Theory, Computation and Experiment on Criticality and Stability of Vortices Separating from Edges

Transcription

1 Theory, Computation and Experiment on Criticality and Stability of Vortices Separating from Edges Ashok Gopalarathnam Department of Mechanical and Aerospace Engineering North Carolina State University AFOSR Flow Interactions and Control Program Review Ballston, VA July 29-31,

2 Personnel Principal Investigators: Ashok Gopalarathnam, NC State Jack R. Edwards, NC State Michael Ol, AFRL-WPAFB Key Collaborators: Kenneth Granlund, AFRL-WPAFB (Post-doctoral scholar) Students: Yoshikazu Hirato, PhD candidate, NC State Minao Shen, PhD student, NC State Sachin Aggarwal, recent MS graduate, NC State 2

3 Outline Background from 2D low-order method for vortex-dominated airfoil flows Spinoff application: Aeroelastic limit-cycle oscillations Related effort: Modeling of dynamic TE separation during lowfrequency pitch oscillations Current effort on low-order method for vortex-dominated wing/rotor flows - Year 1 Progress Next steps 3

4 Background 2D LEV-Dominated Airfoil Flows Effort from previous AFOSR grant FA Theoretical, Computational, and Experimental Studies on the Aerodynamics of Perching Flight, Main objectives: To use integrated theory-cfd-experimental studies to advance understanding of low Reynolds number unsteady aerodynamics of airfoils and flat plates Focus on high-rate, large-amplitude motions where the flows are dominated by leading-edge vortices (LEVs) Phenomenological augmentation of classical theory and low-order models to account for non-linear effects Use directed CFD and experimental studies to guide augmentation of theory 4

5 Background The LDVM Approach Main outcome: the LDVM low-order method for unsteady airfoil flows with intermittent LEV shedding Primarily the PhD work of Dr. Kiran Ramesh (NCSU PhD completed 2014). Kiran is now post-doc at NC State, preparing for academic career. Interested in post-doc/faculty opportunities. Details in recent paper: Ramesh, Gopalarathnam, Granlund, Ol, and Edwards, Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding," Journal of Fluid Mechanics, Volume 751, July 2014, pp Datasets and LDVM code soon from: Extensions to perching and hovering flight in AIAA

6 Background Overview of LDVM LDVM = LESP-modulated Discrete Vortex Method, where LESP = Leading-Edge Separation Parameter Key elements: A large-angle unsteady thin airfoil theory A parameter for monitoring the LE suction: LESP = A 0 A critical value of LESP that controls the maximum suction that a leading edge can support at a given Re Criticality of flow at LE affecting LE stall has been known for some time (Evan & Mort, 1959, Beddoes, 1978, Jones & Platzer, 1997, Ekaterinaris & Platzer, 1998, etc.) Our work connect this idea to the A0 parameter as an LEV switch 6

7 Background Overview of LDVM LESP crit depends only on airfoil and Re; independent of kinematics LEV shedding on when LESP > LESP crit. Else LEV shedding off When LEV shedding is on a discrete vortex released from LE at each time step, with strength such as to maintain LESP at critical value Discrete vortices in flow influence forces and LESP at each time step Key benefit: the intermittent LEV shedding modulated by LESP supercedes ad-hoc criteria for LEV shedding (continuous shedding or shedding determined by critical angle of attack) 7

8 Background Sample Results from LDVM Details in various papers Results shown here for 3 examples: Flat plate undergoing 0-90 deg pitching flow and force comparisons Sinusoidal plunge motion at Re = 100,000 video only Abstraction of a hovering motion plunging in zero-freestream flow 8

9 Example 1 - Motion Flat plate undergoing pitch from 0-90 deg, pivot about LE K = 0.2, Re = 1,000 Results compared to results from Wang and Eldredge (2011) using Eldredge s viscous vortex particle high-order code (couplevpm) LESP a 9

10 Example 1 Flow 10

11 Example 1 Forces 11

12 Background Sample Results from LDVM Results shown here for 3 examples: Flat plate undergoing 0-90 deg pitching flow and force comparisons Sinusoidal plunge motion at Re = 100,000 video only Abstraction of a hovering motion plunging in zero-freestream flow 12

13 Example 2 Video comparison 13

14 Background Sample Results from LDVM Results shown here for 3 examples: Flat plate undergoing 0-90 deg pitching flow and force comparisons Sinusoidal plunge motion at Re = 100,000 video only Abstraction of a hovering motion plunging in zero-freestream flow 14

15 Example 3 - Motion SD7003 airfoil undergoing upward plunge with fixed pitch angle Zero freestream velocity H1 motion consider here More details in AIAA Paper a LESP 15

16 Example 3 - Flows CFD Low-order 16

17 Example 3 - Forces 17

18 Outline Background from 2D low-order method for vortex-dominated airfoil flows Spinoff application: Aero-elastic limit-cycle oscillations Related effort: Modeling of dynamic TE separation during lowfrequency pitch oscillations Current effort on low-order method for vortex-dominated wing/rotor flows - Year 1 Progress Next steps 18

