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Influence of shock waves on supersonic transpiration cooling
International Journal of Heat and Mass Transfer 129 (2019) 965–974
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influence of shock waves on supersonic transpiration cooling Peixue Jiang a, Zhiyuan Liao a, Zheng Huang b, Yanbing Xiong c, Yinhai Zhu a,⇑ a
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China China State Shipbuilding Corporation, Beijing 100048, China c Beijing Institute of Astronautical System Engineering, Beijing 100076, China b
a r t i c l e
i n f o
Article history: Received 19 March 2018 Received in revised form 26 September 2018 Accepted 9 October 2018
Keywords: Transpiration cooling Shock wave Porous sintered plate
a b s t r a c t This paper experimentally and numerically investigates the effect of shock waves on transpiration cooling of a porous plate. The experiments were conducted in a wind tunnel of Mach number 2.8, wherein oblique shock waves were impinged onto the porous plate. A numerical simulation model was used to obtain detailed temperature and flow field distributions near the porous plate surface. The effects of different coolant blowing ratios and shock wave intensities on the transpiration cooling efficiency were studied. The results show that the transpiration cooling efficiency reduces because of the impinging oblique shock waves with the decrease in the fluid velocity near the porous wall, resulting in an increase in the local fluid static temperature. Moreover, the oblique shock waves increase the local static pressure, thus obstructing the coolant outflow and increasing the local wall temperature. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Hypersonic vehicles with a scramjet engine are exposed to an extremely critical thermal environment, thus requiring more efficient and stable active cooling technologies [1]. Transpiration cooling has advantages such as high cooling efficiency, high cooling capacity, and low coolant consumption and is considered one of the most promising active cooling technologies for thermally protecting important parts from extremely high heat loads. Transpiration cooling can be treated as a special case of film cooling, with a porous structure through which a cooling fluid flows onto a heated surface. Owing to the sufficient heat transfer within the porous media and the coolant film over the surface, which thickens the boundary layer, the cooling efficiency of transpiration cooling is higher than those of conventional active cooling methods. Researchers have focused on the thermal and flow mechanisms of transpiration cooling theoretically [2,3], experimentally [4–6], and numerically [7–10]. Liu et al. [11] investigated transpiration cooling using a sintered porous plate in a u = 30 m/s main flow to analyze the influences of the coolant blowing ratio, particle diameter, and porous matrix thermal conductivity. When the main flow is supersonic, the cooling efficiency exhibits a familiar behavior i.e., it increases with the increase in the blowing ratio and porous matrix thermal conductivity [12]. Soller et al. [13] experimentally investigated transpiration cooling for high-speed flight propulsion ⇑ Corresponding author. E-mail address: [email protected] (Y. Zhu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.043 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
systems. The tested sample was subjected to a total temperature of 600 K (T0) and a Mach number of 2.1, and the surface was effectively cooled owing to the cold incoming boundary layer. Meinert et al. [14] and Liu et al. [15] investigated the transpiration cooling efficiency using different coolant gases, and the results show that the gas coolant with a high specific heat is more effective for transpiration cooling. Foreest et al. [16] experimentally compared the transpiration cooling efficiency using liquid water and nitrogen gas, among which liquid water showed a much better performance for transpiration cooling. Shen et al. [17], Shen and Wang [18], Jiang et al. [19], and Huang et al. [20,21] experimentally and numerically investigated transpiration cooling using sintered porous struts, and the results show that with non-uniform coolant flow distributions, the cooling efficiency along the leading edge is higher, and the overall cooling efficiency is more uniform. Most of the studies on supersonic transpiration cooling have considered a uniform main flow. However, in practical applications, such as in the isolator section of a scramjet engine, hypersonic air flows into the engine inlet and is compressed by the fore body shock wave during combustion, and a shock wave chain emerges inevitably at the isolator section [22]. Cavity holders and struts are installed in the engine combustor, which could induce the shock wave and detachment, to improve fuel mixing and ignition. The adverse pressure gradient due to the shock wave could lead to boundary layer separation and considerable pressure loss. Thus, several flow control methods have been proposed to prevent shock-induced separation, improve the efficiency, and reduce the distortion, such as wall bleeding configurations [23] and vortex
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Nomenclature d F L Ma P T u x X
diameter [lm] coolant blowing ratio porous plate length [mm] Mach number pressure [Pa] temperature [K] velocity [m/s] distance from the start on the plate [m] dimensionless distance from the start on the plate
Greek symbols b shock wave angle [°] c specific heat ratio e porosity
generators [24,25]. In supersonic transpiration cooling, which is expected to be applied to hypersonic conditions, the effect of incident oblique shock waves must be taken into consideration. For supersonic film cooling, Juhany and Hunt [26], Kanda et al. [27] and Kanda and Ono [28] showed that an incident shock wave could weaken the cooling effect if the coolant layer static temperature increases. Peng and Jiang [29] and Peng et al. [30] numerically investigated the shock wave influence on supersonic film cooling, and their results show that the shock wave increased the static pressure on the wall, which reduced the local Mach number in the coolant layer and the adiabatic effectiveness, and enhanced the mixing of the main stream and coolant, which was more remarkable with stronger shock wave and lighter gas coolant. Martin et al. [31] numerically studied supersonic film cooling with shock wave interaction using the large-eddy simulation method, and their results show that the film cooling effectiveness decreased by 36% compared to the case with no shock wave within the potential-core region of the cooling stream. Moreover, the shock wave significantly increased the turbulence levels in the boundary layer, resulting in strong temperature fluctuations and more pronounced mixing because the hot main flow is transported toward the wall. Peng et al. [32] numerically studied the threedimensional shock wave effects on film cooling, with the results showing that an uneven shock wave caused a horizontal direction secondary flow, which made the hot mainstream to mix with the cooling film and reduce the cooling film layer thickness. Peng and Jiang [33] numerically investigated a slotted wall structure, and the results show that the slotted wall improves the film cooling after the shock wave is incident. Only few studies have been conducted on the shock wave effect for supersonic transpiration cooling. Nowak et al. [34] and Holden et al. [35] experimentally studied the effects of shock waves on transpiration-cooled nose cones at a Mach number in the range of 12–16 and shear-layer Reynolds number in the range of 104– 106 with both laminar and turbulent shock/shock interactions. The results show that high surface blowing rates enlarge the shock layer and moves the region of peak-heating interaction around the body; however, the shock wave still significantly weakens the cooling performance at the stagnation point. Moreover, the flow field observation showed that weak shocks can destroy the protective coolant layer in film cooling, whereas no significant change was observed after impinging shock waves onto a transpiration cooling plate [36]. Previous studies have shown that transpiration cooling is an effective method for cooling high heat flux surfaces on various structures. However, there is less research on transpiration cooling heat transfer with a nonuniform main flow, especially with an obli-
g h k
q
cooling efficiency wedge angle [°] thermal conductivity [W/(mK)] density [kg/m3]
Subscripts 1 mainstream C coolant e equivalent o total p particle r recovery w wall
que shock wave incident on the surface. Shock waves will occur in the combustion chamber for actual flight conditions which disrupt the protective transpiration cooling film and reduce the cooling efficiency. In this work, the flow and thermal mechanisms of the incident shock wave effect on the transpiration cooling of a porous plate was investigated experimentally and numerically. The porous plate was tested using air as the transpiration coolant in a supersonic wind tunnel (Mach number = 2.8) with a maximum main flow total temperature of 450 K. The experiments were conducted with and without incident shocks generated using wedge-shaped shock generators. The wall temperatures were measured using an infrared camera, and the flow fields were observed using a Schlieren system. Finally, a 2D numerical model was established to simulate the experimental conditions aiming to reveal the shock wave impact mechanism in supersonic transpiration cooling. 2. Experimental investigation 2.1. Experimental system The supersonic wind tunnel used to investigate the shock wave effect on transpiration cooling is the same as the one described in our previous paper [12], as shown in Fig. 1. Air was compressed in a screw compressor at a pressure of 0.75 MPa and then sent through two filters to remove dust and through a condensing drying machine for dehumidification. The compressed dry air was divided into two flow paths in the experimental system. The upper part of the system is the mainstream flow path, and the lower part is the coolant flow path. The mainstream was heated using an electrical heater up to a total temperature of 374 K, and the total pressure was adjusted to 0.46 MPa using an electric pressure regulator. The air then flowed through a specially designed Laval nozzle to be accelerated to a Mach number of 2.8. The wall temperatures were measured using an infrared camera, and the flow fields were observed using a Schlieren system. At the coolant stream path, a pressure regulator and a mass flow meter were used to control the gas pressure for different blowing ratios. The coolant flowed through a reservoir and a flat porous plate before mixing with the mainstream in the test section. The flow velocity decelerated to subsonic in the diffuser and in the subsonic expansion section, and was ultimately exhausted to the surrounding. 2.2. Test section Fig. 2 shows an image of the test section. The test section consists of a rectangular channel with a 20 mm 30 mm cross section
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Fig. 1. Schematic of the experimental system [12].
