Proceedings of the ARO Rotorcraft Wake Prediction Basic Research

Proceedings of the ARO Rotorcraft Wake Prediction Basic Research Workshop

Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332-0150 March 16-17, 2009

Abstracts and Presentation Slides

Contact: N.M. Komerath [email protected] Chee Tung [email protected]

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ARO Rotorcraft Wake Prediction Basic Research Workshop Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia 30332-0150 March 16-17, 2009 Workshop Issues Summary The structure and dynamics of the wakes from rotor blades continue to pose first-order uncertainties in the prediction of hover payload and forward flight speed of rotorcraft. The structure of the rotor wake continues to pose challenges in prediction and measurement. There have been advances in the theory, computational approaches, visualization and measurement capabilities in this field in the past decade, but these have been slow to be translated into first-principles based prediction capability for vehicle design and analysis. Some interesting questions (but by no means all of them) are: 1. What is the structure of the tip vortex at its origin, and what factors influence it? 2. How much of the blade bound vorticity actually ends up in the tip vortex? 3. How fast does the tip vortex diffuse/ dissipate/decay? What is the role of turbulence in these processes? 4. What are the physical phenomena responsible for observed “vortex jitter”? 5. What is the state of computational capability for the tip vortex as a function of age in hover and forward flight? 6. How well are long-age phenomena such as ground vortex rollup, and tail rotor/main rotor interaction captured? 7. What is the status of turbulence modeling for helicopter rotor wakes?

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PROCEEDINGS Authors 1 T. A.Egolf, A.Bagai, N.Tuozzo

Organization Title Sikorsky Vortex Element Wake Modeling Perspectives At Sikorsky

2 T. R. Quackenbush D.A. Wachspress

CDI

Review And Assessment Of Selected Issues In Hovering Rotor Tip Vortex Dynamics

3 H.Tadghighi

Boeing

Current Assessments Of Boeing-Mesa CFD Tools For Applications To Rotor Performance /Wake Computation In Hover Flight

4 R.Narducci

Boeing

Comparison Of Blade Tip Vortex Calculations To Wind Tunnel Measurements

5 S. P´eron, C. Benoit, G. Jeanfaivre 6 F.Massouh I.Dobrev, B.Maalouf

ONERA

High-Order Cartesian Partitioning Method For The Capture Of The Blade Tip Vortex Wake Structure Of A Horizontal-Axis Wind Turbine

7 A.G. Brand 8 S.Y.Wie, K.H. Chung, D.J.Lee

BHTI K.A.R.I.

9 A.Wissink

AFDD

10 S. Schmitz, M. Bhagwat, F.X. Caradonna 11 A.I. Jose, J.D. Baeder 12 V.K. Lakshminarayan J.D. Baeder 13 A. T. Conlisk 14 I. Dobrev, F.Massouh 15 R.B. Haehnel, Y. Wenren, J. Steinhoff 16 J.Steinhoff 17 M. Smith 18 N. Komerath, A.T. Conlisk 19 C.Tung

ENSAM

UCDavis, AMRDEC

The Nature Of Vortex Ring State Numerical Investigation of Rotor Wake and Tip-vortex Dynamics using Free-wake coupled with Vortex-lattice, Potential-panel and CFD method Wake Prediction Using High-Order Adaptive Cartesian Grids In Helios Some Applications and Developments of the Vorticity Embedded Potential Model for Rotor Flow

UMD1

CFD Simulation Of Uh-60 Rotor Wake With Trailing Edge Flaps UMD Numerical Study Of The Effects Of Planform On Micro Hovering Rotor OSU, GIT Wake Interactions for Complex Flight Conditions ENSAM Actuator Disk Model For Interacting Wind Turbine Wakes USA CRREL, A Model To Simulate Rotor Wake Induced Brownout / F.A.I. Whiteout UTSI Status of Vorticity Confinement Technology GIT CFD For Rotor Wakes GIT, OSU Experimental Results On Rotor Wakes Ames RC

Summary Comments

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Overview and Perspectives of Vortex Element Wake Modeling at Sikorsky1 T. Alan Egolf, Ashish Bagai, Nick Tuozzo Abstract This paper presents several Sikorsky engineer’s perspective on vortex element based wake modeling for rotors, including a final emphasis on hybrid CFD/Vortex Element methodology. It briefly reviews some basic aspects of these models, their strengths and weaknesses, modeling issues, and what is needed to improve current hybrid CFD/Vortex Element methodology to support the aerodynamic design and analysis of isolated rotors. It directly or indirectly provides some insight into future research areas for this type of rotor wake modeling. Introduction The discussion and opinions provided in the present paper draw upon direct or indirect experience spanning a period of nearly 40 years with many different wake prediction analyses that gave been used and evaluated at Sikorsky for rotor design and research purposes. These include: F456, F389, F506, G413, CCHAP, RWA, EHPIC, FREEWAKE, ROTORCRAFT, CHARM, 2GCHAS, CAMRAD, RCAS, and MFW. It draws upon related experience with wake prediction methodology that is not necessarily vortex element based, numerous discussions over many years with other experts in the field, documented and undocumented numerical studies, and insight gained from experimental wake data bases of which some not in the public domain. Many of the codes noted above were developed or adapted and modified at The United Technologies Research Center (UTRC) or Sikorsky Aircraft over the years, while some are government or commercial codes. The use of discrete vortex element based wake modeling with non-uniform circulation for rotorcraft applications started in the 1960’s with the advent of the availability of computers in the university, government, and industrial environments and was recognized as a key to accurate rotorcraft performance calculations in that time frame (e.g., Refs. 16). Simpler vortex-ring based or cylindrical sheath type models were available before this period (e.g., Refs. 7-8). Since those early days, the use of such vortex element wake models has become routine. Initially single tip-vortex models with very coarse spatial and temporal discretizations were used and even these taxed the computers of those days. As the computers got faster, research on improving the modeling progressed. Early hover models were empirically based prescribed wake geometries (e.g., Refs. 9-10), while forward flight models were generally based on undistorted wake models. Major improvements in the hover wake 1

Presented at the ARO Rotorcraft Wake Prediction Basic Research Workshop March 16-17, 2009 © Unpublished Work, Sikorsky Aircraft Corporation 2009. All Rights Reserved.

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modeling area came as computers got faster and the understanding of the nature of the hover problem grew, allowing stable distorted wake solutions to be obtained (e.g., Refs. 11-16). In forward flight, undistorted wake models were used in part because of limiting computer resources and because the distortions are less important for much of this flight regime. In fact undistorted wake models in forward flight are still used for performance prediction. Simplified distorted wake models were attempted to keep the computational costs down (e.g., Ref. 17) and a generalized forward flight wake model based on fitting predicted wake distortions was developed (Ref. 18). More recently, with evermore powerful computers, full-span models with near and/or farfield wake elements and distortion of the full wake surface, as opposed to single tip vortex models, have been developed and are routinely used (Refs. 19-26). Figure 1 shows a distorted wake geometry prediction for the Large Swept Tapered (LST) tip using the method of Ref. 22.

Figure 1 Example of Full Span Wake Model Results from the UH-60A Airloads Workshop have shown that the use of Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) coupled solutions is providing improved airloads and blade loads compared with more traditional comprehensive rotor codes that use a combination of aerodynamic models, vortex element wake models, and aeroelastic methodology. The primary benefit is in the better airloads that the CFD simulations provide, coupled with the newer CSD analyses. However, these CFD-based results hint at the need for better resolution of the wake. In the ongoing UH-60A Airloads workshop, both full CFD and hybrid CFD methods have been and are being pursued. The hybrid CFD methods only capture the near wake effects and rely on wake models to model most of the wake influence. With this recent focus on the use of CFD for the rotor blade aerodynamics and the successes observed using full CFD wake capturing, one might question why one would still want to use wake models. The fundamental reason is that the accurate capture or prediction of the discrete wake and its influence is still a challenging computational 2 5

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problem. Full CFD capturing of tip vortex structures from each rotor blade, even with highly efficient block-structured flow solvers with grid adaptation using higher order differencing schemes to mitigate numerical diffusion, is not practical for the conceptual design stage. It also cannot provide highly accurate discrete wake effects for BVI at reasonable cost, and may not do so for many years to come. Background In the rotorcraft field, wake modeling is generally based on the use of potential methods. In this paper, we are focusing on incompressible vortex element models based on purely Lagrangian convection approaches. Thus, the calculation of the influence of the vortex elements and their convection is based on solely on the Biot-Savart law. Reference 27 provides a good overview of vortex methods. Other methods that are combinations of Eulerian and Lagrangian procedures are under development (e.g., Refs. 28-31), but are not discussed herein. It is important to remember that there are two aspects of the wake modeling process. One is obtaining an accurate description of the blade aerodynamic loading distribution, and hence the bound circulation used in defining the wake circulation, i.e., the blade aerodynamic model. For the purposes of this paper, the on-blade vortex elements are considered part of the aerodynamic model. The second aspect is the modeling of the wake off of the blade surface (off-blade vortex elements, see Figure 2.), and this latter aspect is the primary subject of this paper.

Figure 2 Blade and Wake Lattice Model

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There are various types of vortex element models and generally these are used in latticebased methods. The lattice-based models consist of trailed and shed vorticity in the form of discrete elements whose strengths are the trailed and shed circulation (e.g., Refs. 1925), or distributed surface elements with constant or low order variations of the distribution of vorticity on the element surface (Ref. 32). The term lattice comes from the regular ordering of the nodes that describe the wake surface. However, there are other lattice-like methods such as the constant vorticity contour vortex method (Refs. 24-25, 33-34) whose ordering is not regular, but is ordered as function of the wake vorticity distribution as shown in Figure 3.

Figure 3 Constant Vorticity Contour Wake Model (Ref. 24) Another form of discrete vortex element is the point vortex, some times referred to as a vortex particle or vortex blob (e.g., Refs. 35-38 for rotorcraft applications). Wake models based on the point vortex do not require a regular ordering scheme. Most, but not all, wake models used today use vortex segments. The segments can be modeled as straight line or curved segments with constant or varying circulation strengths. Figure 4 is a pictorial of these element types, also showing them in approximate order of computational complexity.

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Figure 4 Vortex Element Types The rotor wake is comprised of vorticity that, in general, is either of the nature of a vortex sheet or a strong vortex such as the tip vortex. The vortices are generally tip vortices and root vortices and a single blade may have multiple 'tip' vortices. Figure 5a is an illustration of a simple wake lattice consisting of root and tip vortices and the sheet being represented as a collection of line vortices without any shed vortex elements, while figure 5b shows the elements for shed vorticity included (Ref. 39).

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(a)

(b) Figure 5 Illustration of Wake Structure Modeling (Ref. 39) The modeling of vortices using the Biot-Savart law results in strong singular behavior. Unless modeled with distributed vorticity elements, the vortex sheets will also have a strong singular behavior just as regular vortices do. Even with distributed elements for the sheet, the behavior is singular at the edges, but it is of lower order. This means that when using vortex element models, the treatment of the cores for either physical behavior or numerical purposes becomes a significant aspect of the methodology for accurate and robust modeling and tip core models have been developed.

