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Effects of wall cooling on performance parameters of hypersonic inlets
Acta Astronautica 65 (2009) 467 – 476 www.elsevier.com/locate/actaastro
Effects of wall cooling on performance parameters of hypersonic inlets Juntao Chang∗ , Wen Bao, Daren Yu, Yi Fan, Yi Shen Harbin Institute of Technology, 150001 Heilongjiang, People’s Republic of China Received 27 July 2008; received in revised form 8 December 2008; accepted 10 February 2009 Available online 12 March 2009
Abstract The internal flowfield of a 2-D mixed-compression hypersonic inlet was simulated numerically at different wall temperatures. The effects of wall cooling on performance parameters of the hypersonic inlet without and with the backpressure, and especially on the maximum backpressure of a fixed-geometry hypersonic inlet were discussed. The inner physical mechanism of wall cooling improving the maximum backpressure of hypersonic inlets was analyzed. In contrast with no wall cooling, the static pressure ratio of hypersonic inlets without backpressure is reduced slightly, but the mass-captured coefficient, total-pressure recovery coefficient and the flow uniformity of hypersonic inlets at the isolator exit are improved by the action of wall cooling. The interaction between boundary layers and shocks is weakened due to wall cooling, which leads to that the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and it can improve the maximum backpressure ratio of hypersonic inlets. With the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient of hypersonic inlets is reduced. Crown Copyright © 2009 Published by Elsevier Ltd. All rights reserved. Keywords: Hypersonic inlet; Wall cooling; Flow control; Performance improvement
1. Introduction The performance of a ramjet–scramjet powered hypersonic vehicle is determined by its inlet efficiency. Specifically, the inlet wave system influences the compression efficiency, mass capturing and combustion stability. The internal flowfield of the compression system features some very complex flow phenomena like shock–shock interaction, shock–boundary layer interaction, separation and so on. The isolator connects the inlet with the combustor and adapts the flow in terms of static pressure delivered by the inlet to the static pressure in
∗ Corresponding author.
E-mail address: [email protected] (J. Chang).
the combustor. The length of the isolator is determined by the need to contain the combustion-induced pressure rise over the entire flight trajectory. If the length of the isolator is short, the isolator cannot contain the shock system induced by the combustor, and the inlet unstart may appear. If the length of the isolator is long, the isolator contributes too much viscous drag and weight to the system performance. An active control system for repositioning shock waves within the isolator should yield a shorter isolator design, which results in the reduced system drag and weight, and the higher propulsive efficiency. There exist many active control measurements for the hypersonic flow, such as boundary layer bleeding, wall cooling and so on. From the viewpoint of the thermal-protection, the overall vehicle and the scramjet engine need the wall cooling [1,2], and the wall
0094-5765/$ - see front matter Crown Copyright © 2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2009.02.005
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Nomenclature Cf Dpt H L Lsep M0 M2 M3 p0 pt0 p2 p3 pb pbmax
the skin friction coefficient the distortion index of the total-pressure recovery coefficient the height of the isolator the length of the isolator the length of the separation zone Mach number of the freestream the mass-weighted averaged Mach number at the entrance of the isolator the mass-weighted averaged Mach number at the exit of the isolator the static pressure of the freestream the total pressure of the freestream the mass-weighted averaged static pressure at the entrance of the isolator the mass-weighted averaged static pressure at the exit of the isolator the backpressure at the exit of the isolator the maximum backpressure at the exit of the isolator
cooling can reduce the viscous drag [3,4] and improve the stabilization of the boundary layer [5–7]. Some papers on the maximum backpressure and the performance parameters of hypersonic inlets have been published. Ding [8] simulated the inner flowfield of the inlet-isolator, and the results show that the maximum backpressure capability is increased with the inlet distortion decreasing. Joe Iannelli [9,10] used a distributed wall mass removal system which can mitigate unstart and expand the operability of the isolator. Tam [11] used a simple method for implementing variable geometry, and several ramp configurations with a backward facing step were used to improve the performance parameter of the isolator. An engineering relationship between the shock-train pressure rise as a function of the correlation parameter (including the isolator length, Reynolds number, etc.) has been developed by Billig [12] and is also reported in Heiser [13]. The effects of different inlet-isolator configurations were discussed in great detail by Emami [14], Reinartz [15] studied the variation of the isolator geometry and its effects on the overall inlet compression efficiency, and the investigation shows that the sustainable backpressure is strongly influenced by the isolator length. However, few papers focused on the effect of wall cooling on performance parameters, especially on the
ps pti p¯ t T0 Tw Re q Q x y i li k
the surface pressure the total-pressure at each of the grid of the isolator height the averaged value of the total-pressure profile the static temperature of the freestream the wall temperature Reynolds number based on the momentum thickness the heat flux the total heat transfer the momentum thickness the mass-captured coefficient the total-pressure recovery coefficient the axis location the vertical location the angle of the wedge the length of the wedge turbulent kinetic energy turbulent dissipation rate
maximum backpressure of a fixed-geometry hypersonic inlet. For the scramjet, the total thrust and ratio of thrust to weight is the important performance parameter. How to improve the total thrust and ratio of thrust to weight is always an important issue for the fixed-geometry scramjet. The bigger the backpressure of the hypersonic inlet that can be sustained, the more the fuel flow allowing to inject into the combustion chamber, and the more the thrust of the scramjet engine. Therefore enhance the maximum backpressure of the hypersonic inlet by taking some measures is an effective way to improve the performance (thrust) of the scramjet engine and hypersonic inlet. One of the active control measurements, wall cooling was used to decrease the static temperature of the wall at the higher Mach number of the freestream. How the wall cooling affects the performance parameters (especially on the maximum backpressure) of the hypersonic inlet? This is our concern problems. And the paper is mainly focused on the effects of wall cooling on performance parameters of hypersonic inlets. To discuss this problem, the inner flowfield of a mixed-compression hypersonic inlet at different wall temperatures was numerically simulated firstly. The performance parameters of hypersonic inlets at different wall temperatures without and with the backpressure were analyzed, respectively, and the inner physical
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469
Fig. 1. Geometric sketch of the inlet model. Table 1 Geometric parameters of the hypersonic inlet.
