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Hypersonic shock tunnel studies of Edney Type III and IV shock interactions
Accepted Manuscript Hypersonic shock tunnel studies of Edney Type III and IV shock interactions
Abhishek Khatta, Gopalan Jagadeesh
PII: DOI: Reference:
S1270-9638(17)30855-6 https://doi.org/10.1016/j.ast.2017.11.001 AESCTE 4276
To appear in:
Aerospace Science and Technology
Received date: Revised date: Accepted date:
12 May 2017 24 October 2017 1 November 2017
Please cite this article in press as: A. Khatta, G. Jagadeesh, Hypersonic shock tunnel studies of Edney Type III and IV shock interactions, Aerosp. Sci. Technol. (2017), https://doi.org/10.1016/j.ast.2017.11.001
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Hypersonic Shock Tunnel Studies of Edney Type III and IV Shock Interactions Abhishek Khatta1 and Gopalan Jagadeesh2 Indian Institute of Science, Bangalore, India – 560012 Of all the possible outcomes of the shock interaction problem, Edney Type-III and Type-IV are considered to be of great importance as they lead to high heat transfer rates on the surface in the vicinity of the interaction. The enhancement in heat transfer occurs because of shear layer attachment in Type-III interaction and impingement of supersonic jet in Type-IV interaction. In this study, unsteady nature of these interactions is studied in conventional shock tunnel at moderate enthalpy condition of 1.07 Mj/kg at flow Mach number of 5.62. A hemispherical model, 50mm in diameter, mounted with thin film Platinum gauges is used along with a 25 wedge to serve as a shock generator. The schlieren images are captured along with the surface convective heat transfer rate measurements for the analysis of flowfield over the model during the test time. The pixel intensity scan is performed along several lines running horizontally to estimate the steadiness of the flowfield. These are correlated with the heat transfer rate measurements to understand the nonsteady nature of the interaction during the small test times offered by the shock tunnel.
1
Research Scholar, Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012
2
Professor, Department of Aerospace Engineering, Indian Institute of Science, Bangalore - 560012
Nomenclature H = stagnation enthalpy, MJ/kg Mࡅ = freestream Mach number Pࡅ = static pressure, kPa R = radius of hemispherical body, m Reࡅ = freestream Reynolds number, /m s = distance along the surface, mm Tࡅ = freestream static temperature, K Uࡅ = freestream velocity, m/s ͳࡅ = freestream density, kg/m3 q = heat transfer rate, W/cm2 ͣ = thermal coefficient of resistance of thin film gauge, C ࡁ1
ͤ = thermal coefficient of resistance of thin film gauge, Ws1/2 /m2K k = thermal conductivity, W/m/K CP = specific heat ratio at constant pressure, J/kg/K E = voltage, V t, Ͷ = time, s x = streamwise coordinate y = normal coordinate Y = derived parameter ࢥ
= independent parameter
I. Introduction Any supersonic flow is accompanied by the shock waves, appearing due to the presence of an obstruction in the path of the flow or due to need to turn the flow. These shock waves when generated from many different obstructions, as in from fin and tail and fore-body of a full scale vehicle, end up interacting with each other, thereby modifying the aerodynamic characteristics of the vehicle. Such inevitability of shock-shock interactions in high speed flows motivates the researchers around the globe to study these phenomenon to better understand the causes and the repercussions of such interactions, leading to the better design of the flight vehicle. The shock-shock interaction problem deals with the observed elevated pressure and heat transfer rates on the surface in close proximity of such interactions. The first detailed experimental analysis of such problem owes to the work of Edney[1], where the surface heat transfer rates were measured using thin film technique and elevated heat flux obtained on the spherical shaped body in the region where an external shock wave interacts with the bow shock wave. Edney[1] conducted experiments in a hypersonic wind tunnel and used spark visualization technique to capture the shock features and this formed the basis of classification of such interactions for all further studies on the problem. The classified interaction patterns are known as Edney Type-I, Edney Type-II, Edney Type-III, Edney Type-IV, Edney Type-V, Edney Type-VI. In his work, the model was injected in the test section and thus the time history of heat flux at a single location for a given configuration was not provided. The classification of such interactions by Edney led to a systematic study on such phenomenon. The later researchers, Hains and Keyes[2], Borovoy et al.[3], Boldyrev et al.[4], investigated the effect of impinging shock strength, body shape, flow Mach number on the amplification obtained in heat transfer rates. It was noticed that the configurations that produce Edney Type-III and Edney Type-IV interactions lead to severe heat transfer rates on the surface of the hemispherical body. Yet, in many experimental work, the temporal variation of heat transfer rates was not discussed and hence the unsteady nature of such interactions was not analyzed. Experiments conducted by Wieting and Holden[5] and Holden[6] revealed some oscillations in the measured quantities for Edney Type-IV interaction and suggested that the nature of such interactions is unsteady within the frequency range of 3 to 10 kHz. Sanderson[7] conducted experiments in a Free Piston Driven Shock Tunnel to study the effect of enthalpy on the heat transfer rates on the blunt body in the presence of interactions and observed unsteadiness in the supersonic jet existing in the Edney Type-
IV interaction. Grasso et al.[8], in their experimental work in R3Ch hypersonic wind tunnel at ONERA focussed on Edney Type-III and Type-IV interactions, with the motive to study the effect of shock impingement location. In the available test time of approximately 10 seconds, the authors observed the change in the supersonic jet from being near normal to the cylinder surface in the beginning of the test time to the jet being curved in space in the later half of test time. Also, the authors conducted some experiments to study hysteresis phenomenon associated with shock interactions. The shock generator was moved continuously with respect to the cylinder and the path was later traced back. It was observed that the pressure values on the surface were not much sensitive to the path followed by the shock generator but the heat transfer values did not come to the same level when the shock generator was traced back on its path. This shed new light and opened many avenues to further study these phenomenon. Riabov et al.[9] performed experimental and numerical investigation of shock impingement flowfields in rarefied environment and concluded that the Type-IV interaction seen in the continuum flow was absent. The results were presented in the form of Stanton number distribution over the surface for various interaction types, but the question of unsteadiness in the observed interactions was left unanswered. Recently, Xiao et al.[10] investigated, both experimentally and numerically, the effect of forward facing step at the stagnation point in the presence of Type-IV interaction. The researcher used a reflected mode shock tunnel at the University of Science and Technology, China, for the experiments and reported that the flow was either steady or unsteady, depending on the location of the impingement of supersonic jet. In case of the unsteady flowfield, they observed a forward and backward motion oscillation and a up and down motion oscillation, both occurring at different frequencies. The unsteadiness in the Edney Type-IV configuration is associated with the supersonic jet which lies very close to the body within the shock layer, and thus it becomes difficult to analyze such phenomenon experimentally, given the sensitivity and the resolution of the experimental equipment. To understand the unsteady nature of the shock-shock interaction phenomenon, many researchers approached the problem through numerical simulation and have over the time added to the understanding of the underlying physics dominating these interactions. Gaitonde and Shang[11] investigated the unsteady nature of Type-IV interaction and focussed on the changes in the structure of the supersonic jet during the limit cycle and estimated the oscillating frequency to be about 30 kHz. The author noticed that during each cycle, the jet exhibits two different configuration, with the jet shock being near normal to the cylinder in one and being parallel in the other. Lind and Lewis[12] performed numerical simulation considering the laminar flow to
understand the unsteadiness of the Type-IV supersonic jet. The authors observed that by changing the impinging shock angle from 18 degree to 19 degree, the supersonic jet tends from a steady to unsteady state. The unsteadiness was characterized by the pressure fluctuation on the model surface with the frequency of oscillation estimated at 1.38 kHz. The authors also commented that by changing the grid resolution, the estimated frequency changed to a higher value of 1.45 kHz. Yamamoto et al.[13] conducted high order numerical simulation for the Type-IV interaction and found that the oscillation in the supersonic jet leads to the unsteady disturbance of the supersonic shear layer and the whole phenomenon leads to the time varying heat transfer and pressure loading on the surface. Chu and Lu[14] solved Navier Stokes Equation with higher order numerical methods for Edney Type-IV interaction. The work focussed on the relationship between the termination jet shock wave with the shear layer instabilities and concluding with proposing a feedback mechanism. It has been noted that though several experimental studies have been devoted to the quantification of high heat transfer rates on the blunt body in the presence of shock-shock interactions, few studies have analyzed the unsteady nature of such interactions. Also, it is evident from the literature that these amplifications are sensitive to many parameters such as impinging shock location, impinging shock strength, body shape and size, freestream flow Mach number and Reynolds number, a unified theory to address the amplification is as of now difficult to put in place. The numerical simulations which have addressed the unsteady nature and the limited experimental studies which analyzed the unsteadiness bring about the oscillation frequency to be within the range of 1 kHz to 30 kHz, which is a wide range and may depend on the factors discussed above. Though the unsteadiness is very evidentally observed experimentally for Edney Type-IV configuration, no such comments have been made for Edney Type-III configuration. In the present study, unsteady nature of Edney Type-III and Edney Type-IV interactions was targeted experimentally in conventional shock tunnel at moderate enthalpy condition. The schlieren images were captured along with the surface convective heat transfer measurements for the analysis of flowfield over the model during the test time. The pixel intensity scan was performed along several lines running horizontally to estimate the steadiness of the flowfield. These were correlated with the heat transfer rate measurements to understand the non-steady nature of the interaction during the small test times in the shock tunnel.
