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Heat transfer by shock-wave/boundary layer interaction on a ﬂat surface with a mounted cylinder Man Sun Yu a, Jiwoon Song a, Ju Chan Bae b, Hyung Hee Cho a,⇑ a b

Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemn-gu, Seoul 120-749, Republic of Korea Agency for Defense Development, Daejeon 305-600, Republic of Korea

a r t i c l e

i n f o

Article history: Received 3 November 2011 Available online 10 December 2011 Keywords: Convective heat transfer coefﬁcient Shock-wave/boundary layer interaction Cylinder IR thermography

a b s t r a c t The detailed convective heat transfer is observed on a ﬂat surface where the cylinder is mounted in a supersonic ﬂow ﬁeld. During the test, the thermal image of a wall temperature distribution is taken by an infra-red camera under the constant heat ﬂux condition on the ﬂat surface. From the measured wall temperature information, heat transfer coefﬁcients are calculated. The shadow graph and the oil ﬂow tests are conducted to examine the shock-wave structure and the surface shear ﬂow around the protruding body, respectively. The entire ﬂow also is simulated numerically. The upstream ﬂow Mach number, total pressure and Reynolds number are about 3, 600 kPa and 2.3 106, respectively. The swept-back effect of a cylinder to the approaching ﬂow is considered in the range from 0° to 30°. From the results, the large increase of heat transfer is observed in a shock-wave/turbulent boundary layer interaction region and the peak heating appeared especially on a ﬂow reattachment region. When the cylinder is swept backward to the main ﬂow, the heat ﬂux promotion decreases as much as its effective area. These results will provide the valuable information for the thermal analysis in a complicated shock-induced separation region. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction In a supersonic speed ﬂight, one of the major problems is the aerodynamic heating due to the shock-wave and boundary layer interaction. This detrimental heating problem could appear on an external skin of aero-vehicles as much as an internal skin of ramjet/scramjet engines. The over-heating of surface material could cause the burn-out of important units protruded into a supersonic ﬂow-ﬁeld. Also, if the heating rates show a steep spatial difference, it could bring a large thermal stress on an inﬂuenced surface, resulting in another kind of damages to the skin material of a vehicle. For last several decades, many experimental investigations about an aerodynamic heating have been conducted. Evans and Smits [1], Mee et al. [2], Shigeru et al. [3], and Edney [4] investigated the aerodynamic heating on the surface and around a solid body protruded to a supersonic ﬂow such as an inclined ramp, a sharp ﬁn and a blunt ﬁn. Especially, Korkegi [5], Stollery [6], and Neumann and Hayes [7] summarized many papers and reports related to the aerodynamic heating problem and also gave a good idea or an inspiration for the necessary research in a next step. ⇑ Corresponding author. Tel.: +82 2 2123 2828; fax: +82 2 312 2159. E-mail address: [email protected] (H.H. Cho). 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.11.033

For the heat transfer around a cylindrical blunt body, Shigeru et al. [3,8] has measured heat ﬂux rates accurately with thin ﬁlm heat ﬂux gauges and showed the increase of a heat transfer in a separated and a reattachment ﬂow regions. However, the results do not include the heat transfer information in the region just in front of a ﬁn leading edge and it takes a long time to observe the two-dimensional distribution only with an array of sensors installed to very limited positions. On the contrary, Schuricht and Roberts [9] took surface temperature images using a TLC (thermochromic liquid crystal) thermography technique to obtain the convective heat transfer coefﬁcient, although they focused only on a laminar ﬂow separation in their experiment. Therefore, even until now, the quantitative data of a heat transfer around a cylindrical blunt body are insufﬁcient due to its difﬁculty for the measurement. In this study, surface temperature images were taken on a ﬂat surface where a cylindrical solid body is mounted using an infrared thermography when the boundary layer separation occurs around the cylinder. To maintain the constant heat ﬂux condition on a temperature-measured surface, a thin foil heater was manufactured and installed on the surface. The measured temperature data were used to obtain the convective heat transfer coefﬁcient. For the understanding of a surface shear ﬂow and a shock-wave structure around a cylinder, the oil ﬁlm and the shadowgraph methods were conducted, respectively. The numerical simulation