2.2. Numerical method
L1 (m)
L2 (m)
L3 (m)
L4 (m)
L5 (m)
L6 (m)
0.212
0.113
0.083
0.157
0.109
0.048
H (m)
1 (deg)
2 (deg)
3 (deg)
4 (deg)
5 (deg)
0.015
6
8.3
9.8
13
14.1
mechanism why the wall cooling can improve the maximum backpressure of hypersonic inlets was discussed. The rest of this paper is organized as follows. Section 2 states inlet model and computations. Section 3 presents the effects of wall cooling on performance parameters of hypersonic inlets. Section 4 presents some conclusions. 2. Inlet model and computations 2.1. Inlet model The main geometric parameters of the hypersonic inlet are referred to Fig. 1 and Table 1, and the length unit is mm, the angle unit is degree. It is a mixedcompression inlet, including three external shocks and two internal shocks. The inlet satisfies the conditions [16] in below: the shock-on-lip condition; the guarantee of the similar strength of the compression ramp shock; the compression ramp shocks converge on the cowl lip, and the reflected shock impinges on the shoulder of the inlet. The compression angle of the three external shocks is 6◦ , 8.3◦ and 9.8◦ , and the compression angle of the two internal shocks is 13◦ and 14.1◦ , respectively. The external contraction ratio is 5.47, and the internal contraction ratio is 1.29, and the total contraction ratio is 7.05. The length of the isolator is seven times the height of the isolator. The design Mach number of the hypersonic inlet is 6.
A Renormalization Group k– turbulence model is implemented for turbulent flows. The boundary condition of the supersonic inflow is far-pressure field, and the freestream conditions can be defined by specifying the boundary conditions. The boundary condition of the exit of the hypersonic inlet is the pressure outlet, and the backpressure can be defined by altering the pressure value. In case of predominant supersonic outflow, the variables are completely extrapolated from the interior to the boundary. Otherwise, the influence of the throttle is simulated with a prescribed backpressure at the outflow boundary and the remaining variables are extrapolated. At solid walls, the no-slip boundary condition is enforced by setting the velocity components to zero. These computations have been performed with the commercial CFD code FLUENT, and the numerical accuracy of this software on the computation of the hypersonic inlet has been validated in Refs. [17–21]. The join calculation of the intake and the isolator is performed in this paper, and the spacing and grid density is different in the two zones. The spacing of the grid in the isolator is relative small, because there are the interaction between the shock and boundary layers. 2.3. Numerical accuracy analysis To ensure the convergence of the numerical solution, the residuals (L2 -norm) are monitored in Fig. 2. The solution can be considered as converged after approximately 75 000 iterations, where the courant number is 0.5. At this stage, the continuity residual, x-velocity residual, y-velocity residual and energy residual reach their minimum values after falling for over four orders of magnitude. The turbulence (k and ) residual have a six orders of magnitude decrease. An additional convergence criterion enforced in this current analysis requires the difference between computed inflow and
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Fig. 2. Residuals for the hypersonic inlet computation.
Fig. 3. Skin friction coefficient distributions at different grid-refinement levels.
outflow mass flux to drop below 0.5%. The evaluation was performed using the medium mesh. The performance of a grid sensitivity analysis confirms that the grid resolution used here is sufficient to capture the physically relevant features. To ensure that the boundary layers, shock interactions, and separation zones are properly resolved, a value of y+ below 5 is realized for the main portion of the wall flow region. To simulate the interaction between the shock and the boundary layer, the intersection and reflection of wave system, calculate the flow field at first, and perform the technology of mesh self-adaptation based on the pressure gradient and continue to compute. In Figs. 3 and 4, the skin friction coefficient and wall heat flux distributions along the cowl and ramp surfaces at the freestream condition (M0 = 6, p0 = 2549 Pa, T0 = 215.5 K, Tw = 1000 K) are shown for three different grid-refinement levels: coarse (744×68), medium (1010×120), and fine (1910×210); where the skin friction coefficient is a non-dimensional parameter defined as the ratio of the wall shear stress and the dynamic pressure of the freestream, and the maximum discrepancy between the three mesh levels is less than 6%. Table 2 shows the performance parameters (mass-captured coefficient, total-pressure recovery coefficient and static pressure ratio) of hypersonic inlets at different grid-refinement levels; and the maximum discrepancy between the three mesh levels is less than 2%, where the performance parameter is referred to the one (mass-weighted averaged) at the exit of the isolator. The calculations were performed on a workstation (CPU 4×2 GHz, Memory 8 GB). The CPU time needed
Fig. 4. Wall heat flux distributions at different grid-refinement levels.
Table 2 Performance parameters of hypersonic inlets at different gridrefinement levels. Grid level
p3 /p0
Coarse Medium Fine
0.9801 0.9873 0.9966
0.4672 0.4564 0.4455
32.5354 32.9849 33.1125
for computation is about 1.5 h for the coarse mesh, 4 h for the medium mesh, and 9 h for the fine mesh. Out of this analysis, the medium grid was selected, and all results shown are computed applying this resolution.
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Fig. 5. Comparison of a schlieren picture (bottom) without throttling and corresponding Mach number contour lines (top) of the computation.
the cowl surface. The reason for the discrepancy is probably the deficiency of the turbulence model, the differences between experiment and computation conditions, or the measurements error of the sensor. In a word, the computation results of the hypersonic inlet accord with the physical conception of the aerodynamics. It can reveal the intersection of oblique shock waves and expansion waves and capture the primary characteristic of internal flowfield. 3. Effects of wall cooling on performance parameters of hypersonic inlets
Fig. 6. Surface pressure distributions of hypersonic inlets.