II. Experimental Facility The experiments were conducted in straight through mode Hypersonic Shock Tunnel-2 (HST-2) at Laboratory for Hypersonic and Shock wave Research (LHSR), IISc, Bangalore. The shock tunnel consists of 2m long driver section and 5.12m long driven section. A metal diaphragm was used to initially separate the driver and driven section. In straight through mode operation, the internal diameter of the shock tube is matched with the inlet of the conical nozzle. The conical nozzle then expands to the test section of dimension 300x300x450mm, as shown schematically in Figure 1.
Figure 1: Schematic drawing of HST2 in straight through mode operation
Two pressure transducers (supplied by PCB Piezotronics, model number - H113A24, sensitivity- 5mV=psi) were mounted flush with the inner wall of the shock tube at 4cm and 42cm from the paper diaphragm station to monitor the passage of the primary shock wave and the subsequent pressure rise. The primary shock wave, after breaking the paper diaphragm, passes through the expanding part of the nozzle followed by the contact surface. The arrival of the contact surface terminates the constant reservoir conditions for the nozzle and thus limits the test time. Figure 2 depicts a typical pressure record obtained
from these two sensors when the tunnel was operated in straight through mode. Data acquisition system was triggered when the primary shock wave passes through the sensor which is located closer to the paper diaphragm station. Since the pressure across the contact surface is constant, the arrival of contact surface, which marks the end of the nozzle reservoir conditions, can not be evaluated from the pressure history. The test time was evaluated by analyzing together the pressure history from the sensors mounted flush with the shock tube, the pressure history from the pitot probe and the schlieren images captured during the experiment. This is discussed in more detail in section IV.
Figure 2: Pressure history recorded from the sensors flush mounted in the driven section of the shock tube near the paper diaphragm
The typical freestream conditions for which the experiments were conducted for the present study are listed in Table 1. Table 1: Typical freestream flow conditions in HST2 straight through mode operation.
M1 [±0.81%] P1, kPa [±3.86%] T1, K [±3.63%] U1, m/s [±1.78%] ȡ (kg/m3) [±5.53%] Re1, (million/m) [±5.13%] H, (MJ/kg) [±3.54%]
5.62 2.094 145.94 1361 0.0499 6.77 1.07
III. Model Details Figure 3 shows the image of the model assembly, which consists of a wedge shape body to serve as the shock generator, a hemispherical body, and movable plates to allow changing the relative distance between the wedge tip and hemispherical body. The diameter of the hemispherical body is 50mm and the wedge angle is 25 . The width of the
shock generator being 100mm. The complete model assembly was mounted in the test section via a cylindrical sting.
Figure 3: Image of complete model assembly
To measure the surface convective heat transfer rates, a slot was cut out from the hemispherical body to mount the MACOR piece, on which Platinum thin films were hand painted. Figure 4 shows the schematic drawing of the hemispherical body. The MACOR piece was cut and shaped accordingly to fit in the slot available on the hemispherical body. Initially 11 thin films were hand painted on the MACOR surface (s/R = 0; ±0.26; ±0.52; ±0.78; ±1.04; ±1.30): To increase the spatial resolution of the surface convective heat transfer measurements, another similar MACOR piece was cut and 10 number of Platinum thin films were painted on its surface (s/R = ±0.13; ±0.39; ±0.65; ±0.914; ±1.17); giving in total 21 discrete location on the surface of the hemispherical body for heat flux measurement. Separate experimental runs were taken under same conditions for models housing different MACOR pieces and the data obtained was analysed together. Figure 5 shows the image of MACOR cut pieces with the Platinum thin films painted on its surface.
Figure 4: Schematic drawing of the hemispherical body with the slots to mount heat transfer gauges
IV. Test Time Evaluation The pitot pressure record serves as the useful measurement to estimate the test time for the experiments in shock tunnels. The experiments in the present study were conducted in the straight
s/R = 0; ±0.26; ±0.52; ±0.78; ±1.04; ±1.30
s/R = ±0.13; ±0.39; ±0.65; ±0.914; ±1.17
Figure 5: Image of MACOR piece with Platinum thin film painted on it
through mode operation of the shock tunnel, where the constant reservoir conditions are terminated by the arrival of the contact surface. In this section, schlieren images captured during the experiment along with the measured reservoir pressure time history and the pitot pressure time history are analyzed to estimate the test time. It is observed that the test time available for the useful measurements depends on the nature of the flowfield around the model. For the current discussion, Edney Type-I interaction is considered as a template case to highlight the importance of more than one diagnostic technique in marking the test time duration. The discussion on the useful test time for the Edney TypeIII and Edney Type-IV interaction is presented, respectively, in sections VI and VII. Figure 6 presents the time history of the pitot pressure recorded using a pitot probe in the test section. The schlieren images were captured using high speed camera Phantom v310, at 40,000 fps and at exposure time of 10 μs and presented in Figure 7. Following Figure 7, along with the pitot pressure history, the duration of transient phenomenon in the tunnel, the establishment and duration of usable test time, and the end of the test time can be
identified. It can be seen that though the pitot pressure starts to build up at 2500 μs, the shock wave appearance, and hence the identification of arrival of the flow, occurs at 2550 μs in the schlieren images. This lag owes to the sensitivity of the schlieren system. Thereafter, from the schlieren images, intensity of the shock wave changes till 2900 μs, which corresponds to the establishment of the flow in the test section. This is also supported by the rising
Figure 6: Pressure history from the pitot probe mounted in the test section
pressure in the pitot pressure signal. From 2900 μs to 3175 μs, small pieces of the paper from the ruptured paper diaphragm are seen in the schlieren images. Also, although the evidence of the paper pieces in the test section is seen for approximately 275 μs, the flowfield is not disturbed because of the the paper diaphragm for this particular run. The pitot pressure also attains a stable value at around 3000 μs. After this, the shock structures in the schlieren images and hence the flowfiled are steady till approximately 3575 μs. Beyond 3575 μs, pitot pressure also observes a change in the value, indicating the end of the test time.
To further support this idea, pixel intensity scan was done using MATLAB on schlieren images to quantify the distance of the shock wave from the body along the line of the scan. The body diameter was taken as the reference length to estimate the pixel length. Figure 8 shows a single schlieren image, for which the pixel intensity scan was done along the centerline and the result is shown in the same figure. Similar intensity scans were performed for all images captured during a particular experiment and the result is presented in Figure 9 for three different experiments for Edney Type-I interaction. The figure also highlights the experiment to experiment variations. It can be seen from Figure 9 that the distance of the shock wave from the body increases till 2900 μs, which constitutes the flow establishment time in the tunnel test section around the model for configuration of Edney Type-I interaction. For both, Run 1 and Run 2, the distance between the shock wave and the body comes to realize a constant value at 2900 μs. In accordance with the pitot pressure history presented in Figure 6, the test time is terminated at around 3575 μs, where the recorded pitot pressure also observes a change.
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Figure 7: Schlieren images for Edney Type-I interaction
(a) Schlieren image
(b) Pixel intensity scan along the centreline of the hemispherical body Figure 8: Edney Type-I interaction
Figure 9: Distance of shock wave from the body along the centerline
This also helps understand that pitot pressure signal is better marker for the end of the test time rather than the beginning of the test time as the duration of pitot rise is a function of the pitot probe’s cavity design and dimension. The uniform flow might be realized well before a cavity based pitot probe equilibrates to steady pressure value. Based on the above arguments, the test time is considered begining at 2900 μs, corresponding to the time when the schlieren images observes a constant shock position, to 3575 μs, consisting of 675 μs of useful test time. Next, to confirm the stability of shock structure and thus the flowfield in the duration evaluated above, the pixel intensity scan was done through several lines running horizontally through the schlieren image as shown in Figure 10. The body diameter was taken as the reference length to estimate the pixel length and the results are presented in Figure 11, where the ‘y’ location mentioned in the caption corresponds to the line running horizontally and whose location is as given in Figure 10. The results are presented for the duration of 675 μs observed as the test time in the previous discussion, beginning from 2900 μs and ending at 3575 μs.
Figure 10: Schlieren image for Edney Type-I showing multiple lines across which intensity scan was performed
Following through Figure 11, though run to run variation is evident, the distance between the shock wave and the hemispherical body do not vary more than one pixel value for any experiment. This is true for the results of intensity scan for all the lines considered, which suggests the stable flowfield features during the test time evaluated.
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Figure 11: Shock wave distance from the body for Edney Type-I interaction
V. Heat Transfer Rate Measurements The thin film Platinum technique was used to measure the surface convective heat transfer rates on the surface of the hemispherical body. A thin film of Platinum was hand painted on the MACOR substrate. The small test times in the shock tunnels allows the assumption for infinite insulation, even for small depths of the substrate[15]. In Figure 12 , region 1 is Platinum thin film of thickness L, and region 2 is MACOR substrate acting as a semiinfinite slab. Applying one-dimensional unsteady heat conduction theory, and following the analysis of Vidal[16] , a general solution for the heat transfer rate can be obtained as in equation 1.
