Sidewall Effects Supersonic

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American Institute of Aeronautics and Astronautics Paper 2002-3777 1 EFFECT OF SIDEWALL CONFIGURATIONS ON THE AERODYNAMIC PERFORMANCE OF SUPERSONIC AIR-INTAKE Y. Watanabe * , A. Murakami and H. Fujiwara National Aerospace Laboratory Tokyo, Japan Abstract The effects of the sidewall variation on the aerodynamic performance for a two dimensional external compression supersonic air-intake were investigated by performing both of wind tunnel tests and numerical simulations. It became clear that one of the major disadvantages of the air-intake with “a larger sidewall” is its comparatively poor pressure recovery and skewed spatial distortion, both of which being caused by the separation vortices induced by the interaction between the sidewall boundary layer and the shock waves. It also became clear that another disadvantage is its comparatively large spillage drag. On the other hand, it turned out to have the advantage of comparatively wide stable range in subcritical operation. The reason for the wide stable range of the air-intake with “a larger sidewall” was investigated in detail using both of the results of the wind tunnel tests and numerical simulations. Nomenclature A 1 = area of throat A 2 = area of exit A c = capture area at full flow condition B = width of stream tube Cd = drag coefficient of intake drag Cd spillage = drag coefficient of spillage drag Cd bleed = drag coefficient of bleed drag Cd cowl = drag coefficient of cowl drag D = diameter of intake exit DC(60) = circumferential distortion parameter DI max , DI min = distortion index H c = capture height at full flow condition H = capture height H t = height of stream line L = length of subsonic diffuser MFR capture = capture mass flow ratio MFR spillage = spillage mass flow ratio p = pressure η exit = pressure recovery at exit plane η slit = pressure recovery behind slit η throat = pressure recovery at intake throat Introduction National Aerospace Laboratory of Japan is promoting the development of two types of Scaled Supersonic Experimental Airplanes (Non-powered Experimental Airplanes and Jet-powered Experimental Airplanes), as well as conducting the research on related technology. The propulsion system for the experimental airplane must have enough net thrust to accelerate the airplane up to the flight speed of M2.0. The air-intake plays a key role on the propulsion in the supersonic flight, the air-intake being required to have high aerodynamic performance such as low total pressure loss, low spatial distortion, low external drag and wide stable operational range. In order to satisfy such requirements, each component constituting the air-intake, such as the ramp for supersonic compression, the sidewall, the subsonic diffuser and the bleed system, should be sophisticated independently and moreover should be working altogether at the highest performance. In this study, special focus was paid on the design of the sidewall configuration for the air-intake. The objective of this study is to clarify the effect of the sidewall configuration on the aerodynamic performance such as the pressure recovery, the spatial distortion, flow stability characteristics and the external drag. Both of the wind tunnel tests and numerical simulations of the air-intake with four types of sidewalls were performed, the results of which were compared to each other. Configuration of Intake Figure 1 illustrates the schematic of the supersonic air-intake. The air-intake is a rectangular and external compression air-intake with three shock system. The design Mach number was 2.0. The total length and capture area was 1663mm and 910cm 2 , respectively, to the scale of the air-intake integrated 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 7-10 July 2002, Indianapolis, Indiana AIAA 2002-3777 Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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sidewall effects supersonic

Transcript of Sidewall Effects Supersonic

  • American Institute of Aeronautics and Astronautics Paper 2002-3777

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    EFFECT OF SIDEWALL CONFIGURATIONS ON THE AERODYNAMIC

    PERFORMANCE OF SUPERSONIC AIR-INTAKE

    Y. Watanabe*, A. Murakami and H. Fujiwara National Aerospace Laboratory

    Tokyo, Japan

    Abstract The effects of the sidewall variation on the

    aerodynamic performance for a two dimensional external compression supersonic air-intake were investigated by performing both of wind tunnel tests and numerical simulations. It became clear that one of the major disadvantages of the air-intake with a larger sidewall is its comparatively poor pressure recovery and skewed spatial distortion, both of which being caused by the separation vortices induced by the interaction between the sidewall boundary layer and the shock waves. It also became clear that another disadvantage is its comparatively large spillage drag. On the other hand, it turned out to have the advantage of comparatively wide stable range in subcritical operation. The reason for the wide stable range of the air-intake with a larger sidewall was investigated in detail using both of the results of the wind tunnel tests and numerical simulations.

