# Modelling Approach

There are 3 basic approaches to modelling two phase flow in piping systems: 1.The experimental (empirical) approach. In this approach correlations are developed from experiments. Using dimensional analysis allows a universal solution to be obtained. These methods can be applied with confidence over the range of conditions obtained, similar to the experiments. 2.The exact solution (rigorous) approach. This approach requires the solution of the energy and momentum equations with the proper boundary conditions. As a practical solution this approach is too complex except in the most simplest of cases. 3.The numerical approach. In this approach the conservation laws are solved numerically. Problems with solution closure occur, and codes tend to be large and time-consuming of processor time. FluidFlow uses a modelling approach which is a hybrid of the empirical and rigorous approaches. By this we mean that we use well known empirical correlations and apply them to a differential pipe length. This is similar to the approach used for gas calculations, however in the case of two phase flow a pressure decrement (rather than a density decrement) is taken and the empirical relationships are applied over the segment length. This approach allows for a flash calculation, liquid holdup and the flow regime to be determined for each segment and acknowledges that the pressure loss per unit length changes as the fluid flows down the pipe. See calculation methods for a more detailed description. There have been many attempts to classify and define flow regimes in two phase flow. The advantage of this approach is that the friction loss relationships can be developed as a function of the flow regime. This is the basis of mechanistic modelling. The available pressure loss relationships that you can use in FluidFlow are: ▪Friedel: This method is based on the paper published by Friedel [21] and utilizes a two phase multiplier to the liquid pressure loss calculation. This correlation uses different equations for horizontal and vertical pipes. ▪Chisholm: Proposed an extensive empirical method (1973), which also uses a two phase multiplier. This is one of the more simplistic two-phase correlations available. ▪Lockhart Martinelli: Proposed a separated flow model, but this should only be applied to horizontal pipe flow. This is also one of the more simplistic two-phase correlations and dates back to the 1970s. Comparison of the above 3 methods to a recent two phase database was made by Whalley who made the following recommendations: (μ L/μ G) < 1000 and a mass flux of < 2000 kg/m2s use the Friedel method. (μ L/μ G) > 1000 and a mass flux of > 100 kg/m2s use the Chisholm method. (μ L/μ G) > 1000 and a mass flux of < 100 kg/m2s use the Lockhart Martinelli method. If you select the Whalley Criteria in the Calculation Options dialog, FluidFlow will select the appropriate method for you. More recently Muller Steinhagen and Heck (2000) made an updated comparison and recommended the MSH correlation as a better approach, particularly for refrigerants and single component fluids. This method loses accuracy at high vapor quality. One of the first approaches based on flow regime was made by Beggs Brill. This correlation is applicable to all pipe orientations. The original method (1973) was extended and FluidFlow uses the extended method. You should probably not use this method for vertical upflow because it underpredicts pressure loss. Drift Flux modelling is accommodated in FluidFlow by using a new correlation published in 2007 [22]. This modelling approach is best suited for vertical and inclined pipes.