The use of a medium grid resolution saves the CPU time greatly. The accuracy of the current numerical investigation is evaluated by comparison with the experimental results [15,22]. Comparison of a schlieren picture without throttling and corresponding Mach number contour lines of the computation is shown in Fig. 5, and it reveals an overall good agreement. The shock wave pattern, the separation, and the approximate boundary-layer thickness of the schlieren picture are also present in the simulation results. The surface pressure distributions shown in Fig. 6, allow for a more quantitative comparison between numerical and experimental results. Here, a discrepancy in the ramp pressure distribution can be seen in the expansion region with subsequent separation. The computed separation appears smaller than experimentally observed, and thus, the separation shock is weaker and impinges downstream of the measured location on
The internal flowfield of the compression system features some very complex flow phenomena like shock–shock interaction, shock–boundary layer interaction, separation, and so on. This separation bubbles cause pressure losses and the falling of performance parameters, and more important, the inlet unstart may appear during flight conditions. Therefore, measures have to be taken to reduce the interaction between shock–boundary layer and the separation bubble. Manipulations of the boundary layer have been studied extensively in attempts to reduce the pressure loss associated with shock/turbulent-boundary-layer interactions. There exist many active control measurements for the hypersonic flow, such as boundary layer bleeding (suction and blowing), wall cooling and so on. From the viewpoint of the thermal-protection, the overall vehicle and the scramjet engine need the wall cooling at higher Mach number, and the wall cooling can reduce the viscous drag and improve the stabilization of the boundary layer. So the effect of the wall cooling on performance parameters of the scramjet and hypersonic inlet should be investigated, which can direct the design and operation of the scramjet or the hypersonic inlet. And this paper is focused on the effects of wall
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Table 3 Performance parameters of hypersonic inlets at different wall temperatures without backpressure. Tw (K)
p3 /p0
M3
1600 1200 800 400
0.9940 1.0125 1.0265 1.0391
0.4465 0.4505 0.4524 0.4514
32.5463 31.7340 30.8686 29.9160
2.5732 2.6008 2.6289 2.6584
cooling on performance parameters of hypersonic inlets with and without backpressure, especially on the effects of wall cooling on the maximum backpressure of a fixed-geometry hypersonic inlet. The effects of wall cooling on performance parameters of hypersonic inlets were discussed in this section. There exist the interaction between the shock and the boundary layer, which leads to the relatively large change of the static temperature of the wall, so it is difficult to make the wall temperature be a fixed value at the action of the wall cooling in practice. From the viewpoint of simplifying the problem, the thermal boundary condition of the wall is defined as the fixed temperature value. The inner flowfield of hypersonic inlets at different wall temperatures (400, 600, 800, 1000, 1200, 1400 and 1600 K) was simulated numerically. 3.1. Effect of wall cooling on performance of hypersonic inlets under no backpressure For a hypersonic inlet, the flow at the exit of the isolator is predominant supersonic outflow with no backpressure, and the variables are completely extrapolated from the interior to the boundary. The performance parameters (mass-weighted averaged) at the exit of the isolator at different wall temperatures are shown in Table 3, where the freestream condition is M0 = 6, p0 = 2549 Pa, T0 = 215.5 K. As can be seen from Table 3, with the wall temperature decreasing, the static pressure ratio decreases, the mass-captured coefficient, the total-pressure recovery coefficient and Mach number at the isolator exit increase slightly. In theory, the wall cooling can weaken the interaction between the boundary layer and the shock. On one hand, the wall cooling can make the speed of sound within the boundary layer decrease, and Mach number within the boundary layer increase; on the other hand, the wall cooling can make the viscosity within the boundary layer decrease, and Reynolds number within the boundary layer increase. These factors can reduce the thickness of the boundary layer, and weaken the effect of the boundary layer on the performance parameter of hypersonic inlets. Fig. 7 shows the
Fig. 7. Velocity vectors and boundary layer edge of the hypersonic inlet at different wall temperatures.
boundary layer edge of the hypersonic inlet at different wall temperatures, where the boundary layer edge can be obtained by creating an isosurface where the velocity magnitude is 99% of the main portion flow. As can be seen from Fig. 7, the thickness of the boundary layer at Tw = 1600 K is bigger than at Tw = 400 K, which cause the mass-captured coefficient decrease. And the shock angle of the oblique shock at Tw = 1600 K is bigger than at Tw = 400 K, which cause the static pressure ratio increase, Mach number and the total-pressure recovery coefficient at the isolator exit decrease. The comparison of the total-pressure recovery coefficient profiles over the height of the isolator exit for the configuration with different wall temperatures is shown in Figs. 8 and 9 shows the variation of the distortion index of total-pressure recovery coefficient with different wall temperatures. The distortion index of the total-pressure N recovery coefficient can be defined by abs( pti − p¯ t / p¯ t ), where pti is the totalD pt = i=1 pressure at each grid of the height of the isolator, p¯ t is the averaged value of the total-pressure profile. As can be seen from Figs. 8 and 9, the distortion index of the total-pressure recovery coefficient at the isolator exit gradually decrease with the wall temperature decreasing. In a word, with the wall temperature decreasing, the static pressure ratio of hypersonic inlets without backpressure is reduced slightly, but the mass-captured coefficient, total-pressure recovery coefficient and the flow uniformity of hypersonic inlets at the isolator exit are improved by the action of the wall cooling.
J. Chang et al. / Acta Astronautica 65 (2009) 467 – 476
Fig. 8. Total-pressure recovery coefficient profiles over the height of the isolator exit at different wall temperatures.
473
Fig. 10. Surface pressure distributions of the hypersonic inlet with different backpressures.
sonic inlet. The effect of wall cooling on performance parameters of hypersonic inlets under backpressure is discussed in this section.
Fig. 9. Variation of the distortion index of the total-pressure recovery coefficient with the wall temperatures.
3.2. Effect of wall cooling on performance parameters of hypersonic inlets under backpressure For a fixed hypersonic inlet, the maximum backpressure of hypersonic inlets is mainly determined by the freestream conditions. If the freestream conditions are fixed, the maximum backpressure of hypersonic inlets is constant. The bigger the backpressure of the hypersonic inlet that can be sustained, the more the fuel flow allowing to inject into the combustion chamber, and the more the thrust of the scramjet engine. Therefore enhance the maximum backpressure of the hypersonic inlet by taking some measures is an effective way to improve the performance (thrust) of the scramjet engine and hyper-
3.2.1. Analysis of backpressure unstart phenomena In scramjet, a precombustion shock system is developed inside the isolator because of the subsequent highpressure combustion zone. To produce a similar shock wave system in the test, the effect of the operating engine is simulated by a specified backpressure. The ramp surface pressure distributions with different backpressures at the boundary condition (M0 = 6, p0 = 2549 Pa, T0 = 215.5 K, Tw = 1000 K) are shown in Fig. 10. The high backpressure leads to the separation of the boundary layer. The pressure buildup proceeds continuously due to the rapidly growing boundary layer. As the backpressure increases, the onset of pressure buildup moves upstream into the isolator. At pb /p0 = 150, the complete isolator contributes to the pressure buildup and the maximum pressure ratio is achieved. After even a slight shift of the operating point (pb /p0 = 150), the pressure rise is pushed forward into the contracting part of the inlet, and the backpressure ratio is defined as the maximum backpressure ratio. A further increase of the backpressure causes a severe flow blockage and results in a strong decrease of captured mass flow. In this condition, the inlet flowfield is unstable and the inlet is no longer started. 3.2.2. Effect of wall cooling on maximum backpressure ratio of hypersonic inlets Fig. 11 shows the variation of the total heat transfer with the wall temperature, where the total heat transfer is referred to the energy which is used to cool the
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J. Chang et al. / Acta Astronautica 65 (2009) 467 – 476 Table 4 Performance parameter of hypersonic inlets at different wall temperatures with backpressure. Tw (K)
p2 /p0
pbmax /p0
1600 1200 800 400
0.9940 1.0125 1.0265 1.0391
0.2429 0.2358 0.2249 0.2145
24.5869 24.2851 23.9564 23.6845
135.5419 145.3118 156.2883 166.6000
Fig. 11. Variation of the total heat transfer with the wall temperature.
