Spectrum Analysis Of SWBLI Under Ramp-Type MVG Control

Transcription

1 Γ Spectrum Analysis Of SWBLI Under Ramp-Type MVG Control Yong Yang Chaoqun Liu Technical Report

2 Spectrum analysis of SWBLI under ramp-type MVG control Yong Yang 1 and Chaoqun Liu. 2 University of Texas at Arlington, Arlington, Texas, USA To do spectrum analysis on SWBLI and reveal the relation between the ring-like vortices and flow separation induced by shock wave, the monotone integrated LES was carried out to solve the unfiltered form of the Navier-Stokes equations. Twenty thousands data sets are recorded and time-averaged flow and the change of several flow quantities in time domain are obtained. The spectrum analysis on these signals will be finished in the full paper and the relation between the ring-like vortices and flow separation induced by shock wave will be revealed in the full paper. Nomenclature M = Mach number Reθ = Reynolds number based on momentum thickness h = micro ramp height δδ 0 = incompressible boundary-layer nominal thickness TT = characteristic time CC = sound speed X, Y, Z = spanwise, normal and streamwise coordinate axes uu, vv, ww = spanwise, normal and streamwise velocity VV = velocity vector (uu, vv, ww) ωω = vorticity ωω xx = streamwise vorticity pp = pressure ρρ = density ψψ = angular speed ff = frequency SSSS = Strouhal number Subscript 0 = inlet w = wall = free stream I. Introduction HOCK wall boundary layer interaction (SWBLI) deteriorates flow quality by inducing large scale flow separation S and can influence aircraft and engine performance significantly and often leads to undesirable effects, such as total pressure loss, making flow unstable and distorted, engine unstart, drag rise and high wall heating. It is still a challenging problem for research. Micro-vortex generators (MVGs) are widely used in the separation control in order to reduce the adverse effects caused by SWBLI. MVG is a kind of low-profile passive control device, which has smaller size (about 10%-40% of boundary layer thickness) in contrast to conventional vortex generators. Because of MVG s small size, it can carry a much lower drag penalty while it still works efficiently in alleviating flow separation. As a kind of miniature and passive device, MVG has clear advantages in terms of low profile drag, lack of intrusiveness and robustness 1. 1 PhD student, Department of Mathematics, AIAA Member. 2 Professor, Department of Mathematics, AIAA Associate Fellow. 1

3 MVGs were first proposed in the 1980s, to increases the performance of flap, which is an aircraft high-lift device 2. It has been successfully used in subsonic regimes to improve aerodynamic performance of aircrafts 3 and it is recently used in supersonic flow to solve the problems caused by SWBLI, especially flow separation 4. In the past decade, a series of experimental and computational investigations on MVG have been carried out. Anderson et al 4 gave the formal and systematic studies about MVG and Babinsky et al 5 made a series of experiments on different kind of MVG and had a detailed study on their control effects. A PIV investigation of the 3D instantaneous flow organization behind a micro-ramp in a supersonic boundary layer was given by Sun et al 6. Wang et al 7 performed an NPLS and PIV experimental study in a low-noise supersonic wind-tunnel. Numerical simulations have been made on MVG for comparative studies and further design purpose, using RANS, hybrid RANS/LES and monotone integrated LES. Rizzetta and Visbal 8 simulated the flow field on a compression corner by implicit LES using a high-order method and Kaenal et al 9 used an approximate de-convolution model developed by Stolz et al 10 to conduct LES on ramp flow. Li and Liu 11 discovered the large scale vortex rings behind MVG by an implicitly implemented LES with fifthorder bandwidth-optimized WENO scheme. Xue et al 12 showed that wake structures of the micro-vanes are quite simpler while the wake structures of micro-ramp are more complicated, including ring-like vortex train and streamwise vortex tubes etc. Wang et al 13 investigated the wake organization downstream of the ramp-type MVG and its function of fluid redistribution with a large-eddy simulation at Mach 2.7. More work on MVG and other flow control tools have been studied recently 14,15. Our previous paper 16 investigated the interaction of vortex rings generated by ramptype MVG with shock and found that the vortex rings have the ability to weaken and alter the shock wave. This paper will study the frequency vortex rings and the shock wave and the relations between them by spectrum method. II. Case setup and code validation To capture details of instantaneous flow structure and reveal the mechanism of interaction between the ring-like vortices and shock wave, the monotone integrated LES 17,18 was carried out to solve the unfiltered form of the Navier- Stokes equations. A. Case setup The dimensions of MVG and half computational domain is displayed in Figure 1. The back edge of MVG is declined to angle 70 to alleviate the difficulty of grid generation while the other dimensions are given same as experiments of Babinsky et al 5 with cc = 7.2h, αα = 24 and ss = 7.5h, where h represents the height of MVG and s represents the distance between the center lines of two adjacent MVG. The geometries of half computational domain are shown in Figure 1(b). According to experiments conducted by Babinsky et al 5, the ratio h/δδ 0 of the models range from 0.3 to 1 and the proper distance between back edge and control region is around 8~19 δδ 0, where δ 0 represents the incompressible boundary layer nominal thickness. In this study, the height of MVG h is supposed to be δδ 0 /2 and the horizontal distance between apex of MVG and ramp corner is set to be 9.75 δδ 0, that is 19.5h. The distance from the ramp corner to the end of ramp is 12.8h and from the inlet of the domain to front edge of MVG is 11.2h. The height of the domain changes from 10h to 15h and the width of half domain is 3.75h. Only half of the grids need to be generated because of the symmetry of the grid distribution. Figure 2 gives the whole computational domain with coordinates, where x, y and z represent the spanwise, normal and streamwise direction respectively. The grid dimensions of whole system are nnnnnnnnnnnnnnnnnn nnnnnnnnnnnnnn nnnnnnnnnnnnnnnnnnssee =

