The Formula of Discharge Coefficient of the Cooling Hole in the Combustion Chamber for a Uniform Penetration Boundary Method

Abstract

Abstract At present, researches on the discharge coefficient of the combustion chamber cooling holes are mostly based on the experimental study of the porous plates considering various geometric structures under different flow conditions. In this method, the average discharge coefficients of multiple holes are obtained. Since the discharge coefficient will be applied to the numerical simulation, it is important to obtain an accurate formula for each cooling hole. Therefore, the discharge coefficient will be associated with some local aerodynamic parameters around the cooling holes and geometric parameters of the cooling holes. In this paper, the geometric parameters consist of length-to-diameter ratio (L/d) and inclination angle (α). The aerodynamic parameters cover the Mach number of cooling flow and mainstream (Mac, Mam), characterizing the flow feature, and the pressure ratio (π) which associates the cooling flow with the mainstream. The purpose of this paper is to study the discharge coefficient of a single circular hole with variable geometries under a cold condition of a combustion chamber, which has low crossflow and low-pressure ratio on both sides of the hole. In this environment, according to the research results, the discharge coefficient is sensitive to the cooling flow Mach number, length-to-diameter ratio and pressure ratio (π ≈ 1.05). Discharge coefficient decreases with L/d linearly, conforms the quadratic function with Mac and changes complexly at π ≈ 1.05. Other parameters have little effect on the discharge coefficient. The data for discharge coefficient of the cylindrical hole considering different parameters is obtained through numerical simulation and the correlations summarized by these data are valid for the following ranges: L/d = 3∼12, α = 20°∼45°, Mac = 0.05∼0.15, Mam = 0∼0.1, π = 1.05∼1.15. Compared with the CFD data, the prediction formula has a maximum error of less than 3% and a mean absolute error of 0.78%.