Fig. 13. Comparison of the maximum backpressure ratio with the Waltrup formula at different wall temperatures.
Fig. 12. Variation of the maximum backpressure ratio of hypersonic inlets with the wall temperature.
wall. With the wall temperature decreasing, the total heat transfer increase, and the relationship between the total heat transfer and the wall temperature is approximately linear. Fig. 12 shows the variation of the maximum backpressure with the wall temperature. The lower the wall temperature, the more the maximum backpressure of the hypersonic inlet. The performance parameters (mass-weighted averaged) at the exit of the isolator at different wall temperatures with the maximum backpressure are shown in Table 4. As can be seen from Table 4, with the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient is reduced.
The maximum backpressure of the isolator can be predicted by the Waltrup formula [12,13,23] (M22 − 1)(L/H )Re0.25 (H/)0.5 = 50( pbmax / p2 − 1) + 170( pbmax / p2 − 1)2 , where M2 and p2 is the massweighted averaged Mach number and static pressure at the entrance of the isolator, pbmax is the maximum backpressure of the isolator, is the boundary-layer momentum thickness, Re is the Reynolds number based on at the entrance of the isolator, H is the height of the isolator, L is the length of the isolator. As can be discussed in part A of Section 3, With Tw decreasing, Re and M2 increase, and decreases. According to the Waltrup formula, the maximum backpressure will be improved with the wall temperature decreasing. The comparison of the maximum backpressure ratio with the Waltrup formula at different wall temperatures is shown in Fig. 13, and the data points agree well with the curve predicted by the Waltrup formula, which proves the validity of the results.
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Fig. 14. Mach number contour of the hypersonic inlet at different wall temperature with pb /p0 = 110. (a) Tw = 400 K; (b) Tw = 800 K; and (c) Tw = 1200 K.
Fig. 15. Variation of the length of separated zones with the wall temperature.
3.3. Inner physical mechanism of wall cooling improving maximum backpressure of hypersonic inlets The inner physical mechanism of wall cooling improving maximum backpressure of the isolator can be explained in blow. The reason why the inlet unstart occurs is that, the rapid development of the boundary layers caused by the high backpressure emerges in the contraction part of the inlet, and it causes the flow sep-
aration and choked in at the entrance of the inlet. Mach number contour of the hypersonic inlet at different wall temperatures with pb /p0 = 110 is shown in Fig. 14, and the variation of the length of the separated zone with the wall temperature is shown in Fig. 15. As can be seen from Figs. 14 and 15, the length of the separated zone of the boundary layer gradually is reduced with the wall temperature decreasing, and the relationship between the length of the separated zone and the wall temperature is approximately linear, and it agrees with Refs. [24,25]. So the wall cooling can make the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and the maximum backpressure ratio of hypersonic inlets can be improved in contrast with no wall cooling. In a word, the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and the maximum backpressure ratio of hypersonic inlets can be improved in contrast with no wall cooling. With the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient is reduced. 4. Conclusions The effect of the wall temperatures on performance parameters of hypersonic inlets is investigated by the
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need for active flow control of hypersonic inlets. For this investigation, the inner flowfield of the hypersonic inlet at different wall temperatures was numerically simulated firstly. The effect of wall cooling on the performance parameter of the hypersonic inlet without and with the backpressure, and especially the effects of wall cooling on the maximum backpressure of a fixed-geometry hypersonic inlet are discussed. The inner physical mechanism of wall cooling improving the maximum backpressure of hypersonic inlets was analyzed. There exist some conclusions. (1) In contrast with no wall cooling, the static pressure ratio of hypersonic inlets without backpressure is reduced slightly, but the mass-captured coefficient, total-pressure recovery coefficient and the flow uniformity of hypersonic inlets at the isolator exit are improved by the action of the wall cooling. (2) The interaction between boundary layers and shocks is weakened at the action of wall cooling, which leads to that the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and it can improve the maximum backpressure ratio. With the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient is reduced. Acknowledgments This work was supported by China National Natural Science Foundation (No. 90816028, No. 90716012), and the authors thank the reviewer’s valuable advices on this paper. References [1] E. Daniau, M. Sicard, Experimental and numerical investigations of an endothermic fuel cooling capacity for scramjet application, AIAA Paper 2005-3404. [2] L.L. Pagel, W.R. Warmbold, Active cooling of a hydrogenfueled scramjet engine, Journal of Aircraft 6 (5) (1969) 472–474. [3] S. Rowan, A. Paull, Viscous drag reduction in a scramjet combustor with film cooling, AIAA Paper 2001-1818. [4] E. Reshotko, Drag reduction by cooling in hydrogen-fueled aircraft, Journal of Aircraft 16 (9) (1979) 584–590. [5] L.H. Back, R.F. Cuffelt, Shock wave/turbulent boundary-layer interactions with and without surface cooling, AIAA Journal 14 (4) (1976) 526–532.