19 Spinoff Aeroelastic LCO of airfoil Collaboration with Dr. Joseba Murua, Lecturer, U. of Surrey Funded by University Global Partnership Network (UGPN) Effort by Kiran Ramesh, co-advised on this effort by Murua and Gopalarathnam Coupling of LDVM with classical 2-DOF structural model for time marching airfoil with intermittent LEV shedding Aerodynamic model (LDVM) Structural model 19

20 Spinoff Aeroelastic LCO of airfoil Sample LCO result due to flow-induced oscillation 20

21 Spinoff Aeroelastic LCO of airfoil This application is an excellent illustration of the need for loworder methods that capture the main flow physics Each data point on the bifurcation curve was an outcome of running the aero-structure model for 1200 convective times (typical) Timing and strength of LEVs is critical for prediction of such oscillations (Kinsey & Dumas, AIAA J, 2008); could be useful for flow-energy harvesting Article in preparation for JFS 21

22 Outline Background from 2D low-order method for vortex-dominated airfoil flows Spinoff application: Aero-elastic limit-cycle oscillations Related effort: Modeling of dynamic TE separation during lowfrequency pitch oscillations Current effort on low-order method for vortex-dominated wing/rotor flows - Year 1 Progress Next steps 22

23 Related Effort Dynamic TE Separation LDVM does not model trailing-edge separation and stall Helicopter-relevant dynamic stall occurs with TE separation preceding dynamic-stall vortex (DSV) or LEV formation New effort to develop a model for dynamic TE separation and combine it with LDVM to develop low-order model for dynamic stall Emphasis on methods rooted in theory, with minimal reliance on empirical parameters Funded by grant from ARO W911NF , PM: Dr. Bryan Glaz Early efforts are focused on modeling dynamic TE stall using a time-lag approach with static airfoil lift data as input 23

24 Related Effort Dynamic TE Separation Sample result hysteresis loop in lift due to a pitching motion Details in Narsipur, S., Gopalarathnam, A., and Edwards, J. R., "A Time-Lag Approach for Prediction of Trailing-Edge Separation in Unsteady Flow," AIAA Paper , June

25 Outline Background from 2D low-order method for vortex-dominated airfoil flows Spinoff application: Aero-elastic limit-cycle oscillations Related effort: Modeling of dynamic TE separation during lowfrequency pitch oscillations Current effort on low-order method for vortex-dominated wing/rotor flows - Year 1 Progress Next steps 25

26 Current Effort Main Goals Continue integrated CFD-experiment-theory effort to address 3D LEV-dominated flows on finite wings and rotors Develop a low-order method for LEV-dominated wing flows Address outstanding questions in wing/rotor flows: How can the LESP concept be extended to 3D? What will the 3D structure of resulting LEVs look like? What is the interplay between LEV, tip vortex and trailingedge starting vortex structures Does planform shape matter? Does vortex burst play a role? Collaborate with other AFOSR PIs to develop and share rich data sets on translating and rotating wings 26

27 Current Effort Year-1 Goals Investigate if LESP concept can be used to identify initiation of LEV formation on finite wing (time instant and spanwise loc.) Approach: Use CFD to study LEV initiation on several wing shapes Use an unsteady vortex lattice (UVLM) method as the inviscid foundation for the low-order method Track time variation of LESP at each strip of the wing For each wing, identify LEV onset from CFD and determine maximum LESP on the wing at that condition Compare spanwise location of max LESP with CFD prediction of LEV initiation Compare maximum LESP from 3D with critical LESP from 2D 27

28 Current Effort Year-1 Goals With AFRL water tunnel back in operation, several 3D-printed wing shapes can be studied Current CFD-experiment comparison for an AR-2 flat plate uses experimental data from T. O. Yilmaz and D. Rockwell (2012). Flow structure on finite-span wings due to pitch-up motion. Journal of Fluid Mechanics, 691, pp Experiment Unsteady RANS with SA turbulence model 28

29 Current Effort Year-1 Goals Inviscid foundation for the low-order method is a UVLM based on the formulation in Katz and Plotkin Currently assumes attached LE flow Goal is to model intermittent and part-span LEV formations 29

30 Results from Year 1: Cases 9 cases studied with CFD and UVLM A 0-45 degree pitch motion is applied to each wing to determine LEV onset Cases Airfoil Re Pivot Taper Twist AR 1, Base SD k 25%c %c %c %c %c 1 10 deg %c 1 10 deg %c P1 Flat plate 10k 25%c P2 75%c

31 Parameter studies Baseline case (case 1) 1. Effect of pivot location (Baseline vs. case 2) 2. Effect of taper ratio (Baseline vs. case 3) 3. Effect of twist (Baseline vs. case 5) 4. Effect of aspect ratio (Baseline vs. case 7) 5. Effect of airfoil (Baseline vs. case P1) 31

