Detached Eddy Simulation on Hypersonic Base Flow Structure of Reentry-F Vehicle

Transcription

1 Available online at ScienceDirect Procedia Engineering 00 (2014) APISAT2014, 2014 Asia-Pacific International Symposium on Aerospace Technology, APISAT2014 Detached Eddy Simulation on Hypersonic Base Flow Structure of Reentry-F Vehicle Chen Zhi*, Zhang Liang, Li Pengfei China Academy of Aerospace Aerodynamics, Beijing , China Abstract A detached eddy simulation of Reentry-F flight vehicle is conducted to investigate its base flow structure. The result shows that DES predicts more accurate heat transfer rates compared to the flight experiment data than laminar and RANS (Spalart-Allmaras model) simulations. The initial vortex surface of base flow field is of toroidal shape, but the decrease of recirculation region cross section area forces the vortex surface first to shrink, then breakdown and reunite, and finally curl to several x-axis elongated vortex surfaces. These x-axis elongated vortex surfaces are origin for the strips distribution of temperature contour on the z=0 plane The Authors. Published by Elsevier Ltd. Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA). Keywords: Detached Eddy Simulation; Base Flow; Flow Structure 1. Introduction Research on hypersonic base flow started in early 1950s, when researchers were interested in the base drag and heating problem of rockets and missiles [1,2]. Though large sets of wind tunnel tests were conducted, reliable data were difficult to obtain because of supporting sting disturbance. Hence, flight experiment takes on more than usual significance in base flow study. In 1968, NASA conducted a flight experiment program named Reentry-F [3]. Though the prime object of the project was to obtain accurate turbulent heat-transfer and transition data, two pressure and four heat-transfer sensors were installed on the spacecraft's base plane to record base pressure and base * Corresponding author. Tel.: ; fax: address: chenzhi@live.cn The Authors. Published by Elsevier Ltd. Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).

2 2 Chen Zhi / Procedia Engineering 00 (2014) heat flux history during the reentry process. Because no sting disturbance is introduced in flight test, these data are ideal for base flow studies both for engineering correlation development and numerical scheme validation. The numerical prediction of base drag and thermal loads has always been difficult for its nature of unsteadiness and large separations. When the flow is turbulent, prediction becomes much more complicated for the adding of the large range of flow scales, which are difficult to resolve directly (in DNS) or modeling (in RANS). In recent years, a technique named Detached Eddy Simulation (DES) becomes more and more popular in large separated flow simulations [4]. DES combines the merits of large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) into one single model. It behaves as LES in separated flow region and RANS in attached boundary layer region. Compared to LES, DES method avoids the direct modeling of large amounts of small scales in boundary layer, which result in a saving of mesh number and computation effort. Compared to RANS, it is capable of handling large separated flow such as base flows. Barnhardt conducted a series of DES simulation on Reentry-F base flow [5,6]. Taking the tiny angle of attack and base supporting ring into consideration, Barnhardt obtained base heating rates result consistent with flight experiment result, which proved the validity of DES method for hypersonic base flow simulation. In the present paper, we performed a detached eddy simulation of Reentry-F base flow at the flight condition of Barnhardt's research, but focus on the wave and vortex structures of hypersonic base flow. 2. Computation Method The simulation was performed with an in-house code "CAAA-HEAT" which was developed and optimized for accurate prediction of the heat environment of hypersonic vehicles. To extend its prediction capability to base flows, SA-DES model is added to the code in the present study. SA-DES model is developed based on the popular RANS model of Spalart-Allmaras (S-A) model. They shares the same transport equation of eddy viscosity (1) and most of the model coefficients. 2 2 ˆ ˆ 1 ˆ ˆ ˆ 2 2 ˆ ˆ Cb u { 1 ˆ ˆ j C b Cb 1S Cw 1 f w } 2 t x j x j x j d x j (1) The only difference is the definition of parameter d. In S-A model, d stands for the wall distance d w, while in SA- DES, it's a length scale and defined as C DES is an adjustable parameter and set to 0.65 in the present study as in Ref [6]. is the maximum cell length, and defined as When grid point is close to wall (d<c DES ), d is equal to the wall distance and the model degenerates to the S-A model. When it is far from the wall and goes to the separated region, d is equal to C DES as a filter length scale, and the model behaves as a subgrid model in LES. The switch between RANS and LES enables DES method to efficiently simulate large separated flows. 3. Computation Setup d min d, C Reentry-F vehicle is a sharp cone with a half cone angle of 5 degree and length of 3.96m, as shown in Fig 1a. To ensure the grid quality and resolution in its base flow region, great efforts have been devoted to the grid generation process and finally a grid of 18 million cells is generated with a cell length of 4mm in the core separation region. The grid topology and surface mesh on base plane are shown in Fig1b. w DES max,, x y z (2) (3)

