Search results for: darcy

Authors: Youssef I. Hafez

Abstract:

Since ancient history rivers have been the fostering and favorite place for people and civilizations to live and exist along river banks. However, due to floods and droughts, especially sever conditions due to global warming and climate change, river channels are completely evolving and moving in the lateral direction changing their plan form either through straightening of curved reaches (meander cut-off) or increasing meandering curvature. The lateral shift or shrink of a river channel affects severely the river banks and the flood plain with tremendous impact on the surrounding environment. Therefore, understanding the formation and the continual processes of river channel meandering is of paramount importance. So far, in spite of the huge number of publications about river-meandering, there has not been a satisfactory theory or approach that provides a clear explanation of the formation of river meanders and the mechanics of their associated geometries. In particular two parameters are often needed to describe meander geometry. The first one is a scale parameter such as the meander arc length. The second is a shape parameter such as the maximum angle a meander path makes with the channel mean down path direction. These two parameters, if known, can determine the meander path and geometry as for example when they are incorporated in the well known sine-generated curve. In this study, a uniform excess energy theory is used to illustrate the origin and mechanics of formation of river meandering. This theory advocates that the longitudinal imbalance between the valley and channel slopes (with the former is greater than the second) leads to formation of curved meander channel in order to reduce the excess energy through its expenditure as transverse energy loss. Two relations are developed based on this theory; one for the determination of river channel radius of curvature at the bend apex (shape parameter) and the other for the determination of river channel sinuosity. The sinuosity equation tested very well when applied to existing available field data. In addition, existing model data were used to develop a relation between the meander arc length and the Darcy-Weisback friction factor. Then, the meander wave length was determined from the equations of the arc length and the sinuosity. The developed equation compared well with available field data. Effects of the transverse bed slope and grain size on river channel sinuosity are addressed. In addition, the concept of maximum channel sinuosity is introduced in order to explain the changes of river channel plan form due to changes in flow discharges and sediment loads induced by global warming and climate changes.

Keywords: river channel meandering, sinuosity, radius of curvature, meander arc length, uniform excess energy theory, transverse energy loss, transverse bed slope, flow discharges, sediment loads, grain size, climate change, global warming

Procedia PDF Downloads 223

Authors: P. Naderi, M. N. Ouarzazi, S. C. Hirata, H. Ben Hamed, H. Beji

Abstract:

The stability of mixed convection in a Newtonian fluid medium heated from below and cooled from above, also known as the Poiseuille-Rayleigh-Bénard problem, has been extensively investigated in the past decades. To our knowledge, mixed convection in porous media has received much less attention in the published literature. The present paper extends the mixed convection problem in porous media for the case of a viscoelastic fluid flow owing to its numerous environmental and industrial applications such as the extrusion of polymer fluids, solidification of liquid crystals, suspension solutions and petroleum activities. Without a superimposed through-flow, the natural convection problem of a viscoelastic fluid in a saturated porous medium has already been treated. The effects of the viscoelastic properties of the fluid on the linear and nonlinear dynamics of the thermoconvective instabilities have also been treated in this work. Consequently, the elasticity of the fluid can lead either to a Hopf bifurcation, giving rise to oscillatory structures in the strongly elastic regime, or to a stationary bifurcation in the weakly elastic regime. The objective of this work is to examine the influence of the main horizontal flow on the linear and characteristics of these two types of instabilities. Under the Boussinesq approximation and Darcy's law extended to a viscoelastic fluid, a temporal stability approach shows that the conditions for the appearance of longitudinal rolls are identical to those found in the absence of through-flow. For the general three-dimensional (3D) perturbations, a Squire transformation allows the deduction of the complex frequencies associated with the 3D problem using those obtained by solving the two-dimensional one. The numerical resolution of the eigenvalue problem concludes that the through-flow has a destabilizing effect and selects a convective configuration organized in purely transversal rolls which oscillate in time and propagate in the direction of the main flow. In addition, by using the mathematical formalism of absolute and convective instabilities, we study the nature of unstable three-dimensional disturbances. It is shown that for a non-vanishing through-flow, general three-dimensional instabilities are convectively unstable which means that in the absence of a continuous noise source these instabilities are drifted outside the porous medium, and no long-term pattern is observed. In contrast, purely transversal rolls may exhibit a transition to absolute instability regime and therefore affect the porous medium everywhere including in the absence of a noise source. The absolute instability threshold, the frequency and the wave number associated with purely transversal rolls are determined as a function of the Péclet number and the viscoelastic parameters. Results are discussed and compared to those obtained from laboratory experiments in the case of Newtonian fluids.