Fig. 2. Test section with a shock wave generator.
and a 220 mm long flat plate made of Bakelite as the bottom. An infrared camera was located on the top of the test section. The upper portion of the test section was made of ZnS for infrared camera observation and the other two sides were made of quartz glass for optical access. The upper wall opened slightly at a 0.5° angle to reduce the influence of the boundary layer. A 50 mm long porous plate made of sintered bronze particles was installed at the center of the Bakelite plate, and a wedge-shaped shock generator was used to produce an oblique shock impingement onto the middle of the porous plate. The wedge angle of the shock generator was adjusted to obtain different shock wave intensities. The coolant reservoir was sealed from the porous plate using a gasket made of low thermal conductivity polytetrafluoroethylene. A plastic gasket was also used for sealing between the coolant reservoir and the test section frame. The thickness of the porous sample was 10 mm, and the porous plate was sintered using bronze particles with an average particle diameter of 90 lm (dp). The sample porosity e was 0.337, and the mean pore diameter dh was 38.8 lm. For the experiment, different wedge angles (h), such as 6, 8, and 10°, were employed, and the shock generator base was 20 mm long. The wedge angle of the shock generator was changed to
obtain different oblique shock wave intensities, which has been often described as a relative static pressure increase after the oblique shock wave, as shown in Eq. (1) [37]. The shock wave intensity was proportional to the wedge angle h.
p2 p1 Dp cMa21 h ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ p p1 Ma21 1
ð1Þ
where the subscripts 1 and 2 represent the parameters before and after the shock wave, respectively. The angle between the induced shock waves and the wall was called the shock wave angle b, as listed in Table 1. The relationship between h and b can be represented as [37]: 2
tanh ¼ 2 cot b
Ma21 sin b 1 Ma21 ð
c þ cos 2bÞ þ 2
ð2Þ
By solving the above implicit equation, the theoretical shock wave angles could be calculated. Table 1 lists the results. The tail edge of the wedge-shaped shock generator is synchronized with the start of the porous plate to make sure that the oblique shock impinges onto the middle of the porous plate, as shown in Fig. 2b.
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Table 1 Shock wave angle b results.
340 Shock wave angle b (°)
335
6 8 10
25.7 27.8 31
330
2.3. Measurement and experimental uncertainty The parameters measured in the experiments included the porous wall temperature, main stream inlet temperature and total pressure, coolant mass flow rate, and coolant inlet temperature. The local wall temperatures on the porous wall were measured using three T-type thermocouples embedded into mini-channels cut into the surface of the porous wall along the centerline with an accuracy of ±0.2 K. The thermocouples were located at x/ L = 0.2, 0.5, and 0.8 in the channels, as shown in Fig. 2. The temperature distribution across the outer porous wall was then measured using an A310 infrared camera from FLIR Inc. after being calibrated using the three thermocouples. The accuracy of the infrared camera was ±2%. A Schlieren system was established for observing the flow field of transpiration cooling with the shock wave effect [19]. As the gas refractive index is proportional to the local gas density, the Schlieren system showed the shock wave structure where the gas density varied dramatically. A ‘‘Z-shaped” optical element arrangement was employed to avoid parallel rays penetrating through the test section repeatedly, which would cause image distortion. A plane mirror was used to reduce the installation space requirement, as shown in Fig. 3. Though the local sintered porous plate surface emissivity varied a little at different positions, the temperature differences between the IR and thermocouple measurements at different coolant injection mass flow rates were less than ±2 K with a constant overall wall emissivity, as shown in Fig. 4. The total temperature of the main stream was measured using a T-type armored thermocouple after the straight flowing section, and the inlet total pressures of the two streams were measured and controlled using two pressure regulators with an accuracy of ±0.1%. Three T-type thermocouples were installed in the coolant reservoir, and the readings were averaged as the coolant inlet temperature. All the T-type thermocou-
Parabolic mirror Plane mirror
Wall temperature, K
Wedge angle h (°)
Bronze plate T0= 374 K Tw1 (TC) Tw1 (IR) Tw2 (TC)
325
Tw2 (IR) Tw3 (TC)
320
Tw3 (IR)
315 310 305 300
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Blowing ratio, % Fig. 4. Calibration of IR imaging system (TC: Thermocouple, IR: Infrared camera).
ples had an accuracy of ±0.2 K. The coolant mass flow rate was controlled using a mass flowmeter from Alicat Inc. with an accuracy of ±0.2%. The blowing ratio for transpiration cooling is defined as the ratio of the mass flow rate per unit area of the cooling fluid and the main flow [37].
Fc ¼
qc uc q1 u1
ð3Þ
where qc is the cooling fluid inlet density, uc is the coolant inlet velocity, q1 is the main stream inlet density, and u1 is the main stream inlet velocity. In supersonic transpiration cooling, the free stream recovery temperature is often used as a substitute for the inlet temperature when defining the cooling effectiveness g.
g¼
Tr Tw Tr Tc
ð4Þ
where Tc is the coolant inlet temperature, and Tw is the wall temperature of the porous plate. The free stream recovery temperature Tr is defined as follows [38].
c1 2 Ma Tr ¼ T1 1 þ r 2
ð5Þ
where r is the recovery factor, and c is the specific heat ratio. According to Eqs. (4) and (5), the uncertainty in the cooling efficiency can be predicted using the following equation. Slit Condenser lens Lamp
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! !2ffi u u T T dT 2 1 dT 2 T r T w dT c w c r w t ¼ þ þ g Tr Tc g ðT r T c Þ2 g ðT r T c Þ2 g
dg
Test section
ð6Þ
Plane mirror
Camera
Knife edge
In this study, the maximum main stream temperature was 374 K, and the lowest cooling efficiency was approximately 0.13. Thus, the maximum uncertainty in the cooling efficiency was ±5.7%. 2.4. Shock wave effect on flow field
Parabolic mirror Fig. 3. Schematic of Schlieren system.
Fig. 5 shows the flow fields for the transpiration cooling with different wedge angles and a coolant blowing ratio (F) in the range of 0.44–2.19%. The main flow direction is from left to right in the figure. Because of the inevitable size difference between the mainstream nozzle section and the test section, two weak oblique shock
P. Jiang et al. / International Journal of Heat and Mass Transfer 129 (2019) 965–974
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Fig. 5. Schlieren images of flow fields with different wedge angles.
waves emerged at the start of the test section, after which the supersonic flow could be considered uniform. The porous plate was installed at the middle of the test section and was not affected by the flow disturbances. Moreover, the injected low-speed cooling gas partially blocked the supersonic mainstream, resulting in an oblique shock wave induced at the beginning of the flat porous plate. The oblique shock wave induced by the injected low-speed cooling gas mixed with these weak shock waves. Therefore, the shock waves were not incident on the porous surface, which means that the boundary layer thickened by the cooling gas was not affected. The intensity of this oblique shock wave increased with the increase in the coolant blowing ratio. The oblique shock wave intensity was controlled by varying the wedge angle h of the shock generator. The measured shock wave angles are compared with the predicted results, as listed in Table 1, and a good agreement is obtained, thus proving the reliability of the experiments. The shock wave intensity increases with the increase in h and the shock wave angle increases as well, thus moving the shock wave impingement position forward. An oblique shock wave emerged at the start of the generator, and a rear expansion wave generated at the trailing part because of the sudden expansion of the main flow channel. Moreover, the expansion wave was reflected and reached the bottom plate without affecting the flow and heat transfer near the porous plate. At the same time, the static pressure of the injected coolant increased with the increase in the blowing ratio F. The decelerated main flow due to the shock wave could be pushed away from the porous surface. For a blowing ratio of 2.19% and a wedge angle of 6°, the incident shock wave was pushed away. However, this phenomenon disappeared when the shock wave intensity increased for a wedge angle of 10°.
Fig. 6. Plate surface temperature contours of different coolant blowing ratios without oblique shock wave effect (Ma = 2.8, T0 = 374 K).
2.5. Shock wave effect on the temperature distribution The experiment was conducted to study the effect of different shock intensities on the transpiration cooling with different wedge angles and varied cooling flow blowing ratios. Fig. 6 shows the plate surface temperature contours of different coolant blowing ratios without incident shock wave effect. When the blowing ratio is low (F = 0.22–0.44%), the covering film of the cooling gas on the porous surface is thin, and the heat transfer between the mainstream and the porous plate is still high. The temperature distribution is relatively uniform because of the high plate conductivity, and the temperature gradient along the flow direction is relatively
low. With the increase in the coolant blowing ratio, the cooling gas film thickness on the surface of the porous media increases, and the wall temperature is gradually reduced. The coolant injected into the mainstream accumulates along the flow direction, thereby reducing the downstream plate surface temperature and increasing the surface temperature gradient. The three temperature disturbances on the temperature distribution contours are the local temperature differences due to the mini-channels in which the T-type thermocouples are embedded (see Fig. 7). The temperature contours show that the wall temperature significantly decreases when the cooling gas is injected into the por-
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1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2 0.0
F =0.22% F =0.66% F =1.10%
T 0= 374 K
0.0
0.2
0.4
X
0.6
0.2
F =0.44% F =0.88% F =1.32%
0.8
0.0
1.0
Fig. 7. Lateral transpiration cooling efficiency variation along the flow direction for different coolant blowing ratios without incident shock wave effect (Ma = 2.8, T0 = 374 K).
ous plate. When the coolant blowing ratio is only 0.22%, the temperature of the plate leading edge is approximately 20 K lower than the mainstream recovery temperature (Tr = 355.8 K). The protective gas film thickness increases with the coolant blowing ratio, thus weakening the heat transferred from the mainstream to the porous plate. When the coolant blowing ratio is 1.1%, the porous plate tail temperature is close to 300 K, which is the inlet temperature of the coolant. The infrared two-dimensional surface temperature distribution contours were quantized to a 320 240 matrix and then processed into the cooling efficiency using Eq. (4). The average cooling effi in the direction parallel to the mainstream flow was calciency g culated to obtain the cooling efficiency distribution along the mainstream flow direction. Fig. 9 shows the variation in the lateral transpiration cooling efficiency along the flow direction for different coolant blowing ratios without incident shock wave effect. The abscissa represents the dimensionless length of the porous surface X = x/L, where x is the distance from the starting position to the local position of the plate surface, and L is the length of the porous plate. The horizontal average cooling efficiency gradually increases
F=0.22%: F=0.44%: F=0.66%: F=0.88%:
0.0
θ θ θ θ
0.2
= 0° = 0° = 0° = 0°
θ = 6° θ = 6° θ = 6° θ = 6°
0.4
θ θ θ θ
X
= 8° = 8° = 8° = 8°
θ θ θ θ
= 10° = 10° = 10° = 10°
0.6
T0= 374 K
0.8
1.0
Fig. 9. Shock wave effect on lateral cooling efficiency distributions under the condition of Ma = 2.8 and T0 = 374 K.
