Pt Analysis Report

Acknowledgement

We thank Dr Sajeer Ahmed, Deputy Head, Experimental Aerodynamics Division and Dr N. B. Mathur for their advice and support through out the project. We also thank the staff of 0.3m tunnel for providing us necessary help during the project.

Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Abstract Experiment on 2-D internal compression inlet with 2-shock system at Mach number 3.0 and total pressure = 60 psi was conducted in 0.3 m trisonic wind tunnel. The simulation of backpressure, which is caused by the combustion process in the engine combustor, is performed by inserting the wedge in the diffuser in upstream direction. By analyzing the pressure distribution along the intake, it was found that at isolator, the maximum rise in static pressure occurs at wedge position, W = 60 mm and minimum energy loss occurs at W = 57.5 mm. Also qualitative analysis is being done on intake model using both viscous (using oil flow technique) and inviscid (theoretically predicted) flow pattern.

Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Contents Page No Acknowledgement

1

Abstract

2

Nomenclature

4

List of Figure

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1. Introduction

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1.1 Inlet Design Parameters

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1.2 Inviscid/Viscous Coupling

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1.3 Boundary Layer Development

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1.4 Shock-Wave Boundary Layer Interaction

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1.5 Starting & Contraction Limits

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1.6 Blunt Leading-Edge

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2. Experimental facility

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3. Model Details

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4. Instrumentation

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5. Test Program

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6. Result & Discussion

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7

6.1 Sidewall pressure distribution

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6.2 Top & bottom wall pressure distribution

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6.3 Distribution of Total pressure

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6.4 Effect of plug position on Total pressure distribution

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6.5 Distribution of Mach number

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6.6 Analysis of Oil flow pattern

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Concluding Remarks

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References

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Appendix

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Figures

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Nomenclature

PS

Local static pressure (psi).

PO

Total or stagnation pressure (psi).

P∝

Free stream static pressure (psi).

q∝

Free stream dynamic pressure (psi).

CP

Pressure coefficient

M

Local Mach number

M∝

Free stream Mach number

γ

Specific heat ratio (=1.4 for air)

X

Distance from the entry (positive downstream) (mm).

W

Wedge position (mm).

Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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List of Figures

