Numerical Simulation of Jet-Wake Vortex Interaction

Transcription

1 Numerical Simulation of Jet-Wake Vortex Interaction Takashi Misaka 1, Shigeru Obayashi 2 Tohoku University, Sendai , Japan Anton Stephan 3, Frank Holzäpfel 4, Thomas Gerz 5 Deutsches Zentrum für Luft- und Raumfahrt (DLR), Oberpfaffenhofen 82234, Germany and Kazuhiro Nakahashi 6 Japan Aerospace Exploration Agency (JAXA), Chofu, Tokyo , Japan The interaction of aircraft exhaust jet and wake vortex is numerically studied. Following the preceding numerical study of wake vortex evolution from roll-up until vortex decay, we aim to simulate the jet-vortex interaction from the early phase until the complete roll-up. For numerical simulation we employ an unstructured mesh Reynolds-averaged Navier- Stokes solver for a flow around an aircraft model, while a Cartesian mesh large-eddy simulation solver implemented on the framework of the Building-Cube Method (BCM) is used for the mid- to far-field wake. Here we investigate a coupling approach of the above solvers to simulate the roll-up of exhaust jet and aircraft wake. The results show that a multi-level Cartesian mesh of the BCM is effective to capture the evolution of aircraft wake including exhaust jet. I. Introduction AKE vortices generated by a flying aircraft pose a potential risk to following aircraft due to the strong and Wcoherent vortical flow structure. 1 In addition, it is pointed out that condensation trails (contrails) originated from the interaction of jet exhaust, wake vortices and the environmental atmosphere may trigger the formation of cirrus clouds (contrail cirrus) which could have an influence on the climate. 2,3 The evolution of aircraft's wake can be divided into several phases, for example, (1) roll-up phase, (2) vortex phase, and (3) dissipation phase. Although large-eddy simulation (LES) or direct numerical simulation (DNS) of a vortex pair provide the detailed insights into the wake vortex evolution and decay in various environmental conditions, 4-6 the impact of the wing load distribution related to aircraft geometry on the resulting wake vortex cannot be evaluated appropriately by using a vortex pair. The simulation bridging the gap between near- and far-field wakes provides the further understanding of the initial appearance of wake vortices. The feasibility of a wake initialization approach has been studied for wing-body and high-lift aircraft configurations, where realistic aircraft wake is generated in a LES domain by sweeping a highfidelity RANS flow field through the domain. 7,8 With the above approach the impact of wake roll-up on the subsequent wake vortex evolution and decay has been investigated. More specifically they investigated the effect of the roll-up process on the evolution of vortex parameters such as average circulation, vortex core radius, and vortex position. In addition, the time evolution of wake vortices initialized by a RANS flow field is compared with that by vortex models such as the Lamb-Oseen model. The approach has also been applied to wake vortices during landing, which successfully reproduces realistic wake vortices in ground proximity including wake vortex ends. 9,10 1 Assistant Professor, Frontier Research Institute for Interdisciplinary Sciences, Katahira 2-1-1, Member AIAA. 2 Professor, Institute of Fluid Science, Katahira 2-1-1, Associate Fellow AIAA. 3 Research Scientist, Institut für Physik der Atmonsphäre, Münchner Straße 20, Member AIAA. 4 Senior Research Scientist, Institut für Physik der Atmonsphäre, Münchner Straße 20, Senior Member AIAA. 5 Research Scientist, Institut für Physik der Atmonsphäre, Münchner Straße Executive Director, Institute of Aeronautical Technology, Associate Fellow AIAA. 1