4 (a) (b) Figure 1. The dimensions of (a) MVG and (b) the half domain Figure 2. The whole computational domain with x and z coordinates. The wall boundary adopts the adiabatic, zero-gradient of pressure and non-slipping conditions and non-reflecting boundary conditions are applied at the upper boundary to avoid possible wave reflection. The conditions of front and rear boundary surfaces in the spanwise direction are set as periodic conditions, since the simulation is for the flow around MVG arrays and only one MVG is simulated. A kind of characteristic-based condition which can handle the outgoing flow without reflection is set at the outflow boundary. To generate inflow conditions, twenty thousand turbulent profiles obtained from DNS results by Liu and Chen 19 are used. Details about generating fully developed turbulent inflow boundary conditions are given by Yan et al 20. The flow before the MVG is fully developed turbulence 3

5 flow by checking the shape factor, which is HH = Figure 3 shows the comparison of the inflow boundary layer velocity profile with DNS results of Guarini et al 21, which indicates the inflow boundary layer velocity profile of LES agrees with the analytical profile. Figure 3. Inflow boundary-layer profile at xx = 00, zz = 8888 comparison with DNS result of Guarini et al. The 5th order bandwidth-optimized WENO scheme 22 is utilized to keep the highly fidelity and the sub-grid stress model is used as the numerical dissipation. The explicit third-order TVD-type Runge-Kutta scheme is employed in time marching. The flow and reference parameters, including Mach number, Reynolds number, etc. are listed in Table 1. MM RRee θθ TT TT ww h ww TT K 300 K 4 mm 850 m/s s Table 1. Flow and reference parameters. B. Code validation The LES code LESUTA has been validated by University of Texas at Arlington and University of Delft researchers 20,23,24. We only give a brief description here. 1. Comparison with experiment by Babinsky et al. Figure 4 gives a quantitative comparison with experiment by Babinsky et al. 5 in the time-averaged velocity profile at xx = 0 and zz = 6.7h. The same pattern is obtained. The difference between LES and the experiment results is considered to be induced by the different Reynolds numbers and back edge degrees of MVG. 4