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Nomenclature D h I L Ma P1 P02 Pr q_ q_ t q_ l r R

diameter of cylinder body convective heat transfer coefﬁcient electric current supplied to heating foil distance from cylinder leading edge along center line free stream Mach number before a pitot probe static pressure in a free stream before a pitot probe pitot pressure Prandtl number heat ﬂux rate emitted from heating foil to free stream total heat generation rate per unit foil area heat loss from heating foil to backup material recovery factor electric resistance of heating foil

was also conducted to observe the ﬂow ﬁeld in a separated region around a cylinder. In the test, the cylinder’s swept-back angle was considered as an experimental parameter and it was changed from 0° to 30°. 2. Experimental apparatus and procedure 2.1. Supersonic blow-down tunnel The free jet type supersonic blow-down wind tunnel is built and used to produce the uniform supersonic ﬂow around a model. Fig. 1 shows the schematic diagram of the wind tunnel. The ﬂow supplement system consisting of an air compressor, a cooler, ﬁlters, and storage tanks is also positioned before the pressure regulator although it does not appear in this ﬁgure. When the test starts, the compressed air is supplied from storage tanks to the stagnation chamber lowering its pressure level down to the operating value by a pressure regulator. In the inlet diffuser of stagnation chamber, the cone-type separator and the 5-stage screen are installed to increase the ﬂow uniformity and lower the turbulence level in a stagnation chamber [10]. The pressure and the temperature in the stagnation chamber are measured during the test by a

Rex St T0 Taw TR TS Tw X, Y

a c

Reynolds number presented by distance from ﬂat plate leading edge, x Stanton number gas total temperature adiabatic wall temperature recovery temperature static temperature in a free stream before a total temperature wall temperature under constant heat ﬂux condition relative position from cylinder leading edge in upstream and span-wise directions, respectively cylinder swept-back angle speciﬁc heat ratio

pressure transducer and an aspiration-type temperature probe installed to the chamber. Stabilized air in the stagnation chamber is accelerated through a supersonic nozzle. The designed Mach number of the nozzle exit section is three and the inner wall proﬁle of a supersonic nozzle is referred to the data provided by Hong [11], who applied the method of characteristic for the supersonic nozzle design. The radius of curvature in a nozzle subsonic part is ﬁve times of a nozzle throat diameter. The exit diameter of nozzle is 80 mm. The accelerated ﬂow is issued into the test chamber where the test model is positioned. In the test chamber, a pressure transducer is installed to measure a static pressure. Circular windows are also prepared to visualize the shock structure during the test. A ﬂat black paint is sprayed on the all surfaces inside the test chamber for the light absorption. Behind of the test chamber, a diffuser and a silencer are positioned for the pressure recovery and the reduction of a noise level, respectively. In the case of a diffuser, the throat diameter and the length are about 100 mm and 905.5 mm, respectively, and the half angle at its convergent and divergent parts is 3.5°. During the test, the stagnation and the static pressures are almost maintained to be about 600 kPa and 12 kPa, respectively, while the chamber temperature decreases due to the gas expansion in storage tanks and the Joule–Thomson effect at the valves and the pressure regulator. To check the ﬂow uniformity in the test section, pitot pressure and total temperature surveys were conducted along a radial direction for the nozzle exit section. The measured pitot pressure is substituted to the Rayleigh supersonic pitot tube equation for the calculation of upstream Mach number as follows: c h iðc1Þ ðc þ 1ÞMa2 =2 P02 ¼ h 1 iðc1Þ P1 2cMa2 cc1 cþ1 þ1

ð1Þ

In Eq. (1), P02 is the measured pitot pressure and P1 is the static pressure value at the nozzle exit calculated with the onedimensional isentropic relation and the measured stagnation chamber pressure, Pch. The measured total temperature is represented as a recovery factor using the following equation:

r¼

TR TS T0 TS

ð2Þ

2.2. Test model and other supplement equipments

Fig. 1. Schematic diagram of supersonic blow-down wind tunnel.

