Computational study of the gas flow through a critical nozzle

Abstract

The critical nozzle is defined as a device to measure the mass flow with only the nozzle supply conditions making use of the flow choking phenomenon at the nozzle throat. The discharge coefficient and critical pressure ratio of the gas flow through the critical nozzle are strongly dependent on the Reynolds number, based on the diameter of the nozzle throat and nozzle supply conditions. Recently a critical nozzle with a small diameter has been extensively used to measure mass flow in a variety of industrial fields. For low Reynolds numbers, prediction of the discharge coefficient and critical pressure is very important since the viscous effects near walls significantly affect the mass flow through the critical nozzle, which is associated with working gas consumption and operation conditions of the critical nozzle. In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through the critical nozzle. In order to investigate the effect of the working gas and turbulence model on the discharge coefficient, several kinds of gases and several turbulence models are employed. The Reynolds number effects are investigated with several nozzles with different throat diameters. The diffuser angle is varied in order to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the standard k-ε turbulence model with the standard wall function gives the best prediction of the discharge coefficient. The discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that the diffuser angle affects the critical pressure ratio.

Numerical analysis of choked converging nozzle flows with surface roughness and heat flux conditions

“…The influence of heat flux is investigated by varying Q in the range of 20-2000 kW/m 2 with the fixed ε/D in value of 0•0125, whereas the surface roughness effects are evaluated through the applied ε/D in range of 0•0025-0•05 by keeping Q at 2000 kW/m 2 . It can be seen from figure 5 that for the negligible Q of 20 kW/m 2 , C d values converge to the 0•988-0•992 interval, which is congenial with the experimental reports of Massier et al (1970) and Kim et al (2003), who ignored the heat transfer through nozzle walls in their investigations; moreover the interval is also in harmony with the ISO 9300 (Paik et al 2000) standardized correlation of C d = f ((Re D ) ex ) for choked nozzles. Ahmad (2001) numerically evaluated the C d of various adiabatic nozzles and proposed (15-16), which characterize the influences of (Re D ) ex and α on C d respectively.…”

“…Park et al (2001) investigated sonic nozzles that are applied to gas flow rate measurements and determined that the critical pressure ratio is highly dependent on the Reynolds number rather than area ratio especially in the cases with low flow velocity. Kim et al (2003) considered several kinds of gases and turbulence models with a wide range of Reynolds numbers on different sonic nozzle geometries. Instabilities in the propulsion of rockets, due to pressure and temperature fluctuations at the upstream of rocket nozzle and the flow geometry, were numerically considered by Assovskii & Rashkovskii (2001).…”

The effect of diffuser angle on the discharge coefficient of a miniature critical nozzle

“…According to one-dimensional gas dynamics theory, the mass flow through a nozzle is given as a function of the pressure and temperature upstream of the nozzle, the nozzle throat diameter, and the specific heat ratio of gas [1]. Critical nozzle is a kind of flow metering device which makes use of the concept of flow choke that occurs at nozzle throat [2], and it is extensively used to precisely measure mass flow rate in a variety of industrial facilities. A considerable number of researches have been carried out to establish the measurement standard of gas flow using critical nozzle.…”

Effect of diffuser angle on the discharge coefficient of miniature critical nozzles

“…According to the one-dimensional gas dynamics theory, mass flow through a nozzle is given as a function of the pressure and temperature upstream of the nozzle, the nozzle throat diameter, and the specific heat ratio of gas [1]. Critical nozzle is a kind of flow metering device that uses the concept of flow choke, which occurs at the nozzle throat [2]. In addition, it is extensively used to precisely measure the mass flow rate in a variety of industrial facilities.…”