NUMERICAL SIMULATION OF THE FREE PITCH OSCILLATION FOR A RE-ENTRY VEHICLE IN TRANSONIC WIND TUNNEL FLOW

Transcription

1 NUMERICAL SIMULATION OF THE FREE PITCH OSCILLATION FOR A RE-ENTRY VEHICLE IN TRANSONIC WIND TUNNEL FLOW Bodo Reimann German Aerospace Center (DLR), Institute of Aerodynamics and Flow Technology, Lilienthalplatz 7, Braunschweig, Germany bodoreimann@dlrde ABSTRACT This paper presents the numerical results carried out by the German Aerospace Center (DLR) in the framework of the ESA Technology Research Program (TRP) Damping Derivatives Assessment for Hypersonic Re-Entry Vehicles Exhibiting High Angle of Attack (DERIVAS) Aim of the study is the simulation of the free pitching oscillation of a re-entry vehicle in transonic wind tunnel conditions The unsteady numerical simulations with strong coupling between the flow around the vehicle and its pitch motion show dynamic unstable behaviour of the vehicle in the transonic regime The presence of the model support, holding the vehicle in the test section has a damping effect on the oscillation Furthermore, the resulting pitch damping sum shows a strong dependency on the amplitude of the pitch oscillation Key words: dynamic stability; pitch damping derivatives; free oscillation technique; flight mechanics coupling; sting effects; CFD; TAU-code; chimera technique 1 INTRODUCTION The entry of a flight vehicle in the atmosphere of a planet comprises a wide range of flow conditions from high speed chemical reacting flow at high altitudes down to low speed close to the landing site Vehicles designed to resist the extreme loads during hypersonic flight often tend to be unstable in the trans- and subsonic flight regime This unstable dynamic behaviour often requires the deployment of a parachute to stabilize the vehicle However for a safe operation the controllability along the entry trajectory is essential For this reason numerical simulations, as well as wind tunnel experiments are used to predict dynamic stability The aim of the study is to compute dynamic pitch damping derivatives of a lifting body type re-entry vehicle in transsonic wind tunnel flow The simulated cases represent wind tunnel conditions of corresponding measurements carried out in the Trisonic Test Section (TMK) at DLR Köln Of special interest is the influence of the support sting holding the model in the test section of the tunnel For this purpose steady-state computations as well as unsteady simulations with full coupling between flow and rigid body motion of the vehicle - so-called free motion technique - have been carried out The simulations have been performed at the Institute of Aerodynamics and Flow Technology of the DLR in Braunschweig The used CFD tool is the DLR TAU-code 2 NUMERICAL METHOD 21 DLR TAU-code The TAU flow solver [7] uses the finite volume method to discretize the Euler or Navier-Stokes equations on unstructured grids Based on this primary grid an edgebased metric called dual-grid is generated in a preprocessing step If multi-grid technique is used, the preprocessor also agglomerates coarser levels of the dual-grid Also domain splitting is done by the preprocessor in case of parallel computations In the CFD (computational fluid dynamics) solver module inviscid terms are computed employing either a second-order central scheme or an AUSMDV upwind scheme using linear reconstruction to get second-order spatial accuracy Viscous terms are generally computed with a second-order central scheme For time integration various explicit Runge-Kutta schemes, as well as an implicite approximate factorization lower-upper symmetric Gauss-Seidel scheme (LU-SGS) is implemented For time accurate computations a Jameson-type dual time stepping approach is employed Additional convergence acceleration is achieved by explicit residual smoothing To simulate turbulent flows the user has the choice between several one- and two-equation turbulence models, a Reynolds stress or a DES model For the present study the perfect gas solver is used For moving grids TAU is written in an arbitrary Eulerian-Lagrangian formulation Chimera technique [2],[3] is an important feature to simulate configurations with movable parts The method