The ﬂat plate model which has a length of 90 mm, a width of 62 mm, and a thickness of 12 mm is used to develop a turbulent

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Fig. 2. Schematic diagram of test model.

10 Numerical Exp. (Dolling14) 8

Pw/Pinf

6

4

2 Fig. 3. Calculation domain and surface mesh near a leading edge of cylinder.

0 -4

-3

-2

-1

0

X/D

4 Numerical 14 Exp. (Dolling ) 3

Pw/Pinf

boundary layer ﬂow on a ﬂat surface. Fig. 2 shows the shape and the dimensions of the test model. The left picture in Fig. 2 shows several dimensions of a model-base made of steel and there is a cubic-shaped hollow space for the installation of a heater and thermal insulators presented in the right picture. As shown in the picture, the Teﬂon block and the mineral wool are inserted into the space of model-base with thicknesses of 5 mm and 1 mm, respectively. To produce the constant heat ﬂux condition on a considered surface around a cylinder, the thin foil heater is designed and manufactured. The electric resistance of heater pattern line can cover the surface around a cylinder effectively. The total thickness of heater is 200 lm while the resistance material is coated on an electric insulated-base with 10 lm thickness. The electric resistance of heater is about 170 X. As a protruding body, a cylinder is positioned in the middle of the ﬂat surface. The diameter of a cylinder is 5 mm and the length is changed from 20 to 23 mm to maintain its height constantly normal to a ﬂat surface for various swept-back angles. According to the empirical result of Westkaemper [12], the length-to-diameter ratio of a cylinder in this study is large enough to ignore length-effect on a shock wave/boundary layer interaction around a cylinder. Finally the ﬂat black paint is sprayed on the test model surface for the light absorption, same with the inner surfaces of test chamber. The emissivity of black paint is found to be about 0.89 from the calibration test and the value is used to calculate the temperature distribution on a surface from the infra-red image. The direct current is supplied to the foil heater by the power supplement system whose maximum voltage and current are 200 V and 20 A, respectively. And the current value is monitored in a test by checking the voltage drop across the shunt positioned in the middle of electric circuit. The most voltage signals from sensors such as pressure transducers and thermocouples are

2

1

0 -4

-2

0

2

4

6

8

X/D

Fig. 4. Surface pressure distribution around a cylinder.

received by a voltmeter (Agilent, HP34970A) and processed in a computer. The surface temperature on a considered surface is measured using an infra-red camera (Jenoptik, Varioscan3011-ST). 2.3. Experimental conditions test procedures As mentioned in the previous chapter, the upstream Mach number is about three and the total pressure is about 600 kPa. During

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main stream due to the very high potential of heat transfer for the high speed ﬂow in contrast to the high thermal resistance of back-up materials. The heat ﬂux value to the main stream is calculated applying the following equation:

q_ ¼ q_ t q_ l

ð3Þ

where

q_ t ¼ I2 R;

Fig. 5. Shock wave structures and static pressure distribution in front of a cylinder.

the test, the unit Reynolds number is calculated to be about 4.8 107/m although it could be changed a little depending on the total temperature. Because the cylinder is positioned at 60 mm downstream from the leading edge of a ﬂat plate, the Reynolds number is calculated to about 2.3 106, which means that the turbulent boundary ﬂow condition is satisﬁed according to the result from He and Morgan [13]. In the beginning of test, when the valve is opened, the electric power is turned on nearly simultaneously supplying the electricity to the foil heater. The most of generating heat is diffused to the