2 Not only the wake vortex itself, but also the interaction of exhaust jet and wake vortex which is relevant to the investigation of contrails requires a consistent approach from the near- to far-field wake. It is because the generation of ice crystals starts immediately after the jet exhaust, where the exhaust jet and wing-tip vortex exist independently before the roll-up of the vorticity sheet behind the main wing. Previous studies of the jet-vortex interaction related to contrails basically investigate the interaction of jet and a rolled-up vortex, therefore, the nearfield evolution of exhaust jet and wing-tip vortex including wake roll-up processes is not well understood. A study of the wake roll-up including exhaust jet has been done by a simple vortex model, 15,16 however, the impact of the detailed aircraft geometry and turbulence behind an aircraft on the jet-vortex interaction would also be of interest. Following the preceding numerical study of the wake vortex evolution from roll-up until vortex decay, we aim to simulate the interaction of exhaust jet and wake vortex from the early phase until the complete roll-up. For numerical simulation we employ a combination of three solvers; an unstructured mesh compressible Reynoldsaveraged Navier-Stokes (RANS) solver, a Cartesian mesh-based compressible and incompressible flow solvers implemented on the framework of the Building-Cube Method (BCM). 17 The BCM realizes the generation of multilevel Cartesian meshes for adapting the detailed aircraft geometry as well as local flow structures. The latter is an important feature to simulate wing-tip vortices and exhaust jets with reasonable accuracy. In this study we use the DLR-F6 model equipped with CFM56-5 type engines. Fan, core and bypass flows are considered as approximated boundary conditions. Here we investigate the feasibility of the coupling approach of the solvers in terms of numerics and computational time. The coupling approach alleviates the difficulty of treating thin boundary layer in Cartesian mesh solvers, while fine vortical structures in the wake are effectively captured by the Cartesian mesh. I. Numerical Methods The near-field including aircraft s boundary layer is simulated by an unstructured mesh computational fluid dynamics (CFD) solver called TAS-code (Tohoku university Aerodynamic Simulation code). 18 RANS equations are discretized by a cell-vertex finite-volume method. The numerical fluxes are computed using an approximate Riemann solver of Harten-Lax-van Leer-Einfeldt-Wada (HLLEW). 19 Second-order spatial accuracy is realized by a linear reconstruction of primitive flow variables with Venkatakrishnan s limiter. 20 The lower/upper symmetric Gauss-Seidel (LU-SGS) implicit method is used for time integration. 21 The SST k-w turbulence model is used for a turbulence closure. 22 A computational mesh is generated by an unstructured mesh generator called MEGG3D. 23,24 Parallel computation is realized by a domain decomposition approach. On the other hand, the mid-field jet-wake vortex interaction is simulated by a Cartesian mesh compressible Navier-Stokes solver implemented on the framework of the BCM. 17 The BCM employs an equally-spaced Cartesian mesh aiming for the simplicity in mesh generation, 25 in the implementation of high-order schemes, 26 and in the post processing. 27 To adapt the detailed aircraft geometry as well as local flow scale without introducing the algorithm complexity, a block-structured Cartesian mesh approach is employed in the BCM. A flow field is discretized by an assemblage of building blocks of cuboids, named cube. All cubes have the same number of computational cells so that the local computational resolution is determined by the cube size. Inviscid fluxes are computed by a hybrid approach 28,29 of a shock capturing scheme based on HLLEW with third-order Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) interpolation 19 and a second-order central difference scheme. The switching is done by Ducros sensor, which enables to capture vortical structure in the wake as well as shock waves. 30 Viscous terms are discretized by a second-order central difference scheme, where Lagrangian dynamic model is employed for a turbulence closure model. 31 Third-order low-storage Runge-Kutta scheme is used for time integration. In addition, the far-field jet-wake vortex interaction is simulated by an incompressible BCM code to alleviate the severe limitation of a time-step size in compressible explicit codes. The pressure term is handled by the fractionalstep method, while the convection and diffusion terms are discretized by a fourth-order central difference scheme. 32 Third-order low-storage Runge-Kutta scheme is used for the time integration. The Lagrangian dynamic model is employed for a sub-grid scale model as in the compressible BCM code. 31 Temperature equation is coupled through a vertical component of momentum equations by the Boussinesq approximation. The coupling of TAS code and compressible BCM code is aiming to avoid an explicit treatment of thin boundary layers in a Cartesian mesh LES. We rather focus on the near- to far-field spatiotemporal development of jet and wake vortex. Even so, it is important to take into account the near flow field to reproduce realistic aircraft wake. As in the previous work, a smooth transition from the RANS to LES is realized by a hyperbolic tangent function. 7,8 The RANS and the LES solutions are equally weighted at the distance of 3 in this paper, where denotes a minimum mesh spacing of LES with the compressible BCM code. In RANS/LES hybrid or zonal LES approaches, turbulent fluctuations modeled in RANS simulation need to be reproduced in the LES domain. The 2

