Three-dimensional simulation of the IAEA 10 MW generic reactor under loss of flow transient is in... more Three-dimensional simulation of the IAEA 10 MW generic reactor under loss of flow transient is introduced using the CFD code, Fluent. The IAEA reactor calculation is a safety-related benchmark problem for an idealized material testing reactor (MTR) pool type specified in order to compare calculational methods used in various research centers. The flow transients considered include fast loss of flow accidents (FLOFA) and slow loss of flow accidents (SLOFA) modeled with exponential flow decay and time constants of 1 and 25 s, respectively. The transients were initiated from a power of 12 MW with a flow trip point at 85% nominal flow and a 200 ms time delay. The simulation shows comparable results as those published by other research groups. However, interesting 3D patterns are shown that are usually lost based on the one-dimensional simulations that other research groups have introduced. In addition, information about the maximum clad surface temperature, the maximum fuel element temperature as well as the location of hot spots in fuel channel is also reported.
Forschung Im Ingenieurwesen-engineering Research, 2008
The present article considers a numerical study on the combined effect of thermal dispersion and ... more The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton–Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.
In this article, the effects of chemical reaction and double dispersion on non-Darcy free convect... more In this article, the effects of chemical reaction and double dispersion on non-Darcy free convection heat and mass transfer from semi-infinite, impermeable vertical wall in a fluid saturated porous medium are investigated. The Forchheimer extension (non-Darcy term) is considered in the flow equations, while the chemical reaction power–law term is considered in the concentration equation. The first order chemical reaction (n = 1) was used as an example of calculations. The Darcy and non-Darcy flow, temperature and concentration fields in this study are observed to be governed by complex interactions among dispersion and natural convection mechanisms. The governing set of partial differential equations were non-dimensionalized and reduced to a set of ordinary differential equations for which Runge–Kutta-based numerical technique were implemented. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) are presented in graphs.
The problem of coupled structural deformation with two-phase flow in porous media is solved numer... more The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cellcentered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.
The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerical... more The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e., viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism.
The flow of two or more immiscible fluids in porous media is ubiquitous particularly in oil indus... more The flow of two or more immiscible fluids in porous media is ubiquitous particularly in oil industry. This includes secondary and tertiary oil recovery, CO 2 sequestration, etc. Accurate predictions of the development of these processes are important in estimating the benefits, e.g., in the form of increased oil extraction, when using certain technology. However, this accurate prediction depends to a large extent on two things; the first is related to our ability to correctly characterize the reservoir with all its complexities and the second depends on our ability to develop robust techniques that solve the governing equations efficiently and accurately. In this work, we introduce a new robust and efficient numerical technique to solving the governing conservation laws which govern the movement of two immiscible fluids in the subsurface. This work will be applied to the problem of CO 2 sequestration in deep saline aquifer; however, it can also be extended to incorporate more cases. The traditional solution algorithms to this problem are based on discretizing the governing laws on a generic cell and then proceed to the other cells within loops. Therefore, it is expected that, calling and iterating these loops several times can take significant amount of CPU time. Furthermore, if this process is done using programming languages which require repeated interpretation each time a loop is called like Matlab, Python or the like, extremely longer time is expected particularly for larger systems. In this new algorithm, the solution is done for all the nodes at once and not within loops. The solution methodology involves manipulating all the variables as column vectors. Then using shifting matrices, these vectors are sifted in such a way that subtracting relevant vectors produces the corresponding difference algorithm. It has been found that this technique significantly reduces the amount of CPU times compared with traditional technique implemented within the framework of Matlab.
The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adja... more The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adjacent to an isothermal cone imbedded in a porous medium with Rosseland diffusion approximation incorporating the variation of permeability and thermal conductivity is numerically investigated. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. Numerical results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed convection parameter χ, the cone angle parameter m, the radiation-conduction parameter R d , and the surface temperature parameter H.
International Journal of Heat and Fluid Flow, 2009
The present article considers a numerical study on the combined effect of thermal dispersion and ... more The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton-Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.
This paper builds the topological and lattice structures of L-fuzzy rough sets by introducing low... more This paper builds the topological and lattice structures of L-fuzzy rough sets by introducing lower and upper sets. In particular, it is shown that when the L-relation is reflexive, the upper (resp. lower) set is equivalent to the lower (resp. upper) L-fuzzy approximation set. Then by the upper (resp. lower) set, it is indicated that an L-preorder is the equivalence condition under which the set of all the lower (resp. upper) L-fuzzy approximation sets and the Alexandrov L-topology are identical. However, associating with an L-preorder, the equivalence condition that L-interior (resp. closure) operator accords with the lower (resp. upper) L-fuzzy approximation operator is investigated. At last, it is proven that the set of all the lower (resp. upper) L-fuzzy approximation sets forms a complete lattice when the L-relation is reflexive.