3 Chen Zhi / Procedia Engineering 00 (2014) a b Fig. 1. Volume Grid Topology and Base Plane Surface Mesh The simulation is conducted at two trajectory points, t=456.0s and t=457.4s, which is consistent with Barnhardt's research. The effect of transition to boundary layer thickness is taken into consideration by directly specifying the transition position in CFD program. The simulation condition is summarized in Table 1. Table 1. Simulation Condition Height(km) Ma Re(1/m) Angel of attack Wall Temperature(K) Transition position m m The base diameter of Reentry-F vehicle is 0.693m and the free stream velocity is about 6000m/s, which results in a characteristic time scale of s. Thus a physical time step of s is chosen for dual time stepping to ensure each characteristic time scale contains more than 100 computation steps to guarantee the time resolution. 4. Results and Discussion With the SA-DES method and aforementioned grid, the heat transfer rate of Reentry-F vehicle is obtained. As a validation of present code, we first exam the predicted heat flux and compare it to the experiment data. Fig. 2 illustrates the predicted forebody heat flux and its comparison with flight data. The predicted heat flux shows good agreement with the flight data except in the transition region. Besides the experiment data, the predicted base heat flux is also compared to laminar and turbulent simulations, as depicted in Fig. 3. As expected, SA-DES predicts the most accurate base heat flux compared to flight test data.

4 4 Chen Zhi / Procedia Engineering 00 (2014) a H=21km H=24km Fig. 2. Predicted heat flux result at forebody b H=21km H=24km Fig. 3. Predicted heat flux result at base plane The base flow wave structure is complicated, to illustrate the wave structures in the base flow region, contour of the dot production of velocity vector and pressure gradient vector ( V P ) on the z=0 plane is shown in Fig. 4. Pressure increases in compression waves in the flow direction which results in a positive V P, while it decreases in expansion waves and result in a negative V P. Thus the sign of V P can be used to distinguish compression waves from expansion waves. Because the rapid change of velocity and pressure is a sign of shock wave, V P 's value can also be used to distinguish shock waves from expansion waves. With this wave structure illustration technique, the wave structure is clearly shown in Fig. 3. It is evident forebody shock wave, the corner expansion wave, the lip shock wave and the recompression shock wave are all evident, which are the typical wave structure of supersonic base flow. But because of strong compression effects in hypersonic flow, it is observed that the lip shock waves and the corner expansion waves are more parallel to the center axis than supersonic cases. V P Forebody Shock Wave Corner Expansion Wave Recompression Shock wave Lip Shock Wave Fig. 4. Wave structure on the z=0 plane The second invariant of velocity gradient tensor (Q2) is an illustration of vortex and is usually used to depict the flow vortex structure. Fig. 5 shows the iso-surfaces of Q2 (colored by static temperature). It can be seen the initial

5 Chen Zhi / Procedia Engineering 00 (2014) base flow vortex is of toroidal shape and is attached to the base edge. But when the flow cross base corner and enters the free shear layer region, the toroidal vortex begins to shrink and break up into short strips. With the decreasing of recirculation region cross section in flow direction, strip vortexes are then compressed and curl and elongate along the x-axis, and finally transform to several x-axised vortex surfaces. Fig. 5. Iso-surfaces of Q2 at base region The development of x-axised vortex is shown in Fig. 6, which illustrates the temperature contour and streamlines on x slices of base flow field. With the decreasing of cross section area of recirculation region, the two large vortexes and several small vortexes on x=4.4 plane are compressed and reassembled to four equal vortexes on x=5.2 plane, which finally combine to two vortexes on x=6.0 plane after the wake neck. x=4.8 x=5.6 Slice position x=4.4 x=5.2 x=6.0 x=4.4 x=4.8 x=5.2 x=5.6 x=6.0 Fig. 6. Streamlines on x slices of base flow field The temperature contour on the z=0 plane is shown in Fig 7. It can be seen at the wake neck of base flow the temperature contour shows a strips distribution, which are both observed in the present simulation and Barnhardt's research [6]. The aforementioned x-axised vortex surfaces are the origin of this phenomenon. 70kft DES 80kft DES Fig.7. Cluster distribution of temperature contour

6 6 Chen Zhi / Procedia Engineering 00 (2014) Conclusions Detached eddy simulation of Reentry-F flight experiment is conducted to investigate the hypersonic base flow structures. The conclusions are as follows: 1.The base heat transfer result is in good agreement with the flight experiment. 2.The initial vortex surface of base flow is of toroidal shape, but the decreasing of recirculation region cross section area forces the vortex surface to breakdown and reunite, and finally forms several x-axis elongated vortex surfaces. 3.These x-axis elongated vortex surfaces are responsible for the cluster distribution of temperature contour. References [1] Martelluci A. Experimental Study of Near Wakes. BSD-TR Vol.1. Data Presentation, November [2] Carpenter P W and Tabakoff W. Survey and Evaluation of Supersonic Base Flow Theories[R]. N , [3] James L D and Howard S C. Analysis of base pressure and base heating on a 5 degree half-angle cone in free flight near mach 20 (reentry f). NASA-TM-X-2468, [4] Spalart P R. Detached-Eddy Simulation[J]. Annual Review Fluid Mechanics, 2009, 41: [5] Michael B and Graham V C. Detached Eddy Simulation of Hypersonic Base Flows During Atmospheric Entry[R]. AIAA Paper , [6] Michael B and Graham V C. Detached Eddy Simulation of the Reentry-F Flight Experiment[R]. AIAA Paper , 2008.