3 random method proposed by Lund et al. is one of simple approaches to realize this. 33 In this study, turbulent fluctuations are generated within the transition region between RANS and LES. Reynolds stress tensors used in the random method are obtained by turbulent variables of the SST k-w turbulence model. On the other hand, the transition from the compressible BCM code to the incompressible BCM code is conducted simply by extracting an arbitrary portion of wake form the compressible BCM results (Fig. 1). Note that the simulation with the compressible BCM code is conducted in the aircraft-fixed frame, while the incompressible BCM code simulates the flow field in the ground-fixed frame by subtracting flight speed from the compressible BCM results. Figure 1. The switching from the mid-field simulation with compressible BCM code to the far-field simulation with incompressible BCM code, (a) the simulation in the aircraft-fixed frame, (b) an extracted wake for the incompressible BCM simulation in the ground-fixed frame. II. Computational Settings Figure 2 shows the DLR-F6 wing-body configuration equipped with CFM56-5 type engines. The nacelle geometry is generated by a combination of analytical functions, 34,35 while the pylon is made based on the one from the DLR-F6 wing-body-nacelle-pylon model with a modification using a CAD software. In RANS simulation using the TAS code, boundary conditions for the engine inlet and outlet are set based on total pressure and total temperature ratios, that is, total pressure ratio of P/P 0 = 1.2 for fan inlet, and total pressure ratios of P/P 0 = 1.93 and 2.43 for core and bypass outlets, respectively. In addition, total temperature ratios of T/T 0 = 2.78 and 1.32 are set for core and bypass outlets, respectively. 35 Mach number of 0.75 and Reynolds number of 3 million are considered, which are close to experimental conditions in a wind tunnel rather than the conditions of actual flight. In addition, an angle of attack is set to one degree. Figure 2. DLR-F6 wing-body configuration equipped with CFM56-5 type engines, (a) overall view, (b) side view around the engine, (c) front view, and (d) rear view. 3

4 A computational mesh for RANS simulation consists of prisms, pyramids and tetrahedra. A total number of grid points is approximately11.4 million, which is shown in Fig. 3(a). Assuming flow symmetry, a half span domain is considered. On the other hand, a multi-level Cartesian mesh based on BCM is used for a region around an aircraft except for boundary layers. The BCM mesh has 6,413 cubes where each cube has 163 grid points, i.e., the total number of grid points is approximately 26.3 million, which is shown in Fig. 3(b). To clearly capture the vortical wake and exhaust jet, cubes are placed uniformly as in Fig. 3(c). The computation using the incompressible BCM code is conducted by extracting a portion of wake from the mesh shown in Fig. 3(c). Here we consider a region from x/b0 = 1.9 to 2.7 from the wing-tip focusing only on the two-dimensional development of the wake, where b0 denotes vortex spacing.1 The region contains 11,152 cubes, i.e., 45.7 million grid points because cubes are uniformly distributed in the vertical direction to capture descending wake vortices. Figure 3. Computational meshes for DLR-F6 wing-body model with CFM56-5 type engines, (a) unstructured mesh used for RANS simulation with the TAS code, (b) cubes and cells for the compressible BCM code, and (c) a view from the top of those cubes. III. Results Figure 4 shows the distribution of surface pressure coefficient Cp obtained from the RANS simulation. A closeup view around an engine is also shown in Fig. 4(b). Figure 5 shows the distributions of (a) streamwise velocity and (b) temperature on a cross-section of the engine. The approximated boundary conditions for core and bypass flows result in high streamwise velocity and temperature behind the engine. The temperature distribution in the near-field wake is the information required for high-fidelity contrail models. The distributions decay quickly due to the increase of mesh resolution as the distance from the engine increases as shown in Fig. 5(c). Unstructured mesh RANS solvers such as the TAS code nicely simulate steady flows around complex geometry, however, LES has advantages in unsteady vortical and jet flows. For this reason, we take a coupling approach in this study. Figure 4. The distribution of surface pressure coefficient Cp obtained from RANS simulation, (a) overall view, (b) close-up view around a nacelle. 4

5 Figure 5. The distributions of (a) streamwise velocity and (b) temperature on a cross-section of the engine, which are obtained from RANS simulation, and (c) unstructured mesh corresponding to the cross-section. Figure 6 shows the distributions of (a) vorticity magnitude and (b) temperature on several downstream crosssections obtained from the simulation with the compressible BCM code. Vortical structures of wing-tip vortex and exhaust jet are captured by the use of a central difference scheme in the vortical regions, while an upwind scheme used in the other regions such as shock waves and boundary layer around the model ensures the stability of the computation. It is also confirmed that the exhaust jet is resolved until downstream by using a fine Cartesian mesh in the wake. Figure 7 shows the iso-surface of axial vorticity obtained from the compressible BCM code. Vortical structures such as wing-tip vortex are well preserved until downstream while reproducing the decay of turbulent jet with the help of a uniform Cartesian mesh distributed in the wake region. On the other hand, numerical oscillations which may appear in the simulation only with a central difference scheme are effectively suppressed. Figure 6. The distributions of (a) vorticity magnitude and (b) temperature on several downstream slices obtained from the simulation with the compressible BCM code. Figure 7. Iso-surface of vorticity magnitude obtained from the compressible BCM code, where vortical structures such as wing-tip vortex and exhaust jet are well preserved until downstream. 5

