Calculation of losses in stage of turbo-expansion engine

Abstract

A topical problem is the elaboration and testing of a method of calculating losses in elements of the through-flow part and stage of turbo-expansion engines as a whole, necessary for the prediction of the efficiency of the planned stage and for the optimization of its geometric and regime relations. This problem in engineering statement was solved by analytical and experimental methods at the AO Kriogenmash. The newly devised method of calculating losses was first: tested, element by element on stands, and was then integrated into the system of automated designing of turbo-expansion engines, and finally the calculated and experimental efficiencies were compared on the investigated industrial stages. The experiments were carried out with stages differing from each other in scale, level of initial pressure, the kind of gas, etc. The results lead to the conclusion that the method is objective and is of scientific and applied interest.Let us consider the main postulates of the method.Components of the Losses. By calculation, almost all the components of the hydraulic losses of the stage are checked: losses in friction and secondary losses in the channel of the diffuser (DF) consisting of a nozzle, the oblique edge, and a radial gap; losses in friction and secondary losses in the channel of the rotor (R) consisting of the channel itself and the oblique edge; losses of partialness in the R on account of detachment of the flow from the wall of the oblique edge of the DF; edge losses in the DF and R; impact losses at the inlet to the R if in the theoretical regime the angle of attack is nonzero; losses at outlet velocity in view of the useful effect of the end diffuser. The losses of power of the stage through disk friction and flow-off are also checked by calculation. The friction losses and the secondary losses in the channel of the nozzle, in the cbannel and the oblique edge of the R are examined by the unidimensional scheme of calculation, in the oblique edge of the DF and in the gap by the plane scheme (jet by je0. Besides that, the type of stage is specified: DF channel type; R radial-axial. According to the experimental data the hydraulic losses and the losses through control in the channel DF are smaller than in the vane DF; the efficiency of the stage with radial-axial R is higher than of the stage with radial R [3].Friction Losses. The calculation of friction losses in the through-flow part is based on Karman's integral equation for the boundary layer; the simplest nongradient alternative of the equation is used, which applies to flows with small pressure gradient, and the expression for calculating the local coefficient of friction losses [4] is known. Such a calculation scheme corresponds fully to flows with small pressure gradient in the oblique edge of the channel of the R. In the channel of the nozzle of the DF and in the channel of the R of the reactive stage, considerable negative pressure gradients act, and it is assumed that their influence on the flow and on the losses are taken into account discretel...