6 Figure 4. Time-averaged velocity profiles at xx = 00, zz = Figure 5. Sketch of main flow features (one side only for clarity), Babinsky et al (2009) Figure 5 shows a sketch of main flow features according to the experiment by Babinsky et al 5. Figure 6 shows the two counter-rotating streamwise vortices in time-averaged view according to our LES results. A new vortex identification criterion called Ω-method 25 is utilized to show the structrues of vortices. The basic idea the Ω-method is vorticity can be decomposed into a vortical part and a non-vortical part since vorticity exists in both rotating flow like vortex and flow without rotation like Blasius solution. And the vortex is the region where the vorticity overtakes the deformation.. Ω is defined as following: TTTTTTTTTT(BB TT BB) Ω = TTTTTTTTTT(AA TT AA) + TTTTTTTTTT(BB TT (1) BB) + εε where AA is the symmetric part of velocity gradient tensor VV, BB is the anti-symmetric part and ε is a small positive number introduced to avoid division by zero: AA = 1 2 VV + VV TT (2) BB = 1 2 VV VV TT (3) According to Liu et al. 25, a vortex can be identified as a connected region where Ω > 0.5 and the iso-surface of Ω = 0.52 can be utilized to indicate the structures of vortices. The green surfaces in Figure 6(a) are the iso-surface of Ω = 0.52 and the colorful plane is the slice zz = 5h which is also shown in details with streamtraces (black lines) in Figure 6(b). Comparing with Figure 5, the structure of primary vortices are found. Also the momentum deficit are conspicuous in the downstream of MVG, see Figure 6(b). 5

7 (a) (b) Figure 6. Two counter-rotating streamwise vortices in time-averaged view. (a) ΩΩ = iso-surface (green) with streamwise momentum distribution at zz = 5555; (b) Streamwise momentum distribution at zz = 5555 with streamtraces (black). 2. Comparison with Sun et al. Figure 7 gives the qualitative comparison with experiment by Sun et al. 15 in the instantaneous structures of vorticity. Comparing the two results, the similar structures of streamwise and spanwise vorticity components can be found, which confirm the existence of ring-like vortices in instantaneous view. (a) (b) Figure 7. Instantaneous structures of vorticity in (a) LES (b) experiment by Sun et al. Orange iso-surface represents spanwise vorticity. Green and purple iso-surface represent streamwise vorticity. 6

8 III. Spectrum analysis of vortex rings and shock waves According to LES results, the large scale vortex rings generated by ramp-type MVG concentrate in the central region along spanwise, see Figure 8(a). The green surface is the iso-surface of Ω = 0.52, which indicates the structures of vortices. From Figure 8(a), we can see the vortex rings behind MVG centralize around xx = 0. Due to the distribution of vortex rings, slice xx = 0 is chosen to carry on the analysis. And twenty thousands files are recorded from tt = 1840TT to tt = 1920TT to give the details of the process. (a) (b) Figure 8. (a)the iso-surface of ΩΩ = and slice xx = 00; (b) The position of slice of xx = 00. A. Time-averaged view The time-averaged quantities are obtained by the following: φφ = 1 tt 2 φφ dddd, tt 2 tt 1 tt 1 where the scalar φφ is the time-averaged quantity and φφ is the instantaneous quantity. The scalar φφ can be referred as ρρ, uu, vv, ww and pp. Figure 9 gives the distributions of time-averaged streamwise velocity ww, density ρρ and pressure pp and the distributions of ρρ, pp and. We can find that there is a low speed and low density zone followed by MVG, see Figure 9(a) and (b); and the pressure in this zone is also lower than the surroundings. The distributions of ρρ, pp given in Figure 9(d) and (e) indicate the postion of shock waves as the shock wave is a discontinuity of density or pressure. Figure 9(f) gives the position of flow separation in time-averaged view, because = 0 at the frontier of the flow separation region on the wall. From Figure 9(f), the flow separates at zz = 15.6h. 7

9 (a) The distribution of streamwise velocity ww. (b) The distribution of density ρρ. (c) The distribution of pressure pp. 8

10 (d) The distribution of the gradient of density ρρ. (e) The distribution of gradient of pressure pp. 9