Figure 12: Schematic drawing showing the use of thin film on MACOR substrate
q (t ) =
β παE f
ª E (t ) « t + ¬
t
1 2
³ 0
E ( t ) − E (τ ) ( t −τ ) ( 3 / 2 )
º » ¼
(1)
where, ȕ is the backing material property defined as
β = kρC P and Į is the temperature coefficient of resistance for the platinum thin film. E(f) is the initial voltage across the thin film and E(t) is the voltage across the thin film at any time ‘t’. The numerical procedure given by Cook and Felderman[17], is used to evaluate the right hand side of equation 1. The initial voltage E(f) is measured before every experiment. The
temperature coefficient of resistance of Platinum, ‘Į’ is calibrated using the oil bath technique. For the present study, the ‘Į’ calibration was done for one gauge and the value of 7X10-4 C-1 was calculated which was used throughout the calculations. The procedure
for obtaining the gauge backing material ȕ is described in detail by Srinivasa[18]. A value of 2200Ws1/2m-2K-1 was determined in the above mentioned work and was used for the present study. Uncertainty in Heat Transfer Rate Measurements The uncertainty analysis was carried out based on the standard method given by Moffat[19]. If Y is a derived quantity which is dependent on several independent variable ࢥ1, ࢥ2, ࢥ3, …, ࢥn, then the uncertainty attributed to Y by the uncertainty in the variable ࢥi is given by :
δYi = ∂∂φY δφi i
(2)
The total uncertainty in the parameter Y is given by square root of sum of squares of each
δ Yi,
δYi =
n
2 ( δ Y ) ¦ i =1
(3)
The errors involved in the measurement of heat transfer rates are, • Error in the output of data acquisition system, including the error in reading the signal is estimated to be ±3.15%. • Error in the measurement of the temperature coefficient of resistance of platinum thin film gauges is ±2.5%. • Error in the measurement of gauge backing material property is ±3.7%. • Error in the measurement of initial voltage for each gauge before the experiment is ±1%. • Error in amplification factor used for the measurement is ±1%.
Total uncertainty = ± 3.15 2 + 2.52 + 3.7 2 + 12 + 12 ≈ ±5.65 ο ο The above methodology is demonstrated by considering the nose point of the hemispherical body in the presence of the simple Edney Type-I interaction, and the results are presented in Figure 13. The raw voltage signal acquired from data acquisition system is filtered and then numerically integrated following the procedure given by Cook and Felderman[17]. The limits of integration are chosen such that it includes the test time. From the plot, showing the raw signal in Figure 13, it can be seen that the rise in voltage starts near 2500 μs, complementing the observations from the pitot measurement.
raw voltage signal acquired from data
filter voltage signal acquired from data
acquisition system
acquisition system
integrated heat flux signal obtained from processing the filtered voltage signal Figure 13: Heat transfer signal for Edney Type-I interaction for a gauge located at s/R = 0
VI. Discussion on Edney Type-III Interaction Edney Type-III interaction pattern appears when the interaction between the bow shock due to the hemispherical body and the planar shock from the wedge is within the sonic circle in front of the body and such that the interaction is between the shock waves of the opposite family. The schematic drawing of such interaction along with the schlieren image captured during this study is presented in Figure 14. A shock wave S1 from the shock generator hits the lower half of the sonic circle, which forms the shock wave S2 , at the point TP1. The flow downstream of the shock wave S2 is subsonic while the flow downstream of the shock wave S1 is supersonic. The flow in region 1 and region 2 are made compatible by the presence of a transmitted shock wave T1 . The freestream flow which goes through a shock system of shock wave S1 and T1 has the same velocity direction and pressure as the freestream which goes through the strong part of the bow shock wave near the vicinity of the triple point TP1 . This type of interaction occurs very close to the body surface and near the centerline. In the cases when the slip line hits the body surface, the supersonic flow which forms one side of the slipline, see a turning of the geometry and another shock wave appears at surface to turn the supersonic flow in the region 3 parallel to the surface.
(a) Schematic drawing of Edney Type-III interaction
(b) Schlieren image of Edney Type-III interaction
Figure 14: Edney Type-III interaction
The schlieren images from two different experiments conducted for the configuration of Edney Type-III interaction are presented in Figure 15 and Figure 16. The images are presented for the test time as evaluated in section IV.
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Figure 15: Schlieren images for Edney Type-III interaction; Run-1
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Figure 16: Schlieren images for Edney Type-III interaction; Run-2
The pixel intensity scan was performed along the horizontal line passing through the nose of the hemispherical body for all the images obtained during the two experiments and the result is presented in Figure 17. The plot reveals lengthier time duration associated with the initial transient phenomenon involved for the Edney Type-III flowfield when compared with that of Edney Type-I flowfield, as presented in Figure 9.
Figure 17: Distance of shock wave from the body along the centerline
Further, to investigate the steadiness of the flow features during the test time, the pixel intensity scans were performed along the multiple lines as shown in Figure 18 and the results are presented in Figure 19. As in the previous case, body diameter was taken as the reference length to estimate the pixel length.
Figure 18: Schlieren image for Edney Type-III showing multiple lines across which intensity scan was performed
From Figure 19, it can be observed that unlike Edney Type-I interaction, where the shock distance from the body stabilizes at the beginning of the test time, for Edney Type-III interaction, the shock wave distance keeps on varying for first 200 μs of the test time. Also, the part of the bow shock wave lying above the centerline is relatively stable. The results of the intensity scans for the lines, y = -5mm; -10mm; -15mm; -20mm, show the fluctuation, though, no orderly or repeated pattern in the fluctuation is observed. The result for line y = -20mm, which lies very close to the triple point show large fluctuation for the case of RUN-2 because of the paper pieces flying through the images close to the area of interest as seen from the schlieren images in Fig. 16. Figure 20 show the hemispherical body with the location of heat transfer gauges along the surface. The s/R location of the gauges is taken positive in the clockwise sense from the centerline. The image reveals the shear layer emanating from the triple point to hit the body surface at the bottom half. Owing to the spatial resolution available, the exact location of the impact of shear layer on the surface can not be determined. The shear layer when reaches the body surface is diffused in space and a reflection off the surface in form of compression waves is seen, which leads to a shock wave at some distance away from the surface. The diffused shear layer impact on the body and the reflection from the surface can be seen from the image to happen in the vicinity of the gauges located at y = -0.78; -0.914; -1.04. Heat flux data, following the methodology described in section V, give additional insight into the flowfield for the Type-III interaction case. The gauge located at s=R = -1.04 is considered and the voltage signal obtained and heat flux deduced is presented in Figure 21, for the duration of 675 μs (as discussed in section IV), which form the test time including the transient phenomenon related to the establishment time for Type-III interaction. The variation in the heat flux is noticed, with the heat flux rising initially, reaching a stable value for about 100 μs, droping to a lower value and then rising again to reach the maximum recorded heat flux at the end of the available test time. Similar observations were made for the gauges located at y = -0.914; -0.78. These observations lead to argue that the shear layer impact on the body produces non-steady heat flux in the vicinity of the impact. Figure 18 and 19 then indicates that the shear layer unsteadiness also affects the upstream bow shock wave but the effect is limited on the bottom half of the shock wave, close to the triple point of the interaction. Figure 22 presents the normalized heat transfer rate distribution on the surface of the hemispherical body for Type-III interaction. The data was normalized by the heat flux
obtained (not presented here) at the centerpoint of body in the absence of shock interaction. The gauges located at y = -1.04; -0.914; -0.78 are marked with two values of heat flux, corresponding to the value obtained in the beginning of the test time and the maximum value obtained during the test time. The maximum heat transfer recorded was obtained at y = -0.914, rising as high as 7 times the undisturbed flow.
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Figure 19: Shock wave distance from the body for Edney Type-III interaction
Figure 20: Schlieren image
raw voltage signal acquired from data
filter voltage signal acquired from data
acquisition system
acquisition system
integrated heat flux signal obtained from processing the filtered voltage signal Figure 21: Heat transfer signal for Edney Type-III interaction for a gauge located at s/R = -1.04
Figure 22: Surface Heat transfer rate distribution for Edney Type-III interaction
VII. Discussion on Edney Type-IV Interaction Edney Type-IV interaction is another shock interaction pattern which appears when the planar shock wave hits the bow shock wave within the sonic circle. Edney Type-IV interaction pattern is not very different from Edney Type-III interaction pattern. Considering Figure 14, where a shock wave S3 is reflected off the solid wall so as to turn the supersonic flow in region 3. When the shock wave S1 moves higher and higher along the bow shock wave S2 , the strength of the shock waves S2 and T1 keeps on increasing and the Mach number in region 3 keeps on decreasing. A situation arises when the supersonic flow in region 3 can no longer turn through the solid wall as the turning required exceeds the maximum deflection limit, the Edney Type-IV configuration appears. The flowfield is depicted in the schematic drawing presented in Figure 23. The interaction is characterized by the presence of a supersonic jet sandwiched between two subsonic flow regions and marked with a series of compression and expansion waves.