along the flow direction. When the coolant blowing ratio increases, the overall cooling efficiency increases but the growth rate decreases. The temperature contours with different oblique shock wave intensities were processed to cooling efficiency contours using the same data processing method, as shown in Fig. 8. The three strips on the bottom-half of the surface are the local temperature differences due to the mini-channels in which the T-type thermocouples are embedded. The efficiency contours show that the cooling efficiency of the central region in the plate is lower than the cooling efficiencies of the upstream and downstream regions. With the increase in the blowing ratio, the cooling efficiency is still relatively low in the middle region, though the overall cooling efficiency increases. Fig. 9 shows the oblique shock wave effects on the variation in the lateral transpiration cooling efficiency along the flow direction with coolant blowing ratios of 0.22, 0.44, 0.66, and 0.88%. With an oblique shock impinging on the plate surface, the overall cooling efficiency is lower, and decreases with the increase in the oblique shock wave intensity. The overall cooling efficiencies with different oblique shock wave intensities were reduced by 15–25% compared to the overall cooling efficiency without the shock wave incidence. The cooling efficiency no longer continuously increases in the flow direction in the range of
Fig. 8. Shock wave effect on surface cooling efficiency contours of different coolant blowing ratios with Ma = 2.8 and T0 = 374 K.
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X = 0.2–0.6, where the cooling efficiency is lower than those of the front and rear regions. With the shock wave effects, the overall cooling efficiency decreases, especially in the downstream region of the shock wave impingement position at low blowing ratios. However, the reduction in the cooling efficiency in the upstream region becomes lower with the increase in the blowing ratio. When the blowing ratio is F = 0.88% or more, the cooling efficiency in the upstream region with or without the shock wave effects remains the same, and the shock wave damage effect on the transpiration cooling efficiency is largely in the downstream region of the shock impingement position. As shown in the results for blowing ratios of 0.66 and 0.88%, the cooling efficiency continues to recovery, and the destructive effects of the incident shock decreases with the increase in the coolant blowing ratio in the upstream region (X < 0.5). However, the reduction in the cooling efficiency remains in the downstream area and reaches approximately 0.2 at the end of the porous plate because of the destructive effects of the incident oblique shock.
The steady-state governing equations for the mainstream fluid region include the continuity, momentum, and energy equations. The equations written in compact Cartesian form are as follows.
@ ðqui Þ ¼ 0 @xi
ð7Þ
@ðqui uj Þ @P @ sij ¼ þ @xi @xi @xj
ð8Þ
@ @T ðui ðqE þ PÞÞ ¼ r k þ uj sij @xi @xi
ð9Þ
where E is the total energy (E = h + u2/2 P/q). The Brinkman–Forchheimer extended Darcy model [39,40] was used to model the coolant flowing through the porous media region.
@ðqeui uj Þ @ðePÞ @ þ ¼ @xi @x @xi
ele
@u e 2 lf e3 qF þ u pffiffiffiffi jUju @xi K K
ð10Þ
where K is the permeability, and F is the inertial coefficient. The per-
3. Numerical analysis 3.1. Numerical model The shock wave effects on the flow and energy transport were analyzed using a 2D numerical model, including the mainstream area, wedge-shaped shock generator, and porous media, as shown in Fig. 10. The constant pressure inlet boundary was used at the channel inlet, and the mainstream air was accelerated to Mach 2.8 via the Laval nozzle. An oblique shock wave was then induced using the wedge-shaped shock generator onto the porous flat surface along the flow path. The wedge angles were 0°, 6°, 8°, and 10° to simulate different incident shock wave intensities. The lengths of the nozzle section and the main channel are 200 mm and 150 mm, respectively, and the height of the channel is 30 mm. The porous media zone is 50 mm in length and 6 mm in thickness. The mesh was refined near the wall and the shock wave according to the pressure gradients. The grid independence was studied for meshes with 263,000, 461,000 and 685,000 elements. The mesh with about 461,000 structured rectangular elements was used as a balance between the computational load and accuracy.
meability K ¼ 1:31 1011 and the inertial coefficient F ¼ 4:68 were obtained from the experiments. The energy equation for the porous region is based on the local thermal equilibrium (LTE) model, which has been proven to be effective for transpiration cooling using gas coolants with the temperature range employed in this study [8,11,12].
@ðqcp eui TÞ @ @T e2 l 2 e3 qF ¼ ðkeff Þþ u þ pffiffiffiffi jUju2 @xi @xi @xi K K
ð11Þ
The effective thermal conductivity keff was calculated using a user defined function, which is defined as:
keff ¼ km þ kd
ð12Þ
where the matrix thermal conductivity km is given by:
# pffiffiffiffiffiffiffiffiffiffiffi " pffiffiffiffiffiffiffiffiffiffiffi 2 1 e ð1 rÞB 1 B þ 1 B 1 km ¼ ð1 1 eÞ þ ln 2 1 rB kf rB 1 rB ð1 rBÞ2 ð13Þ where
Fig. 10. Computational model and the mesh.
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B¼
10 1e 9
e
;
r¼
kf ks
ð14Þ
The thermal dispersion kd has been shown to be significant for convection in porous media and is expressed as follows [41]:
kd ¼ C qf cpf dp U p ð1 eÞ
ð15Þ
C ¼ 1:60 ½Rep Prf ð1 eÞ0:8282
ð16Þ
The control volume method was used to solve the governing equations, and the second-order upwind discretization was used for the convection terms in the momentum, energy, species, and turbulence equations. The Navier–Stokes equations were solved using the standard k-e model with the enhanced two-layer-wall function. The fluid thermodynamic property data for the specific heat, thermal conductivity, and viscosity were obtained from the NIST Database [42]. Throughout the numerical study, the solution methods were included in the commercial software package ANSYS Fluent 14.5 and the effective thermal conductivity was imported using a User Defined Function (UDF). Fig. 11 shows the comparison of the experimental and numerical results of the cooling efficiency distribution with wedge angles of 0° and 10°. For the wall temperature, the numerical results are found to be in good agreement with the experimental data for most areas. At the beginning and ending regions of the porous surface, the experimentally obtained temperature is lower than the numerical one because of the thermal contact resistance between the porous plate and the Bakelite frame. The numerically obtained cooling efficiency drop is higher in the downstream region of the oblique shock wave impingement position, and the overall cooling efficiency (experimental) is more uniform. 3.2. Calculation results and analysis Fig. 12 shows the static temperature distributions for a wedge angle of 10° and without the shock effect. When no shock wave is incident on the porous surface, the coolant overflowing the porous material forms a protective gas film close to the surface, and the heat boundary layer thickens along the mainstream continuously. When the shock wave impinges on the surface, the gas film temperature increases significantly and the gas film thickness decreases after the incident position. The gas film temperature decreases with an increase in the coolant gas blowing ratio but is
1.0
still higher than that without the shock wave. Therefore, the porous wall temperature is higher with an incident shock wave. Fig. 13 shows the static pressure distributions on the porous plate surface with different shock intensities. When no shock wave is incident on the surface, the fluid static pressure near the surface increases with the coolant blowing ratio and decreases along the mainstream flow direction because of the continuously thickening boundary layer. When the shock wave impinges on the surface, the flow velocity after the shock wave decreases, thereby increasing the static pressure. The overall static pressure of the fluid is higher with the shock wave impinging on the porous plate surface than that without the shock wave. The affected area and the magnitude of the static pressure rise both increase with the increase in the shock wave intensity. Similar to a previous study [29], for the analysis of supersonic film cooling, the definition of cooling efficiency (Eq. (4)) is related to the mainstream recovery temperature, wall temperature, and coolant inlet temperature, whereas the mainstream recovery temperature is calculated using Eq. (5). The ratio of the wall surface recovery temperature Tr to the total temperature T1 of the mainstream fluid can be expressed as [38]: 1 1 þ r c1 Ma2 1 Tr 2 r ¼ ¼r 1þ 2 c 1 T1 1 þ 2 Ma Ma2 1 þ c1 2
0.8 0.6 0.4 0.2
Fig. 12. Static temperature distributions for a wedge angle h = 10° and without the shock effect under the condition of Ma = 2.8 and T0 = 374 K.
F =0.22% F =0.44% F =0.66% F =0.88%
0.0 0.0
Exp. Exp. Exp. Exp.
θ=0
0.2
ο
Num. Num. Num. Num.
θ = 10 Exp. Exp. Exp. Exp.
0.4
ο
Num. Num. Num. Num.
x/L
T 0= 374 K
0.6
0.8
1.0
Fig. 11. Comparison of experimental and numerical cooling efficiency distributions on porous surface under the condition of Ma = 2.8 and T0 = 374 K.
