Calculation of the loss of the total pressure in channels with variable cross sectional area in the presence of turbulent mixing

Abstract

The method frequently used to estimate the loss of the total pressure, i.e., summation of the losses associated with the individual elements (struts, expansion of the channel, etc.) is not sufficient, since it does not take into account the fact that the nonuniformlty of the flow resulting from flow separation at a particular element and the associated losses may be changed by subsequent profiling of the channel. The refinement based on integration of the equations of continuity and motion in conjunction with an equation for the turbulent viscosity, as was done, for example, by Lanyuk [1] for nonuniform flow in nozzles, is impossible in many cases of practical interest because of the complexity of the channel configurations and the boundary layer separations that occur. Sekundov [2] has given a method for calculating the mixing in channels used for definite purposes based on a decisive role in the mixing being played by the initial turbulence characteristics. In many cases, however, the turbulence characteristics and the mixing are determined by the local flow conditions. Under such an assumption, a simple method is derived in the present paper for calculating the loss of the total pressure with allowance for mixing in a channel of variable cross sectional area.