| Non-ideal flows through angled orifices occur often in engineering applications such as mass flow meters, blast-wave simulators, gas propulsion devices and projectile launchers. For such flows, a correction factor in the form of a discharge coefficient is required to facilitate good design and efficient operation. The discharge coefficient depends on many parameters including atmospheric to stagnation pressure ratio, gas specific heat ratio, exit to channel area ratio, orifice shape, wall angle and orifice edge rounding. The dependence on these parameters (except edge rounding) was studied numerically by developing a two-dimensional finite-difference computer program that solves the subsonic flowfield in the hodograph plane by a relaxation method and the attached supersonic flowfield, if present, in the physical plane by a method of characteristics, joined together at the sonic surface by matching stream function values. The discharge coefficient was also studied experimentally by developing and testing an experimental facility using a new technique based on the partial blowdown of a pressurized vessel through a short pipe ending with conical orifices of different area ratios, wall angles and orifice edge roundings. Numerical and experimental data from these studies and also from the literature are compared and discussed. A software package called the “ Cd Algorithm” was developed to reproduce quickly the combined numerical and experimental discharge coefficients for the entire set of parameters, and it outperforms previous algorithms in accuracy, efficiency and comprehensiveness. This Cd Algorithm uses analytical, numerical and experimental results at the limits for incompressible, critical and choked flows, and other Cd values between these limits are reproduced by using piecewise cubic polynomial splines. |