! ð17Þ
where r is the recovery factor of air, which can be approximated as r = Pr1/3 under turbulent flow conditions. In the temperature range employed in this study, the Prandtl number of air is unchanged, and the recovery coefficient is approximately constant, i.e., r = 0.898. As shown in the equation, the wall recovery temperature increases with the decrease in the flow velocity near the porous plate surface when the mainstream total temperature remains unchanged. The increase in the wall recovery temperature would therefore reduce the overall transpiration cooling efficiency. Moreover, the decrease in the overall cooling efficiency increases with the increase in the shock wave intensity. The static pressure reaches the maximum near the shock incident location and increases with the increase in the shock intensity. While the cooling fluid enters the porous media from
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(a) F = 0.22%
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the cooling efficiency with shock wave impact. The recovery effect increases with the coolant blowing ratio. Thus, employing a high coolant ratio is an appropriate solution for the shock wave impact on transpiration cooling efficiency. Fig. 14 shows the distribution of the fluid velocity vectors for a coolant blowing ratio of 0.66% with different incident shock intensities. When no shock wave is incident on the surface of the porous plate, the cooling fluid continuously accumulates and the thickness of the boundary layer continuously increases along the main flow direction. When a shock wave is incident on the porous plate surface, the local static pressure at the incident location is the highest, thus hindering the coolant flow. In this case, the boundary layer no longer continuously thickens along the flow direction, thereby reducing the local cooling efficiency. When the shock wave intensity increases, the local static pressure increases and it is more difficult for the cooling fluid to flow out, thus further reducing the cooling efficiency. When the intensity of the shock wave further increases (h = 10°), the boundary layer even separates and results in a fluid backflow in the boundary layer. More coolant flows to the upstream region because of the non-uniform static pressure distribution, and the transpiration cooling efficiency is thus recovered. However, the cooling efficiency is hardly recovered in the downstream area after the incident position of the shock wave. 4. Conclusions
(b) F = 0.66% Fig. 13. Static pressure distributions on the porous surface with different shock wave intensities under the condition of Ma = 2.8 and T0 = 374 K: (a) F = 0.22%, and (b) F = 0.66%.
the reservoir with a constant mass flow rate, the increased and non-uniform static pressure distribution on the porous plate surface causes the cooling fluid to redistribute and flow to the upstream region where the outlet pressure is low. This makes more coolant to flow through the upstream region, helping to recover
A flat porous plate was tested for transpiration cooling in a wind tunnel of Mach number 2.8 with different coolant blowing ratios and incident shock intensities. Wedge-shaped shock wave generators were installed in the test section to induce oblique shock waves with different shock intensities. The porous surface temperature distribution was measured using an infrared camera, and the mainstream flow field was observed using a Schlieren system. A 2D computational model was applied to obtain the detailed temperature and flow field distributions and to analyze the shock wave effect on transpiration cooling. The results show that the transpiration cooling efficiency reduced because of the oblique shock wave impinging on the plate surface. The efficiency decreases with an increase in the shock intensity. The incidence of oblique shock waves causes the flow velocities near the porous surface to decrease and consequently increases the local recovery temperature, thereby reducing the overall cooling efficiency. Moreover, the local static pressure at the shock wave incident location is the highest, thus impeding
Fig. 14. Velocity vector distribution near the porous plate surface under the conditions of Ma = 2.8, T0 = 374 K, and F = 0.66%.
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the cooling fluid flow and further reducing the local cooling efficiency. The overall cooling efficiency reduced, especially in the downstream region of the shock wave impingement position; however, the reduction in the cooling efficiency in the upstream region becomes lower with the increase in the blowing ratio. For a blowing ratio of 0.88%, the cooling efficiencies remains at about 0.75 in the upstream region for various shock intensities, but the cooling efficiency with incident oblique shock is reduced by approximately 0.2 in the downstream area. The overall cooling efficiencies with different oblique shock wave intensities are reduced by 15%25% compared to the overall cooling efficiency without the shock wave incidence. Conflict of interest The authors declared that there is no conflict of interest. Acknowledgments This project was supported by the National Natural Science Foundation of China (No. 51536004) and the Science Fund for Creative Research Groups of NSFC (No. 51621062). References [1] Y.H. Zhu, W. Peng, P.X. Jiang, R.N. Xu, Review on active thermal protection and its heat transfer for airbreathing hypersonic vehicles, Chin. J. Aeronaut. 31 (10) (2018) 1929–1953. [2] X.L. Ouyang, P.X. Jiang, R.N. Xu, Thermal boundary conditions of local thermal non-equilibrium model for convection heat transfer in porous media, Int. J. Heat Mass Transf. 60 (2013) 31–40. [3] J.V. Wolfersdorf, Effect of coolant side heat transfer on transpiration cooling, Heat Mass Transf. 41 (4) (2005) 327–337. [4] P.X. Jiang, L. Yu, J.G. Sun, J. Wang, Experimental and numerical investigation of convection heat transfer in transpiration cooling, Appl. Therm. Eng. 24 (8–9) (2004) 1271–1289. [5] J. Bellettre, F. Bataille, J.C. Rodet, A. Lallemand, Thermal behavior of porous plates subjected to air blowing, J. Thermophys. Heat Transf. 14 (4) (2000) 523– 532. [6] L. Ding, K. Wei, Q. Zhang, J.H. Wang, An experimental investigation on transpiration cooling of porous flat plate, in: 2011 International Conference on Remote Sensing, Environment and Transportation Engineering (RSETE), IEEE, 2011, pp. 5692–5696. [7] Y.B. Xiong, Y.H. Zhu, P.X. Jiang, Numerical simulation of transpiration cooling for sintered metal porous strut of the scramjet combustion chamber, Heat Transf. Eng. 35 (6–8) (2014) 721–729. [8] F. Cheuret, J. Steelant, T. Langener, Numerical investigations on transpiration cooling for scramjet applications using different coolants, in: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2011, p. 2379. [9] J.X. Shi, J.H. Wang, A numerical investigation of transpiration cooling with liquid coolant phase change, Transp. Porous Media 87 (3) (2011) 703–716. [10] W.J. Dong, J.H. Wang, S.Y. Chen, B.C. Ai, X.G. Luo, Modelling and investigation on heat transfer deterioration during transpiration cooling with liquid coolant phase-change, Appl. Therm. Eng. 128 (2018) 381–392. [11] Y.Q. Liu, P.X. Jiang, Y.B. Xiong, Y.P. Wang, Experimental and numerical investigation of transpiration cooling for sintered porous flat plates, Appl. Therm. Eng. 50 (1) (2013) 997–1007. [12] Z. Huang, Y.H. Zhu, Y.B. Xiong, P.X. Jiang, Investigation of supersonic transpiration cooling through sintered metal porous flat plates, J. Porous Media 18 (11) (2015) 1047–1057. [13] S. Soller, C. Kirchberger, M. Kuhn, T. Langener, M. Bouchez, J. Steelant, Experimental investigation of cooling techniques and materials for highspeed flight propulsion systems, in: 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, 2009, p. 7374.