6 Figure 8 shows the temporal evolution of axial vorticity distributions on a slice perpendicular to the flight path, where the superscript * denotes a quantity normalized by wake vortex parameters. 1 In this phase, the incompressible BCM code is employed to alleviate the severe limitation of time-step size in the compressible BCM code. Turbulent fluctuation near exhaust jet decays quickly and is entrained into the vortex oval which realizes weak turbulence distributed within the vortex oval. On the other hand, wake vortices centered at the position of wing-tip vortices gain stable vortical structure at t* = Figure 9 show a similar plot as Fig. 8, but for temperature deviation from the reference. Warm air near exhaust jets are also entrained during roll-up where the magnitude decreases drastically. Figure 8. Temporal evolution of axial vorticity distribution at (a) t* = 0.026, (b) t* = 0.090, and (c) t* = Figure 9. Temporal evolution of temperature distribution at (a) t* = 0.026, (b) t* = 0.090, and (c) t* = Figure 10 shows the comparison of velocity profiles obtained from the incompressible BCM code with Hallock- Burnham, Lamb-Oseen and Jacquin s multi-scale models. Initially, the velocity profile shows keen peak tangential velocity with kink. The keen profile is better represented by Jacquin s multiple scale vortex model. 36 On the other hand, the profile during the roll-up at t* = 0.44 well fits to Lamb-Oseen Vortex model. The profile after the roll-up at t* = rather agrees with Hallock-Burnham vortex model. The results seem to be reasonable because the Jacquin s multiple scale model is derived from the wind tunnel experiment, which measured the near-field wake with high spatial resolution. On the other hand, the Hallock-Burnham vortex model has lower peak tangential velocity compared to that of the Lamb-Oseen model when circulation and core radius are the same. 6

7 Figure 10. The comparison of velocity profiles obtained from the incompressible BCM code with Hallock- Burnham, Lamb-Oseen and Jacquin s multiple scale models. Figure 11. The decay of normalized temperature downstream, where blue line corresponds to the result from compressible BCM code and the red line is for the incompressible BCM code. Black dots represents the result of the wind tunnel experiment which are taken from Paoli et al. 37 The kink of the velocity profiles near the peak at t * = and is due to roll-up process, where the vorticity sheet along the trailing edge of the main wing is rolled-up around a wing-tip vortex realizing the nonaxisymmetric velocity profile. The averaging of the non-axisymmetric velocity profile in rotational direction results in the tangential velocity profiles at t * = and Figure 11 shows the normalized temperature along the jet flow, where the blue line corresponds to the result from the compressible BCM code and the red line is for the incompressible BCM code. The distance from the nacelle shown in the horizontal axis is normalized by the wing span b. Black dots represent the result of the wind tunnel experiment taken from Paoli et al. 37 Quick decay of temperature compares well with the experiment. Note that temperature equation in the incompressible BCM code is treated by the Boussinesq approximation, where the vertical velocity is induced by the deviation of temperature from the reference state. Buoyancy effect was not observed because the temperature increase is not significant in the present setting. IV. Conclusion The interaction of exhaust jet and wake vortex is numerically studied. Following the preceding numerical study of wake vortex evolution from roll-up until vortex decay, we investigate the jet-vortex interaction from the early phase until the complete roll-up. For numerical simulation we employ an unstructured mesh RANS solver for the 7

