INVESTIGATION INTO THE EFFECTS OF FLUID FLOW THROUGH A VENTURI

Investigation into the effects of Fluid Flow through a Venturi

Investigation into the effects of Fluid Flow through a Venturi

1. Introduction

One of the simplest methods of highly accurate measurement of mass flows is the employment of critical nozzles. As a matter of fact, sonic nozzle test rigs are often used as reference flow meters. The guidelines and standards in using these devices are well defined and covered by the ISO Standard 9300. It is valid for toroidal nozzles with critical Reynolds numbers between Re=105 and Re=107. However, critical nozzles of significantly smaller diameter are also in frequent use. In this case, relatively large fluctuations in the mass flow have been observed, making the calibration of these nozzles difficult. In particular, nozzles of diameters <1 mm and Reynolds numbers as small as 3×103 display higher measurement uncertainties. The aim of the present research is to investigate the flow behavior in sonic nozzle test rigs in general, and the instabilities in small sonic nozzles in particular.

In the past, flows in supersonic and transonic nozzles have been studied quite extensively. Due to their significant importance to the aerospace engineering, especially in the area of rocket propulsion, they were investigated numerically and experimentally numerous times. However, most of the research work concentrated on the overall features of these nozzles, assuming steady flow and leaving out some of the unsteady details. Besides, the size, and therefore the Reynolds numbers of these nozzles were significantly larger than considered in the present work. Therefore, the present study could not take advantage of the previous results and findings. Consequently, it was decided by the present authors to carry out a numerical and experimental analysis of the metering nozzles described above (Anderson 1990).

A representative critical nozzle geometry, as recommended by the ISO Standard 9300, was selected for the base line investigation. The nozzle shape is shown in Fig. 2 and Fig. 3. It is a typical convergent-divergent nozzle, with a toroidal throat having a diameter of 10 mm, and a divergent part of 70 mm length, with a divergence wall angle of 4°. The Reynolds number based on the critical conditions and the throat diameter was approx. Re=1.5×105. Additionally, in order to investigate the influence of the critical Reynolds number on the flow behavior, three other Reynolds numbers were used in the numerical study: Re=5.0×105, Re=1.5×106 and Re=1.0×107 (El-Miligui 1991). The nozzle was manufactured out of stainless steel. The physical flow conditions are discussed below.

2. Numerical approach

The governing equations to be solved in the present simulations are the two-dimensional or axisymmetric compressible Navier-Stokes equations. They are, in a simplified vector form in general, body-fitted coordinates ? and ? in the weak conservation law form:

(1)

The above equations are given in more detail by, for example, Steger [4], and will not be repeated here. Eq. (1) is integrated in time by solving its semidiscrete form by means of modified Runge-Kutta (R-K) time stepping. The presently used two stage version of the R-K procedure can ...