Vaneless Diffuser Modeling for Real Gas Supercritical Carbon Dioxide Flows: Need for a Data-Driven Approach

In this work, a real gas-based vaneless diffuser (VLD) differential equation model is presented. The model requires the specification of the skin friction coefficient as input. However, the use of standard VLD friction coefficient estimation expressions require a reexamination for supercritical CO₂ (sCO₂) flows. To establish the skin friction coefficient for real gas sCO₂ flows, computational fluid dynamics (CFD) data are generated using Latin hypercube sampling (LHS), with boundary conditions spanning the typical operating conditions of sCO₂ centrifugal compressors in the kW to MW scale of power generation. The CFD computations are carried out using ansys^® cfx. The corresponding VLD friction coefficient for which the VLD stagnation pressure loss predicted by the one-dimensional (1D) differential equation model matches with the three-dimensional (3D) CFD result is back calculated for the LHS designs. This is carried out using a root finding function in MATLAB^® software. The existing empirical relation that characterizes the VLD skin friction coefficient using the inlet Reynolds number alone shows a poor correlation (R² = 0.26), when compared to the CFD data. It is evident that a data driven approach is required to model the sCO₂ VLD real gas flow for accurate results. Using the LHS data, the efficacy of an artificial neural network (ANN)-based model is demonstrated. A two hidden layer ANN is developed, which accurately predicts the skin friction coefficient for sCO₂ real gas flows (R² = 0.87). This proposed ANN-based VLD model can be easily integrated into existing 1D codes for real gas sCO₂ centrifugal compressor rating and sizing.