A potential barrier to the widespread use of process/CFD co-simulation is that the integration of high-fidelity equipment models may lead to unacceptable co-simulation turnaround times, especially for cases in which one or more CFD models are embedded in the iterative flowsheet solution process. One promising solution is the use of reduced-order models (ROMs) that approximate the CFD-based equipment simulations, while keeping the computational cost manageable. ROMs are equipment models that contain only relevant states or a reduced number of irrelevant states. The advantage is dramatically increased simulation speeds and lower memory requirements.
To obtain ROMs for equipment items with arbitrary geometries, we propose a novel state-space ROM strategy. In contrast to the popular order reduction method of proper orthogonal decomposition (POD), this work focuses on a principal component analysis (PCA) approach. First, the statistical Latin hypercube sampling (LHS) technique is used for experimental design to determine a distribution of plausible sets of operation and boundary conditions for the CFD model. Second, using off-line CFD simulations with the designed cases, we obtain a database consisting of snapshots of the flow-field variables (state variables). Third, selecting the snapshots of one state variable of interest, we formulate a snapshot matrix and implement PCA on it to derive the ranked principal components (PC) and the coordinates of the data elements in the transformed vector space (scores). Fourth, using a neural network formulation, we train a mapping from the inputs of CFD model into the scores. Finally, we assemble the ranked PC and mapping score to develop the ROM.
Two case studies are considered, both based on a 2-D FLUENT CFD model of a gas turbine combustor. One case has a single input, the other one has ten inputs. The PCA-based ROM can be executed within seconds and leads to a CPU savings of two to three orders of magnitude. Replacing the CFD model in the process flowsheet with the ROM through the standard CAPE-OPEN unit operation interface therefore allows APECS process/CFD co-simulations to be solved more efficiently and effectively.