Numerical investigation of an active TPS for a wing leading edge exposed to high temperature air behind a strong bow shock wave
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Abstract
An array of subsonic counter-flow jets is studied as an active thermal protection system (TPS) for wing leading edges of hypersonic vehicles. The performance is numerically estimated in the model case of a circular cylinder on the basis of the 2D compressible Navier-Stokes equations. In contrast to a single subsonic jet, an array of jets is robust against variation of the angle of attack; high cooling effectiveness is confirmed up to 5° variation. The coolant gas (air) discharged from channels embedded in the cylinder covers over a wide range of the front surface of the cylinder. The feasibility of the active TPS is also discussed.
Keywords
Counter-flow jet Hypersonic vehicle Thermal protection system Compressible Navier-Stokes Shock capturing1 Introduction
A hypersonic vehicle must bear harsh aerodynamic heating and the implementation of thermal protection system (TPS) is mandatory in particular around the nose cap and the wing leading edges. Re-usability, low-cost maintenance and life-elongation are now regarded as requisite conditions for future space programs. Existing TPS’s for airframes of hypersonic vehicles such as ablation and reinforced carbon-carbon, however, do not fulfill all of these requirements. For example, the shuttle TPS is said to require about 40,000 h of maintenance between typical flights. An active TPS exploiting a counter-flow jet issuing from around a stagnation point has been considered promising since the early days of space development [1, 2, 3, 4, 5]. In particular, the application of a supersonic jet in the long penetration mode has been attracting a lot of attention lately in connection with drag reduction as well as thermal protection [6, 7, 8]. Nevertheless, such active systems have not yet been put into practice so far, which is in contrast to the well-matured technology of film cooling for turbine blades. The main reason is considered to lie in difficulties in the fulfillment of low mass condition, which is an obvious requirement in space missions.
In the present paper we numerically investigate the performance of an active TPS for wing leading edges of hypersonic vehicles on the basis of the compressible Navier-Stokes equations. Instead of supersonic jets, we consider the application of subsonic jets, which seems advantageous in the light of low mass condition. In fact, our preliminary computations, which were carried out for the model case of a circular cylinder, indicate the achievement of high cooling effectiveness by means of a subsonic counter-flow jet; the high temperature gas coming from behind the bow shock wave formed in front of the cylinder is nearly perfectly blocked by the coolant gas issuing from around the stagnation point despite the occurrence of the Kelvin-Helmholtz instability, which enhances the mixing. These computations, however, were made with the unrealistic boundary condition that the velocity distribution of the jet at the exit was the Poiseuille-flow type for simplicity and the influence of variation of the angle of attack was not examined there. Actual cruise flights of vehicles, however, involve small but appreciable pitching motions and a subsonic counter-flow jet is expected to be easily bent upward or downward. It is also considered that the distribution of the jet at the exit must be markedly different from the Poiseuille-flow type; the Kelvin-Helmholtz instability must also have non-negligible influence on it. The assumption introduced for simplicity is removed in the present study, where an array of subsonic counter-flow jets issuing from channels embedded in the cylinder is considered.
