Transonic flow around NACA0012 — Welcome to LS-DYNA Examples

The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics (NACA, former NASA) in the 1940s. The four digit series define the profile by describing its maximum camber, the location of the maximum camber and the airfoil’s maximum thickness. The NACA 0012 is a symmetrical airfoil frequently used for benchmarking test cases.

In this test case, the Mach number is high enough to reach the so called transonic flow.
Transonic flow occurs when there is mixed subsonic and supersonic local flow in the same
flow field (typically with free stream Mach numbers from M = 0.7 or 0.8 to 1.3). When flowing
over the airfoil’s surface, the flow will accelerate and become locally supersonic resulting in
potential normal shock waves on the upper camber and lower camber. As in this particular
test case, the flow will be considered inviscid, no boundary layer will be developed on the
airfoil’s surface.

References :

D. L. Bonhaus, A HIGHER ORDER ACCURATE FINITE ELEMENT METHOD
FOR VISCOUS COMPRESSIBLE FLOWS, PhD thesis, Virginia Polytechnic Institute
and State University, 1998.

CESE pressure isocontours

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$ Example provided by Iñaki (LSTC)
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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 Transonic flow around NACA0012 profile
*INCLUDE
mesh.k
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$                                                                              $
$                             PARAMETERS                                       $
$                                                                              $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*PARAMETER
R    T_end        20
R  dt_plot       0.5
$
$--- Fluid
$
R dt_fluid    0.0001
Rcfl_fluid       0.7
R M_1           0.80
R P_1      1.1160714
R ro_1           1.0
R cv        2.790179
R cp         3.90625
*PARAMETER_EXPRESSION
Rg,Cp/Cv
*PARAMETER_EXPRESSION
Ra_1,sqrt(g*(P_1/ro_1))
*PARAMETER_EXPRESSION
Ru_1,a_1*M_1
$---+----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         1         2   
*CESE_CONTROL_TIMESTEP
$     iddt       cfl     dtint
         2&cfl_fluid &dt_fluid             
*CESE_CONTROL_LIMITER
$    idlmt      alfa      beta      epsr
         1       1.0       1.0       0.2
$---+----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                   3
*CESE_EOS_IDEAL_GAS
$    eosid        cv        cp
         3       &Cv       &Cp
$---+----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
         3
$   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
         4
$   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_NON_REFLECTIVE_SET
$     ssid
        2
*CESE_BOUNDARY_SOLID_WALL_SET
$     ssid
         5
*CESE_INITIAL
$      uic       vic       wic     rhoic       pic       tic
      &U_1       0.0       0.0     &ro_1      &P_1
$
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
$                                                                              $
$                             DATABASE (OUTPUT)                                $
$                                                                              $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
*DATABASE_BINARY_D3PLOT
&dt_plot
*END