Theoretical and Computational Modeling of Dynamic Stall for Rotorcraft Applications

Transcription

1 Theoretical and Computational Modeling of Dynamic Stall for Rotorcraft Applications Ashok Gopalarathnam and Jack Edwards Department of Mechanical and Aerospace Engineering North Carolina State University 2016 Fluid Dynamics Program Review US Army Research Office Arlington, VA July 19-22,

2 Personnel Principal Investigators: Ashok Gopalarathnam, NC State Jack R. Edwards, NC State Students: Shreyas Narsipur, PhD candidate, NC State Jianghua Ke, PhD graduate (2014), NC State Anupam Kulkarni, PhD candidate, NC State Pranav Hosangadi, PhD candidate, NC State (partial support) Minao Shen, PhD candidate, NC State (partial support) 2

3 Overall Goals Use a combination of existing and new high-order (CFD) and low-order methods (LOM) to improve understanding of and modeling capability for the rotorcraft-relevant dynamic stall CFD: RANS CFD for informing LOM development Hybrid LES/RANS for (hopefully) better predictive capability Low-order method (LOM): With guidance from CFD and experiment, develop physics-based LOM by augmenting inviscid theory for approximate, but fast, analysis capability. 3

4 Outline Computational modeling Theoretical modeling Conclusions 4

5 53 rd Aerospace PHD Final Sciences Defense Meeting Presentation Reynolds-Averaged Navier-Stokes Modeling State of the Practice approach Used to provide data for theoretical modeling effort Various RANS models incorporated into NCSU s REACTMB code Spalart-Allmaras Menter BSL / SST Menter BSL / SST with Menter-Langtry transition formulation Arbitrary Eulerian / Lagrangian formulation for mesh movement Spalart-Allmaras model used for LOM cases presented herein 5

6 53 rd Aerospace PHD Final Sciences Defense Meeting Presentation Large-Eddy / Reynolds-Averaged Navier-Stokes Modeling Goal: Better predictive capability for airfoils / blades / wings near static stall and undergoing dynamic stall Approach: Assessment and further development of NCSU s LES/RANS framework (Gieseking, et al, 2010) in this scope Gieseking s model transitions from RANS to LES ~ where boundary layer changes from logarithmic to wake-like structure t (1 ) t, sgs k Hybrid eddy viscosity 1 1 [1 tanh( ( 2 l g ( max, louter) l l inner d 2 outer inner 1))] Flow-dependent blending function Ratio of turbulence length scales Inner scale l outer 10 C 1/ 2 k k R Outer scale depends on ensembleaveraged data 6

7 53 rd Aerospace PHD Final Sciences Defense Meeting Presentation Large-Eddy / Reynolds-Averaged Navier-Stokes Modeling LES/RANS model variants tested for several experiments: Aerospatiale A airfoil (Gleyzes, et al. (1998) 13.3 A.O.A;) NACA 0012 airfoil near static stall (Pruski, et al. (2013); 16.7 A.O.A) NACA 0012 airfoil undergoing dynamic stall (Pruski, et al. (2013); 11 to 31 A.O.A; k r = 0.1) Sensitivity studies performed (J. Ke, Ph.D. dissertation, 2014; various AIAA papers) LES/RANS model type (including Menter/Langtry transition model) Mesh resolution / topology Spanwise mesh extent Free-air vs. wind-tunnel (static-stall NACA 0012) Gieseking s model successful for mildly separated flows but does not perform well for dynamic cases and for cases that exhibit bifurcation-like behavior 7

8 PHD Final Defense Presentation New LES/RANS modeling approach (AIAA Paper ) Goal: Approach valid for non-statistically stationary turbulent flows Dynamic evolution of RANS-to-LES interface Completely local formulation l outer 10 C t, EVT 1/ 2 Outer scale depends on eddy viscosity determinable from a transport equation ~ t 1 L 2 VK ( ~ u S x t, EVT j x j S x C ~ f j j ) f S 2 p ~ S t 2 ~ R ( t ) x x j j 1 ~ t max( 2 d Eddy viscosity transport equation (Edwards, 1993) Von Kármán length scale used to control excessive eddy-viscosity production due to fluctuating strain rates, C vk 1 L 2 VK ) 8

