Abstract: Through this paper, analyses of components of the unheated/heated turbulent confined jet are introduced and some models to describe them are developed. Turbulence realizable k-<epsilon> model is used to model the turbulence of this problem. Numerical simulations of 2D axisymmetric vertical hot water confined jet into a cylindrical tank have been done. Solutions are obtained for unsteady flow while velocity, pressure, temperature and turbulence distributions inside the water tank are analyzed. For seeking verification, an experiment was conducted for measuring of the temperature of the same system, and comparison between the measured and simulated temperature shows a good agreement. Using the simulated results, some models are developed to describe axial velocity, centerline velocity, radial velocity, dynamic pressure, mass flux, momentum flux and buoyancy flux for both unheated (non-buoyant) and heated (buoyant) jet. Finally, the dynamics of the heated jet in terms of the plume function which is a universal quantity and the source parameter are studied and therefore the maximum velocity can be predicted theoretically.
Abstract: The present article considers a numerical study of the thermal dispersion effect on the non-Darcy natural convection over a vertical flat plate in a fluid saturated porous medium. The Forchheimer extension is considered in the flow equations. The coefficient of thermal diffusivity has been assumed to be the sum of the molecular diffusivity and dispersion thermal diffusivity due to mechanical dispersion. 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 by using the Matlab software packages. Numerical results for the details of the stream function, velocity and temperature contours and profiles as well as heat transfer rate in terms of the Nusselt number, which are shown on graphs, have been presented.
Abstract: In this article, the steady-state concentration boundary layer adjacent to a ceiling wall of
a stagnation-point flow region resulting from hydrogen impinging leakage is investigated.
Flow in neighborhood of the stagnation point is treated as Hiemenz flow, while the
concentration equation governs the concentration distribution in the boundary layer. The
assumptions of the boundary layer theory are invoked to simplify both the momentum and
the concentration equations. Comparison between the CFD simulation and the current
boundary layer approximation shows a good agreement. Both momentum and concentration
boundary layer thicknesses are estimated as well as local friction factor and local
mass transfer. Also, the study is extended to include some cases of unsteady leakage. The
effects of the unsteadiness parameter on the local friction factor and mass transfer rate as
well as momentum and concentration boundary layer thicknesses are analyzed.
Abstract: Hot water heat stores (HWHS) are generally used to overcome the diurnal or seasonal mismatch in the availability and demand of thermal energy. To enhance the system efficiency, good thermal stratification of the HWHS is required. In order to simulate different flow processes in stratified HWHS the effects of stratification on the turbulence are to be considered. Benchmark experiments have been conducted on turbulent flows into a continuously stratified HWHS. Based on these benchmark experiments, different two-equation turbulence transport models namely the RNG (ReNormalizable Group) and the realizable k- turbulence models have been calibrated. The major improvement is provided to the -equation by introducing the effects of the buoyancy field on the turbulence dissipation rate. It is achieved by calibrating the coefficient of the dissipation term (C2 in the RNG and C2 in the realizable k- model) based on the benchmark experiments. A re-definition of the turbulent Prandtl number (Prt) incorporating the effects of stratification on turbulent thermal diffusivity improved the calibration further. The calibrated computational fluid dynamic models are found to predict the charging, discharging and storing processes of typical HWHS with good accuracy.
Abstract: 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 NewtonâRaphson 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.
Abstract: In this paper, we highlight the existence of some instability in finite element method appearing for high values of the Peclet number in the model of hydrogen diffusion in materials. A stabilization technique is used to overcome the instability problem and therefore improve this scheme. We manage to improve the scheme and decrease the instability, and we highlight the strong influence of the stabilization parameter in this particular case.
Abstract: 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 powerâlaw 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 RungeâKutta-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.