[14] J. Meinert, J. Huhn, E. Serbest, O. Haidn, Investigations on the effect of foreign gas transpiration on a turbulent boundary layer, in: 36th AIAA/ASME/SAE/ ASEE Joint Propulsion Conference and Exhibit, 2000, p. 3386. [15] Y.Q. Liu, P.X. Jiang, S.S. Jin, J.G. Sun, Transpiration cooling of a nose cone by various foreign gases, Int. J. Heat Mass Transf. 53 (23–24) (2010) 5364–5372. [16] A.V. Foreest, M. Sippel, A. Gülhan, B. Esser, B.A.C. Ambrosius, K. Sudmeijer, Transpiration cooling using liquid water, J. Thermophys. Heat Transf. 23 (4) (2009) 693. [17] L. Shen, J.H. Wang, W.J. Dong, J. Pu, J.L. Peng, D.J. Qu, L.Z. Chen, An experimental investigation on transpiration cooling with phase change under supersonic condition, Appl. Therm. Eng. 105 (2016) 549–556. [18] L. Shen, J.H. Wang, Numerical investigation on the optimization of local transpiration cooling effectiveness, Appl. Therm. Eng. 127 (2017) 58–69. [19] P.X. Jiang, G. Huang, Y.H. Zhu, Z.Y. Liao, Z. Huang, Experimental investigation of combined transpiration and film cooling for sintered metal porous struts, Int. J. Heat Mass Transf. 108 (2017) 232–243. [20] G. Huang, Y.H. Zhu, Z.Y. Liao, T.J. Lu, P.X. Jiang, Z. Huang, Experimental study on combined cooling method for porous struts in supersonic flow, J. Heat Transf. 140 (2) (2018) 022201. [21] G. Huang, Y.H. Zhu, Z. Huang, P.X. Jiang, Investigation of combined transpiration and opposing jet cooling of sintered metal porous struts, Heat Transf. Eng. 39 (7–8) (2018) 711–723. [22] K. Tani, T. Kanda, K. Kudo, Aerodynamic performance of scramjet inlet models with a single strut, J. Propul. Power 22 (4) (2006) 905–912. [23] J. Häberle, A. Gülhan, Experimental investigation of a two-dimensional and a three-dimensional scramjet inlet at Mach 7, J. Propul. Power 24 (5) (2008) 1023–1034. [24] J.C. Lin, Review of research on low-profile vortex generators to control boundary-layer separation, Prog. Aerosp. Sci. 38 (4) (2002) 389–420. [25] Y. Zhang, H.J. Tan, M.C. Du, D.P. Wang, Control of shock/boundary-layer interaction for hypersonic inlets by highly swept microramps, J. Propul. Power 31 (1) (2014) 133–143. [26] K.A. Juhany, M.L. Hunt, Flowfield measurements in supersonic film cooling including the effect of shock-wave interaction, AIAA J. 32 (3) (1994) 578–585. [27] T. Kanda, F. Ono, M. Takahashi, T. Saito, Y. Wakamatsu, Experimental studies of supersonic film cooling with shock wave interaction, AIAA J. 34 (2) (1996) 265–271. [28] T. Kanda, F. Ono, Experimental studies of supersonic film cooling with shock wave interaction (II), J. Thermophys. Heat Transf. 11 (4) (1997) 590–592. [29] W. Peng, P.X. Jiang, Influence of shock waves on supersonic film cooling, J. Spacecraft Rock. 46 (1) (2009) 67–73. [30] W. Peng, X.K. Sun, P.X. Jiang, Effect of coolant inlet conditions on supersonic film cooling, J. Spacecraft Rock. (2015). [31] M. Konopka, M. Meinke, Wolfgang, Large-eddy simulation of shock/coolingfilm interaction, AIAA J. 50 (10) (2012) 2102–2114. [32] W. Peng, X.K. Sun, P.X. Jiang, J. Wang, Effect of continuous or discrete shock wave generators on supersonic film cooling, Int. J. Heat Mass Transf. 108 (2017) 770–783. [33] W. Peng, P.X. Jiang, Effect of shock waves on supersonic film cooling with a slotted wall, Appl. Therm. Eng. 62 (1) (2014) 187–196. [34] R. Nowak, A. Wieting, M. Holden, Shock/shock interference on a transpiration cooled hemispherical model, in: 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1990, p. 1643. [35] M. Holden, K. Rodriguez, R. Nowak, Studies of shock/shock interaction on smooth and transpiration-cooled hemispherical nosetips in hypersonic flow, in: 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1992, p. 1765. [36] M. Holden, K. Chadwick, Studies of film and transpiration-cooled flows in regions of shock interaction, in: 25th AIAA Fluid Dynamics Conference, 1994, p. 2306. [37] J.D. Anderson Jr., Fundamentals of Aerodynamics, McGraw-Hill Education, Tata, 2010. [38] J.D. Anderson Jr., Hypersonic and high-temperature gas dynamics, Am. Instit. Aeronaut. Astronaut. (2006). [39] K. Vafai, S.J. Kim, On the limitations of the Brinkman-Forchheimer-extended Darcy equation, Int. J. Heat Fluid Flow 16 (1) (1995) 11–15. [40] , Theory Guide. Inc., Canonsburg, PA, 2012. [41] P.X. Jiang, Numerical simulation of forced convection heat transfer in porous plate channels using thermal equilibrium and nonthermal equilibrium models, Numer. Heat Transf.: Part A: Appl. 35 (1) (1999) 99–113. [42] National Institute of Standards and Technology (NIST), Standard Reference Database No. 69, June 2005, NIST Chemistry WebBook: http://webbook. nist.gov/chemistry/.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Influence of shock waves on supersonic transpiration cooling Peixue Jiang a, Zhiyuan Liao a, Zheng Huang b, Yanbing Xiong c, Yinhai Zhu a,⇑ a
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China China State Shipbuilding Corporation, Beijing 100048, China c Beijing Institute of Astronautical System Engineering, Beijing 100076, China b
a r t i c l e
i n f o
Article history: Received 19 March 2018 Received in revised form 26 September 2018 Accepted 9 October 2018
Keywords: Transpiration cooling Shock wave Porous sintered plate
a b s t r a c t This paper experimentally and numerically investigates the effect of shock waves on transpiration cooling of a porous plate. The experiments were conducted in a wind tunnel of Mach number 2.8, wherein oblique shock waves were impinged onto the porous plate. A numerical simulation model was used to obtain detailed temperature and flow field distributions near the porous plate surface. The effects of different coolant blowing ratios and shock wave intensities on the transpiration cooling efficiency were studied. The results show that the transpiration cooling efficiency reduces because of the impinging oblique shock waves with the decrease in the fluid velocity near the porous wall, resulting in an increase in the local fluid static temperature. Moreover, the oblique shock waves increase the local static pressure, thus obstructing the coolant outflow and increasing the local wall temperature. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Hypersonic vehicles with a scramjet engine are exposed to an extremely critical thermal environment, thus requiring more efficient and stable active cooling technologies [1]. Transpiration cooling has advantages such as high cooling efficiency, high cooling capacity, and low coolant consumption and is considered one of the most promising active cooling technologies for thermally protecting important parts from extremely high heat loads. Transpiration cooling can be treated as a special case of film cooling, with a porous structure through which a cooling fluid flows onto a heated surface. Owing to the sufficient heat transfer within the porous media and the coolant film over the surface, which thickens the boundary layer, the cooling efficiency of transpiration cooling is higher than those of conventional active cooling methods. Researchers have focused on the thermal and flow mechanisms of transpiration cooling theoretically [2,3], experimentally [4–6], and numerically [7–10]. Liu et al. [11] investigated transpiration cooling using a sintered porous plate in a u = 30 m/s main flow to analyze the influences of the coolant blowing ratio, particle diameter, and porous matrix thermal conductivity. When the main flow is supersonic, the cooling efficiency exhibits a familiar behavior i.e., it increases with the increase in the blowing ratio and porous matrix thermal conductivity [12]. Soller et al. [13] experimentally investigated transpiration cooling for high-speed flight propulsion ⇑ Corresponding author. E-mail address: [email protected] (Y. Zhu). https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.043 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
systems. The tested sample was subjected to a total temperature of 600 K (T0) and a Mach number of 2.1, and the surface was effectively cooled owing to the cold incoming boundary layer. Meinert et al. [14] and Liu et al. [15] investigated the transpiration cooling efficiency using different coolant gases, and the results show that the gas coolant with a high specific heat is more effective for transpiration cooling. Foreest et al. [16] experimentally compared the transpiration cooling efficiency using liquid water and nitrogen gas, among which liquid water showed a much better performance for transpiration cooling. Shen et al. [17], Shen and Wang [18], Jiang et al. [19], and Huang et al. [20,21] experimentally and numerically investigated transpiration cooling using sintered porous struts, and the results show that with non-uniform coolant flow distributions, the cooling efficiency along the leading edge is higher, and the overall cooling efficiency is more uniform. Most of the studies on supersonic transpiration cooling have considered a uniform main flow. However, in practical applications, such as in the isolator section of a scramjet engine, hypersonic air flows into the engine inlet and is compressed by the fore body shock wave during combustion, and a shock wave chain emerges inevitably at the isolator section [22]. Cavity holders and struts are installed in the engine combustor, which could induce the shock wave and detachment, to improve fuel mixing and ignition. The adverse pressure gradient due to the shock wave could lead to boundary layer separation and considerable pressure loss. Thus, several flow control methods have been proposed to prevent shock-induced separation, improve the efficiency, and reduce the distortion, such as wall bleeding configurations [23] and vortex
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Nomenclature d F L Ma P T u x X
diameter [lm] coolant blowing ratio porous plate length [mm] Mach number pressure [Pa] temperature [K] velocity [m/s] distance from the start on the plate [m] dimensionless distance from the start on the plate
Greek symbols b shock wave angle [°] c specific heat ratio e porosity
generators [24,25]. In supersonic transpiration cooling, which is expected to be applied to hypersonic conditions, the effect of incident oblique shock waves must be taken into consideration. For supersonic film cooling, Juhany and Hunt [26], Kanda et al. [27] and Kanda and Ono [28] showed that an incident shock wave could weaken the cooling effect if the coolant layer static temperature increases. Peng and Jiang [29] and Peng et al. [30] numerically investigated the shock wave influence on supersonic film cooling, and their results show that the shock wave increased the static pressure on the wall, which reduced the local Mach number in the coolant layer and the adiabatic effectiveness, and enhanced the mixing of the main stream and coolant, which was more remarkable with stronger shock wave and lighter gas coolant. Martin et al. [31] numerically studied supersonic film cooling with shock wave interaction using the large-eddy simulation method, and their results show that the film cooling effectiveness decreased by 36% compared to the case with no shock wave within the potential-core region of the cooling stream. Moreover, the shock wave significantly increased the turbulence levels in the boundary layer, resulting in strong temperature fluctuations and more pronounced mixing because the hot main flow is transported toward the wall. Peng et al. [32] numerically studied the threedimensional shock wave effects on film cooling, with the results showing that an uneven shock wave caused a horizontal direction secondary flow, which made the hot mainstream to mix with the cooling film and reduce the cooling film layer thickness. Peng and Jiang [33] numerically investigated a slotted wall structure, and the results show that the slotted wall improves the film cooling after the shock wave is incident. Only few studies have been conducted on the shock wave effect for supersonic transpiration cooling. Nowak et al. [34] and Holden et al. [35] experimentally studied the effects of shock waves on transpiration-cooled nose cones at a Mach number in the range of 12–16 and shear-layer Reynolds number in the range of 104– 106 with both laminar and turbulent shock/shock interactions. The results show that high surface blowing rates enlarge the shock layer and moves the region of peak-heating interaction around the body; however, the shock wave still significantly weakens the cooling performance at the stagnation point. Moreover, the flow field observation showed that weak shocks can destroy the protective coolant layer in film cooling, whereas no significant change was observed after impinging shock waves onto a transpiration cooling plate [36]. Previous studies have shown that transpiration cooling is an effective method for cooling high heat flux surfaces on various structures. However, there is less research on transpiration cooling heat transfer with a nonuniform main flow, especially with an obli-
g h k
q
cooling efficiency wedge angle [°] thermal conductivity [W/(mK)] density [kg/m3]
Subscripts 1 mainstream C coolant e equivalent o total p particle r recovery w wall
que shock wave incident on the surface. Shock waves will occur in the combustion chamber for actual flight conditions which disrupt the protective transpiration cooling film and reduce the cooling efficiency. In this work, the flow and thermal mechanisms of the incident shock wave effect on the transpiration cooling of a porous plate was investigated experimentally and numerically. The porous plate was tested using air as the transpiration coolant in a supersonic wind tunnel (Mach number = 2.8) with a maximum main flow total temperature of 450 K. The experiments were conducted with and without incident shocks generated using wedge-shaped shock generators. The wall temperatures were measured using an infrared camera, and the flow fields were observed using a Schlieren system. Finally, a 2D numerical model was established to simulate the experimental conditions aiming to reveal the shock wave impact mechanism in supersonic transpiration cooling. 2. Experimental investigation 2.1. Experimental system The supersonic wind tunnel used to investigate the shock wave effect on transpiration cooling is the same as the one described in our previous paper [12], as shown in Fig. 1. Air was compressed in a screw compressor at a pressure of 0.75 MPa and then sent through two filters to remove dust and through a condensing drying machine for dehumidification. The compressed dry air was divided into two flow paths in the experimental system. The upper part of the system is the mainstream flow path, and the lower part is the coolant flow path. The mainstream was heated using an electrical heater up to a total temperature of 374 K, and the total pressure was adjusted to 0.46 MPa using an electric pressure regulator. The air then flowed through a specially designed Laval nozzle to be accelerated to a Mach number of 2.8. The wall temperatures were measured using an infrared camera, and the flow fields were observed using a Schlieren system. At the coolant stream path, a pressure regulator and a mass flow meter were used to control the gas pressure for different blowing ratios. The coolant flowed through a reservoir and a flat porous plate before mixing with the mainstream in the test section. The flow velocity decelerated to subsonic in the diffuser and in the subsonic expansion section, and was ultimately exhausted to the surrounding. 2.2. Test section Fig. 2 shows an image of the test section. The test section consists of a rectangular channel with a 20 mm 30 mm cross section
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Fig. 1. Schematic of the experimental system [12].
