SCIENCE CHINA Technological Sciences • RESEARCH PAPER •
May 2012 Vol.55 No.5: 1437–1442 doi: 10.1007/s11431-012-4760-6
Investigation on high angle of attack characteristics of hypersonic space vehicle HUANG Wei*, LI ShiBin, LIU Jun & WANG ZhenGuo* Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China Received October 13, 2011; accepted January 16, 2012; published online March 26, 2012
The high angle of attack characteristics play an important role in the aerodynamic performances of the hypersonic space vehicle. The three-dimensional Reynolds Averaged Navier-Stokes (RANS) equations and the two-equation RNG k- turbulence model have been employed to investigate the influence of the high angle of attack on the lift-to-drag ratio and the flow field characteristics of the hypersonic space vehicle, and the contributions of each component to the aerodynamic forces of the vehicle have been discussed as well. At the same time, in order to validate the numerical method, the predicted results have been compared with the available experimental data of a hypersonic slender vehicle, and the grid independency has been analyzed. The obtained results show that the predicted lift-to-drag ratio and pitching moment coefficient show very good agreement with the experimental data in the open literature, and the grid system makes only a slight difference to the numerical results. There exists an optimal angle of attack for the aerodynamic performance of the hypersonic space vehicle, and its value is 20°. When the angle of attack is 20°, the high pressure does not leak from around the leading edge to the upper surface. With the further increasing of the angle of attack, the high pressure spreads from the wing tips to the central area of the vehicle, and overflows from the leading edge again. Further, the head plays an important role in the drag performance of the vehicle, and the lift percentage of the flaperon is larger than that of the rudderevator. This illustrates that the optimization of the flaperon configuration is a great work for the improvement of the aerodynamic performance of the hypersonic space vehicle, especially for a high lift-to-drag ratio. hypersonic space vehicle, angle of attack characteristic, lift-to-drag ratio, numerical simulation Citation:
1
Huang W, Li S B, Liu J, et al. Investigation on high angle of attack characteristics of hypersonic space vehicle. Sci China Tech Sci, 2012, 55: 1437 1442, doi: 10.1007/s11431-012-4760-6
Introduction
The X-37B space plane spent more than 220 days in orbit since it was launched by the Air Force of the USA on April 22, 2010, and it has drawn an ever increasing attention of many countries for its good aerodynamic and thermal protection characteristics. Its success would quicken the development of the hypersonic propulsion technology and stimulate the combined cycle engine to integrate with the airframe [1]. *Corresponding author (email:
[email protected];
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2012
Ohtake [2] has presented two thermal analysis methods for the re-entry vehicle structure, and Labbe et al. [3] have described the methodologies to characterize the aerodynamic and aerothermodynamic environment of the X-38. However, in the open literature, there are few researches on the aerodynamic performance of the X-37B, especially the effect of the high angle of attack on the lift-to-drag ratio, and it is necessary to study the flow field characteristics around this kind of the vehicle. At the same time, the computational fluid dynamic technology is a valid supplement for the ground experimental data [4], and this is because a significant portion of the hypersonic flight envelope cannot tech.scichina.com
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be simulated experimentally. Park et al. [5] have investigated the asymmetric vortex characteristics of supersonic flow over a body at a high angle of attack numerically, and they have found that the angle of attack, Reynolds number and Mach number all make a great difference to the side force. At the same time, Huang et al. [6] have studied the influence on and contribution of each weighted surface to the integral performance of the hypersonic vehicle with the angle of attack ranging from −8° to 8°, and they have found that under the three different working conditions, namely the inlet closedown, the motor through-flow and ignition, the forces acting on the forebody, the cowl and the upper surface of the airframe have a large impact on the aeropropulsive performance of the vehicle. Further, they have constructed a hypersonic waverider vehicle theoretically, and discussed the effects of the angle of attack, angle of sideslip and the inflow Mach number on the aerodynamic performance of the vehicle numerically [7]. Lin et al. [8] have studied the influence of the angle of attack on the aerodynamic performance of a waveriderbased hypersonic vehicle with finlets, and the waverider geometry has been derived from a perturbed hypersonic flow past a cone with combined transverse and small longitudinal curvature. The obtained results show that this slender waverider with finlets has a high lift-to-drag ratio and an ability to endure a positive angle of attack, and the ability to cruise under a negative angle of attack is poor. Meanwhile, the aerodynamic performances of the sharp and blunt leading edge waveriders at angles of attack ranging from 0° to 5° have been analyzed and compared with the CFD and theoretical predictions [9]. The purpose of the present study is to investigate the high angle of attack characteristics of the hypersonic space vehicle numerically, and the effects of the angle of attack on the lift-to-drag ratio and the flow field characteristics are mainly performed. At the same time, the contributions of each component to the aerodynamic forces of hypersonic space vehicle are discusses as well, and the numerical methods are validated with the available experimental data of a hypersonic slender vehicle.