Three-dimensional simulation of the IAEA 10 MW generic reactor under loss of flow transient is in... more Three-dimensional simulation of the IAEA 10 MW generic reactor under loss of flow transient is introduced using the CFD code, Fluent. The IAEA reactor calculation is a safety-related benchmark problem for an idealized material testing reactor (MTR) pool type specified in order to compare calculational methods used in various research centers. The flow transients considered include fast loss of flow accidents (FLOFA) and slow loss of flow accidents (SLOFA) modeled with exponential flow decay and time constants of 1 and 25 s, respectively. The transients were initiated from a power of 12 MW with a flow trip point at 85% nominal flow and a 200 ms time delay. The simulation shows comparable results as those published by other research groups. However, interesting 3D patterns are shown that are usually lost based on the one-dimensional simulations that other research groups have introduced. In addition, information about the maximum clad surface temperature, the maximum fuel element temperature as well as the location of hot spots in fuel channel is also reported.
Forschung Im Ingenieurwesen-engineering Research, 2008
The present article considers a numerical study on the combined effect of thermal dispersion and ... more The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton–Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.
In this article, the effects of chemical reaction and double dispersion on non-Darcy free convect... more In this article, the effects of chemical reaction and double dispersion on non-Darcy free convection heat and mass transfer from semi-infinite, impermeable vertical wall in a fluid saturated porous medium are investigated. The Forchheimer extension (non-Darcy term) is considered in the flow equations, while the chemical reaction power–law term is considered in the concentration equation. The first order chemical reaction (n = 1) was used as an example of calculations. The Darcy and non-Darcy flow, temperature and concentration fields in this study are observed to be governed by complex interactions among dispersion and natural convection mechanisms. The governing set of partial differential equations were non-dimensionalized and reduced to a set of ordinary differential equations for which Runge–Kutta-based numerical technique were implemented. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) are presented in graphs.
The problem of coupled structural deformation with two-phase flow in porous media is solved numer... more The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cellcentered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.
The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerical... more The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e., viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism.
The flow of two or more immiscible fluids in porous media is ubiquitous particularly in oil indus... more The flow of two or more immiscible fluids in porous media is ubiquitous particularly in oil industry. This includes secondary and tertiary oil recovery, CO 2 sequestration, etc. Accurate predictions of the development of these processes are important in estimating the benefits, e.g., in the form of increased oil extraction, when using certain technology. However, this accurate prediction depends to a large extent on two things; the first is related to our ability to correctly characterize the reservoir with all its complexities and the second depends on our ability to develop robust techniques that solve the governing equations efficiently and accurately. In this work, we introduce a new robust and efficient numerical technique to solving the governing conservation laws which govern the movement of two immiscible fluids in the subsurface. This work will be applied to the problem of CO 2 sequestration in deep saline aquifer; however, it can also be extended to incorporate more cases. The traditional solution algorithms to this problem are based on discretizing the governing laws on a generic cell and then proceed to the other cells within loops. Therefore, it is expected that, calling and iterating these loops several times can take significant amount of CPU time. Furthermore, if this process is done using programming languages which require repeated interpretation each time a loop is called like Matlab, Python or the like, extremely longer time is expected particularly for larger systems. In this new algorithm, the solution is done for all the nodes at once and not within loops. The solution methodology involves manipulating all the variables as column vectors. Then using shifting matrices, these vectors are sifted in such a way that subtracting relevant vectors produces the corresponding difference algorithm. It has been found that this technique significantly reduces the amount of CPU times compared with traditional technique implemented within the framework of Matlab.
The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adja... more The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adjacent to an isothermal cone imbedded in a porous medium with Rosseland diffusion approximation incorporating the variation of permeability and thermal conductivity is numerically investigated. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. Numerical results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed convection parameter χ, the cone angle parameter m, the radiation-conduction parameter R d , and the surface temperature parameter H.
International Journal of Heat and Fluid Flow, 2009
The present article considers a numerical study on the combined effect of thermal dispersion and ... more The present article considers a numerical study on the combined effect of thermal dispersion and thermal radiation on the non-Darcy natural convection flow over a vertical flat plate kept at higher and constant temperature in a fluid saturated porous medium. Forchheimer extension is used in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional governing equations are solved by the finite element method (FEM). The resulting non-linear integral equations are linearized and solved by the Newton-Raphson iteration. The finite element implementations are prepared using Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours as well as heat transfer rates in terms of Nusselt number are presented and discussed.
This paper builds the topological and lattice structures of L-fuzzy rough sets by introducing low... more This paper builds the topological and lattice structures of L-fuzzy rough sets by introducing lower and upper sets. In particular, it is shown that when the L-relation is reflexive, the upper (resp. lower) set is equivalent to the lower (resp. upper) L-fuzzy approximation set. Then by the upper (resp. lower) set, it is indicated that an L-preorder is the equivalence condition under which the set of all the lower (resp. upper) L-fuzzy approximation sets and the Alexandrov L-topology are identical. However, associating with an L-preorder, the equivalence condition that L-interior (resp. closure) operator accords with the lower (resp. upper) L-fuzzy approximation operator is investigated. At last, it is proven that the set of all the lower (resp. upper) L-fuzzy approximation sets forms a complete lattice when the L-relation is reflexive.
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Papers by Amgad Salama