Fig No 1

0.3 M trisonic wind tunnel

Fig No 2

Model details

Fig No 3

Location of ports on the top & bottom plate

Fig No 4

Location of the ports on the side plate

Fig No 5

Conical wedge

Fig No 6

Side plate Cp distribution

Fig No 7

Top plate Cp distribution

Fig No 8

Bottom plate Cp distribution

Fig No 9

Front rake pressure distribution

Fig No 10

Rear rake pressure distribution

Fig No 11

Inviscid flow diagram

Fig No 12

Plot of Mach no, Ps/ Psinf & PO / POinf

Fig No 13

Oil flow pattern for PO = 60 psi

Fig No 14

Oil flow pattern for PO = 70 psi

Fig No 15

Diagram for Interaction of shock wave-boundary layer

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1. Introduction

The primary purpose of an inlet (intake / diffuser) for any air-breathing propulsion system is to capture and compress air for processing by the remaining portion of the engine. Inlets may be classified in accordance with the following descriptions that are not necessarily all-inclusive and are arranged in an arbitrary order: 1. Operating Mach number regime (subsonic, transonic, supersonic, hypersonic, or combinations); 2. Family (axisymmetrical, two dimensional, or three dimensional); 3. Geometry (fixed or variable); 4. Supersonic diffuser form (all external, all internal, or combination external / internal); 5. Supersonic compression complexity (normal shock, single surface, isentropic surface, or multiple surface); 6. Supersonic compression direction [outward (relative to a vehicle body), inward, or downward]; 7. Location on vehicle body (nose, chin, cheek, top, bottom, side, forward, mid, or aft); 8. Number (Single, dual, three, or four); and 9. Interface with combustor [in-line (usually with podded engine) or off-set (flow dumps from inlet into combustor with integral engines)]. In a conventional jet engine the inlet works in combination with a mechanical compressor to provide the proper compression for the entire engine. For vehicles flying at high supersonic (3 < M < 5) or hypersonic (M > 5) speeds, adequate compression can be achieved without a mechanical compressor. A scramjet inlet captures and compresses the air for use in the combustor, so there must be optimum degree of compression. The compression must be sufficiently high that combustion can be sustained, but also sufficiently low that large non-equilibrium chemical losses are not incurred within the combustor and nozzle. Because the airflow and compression ratio for these engines are provided entirely by the inlets, an efficient design of an inlet is crucial to the success of the engine operation. Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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1.1. Inlet Design Parameters The goal in the design of any supersonic / hypersonic inlet is to define a minimum weight geometry that provides an efficient compression process, generates low drag, produces nearly uniform flow entering the combustor, and provides these characteristics over a wide range of flight and engine operating conditions. The design of hypersonic inlets is complicated by the many constrains, both aerodynamic and mechanical, that are imposed on the inlet. Examples of aerodynamic constraints including starting limits, boundary-layer separation limits, and constraints on combustor entrance flow profiles. Examples of mechanical constraints include limits on leading-edge radii, variable geometry flexibility, and cooling system limits. The various aerothermodynamic phenomena that are encountered by scramjet inlets at hypersonic flight are illustrated in fig (1). These phenomena includes blunt leadingedge effects, boundary-layer development issues, transition, inviscid / viscous coupling, shock-shock interactions, shock-boundary-layer interactions, and flow profile effects. For inlets that are designed to operate within a narrow Mach number / altitude envelope, an understanding of a few of these phenomena might be required. For inlets designed to operate over large range of speed and altitude (such as an aerospace plane), nearly all of these aerodynamic issues must be addressed.

The features of a scramjet inlet tend to be different from those of external compression ramjet or turbojet inlets, as illustrated in fig (2). The ramjet or turbojet inlet captures, compresses, and diffuses the air stream to low subsonic speeds. Most of the compression occurs on the external portion of the inlet with little to no internal contraction. These inlets require a large amount of turning to achieve the desired compression ratio, which creates a tradeoff between the external cowl drag and the

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internal aerodynamic performance of the inlet. Along with the high level of total turning, the inlets often use boundary-layer bleed to increase pressure recovery, stabilize shock wave / boundary-layer interactions, and serve as a trap for a terminal shock system.

Scramjet operates at higher speeds than ramjet or turbojet that makes the compression ratio sufficiently high at smaller amount of turning as compared to ramjet or turbojet inlets. In most scramjet inlets design the compression is split between the external and internal portions of the inlet, so that high internal contraction ratios are common. Because these engines are designed to fly at very high speeds, optimum designs possess very low external cowl drag. Although bleed is common in a ramjet or turbojet inlet, the use of boundary layer bleed is uncommon in a scramjet inlet because of the high air temperature encountered and the inherent resistance to separation of hypersonic boundary layers. At high speeds and for low level of heat release, the scramjet inlet will operate with supersonic flow throughout. At lower speed and / or higher values of heat release, a precombustion shock system forms in the inlet throat as a result of the thermal blockage of the combustion process. Depending on the strength of this precombustion shock system, the flow existing in the inlet can be supersonic or subsonic.

1.2. Inviscid/Viscous Coupling Compressive surface located on a hypersonic vehicle serve either to decelerate the flow or to increase the static pressure. The compressive surface shown in fig (3) serves to decelerate the flow prior to reaching the engine inlet and, therefore, to produce acceptable flow velocities in the combustion zone. Although this deceleration can be accomplished

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by a single, normal-shock wave standing just upstream of a pitot-type intake, “the loss in total pressure makes this simple solution unacceptable for flight Mach numbers in excess of M =1.5. In reality, the intake designers use a number of (mostly oblique) shock wave to compress and decelerate the incoming flow”. Consider the flow that has to be turned compressively through some specified angle α, if the turning is accomplished gradually through a series of infinitesimal turns, the deceleration process is isentropic. If the compressive turning of the flow is isentropic, the resultant static pressure is much higher that if the α degrees turn is accomplished by passing the air through a single oblique shock wave. Thus, the local pressure is a function of the freestream Mach number, the local flow direction, the gas-property model, and the process through which the flow is turned.

