This test case consists of an oblique shock wave impacting a solid wall. The flow is considered viscous meaning that a boundary layer will be generated on the solid wall which will result in complex interactions occurring between the oblique shock wave and the boundary layer. Except for very weak shocks, no analytical solutions that accurately describes the behavior of the flow has been provided. Most results and information therefore rely on experimental results making numerical tools very important in order to accurately reproduce and predict complex interactions.
In the case of an oblique shock wave impacting a boundary layer, the boundary layer will thicken and possibly separate in the area of the impact point of the incident shock wave. In the case of a boundary layer separation, the reflected shock wave will be generated upstream of the impact point of the incoming shock wave. On the other hand, after the impact point, the boundary layer’s thickness should diminish generating expansion waves that may accelerate the flow sufficiently enough in order to make it locally supersonic again and generate a second reflected shock wave. Although not the subject of this test case, a possible turbulent transition of the boundary layer may also occur.
References :
G. I. T. L. HAKKINEN, R.J. AND S. ABARBANEL, The interaction of an oblique shock wave with a laminar boundary
layer, NASA Memo 2-18-59W, (1959).
CESE pressure isocontours
*CESE_BOUNDARY_NON_REFLECTIVE_SET *CESE_BOUNDARY_PRESCRIBED_SET *CESE_BOUNDARY_SOLID_WALL_SET *CESE_CONTROL_LIMITER *CESE_CONTROL_SOLVER *CESE_CONTROL_TIMESTEP *CESE_EOS_IDEAL_GAS *CESE_MAT_GAS *CESE_INITIAL *CESE_PART *CONTROL_TERMINATION *DATABASE_BINARY_D3PLOT *ELEMENT_SOLID *KEYWORD *NODE *PARAMETER *PARAMETER_EXPRESSION *TITLE *SET_SEGMENT
$-----------------------------------------------------------------------------
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$ Copyright, 2015 DYNAmore GmbH
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$X------------------------------------------------------------------------------
$X
$X 1. Run file as is.
$X Requires LS-DYNA MPP R8.0.0 (or higher) with double precision
$X
$X------------------------------------------------------------------------------
$# UNITS: Dimensionless
$X------------------------------------------------------------------------------
$X
*KEYWORD
*TITLE
CESE Shock Boundary layer interaction
*INCLUDE
mesh.k
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$ $
$ PARAMETERS $
$ $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*PARAMETER
R T_end 16
R dt_plot 0.5
$
$--- Fluid
$
R M_1 2.00
RBetad 32.6
R P_1 0.1785714
R ro_1 1.0
R Cp 0.625
R Cv 0.446429
R dt_fluid 0.0001
Rcfl_fluid 0.9
Rmu_c1 6.566e-6
Rmu_c2 0.9436
RPrandtl 0.7
$ The oblique shock relations then give the following parameters for a
$ Betad=32.6 degree obloque shock wave :
*PARAMETER_EXPRESSION
Rg,Cp/Cv
*PARAMETER_EXPRESSION
Rgplus,g+1
*PARAMETER_EXPRESSION
Rgmin,g-1
*PARAMETER_EXPRESSION
Rbeta,(Betad*pi)/180
*PARAMETER_EXPRESSION
Rsinb,sin(beta)
*PARAMETER_EXPRESSION
Rcotb,ctn(beta)
*PARAMETER_EXPRESSION
RMn1,M_1*sinb
*PARAMETER_EXPRESSION
Rro_2,ro_1*(gplus*(Mn1*Mn1))/(gmin*(Mn1*Mn1)+2)
*PARAMETER_EXPRESSION
RP_2,P_1+(P_1*2)*(g/gplus)*(Mn1*Mn1-1)
*PARAMETER_EXPRESSION
Rtantheta,2*cotb*((M_1*M_1)*(sinb*sinb)-1)/(2+M_1*M_1*(g+cos(2*beta)))
*PARAMETER_EXPRESSION
Rtheta,atan(tantheta)
*PARAMETER_EXPRESSION
RMn2,sqrt(((Mn1*Mn1)+2/gmin)/(2*(g/gmin)*(Mn1*Mn1)-1))
*PARAMETER_EXPRESSION
RM_2,Mn2/sin(beta-theta)
*PARAMETER_EXPRESSION
RU_2,M_2*sqrt(g*(P_2/ro_2))
*PARAMETER_EXPRESSION
RU_1,M_1*sqrt(g*(P_1/ro_1))
*PARAMETER_EXPRESSION
Ruy_2,-1*(U_2*sin(theta))
*PARAMETER_EXPRESSION
Rux_2,U_2*cos(theta)
$
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$ $
$ CESE CONTROL CARDS $
$ $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*CONTROL_TERMINATION
$ endtim endcyc dtmin endeng endmas
&T_end
*CESE_CONTROL_SOLVER
$ iframe iflow igeom
0 0 2
*CESE_CONTROL_TIMESTEP
$ iddt cfl dtint
2&cfl_fluid &dt_fluid
*CESE_CONTROL_LIMITER
$ idlmt alfa beta epsr
0 0.0 1.0 0.5
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$ $
$ CESE PARTS/ EOS/ MATERIAL $
$ $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*CESE_PART
$ pid mid eosid
1 7 3
*CESE_EOS_IDEAL_GAS
$ eosid cv cp
3 &Cv &Cp
*CESE_MAT_GAS
$ mid c1 c2 prnd
7 &mu_c1 &mu_c2 &prandtl
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$ $
$ CESE BOUNDARY/INITIAL CONDITIONS $
$ $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*CESE_BOUNDARY_PRESCRIBED_SET
$ ssid
1
$ lcid_u lcid_v lcid_w lcid_d lcid_p lcid_t
-1
$ sf_u sf_v sf_w sf_d sf_p sf_t
&U_1 0.0 0.0 &ro_1 &P_1
*CESE_BOUNDARY_PRESCRIBED_SET
$ ssid
5
$ lcid_u lcid_v lcid_w lcid_d lcid_p lcid_t
-1
$ sf_u sf_v sf_w sf_d sf_p sf_t
&Ux_2 &Uy_2 0.0 &ro_2 &P_2
*CESE_BOUNDARY_NON_REFLECTIVE_SET
$ ssid
2
*CESE_BOUNDARY_NON_REFLECTIVE_SET
$ ssid
4
*CESE_BOUNDARY_SOLID_WALL_SET
$ ssid
3
*CESE_INITIAL
$ uic vic wic rhoic pic tic hic
&Ux_2 &Uy_2 0.0 &ro_2 &P_2
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$ $
$ DATABASE (OUTPUT) $
$ $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*DATABASE_BINARY_D3PLOT
&dt_plot
*END