[6] F.W. Spaid, J.C. Frishett, Incipient separation of a supersonic, turbulent boundary layer, including effects of heat transfer, AIAA Journal 10 (7) (1972) 915–922. [7] N.M. El-Hady, A.K. Vermat, Instability of compressible boundary layers along curved walls with suction or cooling, AIAA Journal 22 (2) (1984) 206–213. [8] M. Ding, H. Li, X.Q. Fan, Two-dimensional viscous simulation of a inlet-isolator flows at Mach number 4, AIAA Paper 2001-3883. [9] I. Joe, A distributed wall mass removal system for improving scramjet isolator performance, AIAA Paper 2008-0065. [10] I. Joe, Unstart mitigation in inlet and isolator via wall mass transfer: a computational study, AIAA Paper 2007-5071. [11] C. Tam, K. Lin, Numerical investigations on simple variable geometry for improving scramjet isolator performance, AIAA Paper 2006-4509. [12] F.S. Billig, Research on supersonic combustion, Journal of Propulsion and Power 9 (4) (1993) 499–514. [13] W.H. Heiser, D.T. Pratt, Hypersonic Airbreathing Propulsion, AIAA Education Series, AIAA, Washington, DC, 1993 pp. 153–156. [14] S. Emami, C.A. Trexler, Experimental investigation of inletcombustor isolators for a dual-mode scramjet at a Mach number of 4, NASA Technical Paper 3502, May. [15] B.U. Reinartz, C.D. Herrmann, Aerodynamic performance analysis of a hypersonic inlet isolator using computation and experiment, Journal of Propulsion and Power 19 (5) (2003) 868–875. [16] D.M. VanWie, Scramjet inlets, scramjet propulsion, in: E.T. Curran, S.N.B. Murthy (Eds.), Progress in Astronautics and Aeronautics, vol. 189, AIAA, Reston, VA, 2000, pp. 447–511, (Chapter 7). [17] J. Häberle, A. Gülhan, Internal flowfield investigation of a hypersonic inlet at Mach 6 with bleed, Journal of Propulsion and Power 23 (5) (2007) 1007–1017. [18] J. Häberle, A. Gülhan, Investigation of two-dimensional scramjet inlet flowfield at March 7, Journal of Propulsion and Power 24 (3) (2008) 446–459. [19] D. Yu, J. Chang, W. Bao, Optimal classifications criterions of hypersonic inlet start/unstart, Journal of Propulsion and Power 23 (2) (2007) 310–316. [20] T. Cui, D. Yu, J. Chang, W. Bao, Topological geometry interpretation of hypersonic inlet start/unstart-catastrophe hysteresis and bifurcation, Journal of Aircraft 45 (4) (2008) 1464–1468. [21] J. Chang, D. Yu, W. Bao, L. Qu, Dimensionless analysis of the unstart boundary for 2-D mixed hypersonic inlets, The Aeronautical Journal 112 (1135) (2008) 547–555. [22] C.D. Herrmann, W.W. Koschel, Experimental investigation of the internal compression of a hypersonic intake, AIAA Paper 2002-4130. [23] P.J. Waltrup, F.S. Billig, Prediction of precombustion wall pressure distributions in scramjet engines, Journal of Spacecraft and Rockets 10 (9) (1973) 620–622. [24] H. Olivier, M. Habermann, Use of shock tunnels for hypersonic propulsion testing, AIAA Paper 1999-2447. [25] B.U. Reinartz, Computation of wall heat fluxes in hypersonic inlet flows, AIAA Paper 2002-0506.
Effects of wall cooling on performance parameters of hypersonic inlets Juntao Chang∗ , Wen Bao, Daren Yu, Yi Fan, Yi Shen Harbin Institute of Technology, 150001 Heilongjiang, People’s Republic of China Received 27 July 2008; received in revised form 8 December 2008; accepted 10 February 2009 Available online 12 March 2009
Abstract The internal flowfield of a 2-D mixed-compression hypersonic inlet was simulated numerically at different wall temperatures. The effects of wall cooling on performance parameters of the hypersonic inlet without and with the backpressure, and especially on the maximum backpressure of a fixed-geometry hypersonic inlet were discussed. The inner physical mechanism of wall cooling improving the maximum backpressure of hypersonic inlets was analyzed. In contrast with no wall cooling, the static pressure ratio of hypersonic inlets without backpressure is reduced slightly, but the mass-captured coefficient, total-pressure recovery coefficient and the flow uniformity of hypersonic inlets at the isolator exit are improved by the action of wall cooling. The interaction between boundary layers and shocks is weakened due to wall cooling, which leads to that the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and it can improve the maximum backpressure ratio of hypersonic inlets. With the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient of hypersonic inlets is reduced. Crown Copyright © 2009 Published by Elsevier Ltd. All rights reserved. Keywords: Hypersonic inlet; Wall cooling; Flow control; Performance improvement
1. Introduction The performance of a ramjet–scramjet powered hypersonic vehicle is determined by its inlet efficiency. Specifically, the inlet wave system influences the compression efficiency, mass capturing and combustion stability. The internal flowfield of the compression system features some very complex flow phenomena like shock–shock interaction, shock–boundary layer interaction, separation and so on. The isolator connects the inlet with the combustor and adapts the flow in terms of static pressure delivered by the inlet to the static pressure in
∗ Corresponding author.
E-mail address: [email protected] (J. Chang).
the combustor. The length of the isolator is determined by the need to contain the combustion-induced pressure rise over the entire flight trajectory. If the length of the isolator is short, the isolator cannot contain the shock system induced by the combustor, and the inlet unstart may appear. If the length of the isolator is long, the isolator contributes too much viscous drag and weight to the system performance. An active control system for repositioning shock waves within the isolator should yield a shorter isolator design, which results in the reduced system drag and weight, and the higher propulsive efficiency. There exist many active control measurements for the hypersonic flow, such as boundary layer bleeding, wall cooling and so on. From the viewpoint of the thermal-protection, the overall vehicle and the scramjet engine need the wall cooling [1,2], and the wall
0094-5765/$ - see front matter Crown Copyright © 2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2009.02.005
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Nomenclature Cf Dpt H L Lsep M0 M2 M3 p0 pt0 p2 p3 pb pbmax
the skin friction coefficient the distortion index of the total-pressure recovery coefficient the height of the isolator the length of the isolator the length of the separation zone Mach number of the freestream the mass-weighted averaged Mach number at the entrance of the isolator the mass-weighted averaged Mach number at the exit of the isolator the static pressure of the freestream the total pressure of the freestream the mass-weighted averaged static pressure at the entrance of the isolator the mass-weighted averaged static pressure at the exit of the isolator the backpressure at the exit of the isolator the maximum backpressure at the exit of the isolator
cooling can reduce the viscous drag [3,4] and improve the stabilization of the boundary layer [5–7]. Some papers on the maximum backpressure and the performance parameters of hypersonic inlets have been published. Ding [8] simulated the inner flowfield of the inlet-isolator, and the results show that the maximum backpressure capability is increased with the inlet distortion decreasing. Joe Iannelli [9,10] used a distributed wall mass removal system which can mitigate unstart and expand the operability of the isolator. Tam [11] used a simple method for implementing variable geometry, and several ramp configurations with a backward facing step were used to improve the performance parameter of the isolator. An engineering relationship between the shock-train pressure rise as a function of the correlation parameter (including the isolator length, Reynolds number, etc.) has been developed by Billig [12] and is also reported in Heiser [13]. The effects of different inlet-isolator configurations were discussed in great detail by Emami [14], Reinartz [15] studied the variation of the isolator geometry and its effects on the overall inlet compression efficiency, and the investigation shows that the sustainable backpressure is strongly influenced by the isolator length. However, few papers focused on the effect of wall cooling on performance parameters, especially on the
ps pti p¯ t T0 Tw Re q Q x y i li k
the surface pressure the total-pressure at each of the grid of the isolator height the averaged value of the total-pressure profile the static temperature of the freestream the wall temperature Reynolds number based on the momentum thickness the heat flux the total heat transfer the momentum thickness the mass-captured coefficient the total-pressure recovery coefficient the axis location the vertical location the angle of the wedge the length of the wedge turbulent kinetic energy turbulent dissipation rate
maximum backpressure of a fixed-geometry hypersonic inlet. For the scramjet, the total thrust and ratio of thrust to weight is the important performance parameter. How to improve the total thrust and ratio of thrust to weight is always an important issue for the fixed-geometry scramjet. The bigger the backpressure of the hypersonic inlet that can be sustained, the more the fuel flow allowing to inject into the combustion chamber, and the more the thrust of the scramjet engine. Therefore enhance the maximum backpressure of the hypersonic inlet by taking some measures is an effective way to improve the performance (thrust) of the scramjet engine and hypersonic inlet. One of the active control measurements, wall cooling was used to decrease the static temperature of the wall at the higher Mach number of the freestream. How the wall cooling affects the performance parameters (especially on the maximum backpressure) of the hypersonic inlet? This is our concern problems. And the paper is mainly focused on the effects of wall cooling on performance parameters of hypersonic inlets. To discuss this problem, the inner flowfield of a mixed-compression hypersonic inlet at different wall temperatures was numerically simulated firstly. The performance parameters of hypersonic inlets at different wall temperatures without and with the backpressure were analyzed, respectively, and the inner physical
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Fig. 1. Geometric sketch of the inlet model. Table 1 Geometric parameters of the hypersonic inlet.