Although a totally isentropic inviscid compression process can be designed, these inlets tend to be very long with substantial viscous losses. Viscosity is a property of the fluid that resists shearing motion and is the by-product of the random molecular motion of the particles and their ability to transport momentum. A factor governing the development of viscous flow is the Reynold’s number, Re. Qualitatively; Re is a ratio of the flow momentum to the viscous force trying to retard it. As a compromise between inviscid and viscous losses, discrete oblique shocks are often used in the compression process. After using inviscid tools to construct the basic inlet layout, compensation for the boundary layer must be made. As illustrated in fig (4), the inviscid flow pattern is generated by the combination of the inlet surface and the boundary-layer displacement thickness. The growth of the boundary layer provides compression that is in addition to the turning provided by the inlet surface. The boundary layer also modifies the apparent location of the inviscid shock relative to the actual geometry. Through development of the proper correlations, the inviscid surface can be directly modified to account for the Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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boundary-layer displacement. A coupled inviscid / viscous analysis is then used to verify the inlet design.

1.3 Boundary Layer Development At supersonic and hypersonic speeds the development of the boundary layer within an inlet has a major influence on the performance and operability of the inlet. This influence arises because the growth of the boundary layer adds to the effective compression of the captured flow. In regions of high adverse-pressure gradients, the separation of the boundary layer must be considered and may lead to design constraints on the inlet. Furthermore, the losses as a result of friction within the boundary layer represent the single largest loss mechanism for both supersonic and hypersonic inlets. Due to large amount of losses in the boundary layer in supersonic and hypersonic flows, viscous effects cannot be neglected. Initially from the leading edge, the boundary layer is laminar and then transition from laminar to turbulent boundary layer takes place, where the fluid particles move in random and chaotic fashion. As a laminar boundary layer becomes thicker, it tends to become unstable. Transition is influenced by many factors including local Reynolds number, surface roughness, freestream turbulence, etc, which make the exact transition location very difficult to predict. It is generally believed that boundary-layer transition occurs when some disturbance to the boundary layer grow to a critical amplitude that produces a breakdown of the laminar boundary layer. Not all disturbances produce boundary layer transition. In some instances, the disturbances attenuate and the boundary layer remains laminar. As the disturbances grows, threedimensional unstable waves and hairpin eddies develop and subsequently, turbulent spots occurs, fig (5). The fig indicates that the boundary layer is laminar downstream (as well Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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as upstream) of the turbulent spot. Turbulent boundary layers are characterized by chaotic, unsteady flow often depicted by eddies, but a well defined boundary layer profile still exists if we consider the time average of the velocity.

Because of the desire to compress the captures airstream in a short length, the boundary layer is subjected to high adverse-pressure gradients. Boundary-layer separation is undesirable, and limits are often placed on the design of an inlet such that separation does not exist. Turbulent boundary layers can sustain much larger pressure gradients without separation compared to laminar boundary layers, so that turbulent boundary layers can extend the operational capabilities of the inlet. Unfortunately, turbulent boundary layer also increases the heat loads and frictional losses with in an inlet. Ideally, an inlet would contain just enough turbulent flow to prevent separation yet minimize viscous losses, thus boundary-layer transition is important in inlet design because it can significantly affect the performance and operability. The existence of separated flow in a scramjet inlet is undesirable because of: •

The creation of additional shock wave that may not have been designed as a part of compression process.

•

The losses associated with compression – expansion – recompression of the flow.

•

The existence of a zone of high heat transfer near the reattachment point.

•

The generation of unsteady waves within the inlet that creates loads.

•

The weakening of the boundary layer such that downstream influences are more easily propagated upstream.

•

The generation of an aerodynamic contraction that may cause the inlet to unstart.

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1.4 Shock-Wave Boundary Layer Interaction One of the main problems for the design of scramjet inlet is a shock-wave boundary layer interaction as shown in fig (6). The interactions include nominally two-dimensional interactions, such as those caused by a compression corner or shock reflection, and threedimensional interactions caused by glancing shock wave or swept compression surfaces. In each of these interactions, an incipient separation pressure rise can be defined as the highest-pressure rise that can be sustained without evidence of significant separation. The corresponding turning angle is called the incipient turning angle.