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Because the convection of the rotorcraft wake is generally an unsteady flow problem, the temporal integration generally used to convect the wake has been of concern in the past. Euler integration schemes are common, along with multi-step or predictor-corrector schemes. In hover the convection is driven solely by the induced flow field, while in high-speed forward flight, it is dominated by the kinematics of the blade and freestream flow field. Very early work indicated that the hover wake was unstable (Ref. 11). A later study for hover showed that the state, for an inviscid vortex element based model, is a neutrally stable one at best (Ref. 12). Relaxation schemes, rather than time marching schemes, have been successfully used to overcome this issue (Refs. 13-15, 40), although stable time marching schemes in hover have been now been developed (Refs 14-15). Both approaches work well in forward flight. The use of vortex core growth models introduces damping (diffusion) into the process and mitigates the stability issue in the far wake. Other issues such as vortex stretching, axial flow within the core, initial core size and core growth modeling for dissipation and/or diffusion, the effect of the blade hitting the vortex on core size, and numerical spatial or temporal discretization affect the wake model. As this brief background material indicates, there are many aspects of wake modeling that must be considered for an accurate and robust model. None of the wake models in the codes noted in the introduction are perfect and most of the codes are no longer used because of their limitations. It is not the intent of this paper to identify these codes, but rather to provide our perspective of what to consider in such codes for future application, for refinement of existing codes, or the development of new wake modeling codes with emphasis on hybrid CFD/Vortex Element wake models. Wake Modeling Perspectives Point Vortex vs. Line Segments The point vortex is often used as a simple farfield approximation for the straight or curved segment elements, because the computational complexity is less than that of the straight or curved elements. Figure 6 is an example of a UH-1H rotor whose wake is modeled as an assembly of point vortices for noise prediction (Ref. 35). The advantage of the vortex segment models over the point vortex approach is that the regular ordering, i.e., well defined connectivity of the elements, allows for ease of association of the particular elements with different physical characteristics of the wake structure: that is the tip vortex, the root vortex, and the vortex sheet elements and any treatments used with them. However, this regularity makes it difficult to deal with concepts like vortex merging while maintaining the regular lattice based ordering. Because the point vortex models do not require a specific ordering, they can deal with merging of elements much easier than the lattice methods. However, even though the point vortex models are less costly for the calculation of the induce velocity, there is

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additional computational cost per element to compute the strain field on them to spin and stretch them. In addition, many more elements are needed to approximate a line vortex when the influenced point is near the elements representing the tip vortex. In general the point vortex methods have not been heavily used in the rotorcraft field, but recently there has been renewed interest (e.g., Refs. 35-38).

Figure 6 Particle Vortex Model of Wake of UH-1H Rotor (Ref. 35) Core Models As noted earlier there are fundamentally two types of wake structures that are modeled: vortex sheets and vortices. Regardless of which entity is being modeled with vortex elements, the singular nature of the elements must be dealt with, be it of a physical or numerical nature. The same issues apply to point vortex methods. The tip vortex model is relatively easy to model, because segmented line vortex elements with a core model are a good mathematical analogy for the physically observed tip vortex. Experimental measurements of the tip vortex core radius, primarily in modelscale hover, have given us insight into the core radius and its behavior with wake age. Reference 41 presents a nice summary of the most popular vortex core models and useful insight into the impact of vortex core modeling on hovering rotors. The swirl velocity profiles as a function of radial distance from the core center for some popular models are shown in Figure 7. These are compared with the singular potential flow profile. Based on the work presented in Ref. 41 and other references discussed therein, the Vatistas n=2 model appears to provide a good match to model scale test.

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Figure 7 Popular Vortex Core Models Because the measurements discussed in Ref . 41 have been primarily at model scale, there is some concern as to whether or not the initial vortex core sizes are appropriate for full-scale rotors, and if the observed model scale decay rates are appropriate for full scale. It is also not clear how applicable these hover-based models are for forward flight, particularly after the tip vortex has passed near a blade or is entrained into the lateral “super” vortices. Some of these issues are more important for interactional aerodynamics than for the actual blade aerodynamic loading predictions. This is an area for additional research and refinement. The root vortex is another area where the modeling approach is unclear. Little if any visualization of discrete root vortices exists to help understand this modeling issue. This may be because the root vortex may actually be a much-diffused structure due to the spar and hub affecting the formation of a well-defined root vortex. Discussions with other researchers in this area generally reinforce the belief that this entity should be modeled with a “fat” (diffused) core. This is also an area for research and refinement in our models. Multiple tip vortices have been observed experimentally for a UH-60A-like rotor model in forward flight, shown in Figure 8 and 9 (unpublished) and also for a tail rotor discussed in Ref. 22. Studies for the UH-60A Airloads Workshop with CFD wake

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capturing have indicated their existence. It is probably incorrect to call these tip vortices because by definition there is only one tip vortex, the outermost one, but for convenience we will do so. The core size and core growth models for these vortices are not well understood. It is possible that such physics are also important for the British BERP tip and other unusual blade tip concepts.

Figure 8 Smoke Visualization of Dual Tip Vortices

Figure 9 Experiment (symbols) and Modeling (lines) of Dual Tip Vortices. 10 13

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The vortex sheet modeled with line vortex elements will have a strong singular behavior near the vortex element. This behavior is not physical; it is an artifact of modeling the distributed sheet of vorticity with discrete elements. It is our experience that one possible way to treat the singular behavior of these elements, when modeled with vortex segments, is to use a large core whose size is related to the discretization distance between elements. This is because model problems have shown that introducing a core of this size mitigates the erroneous singular nature when in close proximity of the element, “near” being within the discretization distance noted above. However, the model does not provide the correct tangential flow behavior when in close proximity to the element. It is not clear if one should apply a core growth model for these elements, particularly when one considers the large distortions these entities undergo within the full wake structure of the helicopter rotor. Methods and investigations to deal with this modeling issue may have merit. Distributed Vorticity Elements The use of distributed vorticity elements (panels) can reduce the nature of the singularity and better approximate the local flow field near the vortex sheet. However, their computational cost is much higher than the line vortex segment models and treatment of the lower-order singularity at the edges of these panels is still required in an actual implementation. The errors associated with this treatment are far smaller that those with the vortex point or segment models used to approximate a sheet. Some recent work using quadrilateral panels constructed from semi-infinite vortex sheets of finite span with linearly varying vorticity, shown in Figure 10, have been applied to fixed wings and simple hovering rotors as noted in Ref. 32 to simulate the wake rollup (see Figure 11). Special treatment was still required to deal with the low order numerical singularity. But the method is much less sensitive to the singularity issues than the vortex filament model.

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Figure 10 A Distributed Vorticity Element Construction (Ref. 32)

Figure 11 Application of a Distributed Vorticity Element Model to a Rotor After Three Rotations in Hover (Ref. 32.) 12 15

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Simple quadrilateral elements do not rigorously represent a warped surface such as a rotor wake and exact closed-form analytic solutions for warped elements with nonconstant vorticity distributions are unknown, compounding the difficulty of practical implementation. Efficient hierarchical quadrature integration schemes of the Biot-Savart integral may be a way to deal with this problem, where the induced velocity for points near the element are obtained by numerical integration over the surface of the of element with fine discretization resolution and with course resolution or simpler models when the evaluation point is far away. This may be an area of fruitful research in particular, because it removes the issue of core modeling of the sheet. The computational power of current computers makes this potentially attractive. Wake Discretization and Tip Vortex Strength How the wake is discretized in the spatial or temporal sense can be important. Studies in hover for the prediction of the distorted tip vortex structure have shown that the azimuth discretization should be nominally about 5° or smaller, at least with straight segments (Ref. 42). In forward flight, blade vortex interaction (BVI) passage events occur so quickly that azimuth time steps of 5o are too large to capture the correct impulsive induced flow field and the associated aerodynamic loading. Schemes to deal with the problem of the azimuth discretization for noise prediction have been developed (e.g., Refs 33-34). Other schemes based on interpolation have been developed to enhance the computational speed for high resolution wake prediction, e.g., Ref. 43. For full-span wake models, the radial discretization can have a strong effect on the solution. This is because the strength of the tip vortex is directly related to the local gradient of the circulation on the bound vortex and the number and distribution of elements along the span, unless special treatment is used to define its strength. This complicates the modeling process because the actual physical vortex consists of the entrainment of some of the vorticity shed inboard from the tip into the real vortex. In many models this entrainment is assumed to be all of the vorticity from the location of the peak bound circulation to the tip that is not well modeled with some full span lattice methods. Rollup models that "force" coalescence of the discrete trailing vortex structures into a single tip vortex can be employed to deal with this. However, because these are models, they suffer from the appropriateness of the rules that are used to define them. One benefit of these of models is that they can reduce the computational cost by reducing the number of discrete wake elements. Some numerical work in hover has been done for simple blade models to define the fraction of the peak bound vortex that rolls up into the tip vortex (Ref. 44). Figure 12 shows the predicted growth in the circulation of the tip vortex that appears to only approach 80% of the peak value for a simple rotor planform. This is somewhat substantiated by the experimental work of Ref. 45. However, it is not clear how applicable these particular results are for complex rotor planforms or forward flight. Forward flight introduces additional complexity associated with the azimuth variation of the spanwise loading and the possibility of multiple tip vortices as noted earlier.

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Figure 12 Predicted Evolution of the Tip Vortex Circulation Strength in Hover (Ref. 44) Aerodynamic Coupling It is the observation that the wake models that provide the most consistent and robust results are those that have decoupled the wake radial discretization from the airload model’s radial discretization if the aerodynamic loading model is based on potential methods such as a Prandtl Lifting-Line or the Weissinger Extended Lifting Line. This is related to the issue noted in the previous section. When the radial discretization of the wake lattice and the aerodynamic model are the same, then as the discretization is refined, the strength of the tip vortex becomes weaker and nonphysical unless special treatment is employed. Most of the better wake analyses have dissociated the wake spanwise discretization from the aerodynamic discretization. Again the mapping of the gradient of the bound circulation on to the wake lattice is a modeling process that must be dealt with. Computational Cost As noted, the computational cost per time step of vortex element based models scales with the number of elements squared (n2). For routine application the cost can quickly become unacceptably large using full-span wake models with finer time steps. Methods

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to reduce this cost can be employed, e.g., Ref. 43. Because the calculation of the influence of each element is completely independent of the other elements, parallel computing methods can also be utilized to significantly reduce computational time if available. Schemes that operate on a subset of the elements and then interpolate results to the other elements can be employed. They may use simpler models for elements far away or freeze the far field influence to reduce computational cost. Other schemes such as particle-incell methods, tree codes, and multipole methods can be used that can have very significant cost savings when the number of element is large. Possibly the most common of these approaches are the multipole-based schemes (e.g., Refs. 46-48). These methods employ the concept of treating large number of elements far from the point of interest as a single entity whose strength is based on the combined strengths of the assembly of elements. The mathematics of this process is quite interesting and rigorous. Note that the first order term of the multipole approximation is in fact a point vortex. Simple multipole schemes can be employed that reduce the order from n2 to n1.5 or better, while more sophisticated and rigorous approaches using hierarchical methods can reduce the order to n log(n) while controlling the accuracy of the approximations. For large numbers of elements this reduction can approach many orders of magnitude over the brute force calculation as shown in Figure 13.

Figure 13 Multipole Concept

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Shed Wake Treatment Many wake models ignore the shed wake elements; these elements are related to the time variation of the bound circulation on the blade. The rationale for this treatment is in part due to the use of unsteady aerodynamic models to account for the affects of the near shed wake in the aerodynamic models and, because the strength of the shed elements is generally weak compared with the trailing elements. In addition, the computational cost of these additional elements can double for the same lattice discretization if not done efficiently. This cost was a significant concern in the past but should no longer be a driver. There is some numerical evidence via direct comparison of CFD solutions based on full wake capturing and lattice methods that ignoring the shed wake may not be valid for high speed conditions on the retreating side where the blade runs over a region of strong shed vorticity from the previous blade. Figure 14 shows the inflow at the rotor disk from a full CFD capturing method and CFD-hybrid method for the same condition. The hybrid wake model ignored the shed vorticity. While this effect may not be important for many problems, it probably should not be ignored. The issues with the core treatment in modeling the shed wake are the same as for the trailed elements.

Figure 14 Inflow Comparison Between Wake Capturing and Hybrid CFD/Vortex Element Method Without Shed Vorticity (Sitaraman & Baeder, UMD – Unpublished – UH60-A Airloads Workshop)

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Hybrid Methods As noted in the introduction, one of the purposes of this paper is to discuss the aspects of wake modeling with regard to hybrid CFD/Vortex Element methods. But first a brief overview of these methods is provided. In the context used herein, the hybrid CFD/Vortex Element method consists of solving for the viscous solution in a grid encapsulating the rotor blade and modeling the wake structure outside of this grid using vortex element methods. It should be noted that the hybrid concept is not new, there is earlier work on hybrid approaches based on potential methods in hover (Ref. 49) and forward flight (e.g., Refs. 50-54). The concept is shown in Figure 15. The effects of the other blades and most of the blades own wake are simulated through the vortex element wake model’s influence on the CFD solution in several possible ways: 1) by imposing a partial angle-of-attack as a boundary condition on the blade surface, 2) as an imposed boundary condition on the outer surface of the CFD grid (Boundary Condition approach), 3) as an imposed velocity field on all cells within the grid (Field Velocity approach), or 4) as combination of the latter two methods.