9 PHD Final Defense Presentation New LES/RANS modeling approach (AIAA Paper ) Control of outer-layer length scale: Von Kármán length scale used to increase destruction term in regions of high unsteadiness Controls rate of growth of eddy viscosity used to define instantaneous outer-layer length scale 9

10 PHD Final Defense Presentation New LES/RANS modeling approach (AIAA Paper ) Additional degrees of freedom possible due to decoupling of RANS-to-LES transition location from LES/RANS eddy viscosity: Inclusion of intermittency effect in outer-layer length scale: ~ l 1 l max 0, C outer louter outer 2 2 LVK d Use of extra eddy viscosity to energize buffer layer (improves skin-friction prediction): k t ( 1 ) t, sgs C2 b (1 b ) t, EVT 10

11 PHD Final Defense Presentation Test Cases New LES/RANS model variants tested for several experiments: DeGraaf and Eaton incompressible flat-plate boundary layers (Re θ =2900, Re θ =13000) Elena and Lacharme compressible flat-plate boundary layer (Re θ =4700) Aerospatiale A airfoil (Gleyzes, et al. (1998) 13.3 A.O.A;) Greenblatt, et al. incompressible flow over a 2D hump (underway) 11

12 PHD Final Defense Presentation DeGraaf / Eaton Flat Plate Boundary Layers Re θ =2900 Re θ =13000 Intermittency broadens and shifts the blending function Eddy viscosity increased, velocity in buffer region drops Better results with SST (not shown), but not BSL 12

13 PHD Final Defense Presentation Combating log law mismatch Re θ =13000 Additional degrees of freedom provide improved log-law response Not perfect though an optimal eddy viscosity distribution appears possible 13

14 PHD Final Defense Presentation Aerospatiale A Airfoil Mid-chord velocity Trailing-edge velocity Predictions similar to earlier LES/RANS models 14

15 PHD Final Defense Presentation Turbulent flow over a 2D hump (Greenblatt, et al.) Simulations underway using new LES/RANS formulation 15

16 Outline Computational modeling Theoretical modeling Background LEV-dominated unsteady airfoil flows at low Re Slow vs. Fast unsteady motions Objectives and overview of current approach Modeling dynamic onset of reversed flow using decambering Prediction of LEV initiation Conclusions 16

17 Background: Low-Re LEV-dominated airfoil flows for Fast unsteady motions Research funded by AFOSR ( ), PM: Dr. Doug Smith, Integrated theoretical, computational, and experimental approach PIs: Gopalarathnam, Edwards, and OL (AFRL) Low-order method: We augmented an unsteady thin-airfoil theory for intermittent leading-edge vortex (LEV) shedding We developed a criterion for initiation of LEV formation using a Leading-Edge Suction Parameter or LESP, which can be tracked in unsteady, inviscid methods like unsteady thin-airfoil type theories During unsteady motion, when instantaneous LESP (= A 0 from TAT) exceeds critical LESP, LEV formation is ON, else it is OFF. LEV shedding modeled using discrete vortex shedding. Details in Ramesh et al., JFM, 2014 Key finding: For a given airfoil and Reynolds number, critical LESP is independent of motion kinematics (pitch, plunge, pivot point, rates). This independence is true so long as LEV formation is not preceded by significant flow reversal near the trailing edge. That is, it starts to become invalid for low-rate motions. 17

18 Background: Slow vs. Fast Motions α c Slow pitch up (K = = 0.005) 2V TE Separation, No LEV α c Medium pitch up (K= = 0.05) 2V TE separation, LEV formation α c Fast pitch up (K= = 0.25) 2V No TE Separation, LEV formation 18

19 Outline Computational modeling Theoretical modeling Background Objectives and overview of current approach Modeling dynamic onset of reversed flow using decambering Prediction of LEV initiation Conclusions 19