The separated flow fields for two-dimensional and three-dimensional shock-wave/ boundary-layer interactions are illustrated in fig (7). The two-dimensional interaction is characterized by a separation shock followed by an expansion around the separation bubble and a recompression shock as the flow is turned again parallel to the wall. The three-dimensional interaction results in a complicated flow structure that includes the roll up of a vortex that generates a zone of high heat transfer. This roll up occurs in both sidewall compression inlets and along the sidewalls of two-dimensional inlets.

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There are two prominent techniques for controlling shock-wave/boundary-layer interactions and that are bleeding and blowing. With a bleed system the low-momentum flow near the wall is removed such that the remaining flow can negotiate pressure rise. The disadvantages of a bleed system lie in the substantial drag associated with the bleed air. At hypersonic speeds an additional disadvantage lies in the high temperature of the bleed air, which complicates the design of the bleed system. In a blowing system the flow is injected axially in an attempt to energize the boundary layer such that subsequent adverse pressure gradients can be negotiated. Blowing systems avoid the high drag and internal ducting of a bleed system, but a high-pressure source for the injected fluid must be provided.

1.5 Starting & Contraction Limits For the proper operation all scramjet inlets must operate in a started mode. The term started is used to denote operation under conditions where flow phenomena in the internal portion of the inlet do not alter the capture characteristics of the inlets. An inlet can be unstarted either by over-contracting to the point where the flow chokes at the inlet

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throat or by raising the backpressure beyond the level that can be sustained by the inlet. The flow field of an unstarted hypersonic scramjet inlet can be quite different from that found in a conventional external compression turbojet or ramjet inlet, as illustrated in fig (8). In a ramjet or turbojet inlet the ratio of the boundary layer height to inlet height at the cowl-tip plane is usually small. When this inlet unstarts, a normal shock is expelled, and the flow is spilled subsonically. For hypersonic scramjet inlet a substantial portion of the flow at the cowl tip can be boundary layer. When these inlet unstart, the expelled shock system is sufficiently strong to separate the boundary layer, creating the flow field illustrated in the fig (8). The flow field is characterized by large separation region and supersonic flow spillage. In this condition the portion of the flow that is captured by the

unstarted inlet can be predominantly supersonic. In general, an unstarted inlet captured less airflow with lower efficiency and higher aerodynamic and thermal loads compared to started inlets.

1.6 Blunt Leading-Edge Another important design issue for scramjet inlets concerns the blunting of leading edges on surfaces such as the fore body and cowl tip. These surfaces should be blunted to obtain acceptable heating levels at hypersonic speeds. Unfortunately, the bluntness generally degrades the performance of the inlet. As shown schematically in fig (9), blunt leading edges cause curved bow shocks that generate larger entropy layers. These entropy layers modify the downstream boundary layer development, including transition, and can Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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create significant changes in the inviscid flow field such as the shock positioning and aircaptive characteristics.

Thus it is clear from the above design constraints, design of scramjet inlet is not simple and it requires lot research for successful design.

2. Experimental Facility The 0.3 m trisonic tunnel is an intermittent, blowdown type wind tunnel capable of operating in Mach number range of 0.2 to 3 (Fig 1). Compressed air stored at 10 bar in a large reservoir of about 2830 cubic meter capacity is discharged through the tunnel circuit in a regulated way to achieve the desired mach number in the test section. Pressure regulating wall maintains constant pressure in settling chamber, which in turn ensures constant condition in the test section during the blow down. Supersonic mach numbers are achieved by nozzle block designed and contoured to provide a desired supersonic mach number in a 0.3m x 0.3m test section. At present the tunnel is equipped with nozzle blocks to generate free stream mach numbers (M) of 1.4, 1.6, 1.8, 2.0, 2.2, 2.5 and 3.0. Operating pressure of the tunnel varies with the Mach number and is about 1.79 bar (26 psi) and 4.83 bar (70 psi) at M=3.0. Reynolds number capability of the tunnel based on the operating pressure ranges from 4 to 32 million per meter in Mach number range from 0.2 to 3.0. For the present series of tests M = 3.0 nozzle block is used and a mechanical

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block specially fabricated, is located downstream of the nozzle to mount the internal compression intake model (Fig 2).