Fig. 2. Test section with a shock wave generator.
and a 220 mm long flat plate made of Bakelite as the bottom. An infrared camera was located on the top of the test section. The upper portion of the test section was made of ZnS for infrared camera observation and the other two sides were made of quartz glass for optical access. The upper wall opened slightly at a 0.5° angle to reduce the influence of the boundary layer. A 50 mm long porous plate made of sintered bronze particles was installed at the center of the Bakelite plate, and a wedge-shaped shock generator was used to produce an oblique shock impingement onto the middle of the porous plate. The wedge angle of the shock generator was adjusted to obtain different shock wave intensities. The coolant reservoir was sealed from the porous plate using a gasket made of low thermal conductivity polytetrafluoroethylene. A plastic gasket was also used for sealing between the coolant reservoir and the test section frame. The thickness of the porous sample was 10 mm, and the porous plate was sintered using bronze particles with an average particle diameter of 90 lm (dp). The sample porosity e was 0.337, and the mean pore diameter dh was 38.8 lm. For the experiment, different wedge angles (h), such as 6, 8, and 10°, were employed, and the shock generator base was 20 mm long. The wedge angle of the shock generator was changed to
obtain different oblique shock wave intensities, which has been often described as a relative static pressure increase after the oblique shock wave, as shown in Eq. (1) [37]. The shock wave intensity was proportional to the wedge angle h.
p2 p1 Dp cMa21 h ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ p p1 Ma21 1
ð1Þ
where the subscripts 1 and 2 represent the parameters before and after the shock wave, respectively. The angle between the induced shock waves and the wall was called the shock wave angle b, as listed in Table 1. The relationship between h and b can be represented as [37]: 2
tanh ¼ 2 cot b
Ma21 sin b 1 Ma21 ð
c þ cos 2bÞ þ 2
ð2Þ
By solving the above implicit equation, the theoretical shock wave angles could be calculated. Table 1 lists the results. The tail edge of the wedge-shaped shock generator is synchronized with the start of the porous plate to make sure that the oblique shock impinges onto the middle of the porous plate, as shown in Fig. 2b.
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Table 1 Shock wave angle b results.
340 Shock wave angle b (°)
335
6 8 10
25.7 27.8 31
330
2.3. Measurement and experimental uncertainty The parameters measured in the experiments included the porous wall temperature, main stream inlet temperature and total pressure, coolant mass flow rate, and coolant inlet temperature. The local wall temperatures on the porous wall were measured using three T-type thermocouples embedded into mini-channels cut into the surface of the porous wall along the centerline with an accuracy of ±0.2 K. The thermocouples were located at x/ L = 0.2, 0.5, and 0.8 in the channels, as shown in Fig. 2. The temperature distribution across the outer porous wall was then measured using an A310 infrared camera from FLIR Inc. after being calibrated using the three thermocouples. The accuracy of the infrared camera was ±2%. A Schlieren system was established for observing the flow field of transpiration cooling with the shock wave effect [19]. As the gas refractive index is proportional to the local gas density, the Schlieren system showed the shock wave structure where the gas density varied dramatically. A ‘‘Z-shaped” optical element arrangement was employed to avoid parallel rays penetrating through the test section repeatedly, which would cause image distortion. A plane mirror was used to reduce the installation space requirement, as shown in Fig. 3. Though the local sintered porous plate surface emissivity varied a little at different positions, the temperature differences between the IR and thermocouple measurements at different coolant injection mass flow rates were less than ±2 K with a constant overall wall emissivity, as shown in Fig. 4. The total temperature of the main stream was measured using a T-type armored thermocouple after the straight flowing section, and the inlet total pressures of the two streams were measured and controlled using two pressure regulators with an accuracy of ±0.1%. Three T-type thermocouples were installed in the coolant reservoir, and the readings were averaged as the coolant inlet temperature. All the T-type thermocou-
Parabolic mirror Plane mirror
Wall temperature, K
Wedge angle h (°)
Bronze plate T0= 374 K Tw1 (TC) Tw1 (IR) Tw2 (TC)
325
Tw2 (IR) Tw3 (TC)
320
Tw3 (IR)
315 310 305 300
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Blowing ratio, % Fig. 4. Calibration of IR imaging system (TC: Thermocouple, IR: Infrared camera).
ples had an accuracy of ±0.2 K. The coolant mass flow rate was controlled using a mass flowmeter from Alicat Inc. with an accuracy of ±0.2%. The blowing ratio for transpiration cooling is defined as the ratio of the mass flow rate per unit area of the cooling fluid and the main flow [37].
Fc ¼
qc uc q1 u1
ð3Þ
where qc is the cooling fluid inlet density, uc is the coolant inlet velocity, q1 is the main stream inlet density, and u1 is the main stream inlet velocity. In supersonic transpiration cooling, the free stream recovery temperature is often used as a substitute for the inlet temperature when defining the cooling effectiveness g.
g¼
Tr Tw Tr Tc
ð4Þ
where Tc is the coolant inlet temperature, and Tw is the wall temperature of the porous plate. The free stream recovery temperature Tr is defined as follows [38].
c1 2 Ma Tr ¼ T1 1 þ r 2
ð5Þ
where r is the recovery factor, and c is the specific heat ratio. According to Eqs. (4) and (5), the uncertainty in the cooling efficiency can be predicted using the following equation. Slit Condenser lens Lamp
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! !2ffi u u T T dT 2 1 dT 2 T r T w dT c w c r w t ¼ þ þ g Tr Tc g ðT r T c Þ2 g ðT r T c Þ2 g
dg
Test section
ð6Þ
Plane mirror
Camera
Knife edge
In this study, the maximum main stream temperature was 374 K, and the lowest cooling efficiency was approximately 0.13. Thus, the maximum uncertainty in the cooling efficiency was ±5.7%. 2.4. Shock wave effect on flow field
Parabolic mirror Fig. 3. Schematic of Schlieren system.
Fig. 5 shows the flow fields for the transpiration cooling with different wedge angles and a coolant blowing ratio (F) in the range of 0.44–2.19%. The main flow direction is from left to right in the figure. Because of the inevitable size difference between the mainstream nozzle section and the test section, two weak oblique shock
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Fig. 5. Schlieren images of flow fields with different wedge angles.
waves emerged at the start of the test section, after which the supersonic flow could be considered uniform. The porous plate was installed at the middle of the test section and was not affected by the flow disturbances. Moreover, the injected low-speed cooling gas partially blocked the supersonic mainstream, resulting in an oblique shock wave induced at the beginning of the flat porous plate. The oblique shock wave induced by the injected low-speed cooling gas mixed with these weak shock waves. Therefore, the shock waves were not incident on the porous surface, which means that the boundary layer thickened by the cooling gas was not affected. The intensity of this oblique shock wave increased with the increase in the coolant blowing ratio. The oblique shock wave intensity was controlled by varying the wedge angle h of the shock generator. The measured shock wave angles are compared with the predicted results, as listed in Table 1, and a good agreement is obtained, thus proving the reliability of the experiments. The shock wave intensity increases with the increase in h and the shock wave angle increases as well, thus moving the shock wave impingement position forward. An oblique shock wave emerged at the start of the generator, and a rear expansion wave generated at the trailing part because of the sudden expansion of the main flow channel. Moreover, the expansion wave was reflected and reached the bottom plate without affecting the flow and heat transfer near the porous plate. At the same time, the static pressure of the injected coolant increased with the increase in the blowing ratio F. The decelerated main flow due to the shock wave could be pushed away from the porous surface. For a blowing ratio of 2.19% and a wedge angle of 6°, the incident shock wave was pushed away. However, this phenomenon disappeared when the shock wave intensity increased for a wedge angle of 10°.
