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Three Dimensional Double Diffusive Convection in Saturated Porous Media

Tabrizi Nejad As, Sara | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52243 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Aataiee-Ashtiani, Behzad
  7. Abstract:
  8. Thermal and compositional variations through porous media are the main causes of bringing changes in the density of the fluid in place and arising in density-driven flow. This phenomenon is usually called thermohaline or thermosolutal convection (TC). When the flow is driven by the concentration gradient of two different compositions the problem is called double-diffusive convection (DDC). This phenomenon can be observed in several applications as in geological carbon dioxide sequestration, geothermal systems, underground thermal energy storage, salt mining, salt domes, groundwater management, waste disposal, and seawater intrusion.Despite that TC processes are three-dimensional by nature (due to boundary conditions, domain heterogeneity); all of the investigations about this phenomenon are limited by the assumption of two-dimensional flow. Three-dimensional simulation of TC in porous media is still a challenging task as they required solving simultaneously the coupled nonlinear equations of flow, solute transport and heat transfer under variable density. While numerical models have reached an advanced level of sophistication, it is still not easy to perform three-dimensional simulations which are hampered by computational cost, memory requirement, unphysical oscillations, and convergence issues. Besides, the importance of transient study has been deeply understood due to the dynamic structure of velocity, concentration, and temperature. Due to the high computational cost of the three dimensional and transient problem, a semi-analytical solution has been chosen to solve the problem and in respect of high accuracy and simplicity of Fourier-Galerkin method, this method has been used to solve the problem.In order to solve the problem with Fourier-Galerkin method, the periodic boundary conditions for each unknown were required. The definition of vector potential for expressing periodic boundary conditions for flow has been used. Besides, a change of variable has been defined to create periodic boundary conditions for concentration and temperature. Then, Fourier expansions containing an unknown coefficient and appropriate tragicomic functions satisfying boundary conditions were substituted instead of unknowns and then Galerkin treatment with the same trial functions as the Fourier modes has been applied to the non-linear system and the terms have been integrated whole through the domain and final system with the Fourier coefficient as unknown has been obtained. The results have been verified with a sophisticated software with Finite Element (FE) approach and in the sharp problems containing high Rayleigh numbers where the importance of three-dimensional effects increases, the privilege of Fourier-Galerkin method in solving the problem is observed
  9. Keywords:
  10. Semi-Analytical Solution ; Fourier-Galerkin Method ; Double Diffusive Convection ; Convective Flow ; Porous Media

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