(a) Schematic drawing of Edney Type-IV
(b) Schlieren image of Edney Type-IV
interaction
interaction Figure 23: Edney Type-IV interaction
The schlieren images for two different experiments conducted for the configuration of Edney Type-IV interaction are presented in Figure 24 and Figure 25. The images are presented for the test time as evaluated using the schlieren images for Edney Type-I configuration and the pitot pressure record following the discussion in section IV.
(t=2900 μs)
(t=2925 μs)
(t=2950 μs)
(t=2975 μs)
(t=3000 μs)
(t=3025 μs)
(t=3050 μs)
(t=3100 μs)
(t=3150 μs)
(t=3200 μs)
(t=3250 μs)
(t=3350 μs)
(t=3450 μs)
(t=3550 μs)
Figure 24: Schlieren images for Edney Type-IV interaction; Run-1
(t=2900 μs)
(t=2925 μs)
(t=2950 μs)
(t=2975 μs)
(t=3000 μs)
(t=3025 μs)
(t=3050 μs)
(t=3100 μs)
(t=3150 μs)
(t=3200 μs)
(t=3250 μs)
(t=3350 μs)
(t=3450 μs)
(t=3550 μs)
Figure 25: Schlieren images for Edney Type-IV interaction; Run-2
The pixel intensity scan was performed along the horizontal line passing through the nose of the hemispherical body for all the images captured during the two experiments and the result is presented in Figure 26. The plot reveals that unlike the Edney Type-I or Edney Type-III interaction discussed previously, the distance between the shock wave and the hemispherical body fluctuates for the large part of the test time. Multiple such scans were performed along various lines as shown in Figure 27 and the result is presented in Figure 28. As in previous case hemispherical body diameter was taken as the reference length to estimate the pixel length.
Figure 26: Distance of shock wave from the body along the centerline
Figure 27: Schlieren image for Edney Type-IV showing multiple lines across which intensity scan was performed
From Figure 28, it can be seen that the some part of the test time is disturbed because of the passage of the paper pieces, as seen from the frames for 3000 μs to 3150 μs for RUN 1 in Figure 24 and from frames for 3025 μs to 3250 μs for RUN 2 in Figure 25. In both the experiments, the part of the shock wave lying above the centerline is alone disturbed due to the paper pieces. Figure 28 presents the distance of the oblique shock wave and the part of bow shock above the interaction point, from the hemispherical body, and this distance fluctuates for all the lines for which the intensity scan was performed. During the scan, the distance of the transmitted curved shock from the second triple point was also extracted and plotted in Figure 29. It can be seen that unlike the oblique shock wave, there is no evident fluctuation in the distance of the transmitted shock wave. From this one can argue that the lower side shear layer of the supersonic jet is more stable as compared to observed by Chu and Lu[14]. The supersonic jet emanating from the interaction point can be seen to impact on the hemispherical body in vicinity of the gauges located at s/R = -0.13; -0.26, from Figure 30. The voltage signal acquired for the gauge located at s/R = -0.26 and the heat flux deduced, following the methodology described in section V, is presented in Figure 31. From Figure 28 and Figure 31, arguments can be made about the unsteady nature of the supersonic jet emanating from the Type-IV interaction. Similar observations were made for the gauges located at s/R = -0.13; -0.39; -0.52; -0.65. Figure 32 presents the normalized
heat transfer rate on the surface of the hemispherical body for Type-IV interaction. The data is presented in similar way as for Type-III interaction case, by normalizing using the heat flux (not shown here) obtained at the centerpoint of the body in the absence of the shock interaction. The gauges located at s/R = -0.13; -0.26; -0.39; -0.52; -0.65, are marked with two values of heat flux corresponding to the value obtained at the beginning of the test time and the maximum value obtained during the test time. The maximum heat transfer was recorded for the gauge location s/R = -0.52, reaching 10 times that of undisturbed flow case.
(y = +5mm)
(y = -5mm)
(y = +10mm)
(y = -10mm)
(y = +15mm)
(y = -15mm)
(y = +20mm)
(y = -20mm)
Figure 28: Shock wave distance from the body for Edney Type-IV interaction
(y = -10mm)
(y = -15mm)
(y = -20mm) Figure 29: Shock wave distance from the body for Edney Type-IV interaction
Figure 30: Schlieren image
raw voltage signal acquired from data acquisition system
filter voltage signal acquired from data acquisition system
integrated heat flux signal obtained from processing the filtered voltage signal Figure 31: Heat transfer signal for Edney Type-IV interaction for a gauge located at s/R = -0:26
Figure 32: Surface Heat transfer rate distribution for Edney Type-IV interaction
VIII. Conclusions In the present work, the Edney Type-III and Edney Type-IV interactions were considered by performing experiments in a moderate enthalpy condition using a conventional shock tunnel operated in straight through mode. The short test time available in shock tunnel was critically examined and rigorous analysis was performed to evaluate the useful test time. The importance of two diagnostic technique(pitot pressure time history and schlieren visualization), to estimate the test time was discussed and applied. It was observed that the useful test time varies from Edney Type-I configuration, which is considered as a template case for the comparison, to Edney Type-III and Edney Type-IV configuration, highlighting that the initial transient processes depend on the model configuration and care should be taken in generalizing the test time in shock tunnel for a given condition. The unsteady nature of Edney Type-III and Edney Type-IV interactions was discussed in
detail, by capturing schlieren images at high frequency of 40,000 frames per second and these results were collaborated with surface convective heat transfer rates measured at 21 discrete points on the hemispherical body surface. It was found that the shear layer reattachment on the hemispherical body, present in Edney Type-III case, leads to local unsteadiness in the flowfield. This was seen both in the quantitative information brought out by performing pixel intensity scan through various lines and the time history of the heat transfer rate signals in the vicinity of the shear layer impact. Similar trends were observed in the Edney Type-IV configuration, where the non-steady nature was seen locally at the location of supersonic jet impingement. The schlieren images and the heat transfer rates, for both the cases studied, does not shed light on the pattern or cyclic trend of the non-steady behavior observed. This might owe to the low test times available with the conventional shock tunnels, and need further investigation, for example, in the tailored shock tunnel condition. Finally, the heat transfer rates on the hemispherical body surface were quantified in the case of both Edney Type-III and Edney Type-IV interaction. It was seen that for Edney Type-III interaction the peak heating near the interaction region increases upto seven times that obtained at the nose point of body for Edney Type-I interaction. For Edney Type-IV interaction, the peak heat transfer rate obtained was ten times that obtained at the nose point of body for Edney Type-I interaction. Present work provides the experimental evidence of the unsteady/non-steady nature inherent to the shock-shock interaction phenomenon, when the interaction happens within the sonic circle in front of the blunt body. In the available test time, a repeated or cyclic trend in the temporal variation of the measured quantities was not observed, which hint towards the low frequency associated with the unsteadiness, which strays away from the existing numerical study on the subject where oscillation frequencies as high as 30 kHz are reported.
Funding/Acknowledgement This work was supported by Defence Research and Development Organization (grant number DRDO\IISC-GJ622)
References [1] Edney, B., “Effects of shock impingement on the heat transfer around blunt bodies,” AIAA Journal, Vol 6, No. 1, 1968. [2] Hains, F. D., and Keyes, J. W., “Shock interference heating in hypersonic flws,” AIAA Journal, Vol. 10, No. 11, 1972. [3] Borovoy, V. Ya., Chinilov, Yu., Gusev, V. N., Stuminskaya, I. V., Délery, J., Chanetz, B., “Interference between a cylindrical bow shock and a plane oblique shock,” AIAA Journal, Vol 35, No. 11, 1997. [4] Boldyrev, S. M., Borovoy, V. Ya., Chinilov, Yu., Gusev, V. N., Krutiy, S. N., Stuminskaya, I. V., Yakovleva, L. V., Délery, J., Chanetz, B., “A thourough experimental investigation of shock/shock interferences in high speed flows,” Aerospace Science and technology, 5, 2001. [5] Wieting, A. R., Holden, M. S., “Experimental shock-wave interference heating on a cylinder at Mach 6 and 8,” AIAA Journal, Vol. 27, No. 11, 1989. [6] Holden, M. S., “Special course on three dimensional supersonic/hypersonic flows including separation,” AIAA Journal, Vol. 27, No. 11, 1989. [7] Sanderson, S.R., "Shock wave interactions in hypervelocity flows", PhD Thesis, California Institute of Technology, 1995. [8] Grasso, F., Purpura, C., Chanetz, B., Délery, J., “Type III and Type IV shock/shock interferences: theoretical and experimental aspects,” Aerospace Science and technology, 7, 2003. [9] Riabov, V.V., Botin, A.V., “Numerical and experimental studies of shock interference in hypersonic flows near a cylinder,” 26th International Congress of the Aeronautical Sciences, 2008 [10] Xiao, F., Li, Z., Zhu, Y., Yang, J., “Experimental and numerical study of hypersonic type-IV shock interaction on blunt body with forward facing cavity ,” 20th AIAA International Space Planes and Hypersonic Systems and Technologies Conferences, 2015. [11] Gaitonde, G., Shang, J. S., “On the structure of unsteady Type-IV interaction at Mach 8,” Computers and Fluids, Vol. 24, No. 4, 1995. [12] Lind, C. A., and Lewis, M. J., “Computational analysis of unsteady Type-IV shock interaction of blunt body flows,” Journal of Propulsion and Power, Vol. 12, No. 1, 1996.