    Nomenclature A1 = area of throat A2 = area of exit Ac = capture area at full flow condition B = width of stream tube Cd = drag coefficient of intake drag Cdspillage = drag coefficient of spillage drag Cdbleed = drag coefficient of bleed drag Cdcowl = drag coefficient of cowl drag D = diameter of intake exit DC(60) = circumferential distortion parameter DImax, DImin = distortion index Hc = capture height at full flow condition H = capture height Ht = height of stream line L = length of subsonic diffuser MFRcapture = capture mass flow ratio MFRspillage = spillage mass flow ratio p = pressure exit = pressure recovery at exit plane slit = pressure recovery behind slit

    throat = pressure recovery at intake throat

    Introduction National Aerospace Laboratory of Japan is

    promoting the development of two types of Scaled Supersonic Experimental Airplanes (Non-powered Experimental Airplanes and Jet-powered Experimental Airplanes), as well as conducting the research on related technology. The propulsion system for the experimental airplane must have enough net thrust to accelerate the airplane up to the flight speed of M2.0. The air-intake plays a key role on the propulsion in the supersonic flight, the air-intake being required to have high aerodynamic performance such as low total pressure loss, low spatial distortion, low external drag and wide stable operational range. In order to satisfy such requirements, each component constituting the air-intake, such as the ramp for supersonic compression, the sidewall, the subsonic diffuser and the bleed system, should be sophisticated independently and moreover should be working altogether at the highest performance.

    In this study, special focus was paid on the design of the sidewall configuration for the air-intake. The objective of this study is to clarify the effect of the sidewall configuration on the aerodynamic performance such as the pressure recovery, the spatial distortion, flow stability characteristics and the external drag. Both of the wind tunnel tests and numerical simulations of the air-intake with four types of sidewalls were performed, the results of which were compared to each other.

    Configuration of Intake Figure 1 illustrates the schematic of the

    supersonic air-intake. The air-intake is a rectangular and external compression air-intake with three shock system. The design Mach number was 2.0. The total length and capture area was 1663mm and 910cm2, respectively, to the scale of the air-intake integrated

    38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit7-10 July 2002, Indianapolis, Indiana

    AIAA 2002-3777

    Copyright 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

  • American Institute of Aeronautics and Astronautics Paper 2002-3777

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    into the experimental airplane. Figure 2 shows the cross sectional view of the air-intake. The first ramp, shown as a red area in the supersonic diffuser in Figure 1, consists of a wedge of 3 degrees and an isentropic compression surface of 5 degrees. The second ramp, the green area in the supersonic diffuser in Figure 1, is a variable wedge, the turning angle of which varies from 0 up to 12 degrees. The hinge point location of the movement of the second ramp is shown Figure 2. The oblique shocks and compression waves originating from the first and second ramps focus on the cowl lip at the condition

    Fig.1 Schematic of air-intake

    Fig.2 Cross sectional view of air-intake ( Unit : mm )

    Fig.3 Detail of supersonic diffuser

    Fig.4 Schematic of experimental model

    Fig.5 Experimental model installed in wind tunnel

    Fig.6 Computational grid

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    of the inlet Mach number 2.3. The diffuser ramp, shown as the green area in the subsonic diffuser in Figure 1, is also of a variable type, the turning angle of which is uniquely determined by the position of the second ramp trailing edge. A wide slit is located just downstream of the throat to suck the boundary layer developing on the first and second ramps. Bleed mass flow ratio was varied by changing the bleed exit area. The length-to-exit-diameter ratio of the subsonic diffuser, L/D, was about 3.3. The variation of the cross-sectional shape along the flow direction is shown in the upper part of Figure 2, where it is shown that the shape changes from rectangular to circular while the width D is always constant along the flow direction. The area ratio of the subsonic diffuser A2/A1 depends on the position of the two variable ramps, which was equal to 2.05 at the condition that the turning angle of the second ramp was 12 degrees.

    Four kinds of sidewall configurations were tested shown in Figure 3. The largest sidewall L1 covers most of the supersonic diffuser, the edge line starting from the leading edge of the first ramp. The smallest sidewall was referred to as S1, in which the upstream half area of the sidewall was cut away. The edge line of S1 starts from the corner of the second ramp. The edge line of the sidewall L3 starts from the starting point of the isentropic compression surface, while that of L4 starts from the ending point of the isentropic surface.