Figure 15 Hybrid CFD/Vortex Element Wake Model This last approach may be preferable when one wants to better capture the discrete blade affects when any of the strong vortex elements pass into any of the blade grids. The first approach is the most cost effective, but least accurate and not recommended. The boundary condition approach is the next most cost effective approach, but grid resolution can affect the ability of this approach to accurately capture vortex affects for elements

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passing into the CFD grid. The field velocity approach is the most rigorous in the sense that it best preserves the strong tip vortex effects, but it is the most computationally expensive because of the large number of calculations that are required. Multipole methods make this approach computationally affordable. There are two technical assumptions that are made with these hybrid approaches, 1) it is assumed that incompressible vortex elements are adequate and 2) that blade-to-blade thickness affects can be ignored. A possible concern is that the size of the computational domain can affect the solution, but using characteristic boundary conditions is believed to adequately deal with this concern. With hybrid methods, the technical challenge is how to use the predicted CFD solution information to define the circulation of the vortex elements of the wake model being used. Most of the other issues regarding wake modeling discussed in earlier sections still apply. Most hybrid methods used today use the gradient of the bound circulation based on the lift section obtained from the chordwise integration of the surface pressure to define the wake circulation on a vortex lattice in the same manner as is done with simpler aerodynamic models (e.g., Refs. 55-56). In this standard approach, the airload to circulation mapping issues discussed earlier must still be dealt with for the detached wake circulation model. Related work with a Navier-Stokes/Full-Potential solver in hover that couples the inner viscous solution with the outer full-potential solution integrates the near-field viscous solution to obtain an effective bound circulation, rather than computing the bound circulation from the pressure distribution as noted above (Ref. 57). Some differences were observed in the resulting blade aerodynamic solution compared with the standard approach for blade tips that were stalling, but they were generally small. However, with either of these approaches the core size and strength of the tip vortex are still modeled. There is an approach that removes some aspects of the modeling of the wake, specifically the tip vortex strength and core size along with the strength of the vortex elements used to model the vortex sheet. Rather than directly using the blade aerodynamic solution or the near-field vorticity distribution at the blade, it is possible to define the wake model based on the exiting vorticity distribution in the CFD grid. If the grid resolution is of adequate scale, one can identify vortical structures such as tip vortices and vortex sheets. Furthermore the core size of the tip vortices can be extracted from this information. This approach was demonstrated in forward flight (Ref. 58) as shown in Figure 16, where the field velocity approach was used to include the influence of the wake model.

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Figure 16 Forward Flight Hybrid Method with Tip Vortex Strength and Core Set by the Exiting Vorticity Field Recently the technique of extracting the strength of the vortex elements has been applied in a hybrid method that uses point vortices for the wake structure. The strength of the point vortices is determined by the existing vorticity distribution, but the core size is normally set by the cell size of the grid used to determine the point vortices (Refs. 37-38). This particle vorticity transport method (P-VTM) also includes particle merging. Methods to set the core size for those point vortices that are presumed to represent the tip vortex without artificially affecting the non-tip point vortices are being investigated. Figure 17 shows a low speed condition for the UH-60A rotor.

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Figure 17 Hybrid CFD/Point Vortex Wake Model for UH-60A μ=0.149 (unpublished - UH-60A Airloads Workshop) Another issue with some of the hybrid methods being used today is that when computing the wake distortion, the portion of the wake lattice that emanates from the trailing edge of the blade is not based on the actual position of the vorticity distribution in the CFD grid. While this may be a small error, it can be resolved by treating the vorticity inside the CFD domain as part of the wake lattice. The hybrid approach does not resolve all wake modeling issues. While the strength and core size of the initial tip vortices can be predicted by the viscous solution downstream of the blade as noted above, the core growth must still be modeled with most lattice-based models. And of course the issues discussed earlier regarding modeling of the sheet entities must still be dealt with. This approach fails if the blade grid resolution is inadequate to correctly resolve the size of the exiting tip vortex core. However, with the increasing speed of computers, it is becoming affordable to run very high resolution grids near the blade, also be required in full CFD capturing wake methods if one wants to resolve the tip vortex with high fidelity.

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Concluding Remarks This paper provides some background information on vortex element wake modeling. It highlights many wake modeling issues, and directly or indirectly suggests areas for future work on these issues as perceived by the authors. These areas are: forward flight wake core modeling, root vortex core modeling, better treatment of the vortex sheet, scale effects on the vortex core models, and while not explicitly stated, the need for additional experimental data to provide the information needed to investigate and/or improve some of these modeling features. The paper also presents basic information regarding the Hybrid CFD/VE wake model. It defines an approach for Hybrid CFD/VE wake modeling that removes the fundamental issue of how to set the wake strength and core size when modeling the rotor wake. It is noted that this particular approach is being pursued by at least one researcher, but more would be highly desirable to advance the state-of-the-art. References 1 Piziali, R. A., and Du Waldt, Frank A., “A Method for Computing Rotary Wing Airload Distribution in Forward Flight,” TRECAM TR 62-44, 1962. 2 Piziali, R. A., “A Method for Predicting the Aerodynamic Loads and Dynamic Response of Rotor Blades,” USAAVLABS TR 65-74, 1966. 3 Daughaday, H., and Piziali, R. A. , “An Improved Computational Model for Predicting the Unsteady Aerodynamic Loads of Rotor Blades,” Jour. Amer. Helicopter Soc., Vol. 11, No. 4, Oct. 1966. pp 3-10. 4 Crimi, P., “Theoretical Prediction of the Flow in the Wake of a Helicopter Rotor. Part I. Development of Theory and Results of Computations,” CORNELL AERONAUTICAL LAB, Final Rept., pt. 1 Sept 64-Sep 65. 5 Crimi, P., “Prediction of Rotor Wake Flows,” Cal. USAAVLABS Symposium on Aerodynamic Problems Associated with V/STOL Aircraft. Buffalo, N.Y., June 1966, Vol. I. 6 Landgrebe, A. J., “An Analytical Method for Predicting Rotor Wake Geometry,” AIAA Paper No. 69-196, Feb. 1969. 7 Castles, W. R., and J. H. De Leeuw, “The Normal Component of the Induced Velocity in the Vicinity of a Lifting Rotor and Some Examples of its Application,” NACA Report 1184, 1954. 8 Heyson, H.H., and Katzoff, S., “Induced Velocities Near a Lifting Rotor with Nonuniform Disk Loading,” NACA TR 1319, 1957.

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9 Landgrebe, A. J., “The Wake geometry of a Hovering Helicopter Rotor and its influence on Rotor Performance,” Journal of the American Helicopter Society, Vol. 17, No. 4, October 1972, pp. 3-15. 10 Kocurek, J. D., and Tangler, J. L., “A Prescribed Wake Lifting Surface Hover Performance Analysis,” Journal of the American Helicopter Society, Vol. 22, No. 1, 1977, pp. 24-35. 11 Widnall, S.E., “The stability of a helical vortex filament,” Journal of Fluid Mechanics (1972), vol. 54, no. 4, 641-663. 12 Bliss, Donald B. and Wachspress, Daniel A. and Quackenbush, Todd R., “New Approach to the Free Wake Problem for Hovering Rotors,” Annual Forum Proceedings American Helicopter Society, (1985), 463 – 477. 13 G.L. Crouse, Jr. and J.G. Leishman, "A New Method for Improved Rotor Free-Wake Convergence," Paper AIAA-93-0872, presented at the 31st AIAA Aerospace Sciences Meeting, Reno, Nevada, Jan. 1993. 14 Bagai, A., and Leishman, J.G., "A New Rotor Free-Wake Model using a Pseudoimplicit Methodology," AIAA Paper 94-1918, AIAA Applied Aerodynamics Meeting, Colorado Springs, June 1994. 15 Bhagwat, M. and Leishman, J. G., "On the Aerodynamic Stability of Helicopter Rotor Wakes," American Helicopter Society 56th Annual Forum, Virginia Beach, VA, May 2– 4, 2000. 16 Bhagwat, M. J. and Leishman, J. G., “Stability, Consistency and Convergence of Time-Marching Free-Vortex Rotor Wake Algorithms,” Journal of the American Helicopter Society, Vol. 46, No. 1, 2001. 17 Beddoes, T. S., “A Wake Model for High Resolution Airloads,” Second International Conference on Basic Rotorcraft Research, 1985, Research triangle Park, North Carolina. 18 Egolf, T. A., and Landgrebe, A. J., " Helicopter Rotor Wake Geometry and Its Influence in Forward Flight, Volume 1 - Generalized Wake Geometry and Wake Effect on Rotor Airloads and Performance," NASA CR 3726, October 1983. 19 Bliss, D.B., Quackenbush, T.R. and Bilanin, A.J.: "A New Methodology for Helicopter Free Wake Analyses," Paper No. A-83-39-75-000 presented at the 39th Annual Forum of the American Helicopter Society, May 1983. 20 Bliss, D.B., Teske, M.E., Quackenbush, T.R.: "A New Methodology for Free Wake Analysis Using Curved Vortex Elements," NASA CR 3958, December 1987 (also CDI Report No. 84-6, May 1984).

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21 Johnson, W., “A General Free Wake Geometry Calculation For Wings and Rotors,” Presented at the American Helicopter Society 51st Annual Forum, Fort Worth, Texas, May 9-11, 1995. 22 Egolf T.A., “Helicopter Free-Wake Prediction of Complex Wake Structures Under Blade-Vortex Interaction Operating Conditions,” Proc. 44th Annual Forum American helicopter Society, June 16-18, 1988. 23 Bagai, A. and Leishman J, G, “Rotor Free-Wake Modeling using a Relaxation Technical – Including Comparisons with Experimental Data,” J. of the American Helicopter Society, Vol. 40, No. 3, July 1995, pp. 29-41. 24 Quackenbush, T.R., Bliss, D.B., Wachspress, D.A., Boschitsch, A.H. and Chua K.C., "Computation of Rotor Aerodynamic Loading in Forward Flight using a Full-Span Free Wake Analysis," NASA CR 177611, October 1990 (also CDI Report No. 90-05, Dec. 1990). 25 Quackenbush, T.R., Wachspress, D.A., Boschitsch, A.H. and Curbishley, T.R.: "A Comprehensive Hierarchical Aeromechanics Rotorcraft Model (CHARM) for General Rotor/Surface Interaction," CDI Report 99-03, Final Report for NASA/Ames contract NAS2-14342, January 1999. 26 Johnson, W., “A General Free Wake Geometry Calculation for Wings and Rotors”, st American Helicopter Society 51 Annual Forum, Fort Worth, TX, May 1995. 27 Sethian, J.A., “A Brief Overview of Vortex Methods” in Vortex Methods and Vortex Motion, Society for Industrial and Applied Mathematics, 1991, p. 1-32. 28 Brown, K. D., and Fiddes, S. P., “New Developments in Rotor Wake Methodology,” 22th European Rotorcraft Forum, Brighton, UK, Sept. 1996. 29 Line, A.J. and R.E. Brown, “Efficient High-Resolution Wake Modelling Using the Vorticity Transport Equation,” 60th Annual Forum of the American Helicopter Society. 2004. Baltimore, MD. 30. Ramachandran, K., Tung, C., Caradonna, F. X., “Rotor Hover Performance Prediction Using a Free-Wake, Computational Fluid Dynamics Method,” Journal of Aircraft, vol. 26, Dec. 1989, p. 1105-1110. 31 Bhagwat, M., Moulton, M. and Caradonna, F., "Recent Advances in the EmbeddedWake Approach to Hover Performance Prediction," Proceedings of the American Helicopter Society 4th Decennial Specialists' Conference on Aeromechanics, San Francisco, California, January 21-23, 2004.