[13] Yamamoto, S., Kano, S., and Daiguji, H., “An efficient CFD approach for simulating unsteady hypersonic shock-shock interference flows,” Computers and Fluids, Vol. 27, No. 5-6, 1998. [14] Chu, Y. B., and Lu, X. Y., “Characteristics of unsteady Type-IV shock/shock interaction,” Shock Waves, Vol. 22, 2012. [15] Schultz, D. L. and Jones, T. V., “Heat transfer measurements in short duration hypersonic facilities,” AGARD-AG-165, 1973. [16] Vidal, R. J., “Model instrumentation technique for heat transfer and force measurements in a hypersonic shock tunnel,” Cornell Aerospace Laboratory Report, WADC TN, 1956. [17] Cook, W. J. and Felderman, E. J., “Reduction of data from thin film heat transfer gauge - a concise numerical technique,” AIAA Journal, Vol. 3, No. 4, 1966. [18] Srinivasa, P., “Experimental investigations of hypersonic flow over a bulbous heat shield at Mach number of 6.,” Ph.D. Thesis, Indian Institute of Science, 1991. [19] Moffat, R. J., “Describing the uncertainties in experimental results,” Experimental Thermal and Fluid sciences, Vol. 1, No. 3, 1988.
Abhishek Khatta, Gopalan Jagadeesh
PII: DOI: Reference:
S1270-9638(17)30855-6 https://doi.org/10.1016/j.ast.2017.11.001 AESCTE 4276
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Aerospace Science and Technology
Received date: Revised date: Accepted date:
12 May 2017 24 October 2017 1 November 2017
Please cite this article in press as: A. Khatta, G. Jagadeesh, Hypersonic shock tunnel studies of Edney Type III and IV shock interactions, Aerosp. Sci. Technol. (2017), https://doi.org/10.1016/j.ast.2017.11.001
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Hypersonic Shock Tunnel Studies of Edney Type III and IV Shock Interactions Abhishek Khatta1 and Gopalan Jagadeesh2 Indian Institute of Science, Bangalore, India – 560012 Of all the possible outcomes of the shock interaction problem, Edney Type-III and Type-IV are considered to be of great importance as they lead to high heat transfer rates on the surface in the vicinity of the interaction. The enhancement in heat transfer occurs because of shear layer attachment in Type-III interaction and impingement of supersonic jet in Type-IV interaction. In this study, unsteady nature of these interactions is studied in conventional shock tunnel at moderate enthalpy condition of 1.07 Mj/kg at flow Mach number of 5.62. A hemispherical model, 50mm in diameter, mounted with thin film Platinum gauges is used along with a 25 wedge to serve as a shock generator. The schlieren images are captured along with the surface convective heat transfer rate measurements for the analysis of flowfield over the model during the test time. The pixel intensity scan is performed along several lines running horizontally to estimate the steadiness of the flowfield. These are correlated with the heat transfer rate measurements to understand the nonsteady nature of the interaction during the small test times offered by the shock tunnel.
1
Research Scholar, Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012
2
Professor, Department of Aerospace Engineering, Indian Institute of Science, Bangalore - 560012
Nomenclature H = stagnation enthalpy, MJ/kg Mࡅ = freestream Mach number Pࡅ = static pressure, kPa R = radius of hemispherical body, m Reࡅ = freestream Reynolds number, /m s = distance along the surface, mm Tࡅ = freestream static temperature, K Uࡅ = freestream velocity, m/s ͳࡅ = freestream density, kg/m3 q = heat transfer rate, W/cm2 ͣ = thermal coefficient of resistance of thin film gauge, C ࡁ1
ͤ = thermal coefficient of resistance of thin film gauge, Ws1/2 /m2K k = thermal conductivity, W/m/K CP = specific heat ratio at constant pressure, J/kg/K E = voltage, V t, Ͷ = time, s x = streamwise coordinate y = normal coordinate Y = derived parameter ࢥ
= independent parameter
I. Introduction Any supersonic flow is accompanied by the shock waves, appearing due to the presence of an obstruction in the path of the flow or due to need to turn the flow. These shock waves when generated from many different obstructions, as in from fin and tail and fore-body of a full scale vehicle, end up interacting with each other, thereby modifying the aerodynamic characteristics of the vehicle. Such inevitability of shock-shock interactions in high speed flows motivates the researchers around the globe to study these phenomenon to better understand the causes and the repercussions of such interactions, leading to the better design of the flight vehicle. The shock-shock interaction problem deals with the observed elevated pressure and heat transfer rates on the surface in close proximity of such interactions. The first detailed experimental analysis of such problem owes to the work of Edney[1], where the surface heat transfer rates were measured using thin film technique and elevated heat flux obtained on the spherical shaped body in the region where an external shock wave interacts with the bow shock wave. Edney[1] conducted experiments in a hypersonic wind tunnel and used spark visualization technique to capture the shock features and this formed the basis of classification of such interactions for all further studies on the problem. The classified interaction patterns are known as Edney Type-I, Edney Type-II, Edney Type-III, Edney Type-IV, Edney Type-V, Edney Type-VI. In his work, the model was injected in the test section and thus the time history of heat flux at a single location for a given configuration was not provided. The classification of such interactions by Edney led to a systematic study on such phenomenon. The later researchers, Hains and Keyes[2], Borovoy et al.[3], Boldyrev et al.[4], investigated the effect of impinging shock strength, body shape, flow Mach number on the amplification obtained in heat transfer rates. It was noticed that the configurations that produce Edney Type-III and Edney Type-IV interactions lead to severe heat transfer rates on the surface of the hemispherical body. Yet, in many experimental work, the temporal variation of heat transfer rates was not discussed and hence the unsteady nature of such interactions was not analyzed. Experiments conducted by Wieting and Holden[5] and Holden[6] revealed some oscillations in the measured quantities for Edney Type-IV interaction and suggested that the nature of such interactions is unsteady within the frequency range of 3 to 10 kHz. Sanderson[7] conducted experiments in a Free Piston Driven Shock Tunnel to study the effect of enthalpy on the heat transfer rates on the blunt body in the presence of interactions and observed unsteadiness in the supersonic jet existing in the Edney Type-
IV interaction. Grasso et al.[8], in their experimental work in R3Ch hypersonic wind tunnel at ONERA focussed on Edney Type-III and Type-IV interactions, with the motive to study the effect of shock impingement location. In the available test time of approximately 10 seconds, the authors observed the change in the supersonic jet from being near normal to the cylinder surface in the beginning of the test time to the jet being curved in space in the later half of test time. Also, the authors conducted some experiments to study hysteresis phenomenon associated with shock interactions. The shock generator was moved continuously with respect to the cylinder and the path was later traced back. It was observed that the pressure values on the surface were not much sensitive to the path followed by the shock generator but the heat transfer values did not come to the same level when the shock generator was traced back on its path. This shed new light and opened many avenues to further study these phenomenon. Riabov et al.[9] performed experimental and numerical investigation of shock impingement flowfields in rarefied environment and concluded that the Type-IV interaction seen in the continuum flow was absent. The results were presented in the form of Stanton number distribution over the surface for various interaction types, but the question of unsteadiness in the observed interactions was left unanswered. Recently, Xiao et al.[10] investigated, both experimentally and numerically, the effect of forward facing step at the stagnation point in the presence of Type-IV interaction. The researcher used a reflected mode shock tunnel at the University of Science and Technology, China, for the experiments and reported that the flow was either steady or unsteady, depending on the location of the impingement of supersonic jet. In case of the unsteady flowfield, they observed a forward and backward motion oscillation and a up and down motion oscillation, both occurring at different frequencies. The unsteadiness in the Edney Type-IV configuration is associated with the supersonic jet which lies very close to the body within the shock layer, and thus it becomes difficult to analyze such phenomenon experimentally, given the sensitivity and the resolution of the experimental equipment. To understand the unsteady nature of the shock-shock interaction phenomenon, many researchers approached the problem through numerical simulation and have over the time added to the understanding of the underlying physics dominating these interactions. Gaitonde and Shang[11] investigated the unsteady nature of Type-IV interaction and focussed on the changes in the structure of the supersonic jet during the limit cycle and estimated the oscillating frequency to be about 30 kHz. The author noticed that during each cycle, the jet exhibits two different configuration, with the jet shock being near normal to the cylinder in one and being parallel in the other. Lind and Lewis[12] performed numerical simulation considering the laminar flow to
understand the unsteadiness of the Type-IV supersonic jet. The authors observed that by changing the impinging shock angle from 18 degree to 19 degree, the supersonic jet tends from a steady to unsteady state. The unsteadiness was characterized by the pressure fluctuation on the model surface with the frequency of oscillation estimated at 1.38 kHz. The authors also commented that by changing the grid resolution, the estimated frequency changed to a higher value of 1.45 kHz. Yamamoto et al.[13] conducted high order numerical simulation for the Type-IV interaction and found that the oscillation in the supersonic jet leads to the unsteady disturbance of the supersonic shear layer and the whole phenomenon leads to the time varying heat transfer and pressure loading on the surface. Chu and Lu[14] solved Navier Stokes Equation with higher order numerical methods for Edney Type-IV interaction. The work focussed on the relationship between the termination jet shock wave with the shear layer instabilities and concluding with proposing a feedback mechanism. It has been noted that though several experimental studies have been devoted to the quantification of high heat transfer rates on the blunt body in the presence of shock-shock interactions, few studies have analyzed the unsteady nature of such interactions. Also, it is evident from the literature that these amplifications are sensitive to many parameters such as impinging shock location, impinging shock strength, body shape and size, freestream flow Mach number and Reynolds number, a unified theory to address the amplification is as of now difficult to put in place. The numerical simulations which have addressed the unsteady nature and the limited experimental studies which analyzed the unsteadiness bring about the oscillation frequency to be within the range of 1 kHz to 30 kHz, which is a wide range and may depend on the factors discussed above. Though the unsteadiness is very evidentally observed experimentally for Edney Type-IV configuration, no such comments have been made for Edney Type-III configuration. In the present study, unsteady nature of Edney Type-III and Edney Type-IV interactions was targeted experimentally in conventional shock tunnel at moderate enthalpy condition. The schlieren images were captured along with the surface convective heat transfer measurements for the analysis of flowfield over the model during the test time. The pixel intensity scan was performed along several lines running horizontally to estimate the steadiness of the flowfield. These were correlated with the heat transfer rate measurements to understand the non-steady nature of the interaction during the small test times in the shock tunnel.