2.2. Numerical method
L1 (m)
L2 (m)
L3 (m)
L4 (m)
L5 (m)
L6 (m)
0.212
0.113
0.083
0.157
0.109
0.048
H (m)
1 (deg)
2 (deg)
3 (deg)
4 (deg)
5 (deg)
0.015
6
8.3
9.8
13
14.1
mechanism why the wall cooling can improve the maximum backpressure of hypersonic inlets was discussed. The rest of this paper is organized as follows. Section 2 states inlet model and computations. Section 3 presents the effects of wall cooling on performance parameters of hypersonic inlets. Section 4 presents some conclusions. 2. Inlet model and computations 2.1. Inlet model The main geometric parameters of the hypersonic inlet are referred to Fig. 1 and Table 1, and the length unit is mm, the angle unit is degree. It is a mixedcompression inlet, including three external shocks and two internal shocks. The inlet satisfies the conditions [16] in below: the shock-on-lip condition; the guarantee of the similar strength of the compression ramp shock; the compression ramp shocks converge on the cowl lip, and the reflected shock impinges on the shoulder of the inlet. The compression angle of the three external shocks is 6◦ , 8.3◦ and 9.8◦ , and the compression angle of the two internal shocks is 13◦ and 14.1◦ , respectively. The external contraction ratio is 5.47, and the internal contraction ratio is 1.29, and the total contraction ratio is 7.05. The length of the isolator is seven times the height of the isolator. The design Mach number of the hypersonic inlet is 6.
A Renormalization Group k– turbulence model is implemented for turbulent flows. The boundary condition of the supersonic inflow is far-pressure field, and the freestream conditions can be defined by specifying the boundary conditions. The boundary condition of the exit of the hypersonic inlet is the pressure outlet, and the backpressure can be defined by altering the pressure value. In case of predominant supersonic outflow, the variables are completely extrapolated from the interior to the boundary. Otherwise, the influence of the throttle is simulated with a prescribed backpressure at the outflow boundary and the remaining variables are extrapolated. At solid walls, the no-slip boundary condition is enforced by setting the velocity components to zero. These computations have been performed with the commercial CFD code FLUENT, and the numerical accuracy of this software on the computation of the hypersonic inlet has been validated in Refs. [17–21]. The join calculation of the intake and the isolator is performed in this paper, and the spacing and grid density is different in the two zones. The spacing of the grid in the isolator is relative small, because there are the interaction between the shock and boundary layers. 2.3. Numerical accuracy analysis To ensure the convergence of the numerical solution, the residuals (L2 -norm) are monitored in Fig. 2. The solution can be considered as converged after approximately 75 000 iterations, where the courant number is 0.5. At this stage, the continuity residual, x-velocity residual, y-velocity residual and energy residual reach their minimum values after falling for over four orders of magnitude. The turbulence (k and ) residual have a six orders of magnitude decrease. An additional convergence criterion enforced in this current analysis requires the difference between computed inflow and
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Fig. 2. Residuals for the hypersonic inlet computation.
Fig. 3. Skin friction coefficient distributions at different grid-refinement levels.
outflow mass flux to drop below 0.5%. The evaluation was performed using the medium mesh. The performance of a grid sensitivity analysis confirms that the grid resolution used here is sufficient to capture the physically relevant features. To ensure that the boundary layers, shock interactions, and separation zones are properly resolved, a value of y+ below 5 is realized for the main portion of the wall flow region. To simulate the interaction between the shock and the boundary layer, the intersection and reflection of wave system, calculate the flow field at first, and perform the technology of mesh self-adaptation based on the pressure gradient and continue to compute. In Figs. 3 and 4, the skin friction coefficient and wall heat flux distributions along the cowl and ramp surfaces at the freestream condition (M0 = 6, p0 = 2549 Pa, T0 = 215.5 K, Tw = 1000 K) are shown for three different grid-refinement levels: coarse (744×68), medium (1010×120), and fine (1910×210); where the skin friction coefficient is a non-dimensional parameter defined as the ratio of the wall shear stress and the dynamic pressure of the freestream, and the maximum discrepancy between the three mesh levels is less than 6%. Table 2 shows the performance parameters (mass-captured coefficient, total-pressure recovery coefficient and static pressure ratio) of hypersonic inlets at different grid-refinement levels; and the maximum discrepancy between the three mesh levels is less than 2%, where the performance parameter is referred to the one (mass-weighted averaged) at the exit of the isolator. The calculations were performed on a workstation (CPU 4×2 GHz, Memory 8 GB). The CPU time needed
Fig. 4. Wall heat flux distributions at different grid-refinement levels.
Table 2 Performance parameters of hypersonic inlets at different gridrefinement levels. Grid level
p3 /p0
Coarse Medium Fine
0.9801 0.9873 0.9966
0.4672 0.4564 0.4455
32.5354 32.9849 33.1125
for computation is about 1.5 h for the coarse mesh, 4 h for the medium mesh, and 9 h for the fine mesh. Out of this analysis, the medium grid was selected, and all results shown are computed applying this resolution.
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Fig. 5. Comparison of a schlieren picture (bottom) without throttling and corresponding Mach number contour lines (top) of the computation.
the cowl surface. The reason for the discrepancy is probably the deficiency of the turbulence model, the differences between experiment and computation conditions, or the measurements error of the sensor. In a word, the computation results of the hypersonic inlet accord with the physical conception of the aerodynamics. It can reveal the intersection of oblique shock waves and expansion waves and capture the primary characteristic of internal flowfield. 3. Effects of wall cooling on performance parameters of hypersonic inlets
Fig. 6. Surface pressure distributions of hypersonic inlets.
