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7
On Isolator Performance
Sridhar T, Chandrabose G & Thanigaiarasu S
Dept. of Aerospace Engg., Madras Institute of Technology, Chennai, India.
E-mail: [email protected], [email protected], [email protected]
Abstract – The three dimensional Reynolds Averaged Navier Stokes (RANS) Computational Fluid Dynamics analysis has been employed to study the influence of geometrical shape transition on performance of scramjet isolators. The pre-combustion shock train also called pseudo shock which appears in the subsonic combustion mode in dual mode scramjet isolator is analyzed in shape transitioned isolators. A square isolator and a shape transitioned square to circular isolator configurations having same length and cross sectional areas were considered. The simulations were carried on isolator geometries for inlet conditions of Mach 2 and unit Reynolds number of 12.4x106/m. The pressure rise due to heat addition in combustion chamber is modeled with back pressure 3.8 times higher than the inlet static pressure. The Numerical results match with the experimental data obtained from literature and with the waltrup and Billig correlation. The length of pseudo shock is compared in these isolators and it is found that it is shorter for square to circular configuration.
Index Words - Dual mode Scramjet isolator, Inlet unstart, Pre-combustion shock train, Pseudo shock wave, shape transition
NOMENCLATURE Mi Inlet Mach number P0 Total pressure (kPa) T0 Total temperature (K)
P static pressure at some location (kPa) Pi inlet static pressure (kPa)
Pb static back pressure (kPa) A Cross sectional Area (mm2) H Duct half height
L length of the duct (mm) γ ratio os specific heats PSW Pseudo Shock Wave x Pseudo shock length
Mx Mach number upstream of shock train.
Θ Momentum thickness just upstream of the shock train
α Reynolds number exponent.
Reθ Reynolds number based on momentum thickness just upstream of the shock train.
DH Hydraulic diameter.
Pi/Pb Ratio of pressure across the pseudo shock.
I. INTRODUCTION
The flow path of a dual mode ramjet/scramjet engine consists of an inlet, an isolator, a combustor and a nozzle. The isolator is one of the most critical components and is situated between the inlet and the combustor of a dual-mode ramjet/scramjet engine. Its primary function is to contain the pre-combustion shock train that forms at the entrance of combustion chamber due to the pressure rise caused by the intense turbulent combustion on the low supersonic flow (ramjet mode).This shock train acts as a mechanism to prevent the interaction between the scramjet combustor and the inlet, thereby preventing inlet „unstart‟ condition. The design of an inlet system and isolator plays a key role in hypersonic transportation. In recent trends, the numerical prediction of flow field inside the inlets and isolators has proved an active field of research for the development of a hypersonic vehicle with better performance.
Many researches have been conducted on phenomenon of shock wave boundary layer interactions inside constant area ducts. Neumann and Lustwerk [1, 2] conducted an experiment with a constant area tube and showed that no shock train was formed in the absence of boundary layer case. Carroll and Dutton [3, 4] studied the shock structure in rectangular ducts at Ma
= 1.6 and 2.45 and showed that the level of flow confinement had only a small effect on the shock train.
Balu et al [5] studied the performance of an isolator scramjet engine with inlet Mach number 2.0 and found that for length to height ratio of 4 to 5, shock train can be established with maximum static pressure in the isolator. Allen et al. [6] have studied the shock train leading edge of a scramjet isolator using RANS and LES numerical models and showed RANS model show
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8 reasonably better agreement with experimental results than LES model. The effects of the divergent angle and the back pressure on the shock wave transition and the location of the leading edge of the shock wave train in the scramjet isolator are predicted by Wei Huang et al.
