Kriging meta‐model assisted calibration of computational fluid dynamics models

Abstract

Computational fluid dynamics (CFD) is a simulation technique widely used in chemical and process engineering applications. However, computation has become a bottleneck when calibration of CFD models with experimental data (also known as model parameter estimation) is needed. In this research, the kriging meta-modelling approach (also termed Gaussian process) was coupled with expected improvement (EI) to address this challenge. A new EI measure was developed for the sum of squared errors (SSE) which conforms to a generalised chi-square distribution and hence existing normal distribution-based EI measures are not applicable. The new EI measure is to suggest the CFD model parameter to simulate with, hence minimising SSE and improving match between simulation and experiments. The usefulness of the developed method was demonstrated through a case study of a single-phase flow in both a straight-type and a convergent-divergent-type annular jet pump, where a single model parameter was calibrated with experimental data.Keywords: Calibration, computational fluid dynamics, expected improvement, Gaussian process, parameter estimation Correspondence concerning this article should be addressed to Tao Chen at t.chen@surrey.ac.uk. 2 IntroductionComputational fluid dynamics (CFD) simulations are usually large complex computer programs representing real life fluid systems. The complexity of such simulations can make them quite a herculean task to solve, with the run time associated with the simulation being of great concern. Such simulation run time could be for hours or days.1,2 In addition, large scale or complex systems usually place a great demand on computer memory. 3 Computation is especially a problem when the CFD simulation is required to run for a large number of times, for example when sensitivity analysis is carried out 1,4 , or the models are used within a certain optimisation problem. 4,5 Of particular interest in this research project is calibration of CFD models (also known as model parameter estimation), which can be cast into an optimisation problem.CFD model calibration can be defined as the process of adjusting numerical or physical parameters in the CFD model which, on obtaining the optimal values 6 , helps to improve agreement with experimental data. 7,8,9 The parameters in this context are typically turbulence model coefficients or turbulence model choice. The default values given by CFD software providers for turbulence parameters may apply only in standard circumstances. In this paper, calibration is formulated as an optimisation problem to minimise the mismatch between simulated and experimental outputs (responses). The calibration process may need tens to hundreds of simulation runs to evaluate the objective function, the sum of squared errors (where the errors quantify the differences between the simulated and the experimental outputs) over the region of interest, a requirement that is often infeasible for CFD.These difficulties faced by CFD simulations have led to the application of meta-modelling, whi...

Meta‐Model‐Based Calibration and Sensitivity Studies of Computational Fluid Dynamics Simulation of Jet Pumps

“…In this study, this was based on experience and knowledge of the simulation problem [10]. It is also important to determine the input values to be explored through CFD simulation, a task for the design of experiment (DoE) techniques, where in this work the Hammersley sequence sampling (HSS) was applied.…”

“…(1) is a kriging meta-model type called ordinary kriging [9,10,17]; y * (x * ) 1) is the prediction for a new data point x * , given a vector of input variables with dimension n,…”

“…More recently, we presented the calibration of a single turbulent model parameter in the CFD simulation of annular jet pumps [10]. The present paper aims at further exploring the application of meta-models in the CFD simulation of annular jet pumps.…”

“…Hence, there is a need for proper methodology to deal with the high demand of computation of CFD. In our preliminary study [10], a metamodeling approach was developed and demonstrated on the calibration of a single model parameter. In the present study, this approach has been extended to the calibration of two model parameters, with comparison to our previous study [10].…”

“…Methods reported in the literature include polynomial regression model [7,8], kriging model [9,10], radial basis functions [11], artificial neural network [12,13], support vector machine [14], and multivariate adaptive regression splines [15]. Kriging has been chosen in this study because it provides excellent interpolation compared with other metamodeling techniques [7,16].…”