20 Objectives of current theoretical approach Develop physics-based low-order theoretical approach for helicopterrelevant dynamic stall, focusing on low Mach numbers Augment unsteady thin-airfoil formulation for combinations of unsteady trailing-edge stall and LEV formation Overview of Approach Dissect the dynamic stall process into two phenomena: (a) unsteady trailing-edge flow reversal and (b) LEV formation Theoretically model each separately using physics-based approaches (a) Onset of reversed flow (TE stall) using dynamic decambering Steady flow C n - and C m - used as input (b) LEV formation using the LESP concept adapted from previous AFOSR work Combine the models to handle light and deep dynamic stall Use RANS CFD for guidance and validation of LOM 20

21 Outline Computational modeling Theoretical modeling Background Overview of current approach Modeling dynamic onset of reversed flow using decambering Details of earlier version and results in AIAA Paper Prediction of LEV initiation Conclusions 21

22 Outline Low-order method (LOM) Modeling dynamic onset of reversed flow using dynamic decambering Inviscid foundation Leading-edge suction Model for steady flow (input for unsteady) Time-lag to model boundary-layer convection lag Unsteady flow results 22

23 LOM: Inviscid foundation Based on the time-stepping lumped-vortex element (LVE) algorithm provided by Katz and Plotkin Camberline divided into panels with discrete vortex at quarter chord, zero-normal flow control point at 3c/4 point Arbitrary motions can be handled Takes into account Motion-induced camber effects Wake vorticity (circulation lag) Time variation of LE suction and normal force Augmentation of theory in current work focusses on effects of boundarylayer convection lag in unsteady flow 23

24 LOM: Leading-edge suction Leading-edge suction and the LESP parameter was shown to be critical to LEV formation in fast unsteady flows Hypothesis: LESP is also an important factor for determining flow reversal and its effects Reason: To first order, flow separation/reversal-onset is affected by the pressure difference between LE suction peak and TE pressure (C pdiff ). LESP and C s directly relate to the peak suction and, hence, C pdiff LESP can be used as a substitute for the C pdiff parameter 24

25 Outline Theoretical modeling Modeling dynamic onset of reversed flow using decambering Inviscid foundation Leading-edge suction Model for steady flow (inputs for unsteady) Time-lag to model boundary-layer convection lag Unsteady flow results 25

26 Methodology Model for steady flow (input data for unsteady) Decambering function for an example post-stall δ l m f 0 Beddoes Equation: f 0 = 2 C nviscous C ninviscid 1 2 Decambering function defined using d f and m for f 0 < x < c For each, Newton iteration finds d f and m to match viscous C l and C m data 26

27 Outline Theoretical modeling Modeling dynamic onset of reversed flow using decambering Inviscid foundation RANS CFD for guidance and validation Leading-edge suction Model for steady flow (input for unsteady) Model for boundary-layer convection time lag Unsteady flow results 27

28 Methodology Time lag for unsteady calculation Time-lag equation from modified Goman-Khrabrov (1992) is applied to the separation location from steady-flow input: df τ 1 + f(t) = f Original Goman-Khrabrov dt 0 α(t) τ 2 α (t) equation Model modified to use aerodynamic parameter, LESP or A 0, instead of geometric parameter τ 1 df dt + f(t) = f 0 A 0 (t) τ 2 A 0 (t) Modified Goman-Khrabrov equation τ 1 = relaxation time constant (held constant in this work (= 1)) τ 2 = time delay parameter single value of τ 2 for airfoil determined using CFD or experiment for one case, and used for all other motions Still need to verify if this will work across Reynolds number changes 28

29 Methodology Time stepping in unsteady calculations At time step, t f t, A 0 t, A 0(t) Goman-Khrabrov Equation: τ 1 df dt + f t = f 0 (A 0t τ 2 A 0t) f t+δt = f t + df dt Δt At time step, t+δt Interpolate from steady input to get δ l and m Apply decambering and calculate aerodynamic forces 29

30 Outline Theoretical modeling Modeling dynamic onset of reversed flow using decambering Unsteady flow results Case studies LOM vs. CFD/Exp 30