[7]using three dimensional coupled implicit Reynolds Averaged Navier- Stokes equations and the standard k-ε turbulence model. Kaname Kawatsu et al. [8]
numerically simulated the PSW in straight and diverging ducts with rectangular cross section and observed the separation of boundary layer by the first shock wave of PSW can be seen only near the corners of the duct. In contrast, in the diverging duct case the large separation region appeared at one corner of the upper wall and did not reattach to the wall in the test section. Waltrup and Billing [9]investigated the structure of shock waves in cylindrical ducts in adverse pressure gradients at high Mach numbers and range of Reynolds numbers and confinement levels. At Ma = 1.53 a single normal shock was found. At mach numbers 1.68 to 2.97 a repeated oblique shock was found. Based on the wall static pressure and in-stream pitot pressure distribution obtained from the experiments a simple quadratic relation has been derived to obtain the length of the shock train. This is the only empirical relation available for initial estimate of the isolator length and wall static pressure distribution along the length for a given inlet parameters of mach number, boundary layer parameters, duct diameter and the level of pressure rise across the duct. The above empirical relation was modified for the rectangular ducts based on the study carried out by Sullins et al. and Lin et al. [10], [11]. Numerical simulation and experiments on the Mach 2 PSW in a square duct are performed by Sun et al. [12] on the basis of two-dimensional Navier-Stokes equations, using a Baldwin-Lomax turbulence model, and the Mach 2 supersonic wind tunnel. The numerical results agree well with the experimental results. Based on these investigations, the shock train characteristics, structure, pressure and velocity distributions, and the effect of flow confinement on the interaction are analyzed in detail.
From previous literatures it was found that the effect of Mach number, Reynolds number, boundary layer thickness, adverse pressure gradient on the shock train have been studied intensively, on the other hand the influence of shape transition of isolator geometry on the pseudo shock behaviour has not been investigated numerically.Therefore this study is aimed to numerically investigate the geometrical influence of isolator shape transition on pseudo shock characteristics, the location of leading edge of the PSW, corner flow separation region, the length of shock train and internal drag.
II. COMPUTATIONAL METHODOLOGY A. Physical Model
The Schematic diagram of two isolator configurations namely square and square to circular are shown in Figs 1(a) and 1(b) respectively. The length and height of the square duct are taken as 300 mm and 30mm respectively, the dimensions of square duct are taken with reference from literature[8]. The square to circular configuration has the same square section at entrance and circular section at exit of radius 16.93mm, the radius is chosen to be consistent with the flow cross sectional area of square duct. The cross sectional shapes of square to circular isolator are linear interpolation of end section shapes.
Fig.1 Schematic diagram of isolators B. Numerical Approach
The computational grid of square to circular isolator is shown in Fig 2. Because of the symmetry of the two isolator configurations, only one- quarter portion of the duct is considered for simulation. A nominal three dimensional structured grid with 0.6 million cells is selected as computational domain after the grid independent study and the grid is clustered near the wall to obtain the value of y+~1, the first cell height is 0.05mm off the wall. The numerical analysis is carried out using coupled implicit Reynolds Averaged Navier- Stokes (RANS) equations.
Fig.2 Numerical Grid for Square to circular isolator
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9 The equations are solved using density based finite volume technique. Roe‟s flux difference splitting is used for inviscid fluxes. The flow equations are spatially discretized using monotone upstream-centered scheme for conservative laws (MUSCL) to third accuracy. Dry air using ideal gas approximation is used as the working fluid with constant specific heats with γ =1.4, viscosity is computed using Sutherland‟s formulation. Because of its robustness, the renormalization group (RNG) k-ε turbulence model is incorporated which is capable of capturing the major features of the flow with shock- boundary interactions, corner vortices and separation.
C. Boundary Conditions
The supersonic flow at the inlet of the isolator geometry is defined by imposing boundary conditions given in Table-I. Outlet of the isolator is defined by specification of constant back pressure (Pb) 3.8 times higher than inlet static pressure to simulate the pressure rise due to combustion and remaining variables are extrapolated. Wall boundary condition is specified as no-slip condition and heat flux across the wall is specified as zero to model adiabatic condition. The
„symmetry‟ conditions are applied to symmetry surfaces. Turbulence is specified with intensity and hydraulic diameter. Convergence of the numerical solution is ensured by monitoring the residuals of equations and history of mass flow rate.