II. Experimental Facility The experiments were conducted in straight through mode Hypersonic Shock Tunnel-2 (HST-2) at Laboratory for Hypersonic and Shock wave Research (LHSR), IISc, Bangalore. The shock tunnel consists of 2m long driver section and 5.12m long driven section. A metal diaphragm was used to initially separate the driver and driven section. In straight through mode operation, the internal diameter of the shock tube is matched with the inlet of the conical nozzle. The conical nozzle then expands to the test section of dimension 300x300x450mm, as shown schematically in Figure 1.
Figure 1: Schematic drawing of HST2 in straight through mode operation
Two pressure transducers (supplied by PCB Piezotronics, model number - H113A24, sensitivity- 5mV=psi) were mounted flush with the inner wall of the shock tube at 4cm and 42cm from the paper diaphragm station to monitor the passage of the primary shock wave and the subsequent pressure rise. The primary shock wave, after breaking the paper diaphragm, passes through the expanding part of the nozzle followed by the contact surface. The arrival of the contact surface terminates the constant reservoir conditions for the nozzle and thus limits the test time. Figure 2 depicts a typical pressure record obtained
from these two sensors when the tunnel was operated in straight through mode. Data acquisition system was triggered when the primary shock wave passes through the sensor which is located closer to the paper diaphragm station. Since the pressure across the contact surface is constant, the arrival of contact surface, which marks the end of the nozzle reservoir conditions, can not be evaluated from the pressure history. The test time was evaluated by analyzing together the pressure history from the sensors mounted flush with the shock tube, the pressure history from the pitot probe and the schlieren images captured during the experiment. This is discussed in more detail in section IV.
Figure 2: Pressure history recorded from the sensors flush mounted in the driven section of the shock tube near the paper diaphragm
The typical freestream conditions for which the experiments were conducted for the present study are listed in Table 1. Table 1: Typical freestream flow conditions in HST2 straight through mode operation.
M1 [±0.81%] P1, kPa [±3.86%] T1, K [±3.63%] U1, m/s [±1.78%] ȡ (kg/m3) [±5.53%] Re1, (million/m) [±5.13%] H, (MJ/kg) [±3.54%]
5.62 2.094 145.94 1361 0.0499 6.77 1.07
III. Model Details Figure 3 shows the image of the model assembly, which consists of a wedge shape body to serve as the shock generator, a hemispherical body, and movable plates to allow changing the relative distance between the wedge tip and hemispherical body. The diameter of the hemispherical body is 50mm and the wedge angle is 25 . The width of the
shock generator being 100mm. The complete model assembly was mounted in the test section via a cylindrical sting.
Figure 3: Image of complete model assembly
To measure the surface convective heat transfer rates, a slot was cut out from the hemispherical body to mount the MACOR piece, on which Platinum thin films were hand painted. Figure 4 shows the schematic drawing of the hemispherical body. The MACOR piece was cut and shaped accordingly to fit in the slot available on the hemispherical body. Initially 11 thin films were hand painted on the MACOR surface (s/R = 0; ±0.26; ±0.52; ±0.78; ±1.04; ±1.30): To increase the spatial resolution of the surface convective heat transfer measurements, another similar MACOR piece was cut and 10 number of Platinum thin films were painted on its surface (s/R = ±0.13; ±0.39; ±0.65; ±0.914; ±1.17); giving in total 21 discrete location on the surface of the hemispherical body for heat flux measurement. Separate experimental runs were taken under same conditions for models housing different MACOR pieces and the data obtained was analysed together. Figure 5 shows the image of MACOR cut pieces with the Platinum thin films painted on its surface.
Figure 4: Schematic drawing of the hemispherical body with the slots to mount heat transfer gauges
IV. Test Time Evaluation The pitot pressure record serves as the useful measurement to estimate the test time for the experiments in shock tunnels. The experiments in the present study were conducted in the straight
s/R = 0; ±0.26; ±0.52; ±0.78; ±1.04; ±1.30
s/R = ±0.13; ±0.39; ±0.65; ±0.914; ±1.17
Figure 5: Image of MACOR piece with Platinum thin film painted on it
through mode operation of the shock tunnel, where the constant reservoir conditions are terminated by the arrival of the contact surface. In this section, schlieren images captured during the experiment along with the measured reservoir pressure time history and the pitot pressure time history are analyzed to estimate the test time. It is observed that the test time available for the useful measurements depends on the nature of the flowfield around the model. For the current discussion, Edney Type-I interaction is considered as a template case to highlight the importance of more than one diagnostic technique in marking the test time duration. The discussion on the useful test time for the Edney TypeIII and Edney Type-IV interaction is presented, respectively, in sections VI and VII. Figure 6 presents the time history of the pitot pressure recorded using a pitot probe in the test section. The schlieren images were captured using high speed camera Phantom v310, at 40,000 fps and at exposure time of 10 μs and presented in Figure 7. Following Figure 7, along with the pitot pressure history, the duration of transient phenomenon in the tunnel, the establishment and duration of usable test time, and the end of the test time can be
identified. It can be seen that though the pitot pressure starts to build up at 2500 μs, the shock wave appearance, and hence the identification of arrival of the flow, occurs at 2550 μs in the schlieren images. This lag owes to the sensitivity of the schlieren system. Thereafter, from the schlieren images, intensity of the shock wave changes till 2900 μs, which corresponds to the establishment of the flow in the test section. This is also supported by the rising
Figure 6: Pressure history from the pitot probe mounted in the test section
pressure in the pitot pressure signal. From 2900 μs to 3175 μs, small pieces of the paper from the ruptured paper diaphragm are seen in the schlieren images. Also, although the evidence of the paper pieces in the test section is seen for approximately 275 μs, the flowfield is not disturbed because of the the paper diaphragm for this particular run. The pitot pressure also attains a stable value at around 3000 μs. After this, the shock structures in the schlieren images and hence the flowfiled are steady till approximately 3575 μs. Beyond 3575 μs, pitot pressure also observes a change in the value, indicating the end of the test time.
To further support this idea, pixel intensity scan was done using MATLAB on schlieren images to quantify the distance of the shock wave from the body along the line of the scan. The body diameter was taken as the reference length to estimate the pixel length. Figure 8 shows a single schlieren image, for which the pixel intensity scan was done along the centerline and the result is shown in the same figure. Similar intensity scans were performed for all images captured during a particular experiment and the result is presented in Figure 9 for three different experiments for Edney Type-I interaction. The figure also highlights the experiment to experiment variations. It can be seen from Figure 9 that the distance of the shock wave from the body increases till 2900 μs, which constitutes the flow establishment time in the tunnel test section around the model for configuration of Edney Type-I interaction. For both, Run 1 and Run 2, the distance between the shock wave and the body comes to realize a constant value at 2900 μs. In accordance with the pitot pressure history presented in Figure 6, the test time is terminated at around 3575 μs, where the recorded pitot pressure also observes a change.
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Figure 7: Schlieren images for Edney Type-I interaction
(a) Schlieren image
(b) Pixel intensity scan along the centreline of the hemispherical body Figure 8: Edney Type-I interaction
Figure 9: Distance of shock wave from the body along the centerline
This also helps understand that pitot pressure signal is better marker for the end of the test time rather than the beginning of the test time as the duration of pitot rise is a function of the pitot probe’s cavity design and dimension. The uniform flow might be realized well before a cavity based pitot probe equilibrates to steady pressure value. Based on the above arguments, the test time is considered begining at 2900 μs, corresponding to the time when the schlieren images observes a constant shock position, to 3575 μs, consisting of 675 μs of useful test time. Next, to confirm the stability of shock structure and thus the flowfield in the duration evaluated above, the pixel intensity scan was done through several lines running horizontally through the schlieren image as shown in Figure 10. The body diameter was taken as the reference length to estimate the pixel length and the results are presented in Figure 11, where the ‘y’ location mentioned in the caption corresponds to the line running horizontally and whose location is as given in Figure 10. The results are presented for the duration of 675 μs observed as the test time in the previous discussion, beginning from 2900 μs and ending at 3575 μs.