31 Results Case Studies Case Study Airfoil Reynolds Number Motion Parameters Pivot Nondim. Pitch Rate (K) / Reduced Frequency (k) Reference A NACA e6 0 o -35 o -0 o, pitch-up-return B NACA e6 0 o -20 o -20 o -0 o, pitch-up-hold-return 0%c K = CFD 25%c K = CFD C NACA e6 Plunge 25%c K = CFD D NACA e6 14 o ±10 o sinωt, pitch 25%c k = Exp E NACA e6 0 o -30 o -0 o, pitch-up-return 0%c, 50%c, & 100%c K = 0.01 CFD F NACA e6 Pitch-up-return 100%c K = CFD G NACA e6 Sinusoidal Pitch 25%c k = Exp 31

32 Results - Case Study A (NACA 0012, Re = 3e6, K = 0.005, Pivot = 0%c) 32

33 Results - Case Study A (NACA 0012, Re = 3e6, K = 0.005, Pivot = 0%c) Comparison of dynamic decambering with CFD separation 33

34 Results - Case Study E NACA 0012 Re = 3e6 Motion = 0 o -30 o -0 o, pitch-up-return K = 0.01 Varying pivot locations CFD LOM 34

35 NACA Re = 3e6 Pivot = 100%c Varying motion kinematics Results - Case Study F CFD LOM 35

36 Results - Case Study G NACA 4415 Exp data from OSU tests (Hoffmann et al., 1996) Re = 1.5e6 Pivot = 25%c k = Varying α mean and α max Exp LOM 36

37 Outline Computational modeling Theoretical modeling Background Overview of current approach Modeling dynamic onset of reversed flow using decambering Prediction of LEV initiation for high Re (Details in AIAA ) Critical events leading to LE formation Low vs. high Re number flows Conclusions 37

38 Results Events Leading to LEV Formation Event 1 Event 2 Event 3 38

39 Outline Computational modeling Theoretical modeling Background Overview of current approach Modeling dynamic onset of reversed flow using decambering In progress: Prediction of LEV initiation Critical events leading to LE formation Low vs. high Re number flows Conclusions 39

40 Results Effect of Reynolds Number (SD 7003, K = 0.40, 0 o -90 o -0 o Pitch Up - Return) Reynolds Number = 3x10 4 Reynolds Number = 3x

41 Results Sequence of Events for Re = 3e6 (SD 7003, K = 0.40, 0 o -90 o -0 o Pitch Up - Return) Event 1 Event 2 20% c Event 3 41

42 Results Sequence of Events for Re = 3e4 (SD 7003, K = 0.40, 0 o -90 o -0 o Pitch Up - Return) Event 1 Event 3 10% c Event 2 42

43 Results Variation of LESP with K (SD 7003) * * Variation of LESP with pitch rate at Re = 3e4. Variation of LESP with pitch rate at Re = 3e6. * LEV initiation event. 43

44 Results Variation of LESP with K (SD 7003) * * Variation of LESP with pitch rate at Re = 3e4. Variation of LESP with pitch rate at Re = 3e6. At low Re, LESP variation at LEV initiation (event 3) is small and independent of motion kinematics for a given pitch rate (as observed by Ramesh et al. (2014). At high Re, LESP variation at LEV initiation (event 2) is not independent of kinematics. 44

45 Outline Computational modeling Theoretical modeling Conclusions 45

46 Conclusions and Next Steps CFD effort has resulted in a new LES/RANS model; being tested for attached and separated flows at high Reynolds numbers LOM with time-lagged decambering is seen to be effective at predicting aerodynamics of light-ds cases a single τ 2 can be used for a given airfoil. Effort on-going to study effect of Re on τ 2 Events related to LEV formation identified: LEV initiation points differ between low and high Re. Non-negligible variation in LESP crit at high Reynolds numbers - find a parameter (possibly a modified LESP crit ) for initiation of LEV for high Reynolds number flows. CFD grid sensitivity also being checked. Next step: Integrate TE separation model with LEV model - final method should be capable of simulating any arbitrary airfoil motion within the incompressible flow regime. 46