q_ l ¼ heat losses

The electric current value can be calculated from the voltage drop through the shunt, whose electric resistance is already known. The electric resistance of the heating foil is measured with an ohmmeter to be 170 X. Heat losses can be divided into two parts by the conduction into the backward of a test surface and the radiative heat ﬂux into the test chamber. In this study, the radiation effect can be neglected due to its small value less than 2% of a total heat ﬂux. However, in the case of conduction loss, the magnitude could be large because there is always the temperature difference between the free stream and the test model even in the opposite surface of the ﬂat plate. Especially, in the matter of fact, the testing time of 8–10 s is not long enough to assume the steady conduction process in a backward direction of a heating surface. Therefore, in this study, the magnitude of a total heat ﬂux is determined empirically to minimize the conduction loss and onedimensional transient conduction analysis in back-up materials is conducted for the correction of a practical heat ﬂux value. As the calculated result, about 6% of total heat ﬂux is predicted to be conducted into the backward of test model. This value could decrease in the shock-wave/boundary layer interaction region because of its high potential of a convective heat transfer. The surface temperature image is taken at 8 s after the valve opening and this is enough for the main ﬂow to reach the dynamically-steady condition. The convective heat transfer coefﬁcient is calculated using the following well-known relation:

h¼

q_ T w T aw

ð4Þ

where

T aw ¼ T 0

1 þ r c1 Ma2 2 1 þ c1 Ma2 2

As described in the previous section, the surface temperature, Tw is measured using IRT (infra-red thermography) technique. The total temperature, T0, is assumed to be same to the tempera-

Fig. 6. Path lines around a cylinder for different swept-back angles.

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Fig. 7. Surface pressure (upward) and shear stress (downward) distributions for different swept-back angles.

3.0 1st seperation distance 2nd separation distance

Separation distance (X/D)

2.5 2.0 1.5 1.0 0.5 0.0 0

10

20

30

Fin angle (Deg) Fig. 9. Flow separation distance for different swept-back angles in a center line.

Fig. 8. Oil and lampblack streak patterns for different swept-back angles.

ture measured in the stagnation chamber and this assumption is valid in a short duration blow-down tunnel test. The recovery factor, r, is set to the value for the parallel turbulent ﬂow on a ﬂat surface. The total error for the calculated convective heat transfer value is estimated to be 9.2% in 95% conﬁdence level.

2.4. Domain and boundary conditions for numerical study For the observation of ﬂow ﬁeld around a cylinder, the numerical simulation is conducted with FLUENT vs. 6.1.22. Fig. 3 shows

the calculation domain and the surface grid structure in the region near a leading edge of cylinder. The total number of cells in a domain is about 195,000 and the minimum node spacing in a normal direction to a ﬂat surface is set to 2.5 105 D while the spacing is 2.5 104 D in a normal direction to a cylinder surface. The 1equation turbulence model is applied and from results, y+ values on the considered surface are conﬁrmed to be under the value of 10. The developed turbulent boundary layer is applied to the inlet section and the 1/7th law is assumed to the boundary layer proﬁle. The thickness of boundary layer is assumed to be same to the diameter of cylinder. The inlet pressure, Mach number and static temperature are set to 20 kPa, 2.95, and 95 K, respectively. For the validation of calculated result, the surface pressure distributions on two lines of Y = 0.0 D (center line) and 1.0 D are compared to the experimental result presented by Dolling [16] as shown in Fig. 4. On the centerline in front of a cylinder leading

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1400

Analytic

2

2

1000

X/D=4 X/D=3 X/D=2 X/D=1 X/D=0

1200 h (W/m K)

1200

h (W/m K)

1400

Y/D=0 Y/D=1 Y/D=2 Y/D=3

800

600

1000

800

600

400

400

-2

-1

0

1

2

3

4

-3

-2

-1

0

1

2

3

Y/D

X/D

Fig. 10. Convective heat transfer coefﬁcient distribution on a ﬂat surface.

edge, the numerical result shows a good agreement with an experimental data although the position of initial ﬂow separation is a little closer to the leading edge in the numerical result than the experimental result. The plateau region behind of the separation point is observed and agreed well with the experimental data as much as the abrupt increase of pressure due to the ﬂow reattachment just in front of leading edge. Even in the case of Y = 1.0 D, the numerical result predicts the initial separation point and the pressure increase very well although the ﬂow reattachment position and the pressure peak value do not coincide with the experimental result in spite of the similar pattern.

