Multicomponent turbulent boundary layer on a chemically active surface

When a gaseous mixture flows past chemically active surfaces the boundary layer formed on the wetted body may contain a large number of components with different diffusion properties. This leads to the necessity for studying the diffusion of the components in the multicomponent boundary layer.The use of thebinary boundary layer concept in the general case cannot yield satisfactory results, since replacement of the mutual diffusion coefficients D_ij of the various pairs of components by a single diffusion coefficient D in many cases is a rough approximation.In the general case the number of different diffusion coefficients is equal to N(N–1)/2 (N is the number of components). Usually it is possible to identify groups of components with similar molecular weights. Then the number of different diffusion coefficients may be reduced without large error. However, even in the comparatively simple case when it is possible to divide all the components into two groups with similar molecular weights we must take account of three different diffusion coefficients (one diffusion coefficient in each group and also the diffusion coefficient for the components of one group relative to the components of the other group). Only in particular cases when the gaseous mixture consists of only two components with arbitrary molecular weights, or if all the components of the gaseous mixture have similar molecular weights, can we with justification introduce a single diffusion coefficient (if in this case there are no limitations on the direction of the diffusion).Studies have been published covering the laminar multicomponent boundary layer. An analytic method for solving the equations of the laminar multicomponent boundary layer was developed by Tirskii [1]. There are also studies in which concrete results were obtained by numerical methods with the use of computers (for example, [2, 3]).As far as the author knows, for turbulent flow there are studies (for example, [4, 5]) covering flow with chemical reactions only in the case when all the diffusion coefficients are equal (D_ij=D).The present paper presents a method for calculating the turbulent multicomponent boundary layer with account for several different diffusion coefficients.Notation x, y coordinates - u, v velocity components - density - T temperature - h heat content - H enthalpy - c_i mass concentration of the i-th component - c₁⁽¹⁾ element concentrations in solid body - J_i diffusion flux of the i-th component - m molecular weight - dynamic viscosity coefficient - kinematic viscosity coefficient - heat conduction coefficient - c_p specific heat - adiabatic index - D_ij binary diffusion coefficients - P Prandtl number - S_ij Schmidt number - S_t Stanton number - M Mach number - friction - q radiant thermal flux - boundary layer thickness - D rate of displacement of gas-solid interface - degree of gasification - r_ij weight fraction of element i in component j - _ij stoichiometric coefficients - K_i reaction equilibrium constants - l number of components for which I_i0Indices i, j component number - w quantities for y=0 - * quantities on the edge of the laminar sublayer - ⁽¹⁾ quantities at the solid body - quantities at the outer edge of the boundary layer - molar transport coefficients