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32 Bramesfeld, G, and M. Maughmer, “Relaxed-Wake Vortex-Lattice Method Using Distributed Vorticity Elements,” Journal of Aircraft 2008 0021-8669 vol.45 no.2 (560568). 33 Quackenbush, T.R., Lam C-M.G., Wachspress, D.A.: "Computational Analysis of High Resolution Unsteady Airloads for Rotor Aeroacoustics," NASA CR 194894, May 1994 (also CDI Report No. 93-12, October 1993.) 34 Quackenbush, T. R. and Lam, C.-M. Gordon, Wachspress, D. A. and Bliss, D. B., “Analysis of High Resolution Unsteady Airloads for Helicopter Rotor Blades,” Annual Forum Proceedings - American Helicopter Society, (1994), 1233 – 1248 35 Opoku, D.G, and F. Nitzsche , “Acoustic Validation Of A New Code Using Particle Wake Aerodynamics And Geometrically-Exact Beam structural dynamics,” 29th European Rotorcraft Forum, 2003. 36 Stone C.P. , E.P.N. Duque, and A. Gharakhani, “Towards a Coupled Eulerian/Lagrangian Simulation Method for Rotorcraft Wake Modeling,” AIAA 2008659,46th AIAA Aerospace Sciences Meeting and Exhibit 7 - 10 January 2008, Reno, Nevada. 37 Anusonti-Inthra, P., “Development of Rotorcraft Wake Capturing Methodology Using Fully Coupled CFD and Particle Vortex Transport Method,” Proceedings of the 62nd AHS Annual Forum, Phoenix, AZ, 2006. 38 Anusonti-Inthra , P., and M. Floros, “Coupled CFD and Particle Vortex Transport Method: Wing Performance and Wake Validations,” 38th Fluid Dynamics Conference and Exhibit, Seattle, June 2008 AIAA paper 2008-4177. 39 Conlisk A.T., “Modern helicopter rotor aerodynamics,” Progress in Aerospace Sciences, Volume 37, Number 5, July 2001, pp. 419-476(58). 40 Miller, W. O. and Bliss, D. B., “Direct Periodic Solutions of Rotor Free Wake Calculations by Inversion of a Linear Periodic System,” Annual Forum Proceedings American Helicopter Society, (1990), 757 – 769. 41 Bhagwat, M.J., and Leishman, J. G., “Generalized Viscous Vortex Model for Application to Free-Vortex Wake And Aeroacoustic Calculations,” Annual Forum Proceedings,” American Helicopter Society, 2002, VOL 58; PART 2, pages 2042-2057. 42 Gupta, S. and J.G. Leishman, “Accuracy of the Induced Velocity from Helicoidal Vortices Using Straight-Line Segmentation,” AIAA JOURNAL, Vol. 43, No. 1, January 2005.

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43 Bagai, A. and J.G Leishman, “Adaptive Grid Sequencing and Interpolation Schemes for Helicopter Rotor Wake Analyses,” AIAA Journal, 1998, 0001-1452 vol. 36, no. 9, pp. 1593-1602. 44 Hui Li., O. R. Burggraf, and A. T. Conlisk, “Formation of a Rotor Tip Vortex,” JOURNAL OF AIRCRAFT, Vol. 39, No. 5, September–October 2002. 45 Bhagwat, M.J., and Leishman, “Measurements of Bound and Wake Circulation on a Helicopter Rotor,” Journal of Aircraft 2000, 0021-8669, vol.37 no.2 (227-234). 46 Greengaard, L. and V. Rohlin, “A Fast Algorithm for Particle Simulations,” Journal Of Computational Physics 73, 315-348 (1987). 47 Greengaard, L. and V. Rohlin, “A Fast Algorithm for Vortex Methods,” A Collection of Papers, 1st National Fluid Dynamics Congress, 88-3574-CP, Cincinnati, Ohio, July 2528, 1988. 48 Chua K., and T. R. Quackenbush , “A fast vortex method for the simulation of threedimensional flows on parallel computers,” Proceedings of the conference on Parallel computational fluid dynamics, (1992) 87 - 98 , 1993. 49 Egolf, T. A. and S. P. Sparks, “Hovering Rotor Airload Prediction Using a Full Potential Flow Analysis with Realistic Wake Geometry ,” American Helicopter Society, Annual Forum, 41st, May 15-17, 1985, Proceedings, p. 515-530. 50 Sankar, L. N. and Prichard, D., “Solution of Transonic Flow past rotor blades using the Conservative Full Potential Equation,” AIAA Paper 85-5012, October 1985. 51 Egolf, T. A. and Sparks, S.P., “A Full Potential Rotor Analysis with Wake Influence using an Inner-Outer Domain Technique,” 42nd Annual AHS Forum, June 1986. 52 Strawn, R.C., “Numerical Modeling of Rotor Flows with a Conservative Form of the Full Potential Equation,” AIAA Paper 86-0079, July 1986. 53 Bridgeman, J. O., Strawn, R. C. and Caradonna, F. X., “An Entropy and Viscosity Corrected Potential Method for Rotor Performance prediction,” 44th Annual AHS Forum, June 1988. 54 Strawn, R. C. and Caradonna, F. X., "Conservative Full Potential Model for Unsteady Transonic Rotor Flows, " AIAA Journal, Vol. 25, February 1987, pp. 193-198. 55 Rajmohan, N. , Sankar, L., Charles, B., Makinen, S. M., Egolf, T. A., “Application of Hybrid Methodology to Rotors in Steady and Maneuvering Flight,” Proceedings of the American Helicopter Society 64th Annual Forum, April 29 – May 1, 2008.

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56 Sitaraman, J., Baeder, J. D., and Chopra, I., “Validation of UH-60 Rotor Blade Aerodynamic Characteristics using CFD,” 59th Annual Forum of the American Helicopter Society, May 6-8, 2003. 57 Schmitz S., J. J. Chattot, M. Bhagwat, M. Moulton, F. Caradonna, , “The Prediction and Validation of Hover Performance and Detailed Blade Loads,” AHS Aeromechanics Specialist's Conference, San Francisco, CA, Jan. 2008. 58 Egolf, T.A., “Improved Aerodynamic Methodology for Hover and Forward Flight Aeromechanics/Dynamic System Modeling & Analysis Methodology.” Final Report, NASA Cooperative Agreement # NCC2-9019 Entitled Advanced Rotorcraft Technology, WBS 05-B-01-02.1, Feb. 16 2006.

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© Unpublished Work, Sikorsky Aircraft Corporation 2009. All Rights Reserved.

ARO Wake Workshop 3/16/2009

T. Alan Egolf, Ashish Bagai, Nick Tuozzo Sikorsky Aircraft

Overview and Perspectives of Vortex Element Wake Modeling at Sikorsky

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

• • • • • •

31

Motivation Background Vortex Element (VE) Modeling Perspectives on Various Aspects of Wake Modeling Thoughts on Hybrid CFD/VE Wake Modeling Concluding Remarks

Outline

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

32

• Provide perspective on vortex element (VE) wake modeling • Provide insight regarding current VE wake modeling • Spark innovation for future VE wake modeling • Identify areas for future research • Highlight areas for Hybrid CFD/VE wake modeling

Motivation

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33

• Based on nearly 40 years of work in this area • Application of many codes, primarily inhouse and commercial • Published and unpublished data and research activities • Interactions with other experts • Work with other related methodology

Background

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

34

– On-blade aerodynamic model – defining the circulation – Off-blade wake model – convection

• Two aspects:

– Vortex segments – straight & curved – Distributed vorticity elements – Point vortex (vortex blob or vortex particles)

• Lagrangian based only for this presentation

– Hover & Forward Flight (FF) – Prescribed wake models – Distorted wake models

• Model sophistication driven by computer capabilities –1960’s to date

Vortex Element Wake Model

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35

Blade Circulation & Off-blade Elements

Vortex Element Wake Model

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Vortex Element Types

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• Full-span or single tip models • Generally a discrete tip vortex • May include root vortex • May include shed vorticity

• known connectivity • straight or curved elements

• Line-segment based

Vortex Lattice Examples

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Hover

38

Forward Flight

Sikorsky Full-Span Coaxial Simulations

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

• Recent renewed interest • Very amendable to multipole methods • Leading term in multipole expansion for constant strength vortex segment

39

UH-1H Wake at 100 kts.

• Often used as a far field approximation – lower computational cost • No connectivity required – good for element merging

Point Vortex Model

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

• Applicability to fullscale & forward flight • Root vortex • Sheet vortex • Multiple tip vortices

• Current models based on model-scale hover results • Some issues:

• Swirl profile – Vatistas n=2 • Core growth

40

• Possibly the most significant aspect of vortex element modeling today • Singular behavior – physical and numerical • Core size

Vortex Core Modeling

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

41

• Multiple Peak Roll-up & Core Models

• Capture with full-span model • Prescribe in some manner – local circulation centroid

• Geometry modeling

• Experiment and prediction have shown existence of co-rotating tip vortices for UH-60A or UH-60A like rotors

Multiple Tip Vortices

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

42

• No physical core modeling issue – but must deal with edges • Very costly relative to linesegment models

• Reduces order of singularity • Useful for vortex sheet

• Linear spanwise vorticity • Analytic sum of two semi-infinite sheets • Reduced farfield fluctuations for improved convergence

• Recent hover work for single blade:

Distributed Vorticity Element

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

43

• Without proper treatment, tip vortex strength dependent on gradient of *B - no roll-up! • Hover calculations & experiment indicate ~70-80% of peak *B • FF generally assumes first peak from tip, but is this correct?

• Spanwise (full-span wakes)

• Numerical hover studies have indicated need for '\ of 5o • BVI events occur rapidly and for modern rotors 1 chord length is equivalent ~ 5o near tip => need finer '\ for this problem • Methods have been developed to handle high fidelity wakes for BVI

• Temporal

Wake Discretization & Tip Vortex Strength

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

• Used in many modern codes: CPU much less of a concern today

• Orders of magnitude reduction possible

• Multipole based schemes very successful ~ n ln(n)

• Numerous methods used to reduced cost

• Computational cost scales with n2 per time step for distorted wake

44

Computational Cost

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

• Need better understanding of the shed vorticity impact for these conditions

• Evidence from CFD wake capturing method compared with Hybrid CFD/VE wake method imply that shed wake may be important for highly stalled flight conditions on retreating side

• Many methods in use ignore the far shed wake

45

Inflow from wake capturing & Hybrid method without shed wake from UH-60A Airloads Workshop

Shed Wake

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

• Hybrid CFD/Vortex Element wake methods are one to two orders of magnitude less costly than CFD wake capturing methods for highly resolved wake structures

• Need for CFD blade airloads demonstrated in UH-60A Airloads Workshop for many conditions

46

• Boundary Condition • Field Velocity (grid velocity)

Hybrid Method • Blade circulation obtained from CFD in blade grid • Wake structure and strength modeled with Vortex Elements • Influence of wake

Hybrid CFD/Vortex Element Methods

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

• An alternative approach is to use the exiting flow field to set the core size and vortex strength, removing some modeling assumptions

• Most Hybrid methods use bound circulation distribution to define the wake circulation – hence suffer from many of the modeling issues noted earlier

47

Forward flight simulation using the field velocity approach with multiple core size and strength extracted from CFD solution as shown below

Hybrid CFD/Vortex Element Methods

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• Recent Hybrid CFD/Point Vortex method • Strength of point vortices set by exiting vorticity distribution

Hybrid CFD/Vortex Element Methods

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

•Core size •Circulation strengths 49

Current Hybrid CFD/VE wake methodology was discussed with an alternative approach that removes two key parts of the tip vortex modeling process:

• Core modeling for root vortex and multiple tip vortices • Sheet modeling • Scale effects on core models • Circulation strength • Shed wake modeling • Computational cost • Additional test data to support model improvements

A brief overview and perspective was provided for key aspects of the wake modeling methodology with inferred needs and future work in the following areas:

Concluding Remarks

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Review and Assessment of Selected Issues in Hovering Rotor Tip Vortex Dynamics T. R. Quackenbush and D.A. Wachspress, Continuum Dynamics, Inc.

This discussion will briefly outline previously developed (though still relevant) methods of analysis of vortex instabilities in hovering rotor wakes, derived from the linearized dynamics of self-preserving wake solutions. The behavior of OGE rotor wakes will be discussed and the relationship of computed measures of wake instabilities to prior analytical and experimental results from other investigators will be noted. The ability of current methods to capture noteworthy behaviors in the wakes of IGE hovering rotors will also be described, including the appearance of long-period pulsations in wake-induced velocity and vortex bundling.