3. Results and discussion 3.1. Flow ﬁeld around a cylinder Fig. 5(a) shows the shock wave structure in front of a cylinder, which is photographed by a shadowgraph method. In front of a cylinder, the stand-off shock wave is observed well as a thick vertical line. Near a ﬂat surface, an inclined shock wave is shown and it is also called as the name of ‘‘separation shock wave’’ because the boundary layer separation is known to occur near the foot of this shock wave. The interaction between the stand-off and the separation shock waves results in the lambda-shaped shock wave

structure. From the numerical result for a static pressure distribution in a symmetric surface, the pressure increase due to these shock wave structures can be observed as shown in Fig. 5(b). Also, high pressure region (P1) is shown locally behind of the triple point ahead of a cylinder leading edge. The peak pressure region behind of the triple point is induced by the impingement of supersonic jet ﬂow which is positioned in a gap between two normal shock waves of lambda shock structure and it has been conﬁrmed well by the experimental result of Edney [4]. Another peak pressure region (P2) on a ﬂat surface appears due to the impingement of horseshoe vortex ﬂow. For better understanding of the vortex ﬂow around a cylinder, stream lines are shown in Fig. 6 for different swept-back angles. In the picture, the stream lines are shown only in the half side of cylinder for convenience. At far upstream of a cylinder body, ﬂow goes downstream straightly without any direction change. However, when the adverse pressure gradient in front of a cylinder affects the upstream ﬂow through the subsonic part in a boundary layer, the ﬂow goes upward from the bottom surface resulting in the boundary layer separation. Eventually, the separated ﬂow rolls down again and reattaches to the surface while it moves to lateral surface showing the horseshoe vortex pattern. As a cylinder is swept back, the vortex structure becomes small as much as the separation region around a cylinder. This ﬂow pattern has been well-known by other researchers for decades and the sweep of

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4.0 Y/D=0.0 Y/D=0.5 Y/D=1.0 Y/D=1.5 Y/D=2.0

Bow shock

3.5

h/href

3.0 2.5 2nd sep.

2.0

1st sep.

1.5 1.0 -2

-1

0

1

2

3

4

X/D

4.0

4.0

X/D=-2.0 X/D=-1.0 X/D=0.0 X/D=1.0 X/D=2.0 X/D=3.0

h/href at Y/D=0.0 h/href at Y/D=1.0

3.5

3.5

14 14

PS/Pref at Y/D=1.0 (Dolling )

3.0

3.0 h/href

h/href or PS/Pref

PS/Pref at Y/D=0.0 (Dolling )

2.5

2.5

2.0

2.0

1.5

1.5

1.0 -2

-1

0

1

2

3

4

X/D

1.0 -3

-2

-1

0

1

2

3

Y/D

Fig. 11. Convective heat transfer coefﬁcient distribution for a swept-back angle of 0°.

cylinder has been known to be the best way to control the ﬂow separation around a three-dimensional blunt ﬁn [15]. Although it is not presented here, the small vortex is also observed near the base of cylinder leading edge and it moves along the cylinder surface rotating reversely with the primary vortex. This seems to be the reason the peak surface pressure appears a little detached from the cylinder leading edge in Fig. 4(a). Surface pressure and shear stress distributions around a cylinder are shown together in Fig. 7 and the upper side of each picture represents the surface pressure distribution. For the pictures of surface shear stress distribution in a lower side, bow-shaped regions of low shear stress are observed and the ﬂow separation is supposed to occur in these areas, especially near the white dotted lines representing the lowest shear stress. Surface pressure starts to increase a little upstream of these ﬂow separation lines due to the high pressure propagation to the upstream through the boundary layer. In a ﬂow separated region, there is a low pressure valley or a plateau until the peak surface pressure appears just in front of a cylinder due to the vortex ﬂow impingement. As a cylinder is swept back, the ﬂow separation is retarded and the separation line becomes close to the cylinder with the increase of a cylinder swept-back angle. Also, the magnitude of peak pressure due to the ﬂow reattachment decreases as the cylinder is swept back. The conﬁrmation of ﬂow separation is also possible experimentally by the oil ﬁlm method and results are shown in Fig. 8. Around a cylinder, two ﬂow separation lines are observed well in most of cases. Especially, when the cylinder is in vertical direction (h = 0°), the ﬁrst ﬂow separation point in a center line is expected to about 2.62 times cylinder diameter upstream of a cylinder

