A simulated annealing-based inverse computational fluid dynamics model for unknown parameter estimation in fluid flow problem

In this paper, a simulated annealing (SA)-based optimisation is carried out for simultaneous estimation of the Reynolds number (Re) and the dimensions of the enclosure (lx, ly ) from the knowledge of centreline velocity field. For demonstrating the retrieval methodology, the required centreline velocity field is first obtained from a forward method using some known values of the unknowns, which are ultimately estimated by the inverse method. SA is used to optimise the objective function represented by the square of the difference between the known field and an arbitrary guessed field (calculated using some guessed value of the unknowns). For studying the sensitivity of the estimated parameters, the effect of random errors has been investigated and the suitability of the SA has been checked for different initial guesses. The algorithm reported in the present work is useful in estimating the above unknowns (Re, lx, ly ) for a given velocity field.

[1]  J. Marsden,et al.  A mathematical introduction to fluid mechanics , 1979 .

[2]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[3]  C. Brücker,et al.  Experimental and numerical investigations of a turbulent round jet into a cavity , 2008 .

[4]  Woo Il Lee,et al.  Inverse estimation of thermophysical properties for anisotropic composite , 2003 .

[5]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

[6]  D. Birchall,et al.  Computational Fluid Dynamics , 2020, Radial Flow Turbocompressors.

[7]  D. Arumuga Perumal,et al.  Simulation Of Flow In Two-sidedLid-driven Square Cavities By TheLattice Boltzmann Method , 2008 .

[8]  Alfred S Carasso,et al.  Space marching difference schemes in the nonlinear inverse heat conduction problem , 1990 .

[9]  Ranjan Das.  Estimation of Radius Ratio in a Fin Using Inverse CFD Model , 2011 .

[10]  Subhash C. Mishra,et al.  An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm , 2008 .

[11]  Stephen Malkin,et al.  Inverse heat transfer analysis of grinding, Part 1: Methods , 1996 .

[12]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[13]  C. Bruneau,et al.  The 2D lid-driven cavity problem revisited , 2006 .

[14]  M. Chahine.  Inverse Problems in Radiative Transfer: Determination of Atmospheric Parameters , 1970 .

[15]  Gilbert Strang,et al.  Computational Science and Engineering , 2007 .

[16]  Giampietro Fabbri.  Optimum performances of longitudinal convective fins with symmetrical and asymmetrical profiles , 1999 .

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[18]  B. Shi,et al.  Lattice BGK model for incompressible Navier-Stokes equation , 2000 .

[19]  A. Keane,et al.  The development of a hybridized particle swarm for kriging hyperparameter tuning , 2011 .

[20]  Ralf Salomon,et al.  Evolutionary algorithms and gradient search: similarities and differences , 1998, IEEE Trans. Evol. Comput..

[21]  Motohiko Nohmi,et al.  Hydrodynamic Design System for Pumps Based on 3-D CAD, CFD, and Inverse Design Method , 2002 .

[22]  LiuZu-yuan,et al.  LATTICE BGK MODEL FOR THE INCOMPRESSIBLE NAVIER—STOKES EQUATION , 2003 .

[23]  R. Das,et al.  Retrieval of thermal properties in a transient conduction–radiation problem with variable thermal conductivity , 2009 .

[24]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[25]  Aleksander Nawrat,et al.  Inverse approach and sensitivity analysis for identification of ingot-mould thermal resistance in continuous casting of metals , 2005 .

[26]  Giampietro Fabbri,et al.  Optimization of heat transfer through finned dissipators cooled by laminar flow , 1998 .

[27]  M. Schafer,et al.  Comparison of trust-region-based and evolutionary methods for optimization of flow geometries , 2007 .

[28]  T. Taylor,et al.  Pseudospectral methods for solution of the incompressible Navier-Stokes equations , 1987 .

[29]  L. Perelman,et al.  A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers , 1997 .

[30]  M. Raynaud,et al.  A NEW FINITE-DIFFERENCE METHOD FOR THE NONLINEAR INVERSE HEAT CONDUCTION PROBLEM , 1986 .

[31]  Krishnamurthy Muralidhar,et al.  Computational Fluid Flow and Heat Transfer , 2003 .

[32]  Ofodike A. Ezekoye,et al.  Inverse design model for radiative heat transfer , 2000 .

[33]  Ernesto Tarantino,et al.  Evolutionary Algorithms for Aerofoil Design , 1998 .

[34]  T. H. Tsang,et al.  Transient solutions for three‐dimensional lid‐driven cavity flows by a least‐squares finite element method , 1995 .

[35]  Brian D. Sleeman,et al.  The Inverse Problem of Acoustic Scattering , 1982 .

[36]  E. Barragy,et al.  STREAM FUNCTION-VORTICITY DRIVEN CAVITY SOLUTION USING p FINITE ELEMENTS , 1997 .

[37]  Farhad Kolahan,et al.  Simulated Annealing Application for Structural Optimization , 2007 .

[38]  Farid Bakir,et al.  Inverse Design Method for Centrifugal Impellers and Comparison with Numerical Simulation Tools , 2004 .

[39]  Richard E. Ewing,et al.  A class of parameter estimation techniques for fluid flow in porous media , 1991 .

[40]  R. Das,et al.  Inverse analysis of Navier–Stokes equations using simplex search method , 2012 .