Transonic flow around NACA0012

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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$X
$X 1. Run file as is.
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$# UNITS: Dimensionless
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*KEYWORD
*TITLE
CESE Transonic flow around NACA0012 profile
*INCLUDE
mesh.k
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
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$                             PARAMETERS                                       $
$                                                                              $
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
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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
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Rg,Cp/Cv
*PARAMETER_EXPRESSION
Ra_1,sqrt(g*(P_1/ro_1))
*PARAMETER_EXPRESSION
Ru_1,a_1*M_1
$---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
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$                           CESE CONTROL CARDS                                 $
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    &T_end   
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*CESE_CONTROL_LIMITER
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         1       1.0       1.0       0.2
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$                       CESE PARTS/ EOS/ MATERIAL                              $
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         1                   3
*CESE_EOS_IDEAL_GAS
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         3       &Cv       &Cp
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$                    CESE BOUNDARY/INITIAL CONDITIONS                          $
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         1
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                                                          -1
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         3
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                                                          -1
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*CESE_BOUNDARY_PRESCRIBED_SET
$     ssid
         4
$   lcid_u    lcid_v    lcid_w    lcid_d    lcid_p    lcid_t
                                                          -1
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*CESE_BOUNDARY_NON_REFLECTIVE_SET
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         5
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