    Wind tunnel test Figure 4 shows the schematic of the

    experimental model. It was a 19.2% scale model of the actual air-intake used for the experimental airplane. The exit diameter of the air-intake is 70mm. In the wind tunnel test, two kinds of sidewall, S1 and L1, were tested. The bleed exit area was set 8 percents of the capture area, Ac. A flow plug was used to control the mass flow ratio. A spatially high resolution measurement of the total pressure distribution at the air-intake exit was performed by means of rotatory pitot rakes. For steady pressure measurements, three electrical scanners (PRESSURE SYSTEMS Inc.) were used, each of which contains 64 pressure transducers. For unsteady pressure measurements, high response pressure transducers (Kulite XCQ-062) were used. The unsteady pressure transducers were set at the two locations, one of which was near and inside the cowl lip and another was at the center of the air-intake exit surface. Figure 5 shows the picture of the experimental model installed in the 1m1m blowdown type supersonic wind tunnel of National Aerospace Laboratory of

    Japan. The wind tunnel tests were performed with the free stream Mach numbers ranging from 1.5 to 2.0. The duration time of a blow was 36 seconds. The color schlieren method and the oil flow technique were applied to visualize the flow fields in and around the supersonic diffuser.

    The pressure recovery and the total pressure distortion were obtained based on the results of the total pressure distribution measurements. The pressure recovery is defined as,

    = PPf / (1)

    where Pf is the spatial average of the total pressure on the air-intake exit surface while P is the total pressure of the free stream. Two kinds of distortion parameter were used in this study, one of which is the distortion index (D.I.) used for the guideline to determine the engine operation limit. The maximum and minimum values of the D.I. are defined as,

    ( )

    = PPP f /D.I. maxmax (2)

    ( )

    = PPP f /D.I. minmin (3)

    where Pmax and Pmin are the maximum and minimum values of the total pressure within the region of the air-intake exit surface excluding the outer 1.5 percents region near the wall. Another distortion parameter is the circumferential distortion parameter DC(60) which is defined as,

    ( ) ff qPP /DC(60) 60= (4) where qf is the mean dynamic pressure at the air-intake exit while P60 is the spatial average of the mean total pressure obtained in the worst 60 degrees sector of the exit. In order to detect the buzz, the pressure fluctuation was monitored, the pressure being measured through the high response pressure transducers explained above. The mass flow through the subsonic diffuser was calculated on the choked area of the flow plug using both of the free stream total temperature and the total pressure just upstream of the flow plug. The bleed mass flow was calculated based on the total pressure and the static pressure at the bleed exit.

    Numerical simulation methods The steady, compressible, Reynolds-averaged

    Navier-Stokes equations were solved for the flow through the supersonic air-intake. The turbulence viscosity was evaluated with the low Reynolds number k-epsilon model developed by Myong and Kasagi2. Spatial difference was evaluated by a third order upwind biased Roe scheme3 with a TVD

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    limiter of Chakravathy and Osher type4. For the time advancement, an implicit method was adopted.

    Figure 6 illustrates the computational grid in and around the air-intake. The computational domain was decomposed into four regions. The total number of grid points was 450,000. A straight duct and a variable second throat was located downstream of the air-intake to control the capture mass flow ratio corresponding to the flow plug in the wind tunnel test. The internal flow through the bleed chamber for boundary layer removal was also simulated. The bleed chamber was connected to the main duct through the slit located just downstream of the throat. The bleed exit area was 9 percents of the capture area Ac of the air-intake. Four kinds of sidewall configuration shown in Figure 3 were investigated in the present numerical simulations.