50

Continuum Dynamics, Inc. 51

ARO Rotorcraft Wake Prediction Basic Research Workshop Georgia Institute of Technology Atlanta, GA

Presented at

March 16, 2009

Todd R. Quackenbush, Daniel A. Wachspress and Glen R. Whitehouse

Presented by

Review And Assessment Of Selected Issues In Hovering Rotor Tip Vortex Dynamics

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc.

Peer investigators, past and present:

52

too numerous to mention…..

Sponsors: NASA/Ames (Fort Felker, Bill Warmbrodt, Tom Norman, Jeff Light, Wayne Johnson); NASA/Langley (Tom Brooks, Casey Burley, Earl Booth); U.S. Army AFDD and ARO (Chee Tung, Tom Doligalski)

Collaborators: Don Bliss, Milt Teske, Alex Boschitsch, Richard Brown

Acknowledgements (for past and ongoing support)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 53

• Observations and open questions

• Relation to current IGE wake behavior of interest

• Analysis with successor wake modeling tools

- time domain and relaxation solution methods - early observations on wake instabilities - seeds for later questions

• Highlights of CDI investigations 1983-95

• Historical excerpts: hover wake analysis (nonexhaustive)

Outline

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc.

Long Track flow viz rig

54

1-bladed rotor

• Vortex wake observations in hover/low speed (Gray 1956)

Snapshot of rotor wake in descent (Drees 1948)

Tip vortex visualization

• Early observations of unsteady wake structure include Drees, et al. large scale rotor wake behavior in axial flight

Historical Highlights (nonexhaustive)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

55

Identification of “stable” (left) and “unstable” (right) wake structures (Landgrebe, USAAMRDL TR 71-24)

Continuum Dynamics, Inc.

Hover wake schematic (Gray 1956)

• Canonical model used by initial free wake investigators (e.g. Crimi 1965, Clark/Leiper 1969, Landgrebe 1971, Scully 1975)

• Tip vortex / inboard vortex sheet model widely adopted.

Wake Structure and Initial Computations

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 56

Computation of looping behavior of far wake of rotors in hover (Landgrebe, USAAMRDL TR 71-24)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

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- review of Widnall 1972, Loewy and Gupta 1974 provided background on helical vortex instabilities

-inspection of Landgrebe results suggests similar behavior

• Failure of convergence encountered:

• Hovering rotor computations intended as a “simple” demonstration case.

3958 (1987)

(Refs: Bliss et al. AHS Forum (1983), NASA CR

• Development of curved vortex wake elements (1982-85) – Basic Curved Vortex Element (BCVE) for general rotor wake computations.

Parabolic vortex Element (BCVE)

BCVEs plus special self-induction element used to model a filament

Early Investigations at CDI

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc.

Vortex helix

Vortex pair

58

Vortex ring

• Alternative solution method required.

Self-preserving wake geometry for a rotor wake in hover (solid) vs. “typical” time domain deviations (dashed)

• Postulate existence of a self-preserving, dynamically free vortex wake solution, analogous to other vortical artifacts.

Observations on Hovering Rotor Wake Stability

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 59

(Refs: Bliss, et al. AHS Forum Paper 1985; Quackenbush et al. AIAA Journal 1989; Quackenbush et al. NASA CR 4309 1990)

• NASA/Ames sponsored research establishes feasibility (1983-84) and begins full scale model development for lifting rotors (1985-87).

- direct solution for force free wake composed of multiple trailers - systematic perturbation of vortex filament positions - assembly of matrix, execution of iterative solutions

• Alternative – formulation of “influence coefficient” (IC) approach:

• Evident that multiple numerical schemes (e.g., upwinding) can be applied to stabilize wake – however, nonphysical effects introduced.

Time Domain and Relaxation Methods

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc.

• Assess velocity perturbations and construct IC matrix.

• Normal/binormal perturbations

60

• Null velocity in crossflow planes.

• Single (later multiple) contracting tip vortex from each blade

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc.

Full influence coefficient matrix including blade bound circulation

61

• Embodied in CDI EHPIC model (1987)

• Overall wake structure with free near field and semi-free far field

• Bound circulation coupled into solution

Schematic of complete hover wake

Integrated Lifting Rotor Free Wake Model for Hover

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

modal decomposition

62

(Ref.:Quackenbush et al. NASA CR 177523 1989, Continuum Dynamics, Inc. CR 4309 1990)

• Wake looping behavior observed when self-preserving solution released

- frequencies scale in a manner similar to analysis of Widnall and Loewy/Gupta (*/hf2 or CT1/2/Nb for rotors).

- numerous unstable modes present (positive real exponents)

• Observations from limited studies:

linearized kinematic equation governing wake distortion

• Follow-on NASA-sponsored research includes formal eigensystem solutions for the influence coefficient matrix.

Eigenanalysis of Hovering Rotor Wake

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

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Side note: similar departures observed for converged vortices in IGE hovering wakes – not pursued.

Departures of vortex trajectory from the converged, self-preserving wake geometry for an OGE hovering rotor (single tip filament, one bladed rotor, five free turns of wake) when evolved in time.

(Ref.: Quackenbush et al. NASA CR 4309 1990)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

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Well-defined vortices evident in IGE cases even for low Re tests (Lee et al. 2008)

Unsteadiness in low speed forward flight (Saijo et al. 2003)

Rotor

Invisicid Eulerian CFD models (e.g., Brown, Whitehouse et al. 2003/4) show success in capturing major OGEIGE flow phenomena

Hove r

• Numerous investigations of rotor wake dynamics in hover and axial flight from the mid-90s to date (led by Leishman, Komerath, Caradonna, Brown and others) offer insights into structure, time variation of IGE wakes.

Subsequent Related Investigations (abridged)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc.

• IGE calculations possible for hover / near-hover cases.

• Bodies / surfaces can be modeled, including ground planes/enclosures.

• Widely validated for rotor loads and flow fields (e.g., Wachspress et al. 2003 AHS Forum)

• Unsteady, inviscid, time domain

• Full span free vortex wake model

• CDI CHARM model – comprehensive rotor analysis

65

AH-64 full multi-rotor analysis

Isolated Lynx main rotor

General Inviscid Lagrangian Wake Model

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

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EH-101: h/R = 0.8 (near hover at CT = .008, P* = 0.2)

Side view of velocity scan plane (CDI CHARM model)

Rotorcraft Wake Behavior in Hover/Near-Hover IGE

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Continuum Dynamics, Inc. 67

EH-101: h/R = 0.8 (near hover at CT = .008)

Top view of velocity scan plane (CDI CHARM model)

Rotorcraft Wake Behavior in Hover/Near-Hover IGE

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Continuum Dynamics, Inc. 68

Also observed in full scale flight situations (e.g., UH/SH-60 over water) and full-scale time domain outwash data (e.g., CH-53)

Aggregation/pulsations evident with partial ground plane

CHARM model of SH-60 rotor

Rotorcraft Wake Behavior in Hover IGE

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Aggregation appears in this simple model problem

Strength, spacing and release timing arranged to mimic typical rotor parameters

Simple 2D model problem constructed to illustrate abiilty of inviscid model to capture vortex aggregation/bundling

2D Model Problem

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• A complement to experimental studies and RANS modeling.

- role of aggregated features in observed outwash, entrainment problems?

- factors affecting formation of aggregated features in time domain wakes?

- formal studies of IGE wake stability (path to recirculation behavior?)

• Timely for application to current problems of IGE rotor aerodynamics (e.g., brownout):

Sea King IGE in near brownout conditions

• Lagrangian free vortex wake models have offered significant insight into wake dynamics in past investigations

Observations and Open Questions

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

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END

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc.

Modes with positive real parts indicate instabilities

72

(Ref.: Quackenbush et al. NASA CR 4309 1990)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

•

Continuum Dynamics, Inc.

• Limited studies of singlefilament vortex wake eigensystem for IGE rotors.

• Solution scheme extended to vortex wakes in ground effect.

73

(Typical multifilament hovering rotor free wake solution in ground effect – OH-6 main rotor at h/D – 0.75)

Rotors in Ground Effect

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 74

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 75

Schematic of “stable” and “unstable” tip vortex (Landgrebe 1971)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 76

• • Adaptation works well….

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 77

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Continuum Dynamics, Inc. 78

• Connection to far wake (leapfrogging) behavior

• Landgrebe: observations of lack of convergence in calculations

• Early free wake calculations

• Landgrebe, Kocurek

• Prescribed wake (Kocurek and Tangler 1978) and generalized wake models

Follow-On Free / Prescribed Wake Investigations

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Current Assessments Of Boeing-Mesa CFD Tools For Applications To Rotor Performance /Wake Computation In Hover Flight

Hormoz Tadghighi Boeing Company Mesa, Arizona

The presentation will provide detailed information pertaining to the coupling techniques of Vortran-M model developed originally by Professor Brown (University of Glassgow, UK) with the OVERFLOW solver. Under this approach, the main goal is to tightly couple the techniques used in the Vorticity Transport Model (VTM) with the OVERFLOW solver in order to enhance the rotor wake capturing for both hover and forward flight regimes, specially BVI flows. As the result, the computational grid needed for a typical rotor aerodynamics performance computation can be kept to an optimum size in comparison to the historically very large grid size needed in the past in order to obtain a reasonable estimation of rotor, say, Figure-Of-Merit values. This approach will also offer a reduction in both memory requirements and CPUs resources. Therefore, it enables a much larger run matrix to be performed over a reasonable time frame. In its final form, it is expected that the newly developed OV_VTM solver will become a more practical CFD tool for preliminary design applications. Further, the past results obtained for 500E aircraft main rotor performance using OVERFLOW solver will be presented in order to enable a fair assessment of its capabilities in computing the rotor hover performance in the absent of the VTM model.

79

80

Mesa, Arizona March, 2009

Hormoz Tadghighi Technical Fellow The Boeing Company

Boeing Mesa CFD Tools For Applications To Rotor Performance /Wake Computation In Hover Flight

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Rotor blade R = 30’ radius airfoil: VR-X (as designed)

Establishing relative accuracy of the CFD hover prediction tool

VR-X airfoil 2D Wind tunnel data

81

X- rotor Hover performance predictions

CFD Hover performance improvement

X-Rotor

Flight Test Data

Rotor Hover Performance Prediction Using CFD

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Production Rotor blade R = 30+/-r radius airfoil: Vr-xx



Main Rotor – Hover  Detectable only 1 Revs of rotor wake

82

Computed Wake Geometry – Current Status

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

   

83

Accurate wake prediction -challenges Rotor overall Blade Aerodynamic Forces and Moments Blade Loading – chordwise and Spanwise CFD as a diagnostic tools for Troubleshooting

Outstanding Issues – Hover CFD analysis

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

 

84

Reasonable size computational grid (practicality - CPU time and memory requirements) Hybrid Navier-Stokes (Steinhoff, Sankar) – Helix-Turns & Hybrid Coupled VorTran-M (Vorticity Transport Method) Navier Stokes with OVERFLOW GD Discontinuous Galerkin grid adaptation – Unstructured grid Solution adaptive grids: CHIMERA (Meakin)



 

Solution algorithms numerical diffusion  (grid resolution is a major contributing factor)



$FFXUDWH³ZDNH´ SUHGLFWLRQ

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009





85

Modeling:  Vortex wake dynamics (capturing/minimum diffusion)  Secondary vortex structures (capturing/min. diffusion)  Transverse jets (suitable turbulence model)  Time and spatial accuracy (higher-order schemes) Implementation:  Design complexity (discriminator among various concepts)  Packaging (small volume limitations)  Cost (very important factor)  Maintainability (equally important)  Suitability for the rotor environment - ultimate discriminator

Technical/Design Challenges

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Time integration: 3rd-order accurate (TVD-RK) Solution method: cell-based, Discontinuous Galerkin Solution acceleration: multi-grid Grid topology: unstructured, hexahedral elements Grid adaptation: anisotropic h-refinement/coarsening

  

86

Euler based solver Single rotor – lacking multi-rotor and rotor/fuselage interactional aerodynamic capability Shared Memory rather than MPI capability

 Limitations

    

 Solver: Finite-element, 3-D, Unsteady Euler

Boeing/NLR Rotor Solver

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



Multi-Block Hex Grid

87

Boeing/NLR Rotor Solver (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



Caradonna Tung Rotor Model

Caradonna Tung Rotor Model

88

Boeing/NLR Rotor Solver (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



Rotor Wake history  2 Revs.