11 (f) The distribution of streamwise velocity gradient along normal direction. Figure 9. The distributions of time-averaged quantities on the slice xx = 00. B. The signals in time domain 1. Shock osillation According to the position of the shock wave indicated in Figure 9(d) and (e), five positions are chosen to probe the change of flow quantities, see Figure 10. The details of five points are listed in Table 2. Figure 10. The positions of 5 probing points with the distribution of ρρ. A B C D E Z/h Y/h Table 2. The positions of points A,B,C,D and E. The signals of ρρ, pp probed at points A, B, C, D and E are shown in Figure 11. It is easy to see that the frequencies of ρρ, pp have the order AA < BB < CC < DD < EE and the magnitude of ρρ, pp have the order AA BB > CC > DD > EE, which indicate that the top section of the shock wave is more stable and stronger while the bottom section of the shock wave is more unstable and weaker. 10

12 (a) (b) (c) (d) 11

13 (e) Figure 11. The signals of ρρ, pp probed at points A,B,C,D and E. 2. Flow separation region oscillation Figure 12 gives the schematic of the position of the leading edge of the flow separation region. In Figure 12, the blue region represents < 0 and the red region represents > 0. The position indicated by red arrow represents the leading edge of the flow separation region. Figure 13 gives the change of the leading edge of the flow separation region with time. Figure 12. The schematic of the position of the leading edge of the flow separation region. Figure 13. The change of the leading edge of the flow separation region. 3. Frequency of vortex rings Figure 14 shows the positions of probing vortex rings with the distribution of streamwise velocity. From Figure 7, we can see the vortex ring head is along with great positive spanwise vorticity ωω xx, thence we record the maximum ωω xx laying on each blue line marked as H, L, M, N, Q and S in Figure 14, to record the vortex rings passing through these different streamwise positions. For every blue line, the bottom is at yy = 0.9h and the top is at xx = 4.0h. And the details of streamwise position of these lines are listed in Table 3. Figure 15 shows the changes of the maximal ωω xx along lines H, L, M, N, Q and S. 12

14 Figure 14. The positions of probing vortex rings. H L M N Q S Z= 8h 10h 12h 14h 16h 18h Table 3. The streamwise position of lines H, L, M, N, Q and S. (a) (b) (c) 13

15 (d) (e) C. Spectrum analysis on the signals 1. Shock oscillation Will be finished in full paper. 2. Flow separation region oscillation Will be finished in full paper. 3. Frequency of vortex rings Will be finished in full paper. (f) Figure 15. The change of maximal ωω xx along line H, L, M, N, Q and S. IV. Conclusion To do spectrum analysis on SWBLI and reveal the relation between the ring-like vortices and flow separation induced by shock wave, the monotone integrated LES was carried out to solve the unfiltered form of the Navier-Stokes equations. Twenty thousands data sets are recorded in 80TT and time-averaged flow and the change of several flow quantities in time domain are obtained. The spectrum analysis on these signals will be finished in the full paper and the relation between the ring-like vortices and flow separation induced by shock wave will be revealed in the full paper. Acknowledgments This work was originally supported by AFOSR grant FA supervised by Dr. John Schmisseur and then the Department of Mathematics at University of Texas at Arlington. The authors are grateful to Texas Advanced 14

