# Discharge Coefficients of a Heavy Suspension Nozzle
## 1 Introduction
They also noticed that, due to real gas effects, the fluid density at the nozzle throat became smaller than the theoretical one. In most of the research undertaken previously, the theoretical work was not supported by an experimental method, which could allow working directly with the experimental data. These aspects were covered in Reference [13], where, for constant section short nozzles, an expression defining the discharge coefficient was developed using an experimental method and a gas flow model based on the Lee-Kesler equation of state [14]. Experimental results were compared with the ones obtained from the new developed equation, observing that, for tests performed using nitrogen up to 7.6 MPa pressure differential, a good correlation was obtained. Computational Fluid Dynamic (CFD) applications are gaining reliability every day. The consideration of the gas as real and compressible, under sonic or supersonic flow conditions, is still not fully extended. In reality, turbulent models quite often have some difficulties in dealing with such kind of flows. Nevertheless, there are many industrial applications where sonic, and even supersonic, flow is used. CFD simulations on compressible flow through valves, whether purging or relief ones, have recently been performed  
Figure 1: Scheme of a typical heavy vehicle suspension. in Reference [15; 16]. The modeling of flow ejectors under sonic flow conditions was considered in Reference [17; 18; 19; 20; 21]. Some of the recent papers simulating compressible flow conditions at high Mach numbers inside nozzles are Reference [22; 23; 24; 25]. From all these studies, it is particularly relevant to highlight the work done by [PERSON] et al. [15], where they numerically evaluated the exit flow of natural gas through a purging valve, during its opening time. They considered the gas as real and compressible, being the maximum pressure differential of 3.5 MPa. As a turbulent model, the standard \(k-\epsilon\) was selected. They concluded supersonic flow was to be expected at the pipe outlet. [PERSON] et al. [16] performed CFD simulations on air valves under compressible flow condition. They showed how CFD models are efficient to represent the behavior of air entering and leaving the valve. The maximum pressure differential studied was 0.1 MPa. In their analysis, they used the realizable \(k-\epsilon\) turbulent model and their results matched very well with the experimental data. [PERSON] et al. [17] performed numerical and experimental analyses in order to check the effectiveness of the commonly-used computational techniques when predicting ejector flow characteristics at supersonic flow conditions. For the numerical part, they considered the working fluid as an ideal gas. They tested different Reynolds-averaged Navier-Stokes (RANS) turbulent models, among them, the \(k-\omega\) SST and \(k-\epsilon\) realizable ones, and observed that, in general, all turbulent models generated very similar results, although epsilon-based models were more accurate at low pressure differentials (around 0.2 MPa). The different pressure differentials they evaluated were of 0.2, 0.35, and 0.5 MPa. On the other hand, they stated that the main differences between the numerical and experimental results appeared when comparing 2D and 3D models. [PERSON] et al. [18] performed a compressible 2D RANS simulation on an air ejector pump. In their analysis, they assumed the working fluid as ideal gas and the walls were treated as adiabatic. Pressure differentials of 0.5, 0.6, 0.7, and 0.8 MPa were considered. They used a \(k-\epsilon\) realizable turbulent model along with a wall function and a very good agreement with experimental data was obtained. They concluded that the main sources of entropy are the mixing and normal shock occurred in the mixing chamber and diffuser, respectively. [PERSON] and [PERSON] [21] used CFD to develop a 3D model of compressible flow across a venturi in which obstacles were located inside. Air was considered as compressible and was treated as ideal gas.