2 handles the data exchange in the overlapping region The current implementation of the Chimera technique covers steady and unsteady simulations for inviscid and viscous flows with multiple moving bodies, and is also available in parallel mode 22 Flight mechanic coupling The motion of the rigid body is computed in the RBD (rigid body dynamics) module solving Newtons second law and the Euler equation of rotational dynamics The coupled CFD/RBD problem is solved in a partitioned manner A so-called strong coupling scheme is used [6] Strong coupling means that the coupled equations are iteratively solved within each physical time step by repeatedly solving the involved disciplines CFD and RBD separately based on the exchanged coupling quatities These are on CFD side aerodynamic loads (forces and moments) and on RBD side the motion state (position and velocities) Figure 1 shows a operation chart of a strong coupled simulation Figure 1 Scheme of the strong coupling between CFD and RBD 23 Figure 2 Chimera blocks Shown are the surface and farfield boundary of the sting mesh (blue) and the surface boundary of the vehicle (grey) The farfield boundary of the vehicle mesh is not visible during the run [1] The cross flexure has not been taken into account for the simulations The Chimera mesh consist of two blocks (separate grids), one for the vehicle and one for the sting Figure 2 shows the two parts of the mesh Two additional grids so-called hole grids are needed to cut a hole for the body in the volumetric grid of the other block, respectively Figure 3 shows the hole definition of the Chimera mesh In order to ensure enough overlap for the interpolation between the Chimera grids, and due to the fact that the gap between sting and vehicle Computational domain As input for the generation of the computational grids ESA provided a CAD file of the geometry of the vehicle based on the Intermediate Experimental Vehicle (IXV) aeroshape 22 Flap deflection is not considered Minor corrections to avoid tiny surface panels and to guarantee a watertight contour have been introduced by DLR The CAD description of the wind tunnel sting holding the model in the test section has been constructed by DLR Several details of the mounting mechanism have been simplified for the meshing process The meshing itself has been done with the commercial mesh generating software CENTAUR Two types of grids have been generated, one for the flight configuration which comprises only the vehicle, and one for the wind tunnel configuration which also includes the model support sting To simulate the rotation of the vehicle around its y-axis with respect to the sting the method of overlapping grids (Chimera technique) has been applied for the wind tunnel configuration In the experiments the vehicle is attached to the sting in the center of rotation (CoR) by a cross flexure which allows the vehicle to oscillate around the y-axis Figure 3 Chimera hole boundaries The vehicle hole definition (red) cuts out the vehicle surface from the mesh around the support sting The sting hole (green) cuts out the sting surface from the vehicle mesh

3 have than been used for the generation of the wind tunnel mesh, so that the resolution of both final meshes is similar The final grid for the free flight has 537 million points (2089 million primary grid cells), with the support sting included the number of points rises to 1771 million points (6802 million primary grid cells) Figures 4 to 6 gives an impression of the final primary meshes 24 Figure 4 Computational mesh for the wind tunnel configuration Shown is the vehicle mesh (black) the vehicle surface (red) and the mesh around the model support sting (blue) The farfield sphere has a diameter of 375 m Test conditions The freestream conditions of the TMK used for the simulations are given in Tab 1 The gas is assumed to be calorically perfect air with γ = 14 and R = 287 J/(kg K) The wall is modeled as adiabatic no slip boundary All simulation are carried out with a turbulent flow solver with implemented Menter SST k-ω turbulence model [4] The reference length of the vehicle is Lref = 0125 m The reference relation area for the half model is Aref = m2 The cordinates of the center of rotation are xcor = m, ycor = 00 m and zcor = m The moment of inertia for the half model around the y-axis is computed with Iyy = kg m2 In wind tunnel tests the angle of attack α is identical to the pitch angle θ The vehicle model is very small, only a maximum pitch amplitude of ±2 can be simulated The size of the vehicle is 0125 m The spherical farfield of the computational domain has a diameter of 375 m Only one half side of the domain is computed exploiting the symmetry of the model For the free flight grid the notch for the support sting on the top of the vehicle does not exit The main part of the primary volumetric mesh consist of tetraedras and pyramids Boundary layers are resolved using a stack of prismatic cells perpendicular to the triangulated viscous walls In regions of interest the grid points are clustered to increase the resolution of the flowfield A grid convergence study has been performed for the free flight case The findings Table 1 Simulated conditions of the freestream in TMK Figure 5 Detailed view of the mesh for the wind tunnel configuration Figure 6 Detailed view of the mesh for the free flight configuration M Re [ 106 ] u [m/s] ρ [kg/m3 ] T [K] run 18 run19 run 23 run