16 Computing Center (TACC) for providing computation hours. This work is accomplished by using Code LESUTA which was developed by Drs. Q. Li and C. Liu at University of Texas at Arlington. References 1 Lu, F. K., Li, Q., and Liu, C., Microvortex generators in high-speed flow, Progress in Aerospace Sciences, vol. 53, Aug. 2012, pp Lin, J. C., Howard, F. G., and Selby, G. V., Turbulent flow separation control through passive techniques, 2nd Shear Flow Conference, Bohannon, K. S., Passive Flow Control on Civil Aircraft Flaps Using Sub-Boundary Layer Vortex Generators in the AWIATOR Programme, 3rd AIAA Flow Control Conference, 2006, p Anderson, B., Tinapple, J., and Surber, L., Optimal Control of Shock Wave Turbulent Boundary Layer Interactions Using Micro-Array Actuation, 3rd AIAA Flow Control Conference, San Francisco, California: American Institute of Aeronautics and Astronautics, 2006, p Babinsky, H., Li, Y., and Pitt Ford, C. W., Microramp Control of Supersonic Oblique Shock-Wave/Boundary-Layer Interactions, AIAA Journal, vol. 47, Mar. 2009, pp Sun, Z., Schrijer, F. F. J., Scarano, F., and van Oudheusden, B. W., PIV Investigation of the 3D Instantaneous Flow Organization behind a Micro-ramp in a Supersonic Boundary Layer, 28th International Symposium on Shock Waves, Berlin, Heidelberg: Springer Berlin Heidelberg, 2012, pp Wang, B., Liu, W., Zhao, Y., Fan, X., and Wang, C., Experimental investigation of the micro-ramp based shock wave and turbulent boundary layer interaction control, Physics of Fluids, vol. 24, 2012, p Rizzetta, D. P., Visbal, M. R., and Gaitonde, D. V., Large-eddy simulation of supersonic compression-ramp flow by high-order method, AIAA Journal, vol. 39, Jan. 2001, pp Kaenel, R. Von, Kleiser, L., Adams, N. A., and Vos, J. B., Large-Eddy Simulation of Shock-Turbulence Interaction, AIAA Journal, vol. 42, Dec. 2004, pp Stolz, S., Adams, N. A., and Kleiser, L., The approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent-boundary-layer interaction, Physics of Fluids, vol. 13, 2001, p Li, Q., and Liu, C., LES for Supersonic Ramp Control Flow Using MVG at M=2.5 and Re_theta=1440, 48th AIAA Aerospace Sciences Meeting, Orlando, Florida: 2010, pp Xue, D., Chen, Z., Jiang, X., and Fan, B., Numerical investigations on the wake structures of micro-ramp and microvanes, Fluid Dynamics Research, vol. 46, Feb. 2014, p Wang, B., Liu, W. D., Sun, M. B., and Zhao, Y. X., Fluid Redistribution in the Turbulent Boundary Layer Under the Microramp Control, AIAA Journal, vol. 53, Dec. 2015, pp Saad, R., Erdem, E., Yang, L., and Kontis, K., Experimental Studies on Micro-ramps at Mach 5, 28th International Symposium on Shock Waves, Berlin, Heidelberg: Springer Berlin Heidelberg, 2012, pp Sun, Z., Schrijer, F. F. J., Scarano, F., and van Oudheusden, B. W., The three-dimensional flow organization past a microramp in a supersonic boundary layer, Physics of Fluids, vol. 24, 2012, p Yang, Y., Yan, Y., and Liu, C., LES Study on Mechanism of Reduction of Shock Induced Flow Separation by MVG, 53rd AIAA Aerospace Sciences Meeting, Orlando, Florida:, 2015, pp Lee, C., and Li, R., Dominant structure for turbulent production in a transitional boundary layer, Journal of Turbulence, vol. 8, Jan. 2007, p. N Grinstein, F. F., Margolin, L. G., and Rider, W. J., Implicit Large Eddy Simulation, Liu, C., and Chen, L., Parallel DNS for vortex structure of late stages of flow transition, Computers and Fluids, vol. 45, 2011, pp Yan, Y., Chen, C., Wang, X., and Liu, C., LES and analyses on the vortex structure behind supersonic MVG with turbulent inflow, Applied Mathematical Modelling, vol. 38, 2014, pp Guarini, S. E., Moser, R. D., Shariff, K., and Wray, A., Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5, Journal of Fluid Mechanics, vol. 414, 2000, pp Jiang, G.-S., and Shu, C.-W., Efficient implementation of weighted ENO schemes, Journal of Computational Physics, vol. 126, 1996, pp Sun, Z., Micro Vortex Generators for Boundary Layer Control: Principles and Applications, International Journal of Flow Control, vol. 7, Jun. 2015, pp Li, Q., and Liu, C., Implicit LES for Supersonic Microramp Vortex Generator: New Discoveries and New Mechanisms, Modelling and Simulation in Engineering, vol. 2011, 2011, pp Liu, C., Wang, Y., Yang, Y., and Duan, Z., New Omega Vortex Identification Method, SCIENCE CHINA Physics, Mechanics & Astronomy, vol. 59, 2016, p