The use of a medium grid resolution saves the CPU time greatly. The accuracy of the current numerical investigation is evaluated by comparison with the experimental results [15,22]. Comparison of a schlieren picture without throttling and corresponding Mach number contour lines of the computation is shown in Fig. 5, and it reveals an overall good agreement. The shock wave pattern, the separation, and the approximate boundary-layer thickness of the schlieren picture are also present in the simulation results. The surface pressure distributions shown in Fig. 6, allow for a more quantitative comparison between numerical and experimental results. Here, a discrepancy in the ramp pressure distribution can be seen in the expansion region with subsequent separation. The computed separation appears smaller than experimentally observed, and thus, the separation shock is weaker and impinges downstream of the measured location on
The internal flowfield of the compression system features some very complex flow phenomena like shock–shock interaction, shock–boundary layer interaction, separation, and so on. This separation bubbles cause pressure losses and the falling of performance parameters, and more important, the inlet unstart may appear during flight conditions. Therefore, measures have to be taken to reduce the interaction between shock–boundary layer and the separation bubble. Manipulations of the boundary layer have been studied extensively in attempts to reduce the pressure loss associated with shock/turbulent-boundary-layer interactions. There exist many active control measurements for the hypersonic flow, such as boundary layer bleeding (suction and blowing), wall cooling and so on. From the viewpoint of the thermal-protection, the overall vehicle and the scramjet engine need the wall cooling at higher Mach number, and the wall cooling can reduce the viscous drag and improve the stabilization of the boundary layer. So the effect of the wall cooling on performance parameters of the scramjet and hypersonic inlet should be investigated, which can direct the design and operation of the scramjet or the hypersonic inlet. And this paper is focused on the effects of wall
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Table 3 Performance parameters of hypersonic inlets at different wall temperatures without backpressure. Tw (K)
p3 /p0
M3
1600 1200 800 400
0.9940 1.0125 1.0265 1.0391
0.4465 0.4505 0.4524 0.4514
32.5463 31.7340 30.8686 29.9160
2.5732 2.6008 2.6289 2.6584
cooling on performance parameters of hypersonic inlets with and without backpressure, especially on the effects of wall cooling on the maximum backpressure of a fixed-geometry hypersonic inlet. The effects of wall cooling on performance parameters of hypersonic inlets were discussed in this section. There exist the interaction between the shock and the boundary layer, which leads to the relatively large change of the static temperature of the wall, so it is difficult to make the wall temperature be a fixed value at the action of the wall cooling in practice. From the viewpoint of simplifying the problem, the thermal boundary condition of the wall is defined as the fixed temperature value. The inner flowfield of hypersonic inlets at different wall temperatures (400, 600, 800, 1000, 1200, 1400 and 1600 K) was simulated numerically. 3.1. Effect of wall cooling on performance of hypersonic inlets under no backpressure For a hypersonic inlet, the flow at the exit of the isolator is predominant supersonic outflow with no backpressure, and the variables are completely extrapolated from the interior to the boundary. The performance parameters (mass-weighted averaged) at the exit of the isolator at different wall temperatures are shown in Table 3, where the freestream condition is M0 = 6, p0 = 2549 Pa, T0 = 215.5 K. As can be seen from Table 3, with the wall temperature decreasing, the static pressure ratio decreases, the mass-captured coefficient, the total-pressure recovery coefficient and Mach number at the isolator exit increase slightly. In theory, the wall cooling can weaken the interaction between the boundary layer and the shock. On one hand, the wall cooling can make the speed of sound within the boundary layer decrease, and Mach number within the boundary layer increase; on the other hand, the wall cooling can make the viscosity within the boundary layer decrease, and Reynolds number within the boundary layer increase. These factors can reduce the thickness of the boundary layer, and weaken the effect of the boundary layer on the performance parameter of hypersonic inlets. Fig. 7 shows the
Fig. 7. Velocity vectors and boundary layer edge of the hypersonic inlet at different wall temperatures.
boundary layer edge of the hypersonic inlet at different wall temperatures, where the boundary layer edge can be obtained by creating an isosurface where the velocity magnitude is 99% of the main portion flow. As can be seen from Fig. 7, the thickness of the boundary layer at Tw = 1600 K is bigger than at Tw = 400 K, which cause the mass-captured coefficient decrease. And the shock angle of the oblique shock at Tw = 1600 K is bigger than at Tw = 400 K, which cause the static pressure ratio increase, Mach number and the total-pressure recovery coefficient at the isolator exit decrease. The comparison of the total-pressure recovery coefficient profiles over the height of the isolator exit for the configuration with different wall temperatures is shown in Figs. 8 and 9 shows the variation of the distortion index of total-pressure recovery coefficient with different wall temperatures. The distortion index of the total-pressure N recovery coefficient can be defined by abs( pti − p¯ t / p¯ t ), where pti is the totalD pt = i=1 pressure at each grid of the height of the isolator, p¯ t is the averaged value of the total-pressure profile. As can be seen from Figs. 8 and 9, the distortion index of the total-pressure recovery coefficient at the isolator exit gradually decrease with the wall temperature decreasing. In a word, with the wall temperature decreasing, the static pressure ratio of hypersonic inlets without backpressure is reduced slightly, but the mass-captured coefficient, total-pressure recovery coefficient and the flow uniformity of hypersonic inlets at the isolator exit are improved by the action of the wall cooling.
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Fig. 8. Total-pressure recovery coefficient profiles over the height of the isolator exit at different wall temperatures.
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Fig. 10. Surface pressure distributions of the hypersonic inlet with different backpressures.
sonic inlet. The effect of wall cooling on performance parameters of hypersonic inlets under backpressure is discussed in this section.
Fig. 9. Variation of the distortion index of the total-pressure recovery coefficient with the wall temperatures.