89

Boeing/NLR Rotor Solver (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



Caradonna Tung Model Rotor  Depicted only 2 Revs of rotor wake

90

Boeing/NLR Rotor Solver (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

        

91

3D, time marching implicit Navier-Stokes Structured overset chimera grid topology Extensive inviscid flux implicit algorithms Option for thin layer or full viscous terms Total of six boundary layers including one-equation and two-equation models Low speed preconditioning model Supports bodies in relative motion – six-degrees-of-freedom Periodic boundary condition - Hover Efficient MPI scalability

 OVERFLOW2.1v

OVERFLOW Solver – Hover Application

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009





  500E, AH64D, MELB and CMRB(AH-64D Block III rotor).

Aircrafts: Hover flight condition

  

Requires a very large volume grid density for hover analysis. Large set of input flags – Require experienced users Lack of robustness for multi-grid level analysis.

Current outstanding issues:

92

Achieved efficient wake capturing by using an overset-meshes topology.



Ranged from very good to fair correlations against measured data:



Applications

OVERFLOW (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

  

Grid size: 257x139x81 Turbulence model: Spalart-Allmaras OGE

0

100

200

300

400

500

600

700

800

0

93

1000

2000

-9.34 Twist, NACA0015, sq tip

3000 Thrust [lbs]

4000

5000

OVERFLOW Flight Test Data

6000

500E Main Rotor - Hover Performance [OVERFLOW]

OVERFLOW Solver – Hover Application (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Power [hp]

     

94

Overset structured mesh solver (OVERset Transonic Unsteady Rotor Navier-Stokes). Second order backward difference for time integration. Lower-Upper Symmetric Gauss Seidel (LUSGS). Upwind based scheme that uses Roe's flux differencing with MUSCL type limiting. Viscous fluxes based on second order central differencing. Turbulence models: Baldwin-Lomax and Spalart-Allmaras

 OVERTURNS:

OVERTURNS Solver – Background

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009





  500E, 600N, MD900, AH-64D, and MELB.

Aircrafts: Hover flight condition

  

Limited advanced turbulence models. Lack of good mesh generation tools high quality assurance. Lack of parallel processing (Hover version) – Very Expensive CPU run time.

Current outstanding issues:

95

Achieved efficient wake capturing by using an overset-meshes topology.



Overall good correlations against measured data:



Applications

OVERTURNS (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



 

Grid size: 259x189x81 Turbulence model: Baldwin-Lomax OGE

0

100

200

300

400

500

600

700

800

0

1000

96

2000

-9.34 Twist, NACA0015, sq tip

3000 Thrust [lbs]

4000

5000

Flight Test Data OVERTURNS

6000

500E Main Rotor - Hover Performance [OVERTURNS]

OVERTURNS Solver – Hover Application (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Power [hp]





 Explicitly conserves vorticity 2nd order in space and time Cell-centered finite volume Fully adaptive mesh Fast Multipole Biot-Savart induced velocity calculation Viscous dissipation terms (suitable for rotor hover flow analysis)



 

97

VorTran-M grid system functions as off body grid CFD solver interfaces with VorTran-M in the overlap between the near body region and VorTran-M grid VorTran-M feeds back to the CFD solver at the near body boundary

Pseudo overset coupling

     

VorTran-M is based on vorticity-velocity form of Navier-Stokes equations:

Coupling architecture – Summary

OVERFLOW VorTran-M Module Coupling - In Collaboration with CDI (Dr. Glen Whitehouse of CDI)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009









The CFD solver is capable of preserving vorticity in the near body region If using incompressible inviscid VorTran-M then near body domain must large enough to handle compressibility and viscous effects The flow outside of the near body region is represented entirely by the vorticity transport equations (i.e. VorTran-M) CFD solver must complete time step before calling VorTran-M Requires resynchronization between CFD & VorTran-M prior before and after VorTran-M time advance

98

Overall cost should be reduced since the total number of grid cells (CFD + VorTran-M) required will be less than equivalent CFD computation

 

VorTran-M employs explicit time stepping (CFL < 1)



 

Small fine mesh region near the body

Assumptions

OVERFLOW VorTran-M Module Coupling (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009





Requires custom routines to couple with OVERFLOW BC’s OVERFLOW near body grid domain

  Exiting and entering vorticity Eliminate double counting

99

Selection of pseudo overset approach to address

 

BCs issues  VorTran-M functions as off-body grid system

OVERFLOW VorTran-M Module Coupling (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



Ω1 – CFD domain (handled solely by the CFD solver)

100

4 Regions  Region W1 is within the CFD domain, and is handled solely by the CFD solver  Region W2 is within the CFD domain, surrounds region W1. Vorticity is prescribed from the CFD solver to VorTran-M  Region W3 is the remaining CFD domain outside of W2. The outer boundary Ω2 – CFD solver prescribes condition is set by VorTran-M vorticity in VorTran-M Ω4 –VorTran-M domain  Region W4 is the remaining domain outside the CFD domain where VorTranΩ3 – Remaining CFD domain. VorTran-M sets the boundary conditions M is responsible for vorticity transport

Overlap Regions

OVERFLOW VorTran-M Module Coupling (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009





Sequencing and Flow of Information

Solver Sequencing

101

Compute ωn+1CFD Overwrite (for R∈ Ω2) ωn+1VTM(R) ĸ ωn+1CFD(R)

2. 3.

No Done?

Yes

Advance time step tn ĺ tn+1

Define Ω2

1.

Stop

Sub-iterate CFD solution qn ĺ qn+1

Compute CFD boundary solution using VorTran-M qnex( (Rn+1i;ωn+1VTM )

Update CFD grid Rni ĺ Rn+1i

Advance CFD solution

Advance VorTran-M solution ωnVTM ĺ ωn+1VTM

Overwrite VorTran-M solution in Ω 2

Known at time, tn ωnVTM; qn & Rn

Initialize VorTran-M & CFD solutions

OVERFLOW VorTran-M Module Coupling (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



Schematic representation of the coupling approach between OVERFLOW and VorTran-M

102

CFD grid uses VorTran-M to specify velocities on boundary

CFD calculates a vorticity distribution to initialize the VorTran-M solution

VorTran-M domain

OVERFLOW VorTran-M Module Coupling (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009



CFD specs  R=197.5cm, 10o twist, VR-12, qtip =11o  Blades meshed individually  72K tets  Open root boundary condition

Vorticity iso-surfaces of the wake and pressure contours on RSA3D PV CFD boundary for an ascending rotor

2-bladed untrimmed rotor in hover

Coupled to RSA3D

103

OVERFLOW VorTran-M Module Coupling (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009





Still remain many gray areas such grid sensitivity, suitable type of schemes, turbulence models etc. There exist somewhat limited high quality CFD database against measured data. New tasks must be encouraged under various joint government/industry programs such as NRTC/CRI and others to pave the way of the utilization of these tools in the preliminary design stage.



104

Yet extensive validations require before they emerge as a CFD tools for any design applications.

Hybrid/coupled CFD solvers offer an attractive extension to the existing legacy solvers.

 



Legacy CFD solvers provide fair to good estimation of rotor overall aerodynamic performance in terms of forces and moments.

Conclusions

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Comparison of Blade Tip Vortex Calculations to Wind Tunnel Measurements Robert Narducci, Ph.D. Associate Technical Fellow The Boeing Company

ARO Rotorcraft Wake Prediction Basic Research Workshop School of Aerospace Engineering, Georgia Institute of Technology Atlanta, GA March 16 – 17, 2009 BOEING is a trademark of Boeing Management Company. Copyright © 2009 Boeing. All rights reserved.

Accurate calculations of blade tip vortices by computational fluid dynamics methods is of ever-increasing importance to the rotorcraft community. Increasing demand for rotor performance requires design and evaluation of rotor systems with high-fidelity methods for helicopter manufacturers to remain competitive. Generally, CFD can provide accurate near-field solutions that capture key physical elements since they are based on first principles. However, CFD methods are notorious for premature dissipation when it comes to far field wakes. The implication is that in the rotor environment blade tip vortices are weakened or washed out completely prior to the arrival of the proceeding blade. The result is improper prediction of blade loads on the outboard section and ultimately poor rotor performance prediction. Calculations are made on a stationary rotor blade in Mach 0.15 flow for the purpose of benchmarking the ability of steady Reynolds Average Navier Stokes methods to compute blade tip vortices. Several spatial discretization schemes and gridding strategies are investigated. Computed results are compared against measurements made by the quantitative wake survey system (QWSS) in the Boeing-Vertol Wind Tunnel.

1 105

BOEING is a trademark of Boeing Management Company. Copyright © 2009 Boeing. All rights reserved.

106

March 16 – 17, 2009

ARO Rotorcraft Wake Prediction Basic Research Workshop School of Aerospace Engineering, Georgia Institute of Technology Atlanta, GA

Robert Narducci, Ph.D. Associate Technical Fellow The Boeing Company

Comparison of Blade Tip Vortex Calculations to Wind Tunnel Measurements

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

107

ARO Rotorcraft Wake Prediction Workshop | 2

The author wishes to thank NTRC/RITA for support in acquiring the wind tunnel data and allowing its use in validating CFD methods

Acknowledgements

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ƒ Conclusions 108

ƒ Practical Application to Hover Analysis

ƒ Results and Findings

ƒ Several Approaches to CFD Calculations

ƒ BVWT Test 433 Segmented Blade Test

ƒ Motivation

Outline

ARO Rotorcraft Wake Prediction Workshop | 3

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

109

ARO Rotorcraft Wake Prediction Workshop | 4

ƒ The result is improper prediction of blade loads on the outboard section and ultimately poor rotor performance prediction

ƒ The implication is that in the rotor environment blade tip vortices are weakened or washed out completely prior to the arrival of the following blade

ƒ However, CFD methods are notorious for premature dissipation when it comes to far field wakes

ƒ Generally, CFD can provide accurate near-field solutions that capture key physical elements

ƒ Accurate calculations of blade tip vortices by CFD methods are of everincreasing importance to the rotorcraft community

Motivation

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

110

ARO Rotorcraft Wake Prediction Workshop | 5

system (QWSS) in the Boeing-Vertol Wind Tunnel.

compared against measurements made by the quantitative wake survey

schemes and gridding strategies are investigated. Computed results are

Stokes methods to compute blade tip vortices. Several spatial discretization

purpose of benchmarking the ability of steady Reynolds-Averaged Navier-

Calculations are made of a stationary rotor blade in Mach 0.15 flow for the

Motivation (Continued)

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

30

24

19

Chinook

Apache

V-22

R

C

ircu m fe

60

86

70

adi u s (ft)

20.0

21.5

23.3

111

ARO Rotorcraft Wake Prediction Workshop | 6

Maintaining Vorticity Requirements

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

D

r e n ce

(

cho r d s) ista n c e

to n ext

b l a de ( cho r d s)

Balance system at root

112

Multi-segment wing with pressure taps

Traverse Mechanism

ARO Rotorcraft Wake Prediction Workshop | 7

5-hole probe

Experimental Test Setup in Wind Tunnel

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Tip balance

Wake survey probe

113

Pitch Actuator

ARO Rotorcraft Wake Prediction Workshop | 8

Multi-segment blade with pressure taps and removable tip

Root Balance

Experimental Test Setup in Wind Tunnel

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ƒ Flow measurements were made between 2’ and 20’ downstream to measure the vortex structure and span loading

ƒ The model was instrumented with a 5-component balance at the root and several static pressure taps

ƒ The blade was segmented in 2” sections to simulate rotor blade span loading by dialing-in twist

ƒ The model represents a generic tiltrotor blade built to approximately ½ scale of the V-22

Wind Tunnel Model

114

ARO Rotorcraft Wake Prediction Workshop | 9

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Twist

Bound Circulation

115

r/R

ARO Rotorcraft Wake Prediction Workshop | 10

ƒ The blade was twisted to produce a circulation representative of a rotor in hover

BVWT 433 Twist

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Wing Wing Tip Vortex Far Field

71 x 209 x 59 O-H

Far field extends to 20 span length (tunnel walls are not modeled)

– – – –

4-Block Grid

116

101 x 101 x 101 Cartesian

Euler Equations

Basic CFD Approach

ARO Rotorcraft Wake Prediction Workshop | 11

N-S Equations

Total points 6.7 million 30 chords

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

117

ARO Rotorcraft Wake Prediction Workshop | 12

Solutions are run with Baldwin-Barth turbulence model

ƒ Angle of Attack = 6.5q

ƒ Pressure = 14.696 psi

ƒ Temperature = 59 °F

ƒ Mach = 0.15

Flow Conditions

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ƒ Vortex position

ƒ Vortex shape

ƒ Vortex strength

CFD Comparisons

118

ARO Rotorcraft Wake Prediction Workshop | 13

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vertical Distance from Core (in)

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0.6

0.2

0.0

-0.2

-0.4

Normalized Horizontal Velocity

0.4

-0.6

Experiment 2nd order 4th order 6th order

119

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

15

5

0

-5

-10

ARO Rotorcraft Wake Prediction Workshop | 14

Horizontal Distance from Core (in)

10

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Distancefrom from¼ ¼chord: chord:17.8 10.7 14.1 4.0 7.1 Distance 2.0 cctiptip

2nd, 4th & 6th Order Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Normalized Veritcal Velocity .

