Nozzle flow model

The discharge coefficient is in general determined experimentally by the valve manufacturer for a fixed nominal lift. It corresponds to the average value of the ratio from mass flows measured and calculated with the nozzle flow model [1]. At least... 

Figure 15.6 Sizing coefficient versus reduced inlet stagnation pressure calculated according to EN-ISO 4126-7 and a nozzle flow model including real gas effects for ethylene at inlet stagnation temperatures of 300 and 443 K.

The REAL nozzle flow model was validated with measurements performed on a high-pressure nozzle with nitrogen at a test facility of BASF. The measurements were conducted at inlet pressures of up to 1000 bar [15]. In addition, the calculations agree very accurately with the values in DIN EN ISO 9300 [13], based on many measurements on nozzles performed worldwide at pressures below 200 bar. Moreover, Beune [6] has intensively studied the flow behavior through high-pressure safety valves by numerical simulations with ANSYS CFX. He underlined the precision of the real gas nozzle flow model. In addition, he verified experimentally for a certain valve type that the discharge coefficient of the safety valve in combination with the REAL nozzle flow model can be regarded as constant as is presently stated in EN-ISO 4126-7. 

Applying the REAL nozzle flow model, care must be taken for averaging the parameter. Close to the thermodynamic critical point, it might be necessary to stepwise average the parameter or to solve the equation numerically. 

Appendix 15. A Calculation of Sizing Coefficient According to EN-ISO 4126-7 and a Real Gas Nozzle Flow Model... 

Most, if not all, solutions of the nozzle expansion problem have used equilibrium composition chamber conditions as the initial condition for nozzle solution. The feature is common to all of the nozzle flow solutions that is, the equilibrium composition expansion, frozen composition expansion, Bray freezing model, and kinetic rate solutions have all invoked the assumption of equilibrium composition at the beginning of the expansion process. While the failure to obtain equilibrium composition predicted performance, in terms of experimental characteristic velocities, has suggested a departure from equilibrium in the combustion chamber, only recently have non-equilibrium compositions been measured directly (31). 

Summary of the nozzle-based model for gas flow through the control valve... 

Appendix 4 gives a detailed comparison of the FUGSE with the nozzle-based model of gas flow through the... 

We may generate a comparison between the modified liquid-flow model and the nozzle-based model by taking out the factor, C VPiAi from both equation (9.59) and equation (9.34). The modified liquid-flow function, fun, emerges as ... 

The graph shows that the modified liquid-flow model can give results that are reasonably close to those of the nozzle-based model, although the approach to choked flow is predicted to happen at higher valve pressure... 

Appendix 4 Comparison of Fisher Universal Gas Sizing Equation, FUGSE, with the nozzle-based model for control valve gas flow... 

Another type of cold flow modeling is designed to test particular equipment components. For example, if there is concern about erosion of a nozzle by entrained solids, it is possible to design a cold flow model to evaluate how fast (and where) the nozzle is likely to erode. Atomization by a burner can be measured by operating the burner under appropriate (scaled) conditions. These tests are typically done as final validation of the design before installation at a customer s furnace. 

In summary, for a prescribed nozzle profile A(x) and inlet conditions, the area-Mach relation Eq. 3 and isentropic flow relations Eqs. 4,5 and 6 are sufficient to completely determine the nozzle flow field under the quasi-ID model. 

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