4 25 Simulation procedure Several steady-state computations have been carried out to find the trim angle α trim of each configuration where the pitching moment coefficient is equal to zero A solution close to the trim position (θ init ) is used as the initial restart solution for the unsteady coupled CFD/RBD simulation The pitch damping sum q + α can than computed from the time-history of the pitch oscillation amplitude θ(t) [5], 2 u q + α = 1 2 ρ u 2 A ref L 2 f(θ 0 ) (1) ref using logarithmic decrements f(θ 0 ) = 2 I yy t 0,i+1 t 0,i ln ( θ0,i+1 θ 0,i ) (2) θ 0,i describes the i-th local extremum of the pitch oscillation amplitude and (t 0,i+1 t 0,i ) the time between two succeeding extremal values The pitching moment slope α is computed from the fitted steady-state results Angular frequencies ω expected close to the trim point result from ω = 3 RESULTS Cmα 31 Grid convergence study I 1 2 ρ u 2 A ref L ref (3) As already mentioned a grid convergence study has been performed for the free flight case On several grids with increasing spatial resolution steady-state computations for various angles of attack have been executed for run 19 Figure 7 shows the pitching moment coefficient versus the angle of attack for the six grids There is no x10 6 grid points 103x10 6 grid points 207x10 6 grid points 396x10 6 grid points 537x10 6 grid points 895x10 6 grid points Figure 7 Pitching moment coefficient for run 19 (M = 095) versus angle of attack computed on different grids time steps Figure 8 Pitching moment coefficient for run 19 (M = 095) versus number of time steps significant difference between the three finest grids For the further study the grid with 537 million points have been used The grid including the support sting has a similar resolution Figure 8 shows the evolution of the pitching moment coefficient during the numerical iteration process At the end of each physical time step the flow solution is converged The numerical convergence for the wind tunnel case is much worse compared to the convergence of the free flight simulation The number of inner iteration for the dual time stepping scheme is nearly three times higher It is supposed that this is caused by the higher complexity of the model geometry and the application of the Chimera technique 32 Steady-state results For both configurations and all flow conditions steadystate simulations have been carried out for different angles of attack The results for the pitching moment for run 18, 19, 23 and 10 are shown in Fig 9 12 The values of the pitching moment are fitted by a second order poly Fitted steady-state CFD with sting Fitted steady-state CFD w/o sting Figure 9 Steady-state pitching moment coefficient versus angle of attack for run 18 (M = 080)

5 Fitted steady-state CFD with sting Fitted steady-state CFD w/o sting Fitted steady-state CFD with sting Fitted steady-state CFD w/o sting Figure 10 Steady-state pitching moment coefficient versus angle of attack for run 19 (M = 095) Figure 12 Steady-state pitching moment coefficient versus angle of attack for run 10 (M = 201) Fitted steady-state CFD with sting Fitted steady-state CFD w/o sting effect for the subsonic cases run 18, 19 and 23 For run 18 and 19 the sting induces an increase of the trim angle of about 4 For run 23 the presence of the support sting leads to indifferent static behavior of the vehicle There is no significant influence of the wind tunnel support sting in supersonic flow 33 Unsteady coupled results Figure 11 Steady-state pitching moment coefficient versus angle of attack for run 23 (M = 110) nomial Trim angles, pitching moment slopes, expected angular frequencies and the inital pitch angles for the coupled simulations are summarized in Tab 2 In the considered range of angle of attack the sting has the largest Table 2 Steady-state results for free flight (FF) and wind tunnel (WT) configuration run 18 run19 run 23 run 10 M α trim [ ] FF WT α [1/rad] FF WT ω [1/s] FF WT θ init [ ] FF /500 WT To ensure to have a sufficient number of sampling point for the simulation of the unsteady pitch oscillation a physical time step of 2 ms has been chosen Figure 13 to 16 show in comparison the pitch oscillation history for the free flight and wind tunnel configuration for each flow condition In all cases the vehicle oscillates around the trim position In addition to the physical time step of 2 ms a simulation with a time step size of 1 ms has been carried out for run 19 (Fig 13) Also for large oscillation amplitudes the difference is small For the transonic cases run 18 and 19 the pitch oscillation amplitude escalates with time Figure 13 and 14 show that the escalation rate is much higher for the free flight configuration compared to the wind tunnel configuration with sting The support sting has a damping effect on the pitch oscillation Nevertheless the dynamic behavior for both configurations in this flow condition is dynamically unstable For an increasing Mach number a change of the unstable dynamic behavior without sting to a slightly stable type of pitch motion with sting is observed for run 23 in Fig 15 For the supersonic case run 10 the pitch oscillation amplitude decreases in time Both configurations are dynamically stable In order get data for large oscillation amplitudes for run 10 a second simulation with an initial pitch angle of 50 has been performed The results are also shown in Fig16 Due to the fact that the initial starting solution for the simulation of run 18 was very close to the trim angle

6 θ [ ] Trim angle with sting Trim angle w/o sting Figure 13 Time-history of pitch oscillation amplitude for run 18 (M = 080) t [s] θ [ ] Trim angle with sting (θ init = 43 ) (θ init = 50 ) Trim angle w/o sting Figure 16 Time-history of pitch oscillation amplitude for run 10 (M = 201) t [s] Trim angle with sting ( t = 2ms) ( t = 1ms) Trim angle w/o sting θ [ ] q +α Figure 14 Time-history of pitch oscillation amplitude for run 19 (M = 095) The small picture shows the difference between the two simulated physical time step of 2 ms and 1 ms t [s] θ 0 [ ] Figure 17 Pitch damping sum versus pitch oscillation amplitude for run Trim angle w/o sting θ [ ] t [s] q +α θ 0 [ ] Figure 15 Time-history of pitch oscillation amplitude for run 23 (M = 110) Figure 18 Pitch damping sum versus pitch oscillation amplitude for run 19 (M = 095)

