An Exploration of Numerical Methods for Thermally-Induced Convection in Storage Tanks and Films
Date
2021-07-19
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Abstract
The study is on conditions for onset of convection, the transient and steady states velocity and temperature patterns in 2D and 3D coordinates for fluids in vertical cylindrical storage tanks. The Navier-Stokes and energy equations are formulated using vorticity, stream function (2D) / vector potential (3D) and temperature as the dependent variables, with and without dynamic free surfaces. Solving the transport equations and exploring conditions for multiple solutions, of which only certain patterns may be realizable, is time-consuming. The development of computationally efficient algorithms is crucial to reduce computation overheads. In this work, software package for the simulation of 2D and 3D problems with parallel implementation was developed. For 2D simulation, the numerical methods in package include Gauss-Seidel with Red-Black (GS-RB) ordering, Alternating Direction Implicit with Fast Fourier Transform (ADI + FFT) and with Evolutionary Factorization with Logarithmic time step (ADI+EFL), Geometric Multigrid (GMG), Jacobian Free Newton-Krylov (JFNK). For 3D simulation, GS-RB (parallel) and ADI-EF (Samarskii-Andreev) with FFT for the vector potential equations were developed. The non-linear systems of PDE were approximated using central (CFD) and monotonic - conservative (MCFD) finite differences schemes.
The boundary conditions for vorticity in 3D were derived using the one grid step methods for a second order accuracy. For 2D simulations, the Polezhaev - Gryaznov method was extended for the axisymmetric domain. These approaches significantly improved CPU performance.
The investigation was restricted to one component liquids, and cylindrical tanks with evaporation at the free surfaces were of primary interest. Specification of appropriate boundary conditions for the free surface is difficult as the interface may be deformed due to the inertia of ascending and descending streams and gradients of the interfacial tension. The contour is unknown a priori. In lien of detailed calculations, evaporation was incorporated through the application of Hashemi-Wesson’s empirical correlation between vaporization rates and the local surface temperature. To understand the interfacial dynamics and to develop the numerical scheme for modeling evolving surface contours, deformation of thin liquid layers locally heated along strips was explored.
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Keywords
Numerical Methods, Thermally Induced Convection, Vertical Cylindrical Storage Tanks, Films, ADI, Gauss-Seidel, Polezhaev-Gryaznov, boundary conditions for vorticity, monotonic conservative difference scheme, parallel algorithm, buoyancy convection, vertical cylinder, transient, steady state, efficient algorithm, JFNK
Citation
Pletnyov, F. (2021). An Exploration of Numerical Methods for Thermally-Induced Convection in Storage Tanks and Films (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.