    Results and Discussions Flow fields around the air-intake

    Figures 7 and 8 show the flow fields through the air-intake with the largest sidewall L1 obtained by performing the numerical simulations with different mass flow ratio. The inlet Mach number was 2.0. The operation conditions shown in Figure 7 and 8 are nearly critical and subcritical, respectively. As is shown in Figure 7(a), the oblique shock waves and the compression waves cross the terminal shock wave above the cowl lip at critical operation. Figure 7(b) shows that large longitudinal vortices were induced in the subsonic diffuser. This is due to the shock boundary layer interaction on the large sidewalls. These vortices still remained in the subcritical operation shown in Figure 8(b). The results of the smallest sidewall S1 with different mass flow ratios are shown in Figures 9 and 10. Note that the mass flow ratio of the flow shown in Figure 9 is nearly equal to that of the flow shown in Figure 7. In the case with S1 sidewall at critical condition shown in Figure.9(b), the vortices induced in the subsonic diffuser were fairly small compared to the previous large sidewall case shown in Figure 7(b). The reason for the difference lies on the thickness of the sidewall boundary layer upstream of its interaction with the shock waves. It can be easily estimated that the thickness of the sidewall boundary layer on the large sidewall was larger than that on the small sidewall one, which naturally resulted in the larger longitudinal vortices downstream of the shock boundary layer interaction as long as the strength of the shock waves is almost the same. Figure 10 shows the flow field through the air-intake with the smallest sidewall S1 in subcritical operation.

    Note that the mass flow ratio of the flow shown in Figure 10 is nearly equal to that of the flow shown in Figure 8. Although the location of the terminal shock wave in the flow field shown in Figure 10(a) is approximately the same as that in Figure 8(a), there exists a clear difference between these two flows, especially on the cowl side of the subsonic diffuser. In the case with the small sidewall, Figure 10(b) shows the existence of the low total pressure region on the cowl side of the diffuser, which turned out to be caused by the shear layer ingestion, the shear layer originating from the intersection point of the shock waves (referred to as Triple point in the figures). On the other hand, in the case with the large sidewall, no such low total pressure region could be observed on the cowl side as is shown in Figure 8(b). The reason of this difference will be explained later.

    Figure 11 compares the oil flow pictures on the first and second ramps for the air-intakes with S1 and L1 sidewalls. In the case with S1 sidewall, streamlines on the first ramp are diverted outside indicating that sideways spillage occurred, on the other hand, streamlines are nearly straight in the case with the large sidewall L1 indicating that the sideways spillage was negligible. This is simply due to the effect of the large solid sidewall preventing the flow from going outside. Pressure recovery

    Figure 12 shows the pressure recovery plotted as a function of the mass flow ratio obtained in the numerical simulations for four sidewall configurations. The wind tunnel test result for only S1 sidewall case is also plotted in the same figure. The mass flow ratio is defined by the ratio of the mass flow going through the throat to the captured mass flow. The inlet Mach number was 2.0. The numerical result for S1 sidewall agrees fairly well with the corresponding wind tunnel test result. The results of the numerical simulations with different sidewalls show a large difference of the recovery. The pressure recovery for L4 sidewall is nearly equal to that for S1. On the other hand, both of the recoveries for the sidewalls L1 and L3 are clearly smaller than that for S1.

    In the cases of the larger sidewalls, L1 and L3, the sidewall boundary layer became too thick, due to the shock boundary layer interaction, to be sucked into the bleed chamber completely, which resulted in the appearance of the large longitudinal vortices finally causing the reduction of the pressure recovery.

    It was interesting that the pressure recovery for the larger sidewall cases, L1 and L3, increased with

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    (a) Cross sectional view of Mach number contour