2 Physical model and numerical method The hypersonic space vehicle is reconstructed from the X-37B, and it includes 6 main components, namely the head, the forward and backward bodies, the flaperon, the rudderevator and the base face (see Figure 1). The length of the hypersonic space vehicle is 8.9 m, and its height is 2.9 m. The wingspan for the flaperons is 4.5 m, and the angle between the rudderevators is 82° [10]. The supersonic air flows from left to right with the freestream Mach number 8.2, the static pressure 951.5 Pa and the static temperature 89.3 K. At the outflow, all the physical variables are extrapolated
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Figure 1
A sketch of the hypersonic space vehicle.
from the internal cells due to the flow being supersonic. The three-dimensional coupled implicit Reynolds Averaged Navier-Stokes (RANS) equations and the two-equation RNG k- turbulence model have been employed to numerically simulate the flow fields around the hypersonic space vehicle, and the appropriate system of equations, which governs the turbulence flow of a compressible gas, may be written as [11]: (a) mass conservation equation ui 0, , i=1, 2, 3; t xi
(1)
(b) momentum conservation equation P ij ui u j Fbi , ui t x j xi x j
i, j=1, 2, 3;
(2)
(c) energy equation
q D u 2 P ij ui i Fbj u j Q, h Dt 2 t x j xi i, j=1, 2, 3; (3)
(d) turbulent kinetic energy (k) equation k kui k eff Gk YM , xi x j x j
i, j=1, 2, 3;
(4)
(e) rate of dissipation of turbulent kinetic energy () equation 2 ui eff C1 Gk C2 R , xi x j x j k k i, j=1, 2, 3 (5)
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with R
C 3 1 / 0 2 1 3
k
,
(6)
Sk ,
(7)
0 4.38, 0.012,
(8)
where , ui, P, ij, Fbi, Q and C are the density, velocity components, pressure, turbulent shear stress, body force components, bulk heat addition and eddy viscosity, respectively. Gk, YM and S are respectively the production of turbulence kinetic energy due to velocity gradients [12], the contribution of dilatation-dissipation in compressible turbulence and the modulus of the mean strain tensor [13]. k and are respectively the turbulence Prandtl numbers for k and equations. In the same way, the model constants are also derived analytically: C1=1.42, C2=1.68 [14]. The viscosity and thermal conductivity are evaluated using a mass-weighted mixing law, and a no-slip and adiabatic boundary condition is imposed along the walls of the hypersonic space vehicle [15]. Because of the symmetry of the geometric configuration, only half of the region of the flow field is required in order to perform the numerical simulations of the hypersonic space vehicle. The standard wall functions are introduced to model the near-wall region flow, and the air is assumed to be a thermally and calorically perfect gas. The solutions can be considered as converged when the residuals reach their minimum values after falling for more than three orders of magnitude, and the difference between the computed inflow and the outflow mass flux is required to drop below 0.001 kg s1.
3 Code validation
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process, the lift-to-drag ratios for different angles of attack, i.e. 3°, 0°, 3°, 5°, 7° and 10°, are obtained. At the same time, in order to analyze the grid independency, four grid scales are introduced in this study, namely Grids 1−4. Grids 1−3 use the structured grid cells, and the last one uses the unstructured grid cells. The detailed information for grid systems is illustrated in Table 1. Figures 3 and 4 present the lift-to-drag ratio and pitching moment coefficient versus angle of attack for different grid scales respectively, and the solid symbol represents the experimental data from ref. [16]. It is clear that the predicted lift-to-drag ratios show very good agreement with the experimental data for all grid scales, especially Grid 4 (see Figure 3), and the lift-to-drag ratio increases monotonically with the increasing of the angle of attack in the range considered in the experiment. This implies that the numerical methods employed in this paper are with confidence to investigate the aerodynamic characteristics of hypersonic vehicles, and the grid scale makes only a slight difference to the predicted results. At the same time, we have observed that the predicted pitching moment coefficients for all grid scales match very well with the experimental data in ref. [16] (see Figure 4), and this validates the accuracy of the present code further. Thus, in the following sections, the unstructured grid system with 936721 cells is applied to obtain the high angle of attack characteristics of the hypersonic space vehicle. Table 1
Information for grid systems Type
Number of cells
y+
Grid 1
structured
389400