Figure 10: Schlieren image for Edney Type-I showing multiple lines across which intensity scan was performed
Following through Figure 11, though run to run variation is evident, the distance between the shock wave and the hemispherical body do not vary more than one pixel value for any experiment. This is true for the results of intensity scan for all the lines considered, which suggests the stable flowfield features during the test time evaluated.
(y = +5mm)
(y = -5mm)
(y = +10 mm)
(y = -10 mm)
(y = +15 mm)
(y = -15 mm)
(y = +20 mm)
(y = -20 mm)
Figure 11: Shock wave distance from the body for Edney Type-I interaction
V. Heat Transfer Rate Measurements The thin film Platinum technique was used to measure the surface convective heat transfer rates on the surface of the hemispherical body. A thin film of Platinum was hand painted on the MACOR substrate. The small test times in the shock tunnels allows the assumption for infinite insulation, even for small depths of the substrate[15]. In Figure 12 , region 1 is Platinum thin film of thickness L, and region 2 is MACOR substrate acting as a semiinfinite slab. Applying one-dimensional unsteady heat conduction theory, and following the analysis of Vidal[16] , a general solution for the heat transfer rate can be obtained as in equation 1.
Figure 12: Schematic drawing showing the use of thin film on MACOR substrate
q (t ) =
β παE f
ª E (t ) « t + ¬
t
1 2
³ 0
E ( t ) − E (τ ) ( t −τ ) ( 3 / 2 )
º » ¼
(1)
where, ȕ is the backing material property defined as
β = kρC P and Į is the temperature coefficient of resistance for the platinum thin film. E(f) is the initial voltage across the thin film and E(t) is the voltage across the thin film at any time ‘t’. The numerical procedure given by Cook and Felderman[17], is used to evaluate the right hand side of equation 1. The initial voltage E(f) is measured before every experiment. The
temperature coefficient of resistance of Platinum, ‘Į’ is calibrated using the oil bath technique. For the present study, the ‘Į’ calibration was done for one gauge and the value of 7X10-4 C-1 was calculated which was used throughout the calculations. The procedure
for obtaining the gauge backing material ȕ is described in detail by Srinivasa[18]. A value of 2200Ws1/2m-2K-1 was determined in the above mentioned work and was used for the present study. Uncertainty in Heat Transfer Rate Measurements The uncertainty analysis was carried out based on the standard method given by Moffat[19]. If Y is a derived quantity which is dependent on several independent variable ࢥ1, ࢥ2, ࢥ3, …, ࢥn, then the uncertainty attributed to Y by the uncertainty in the variable ࢥi is given by :
δYi = ∂∂φY δφi i
(2)
The total uncertainty in the parameter Y is given by square root of sum of squares of each
δ Yi,
δYi =
n
2 ( δ Y ) ¦ i =1
(3)
The errors involved in the measurement of heat transfer rates are, • Error in the output of data acquisition system, including the error in reading the signal is estimated to be ±3.15%. • Error in the measurement of the temperature coefficient of resistance of platinum thin film gauges is ±2.5%. • Error in the measurement of gauge backing material property is ±3.7%. • Error in the measurement of initial voltage for each gauge before the experiment is ±1%. • Error in amplification factor used for the measurement is ±1%.
Total uncertainty = ± 3.15 2 + 2.52 + 3.7 2 + 12 + 12 ≈ ±5.65 ο ο The above methodology is demonstrated by considering the nose point of the hemispherical body in the presence of the simple Edney Type-I interaction, and the results are presented in Figure 13. The raw voltage signal acquired from data acquisition system is filtered and then numerically integrated following the procedure given by Cook and Felderman[17]. The limits of integration are chosen such that it includes the test time. From the plot, showing the raw signal in Figure 13, it can be seen that the rise in voltage starts near 2500 μs, complementing the observations from the pitot measurement.
raw voltage signal acquired from data
filter voltage signal acquired from data
acquisition system
acquisition system
integrated heat flux signal obtained from processing the filtered voltage signal Figure 13: Heat transfer signal for Edney Type-I interaction for a gauge located at s/R = 0
VI. Discussion on Edney Type-III Interaction Edney Type-III interaction pattern appears when the interaction between the bow shock due to the hemispherical body and the planar shock from the wedge is within the sonic circle in front of the body and such that the interaction is between the shock waves of the opposite family. The schematic drawing of such interaction along with the schlieren image captured during this study is presented in Figure 14. A shock wave S1 from the shock generator hits the lower half of the sonic circle, which forms the shock wave S2 , at the point TP1. The flow downstream of the shock wave S2 is subsonic while the flow downstream of the shock wave S1 is supersonic. The flow in region 1 and region 2 are made compatible by the presence of a transmitted shock wave T1 . The freestream flow which goes through a shock system of shock wave S1 and T1 has the same velocity direction and pressure as the freestream which goes through the strong part of the bow shock wave near the vicinity of the triple point TP1 . This type of interaction occurs very close to the body surface and near the centerline. In the cases when the slip line hits the body surface, the supersonic flow which forms one side of the slipline, see a turning of the geometry and another shock wave appears at surface to turn the supersonic flow in the region 3 parallel to the surface.
(a) Schematic drawing of Edney Type-III interaction
(b) Schlieren image of Edney Type-III interaction
Figure 14: Edney Type-III interaction
The schlieren images from two different experiments conducted for the configuration of Edney Type-III interaction are presented in Figure 15 and Figure 16. The images are presented for the test time as evaluated in section IV.
(t=2900 μs)
(t=2925 μs)
(t=2950 μs)
(t=2975 μs)
(t=3000 μs)
(t=3025 μs)
(t=3050 μs)
(t=3100 μs)
(t=3150 μs)
(t=3200 μs)
(t=3250 μs)
(t=3350 μs)
(t=3450 μs)
(t=3550 μs)
Figure 15: Schlieren images for Edney Type-III interaction; Run-1
(t=2900 μs)
(t=2925 μs)
(t=2950 μs)
(t=2975 μs)
(t=3000 μs)
(t=3025 μs)
(t=3050 μs)
(t=3100 μs)
(t=3150 μs)
(t=3200 μs)
(t=3250 μs)
(t=3350 μs)
(t=3450 μs)
(t=3550 μs)
Figure 16: Schlieren images for Edney Type-III interaction; Run-2
The pixel intensity scan was performed along the horizontal line passing through the nose of the hemispherical body for all the images obtained during the two experiments and the result is presented in Figure 17. The plot reveals lengthier time duration associated with the initial transient phenomenon involved for the Edney Type-III flowfield when compared with that of Edney Type-I flowfield, as presented in Figure 9.
Figure 17: Distance of shock wave from the body along the centerline
Further, to investigate the steadiness of the flow features during the test time, the pixel intensity scans were performed along the multiple lines as shown in Figure 18 and the results are presented in Figure 19. As in the previous case, body diameter was taken as the reference length to estimate the pixel length.
Figure 18: Schlieren image for Edney Type-III showing multiple lines across which intensity scan was performed
From Figure 19, it can be observed that unlike Edney Type-I interaction, where the shock distance from the body stabilizes at the beginning of the test time, for Edney Type-III interaction, the shock wave distance keeps on varying for first 200 μs of the test time. Also, the part of the bow shock wave lying above the centerline is relatively stable. The results of the intensity scans for the lines, y = -5mm; -10mm; -15mm; -20mm, show the fluctuation, though, no orderly or repeated pattern in the fluctuation is observed. The result for line y = -20mm, which lies very close to the triple point show large fluctuation for the case of RUN-2 because of the paper pieces flying through the images close to the area of interest as seen from the schlieren images in Fig. 16. Figure 20 show the hemispherical body with the location of heat transfer gauges along the surface. The s/R location of the gauges is taken positive in the clockwise sense from the centerline. The image reveals the shear layer emanating from the triple point to hit the body surface at the bottom half. Owing to the spatial resolution available, the exact location of the impact of shear layer on the surface can not be determined. The shear layer when reaches the body surface is diffused in space and a reflection off the surface in form of compression waves is seen, which leads to a shock wave at some distance away from the surface. The diffused shear layer impact on the body and the reflection from the surface can be seen from the image to happen in the vicinity of the gauges located at y = -0.78; -0.914; -1.04. Heat flux data, following the methodology described in section V, give additional insight into the flowfield for the Type-III interaction case. The gauge located at s=R = -1.04 is considered and the voltage signal obtained and heat flux deduced is presented in Figure 21, for the duration of 675 μs (as discussed in section IV), which form the test time including the transient phenomenon related to the establishment time for Type-III interaction. The variation in the heat flux is noticed, with the heat flux rising initially, reaching a stable value for about 100 μs, droping to a lower value and then rising again to reach the maximum recorded heat flux at the end of the available test time. Similar observations were made for the gauges located at y = -0.914; -0.78. These observations lead to argue that the shear layer impact on the body produces non-steady heat flux in the vicinity of the impact. Figure 18 and 19 then indicates that the shear layer unsteadiness also affects the upstream bow shock wave but the effect is limited on the bottom half of the shock wave, close to the triple point of the interaction. Figure 22 presents the normalized heat transfer rate distribution on the surface of the hemispherical body for Type-III interaction. The data was normalized by the heat flux
obtained (not presented here) at the centerpoint of body in the absence of shock interaction. The gauges located at y = -1.04; -0.914; -0.78 are marked with two values of heat flux, corresponding to the value obtained in the beginning of the test time and the maximum value obtained during the test time. The maximum heat transfer recorded was obtained at y = -0.914, rising as high as 7 times the undisturbed flow.