Fig. 6. Plate surface temperature contours of different coolant blowing ratios without oblique shock wave effect (Ma = 2.8, T0 = 374 K).
2.5. Shock wave effect on the temperature distribution The experiment was conducted to study the effect of different shock intensities on the transpiration cooling with different wedge angles and varied cooling flow blowing ratios. Fig. 6 shows the plate surface temperature contours of different coolant blowing ratios without incident shock wave effect. When the blowing ratio is low (F = 0.22–0.44%), the covering film of the cooling gas on the porous surface is thin, and the heat transfer between the mainstream and the porous plate is still high. The temperature distribution is relatively uniform because of the high plate conductivity, and the temperature gradient along the flow direction is relatively
low. With the increase in the coolant blowing ratio, the cooling gas film thickness on the surface of the porous media increases, and the wall temperature is gradually reduced. The coolant injected into the mainstream accumulates along the flow direction, thereby reducing the downstream plate surface temperature and increasing the surface temperature gradient. The three temperature disturbances on the temperature distribution contours are the local temperature differences due to the mini-channels in which the T-type thermocouples are embedded (see Fig. 7). The temperature contours show that the wall temperature significantly decreases when the cooling gas is injected into the por-
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1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2 0.0
F =0.22% F =0.66% F =1.10%
T 0= 374 K
0.0
0.2
0.4
X
0.6
0.2
F =0.44% F =0.88% F =1.32%
0.8
0.0
1.0
Fig. 7. Lateral transpiration cooling efficiency variation along the flow direction for different coolant blowing ratios without incident shock wave effect (Ma = 2.8, T0 = 374 K).
ous plate. When the coolant blowing ratio is only 0.22%, the temperature of the plate leading edge is approximately 20 K lower than the mainstream recovery temperature (Tr = 355.8 K). The protective gas film thickness increases with the coolant blowing ratio, thus weakening the heat transferred from the mainstream to the porous plate. When the coolant blowing ratio is 1.1%, the porous plate tail temperature is close to 300 K, which is the inlet temperature of the coolant. The infrared two-dimensional surface temperature distribution contours were quantized to a 320 240 matrix and then processed into the cooling efficiency using Eq. (4). The average cooling effi in the direction parallel to the mainstream flow was calciency g culated to obtain the cooling efficiency distribution along the mainstream flow direction. Fig. 9 shows the variation in the lateral transpiration cooling efficiency along the flow direction for different coolant blowing ratios without incident shock wave effect. The abscissa represents the dimensionless length of the porous surface X = x/L, where x is the distance from the starting position to the local position of the plate surface, and L is the length of the porous plate. The horizontal average cooling efficiency gradually increases
F=0.22%: F=0.44%: F=0.66%: F=0.88%:
0.0
θ θ θ θ
0.2
= 0° = 0° = 0° = 0°
θ = 6° θ = 6° θ = 6° θ = 6°
0.4
θ θ θ θ
X
= 8° = 8° = 8° = 8°
θ θ θ θ
= 10° = 10° = 10° = 10°
0.6
T0= 374 K
0.8
1.0
Fig. 9. Shock wave effect on lateral cooling efficiency distributions under the condition of Ma = 2.8 and T0 = 374 K.
along the flow direction. When the coolant blowing ratio increases, the overall cooling efficiency increases but the growth rate decreases. The temperature contours with different oblique shock wave intensities were processed to cooling efficiency contours using the same data processing method, as shown in Fig. 8. The three strips on the bottom-half of the surface are the local temperature differences due to the mini-channels in which the T-type thermocouples are embedded. The efficiency contours show that the cooling efficiency of the central region in the plate is lower than the cooling efficiencies of the upstream and downstream regions. With the increase in the blowing ratio, the cooling efficiency is still relatively low in the middle region, though the overall cooling efficiency increases. Fig. 9 shows the oblique shock wave effects on the variation in the lateral transpiration cooling efficiency along the flow direction with coolant blowing ratios of 0.22, 0.44, 0.66, and 0.88%. With an oblique shock impinging on the plate surface, the overall cooling efficiency is lower, and decreases with the increase in the oblique shock wave intensity. The overall cooling efficiencies with different oblique shock wave intensities were reduced by 15–25% compared to the overall cooling efficiency without the shock wave incidence. The cooling efficiency no longer continuously increases in the flow direction in the range of
Fig. 8. Shock wave effect on surface cooling efficiency contours of different coolant blowing ratios with Ma = 2.8 and T0 = 374 K.
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X = 0.2–0.6, where the cooling efficiency is lower than those of the front and rear regions. With the shock wave effects, the overall cooling efficiency decreases, especially in the downstream region of the shock wave impingement position at low blowing ratios. However, the reduction in the cooling efficiency in the upstream region becomes lower with the increase in the blowing ratio. When the blowing ratio is F = 0.88% or more, the cooling efficiency in the upstream region with or without the shock wave effects remains the same, and the shock wave damage effect on the transpiration cooling efficiency is largely in the downstream region of the shock impingement position. As shown in the results for blowing ratios of 0.66 and 0.88%, the cooling efficiency continues to recovery, and the destructive effects of the incident shock decreases with the increase in the coolant blowing ratio in the upstream region (X < 0.5). However, the reduction in the cooling efficiency remains in the downstream area and reaches approximately 0.2 at the end of the porous plate because of the destructive effects of the incident oblique shock.
The steady-state governing equations for the mainstream fluid region include the continuity, momentum, and energy equations. The equations written in compact Cartesian form are as follows.
@ ðqui Þ ¼ 0 @xi
ð7Þ
@ðqui uj Þ @P @ sij ¼ þ @xi @xi @xj
ð8Þ
@ @T ðui ðqE þ PÞÞ ¼ r k þ uj sij @xi @xi
ð9Þ
where E is the total energy (E = h + u2/2 P/q). The Brinkman–Forchheimer extended Darcy model [39,40] was used to model the coolant flowing through the porous media region.
@ðqeui uj Þ @ðePÞ @ þ ¼ @xi @x @xi
ele
@u e 2 lf e3 qF þ u pffiffiffiffi jUju @xi K K
ð10Þ
where K is the permeability, and F is the inertial coefficient. The per-
3. Numerical analysis 3.1. Numerical model The shock wave effects on the flow and energy transport were analyzed using a 2D numerical model, including the mainstream area, wedge-shaped shock generator, and porous media, as shown in Fig. 10. The constant pressure inlet boundary was used at the channel inlet, and the mainstream air was accelerated to Mach 2.8 via the Laval nozzle. An oblique shock wave was then induced using the wedge-shaped shock generator onto the porous flat surface along the flow path. The wedge angles were 0°, 6°, 8°, and 10° to simulate different incident shock wave intensities. The lengths of the nozzle section and the main channel are 200 mm and 150 mm, respectively, and the height of the channel is 30 mm. The porous media zone is 50 mm in length and 6 mm in thickness. The mesh was refined near the wall and the shock wave according to the pressure gradients. The grid independence was studied for meshes with 263,000, 461,000 and 685,000 elements. The mesh with about 461,000 structured rectangular elements was used as a balance between the computational load and accuracy.
meability K ¼ 1:31 1011 and the inertial coefficient F ¼ 4:68 were obtained from the experiments. The energy equation for the porous region is based on the local thermal equilibrium (LTE) model, which has been proven to be effective for transpiration cooling using gas coolants with the temperature range employed in this study [8,11,12].
@ðqcp eui TÞ @ @T e2 l 2 e3 qF ¼ ðkeff Þþ u þ pffiffiffiffi jUju2 @xi @xi @xi K K
ð11Þ
The effective thermal conductivity keff was calculated using a user defined function, which is defined as:
keff ¼ km þ kd
ð12Þ
where the matrix thermal conductivity km is given by:
# pffiffiffiffiffiffiffiffiffiffiffi " pffiffiffiffiffiffiffiffiffiffiffi 2 1 e ð1 rÞB 1 B þ 1 B 1 km ¼ ð1 1 eÞ þ ln 2 1 rB kf rB 1 rB ð1 rBÞ2 ð13Þ where
Fig. 10. Computational model and the mesh.