Keywords: instability, mixed convection, porous media, and viscoelastic fluid

Procedia PDF Downloads 341

Authors: Qaisar Ali, Waqar A. Khan, Shafiq R. Qureshi

Abstract:

Heat transfer in Power Law Fluids across cylindrical surfaces has copious engineering applications. These applications comprises of areas such as underwater pollution, bio medical engineering, filtration systems, chemical, petroleum, polymer, food processing, recovery of geothermal energy, crude oil extraction, pharmaceutical and thermal energy storage. The quantum of research work with diversified conditions to study the effects of combined heat transfer and fluid flow across porous media has increased considerably over last few decades. The most non-Newtonian fluids of practical interest are highly viscous and therefore are often processed in the laminar flow regime. Several studies have been performed to investigate the effects of free and mixed convection in Newtonian fluids along vertical and horizontal cylinder embedded in a saturated porous medium, whereas very few analysis have been performed on Power law fluids along wedge. In this study, boundary layer analysis under the effects of radiation-mixed convection in power law fluids along vertical wedge in porous medium have been investigated using an implicit finite difference method (Keller box method). Steady, 2-D laminar flow has been considered under prescribed surface heat flux condition. Darcy, Boussinesq and Roseland approximations are assumed to be valid. Neglecting viscous dissipation effects and the radiate heat flux in the flow direction, the boundary layer equations governing mixed convection flow over a vertical wedge are transformed into dimensionless form. The single mathematical model represents the case for vertical wedge, cone and plate by introducing the geometry parameter. Both similar and Non- similar solutions have been obtained and results for Non similar case have been presented/ plotted. Effects of radiation parameter, variable heat flux parameter, wedge angle parameter ‘m’ and mixed convection parameter have been studied for both Newtonian and Non-Newtonian fluids. The results are also compared with the available data for the analysis of heat transfer in the prescribed range of parameters and found in good agreement. Results for the details of dimensionless local Nusselt number, temperature and velocity fields have also been presented for both Newtonian and Non-Newtonian fluids. Analysis of data revealed that as the radiation parameter or wedge angle is increased, the Nusselt number decreases whereas it increases with increase in the value of heat flux parameter at a given value of mixed convection parameter. Also, it is observed that as viscosity increases, the skin friction co-efficient increases which tends to reduce the velocity. Moreover, pseudo plastic fluids are more heat conductive than Newtonian and dilatant fluids respectively. All fluids behave identically in pure forced convection domain.

Keywords: porous medium, power law fluids, surface heat flux, vertical wedge

Procedia PDF Downloads 312

Authors: A. Odoom, A. Salama, H. Ibrahim

Abstract:

Hydrogen is a clean source of energy for power production and transportation. The main source of hydrogen in this research is biodiesel. Glycerol also called glycerine is a by-product of biodiesel production by transesterification of vegetable oils and methanol. This is a reliable and environmentally-friendly source of hydrogen production than fossil fuels. A typical composition of crude glycerol comprises of glycerol, water, organic and inorganic salts, soap, methanol and small amounts of glycerides. Crude glycerol has limited industrial application due to its low purity thus, the usage of crude glycerol can significantly enhance the sustainability and production of biodiesel. Reforming techniques is an approach for hydrogen production mainly Steam Reforming (SR), Autothermal Reforming (ATR) and Partial Oxidation Reforming (POR). SR produces high hydrogen conversions and yield but is highly endothermic whereas POR is exothermic. On the downside, PO yields lower hydrogen as well as large amount of side reactions. ATR which is a fusion of partial oxidation reforming and steam reforming is thermally neutral because net reactor heat duty is zero. It has relatively high hydrogen yield, selectivity as well as limits coke formation. The complex chemical processes that take place during the production phases makes it relatively difficult to construct a reliable and robust numerical model. Numerical model is a tool to mimic reality and provide insight into the influence of the parameters. In this work, we introduce a finite volume numerical study for an 'in-house' lab-scale experiment of ATR. Previous numerical studies on this process have considered either using Comsol or nodal finite difference analysis. Since Comsol is a commercial package which is not readily available everywhere and lab-scale experiment can be considered well mixed in the radial direction. One spatial dimension suffices to capture the essential feature of ATR, in this work, we consider developing our own numerical approach using MATLAB. A continuum fixed bed reactor is modelled using MATLAB with both pseudo homogeneous and heterogeneous models. The drawback of nodal finite difference formulation is that it is not locally conservative which means that materials and momenta can be generated inside the domain as an artifact of the discretization. Control volume, on the other hand, is locally conservative and suites very well problems where materials are generated and consumed inside the domain. In this work, species mass balance, Darcy’s equation and energy equations are solved using operator splitting technique. Therefore, diffusion-like terms are discretized implicitly while advection-like terms are discretized explicitly. An upwind scheme is adapted for the advection term to ensure accuracy and positivity. Comparisons with the experimental data show very good agreements which build confidence in our modeling approach. The models obtained were validated and optimized for better results.

Keywords: autothermal reforming, crude glycerol, hydrogen, numerical model

Procedia PDF Downloads 140