Abstract: Hydrogen leakage is serious problem and considered to be an important safety issue since when it mixes with air, fire or explosion can result [1]-[6]. The expected extensive usage of hydrogen increases the probability of its accidental release from hydrogen vessel infrastructure. Hydrogen leaks may occur from loose fittings, o-ring seals, pinholes, or vents on hydrogen-containing vehicles, buildings, storage facilities, or other hydrogen-based systems. The current article is devoted to introduce mathematical and physical analyses with numerical investigation of a horizontal axisymmetric non-Boussinesq buoyant jet resulting from hydrogen leakage in air (H2-air jet) as an example of injecting a low-density gas jet into high-density ambient. The density of the mixture is a function of the concentration only, the binary gas mixture is assumed to be of a linear mixing type and the rate of entrainment is assumed to be a function of the plume centerline velocity and the ratio of the mean plume and ambient densities. On the other hand, the local rate of entrainment may be considered to be consisted from two components; one is the component of entrainment due to jet momentum while the other is the component of entrainment due to buoyancy. The integral models of the mass, momentum and concentration fluxes are obtained and transformed to a set of ordinary differential equations using some non-dimensional transformations known as similarity transformations. The given ordinary differential system is integrated numerically and the mean centerline mass fraction, jet width and mean centerline velocity are obtained. In the second step, the mean axial velocity, mean concentration and mean density of the jet are obtained. Finally in the third step of this article, several quantities of interest, including the cross-stream velocity, Reynolds stress, velocity-concentration correlation (radial flux), turbulent eddy viscosity and turbulent eddy diffusivity, are obtained. In addition, the turbulent Schmidt number is estimated and the normalized jet-feed material density and the normalized momentum flux density are correlated.
References
1. M.F. El-Amin, H. Kanayama, Int. J. Hydrogen Energy 33 (2008) 6393.
2. M.F. El-Amin, M. Inoue, H. Kanayama, Int. J. Hydrogen Energy 33 (2008) 7642.
3. M.F. El-Amin, H. Kanayama, Int. J. Hydrogen Energy 34 (2009) 5803.
4. M.F. El-Amin, Int. J. Hydrogen Energy 34 (2009) 7873.
5. M.F. El-Amin, H. Kanayama, Int. J. Hydrogen Energy 34 (2009) 1620.
6. M.F. El-Amin, H. Kanayama, Int. J. Hydrogen Energy 34 (2009) 1607.
Abstract: In most of real-world applications, such as the case of heat storages, inlet is not kept at a constant temperature but it may vary with time during charging process. In this paper, a vertical water jet injected into a rectangular storage tank is measured experimentally and simulated numerically. Two cases of study are considered; one is a hot water jet with uniform inlet temperature (UIT) injected into a cold water tank, and the other is a cold water jet with non-uniform inlet temperature (NUIT) injected into a hot water tank. Three different temperature differences and three different flow rates are studied for the hot water jet with UIT which is injected into a cold water tank. Also, three different initial temperatures with constant flow rate as well as three different flow rates with constant initial temperature are considered for the cold jet with NUIT which is injected into a hot water tank. Turbulence intensity at the inlet as well as Reynolds number for the NUIT cases are therefore functions of inlet temperature and time. Both experimental measurements and numerical calculations are carried out for the same measured flow and thermal conditions. The realizable model is used for modeling the turbulent flow. Numerical solutions are obtained for unsteady flow while pressure, velocity, temperature and turbulence distributions inside the water tank are analyzed. The simulated results are compared to the measured results, and they show a good agreement at low temperatures.
Abstract: Scaling laws of laboratory imbibition experiments are very important to be used to predict oil recovery from matrix blocks. The importance of this concept being the oil recovery from reservoir matrix blocks in the field can be predicted experimentally from tests on small samples in laboratory. Laboratory results of oil recovery are commonly represented as a function of dimensionless time which in turn is a universal parameter including several physical parameters of fluids and rocks. It is considered as a good scaling group if the measured oil recovery is represented in a single universal curve with sharing less primary physical parameters.
In the present work, we introduce a new dimensionless time formula in terms of characteristic velocity (e.g. injection velocity) which in turn is very important of some enhanced oil recovery (EOR) mechanisms such as water injection stage. In the first part of this article, we derive a power-law formula for dimensionless time that reduces the number of complexities in characterizing two-phase imbibition through a porous medium. The theory and characteristic velocity function is tested against some oil recovery experimental data for oil-water system from the literature. Through a comprehensive evaluation of available time scaling formulas, a simplified tool is provided for characterizing two-phase flow, through the use of a reference capillary number. In this context, the second part of the paper, we introduce a theoretical analysis and numerical computations of the counter-current imbibition. The one-dimensional macroscopic governing equation is transformed into a non-dimensional form which includes the dimensionless physical parameters (capillary number Ca and Darcy number Da). Additionally, numerical experiments are performed for wide ranges of values of capillary and Darcy numbers to illustrate their influences on water saturation as well as relative water/oil permeabilities.