2 Problem
3 Numerical method
The numerical method employed in the present study is a simplified version of the shock-capturing finite volume method developed in Ref. [9]. The numerical flux corresponding to the Euler equations is computed as a convex combination of three parts, namely F^{A}, F^{D} and F^{C}, in the original scheme. The F^{A} is dissipative and F^{D} and F^{C} are less dissipative. The arguments of F^{A} and F^{D} are computed by MUSCL (the van-Leer slope limiter) and those of F^{C} are done by fifth order accurate Lagrange’s polynomial approximation. The weights of the convex combination vary smoothly according to physical situations such that F^{A}, F^{D} and F^{C}, respectively, become dominant around shock waves, around contact discontinuities and in smooth regions. The Euler flux of the simplified scheme comprises F^{A} and F^{D}; the former takes charge of regions around shocks and the latter does of those around contact discontinuities and smooth regions. The diffusive numerical flux is common for both of the schemes and is computed by the standard second order accurate central finite difference approximation; second order accuracy is considered to suffice even in the original scheme in view of the smallness of the diffusive terms, which are multiplied by the inverse of the Reynolds number. The standard RK-4 and RK-2 are employed in the original scheme and the simplified one, respectively. The robustness of the original scheme against shock anomalies such as carbuncle phenomenon and post shock oscillations is drastically enhanced by a simple procedure at the preprocessing level and its side effect appears as one-cell increase in thickness of a numerically captured shock [10]. The simplified scheme inherits the strong robustness against shock anomalies from the original scheme. The performance of the original scheme is largely comparable to that of WENO5-Rusanov, while its computational cost is 30~40% less than of that of the advanced scheme; the time consuming local characteristic decomposition is not necessary in shock capturing with MUSCL. The simplified scheme is more than 6 times as fast as the original scheme. In the present study, we put the speed of computation before the order of formal accuracy of computation, which is meaningful only if the resolution is sufficiently high.
4 Results and discussions
The upstream condition, the stagnation pressure and the reservoir pressure
M_{∞} | Re_{∞} | T_{∞} [K] | P_{∞} [Pa] | P_{sta} [Pa] | P_{res} [Pa] | |
---|---|---|---|---|---|---|
Case-A | 5 | 460,000 | 230 | 1000 | 3.26E+ 4 | 3.29E+ 4 |
Case-B | 27 | 2600 | 200 | 1 | 9.44E+ 2 | 1.20E+ 3 |
Case-C | 7.5 | 34,000 | 270 | 76 | 5.54E+ 3 | 5.85E+ 3 |
The achievement of high cooling effectiveness is confirmed up to 5° variation of the angle of attack in the 2D numerical computations of an array of subsonic counter-flow jets. Because the prediction of the cooling effectiveness is sensitive to the numerical behavior of the Kelvin-Helmholtz instability, more detailed numerical computations are needed. Even if the present 2D computations capture the actual flows well, it does not immediately prove the feasibility of the active TPS, however. Suppose a hypersonic vehicle with a wingspan of 20 m (e.g. X-30 and space shuttle orbiter). In Case-A, the active TPS consumes about 2.6 kg of air per second as the coolant; the total air consumed in a cruise flight of 5000 km amounts to about 10 t. It is not reasonable to load the vehicle with such amount of air and the suction of the outside air is considered to be mandatory. The total temperature of the outside air, however, is about 1400 K; the kinetic energy of molecules constituting the air at upstream, which is transformed to the internal energy during the deceleration, should be absorbed in some appropriate way. In the case of the cooling by means of water spray, where the kinetic energy is consumed as the latent heat and the coolant gas is a mixture of air and water vapor, the amount of water necessary for the flight is estimated to be about 2.9 t, which is about 2% of the gross weight of X-30; it is reduced to 1.6 t when the total temperature of the jets is increased to 800 K. Similarly, it is estimated from the results of Case-B and Case-C, though just for reference, that the amount of the coolant air consumed during 800 s of the peak heating period in a typical shuttle re-entry is about 500 kg, which is about 2% of the payload.
5 Conclusions
Subsonic jets are preferable to supersonic ones as an active TPS for hypersonic vehicles in the light of low mass condition. However, they are not robust enough against small variation of the angle of attack. The present study proposes a solution method which overcomes the weakness. It is also suggested that hypersonic passenger vehicles require another type of cooling system for the supply of the coolant. It is worth while further exploring the feasibility of active TPS’s exploiting subsonic counter-flow jets. The corresponding 3D computations are now under way.
Notes
Acknowledgements
Funding from the Kyoto University Foundation is gratefully acknowledged.
Funding
The Kyoto University Foundation.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Authors’ contributions
TO is responsible for the formulation of the problem, the analyses of numerical results and the writing. TS carried out the numerical computation and TK was engaged in the preliminary numerical computation for the present study. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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