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B¼
10 1e 9
e
;
r¼
kf ks
ð14Þ
The thermal dispersion kd has been shown to be significant for convection in porous media and is expressed as follows [41]:
kd ¼ C qf cpf dp U p ð1 eÞ
ð15Þ
C ¼ 1:60 ½Rep Prf ð1 eÞ0:8282
ð16Þ
The control volume method was used to solve the governing equations, and the second-order upwind discretization was used for the convection terms in the momentum, energy, species, and turbulence equations. The Navier–Stokes equations were solved using the standard k-e model with the enhanced two-layer-wall function. The fluid thermodynamic property data for the specific heat, thermal conductivity, and viscosity were obtained from the NIST Database [42]. Throughout the numerical study, the solution methods were included in the commercial software package ANSYS Fluent 14.5 and the effective thermal conductivity was imported using a User Defined Function (UDF). Fig. 11 shows the comparison of the experimental and numerical results of the cooling efficiency distribution with wedge angles of 0° and 10°. For the wall temperature, the numerical results are found to be in good agreement with the experimental data for most areas. At the beginning and ending regions of the porous surface, the experimentally obtained temperature is lower than the numerical one because of the thermal contact resistance between the porous plate and the Bakelite frame. The numerically obtained cooling efficiency drop is higher in the downstream region of the oblique shock wave impingement position, and the overall cooling efficiency (experimental) is more uniform. 3.2. Calculation results and analysis Fig. 12 shows the static temperature distributions for a wedge angle of 10° and without the shock effect. When no shock wave is incident on the porous surface, the coolant overflowing the porous material forms a protective gas film close to the surface, and the heat boundary layer thickens along the mainstream continuously. When the shock wave impinges on the surface, the gas film temperature increases significantly and the gas film thickness decreases after the incident position. The gas film temperature decreases with an increase in the coolant gas blowing ratio but is
1.0
still higher than that without the shock wave. Therefore, the porous wall temperature is higher with an incident shock wave. Fig. 13 shows the static pressure distributions on the porous plate surface with different shock intensities. When no shock wave is incident on the surface, the fluid static pressure near the surface increases with the coolant blowing ratio and decreases along the mainstream flow direction because of the continuously thickening boundary layer. When the shock wave impinges on the surface, the flow velocity after the shock wave decreases, thereby increasing the static pressure. The overall static pressure of the fluid is higher with the shock wave impinging on the porous plate surface than that without the shock wave. The affected area and the magnitude of the static pressure rise both increase with the increase in the shock wave intensity. Similar to a previous study [29], for the analysis of supersonic film cooling, the definition of cooling efficiency (Eq. (4)) is related to the mainstream recovery temperature, wall temperature, and coolant inlet temperature, whereas the mainstream recovery temperature is calculated using Eq. (5). The ratio of the wall surface recovery temperature Tr to the total temperature T1 of the mainstream fluid can be expressed as [38]: 1 1 þ r c1 Ma2 1 Tr 2 r ¼ ¼r 1þ 2 c 1 T1 1 þ 2 Ma Ma2 1 þ c1 2
0.8 0.6 0.4 0.2
Fig. 12. Static temperature distributions for a wedge angle h = 10° and without the shock effect under the condition of Ma = 2.8 and T0 = 374 K.
F =0.22% F =0.44% F =0.66% F =0.88%
0.0 0.0
Exp. Exp. Exp. Exp.
θ=0
0.2
ο
Num. Num. Num. Num.
θ = 10 Exp. Exp. Exp. Exp.
0.4
ο
Num. Num. Num. Num.
x/L
T 0= 374 K
0.6
0.8
1.0
Fig. 11. Comparison of experimental and numerical cooling efficiency distributions on porous surface under the condition of Ma = 2.8 and T0 = 374 K.
! ð17Þ
where r is the recovery factor of air, which can be approximated as r = Pr1/3 under turbulent flow conditions. In the temperature range employed in this study, the Prandtl number of air is unchanged, and the recovery coefficient is approximately constant, i.e., r = 0.898. As shown in the equation, the wall recovery temperature increases with the decrease in the flow velocity near the porous plate surface when the mainstream total temperature remains unchanged. The increase in the wall recovery temperature would therefore reduce the overall transpiration cooling efficiency. Moreover, the decrease in the overall cooling efficiency increases with the increase in the shock wave intensity. The static pressure reaches the maximum near the shock incident location and increases with the increase in the shock intensity. While the cooling fluid enters the porous media from
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(a) F = 0.22%
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the cooling efficiency with shock wave impact. The recovery effect increases with the coolant blowing ratio. Thus, employing a high coolant ratio is an appropriate solution for the shock wave impact on transpiration cooling efficiency. Fig. 14 shows the distribution of the fluid velocity vectors for a coolant blowing ratio of 0.66% with different incident shock intensities. When no shock wave is incident on the surface of the porous plate, the cooling fluid continuously accumulates and the thickness of the boundary layer continuously increases along the main flow direction. When a shock wave is incident on the porous plate surface, the local static pressure at the incident location is the highest, thus hindering the coolant flow. In this case, the boundary layer no longer continuously thickens along the flow direction, thereby reducing the local cooling efficiency. When the shock wave intensity increases, the local static pressure increases and it is more difficult for the cooling fluid to flow out, thus further reducing the cooling efficiency. When the intensity of the shock wave further increases (h = 10°), the boundary layer even separates and results in a fluid backflow in the boundary layer. More coolant flows to the upstream region because of the non-uniform static pressure distribution, and the transpiration cooling efficiency is thus recovered. However, the cooling efficiency is hardly recovered in the downstream area after the incident position of the shock wave. 4. Conclusions
(b) F = 0.66% Fig. 13. Static pressure distributions on the porous surface with different shock wave intensities under the condition of Ma = 2.8 and T0 = 374 K: (a) F = 0.22%, and (b) F = 0.66%.
the reservoir with a constant mass flow rate, the increased and non-uniform static pressure distribution on the porous plate surface causes the cooling fluid to redistribute and flow to the upstream region where the outlet pressure is low. This makes more coolant to flow through the upstream region, helping to recover
A flat porous plate was tested for transpiration cooling in a wind tunnel of Mach number 2.8 with different coolant blowing ratios and incident shock intensities. Wedge-shaped shock wave generators were installed in the test section to induce oblique shock waves with different shock intensities. The porous surface temperature distribution was measured using an infrared camera, and the mainstream flow field was observed using a Schlieren system. A 2D computational model was applied to obtain the detailed temperature and flow field distributions and to analyze the shock wave effect on transpiration cooling. The results show that the transpiration cooling efficiency reduced because of the oblique shock wave impinging on the plate surface. The efficiency decreases with an increase in the shock intensity. The incidence of oblique shock waves causes the flow velocities near the porous surface to decrease and consequently increases the local recovery temperature, thereby reducing the overall cooling efficiency. Moreover, the local static pressure at the shock wave incident location is the highest, thus impeding
Fig. 14. Velocity vector distribution near the porous plate surface under the conditions of Ma = 2.8, T0 = 374 K, and F = 0.66%.
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the cooling fluid flow and further reducing the local cooling efficiency. The overall cooling efficiency reduced, especially in the downstream region of the shock wave impingement position; however, the reduction in the cooling efficiency in the upstream region becomes lower with the increase in the blowing ratio. For a blowing ratio of 0.88%, the cooling efficiencies remains at about 0.75 in the upstream region for various shock intensities, but the cooling efficiency with incident oblique shock is reduced by approximately 0.2 in the downstream area. The overall cooling efficiencies with different oblique shock wave intensities are reduced by 15%25% compared to the overall cooling efficiency without the shock wave incidence. Conflict of interest The authors declared that there is no conflict of interest. Acknowledgments This project was supported by the National Natural Science Foundation of China (No. 51536004) and the Science Fund for Creative Research Groups of NSFC (No. 51621062). References [1] Y.H. Zhu, W. Peng, P.X. Jiang, R.N. Xu, Review on active thermal protection and its heat transfer for airbreathing hypersonic vehicles, Chin. J. Aeronaut. 31 (10) (2018) 1929–1953. [2] X.L. Ouyang, P.X. Jiang, R.N. Xu, Thermal boundary conditions of local thermal non-equilibrium model for convection heat transfer in porous media, Int. J. Heat Mass Transf. 60 (2013) 31–40. [3] J.V. Wolfersdorf, Effect of coolant side heat transfer on transpiration cooling, Heat Mass Transf. 41 (4) (2005) 327–337. [4] P.X. Jiang, L. Yu, J.G. Sun, J. Wang, Experimental and numerical investigation of convection heat transfer in transpiration cooling, Appl. Therm. Eng. 24 (8–9) (2004) 1271–1289. [5] J. Bellettre, F. Bataille, J.C. Rodet, A. Lallemand, Thermal behavior of porous plates subjected to air blowing, J. Thermophys. Heat Transf. 14 (4) (2000) 523– 532. [6] L. Ding, K. Wei, Q. Zhang, J.H. Wang, An experimental investigation on transpiration cooling of porous flat plate, in: 2011 International Conference on Remote Sensing, Environment and Transportation Engineering (RSETE), IEEE, 2011, pp. 5692–5696. [7] Y.B. Xiong, Y.H. Zhu, P.X. Jiang, Numerical simulation of transpiration cooling for sintered metal porous strut of the scramjet combustion chamber, Heat Transf. Eng. 35 (6–8) (2014) 721–729. [8] F. Cheuret, J. Steelant, T. Langener, Numerical investigations on transpiration cooling for scramjet applications using different coolants, in: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2011, p. 2379. [9] J.X. Shi, J.H. Wang, A numerical investigation of transpiration cooling with liquid coolant phase change, Transp. Porous Media 87 (3) (2011) 703–716. [10] W.J. Dong, J.H. Wang, S.Y. Chen, B.C. Ai, X.G. Luo, Modelling and investigation on heat transfer deterioration during transpiration cooling with liquid coolant phase-change, Appl. Therm. Eng. 128 (2018) 381–392. [11] Y.Q. Liu, P.X. Jiang, Y.B. Xiong, Y.P. Wang, Experimental and numerical investigation of transpiration cooling for sintered porous flat plates, Appl. Therm. Eng. 50 (1) (2013) 997–1007. [12] Z. Huang, Y.H. Zhu, Y.B. Xiong, P.X. Jiang, Investigation of supersonic transpiration cooling through sintered metal porous flat plates, J. Porous Media 18 (11) (2015) 1047–1057. [13] S. Soller, C. Kirchberger, M. Kuhn, T. Langener, M. Bouchez, J. Steelant, Experimental investigation of cooling techniques and materials for highspeed flight propulsion systems, in: 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference, 2009, p. 7374.
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