Transonic shock-wave/turbulent boundary-layer interactions in a circular duct

Om, Deepak; Viegas, J. R.; Childs, M. E.

doi:10.2514/3.8974

Cited by 30 publications

(11 citation statements)

References 12 publications

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“…This choice is due to the fact that the axisymmetric configuration minimises the three-dimensional effects from the shock wave/boundary layer interactions encountered in rectangular channels. 30 The numerical and experimental results by Kawatsu et al 31 reported that in rectangular ducts, the boundary layer separation occurs only near the corners of the duct but not at the centre plane of the test section, as it is observed with schlieren photography. Although Billig et al 32 stated that since the trend of the pressure rise for cylindrical and rectangular cross-sections is quite similar then the shock train characteristics may also be similar, no similarity law linking different cross-sectional geometries have been reported.…”

Section: Introductionmentioning

confidence: 92%

Numerical investigation on three-dimensional shock train structures in rectangular isolators

Gnani

Zare‐Behtash

White

et al. 2018

European Journal of Mechanics - B/Fluids

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The understanding of the formation of shock trains in high-speed engines is vital for the improvement of engine design. The formation of these flow structures in a narrow duct, driven by the presence of the viscous effects on the walls, is an extremely complex process that is not fully understood. This investigation demonstrates the high sensitivity of the shock train to the solving equations. The establishment of the shock train in the duct mainly depends on the way that the boundary layer develops on the walls. The k-ω Wilcox model confirms to be the most suitable to accurately reproduce the subtle features close to the solid boundary. The assumption of two-dimensional flow is not completely accurate for describing internal flows where the threedimensional effects from the shock wave/boundary layer interactions cannot be neglected. The centreline flow properties show that the first shock wave has the same strength in the two-and three-dimensional cases. However, in the three-dimensional case the thinner boundary layer behind the leading shock allows the flow to expand more in the subsonic region causing a stronger deceleration of the flow behind the first shock.

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Section: Introductionmentioning

confidence: 92%

Numerical investigation on three-dimensional shock train structures in rectangular isolators

Gnani

Zare‐Behtash

White

et al. 2018

European Journal of Mechanics - B/Fluids

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“…Moreover, the effect of blockage is to reduce the extent of separation for transonic interactions. 3 This further justifies the use of the above assumption for internal flows. The initial positive perturbation is taken to be the minimum *> ref perturbation that produces a continuous supersonic compression at the boundary-layer edge.…”

Section: Initial Pressure Perturbationmentioning

confidence: 80%

“…of the duct and very mild streamline curvatures. 3 ' 12 Based on this observation, it was decided that one-dimensional inviscid flow assumption should be a reasonable approximation for the inviscid flow in tin's region.…”

Section: Analytical Flow Modelmentioning

confidence: 98%

“…Increased blockage in internal flows produces a larger embedded supersonic region than is found for interactions in planar flows. 3 The treatment of the turning process of the flow in this region is presented in the section entitled Auxiliary Functions for C f and *> ref .…”

Section: Analytical Flow Modelmentioning

confidence: 99%

“…1 ' 3 The effect of blockage is to produce a lower pressure recovery, a less retarded boundary-layer flow, and a larger embedded supersonic region. 3 (The embedded supersonic region was termed "supersonic tongue" by Seddon. 1 )…”

Section: Introductionmentioning

confidence: 99%

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Integral analysis of transonic shock wave/boundary-layer interactionin internal flow

Childs

1985

Journal of Propulsion and Power

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An approximate integral viscous-inviscid interaction method ispresented for calculating the development of a turbulent boundary layer subjected to a normal shock wave in an internal flow. The inflow conditions and the downstream pressure are provided for the computation. In the supersonic region of shock pressure rise, the Prandtl-Meyer function is used to couple the viscous and inviscid flows. An analytical model for the coupling process is postulated and appropriate equations are defined. Downstream of the sonic point, onedimensional inviscid flow is assumed for coupling with the viscous flow. The viscous flow is calculated using Green's integral lag-entrainment boundary-layer method. Comparisons of the solutions with the experimental data are made for interactions which are unseparated, near separation, and separated. For comparison purposes, solutions to the time-dependent, mass-averaged Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model are also presented. The computed results from the integral method show good agreement with experimental data for unseparated interactions and reasonable agreement with the trend of the viscous effects when the interaction becomes increasingly separated. Nomenclature C E =entrainment coefficient Cf = skin-friction coefficient, 2r^/p e u 2 e C T = shear-stress coefficient F _ = function of C E and C f H,H l ,H = velocity profile shape parameters H k = kinematic value of H M = Mach number n = exponent in *> ref model P = pressure R = radius of the duct Re -Reynolds number T = temperature u = streamwise velocity x_ = axial distance X = (x-x u )/d u A = mass-flow thickness 6 = boundary-layer thickness 6* = boundary-layer displacement thickness 7 = specific heat ratio (=1.4) 0 = boundary-layer momentum thickness X = scaling parameter for secondary influences on turbulence structure v = Prandtl-Meyer function p = density r = shear stress =flow angle at the boundary-layer edge Subscripts 0 EQ = stagnation condition = equilibrium conditions EQ 0 = equilibrium conditions in absence of secondary influence on turbulence structure e = boundary-layer edge F ="ref = 0 r = recovery condition ref = reference condition u = start of interaction oo = freestream condition at the start of interaction

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