    (b) Total pressure distribution in subsonic diffuser

    Fig.7 Flow field around L1 air-intake in critical

    operation at M 2.0; MFRcapture = 0.830

    (a) Cross sectional view of Mach number contour

    (b) Total pressure distribution in subsonic diffuser

    Fig.8 Flow field around L1 air-intake in subcritical

    operation at M 2.0; MFRcapture = 0.795

    (a) Cross sectional view of Mach number contour

    (b) Total pressure distribution in subsonic diffuser

    Fig.9 Flow field around S1 air-intake in critical

    operation at M 2.0; MFRcapture = 0.833

    (a) Cross sectional view of Mach number contour

    (b) Total pressure distribution in subsonic diffuser

    Fig.10 Flow field around S1 air-intake in subcritical

    operation at M 2.0; MFRcapture = 0.793

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    the reduction of the mass flow ratio (MFR) in the subcritical operation with the MFR lower than about 0.82 shown in Figure 12. This was not the case with the simulations with the smaller sidewalls where the pressure recovery was nearly constant except the state of buzz. The increase in the recovery for the larger sidewall cases in the subcritical operation can be explained as follows; the pressure in the bleed chamber became higher as the MFR was reduced until the flow went into the state of buzz. This pressure rise had an effect to increase the bleed mass flow as long as the bleed exit area was fixed. As the results, the bleed chamber was able to suck more boundary layer than before which improved the pressure recovery. Figure 13 shows the pressure recoveries at the throat and at the location just downstream of the slit for bleed for the case with the sidewall L1. The former corresponds to the recovery just before the boundary layer bleed, while the latter corresponds to the recovery after the bleed. The figure shows that the recovery after the bleed increased with the decrease in the MFR even though the recovery before the bleed decreased with the decrease in the MFR. This clearly indicates that the pressure recovery was improved due to the increase in the bleed of the boundary layer.

    Similar investigation was performed for the inlet Mach number 1.7. Figure 14 shows the pressure recovery vs the MFR. The sensitivity of the size of the side wall to the pressure recovery is much less compared to the M2.0 cases just because the shock waves amplifying the boundary layer thickness became weaker. Figure 15 shows the total pressure distribution for the air-intake with L1 sidewall, which corresponds to Figures 7(b) and 8(b) for M2.0 cases. The longitudinal vortices actually became small even in the case with the largest sidewall at the inlet Mach number 1.7. Spatial distortion index

    Figure 16 shows a diagram of the maximum and minimum distortion indices at the inlet Mach number of 2.0 obtained in the numerical simulations. In all cases except in supercritical operation the distortion indices were within the range of 7.5% which is one of the requirements of the operation of the engine used for the experimental airplane. Comparison of the distortion indices with different sidewalls shows a clear tendency that the distortion was larger with larger sidewalls. This is due to the large longitudinal vortices induced by the shock boundary layer interaction explained above. The circumferential distortion parameter DC(60) is shown in Figure 17, where the flows with the four

    Fig.11 Oil flow picture on ramp at M 2.0

    Fig.12 Variation of pressure recovery against capture

    mass flow ratio at M 2.0

    Fig.13 Pressure recovery at throat and behind slit of

    air-intake at M 2.0

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    different sidewalls can be divided into two groups, one was the air-intakes with the smaller sidewall, S1 and L4, and another with the larger sidewall, L1 and L3. The former shows a clear reduction of DC(60) near critical and subcritical range and shows rapid increase in DC(60) when the shear layer was ingested into the diffuser, while the latter shows that DC(60) kept nearly constant at high value at any MFR. Figure 18 shows the circumferential distortion index diagram in the case of the inlet Mach number of 1.7. The sensitivity of the size of the side wall to DC(60) was weaker compared to the M2.0 cases although it shows DC(60) a rapid increase with the ingestion of the shear layer for the cases with the smaller sidewalls shows. Instability of the intake flow

    Instability of an air-intake flow, which is often described as a time distortion, is also an important characteristic of an air-intake, which directly related to the stable operation margin of an engine. In subcritical operation below a certain value of the mass flow ratio, there might to be occurred serious shock wave oscillation phenomena well known as buzz. Figure 19 shows the schlieren photographs taken in the wind tunnel tests with the sidewalls L1 and S1 both of which operating at supercritical conditions. The chocked exit area controlled by the flow plug was almost the same for the two cases. The similar photographs at subcritical conditions are shown in Figure 20. At supercritical conditions shown in Figure 19, shock system was stable in both cases. At the subcritical condition shown in Figure 20, flow field in the air-intake with L1 was still stable, while in the air-intake with S1, the oscillation of the terminal shock wave occurred. Further reducing the mass flow ratio, both of the flow fields went into the state shown in the schlieren photographs of Figure 21. Significant shock oscillations were observed in both cases. Figure 22 shows the root mean square values of the pressure fluctuation measured near the cowl lip in the subsonic diffuser. As is shown in the figure, the unsteady flow characteristics of the air-intake with S1 sidewall is different especially in the operation condition with the spillage mass flow ratio ranging from about 0.14 to 0.23 in which the flow with the sidewall S1 showed a higher level of oscillation compared to the flow with L1 sidewall.