7 q +α Table 3 Steady-state results for free flight (FF) and wind tunnel (WT) configuration run 18 run19 run 23 run 10 M q + α FF (1 ) [1/rad] WT (1 ) FF (3 ) WT (2 ) θ 0 [ ] Figure 19 Pitch damping sum versus pitch oscillation amplitude for run 23 (M = 110) q +α (θ init = 43 ) (θ init = 50 ) θ 0 [ ] Figure 20 Pitch damping sum versus pitch oscillation amplitude for run 10 (M = 201) 25 the reached maximum amplitude is very small For all freestream conditions the sting has a small influence on the frequency of the oscillation Figure 17 to 20 show the pitch damping sum computed from the time-historie data using Eq (2) and (3) The analysis has been done for local maxima and minima separately For the transonic freesteam the pitch damping sum decreases rapidly with increasing oscillation amplitudes this is mainly observed for the free flight cases where higher amplitudes have been achieved For run 18, 19 and 23 the pitch damping sum is reduced by a factor of two for an oscillation amplitude of ±10 compared to oscillations with very small amplitudes For practical reasons the pitch damping sum is averaged in a region around the trim angle The averaging has been done for two ranges of amplitude, one for small oscillations up to 1 and one for larger oscillations up to 3, if data available The averaged values are listed in Tab 3 and plotted versus Mach number in Fig 21 The plot shows that the suport sting has a stabilizing effect on the pitch oscillation for all transonic cases Especially for run 23 the pitch damping sum changes the sign from positive to negative what means that the behavior changes from unstable to slightly stable It also shows a higher damping for larger oscillation amplitudes For the supersonic case the dependancy of the pitch damping sum from the oscillation amplitude is less severe It seems that the support sting decreases the damping slightly Oscillation amplitude <1 with sting Oscillation amplitude 2 with sting Oscillation amplitude 1 w/o sting Oscillation amplitude 3 w/o sting 4 CONCLUSION q +α dynamically unstable dynamically stable Figure 21 Averaged pitch damping sum versus Mach number for diiferent pitch oscillation amplitudes M Steady-state as well as fully coupled CFD/RBD simulations have been carried out to investigate the static and dynamic stability of a re-entry vehicle in transonic and low supersonic flow at high angles of attack The study focusses on the influence of the support sting, holding the vehicle in the wind tunnel, to the pitch damping derivatives For all investigated transonic cases the results show that the vehicle is dynamically unstable The presence of the sting increases the trim angle and decreases the escalation rate of the pitch oscillation The results also show a strong dependancy of the pitch damping derivative on the pitch oscillation amplitude The pitch damping sum decreases with larger pitch oscillation amplitudes In supersonic flow the influence of the sting and the the oscil-

8 lation amplitude is small ACKNOWLEDGMENTS These activities have been carried out in the framework of the Technology Research Program of the European Space Agency The author would like to thanks ESA for the support and for the funding of this project REFERENCES [1] Gülhan, A, Klevanski, J & Willems, S(2011) Experimental study of the dynamic stability of the EXOMARS capsule 7th European Symposium on Aerothermodynamics, Brugge, Belgium [2] Madrane, A, Heinrich, R & Gerhold T (2002) Implementation of the chimera method in the unstructured hybrid DLR fine volume TAU-code 6th Overset Composite Grid and Solution Technology Symposium, Ft Walton Beach, USA [3] Madrane, A, Raichle, A & Stürmer, A (2004) Parallel Implementation of a Dynamic Overset Unstructured Grid Approach ECCOMAS 2004, Jyväskylä, Finland [4] Menter, F R (1994) Two-equation eddy-viscosity turbulence models for engineering applications AIAA Journal 32(8), [5] Redd, B, Olsen, D M & Barton, R L (1965) Relationship between the aerodynamic damping derivatives measured as a function of instantaneous angular displacement and the aerodynamic damping derivatives measured as a function of oscillation amplitude NASA TN D-2855, USA [6] Reimer, L, Heinrich, R & Meurer, R (2014) Validation of a Time-Domain TAU-Flight Dynamics Coupling Based on Store Relation Scenarios Notes on Numerical Fluid Mechanics an Multidisciplinary Design 124, , Springer [7] Schwamborn, D, Gerhold, T & Heinrich, R (2006) The DLR TAU-Code: Recent Applications in Research and Industry ECCOMAS 2006, Delft, The Netherlands