leading edge and this value is comparable with the value of 2.65 times cylinder diameter suggested by Westkaemper [12]. It is quite interesting that the secondary ﬂow separation is not simulated in a numerical analysis although it appears clearly in an oil streak pattern. This secondary separation has been already observed by other researchers’ data [3,16] although it is expected not to have a large effect to the ﬂow characteristic because it induces only a small counter-rotating vortex ﬂow compared to the large primary horseshoe vortex. Consequently, surface pressure distributions from the numerical and the experimental results show good agreement each other as mentioned in Fig. 4. For the quantitative investigation of the cylinder sweeping effect to the ﬂow separation, the separation distances in a center line for different swept-back angles are shown in Fig. 9 and the separation distance is deﬁned as the distance from a cylinder leading edge to the ﬂow separation point in a center line. From the graph, a good linear relation appears between the swept-back angle and the separation distance and the relations are expressed by linear equations as follows:

L1st sep: =D ¼ 2:65 0:046a L2nd sep: =D ¼ 1:38 0:037a

ð5Þ

3.2. Convective heat transfer coefﬁcients around a cylinder As mentioned in the previous section, the experiment is conducted for measuring the surface temperature distribution in a ﬂow separated region around a cylinder under the constant heat ﬂux condition. The convective heat transfer coefﬁcient is calculated

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4.0 ο

α=0

3.5

h/href

3.0

α=10

ο

α=20

ο

α=30

o

2.5 2.0 1.5 1.0 -3

-2

-1

0 Y/D

1

2

3

4.0 o

α=0

4.0

3.5 3.5

α=0

3.0

α=10

o

o

h/href

α=20o

2.5

α=20

3.0

o

h/href

o

α=10

α=30o

o

α=30

2.5 2.0

2.0

1.5

1.5

1.0

1.0 0

1

2

3

4

-3

-2

-1

0

1

2

3

Y/D

X/D

Fig. 12. Convective heat transfer coefﬁcient distribution for various swept-back angles.

from the result. However, at ﬁrst, the test is conducted for the base case of a non-disturbed ﬂow on a ﬂat surface without a cylinder and the result is shown in Fig. 10. In a contour shown in Fig. 10(a), the white elliptic region does not have any meaningful data because the hole blocked for the test for a cylinder insertion is positioned there. In the contour, it can be found that the heat transfer decreases gradually in a downstream direction as the boundary layer develops and the span-wise uniformity is good. For more detailed observation, the heat transfer coefﬁcient is plotted along both the downstream and the span-wise directions in Fig. 10(b). The value is ranged from about 500 to 700 W/m2 K and the conspicuous high heat transfer is observed at both sides in an upstream region. This abnormal high heat transfer coefﬁcient seems to appear due to the relative large heat loss to the backup material. Actually, the region where the high heat transfer coefﬁcient appears is positioned near the non-heated cold region. In other regions, the distribution shows a good uniformity in a lateral direction. In a next step, a cylinder body is mounted on a model surface without an inclination and the heat transfer coefﬁcient distribution around the protruding body is measured as shown in Fig. 11. In the ﬁgure, the heat transfer coefﬁcient is presented as the normalized value by a reference value, which is deﬁned as the heat transfer coefﬁcient on the ﬂat surface without a protruding body. The reference heat transfer coefﬁcient is calculated using the analytic relation suggested by Kays and Crawford [17]. It shows a good

agreement with an experimental result (Fig. 10(b)) in a considered domain.