3. Model Description The intake model is made of 4 detachable plates (the top plate, the bottom plate and two side plates) as shown in the fig (3 & 4). The plates are made of mild steel and coated with black paint. Holes are drilled on these plates to bolt them together. The 3 main parts of the model are the intake, the isolator and the diffuser. The intake extends to a length of 130 mm measured from the tip of the top plate. The intake is followed by an isolator, which has a length of 120 mm and finally the diffuser of length 100 mm. There are ports along the top plate, bottom plate and one of the side plates for measuring the static pressures. Two rakes are fixed just at the beginning of the isolator and the diffuser respectively for measuring the total pressures. The former is called the front rake and latter the rear rake. A wedge, which can be moved inside and outside from the rear portion of the diffuser control the mass flow in the model (Fig 5). The wedge is actually simulating the backpressure, which occurs in the real situations. The whole model is mounted on a strut at an angle of 13.2 degrees so that the incoming flow is parallel to the initial portion of the bottom plate. The strut is in turn fixed on to a tunnel-mounting block inside the test section of the wind tunnel.

4. Instrumentation Static pressure ports were located along the top, bottom and sidewall of the model. Schematic of pressure ports location is shown in fig (0) and the distance of pressure port from the intake entry are given in the tables. The pressure ports are of 0.5 mm internal diameter. Polythene tubes from the steel tube located at the end of brass bush connect the port to the ESP scanner of range +/- 10 psid. Pressure data from each of the tube is acquired and processed and presented in the form of pressure coefficient. Free stream total pressure was measured through a pitot tube located at settling chamber using 0 to 100 psid DRUCK transducer and the tunnel wall static pressure was measured using a +/10 psid DRUCK transducer. For the measurement of total pressure inside the model two rakes were used. Rake pressures were measured using ESP scanner of range +/-30 psid. Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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5. Test Program Experiments were carried out at a free stream mach number of 3.0 for different mass flow conditions through the model. By varying the position of the plug located at the exit of the model, mass flow through the duct is varied. The position of plug is expressed as the ratio of geometrical area it subtends at the exit plane of the model to the cross section area of the diffuser exit. Flow field inside the model was visualized using the Oil flow technique and the photographs were taken for the different positions of the plug (W = 0, 20, 40, 50, 55, 57.5, 60, 80, 100 mm). At the different plug positions static pressure, total pressure from the rake and the surface flow pattern on all the four walls were obtained. Pressure recovery of the flow at different exit areas was determined by measuring the total pressure profile of the flow inside the model using the rake. To get the surface flow patterns a mixture of Oleic acid, Vacuum pump oil and Titanium dioxide in the ratio of 1:5:10 by volume were used.

6. Results & Discussion

6.1 Side wall pressure distribution The CP distribution is very similar for the wedge positions, W = 0, 20 and 40mm. In this three cases the CP value increase steadily but gradually till X = 95mm. Then there is a sudden decrease in CP value at near about X = 185mm. This sudden decrease can be due to the expansion wave caused by the reflection of shock wave from the boundary layer. Then there is an alternate increase and decrease of CP (Fig 6) along the length of the intake. That is due to reflected shock and expansion waves. For the wedge position W = 50, 55 and 57.5 mm the trend is similar to the previous positions of the wedge till about X = 220 mm (Fig 6). But after that the CP value increases at a faster rate. It can be seen from the fig that the shock is moving upstream as the wedge is moved further inside. For the wedge position W = 60 and 80 mm, unlike the previous cases the CP value rises very rapidly till X = 170 mm. Further in the intake there is alternate rise and drop in CP as in the previous cases. But the magnitude of the fluctuations is comparatively smaller. Maximum static position rise is obtained for wedge position, W = 60 mm. In the case of

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wedge position, W = 100mm, initially there is a sharp increase in CP but after that in becomes almost constant.

6.2 Top and Bottom wall pressure distribution The top and bottom wall pressure distribution are given in (Figs 7 & 8). This concurs with the pressure distribution on the sidewall. 6.3 Distribution of Total Pressure The total pressure is measured experimentally only at the two rakes. Total pressure is decreasing downstream along the length of intake model. This is due to the pressure loss across the reflected shock train. But towards the end of the model there is a considerable fall in total pressure (Figs 9 & 10).