-15

Peak-to-Peak Spanwise Velocity

0.0

0.2

0.4

0.6

0.8

1.0

0.0

8.0

12.0

16.0

Down Stream Distance (Chords)

4.0

20.0

120

0.0

0.2

0.4

0.6

0.8

1.0

0.0

8.0

12.0

16.0

Experiment 2nd order 4th order 6th order

20.0

ARO Rotorcraft Wake Prediction Workshop | 15

Down Stream Distance (Chords)

4.0

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Strength

2nd, 4th & 6th Order Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Peak-to-Peak Vertical Velocity .

Vortex Height

4.0

8.0

12.0

16.0

20.0

Down Stream Distance (Chords)

121

0.0

0.0

0.0

4.0

8.0

12.0

16.0

4.0

8.0

12.0

16.0

0.0

8.0

12.0

16.0

20.0

ARO Rotorcraft Wake Prediction Workshop | 16

Down Stream Distance (Chords)

4.0

Experiment 2nd order 4th order 6th order

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Shape

2nd, 4th & 6th Order Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vortex Breadth

Lateral Distance

4.0

8.0

12.0

16.0

20.0

Chord Length Downstream

122

-3.0

106.0

0.0

-2.0

-1.0

0.0

1.0

2.0

3.0

107.0

108.0

109.0

110.0

111.0

112.0

0.0

8.0

12.0

16.0

Experiment 2nd order 4th order 6th order

20.0

ARO Rotorcraft Wake Prediction Workshop | 17

Chord Length Downstream

4.0

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Position

2nd, 4th & 6th Order Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vertical Distance

Observations

123

ARO Rotorcraft Wake Prediction Workshop | 18

ƒ Higher-order methods behave as expected bringing more accuracy to the solution by maintaining vortex strength & size further downstream

ƒ Vortex is diffusing spatially, most evident in the lower order methods

ƒ Vortex strength is missed by about the same amount 2 chord downstream as it is 20 chord downstream

2nd, 4th & 6th Order Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

OVERFLOW-D

Final Solution

-16.00

-14.00

-12.00

-10.00

-8.00

-6.00

-4.00

0

124

Arvin Shmilovich & Yoram Yadlin (Boeing PW – Huntington Beach)

Converged?

(several 1000 iterations)

OVERFLOW-D

Grid Adaptation

Vortex Tracking

(several 1000 iterations)

Initial Grid

Grid Adaptation Process

Grid Adaptation

ARO Rotorcraft Wake Prediction Workshop | 19

Iterations

5000 10000 15000 20000 25000

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

L2 Norm of Resid

No Adaptation

125

ARO Rotorcraft Wake Prediction Workshop | 20

Adaptation

Contours of Axial-Component of Vorticity

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vertical Distance from Core (in)

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0.6

0.2

0.0

-0.2

-0.4

Normalized Horizontal Velocity

0.4

-0.6

126

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

15

5

0

-5

-10

Experiment Experiment th th 4th 4order order th th 4 4order order Adapted Adapted

ARO Rotorcraft Wake Prediction Workshop | 21

Horizontal Distance from Core (in)

10

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Distance 14.1 17.8 Distancefrom from¼ ¼chord: chord:10.7 2.0 cctiptip 4.0 7.1

4th Order Adapted Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Normalized Normalized Veritcal Veritcal Velocity Velocity ..

-15

Peak-to-Peak Spanwise Velocity

0.0

0.2

0.4

0.6

0.8

1.0

0.0

8.0

12.0

16.0

Down Stream Distance (Chords)

4.0

20.0

127

0.0

0.2

0.4

0.6

0.8

1.0

0.0

8.0

12.0

16.0

Experiment 4th order 4th order Adapted

20.0

ARO Rotorcraft Wake Prediction Workshop | 22

Down Stream Distance (Chords)

4.0

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Strength

4th Order Adapted Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Peak-to-Peak Vertical Velocity .

Vortex Height

4.0

8.0

12.0

16.0

20.0

Down Stream Distance (Chords)

128

0.0

0.0

0.0

4.0

8.0

12.0

16.0

4.0

8.0

12.0

16.0

0.0

8.0

12.0

16.0

20.0

ARO Rotorcraft Wake Prediction Workshop | 23

Down Stream Distance (Chords)

4.0

Experiment 4th order 4th order Adapted

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Shape

4th Order Adapted Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vortex Breadth

Lateral Distance

4.0

8.0

12.0

16.0

20.0

Chord Length Downstream

129

-3.0

106.0

0.0

-2.0

-1.0

0.0

1.0

2.0

3.0

107.0

108.0

109.0

110.0

111.0

112.0

0.0

8.0

12.0

16.0

ARO Rotorcraft Wake Prediction Workshop | 24

20.0

Experiment 4th order 4th order Adapted

Chord Length Downstream

4.0

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Position

4th Order Adapted Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vertical Distance

Same number of cells in 1/16 of the area 130

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Tighter Grid Spacing in the Embedded Block

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vertical Distance from Core (in)

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

0.6

0.2

0.0

-0.2

-0.4

Normalized Horizontal Velocity

0.4

-0.6

131

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

15

5

0

-5

-10

ARO Rotorcraft Wake Prediction Workshop | 26

-15

Experiment Coarse Fine

Horizontal Distance from Core (in)

10

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Distance 14.1 Distancefrom from¼ ¼chord: chord:17.8 10.7 2.0 cctiptip 4.0 7.1

4th Order Adapted Solutions with Refined Grid

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Normalized Veritcal Velocity .

Peak-to-Peak Spanwise Velocity

0.0

0.2

0.4

0.6

0.8

1.0

0.0

8.0

12.0

16.0

Down Stream Distance (Chords)

4.0

20.0

132

0.0

0.2

0.4

0.6

0.8

1.0

0.0

8.0

12.0

16.0

Experiment Coarse Fine

20.0

ARO Rotorcraft Wake Prediction Workshop | 27

Down Stream Distance (Chords)

4.0

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Strength

4th Order Adapted Solutions with Refined Grid

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Peak-to-Peak Vertical Velocity .

Vortex Height

4.0

8.0

12.0

16.0

20.0

Down Stream Distance (Chords)

133

0.0

0.0

0.0

4.0

8.0

12.0

16.0

4.0

8.0

12.0

16.0

0.0

8.0

12.0

16.0

20.0

ARO Rotorcraft Wake Prediction Workshop | 28

Down Stream Distance (Chords)

4.0

Experiment Coarse Fine

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Shape

4th Order Adapted Solutions with Refined Grid

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vortex Breadth

Lateral Distance

4.0

8.0

12.0

16.0

20.0

Chord Length Downstream

134

-3.0

106.0

0.0

-2.0

-1.0

0.0

1.0

2.0

3.0

107.0

108.0

109.0

110.0

111.0

112.0

0.0

8.0

12.0

16.0

Experiment Coarse Fine

20.0

ARO Rotorcraft Wake Prediction Workshop | 29

Chord Length Downstream

4.0

Mf = 0.15, Tf = 518 °R, Pf = 14.696 psi, D = 6.5° Vortex Position

4th Order Adapted Solutions with Refined Grid

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Vertical Distance

Observations

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ƒ Adequate overlap for communication among blocks can become an issue with the adaptive block

ƒ The process improved the resolution of the vortex

ƒ Adaptation allows for greater grid resolution near the vortex

ƒ Grid adaptation process aligned the grid with the vortex center

4th Order Adapted Solutions

Vortex Prediction Compared to WT Data

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ƒ Figure of merit is not a good convergence metric

ƒ Rotor wake must remain as much as possible within a single grid block and away from fringe points to avoid convergence hang ups

ƒ Cylindrical grids naturally have finer cell volumes near the rotor

ƒ Steady calculations using pie-slice domain

ƒ Judicious use of points is critical to efficiently predict hover performance

Application to Hover

136

1 2 3 4

1 2 3 4

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ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ƒ Restarts become less effective for hover cases

ƒ Adequate overlap for communication among blocks can become an issue with the adaptive block

ƒ Particularly for low thrust cases, vortices can bunch up and grid adaptation schemes can get confused on which vortex to center on

ƒ Grid adaptation to a rotor in hover is tricky… too many vortices to track!

137

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Application to Hover Analysis

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138

ƒ Laminar to turbulence boundary layer transition

ƒ Aeroelastic wind up

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Other Challenges for Hover Performance

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ƒ Adaptation in the fix-wing problem is straight-forward compared to rotors in hover

ƒ RANS methods with standard turbulence models in the near field and Euler solutions in the wake are capable of predicting vortices accurate to 20 chord length behind the ¼ chord with higher order methods and grid adaptation

ƒ The BVWT data is useful to benchmark methods for vortex prediction, though measurements only went 20 chord lengths behind the ¼ chord

Summary and Conclusions

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This project was funded by the Center for Rotorcraft Innovation (CRI) and the National Rotorcraft Technology Center (NRTC), U.S. Army Aviation and Missile Research, Development and Engineering Center (AMRDEC) under Technology Investment Agreement W911W6-06-2-0002, entitled National Rotorcraft Technology Center Research Program. The authors would like to acknowledge that this research and development was accomplished with the support and guidance of the NRTC and CRI. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the AMRDEC or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.

Acknowledgements

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ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

ARO Rotorcraft Wake Prediction Basic Research Workshop March 16 - 17, 2009 - Georgia Institute of Technology - Atlanta High-order Cartesian partitioning method for the capture of the blade tip vortex S. P´ eron1 , C. Benoit1 , G. Jeanfaivre1 , T. Renaud2 , ONERA 1 CFD

and Aeroacoustics Department 29, Avenue de la Division Leclerc, BP 72, 92322 Chˆ atillon Cedex, France [email protected], [email protected], [email protected] 2

Applied Aerodynamics Department 8, rue des Vertugadins, 92190 Meudon, France [email protected]

In the past few years, we have developed a Cartesian overset mesh adaptation method for the simulation of inviscid or viscous flows, based on the original work of Meakin [1]. This technique starts from a set of near-body curvilinear grids, describing the bodies involved in the simulation. A set of overset Cartesian grids is then automatically generated to discretize the remaining part of the computational domain. This set of grids is periodically regenerated to adapt to the flow features. Classical Chimera transfers are used between the body curvilinear grids and the Cartesian grids, and between overset Cartesian grids as well. Originally, the 2nd -order Jameson solver and 2nd -order interpolations for Chimera transfers were used. This technique has been first applied to the inviscid simulation of rotors in hover in [2], and later on, of a realistic rotor in descent flight [3]. Results on the HART test-case concerning the capture of the BVI will be presented at the workshop. Some success was achieved in capturing the blade-vortex interaction involved in this problem. More recently, this method has been extended to the 3rd order of accuracy by modifying the Jameson solver and using 3rd order interpolations [4]. An extension of this technique to the fifth order of spatial accuracy has been achieved on Cartesian grids. Our contribution to the workshop is to investigate the influence of the accuracy of the solver on the capture of the tip vortex of an isolated blade in hover. It is proposed here to analyze in more details results of [4] focusing on the vortex structure in its early advection. The chosen test-case is a 7A blade in hover, with a span equal to R = 15 c, where c denotes the chord length. The tip Mach number is equal to 0.617, and the dimensionless rotating velocity is equal to 0.4113. The collective pitch is θ = 10◦ , the conicity angle is β = 3◦ , and the linear twist slope is α = −8.3. The blade mesh is a C-type mesh, with 141 × 27 × 18 nodes, such that the mesh is artificially closed on the last cell of the tip (fig. 1). Three inviscid simulations are performed, corresponding to 2nd , 3rd and 5th -order solvers respectively. First, a 2nd -order Finite-Volume Jameson space-centered scheme is used. A scalar artificial dissipation is used on the blade grid, with coefficients k2 = 0.5 and k4 = 0.032, whereas a matrix dissipation is set on Cartesian grids, with k2 = 0.5 and k4 = 0.016. Then, 1 143