(y = +5mm)
(y = +10mm)
(y = +15mm)
(y = +20mm)
(y = -5mm)
(y = -10mm)
(y = -15mm)
(y = -20mm)
Figure 19: Shock wave distance from the body for Edney Type-III interaction
Figure 20: Schlieren image
raw voltage signal acquired from data
filter voltage signal acquired from data
acquisition system
acquisition system
integrated heat flux signal obtained from processing the filtered voltage signal Figure 21: Heat transfer signal for Edney Type-III interaction for a gauge located at s/R = -1.04
Figure 22: Surface Heat transfer rate distribution for Edney Type-III interaction
VII. Discussion on Edney Type-IV Interaction Edney Type-IV interaction is another shock interaction pattern which appears when the planar shock wave hits the bow shock wave within the sonic circle. Edney Type-IV interaction pattern is not very different from Edney Type-III interaction pattern. Considering Figure 14, where a shock wave S3 is reflected off the solid wall so as to turn the supersonic flow in region 3. When the shock wave S1 moves higher and higher along the bow shock wave S2 , the strength of the shock waves S2 and T1 keeps on increasing and the Mach number in region 3 keeps on decreasing. A situation arises when the supersonic flow in region 3 can no longer turn through the solid wall as the turning required exceeds the maximum deflection limit, the Edney Type-IV configuration appears. The flowfield is depicted in the schematic drawing presented in Figure 23. The interaction is characterized by the presence of a supersonic jet sandwiched between two subsonic flow regions and marked with a series of compression and expansion waves.
(a) Schematic drawing of Edney Type-IV
(b) Schlieren image of Edney Type-IV
interaction
interaction Figure 23: Edney Type-IV interaction
The schlieren images for two different experiments conducted for the configuration of Edney Type-IV interaction are presented in Figure 24 and Figure 25. The images are presented for the test time as evaluated using the schlieren images for Edney Type-I configuration and the pitot pressure record following the discussion in section IV.
(t=2900 μs)
(t=2925 μs)
(t=2950 μs)
(t=2975 μs)
(t=3000 μs)
(t=3025 μs)
(t=3050 μs)
(t=3100 μs)
(t=3150 μs)
(t=3200 μs)
(t=3250 μs)
(t=3350 μs)
(t=3450 μs)
(t=3550 μs)
Figure 24: Schlieren images for Edney Type-IV interaction; Run-1
(t=2900 μs)
(t=2925 μs)
(t=2950 μs)
(t=2975 μs)
(t=3000 μs)
(t=3025 μs)
(t=3050 μs)
(t=3100 μs)
(t=3150 μs)
(t=3200 μs)
(t=3250 μs)
(t=3350 μs)
(t=3450 μs)
(t=3550 μs)
Figure 25: Schlieren images for Edney Type-IV interaction; Run-2
The pixel intensity scan was performed along the horizontal line passing through the nose of the hemispherical body for all the images captured during the two experiments and the result is presented in Figure 26. The plot reveals that unlike the Edney Type-I or Edney Type-III interaction discussed previously, the distance between the shock wave and the hemispherical body fluctuates for the large part of the test time. Multiple such scans were performed along various lines as shown in Figure 27 and the result is presented in Figure 28. As in previous case hemispherical body diameter was taken as the reference length to estimate the pixel length.
Figure 26: Distance of shock wave from the body along the centerline
Figure 27: Schlieren image for Edney Type-IV showing multiple lines across which intensity scan was performed
From Figure 28, it can be seen that the some part of the test time is disturbed because of the passage of the paper pieces, as seen from the frames for 3000 μs to 3150 μs for RUN 1 in Figure 24 and from frames for 3025 μs to 3250 μs for RUN 2 in Figure 25. In both the experiments, the part of the shock wave lying above the centerline is alone disturbed due to the paper pieces. Figure 28 presents the distance of the oblique shock wave and the part of bow shock above the interaction point, from the hemispherical body, and this distance fluctuates for all the lines for which the intensity scan was performed. During the scan, the distance of the transmitted curved shock from the second triple point was also extracted and plotted in Figure 29. It can be seen that unlike the oblique shock wave, there is no evident fluctuation in the distance of the transmitted shock wave. From this one can argue that the lower side shear layer of the supersonic jet is more stable as compared to observed by Chu and Lu[14]. The supersonic jet emanating from the interaction point can be seen to impact on the hemispherical body in vicinity of the gauges located at s/R = -0.13; -0.26, from Figure 30. The voltage signal acquired for the gauge located at s/R = -0.26 and the heat flux deduced, following the methodology described in section V, is presented in Figure 31. From Figure 28 and Figure 31, arguments can be made about the unsteady nature of the supersonic jet emanating from the Type-IV interaction. Similar observations were made for the gauges located at s/R = -0.13; -0.39; -0.52; -0.65. Figure 32 presents the normalized
heat transfer rate on the surface of the hemispherical body for Type-IV interaction. The data is presented in similar way as for Type-III interaction case, by normalizing using the heat flux (not shown here) obtained at the centerpoint of the body in the absence of the shock interaction. The gauges located at s/R = -0.13; -0.26; -0.39; -0.52; -0.65, are marked with two values of heat flux corresponding to the value obtained at the beginning of the test time and the maximum value obtained during the test time. The maximum heat transfer was recorded for the gauge location s/R = -0.52, reaching 10 times that of undisturbed flow case.
(y = +5mm)
(y = -5mm)
(y = +10mm)
(y = -10mm)
(y = +15mm)
(y = -15mm)
(y = +20mm)
(y = -20mm)
Figure 28: Shock wave distance from the body for Edney Type-IV interaction
(y = -10mm)
(y = -15mm)
(y = -20mm) Figure 29: Shock wave distance from the body for Edney Type-IV interaction
Figure 30: Schlieren image
raw voltage signal acquired from data acquisition system
filter voltage signal acquired from data acquisition system
integrated heat flux signal obtained from processing the filtered voltage signal Figure 31: Heat transfer signal for Edney Type-IV interaction for a gauge located at s/R = -0:26
Figure 32: Surface Heat transfer rate distribution for Edney Type-IV interaction
VIII. Conclusions In the present work, the Edney Type-III and Edney Type-IV interactions were considered by performing experiments in a moderate enthalpy condition using a conventional shock tunnel operated in straight through mode. The short test time available in shock tunnel was critically examined and rigorous analysis was performed to evaluate the useful test time. The importance of two diagnostic technique(pitot pressure time history and schlieren visualization), to estimate the test time was discussed and applied. It was observed that the useful test time varies from Edney Type-I configuration, which is considered as a template case for the comparison, to Edney Type-III and Edney Type-IV configuration, highlighting that the initial transient processes depend on the model configuration and care should be taken in generalizing the test time in shock tunnel for a given condition. The unsteady nature of Edney Type-III and Edney Type-IV interactions was discussed in
detail, by capturing schlieren images at high frequency of 40,000 frames per second and these results were collaborated with surface convective heat transfer rates measured at 21 discrete points on the hemispherical body surface. It was found that the shear layer reattachment on the hemispherical body, present in Edney Type-III case, leads to local unsteadiness in the flowfield. This was seen both in the quantitative information brought out by performing pixel intensity scan through various lines and the time history of the heat transfer rate signals in the vicinity of the shear layer impact. Similar trends were observed in the Edney Type-IV configuration, where the non-steady nature was seen locally at the location of supersonic jet impingement. The schlieren images and the heat transfer rates, for both the cases studied, does not shed light on the pattern or cyclic trend of the non-steady behavior observed. This might owe to the low test times available with the conventional shock tunnels, and need further investigation, for example, in the tailored shock tunnel condition. Finally, the heat transfer rates on the hemispherical body surface were quantified in the case of both Edney Type-III and Edney Type-IV interaction. It was seen that for Edney Type-III interaction the peak heating near the interaction region increases upto seven times that obtained at the nose point of body for Edney Type-I interaction. For Edney Type-IV interaction, the peak heat transfer rate obtained was ten times that obtained at the nose point of body for Edney Type-I interaction. Present work provides the experimental evidence of the unsteady/non-steady nature inherent to the shock-shock interaction phenomenon, when the interaction happens within the sonic circle in front of the blunt body. In the available test time, a repeated or cyclic trend in the temporal variation of the measured quantities was not observed, which hint towards the low frequency associated with the unsteadiness, which strays away from the existing numerical study on the subject where oscillation frequencies as high as 30 kHz are reported.
Funding/Acknowledgement This work was supported by Defence Research and Development Organization (grant number DRDO\IISC-GJ622)
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