6.4 Effect of plug position on Total pressure distribution As the plug advances into the diffuser, the exit area is decreased (thereby increasing the back pressure) causing decrease of total pressure. This can be seen from the total pressure measured at the rakes for the different plug positions (Figs 9 & 10).

6.5 Distribution of Mach number From the total pressures measured at the rakes and the static pressures measured 3 mm ahead of the rakes the Mach number was calculated using the Rayleigh-Pitot formula (appendix). The Mach numbers at the various locations were calculated theoretically using these two experimental values and considering the inviscid shock diagram (Fig. 11) (Table) & (Fig. 12). It is seen that Mach number decreases downstream along the length of the intake and as the plug is moved more inside it is observed that the shock at the beginning of the intake becomes stronger and the flow becomes subsonic very early inside the model.

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6.6 Analysis of Oil flow pattern Photographs of the oil flow pattern on the top, bottom and two side plates at two different inlet total pressure i.e. Po = 60 psi (Fig. 13) and Po = 70 psi (Fig. 14) are available. The observations that can be made from the two photographs are given below

Po = 70 psi The oil flow pattern on the side plates (Fig. 14) is typical and in good accordance with the inviscid flow theory. However there is a big separated zone just after the first expansion corner at the bottom plate. An examination of the bottom plate oil flow pattern clearly shows this separation. This phenomenon is however can be explained if we take into account the boundary layer and its interaction with shock waves. According to the shock boundary layer interaction theory this separation is caused due to high adverse pressure gradient. Due to shock there is pressure rise outside the boundary layer however there is no such pressure rise in the subsonic region of the boundary layer which causes high pressure gradient and the subsequent separation. On reflection of the shock wave from the boundary layer expansion waves are formed which turns the flow towards the wall, reattaching the flow to the wall. This phenomenon can be understood from the figure attached (Fig. 15). This whole phenomenon can be seen in the oil flow pattern. Oil flow pattern downstream shows the formation of shock waves at location, which are at good accordance with the prediction of the inviscid theory.

Po = 60 psi The oil flow pattern for PO = 60 psi (Fig. 13) is different from what is predicted by the inviscid flow theory. Initially there is a shockwave and expansion wave at the corners. Also there is separation at the first expansion corner as predicted by the shock-boundarylayer interaction theory if we take into account the viscous effects. An examination of the bottom plate shows the separation of the flow at the expansion corner. However the thickness of the separated zone is not as big on the side plate of PO = 60 psi as compared to the side plate oil flow pattern for PO = 70 psi. The oil flow pattern downstream is a bit different from the oil flow pattern predicted by the inviscid flow theory. This difference maybe due to effect of boundary layer, which modifies the apparent location of the Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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inviscid shock relative to the actual geometry. Thus we get a pattern different from the inviscid prediction. The effect of the boundary layer on the flow is governed by the Reynolds number of the flow so this maybe the reason why oil flow pattern for PO = 70 psi & PO = 60 psi differ from each other.

7. Concluding Remarks To understand the flow field associated with internal compression intake at supersonic speeds an experimental program is initiated in the 0.3 m tunnel. An arrangement was made to mount the model inside the test section of the tunnel. The flow variation at the different exit areas was studied through measurement of surface pressures, rake pressures and flow visualization. Pressure distribution inside the model for different wedge positions have revealed that the flow separation occurs just at the beginning of the intake. This causes the efficiency of intake to fall considerably. The separation can be due to shock-boundary-layer interaction. Experimental studies also revealed that maximum static pressure rise was obtained for wedge position, W = 60 mm and minimum total pressure loss was obtained for the wedge position, W = 57.5 mm. The variation of pressure distribution inside the model due to the change of back pressure is reasonably understood. But the separation caused by oblique shock wave and boundary layer interaction is yet to be understood fully.