Table-I Boundary conditions at the inlet of isolators Ma T0 (K) P0 (kPa) Pi (kPa)
2 298 100 12.78
III. VALIDATION CASE
Fig.3 Comparison of Numerical and Experimental results
The validation case considered here is from literature [8] where the experimental investigation of pseudo shock is conducted in square test section of
30mmx30mm in intermittent suction type supersonic wind tunnel. The test section Mach number is kept at 2.3 and plenum pressure is 100kPa and temperature is 298K. The back pressure is applied by means of butterfly valve placed at the end of tunnel section which is applied to produce a ratio of 3.8 between outlet and inlet static pressures. The comparison of Numerical and experimental data of static pressure along the center line of isolator bottom wall is shown in Fig.3. The pressure in the plot is normalized with isolator entrance total pressure value of 100kPa and the position is normalized with height of the isolator which is 30mm. It can be seen that numerical results matches well with the experimental data, the position of pressure rise i.e. the leading edge of pseudo shock is predicted closely by simulation. The pressure values are slightly higher than experimental data in the shock free region (X/H of 0 to 5). This may be due to uniform conditions assumed in the boundary conditions and unavailability of wind tunnel turbulent parameters, although it agrees well in the pseudo shock region (X/H of 5 to 10). Hence validation indicates that acquired computational methodology and turbulence model can be utilized in solving the shock train flow field inside isolator.
IV. RESULTS AND DISCUSSION
The contours of static pressure and Mach number along the symmetry plane are shown in Figs 4 and 5 respectively. These contours confirms the formation of pseudo shock inside the isolator configurations and also shock train region contains series of bifurcated normal shocks i.e. the normal shock is bifurcated by the lambda shock emanating from the boundary layer. Behind each bi-furcated shock, there forms a diamond shaped expansion region as seen from Figs 4 and 5. The shock wave and expansion wave pattern resembles similar in symmetry plane for two isolator configurations regardless of the shape transition, although changes were observed in planes offset from symmetry. The normal shock portion in the bifurcated shock system is minimal for the first shock and increases downstream.
Fig.4 static Pressure contours in the symmetry plane
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10 A series of four clearly visible shock-expansion pairs were observed regardless of the length of pseudo shock region. The thickness of boundary layer increased rapidly after its encounter with leading leg of lambda shock at the foot of first shock as seen in Fig.5. This rapid growth was reduced aft of the trailing lambda leg at the foot of first shock decreasing boundary layer thickness which results in divergence of effective flow area confined by boundary layer. The result is flow expansion after shock wave which accelerates the core flow to supersonic creating successive shock waves.
Fig.5 Mach number contours in the symmetry plane The interval between shock wave and expansion wave and level of expansion decreases whereas the thickness of boundary layer increases downstream through the shock train as shown in Fig.5. It is also observed that the rate of boundary layer growth is maximum at the foot of first shock wave compared to successive shocks. This shows that the strength of interaction is strong at leading edge of pseudo shock and is weak at the trailing edge. The supersonic flow region was confined to the center region of isolator whereas the subsonic flow region was observed to be spread out from the wall to the core as seen in Fig 5.
This subsonic flow region was dominant downstream of shock train, thus, the boundary layer edge rearwards of the shock train has mixed supersonic and subsonic flow.
The plot of static pressure along the isolator center axis is shown in Fig 6. The repeated rise and fall in pressure plot shows formation of normal shock and expansion wave at the core of shock train. The oscillations in the plot dies out and levels downstream marking the end of shock train region, although some slight undulations are observed. The Mach number distribution followed the inverse trend of static pressure.
The distribution of static pressure along the center line of bottom wall is shown in Fig 7. This plot is significant as it displays the length of the pseudo shock.
The leading edge position of pseudo shock is identified by sudden rise in wall static pressure. The curve
increases monotonically through the shock train region and levels off near the aft region of pseudo shock reaching the value of back pressure. As seen from Fig 7, the pseudo shock length is the longest for square isolator and is the least for square to circular isolator.
The position is normalized with length of the isolator which is 300mm.
Fig.6 Static pressure distribution along isolator center line
Fig.7 Static pressure distribution along isolator wall center line
Compared with the square isolator the square to circular isolator have less separation region influenced by corner vortices as noticed from Fig 8; the low pressure corner region was found throughout the square isolator duct due to inherent presence of geometrical corner in square cross section. As a result of shape transition, the geometrical corner was eliminated downstream in square to circular isolator. Also seen the separation region was thinner and longer for square configuration whereas it was wider and shorter in square to circular configuration.
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11 Fig.8 wall shear stress contour of isolators
In order to assess the performance of the two isolator configurations the following parameters are considered. They are pseudo shock leading edge position, pseudo shock length, shock train distribution inside pseudo shock, shock train length, internal drag, total pressure recovery and Mass weighed Mach number at duct exit. The parameters are summarized in the Table-II. The shock train distribution inside the pseudo shock and its position are calculated by observing undulations in Fig.7.