St ¼ 0:0287 Pr0:4 Re0:2 x

ð6Þ

In the contour, two curved white lines mean the ﬁrst and the second ﬂow separation lines which are conﬁrmed by the oil ﬁlm method. The gradual increase of heat transfer coefﬁcient is observed downstream of the ﬁrst ﬂow separation line. The increase of turbulent level in a shear layer which is formed behind a separation shock wave seems like the reason of this heat transfer intensiﬁcation. Secondary ﬂow separation does not show any dominant effect to the surface heat transfer as much as the surface pressure distribution mentioned in the previous paragraph. There is a bow-shaped valley having relative low heat transfer coefﬁcients between the secondary separation line and the circular edge of a cylinder. Interestingly, this low heat transfer characteristic appears at the similar region where the low surface pressure is observed as shown in Fig. 11(b). Fig. 11(b) shows the heat transfer distribution together with the surface pressure for comparison and the surface pressure data is referred from the result suggested by Dolling [14]. Besides of the coincidence of positions where the low values appear, it is noticeable that the overall pattern is very similar each other. The normalized heat transfer coefﬁcient distributions are also plotted in a downstream direction for several span-wise positions in Fig. 11(c). For convenience, the ﬁrst and

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the second ﬂow separation positions and the inviscid bow shock wave position in the center line are indicated. In the center line, the heat transfer is intensiﬁed downstream of the ﬁrst ﬂow separation and the peak heat transfer appears on the ﬂow reattachment region near X/D = 0.0. The heat transfer coefﬁcient seems to be over three times of the non-separated value. As the distance from the center line increase in a span-wise direction, overall heat transfer coefﬁcient decreases and the peak heating position moves downstream as much as the valley or the plateau region of heat. For the case of Y/D = 1.0, it is shown that the heat transfer coefﬁcient decreases gradually again behind of the peak heating point (X/ D = 1.0) as the attached ﬂow develops in a downstream direction. Heat transfer coefﬁcient is also plotted in a span-wise direction for various stream-wise positions in Fig. 11(d). Ahead of a cylinder such as X/D = 3.0, 2.0, and 1.0, the peak heating occurs at the center position and the heat transfer coefﬁcient decreases gradually in a spanwise direction. However, in a downstream of a cylinder leading edge (X/D = 1.0 and 2.0), this ‘K’-shaped distribution does not appear anymore and two peaks of heat transfer are observed at both sides, where the horse-shoe vortex impingements are expected. Heat transfer coefﬁcient distributions for various cylinder swept-back angles are shown in Fig. 12. As mentioned in the previous paragraph, the region where the cylinder is positioned and downstream of it does not have any meaningful data although the white region is enlarged as the cylinder swept-back angle increases. In the contour, as the cylinder swept-back angle increases, the heat transfer level in the ﬂow separation region decreases and the ﬂow separation effect is also limited to the area close to the cylinder. Also, the bow-shaped region with the relative low heat transfer coefﬁcient in front of a cylinder disappears when the swept-back angle is over 20°. This phenomenon can be conﬁrmed more evidently in Fig. 12(b), which shows the heat transfer coefﬁcient distribution on the center line. The position of relative low heat transfer valley moves from X 0.6 D in a = 0° to X 0.35 D in a = 10° and the heat transfer coefﬁcient increases monotonously in cases of a = 20° and a = 30°. Also, in Fig. 12(b), the initial heat transfer increase position moves downstream and the overall heat transfer level decreases when the cylinder is swept back. The spanwise distributions of heat transfer coefﬁcient are shown in Fig. 12(c) and (d) for the stream-wise positions ahead and behind of a cylinder (X/D = 1.0, and 2.0). From the results, the width of high heat transfer region is reduced as much as its level with increasing swept-back angle. However, despite of this effective depression of heat transfer around a cylinder, the heat transfer coefﬁcient in the area near the cylinder edge is increased with increasing swept-back angle at X/D = 2.0, that is, the stream-wise position behind of a cylinder and this locally large difference of heat transfer could make the severe thermal stress at the corner between a cylinder and a ﬂat plate. 4. Conclusion Experimental study on the heat transfer in a separated ﬂow by the interaction of shock wave/turbulent boundary layer is