47 PHD Final Defense Presentation Extra / Backup slides 47

48 PHD Final Defense Presentation A airfoil (α = 13.3 deg.; Gleyzes, et al) 3020x180x72 Skin Friction Trailing-edge velocity Swirl-strength iso-surfaces showing development of boundary-layer eddy structures Three LES/RANS models: Choi, et al (2008), Gieseking et al. (2010), and Gieseking et al. with Menter / Langtry transition model Inclusion of M-L transition improves initial skinfriction response but overly-energizes boundary layer Good results for velocity profiles near trailing edge for models without Menter/Langtry transition 48

49 PHD Final Defense Presentation NACA 0012 Static Stall (α = 16.7 deg.; Pruski, et al) Bifurcation-type response, depending on mesh resolution: 1152 x 224 x x 224 x x 224 x 256 Stabilized LEV on coarse mesh LEV detaches on fine meshes 16.7 PIV Leading edge axial velocity Image from 49

50 PHD Final Defense Presentation NACA 0012 Dynamic Stall (Pruski, et al) α varies from 11 to 31 ; reduced frequency = 0.1 Phase-locked PIV data available at α =16.7 during upstroke / downstroke 1152 x 224 x x 224 x 128 Upstroke experiment Trends similar to those shown for static-stall case Spanwise mesh refinement promotes flow attachment to the leading edge LES/RANS models use ensemble-averaging: not defined well for dynamic motion events Downstroke 50

51 Backup Issue with Flow Reattachment C n prediction on the SC1095 and HH-02 airfoil sections (Leishman et al. (1989)). Modeling the aerodynamic coefficients during the return motion has been an issue in all unsteady models. Most models apply modifications to the time lag equations to correctly predict reattachment. For example, the Beddoes-Leishman model uses a different value of time lag during the return motion to model reattachment to some degree of success

52 PHD Final Defense Presentation Old/Backup slides 52

53 Background: Low-Re LEV-dominated airfoil flows for Fast unsteady motions Unsteady thin airfoil theory was augmented with discrete vortex method for modeling intermittent LEV shedding: The method is called LDVM: LESP-modulated Discrete Vortex Method LESP criterion used as LEV formation on/off switch supersedes ad-hoc criteria in the literature works for rounded leading edges When LESP > LESP crit, LEV shedding is on, else off Details in Ramesh et. al, Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding, Journal of Fluid Mechanics, July LDVM code: 53

54 Background: Low-Re LEV-dominated airfoil flows for Fast unsteady motions 54

55 Methodology BL Convection Time Lag As pitch rate (K)/reduced frequency (k) varied for the motions, the maximum value of da 0 /dt for all motions was taken to compare the variation in τ 2. Calculated τ 2 values of various arbitrary motions for the NACA airfoil (CFD): α-lag A 0 -Lag 57

56 Methodology BL Convection Time Lag Calculated τ 2 values of various arbitrary motions for: NACA 0012 (CFD) α-lag A 0 -Lag NACA 4415 (Exp) 60

57 Methodology BL Convection Time Lag As pitch rate (K)/reduced frequency (k) varied for the motions, the maximum value of da 0 /dt for all motions was taken to compare the variation in τ 2. Calculated τ 2 values of various arbitrary motions for the NACA airfoil (CFD): α-lag A 0 -Lag 61

58 Methodology BL Convection Time Lag As pitch rate (K)/reduced frequency (k) varied for the motions, the maximum value of da 0 /dt for all motions was taken to compare the variation in τ 2. Calculated τ 2 values of various arbitrary motions for the NACA airfoil (CFD): Varying Pivot Varying Pivot α-lag A 0 -Lag 62

59 Methodology BL Convection Time Lag Calculated τ 2 values of various arbitrary motions for: NACA 0012 (CFD) α-lag A 0 -Lag NACA 4415 (Exp) 63

60 Results - Case Study B (NACA 0012, Re = 3e6, K = 0.005, Pivot = 25%c) 64

61 Results - Case Study C (NACA 23012, Re = 3e6, K = , Plunge) 65

62 Results - Case Study D (NACA 4415, Re = 1.5e6, k = 0.019, Pivot = 25%c) 66