3.2. Effect of wall cooling on performance parameters of hypersonic inlets under backpressure For a fixed hypersonic inlet, the maximum backpressure of hypersonic inlets is mainly determined by the freestream conditions. If the freestream conditions are fixed, the maximum backpressure of hypersonic inlets is constant. The bigger the backpressure of the hypersonic inlet that can be sustained, the more the fuel flow allowing to inject into the combustion chamber, and the more the thrust of the scramjet engine. Therefore enhance the maximum backpressure of the hypersonic inlet by taking some measures is an effective way to improve the performance (thrust) of the scramjet engine and hyper-
3.2.1. Analysis of backpressure unstart phenomena In scramjet, a precombustion shock system is developed inside the isolator because of the subsequent highpressure combustion zone. To produce a similar shock wave system in the test, the effect of the operating engine is simulated by a specified backpressure. The ramp surface pressure distributions with different backpressures at the boundary condition (M0 = 6, p0 = 2549 Pa, T0 = 215.5 K, Tw = 1000 K) are shown in Fig. 10. The high backpressure leads to the separation of the boundary layer. The pressure buildup proceeds continuously due to the rapidly growing boundary layer. As the backpressure increases, the onset of pressure buildup moves upstream into the isolator. At pb /p0 = 150, the complete isolator contributes to the pressure buildup and the maximum pressure ratio is achieved. After even a slight shift of the operating point (pb /p0 = 150), the pressure rise is pushed forward into the contracting part of the inlet, and the backpressure ratio is defined as the maximum backpressure ratio. A further increase of the backpressure causes a severe flow blockage and results in a strong decrease of captured mass flow. In this condition, the inlet flowfield is unstable and the inlet is no longer started. 3.2.2. Effect of wall cooling on maximum backpressure ratio of hypersonic inlets Fig. 11 shows the variation of the total heat transfer with the wall temperature, where the total heat transfer is referred to the energy which is used to cool the
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J. Chang et al. / Acta Astronautica 65 (2009) 467 – 476 Table 4 Performance parameter of hypersonic inlets at different wall temperatures with backpressure. Tw (K)
p2 /p0
pbmax /p0
1600 1200 800 400
0.9940 1.0125 1.0265 1.0391
0.2429 0.2358 0.2249 0.2145
24.5869 24.2851 23.9564 23.6845
135.5419 145.3118 156.2883 166.6000
Fig. 11. Variation of the total heat transfer with the wall temperature.
Fig. 13. Comparison of the maximum backpressure ratio with the Waltrup formula at different wall temperatures.
Fig. 12. Variation of the maximum backpressure ratio of hypersonic inlets with the wall temperature.
wall. With the wall temperature decreasing, the total heat transfer increase, and the relationship between the total heat transfer and the wall temperature is approximately linear. Fig. 12 shows the variation of the maximum backpressure with the wall temperature. The lower the wall temperature, the more the maximum backpressure of the hypersonic inlet. The performance parameters (mass-weighted averaged) at the exit of the isolator at different wall temperatures with the maximum backpressure are shown in Table 4. As can be seen from Table 4, with the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient is reduced.
The maximum backpressure of the isolator can be predicted by the Waltrup formula [12,13,23] (M22 − 1)(L/H )Re0.25 (H/)0.5 = 50( pbmax / p2 − 1) + 170( pbmax / p2 − 1)2 , where M2 and p2 is the massweighted averaged Mach number and static pressure at the entrance of the isolator, pbmax is the maximum backpressure of the isolator, is the boundary-layer momentum thickness, Re is the Reynolds number based on at the entrance of the isolator, H is the height of the isolator, L is the length of the isolator. As can be discussed in part A of Section 3, With Tw decreasing, Re and M2 increase, and decreases. According to the Waltrup formula, the maximum backpressure will be improved with the wall temperature decreasing. The comparison of the maximum backpressure ratio with the Waltrup formula at different wall temperatures is shown in Fig. 13, and the data points agree well with the curve predicted by the Waltrup formula, which proves the validity of the results.
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Fig. 14. Mach number contour of the hypersonic inlet at different wall temperature with pb /p0 = 110. (a) Tw = 400 K; (b) Tw = 800 K; and (c) Tw = 1200 K.
Fig. 15. Variation of the length of separated zones with the wall temperature.
3.3. Inner physical mechanism of wall cooling improving maximum backpressure of hypersonic inlets The inner physical mechanism of wall cooling improving maximum backpressure of the isolator can be explained in blow. The reason why the inlet unstart occurs is that, the rapid development of the boundary layers caused by the high backpressure emerges in the contraction part of the inlet, and it causes the flow sep-
aration and choked in at the entrance of the inlet. Mach number contour of the hypersonic inlet at different wall temperatures with pb /p0 = 110 is shown in Fig. 14, and the variation of the length of the separated zone with the wall temperature is shown in Fig. 15. As can be seen from Figs. 14 and 15, the length of the separated zone of the boundary layer gradually is reduced with the wall temperature decreasing, and the relationship between the length of the separated zone and the wall temperature is approximately linear, and it agrees with Refs. [24,25]. So the wall cooling can make the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and the maximum backpressure ratio of hypersonic inlets can be improved in contrast with no wall cooling. In a word, the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and the maximum backpressure ratio of hypersonic inlets can be improved in contrast with no wall cooling. With the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient is reduced. 4. Conclusions The effect of the wall temperatures on performance parameters of hypersonic inlets is investigated by the
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need for active flow control of hypersonic inlets. For this investigation, the inner flowfield of the hypersonic inlet at different wall temperatures was numerically simulated firstly. The effect of wall cooling on the performance parameter of the hypersonic inlet without and with the backpressure, and especially the effects of wall cooling on the maximum backpressure of a fixed-geometry hypersonic inlet are discussed. The inner physical mechanism of wall cooling improving the maximum backpressure of hypersonic inlets was analyzed. There exist some conclusions. (1) In contrast with no wall cooling, the static pressure ratio of hypersonic inlets without backpressure is reduced slightly, but the mass-captured coefficient, total-pressure recovery coefficient and the flow uniformity of hypersonic inlets at the isolator exit are improved by the action of the wall cooling. (2) The interaction between boundary layers and shocks is weakened at the action of wall cooling, which leads to that the boundary layers separations at the entrance of the isolator caused by the high backpressure occur later, and it can improve the maximum backpressure ratio. With the wall temperatures decreasing, the maximum backpressure ratio and mass-captured coefficient are added, and the total-pressure recovery coefficient is reduced. Acknowledgments This work was supported by China National Natural Science Foundation (No. 90816028, No. 90716012), and the authors thank the reviewer’s valuable advices on this paper. References [1] E. Daniau, M. Sicard, Experimental and numerical investigations of an endothermic fuel cooling capacity for scramjet application, AIAA Paper 2005-3404. [2] L.L. Pagel, W.R. Warmbold, Active cooling of a hydrogenfueled scramjet engine, Journal of Aircraft 6 (5) (1969) 472–474. [3] S. Rowan, A. Paull, Viscous drag reduction in a scramjet combustor with film cooling, AIAA Paper 2001-1818. [4] E. Reshotko, Drag reduction by cooling in hydrogen-fueled aircraft, Journal of Aircraft 16 (9) (1979) 584–590. [5] L.H. Back, R.F. Cuffelt, Shock wave/turbulent boundary-layer interactions with and without surface cooling, AIAA Journal 14 (4) (1976) 526–532.
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