Three-dimensional laminar boundary layer on a permeable surface in the neighborhood of a symmetry plane (original) (raw)
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Fluid Dynamics, 1990
An approximate method of determining the heat transfer and friction stress in three-dimensional flow problems using the two-dimensional and one-dimensional solutions is proposed. This method is applicable over a wide range of Reynolds numbers --from low to high. On the basis of a theoretical analysis of the approximate analytic solution of the equations of a three-dimensional viscous shock layer it is shown that the problem of determining the heat flux in the neighborhood of the plane of symmetry of bodies inclined to the flow at an angle of attack can be reduced, firstly, to the problem of determining that quantity for an axisymmetric body and, secondly, to the problem of determining the heat transfer to an axisymmetric stagnation point. On the basis of an analysis of the results of a numerical solution of the problem it is shown that corresponding analogs can also be used for the friction stress. The accuracy of the similarity relations established is estimated by solving the problem by a finite-difference method. A similarity relation of the same kind was previously obtained in [i] for a double-curvature stagnation point.
Fluid Dynamics, 1990
The three-dimensional supersonic flow of nonequilibrium dissociating air past smooth blunt bodies on whose surface heterogeneous chemical reactions are taking place is investigated within the framework of thin viscous shock layer theory. An economical numerical method of solving the equations with an improved order of approximation with respect to the normal coordinate is employed. This method does not require the preliminary solution of the Stefan--Maxwell relations for the diffusion fluxes and makes it possible to calculate flows that do not possess a plane of symmetry. The effect of the angles of attack and yaw, the catalytic reaction model and a number of other parameters of the problem on the pressure, heat flux and equilibrium surface temperature distributions is analyzed with reference to the example of flow past a triaxial ellipsoid.
Supersonic nonuniform gas flow around elongated axisymmetric bodies
Journal of Applied Mechanics and Technical Physics, 1990
The equations for a thin viscous shock layer near elongated hyperboloids of revolution oriented at zero angle of attack in a nonuniform gas flow are solved numerically in a wide range of values of the determining parameters of the problem.
Interaction between Boundary Layer and Shock in Hypersonic Flows with chemical real gas effects
In this paper, viscous interaction phenomenon in hypersonic flows with chemical reactions is numerically simulated. Two-dimensional Navier-Stokes equations are solved to simulate this phenomenon. Inviscid fluxes are approximated using Van Leer flux vector splitting method and to increase the accuracy of this approximation, MUSCL approach with Van albada limiters is applied. Chemical reactions are considered to be in equilibrium conditions. With this assumption there is no closed form for equation of state for the gas (air) and relation between thermodynamic properties are calculated from thermodynamic tables. In addition, transport properties (viscosity and conductivity) are functions of two independent thermodynamic properties. These functions are calculated using kinetic theory. To evaluate the performance of the model used in this research, some test cases are studied. First test case is flow over a ramp with various angles. The results of this test case are compared with the results of other numerical methods and the effect of geometry on separation length is studied. The second case is a hypersonic flow over a 15-degree ramp. The results are in good agreement compared with experimental data. In addition, there results are compared with the results of ideal gas (nonreacting flow) calculations. It can be seen that ideal gas assumption for air introduces considerable deviation form experimental data.