    The ingestion of the shear layer is one of the important factors of the occurrence of flow instability. The instability of this type is referred to as Ferri instability5. Although the ingestion of the shear layer is not a sufficient condition for the

    occurrence of buzz6, it is a useful criterion to determine the safety limit of the air-intake operation. Figure 23 illustrates the streamlines of the flow through a supersonic air-intake. The height Hc indicates the height of the cowl lip while the height

    Fig.14 Variation of pressure recovery against capture

    mass flow ratio at M 1.7

    Fig.15 Total pressure distribution in L1 air-intake

    at M 1.7; MFRcapture = 0.797

    Fig.16 Variation of distortion index against capture

    mass flow ratio at M 2.0

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    Fig.17 Variation of circumferential distortion

    parameter against capture mass flow ratio at M 2.0

    Fig.18 Variation of circumferential distortion

    parameter against capture mass flow ratio at M 1.7

    Fig.19 Schlieren photos in supercritical operation at

    M 2.0

    Fig.20 Schlieren photos in subcritical operation at

    M 2.0

    Fig.21 Schlieren photos of buzz in subcritical

    operation at M 2.0

    Fig.22 R.M.S. value of pressure fluctuation at M 2.0

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    H indicates the capture height and the height Ht indicates the height of the streamline passing through the intersection point between the second ramp shock and the terminal shock waves, respectively. The shear layer is ingested into the subsonic diffuser when Ht is smaller than H. The relations between the heights Ht and H at the inlet Mach numbers 2.0 and 1.7 were shown in Figures 24 and 25, respectively. Both of the heights Ht and Hdecreased as the spillage mass flow ratio increased. The capture height H was larger in the cases of smaller sidewall configurations, while the height Ht was smaller in the cases of smaller sidewall configurations. The minimum mass flow ratio without the ingestion of the shear layer was thereby dependent on the sidewall configuration. Assuming that buzz always occurs when the shear layer is ingested, the subcritical stability margin measured by the mass flow ratio increases by about 3 percents when the S1 sidewall is replaced by L1 at the inlet Mach number of 2.0. In the case of M1.7 it increases by 7 percents.

    Figures 26 and 27 show the stream tubes going into the subsonic diffuser in the cases of L1 and S1 sidewalls, respectively. The inlet Mach number was 2.0. The cross sectional area of the captured flow at the infinite upstream, which is approximated by the product of B and H, was almost the same in both

    Fig.23 Definition of height of stream line

    Fig.24 Variation of heights of stream line against

    spillage mass flow ratio at M 2.0

    of the cases because the spillage (or equivalently captured) mass flow ratio was almost the same. In the case of L1 sidewall air-intake, the sideways spillage mass flow was much smaller than the mass flow of the subsonic spillage escaping upward over the cowl lip. On the other hand, in the case of S1

    Fig.25 Variation of heights of stream line against

    spillage mass flow ratio at M 1.7

    Fig.26 Shape of capture stream tube of L1 air-intake

    at M 2.0; MFRcapture = 0.795

    Fig.27 Shape of capture stream tube of S1 air-intake

    at M 2.0; MFRcapture = 0.793

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    sidewall air-intake, the ratio of the sideways spillage mass flow to the total spillage mass flow is larger compared to the air-intake with L1 sidewall. The increase in the sideways spillage made the width of the stream tube B smaller causing the increase in the capture height H as long as the captured mass flow or the product of B and H was constant. The height H for S1 sidewall air-intake thereby became higher than that of L1 which explains the difference of S1 and L1 in Figure 24.

    The sideways spillage, in addition, exhibits the influence on the local Mach number distribution. The expansion waves generated by the sideways spillage propagated inside of the supersonic diffuser for spanwise direction. The flow upstream of the second ramp shock was accelerated by the expansion waves making the shock angle of the second ramp shock, shown in Figure 23, smaller. As a result, the intersection point between the second ramp shock and the terminal shock shifted lower. This made the difference larger in the height Ht with the sidewall configuration shown in Figure 24 and 25. External drag of the air-intake

    Figure 28 shows the air-intake total drag coefficient and its three components, a spillage drag, a bleed drag and a cowl drag, for the S1 and L1 sidewall air-intakes. The total drag of L1 sidewall air-intake was larger than that of S1 sidewall air-intake mainly because the spillage drag was different, while the other two components were almost the same.