Table-II Performance comparison of isolators Parameters Square Square to
Circular Pseudo shock leading
edge position 0.08 m 0.12 m Pseudo shock length
(x/L) (in percentage of duct
length)
0.733
(73.3%) 0.6 (60%) Shock train
distribution inside pseudo shock (in percentage of duct
length)
0.08 m – 0.22 m
0.12 m – 0.22 m
46.6% 33.3%
Shock train length
(x/L) 0.466 0.333
Internal Drag
Pressure
Drag 0 N 0.279N
Viscous
Drag 2.81N 2.743N
Total
Drag 2.81N 3.022N
Mach Number at
center of exit plane 0.9913 1.0156
Mach number at exit plane (Mass weighed
average)
0.709 0.717 Total pressure
recovery 0.703 0.704
It is noticed from the above comparison that the pseudo shock length in the square to circular duct was least compared to square duct and the position of its leading edge is located well aft wards i.e. 40% of duct length from the entrance compared with 26.67% of square duct. The shock train distribution in pseudo shock of square to circular duct was also the least compared with square duct. The internal drag was the least for square duct, this may be due to the fact that only viscous forces contribute for internal drag in square isolator, whereas both viscous and pressure forces contribute in square to circular isolator. It may be accounted to the presence of axial geometrical divergence and shrinkage of wall surfaces in latter in transforming from square to circular shape.
The Mach number at the center of exit plane is comparable and is near sonic for both configurations, which shows the thermal chocking of low supersonic flow due to the heat addition inside combustion chamber. The mass weighed average of Mach number at isolator exit plane are nearly same around 0.7 indicating presence of maximum subsonic portion compared to supersonic portion and this shows the mixing of subsonic and supersonic flows in aft region of pseudo shock. Total pressure recovery is almost same for the two isolators regardless of shock train distribution inside pseudo shock length and its length, hence the presence of pre-combustion shock train costs 30% of total pressure, thus the loss in energy.
V. COMPARISON OF NUMERICAL RESULTS WITH WALTRUP AND BILLING
CORRELATION
Fig.9 Comparison of Pseudo shock length
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12 The obtained pseudo shock length from numerical results is compared with the experimental correlation formula given by Waltrup and Billing [8], they developed a well-known empirical relationship between the pressure distribution in the pseudo shock and several circular duct flow parameters. This relation is modified where the Reynolds number exponent is obtained by average values of square and circular ducts .i.e.α=0.225. The correlation is given below
As seen from Fig.9, the pseudo shock lengths acquired from Numerical simulation for square and square to circular isolator configuration agrees with the pseudo shock length obtained from experimental correlation formula. This shows that the correlation may be used to estimate the preliminary isolator length required to contain the pseudo shock.
VI. CONCLUSION
The computational analyses were carried out over square and square to circular isolator configurations to study the influence of shape transition on their performance.
The numerically obtained pseudo shock lengths for square and square to circular configurations were verified with the Waltrup and Billing experimental correlation and were found to match with correlated pseudo shock length.
The square to circular isolator contained the shortest pseudo shock length for given isolator pressure ratio of 3.8 and given isolator length of 300mm. The influence of corner vortices remained less for square to circular isolator and posed shorter wider separation region compared to square configuration. The internal drag of square to circular isolator was higher than the square isolator. The exit Mach number and total pressure recovery were comparable for two isolator configurations.
It is found that owing to shape transition the square to circular configuration outperforms over the square configuration. Hence from the point of given isolator length and pressure ratio, the square to circular isolator is favorable in order to permit continuous inlet operation, containing within it the shorter pre- combustion shock train in ramjet mode of combustion.
Hence it can allow pressure rise more than the imposed back pressure by enclosing the complete shock train and prevent it from interacting with inlet causing unstart condition.
VII. REFERENCE
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[3]. Carroll B.F and Dutton J.C, "Characteristics of multiple shock wave/turbulent boundary layer interactions in rectangular ducts", J.Propulsion Power, 1990, Vol. 6(2), pp. 186 - 193.
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[5]. Balu G., Sumeet Gupta, Nischal Srivastava, Panneerselvam and Rathakrishnan E.,
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[8]. Kawatsu K, Koike S, Kumasaka T, Masuya G and Takita K, "Pseudo-shock wave produced by backpressure in straight and diverging rectangular ", AIAA paper 2005-3285, 2005.
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