32 Baseline Case Baseline case: Rectangular wing Aspect ratio 2 SD 7003 airfoil section Zero twist Pivot at quarter chord Max LESP LESP Baseline LE Pitch up from 0 to 45 deg Non-dim pitch rate of K = TE 32

33 1. Effect of Pivot Location Max LESP Baseline, c/4 pivot Max LESP Case 2, 3c/4 pivot LESP LESP 33

34 2. Effect of Taper Ratio (Tip-to-Root Chord) Max LESP Baseline, Taper ratio = 1 Case 3, Taper ratio = 0.5 Max LESP LESP LESP 34

35 3. Effect of Wingtip Twist Max LESP Baseline, twist = 0 Case 5, twist = 10 deg (washin) Max LESP LESP LESP 35

36 4. Effect of Aspect Ratio Max LESP Baseline, aspect ratio = 2 Max LESP Case 7, aspect ratio = 4 LESP LESP 36

37 5. Effect of Airfoil Shape Max LESP Baseline, SD 7003 airfoil Case P1, flat plate airfoil LESP Max LESP LESP Case 5, twist = 10 deg (washin) 37

38 Maximum LESP (3D) vs. Critical LESP (2D): AR-2 plate (cases P1 and P2): The maximum LESP for the two wings are very close The maximum LESP is also close to the critical LESP for 2D flat plate at the same Re LESP crit from 2D can be used to predict LEV initiation on wings AR 2 plate Critical LESP (2D) Max LESP (3D) LESP 38

39 Maximum LESP (3D) vs. Critical LESP (2D): AR-2 plate (cases P1 and P2): LESP crit from 2D can be used to predict LEV initiation on wings AR 2 plate and AR 4 SD 7003 Critical LESP (2D) Max LESP (3D) AR-4 SD 7003 (case 7): Max LESP is close to critical LESP for 2D SD 7003 at this Re Again, LESP crit from 2D can be used to predict wing LEV initiation LESP 39

40 Maximum LESP (3D) vs. Critical LESP (2D): AR 2 plate, AR 2 SD 7003, and AR 2 SD 7003 AR-2 plate (cases P1 and P2): LESP crit from 2D can be used to predict LEV initiation on wings AR-4 SD 7003 (case 7): Again, LESP crit from 2D can be used to predict wing LEV initiation AR-2 SD 7003 (cases 1-6): Max LESP values are close, but have a spread of This spread is not too bad considering the pitch angle for LEV initiation differs by nearly 11 degrees Max LESP values differ from LESP crit by nearly What is the reason for this discrepancy just for this set of cases? Critical LESP (2D) LESP Max LESP (3D) 40

41 Discrepancy for AR-2 SD 7003 cases Comparison of generic low-ar flow from experiment, CFD, UVLM We see that the tip vortex is clearly lifted up in experiment and CFD. In the UVLM, the tip vortex is modeled as attached to the tip. The effect of not modeling the lifted-up tip vortex will start to become noticeable at higher pitch angles and for lower AR. Conjecture: The AR-2 SD 7003 cases are affected by this modeling deficiency. This can be easily corrected. It is anticipated that the LESP max results for 3D will better match LESP crit for 2D. 41

42 Next Steps A key idea towards our path to 3D low-order modeling is extending the LESP idea from leading edges to other edges (tip, TE) in general Continue to use CFD and experiment to guide low-order method development. Explore collaborations with other PIs in FIC program for experimental support / data: Jones, Ringuette, Buchholz, and Rockwell Extend LESP to a general Edge Separation Parameter ( ESP ) How will LESP/ESP be affected by leading-edge sweep, tip shape, spanwise gradient of bound vorticity at the wing tip? Use directed CFD and experimental studies to determine trends 42

43 Next Steps How do we develop a low-order model for finite wing flows with LEVs using a strip-theory type approach? We propose to develop a new element for use in vortex-lattice formulations: a horseshoe LEV element Early stage, During formation Late stage, During convection The formation of the LEV element will be mediated by the local ESP This horseshoe LEV element s strength and location will be dynamically altered in an unsteady flow by time stepping A plausible shape for a late-stage LEV element could be a structure resembling the arch vortex studied by Visbal s, Rockwell s groups 43

44 Year-3 Plans By developing a hybrid 2D-3D formulation with horseshoe LEV element on each wing strip of an arbitrary wing undergoing translation or rotation Spanwise component of induced velocity could be used to transport vorticity in the spanwise direction from one strip to its neighbor 44

45 Summary of Progress Year 1 Completed study of several wings undergoing pitch-up motion using RANS and UVLM Results show that the LESP concept, applied to each strip of a finite wing, can be used to predict initiation of LEV formation even for low AR of 2! Maximum LESP for a wing is nearly the same as the critical LESP for the corresponding airfoil, with some exceptions Exceptions were traced to a modeling deficiency of the tip-vortex structure in low-ar wings. This deficiency will be addressed next. Follow-on CFD, experimental, and low-order studies will focus on LEV formation, evolution and interaction with tip and TE vortices Going forward, the mantra is Doing more with LESP 45