NUMERICAL SOLUTION OF COMPRESSIBLE STEADY FLOWS IN A 2 D GAMM CHANNEL AND DCA 18 % PROFILE

• Ing. Pavel Kryštůfek, Czech Technical University of Liberec, Faculty of Mechanical Engineering, Dept. of Power Engineering Equipment, Studentská 2, 461 17 Liberec 1, pavel.krystufek@tul.cz prof. RNDr. Karel KOZEL DrSc., Czech Technical University in Prague, Faculty of Mechanical Engineering, Karlovo náměstí 13, 121 35 Prague 2; karel.kozel@fs.cvut.cz EPJ Web of Conferences , 010 (2012) DOI: 10.1051/epjconf/201225010 © Owned by the authors, published by EDP Sciences, 2012


INTRODUCTION
A numerical code has been developed for simulating transonic flow field in GAMM channel and around half DCA 18% profiles.For future simulating mesh generator type C has been developed.In this case mesh has been created for numerical solution over profile NACA 0012.

MATHEMATICAL MODELS
The 2D flow of an inviscid compressible fluid is described by the system of Euler equations.
( ) ( ) where , ( ) ( ) ( ) ( ) In the above equations, W is conservative variable, F , G are function of inviscid physical fluxes, ρ denotes density, 1 w , 2 w are components of velocity in the direction of axis x , y , p is pressure, e is total energy per unit volume.The parameter is the adiabatic exponent.

SPECIFICATION OF TEST CASES
We selected for numerical solution a structured mesh formed by quadrilateral finite volumes.Mesh for GAMM channel with selecting parameters is presented in Fig. 1.Mesh with half DCA 18% profile with selecting parameters is presented in Fig. 2. A program for generating mesh makes it possible any thickening of mesh in x direction.In y direction is controlled density only one parameter.( ) EPJ Web of Conferences

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Corrector: ( ) The Jameson's artificial dissipation AD damps undesirable oscillations and improves the stability of the method ( ) ( ) ( ) The convergence to the steady state is followed by log L2 residual defined by Re where N is a number of all elements in the computational domain.
At inlet part set values are considered for flow at infinity.At outlet p is given and other values are extrapolated.On wall zero derivatives of velocity vector along normal is considered.
The initial conditions must agree with request of even input approaching flow.That was defined by Mach number Ma , size of density and absolute size of velocity, where α is an angle between centers neighboring cells in x direction.

NUMERICAL RESULTS
For a 2D numerical simulation of flows of an inviscid compressible fluid in the GAMM channel and around half DCA 18% profile, the authors applied LW numerical schemes in McCormack's modification on a structured grid with 400 x 200 cells.

MESHES PREPARATION OF PROFILES WITH A BLUNT LEADING EDGE
The grid around profiles (wing) usually consists of a C-grid in the flow direction (Fig. 7.).In the case of the C-topology (Fig. 7.) the aerodynamics body is enclosed by one family grid lines, which also form the wake region.The situation is sketched in Fig. 8.
Examples of grid created by ours program were presented in Fig. 9.

CONCLUSIONS
Numerical solution has been applied on structured meshes with 400x200 elements.The LW-MC sheme has been used for GAMM channel and half DCA 18% airfoil.Then results were compared with other authors [7], [12].The mesh generator of the type C for profile with a blunt leading edge has been programed.

Fig 5 and Fig. 6 .
The result of pressure coefficient p C (Fig.6) is compared with G. S. Deiwert obtained by finitediference method with computational grid 50 x 38 cells.Progress of the pressure coefficient p C for inviscid flow from Deiwert is coarser and does not show details that are visible in our results.EFM11 01043-p.3

Figure 7 :
Figure 7: Structured surface and volume grid of a wing-body configuration (Courtesy O.Brodersen, DLR, Germany)