conducted. The cylinder body is considered as a protruding body which makes the shock wave for the interaction with a boundary layer and its swept-back angle is selected as a parameter. The complicated two-dimensional distribution of the convective heat transfer coefﬁcient is presented as an image by means of an infra-red thermography. The shadowgraph and the oil-ﬁlm methods are also used for the understanding of a ﬂow characteristic especially in a separated region and the linear relation between the swept-back angle and the separation point in a center line is found additionally. From the results, a bow-shaped valley with relative low heat transfer coefﬁcient is discovered in front of a cylinder and it disappears when the cylinder is swept back over 20°. The sweeping of a cylinder is found to be a good way for the depression of heat transfer increase around a cylinder and the reduction of the separation area although the locally high heat transfer difference is predicted near the corner between the cylinder and the ﬂat surfaces at a high swept-back angle. References [1] T.T. Evans, A.J. Smits, Measurements of the mean heat transfer in a shock wave–turbulent boundary layer interaction, Exp. Therm. Fluid Sci. 12 (1996) 87–97. [2] D.J. Mee, H.S. Chiu, P.T. Ireland, Techniques for detailed heat transfer measurements in cold supersonic blowdown tunnels using thermochromic liquid crystals, Int. J. Heat Mass Transfer 45 (2002) 3287–3297. [3] A. Shigeru, H. Masanori, T. Anzhong, The structure of aerodynamic heating in three-dimensional shock wave/turbulent boundary layer interactions induced by sharp and blunt ﬁns, in: AIAA 20th Fluid Dynamics, Plasma Dynamics and Lasers Conference, AIAA-89-1854, 1989. [4] B.E. Edney, Effects of shock impingement on the heat transfer around blunt bodies, AIAA J. 6 (1968) 15–21. [5] R.H. Korkegi, Survey of viscous interactions associated with high mach number ﬂight, AIAA J. 9 (1971) 771–784. [6] J.L. Stollery, Some aspects of shock wave boundary layer interaction relevant to intake ﬂows, in: Proceeding of AGARD Conferences – Aerodynamics of Hypersonic Lifting Vehicles, CP-428, 1987. [7] R.D. Neumann, J.R. Hayes, Introduction to aerodynamic heating analysis of supersonic missiles, tactical missile aerodynamics, Hemsch, M., Prog. Astronaut. Aeronaut. V-141 (1992) 421–481. [8] A. Shiegeru, K. Seishi, N. Shigehide, Aerodynamic heating phenomena in three dimensional shock wave/turbulent boundary layer interactions induced by sweptback blunt ﬁns, in: AIAA 28th Aerospace Sciences Meeting AIAA-1990381, 1990. [9] P.H. Schuricht, G.T. Roberts, Hypersonic interference heating induced by a blunt ﬁn, in: AIAA Eigth International Space Planes and Hypersonic Systems and Technologies Conference AIAA-1998-1579, 1998. [10] A. Pope, K.L. Goin, High Speed Wind Tunnel Testing, John Wileys & Sons, 1965. [11] Y.S. Hong, Engineering of Space Propulsion, Chong-Mun-Gak, 1992. [12] J.C. Westkaemper, Turbulent boundary layer separation ahead of cylinder, AIAA J. 6 (1969) 1352–1355. [13] Y. He, R.G. Morgan, Transition of compressible high enthalpy boundary layer ﬂow over a ﬂat plate, Aeronaut. J. 98 (1994) 25–34. [14] D.S. Dolling, Blunt ﬁn-induced shock wave/turbulent boundary layer interaction, AIAA J. 20 (1982) 1674–1680. [15] P.K. Chang, Control of Flow Separation: Energy Conservation, Operational Efﬁciency, and Safety, McGraw-Hill Book Company, 1976. [16] N.R. Fomison, J.L. Stollery, The effects of sweep and bluntness on a glancing shock wave turbulent boundary layer interaction, transition of compressible high enthalpy boundary layer ﬂow over a ﬂat plate, in: Proceeding of AGARD Conferences – Aerodynamics of Hypersonic Lifting Vehicles, CP-428, AGARDograph 8-1-8-18, 1987. [17] W.M. Kays, M.E. Crawford, Convective Heat and Mass Transfer, second ed., McGraw-Hill Book Company, 1980. p. 213.

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