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009 rd

a 3 -order space-centered scheme is used on both Cartesian and curvilinear grids, using the same artificial dissipation as for the 2nd -order scheme. The last simulation is based on a 5th -order space-centered scheme, using a Finite-Difference approach [5] on Cartesian grids and the previous 3rd -order space-centered scheme on curvilinear grids, with a 6th -order linear 1 artificial viscosity, with coefficient k4 = . 60 Chimera interpolations are of a 2nd -order of accuracy for the 2nd -order computation, and of a 3rd order of accuracy for higher-order computations. The stencil is corrected for one layer of interpolated cells at overlap borders and at the fringe of blanked cells, in order to get 2nd -order formulations locally. A backward Euler scheme, with a LDU implicit phase, is used for time integration, with a CFL number equal to 25 and 8 for the 2nd and higher-order solvers respectively. The Cartesian grids are adapted to the solution every 1000 iterations, using the vorticity as the refinement indicator. The number of points is multiplied by 1.4 at each remeshing, resulting in 20 million points after 6 remeshings. The spatial step in the finer Cartesian grid roughly equal to 3% of the chord length.

Figure 1: View of the blade surface mesh in the blade tip region.

The blade tip vortex is captured during more than half a revolution for both simulations, which is illustrated by the isosurface ω = 10 of the vorticity magnitude on figures 2 to 4). Note that the mesh adaptation is located in the blade wake. Slices at several distances past the blade have been performed (figs. 5 to 13). It appears clearly that the blade tip vortex is more intense and more confined if higher-order solvers are used, and that its structure is more elliptic. The vorticity magnitude in the core is roughly equal to 19.3, 19.6 and 19.8 respectively for the 2nd , 3rd and 5th -order computations until 4 chords past the trailing edge, and decreases to a value of 17.6 for the 2nd -order solver 9 chords past the blade trailing edge, whereas the vorticity magnitude is equal to 19.4 for the 5th -order solver at the same distance.

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ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Figure 2: 2nd -order computation, isosurface ω = 10.

Figure 3: 3rd -order computation, isosurface ω = 10.

Figure 4: 5th -order computation, isosurface ω = 10.

3

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ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Figure 5: 2nd -order computation, isovalues of vorticity magnitude, one chord past the trailing edge of the blade.

Figure 6: 3rd -order computation, isovalues of vorticity magnitude, one chord past the trailing edge of the blade.

Figure 7: 5th -order computation, isovalues of vorticity magnitude, one chord past the trailing edge of the blade.

4

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ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Figure 8: 2nd -order computation, isovalues of vorticity magnitude, 4 chords past the trailing edge of the blade.

Figure 9: 3rd -order computation, isovalues of vorticity magnitude, 4 chords past the trailing edge of the blade.

Figure 10: 5th -order computation, isovalues of vorticity magnitude, 4 chords past the trailing edge of the blade.

5

147

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

Figure 11: 2nd -order computation, isovalues of vorticity magnitude, 9 chords past the trailing edge of the blade.

Figure 12: 3rd -order computation, isovalues of vorticity magnitude, 9 chords past the trailing edge of the blade.

Figure 13: 5th -order computation, isovalues of vorticity magnitude, 9 chords past the trailing edge of the blade.

6

148

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References [1] R. Meakin, Adaptive Spatial Partitioning and Refinement for Overset Structured Grids, Computer Methods in Applied Mechanics and Engineering, vol. 189, pp 1077-1117 (2000). [2] C. Benoit and G. Jeanfaivre, Three Dimensional Inviscid Isolated Rotor Calculations Using Chimera and Automatic Cartesian Partitioning Methods, Journal of the American Helicopter Society, pp 128-138 (2003). [3] Renaud T., Perez G., Benoit C., Jeanfaivre G., P´eron S., Blade-Vortex Interaction Capture by CFD, 34th European Rotorcraft Forum (2008). [4] O. Saunier, C. Benoit, G. Jeanfaivre, A. Lerat, Third-order Cartesian overset mesh adaptation for solving steady compressible flows, International Journal for Numerical Methods in Fluids, vol. 57, pp 811-838 (2007). [5] Lerat A., Corre C., High-order residual-based compact schemes on structured grids, CFD Higher-Order Discretization Methods, Von Karmann Institute LS 2006-01, pp 1-105 (2006).

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Figure 1: Isosurface of Q criterion and slice of the adapted mesh in the blade tip region.

2

150

1

Direction - Conférence

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152

S. Peron, C. Benoit, G. Jeanfaivre, T. Renaud, O. Saunier

High-order Cartesian partitioning for the capture of the blade tip vortex

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

3

Direction - Conférence

•

•

Accurate and efficient capture of the blade tip vortex of an isolated blade in hover Capture of the blade-vortex interaction of a multibladed rotor in forward flight

•

•

•

153

• Optimized schemes (no metric storage,…) • High-order solver easy to implement • Optimized Chimera interpolations

Chimera technique: bodies in relative motion Automatic Cartesian mesh generation and adaptation Specific solver for Cartesian grids:

CFD tools:

•

•

Aims:

Outline

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

4

Direction - Conférence

•

•

Fine description of the geometry Short extension

•

•

•

•

Discretize the computational domain Automatically generated Regular grids (constant step on each level) Can be adapted to the flow features

Cartesian grids:

•

•

Body grids given by the user:

154

Cartesian mesh generation

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

5

Direction - Conférence

•

•

•

Finite-Volume formulation on both curvilinear and Cartesian grids 2nd order nonlinear artificial viscosity,4th order linear artificial viscosity Chimera joins between all grids

Correction of the dispersive error of Jameson’s scheme Finite-Volume formulation on curvilinear grids Finite-Difference approach on Cartesian grids Same dissipation as for Jameson’s scheme 3rd order interpolation between Cartesian grids

•

•

•

•

155

3rd order Finite-Volume formulation on curvilinear grids 6th order directional scheme on Cartesian grids (Lerat, Corre) 6th order linear artificial viscosity 3rd order interpolations on Cartesian grids

5th order scheme

•

•

•

•

•

3rd order on curvilinear and Cartesian grids (Lerat, Cinnella)

•

•

•

2nd order (Jameson)

High-order solver for the Euler equations

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

6

Direction - Conférence

•

•

•

Mtip=0.617

:=0.4113 (dimensionless)

•

•

C-type 141x27x18 nodes

156

Evaluation of high-order solver capabilities in capturing the blade tip vortex

•

•

Blade mesh

T=10º, E=3º, D=-8.3 (linear twist)

•

7A isolated blade in hover

Application to the capture of the blade tip vortex

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

7

Direction - Conférence

•

•

•

Refinement indicator: vorticity

2nd order accurate solver, with matrix diss. on Cartesian grids 3rd order accurate solver, with matrix diss. on Cartesian grids 5th order accurate solver, with 6th order linear dissipation

•

•

157

One layer of interpolated cells at overlap borders, and at the fringe of blanked cells. 2nd and 3rd order interpolations

Chimera technique:

•

•

•

Spatial discretization solvers:

•

Cartesian partitioning technique:

Numerical methods

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

8

Direction - Conférence

•

•

Coarse mesh : 'h=15% chord on finest Cartesian grids (5M pts) Medium mesh : 'h=7.5% chord on finest Cartesian grids (11 M pts) Fine mesh : 'h=3.5% chord on finest Cartesian grids (44 M pts)

•

•

Focus: early age of the vortex 'h=3% chord, 20 M pts

158

Comparison of simulations of increasing orders of accuracy on a fine mesh :

•

•

•

Comparison of simulations of different grid resolutions

Inviscid simulations of an isolated blade in hover

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

9

Direction - Conférence

2nd order

159

3rd order

5th order

View of the adapted mesh and isosurface of vorticity =5

• 2 points in the vortex core • Better preservation of the vortex with the 5th order solver

Inviscid simulations on medium mesh

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

10

Direction - Conférence

Medium mesh

Fine mesh

160

resolution) • < > 30 deg: regular loss due to numerical diffusion, and mesh resolution

• 0 < < < 30 deg: 40% of vorticity loss (independent on the mesh

Coarse mesh

Vortex age in the vortex core

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

11

Direction - Conférence

2nd order

161

3rd order

5th order

View of the adapted mesh and isosurface of vorticity =10

• 4 points in the vortex core • Adaptation located in the wake region • Wake preserved during ¾ a revolution

Study of the early-aged vortex: inviscid simulations on a fine mesh

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

12

Direction - Conférence

2nd order: core = 19.4

162

3rd order: core = 21.3

• 1 chord past the trailing edge of the blade

Comparison of the vortex shape

5th order: core = 19.6

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

13

Direction - Conférence

2nd order: core = 19.3

• < = 30 deg

163

3rd order: core = 19.6

Comparison of the vortex shape

5th order: core = 19.6

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

14

Direction - Conférence

2nd order: core = 17.6

• < = 45 deg

164

3rd order: core = 18.6

Comparison of the vortex shape

5th order: core = 19.3

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

15

Direction - Conférence

2nd order: core = 11.7

• < = 90 deg

165

3rd order: core = 12.4

Comparison of the vortex shape

5th order: core = 15.3

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

16

Direction - Conférence

•

•

Better wake-capturing Higher levels of vorticity More accurate vortex evolution (considering Euler equations) CPU time increase of only 15 %

166

Promising technique for the capture of the BVI

•

•

•

•

High-order solvers using Cartesian partitioning provide:

Conclusions

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

17

Direction - Conférence

•

•

BO105 rotor in descent flight rigid blade assumption Dq=-4.2º, P=0.15, Zb=11.22, Mtip=0.635

•

•

167

2nd order accurate computations on Chimera coarse / medium / fine meshes 3rd order accurate computations on a Cartesian adapted medium mesh

Inviscid unsteady computations, 'D 1 > E 3 F G. "   H  9   / . ,) "  I  J   .+-2;(BB: %(' 2 H     K 3  GH ,L   1

  2    3       ,F F"   J     .+&2((BB+ %*'3 /2 #M KG2 3  F3   I    7  / 9   . 79 J            .&;2&&NN;

%+'  1 7  G   F 9     # 3   H  J    .*;2&(BBB %-'M7O #MK G1              J           .&A ((BB:

263

264

ARO Rotorcraft Wake Prediction Basic Research Workshop

Mar.16-17, 2009, Georgia Institute of Technology

*Department of Aerospace Engineering, KAIST, Korea ** Rotor Department, KARI, Korea

Duck Joo Lee*, Seong Yong Wie*, Ki hoon Chung**

Numerical Investigation of Rotor Wake and Tip-vortex Dynamics using Free-wake Coupled with Vortex-Lattice, Potential-Panel and CFD Method

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

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ARO Rotorcraft Wake Prediction Basic Research Workshop

9 Wake is a key to predict the unsteady aerodynamics of helicopter

• Helicopter rotor aerodynamics

Introduction

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

F (t )

Usteady loading F (t )dt

dF (t ) dt

266

Noise

mx(t )  cx (t )  kx(t )

Vibration

0

³

T

Performance

F (t )

Vinduced _ wake

ARO Rotorcraft Wake Prediction Basic Research Workshop

V

VFreestream

– Unsteady loading is affected by rotor wake Æ performance, vibration, noise of rotor – Effective angle of attack is changed by induced velocity

• The importance of rotor wake

Introduction

ARO Rotorcraft Wake Prediction Basic Research Workshop, March 16-17, 2009

– Wake Simulation: Good – Fast computation – Incompressible(M