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Reference:

1. Van Wie, D.M., “Scramjet Engine”, Progress in Aerospace and Aeronautics, AIAA Washington, D.C., 2001, PP: 447-511. 2. Bertin, J.J., “Hypersonic Aerothermodynamics”, AIAA Education Series, AIAA Washington, D.C., 1994. 3. Mahoney, J.J., “Inlets for Supersonic Missiles”, AIAA Education Series, AIAA Washington, D.C., 1990. 4. Young, A.D., “Boundary Layer”, AIAA Education Series, AIAA Washington, D.C., 1989. 5. Chew, Y.T., “Shockwave and Boundary Layer Interaction in the Presence of an Expansion Corner”, Aeronautical Quarterly, Vol-30, 1979, PP: 506-527. 6. Mattingly, J.D.; William, H.H.; Daniel, H.D., “Aircraft Engine Design”, AIAA Education Series, AIAA Washington, D.C., 1987. 7. Gadd, G.E., “Interaction Between Wholly Laminar or Wholly Turbulent Boundary Layers and Shock Wave Strong Enough to Cause Separation”, Journal of Aeronautical Sciences, Vol-20, No-11, November 1953. 8. Gadd, G.E., “A Theoretical Investigation of Laminar Separation in Supersonic Flow”, Journal of Aeronautical Sciences, October 1957. 9. Oosthuizen, P.H., “An Analysis of the Interaction of Boundary Layer and the Corner Expansion Wave in Supersonic Flow”, UTIAS Tech Note 117, 1967. 10. Curle, N., “Shock-Induced Separation of a Laminar Boundary Layer in Supersonic flow past a Convex Corner”, The Aeronautical Quarterly, February 1965. 11. Westphal, R.V., Jonston, J.P., and Easton, J.K., 1984. “Experimental Study of Flow Reattachment in a Single-Sided Sudden-Expansion,” NASA CR 3765. 12. Mirua, H., “Prandtl-Mayer Flow of a Dusty Gas with a Small Deflection Angle,” Phys. Soc. Japan, 37 (1974) 1145-52. 13. Miura, H., and Glass, I.I., “Supersonic Expansion of a Dusty Gas Around a Sharp Corner,” Proc. Roy. Soc. London, A415 (1988), pp. 91- 105.

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14. Delery, J.M., “Shock-Wave/Turbulent Boundary Interaction and its Control,” Progress in Aerospace Sciences, Vol-22, 1985, pp. 209-280. 15. Stollery, J.L., “Some Aspect of Shock-Wave/Boundary-Layer Interaction Relevant to Intake Flows,” Hypersonic Combined Cycle Propulsion, AGARDCP-479, June 1990.

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Appendix Procedure for calculating the Mach number upstream of the rake

Mach number measurements were made using the top wall mounted total pressure rakes connected to an ESP scanner of range +/- 30 psid and ports on the sidewall, which measures static pressure. The side wall ports were 3mm ahead of the plane of rakes so that the static pressure measured was upstream of the detached shock (due to the rake) and the total pressure measured was after the detached shock.. 1. Calculate the local Mach number before the rake using Raleigh-Pitot formula

1 γ − 1 ⎛ 2γ ⎞ γ − 1 ⎜⎜ ⎟⎟ M 2 − γ + 1⎠ ⎛ Ps ⎞ ⎝ γ + 1 ⎜ ⎟ = γ ⎝ Po ⎠ γ −1 ⎛ γ + 1 ⎞ M 2 ⎟ ⎜ 2 ⎝ ⎠

−1 3.44 ⎫ ⎧ ⎪⎛ Ps ⎞ 2 ⎪ ⎛ Ps ⎞ ⎡ Ps ⎤ M = ⎨0.88185 − 0.2147 ⎜ + 0.06 ⎥ ⎟ ⎟ − 0.2478 ⎢ ⎬⎜ ⎝ Po ⎠ ⎣ Po ⎦ ⎪⎭⎝ Po ⎠ ⎪⎩

2. Calculate the local Total pressure upstream of the rake using isentropic formula.

⎛ Po ⎞ ⎡ (γ − 1) 2 ⎤ M ⎥ ⎜ ⎟ = ⎢1 + 2 ⎝ Ps ⎠ ⎣ ⎦

Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Figures

Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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Submitted to Department of Aerospace, IIT Bombay By: Ashish Gupta (99D01003) and Moble Benedict (99D010011)

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