A Solution of Shock-Induced Boundary-Layer Interaction Problems by an Integral Method

1971 ◽  
Vol 38 (4) ◽  
pp. 775-782
Author(s):  
J. W. Murdock
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Shear Stress ◽  
Exact Solutions ◽  
Relative Proportion ◽  
Leading Edge ◽  
Momentum Equation ◽  
Layer Interaction ◽  
Boundary Layer Interaction ◽  
Layer Region

An integral technique is developed to solve a general class of shock-induced boundary-layer interaction problems. Included in this class is the boundary layer which grows downstream of the leading edge of a semi-infinite flat plate with a shock wave propagating over it, and the boundary-layer region in a shock tube that is dependent upon both the shock wave and the expansion wave. The integral equations used to solve the Howarth transformed (incompressible) momentum equation are formulated in terms of a general two-parameter family of velocity profiles. These equations are solved for a velocity profile which is a linear combination of the two exact solutions valid at either end of the interaction region. The relative proportion of these two solutions is controlled by a shape factor similar to the Karman-Pohlhausen one in that it is controlled by the degree of unsteadiness in the boundary layer rather than by the pressure gradient. The solutions generated are in excellent agreement with published exact solutions, and all discontinuities in the slope of the shear stress present in earlier similar integral solutions are eliminated. The momentum and displacement thicknesses and the wall shear stress are predicted to within one percent of the exact values.

Simulation of blunt-fin-induced shock-wave and turbulent boundary-layer interaction

1985 ◽  
Vol 154 ◽  
pp. 163-185 ◽  
Author(s):  
Ching-Mao Hung ◽  
Pieter G. Buning
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Flat Plate ◽  
High Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Horseshoe Vortex ◽  
Layer Interaction ◽  
Boundary Layer Interaction

The Reynolds-averaged Navier–Stokes equations are solved numerically for supersonic flow over a blunt fin mounted on a flat plate. The fin shock causes the boundary layer to separate, which results in a complicated, three-dimensional shock-wave and boundary-layer interaction. The computed results are in good agreement with the mean static pressure measured on the fin and the flat plate. The main features, such as peak pressure on the fin leading edge and a double peak on the plate, are predicted well. The role of the horseshoe vortex is discussed. This vortex leads to the development of high-speed flow and, hence, low-pressure regions on the fin and the plate. Different thicknesses of the incoming boundary layer have been studied. Varying the thicknesses by an order of magnitude shows that the size of the horseshoe vortex and, therefore, the spatial extent of the interaction are dominated by inviscid flow and only weakly dependent on the Reynolds number. Coloured graphics are used to show details of the interaction flow field.

Study of Shock/Blade Tip Leakage Vortex/Boundary Layer Interaction in a Transonic Rotor With IDDES Method

2013 ◽  
Author(s):  
Ke Shi ◽  
Song Fu
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Vortex Breakdown ◽  
Leading Edge ◽  
Wave Surface ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Layer Interaction ◽  
Boundary Layer Interaction ◽  
Blade Tip

In the present study, Improved Delayed Detached Eddy Simulation (IDDES) based on k-ω-SST turbulence model is applied to study the unsteady phenomenon in a transonic compressor rotor. Particular emphasis is on the understanding of the complex underlying mechanisms for the flow unsteadiness caused by the interaction of passage shock, blade tip leakage vortex (BTLV) and the blade boundary layer. The sources of the significant unsteadiness of the flow are shown. At the lower span height, where the BTLV is far away, the shock wave ahead of the blade leading edge impinges on the suction surface boundary layer of the adjacent blade, causing the shock wave/boundary layer interaction (SWBLI). Boundary layer thickness grows, while flow separates after the interaction. Predicted by IDDES calculation, this shock-induced separation exists as a separation bubble. The flow reattaches very soon after separation. At the near tip region, the shock wave surface deforms due to the strong interaction between the shock and the BTLV. Oscillation of the shock wave surface near the vortex core infers an unsteady contend between the shock and the vortex. Iso-surfaces of the Q parameter are applied to identify the vortex and its structure. Normally, the vortex breakdown in the rotor passage will lead to stall. However, in the present transonic case, the vortex breakdown was observed even at the near peak efficiency point. While the mass flow rate decreases, the shock waves formed ahead of the rotor blade leading edge were pushed upstream, causing earlier casing wall boundary layer separation. Upstream moving behavior of the shock is considered a new stall process.

Separation mitigation using pressure feedback technique for hypersonic shock wave boundary layer interaction

2018 ◽  
Vol 233 (10) ◽  
pp. 3519-3533 ◽  
Author(s):  
Siddesh Desai ◽  
Vinayak Kulkarni ◽  
Hrishikesh Gadgil
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Leading Edge ◽  
Separation Control ◽  
Feedback Channel ◽  
Layer Interaction ◽  
Boundary Layer Interaction ◽  
Pressure Feedback ◽  
Wave Boundary ◽  
Separation Size

Present studies are focused on the use of pressure feedback technique as a separation control technique for ramp induced flow separation at hypersonic speed. Numerical simulations portrayed that though pressure feedback technique can reduce the flow separation, further cooling of the feedback channel enhances its potential for separation control. Marginal cooling of channel walls to 175 K has reduced separation bubble size by 18.18% while strong cooling of those walls to 50 K reduced the separation by 30%. Such low enthalpy perfect gas simulations also showed the lower effectiveness of pressure feedback technique with increased ramp angle. Further, it has been noticed from the perfect and nonequilibrium gas flow simulations that the cooling of pressure feedback channel introduces differential separation size for the same wall-to-total temperature ratio cases. Integration of cooled pressure feedback channel with blunt leading edge configuration showed reduced separation size for any bluntness radius. Effectiveness of this integration is seen in lowering the values of inversion and equivalent radii. Thus, use of cooled pressure feedback technique in conjunction with leading edge bluntness is not only seen to have reduced the intensity of shock wave boundary layer interaction but also has enhanced the controllability of blunted leading edge without altering the entropy layer–boundary layer interaction.

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