8 near-field including the boundary layer around an aircraft, while Cartesian mesh LES solvers implemented on the framework of the BCM are used for the mid- to far-field wake development, i.e., the compressible BCM code for mid-field wake and the incompressible BCM code for the far-field wake. Here we investigate the coupling approach of the above solvers to simulate the entire process of jet-wake vortex from the early phase until the complete roll-up. Overall procedure was demonstrated and found fairly feasible in terms of numerics and computational time. The results show that a multi-level Cartesian mesh of the BCM is effective to simulate the fine wing-tip vortices as well as defusing exhaust jet. The velocity profiles agree with several vortex models depending on those ages. Temperature from the modeled exhaust jet drastically decays downstream, which agrees with experiment. Acknowledgments We would like to thank Prof. Kanazaki (Tokyo Metropolitan University) and his students for providing a code for generating generic nacelle geometry. Computer time provided by the Advanced Fluid Informatics Research Center, Institute of Fluid Science, Tohoku University is greatly acknowledged. Part of the work was carried out under the Collaborative Research Project of the Institute of Fluid Science. In addition, this work was partially supported by JSPS KAKENHI Grant-in-Aid for Young Scientists (B), Grant Number References 1 Gerz, T., Holzäpfel, F., and Darracq, D., Commercial Aircraft Wake Vortices, Progress in Aerospace Science, Vol. 38, No. 3, 2002, pp Minnis, P., Young, D. F., Ngyuen, L., Garber, D. P., Jr., W. L. S., and Palikonda, R., Transformation of Contrails into Cirrus during SUCCESS, Geophysical Research Letters, Vol. 25, No. 8, 1998, pp Schumann, U., Graf, K., and Mannstein, H., Potential to Reduce the Climate Impact of Aviation by Flight Level Changes, AIAA Paper , Proctor, F. H., Hamilton, D. W., and Han, J., Wake Vortex Transport and Decay in Ground Effect: Vortex Linking with the Ground, AIAA Paper , Holzäpfel, F., Gerz, T., and Baumann, R., The Turbulent Decay of Trailing Vortex Pairs in Stably Stratified Environments, Aerospace Science and Technology, Vol. 5, No. 2, 2001, pp Misaka, T., Holzäpfel, F., and Gerz, T., Manhart, M., and Schwertfirm, F., Vortex Bursting and Tracer Transport of a Counter-Rotating Vortex Pair, Physics of Fluids, Vol. 24, No. 2, 2012, pp (1) (21). 7 Misaka, T., Holzäpfel, F., and Gerz, T., Wake Evolution of Wing-Body Configuration from Roll-Up to Vortex Decay, AIAA Paper , Misaka T., Holzäpfel F., Gerz T., Wake Evolution of High-Lift Configuration from Roll-Up to Vortex Decay, AIAA Paper , Stephan A., Holzäpfel F., and Misaka T., Towards Realistic Simulation of Wake-Vortex Evolution During Landing With Flat and Complex Terrain, 8th International Symposium on Turbulence and Shear Flow Phenomena, AER1A, August 28-30, 2013 Poitiers, France. 10 Stephan, A., Holzäpfel, F., and Misaka, T., Hybrid Simulation of Wake-Vortex Evolution During Landing on Flat Terrain and with Plate Line, submitted for publication in International Journal of Heat and Fluid Flow. 11 Schumann, U. (Ed.), Atmospheric Physics: Background Methods Trends, Springer, Unterstrasser, S. and Gierens, K., Numerical simulations of contrail-to-cirrus transition - Part 1: An extensive parametric study, Atmospheric Chemistry and Physics, Vol. 10, 2010, pp Paugam, R., Paoli, R., and Cariolle, D., Influence of Vortex Dynamics and Atmospheric Turbulence on the Early Evolution of a Contrail, Atmospheric Chemistry and Physics, Vol. 10, 2010, pp Naiman A., Lele S., Jacobson M., Large Eddy Simulations of Persistent Aircraft Contrails, AIAA Paper , Rossow V. J., and Brown A. P., Effect of Jet-Exhaust Streams on Structure of Vortex Wakes, Journal of Aircraft, Vol. 47, No. 3, 2010, pp Dedesh, V. T., Zamyatin, A. N., Grigoryev, M. A., Zuev, S. A., and Zhelannikov, A. I., Researches of Interaction of Aircraft Wake Vortices and Condensation Trails, AIAA Paper , Nakahashi, K., High-Density Mesh Flow Computations with Pre-/Post-Data Compressions, AIAA Paper , Nakahashi, K., Ito, Y., and Togashi, F., Some Challenges of Realistic Flow Simulations by Unstructured Grid CFD, International Journal for Numerical Methods in Fluids, Vol. 43, No. 6-7, pp , Obayashi, S., and Guruswamy, G. P., Convergence Acceleration of an Aeroelastic Navier-Stokes Solver, AIAA Journal, Vol. 33, No. 6, 1994, pp Venkatakrishnan, V., Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters, Journal of Computational Physics, Vol. 118, No. 1, pp , Sharov, D., and Nakahashi, K., Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss-Seidel Computations, AIAA Journal, Vol. 36, No. 3, pp ,

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