    Spillage drag is determined by the integral of the pressure on the surface covering the capture stream tube. Figure 29 illustrates the top view of the pressure distribution on the surface of the capture stream tube. The upper half of Figure 29 shows the result of L1 sidewall air-intake while the lower half shows the result of S1 sidewall air-intake. It is

    Fig.28 Drag coefficient of air-intake at M 2.0

    clearly shown that the high pressure area in the case of L1 air-intake pushing the internal flow downstream to increase the drag is wider than that of the a ir - in take with S1 s idewal l . Another interpretation of the difference of the total spillage drag with different sidewalls can be written as follows. The sideways spillage flow is mainly supersonic because it goes through only oblique

    Fig.29 Pressure distribution on capture stream tube

    Fig.30 Operational range at M 2.0

    Fig.31 Operational range at M 1.7

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    shock waves. In contrast, the spillage flow escaping upward over the cowl lip is subsonic because it is decelerated and compressed going through both of the oblique and terminal shock waves. This compression caused larger drag per unit mass flow of the subsonic spillage compared to the sideways supersonic spillage. The larger portion of the subsonic spillage than the supersonic spillage in the case of L1 sidewall air-intake was one of the main reasons for the larger total spillage drag. Engine matching

    It is usual that the occurrence of the ingestion of the shear layer determines the low MFR operation criterion, while the spatial distortion determines the higher MFR operation criterion. In accordance with these criteria the data points in Figure 12 without the stable operation range were eliminated and only the points within the stable operation range were re-plotted in Figure 30. There was no supercritical operation margin in the case of L1 and L3 sidewall air-intakes. The air-intake with no supercritical margin must be operated at subciritical condition with additional spillage drag. The pressure recoveries of the air-intakes with the larger sidewalls, L1 and L3, were worse than those of the smaller sidewalls, S1 and L4. Using an air-intake with large spillage drag and low pressure recovery causes the aggravation of the net thrust of propulsion system. As the results, S1 or L4 sidewall configurations were better in the present study at the condition for the Mach number of 2.0.

    Similar consideration was done for M1.7. Figure 31 shows that there was no subcritical operation margin in the case of S1 air-intake at the inlet Mach number of 1.7. Subcritical operational margins were wider in the case of the larger sidewall configurations, L3 and L4, however, there was no operation margin at supercritical condition either.

    Conclusion In this study, the effects of the sidewall

    configurations on the aerodynamic performance of the rectangular external compression air-intake were investigated experimentally and numerically at two Mach numbers of 1.7 and 2.0.

    In the case with the large sidewall, the interaction of the shock waves with the sidewall boundary layer induced the longitudinal vortices in the subsonic diffuser, which caused serious pressure loss especially at Mach number 2.0. The pressure recovery and the distortion indices were aggravated by the longitudinal vortices especially at higher

    capture mass flow ratio in the case with the large sidewalls.

    The shear layer originating from the intersection point of the oblique and terminal shock waves was ingested into the air-intake in subcritical operation below a certain value of the mass flow ratio. The minimum mass flow ratio without the shear layer ingestion was higher for the air-intake with the smaller sidewall. The stable operation margin in subcritical condition was reduced more by the shear layer ingestion in the case of the smaller sidewall.

    The external drag was larger in the cases with the larger sidewalls due to the influence of the relatively high ratio of the subsonic spillage compared to the sideways supersonic spillage.

    In short, at the inlet Mach number 2.0, the air-intake with the smaller sidewalls have the advantage of high pressure recovery, low distortion and low external drag, while the air-intake with the larger sidewalls have the advantage of their wide range of safety operation range in subciritical condition. At the inlet Mach number 1.7, the differences in the pressure recovery and distortion were smaller compared to M2.0 because the interaction of the sidewall boundary layer and the shock waves was softened in the case of M1.7 compared to M2.0.

    References 1. Seddon, J. and Goldsmith, E.L., Intake

    Aerodynamics, AIAA Education Series ISBN 0-93040-03-7, 1985.

    2. Myong, H.K. and Kasagi, N., A new approach to the improvement of k-epsilon turbulence model for wall-bounded shear flow, JSME International Journal of Fluid Engineering, Vol. 109, 1990, pp.156-160.

    3. Roe, P.L., Approximates Riemann Solvers, Parameter Vectors and Difference Schemes, Journal of Computational Physics, Vol.43, 1981, pp.357-372.

    4. Chakravarthy, S.R. and Osher, S., A new class of high accuracy TVD schemes for hyperbolic conservation laws, AIAA paper 85-0243, 1985.

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