Turbulent flow in a composite channel

Numerical solutions for turbulent flow in a composite channel are presented. Here, a channel with a centered porous material is considered. The interface between the porous medium and the clear flow was assumed to have different transversal positions and the porous matrix was simulated with distinct permeabilities. Governing equations were discretized and solved for both domains making use of one unique numerical methodology. Increasing the size of the porous material pushes the flow outwards, increasing the levels of turbulent kinetic energy at the macroscopic interface. For high permeability media, a large amount of mechanical energy is converted into turbulence inside the porous structure.     

Turbulent flow with combustion in a moving bed

This paper presents a mathematical model for treating turbulent combusting flows in a moving porous bed, which might be useful to design and analysis of modern and advanced biomass gasification systems. Here, one explicitly considers the intra-pore levels of turbulent kinetic energy and the movement of the rigid solid matrix is considered to occur at a steady speed. Transport equations are written in their time-and-volume-averaged form and a volume-based statistical turbulence model is applied to simulate turbulence generation due to the porous matrix. The rate of fuel consumption is described by an Arrhenius expression involving the product of the fuel and oxidant mass fractions. Results indicate that fixing the gas speed and increasing the speed of the solid matrix pushes the flame front towards the end of the reactor. Also, since the rate of production of turbulence is dependent on the relative velocity between phases, as the solid velocity approaches that of the gas stream, the level of turbulence in the flow is reduced.     

The stability of flow in a channel or duct occupied by a porous medium

The hydrodynamic stability of flow of an incompressible fluid through a plane-parallel channel or circular duct filled with a saturated porous medium, modeled by the Brinkman equation, is discussed on the basis of an analogy with a magneto-hydrodynamic problem (Hartmann flow). Flow in a circular duct is found to be stable to small disturbances for all values of the Reynolds number, but for a plane-parallel channel the flow is unstable if the Reynolds number exceeds a critical value, dependent on a Darcy number.     

Turbulent natural convection in a porous square cavity computed with a macroscopic κ–ε model

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic κ–ε turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Computations covered the range 10 < Ra_m < 10⁶ and 10⁻⁷ < Da  < 10⁻¹⁰ and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m and for Ra_m less than a certain critical Rayleigh number, Ra_cr. This convergence of results as Ra_m decreases can be seen as a characterization of the laminarization phenomenon. For Ra_m values less than around 10⁴, both laminar and turbulent flow solutions merge, indicating that such critical value for Ra_m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra_m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.     

Turbulent kinetic energy in a moving porous bed

This paper presents a set of transport equations for solving problems involving turbulent flow in a moving bed reactor. The reactor is seen as a porous matrix with a moving solid phase. Equations are time-and-volume averaged and the solid phase is considered to have an imposed constant velocity. Additional drag terms appearing in the momentum equation are assumed to be a function of the relative velocity between the fluid and solid phase. Turbulence equations are influenced by the speed of the solid phase in relation to that of the flowing fluid. Results show the decrease of turbulent kinetic energy levels as the solid speed approaches the speed of the moving bed.     

Double-diffusive turbulent natural convection in a porous square cavity with opposing temperature and concentration gradients

This paper presents results for coupled heat and mass transport under laminar and turbulent flow regimes in porous cavities. Two driving mechanisms are considered to contribute to the overall momentum transport, namely temperature driven and concentration driven mass fluxes. Aiding and opposing flows are considered, where temperature and concentration gradients are either in the same direction or of different sign, respectively. Modeled equations are presented based on the double-decomposition concept, which considers both time fluctuations and spatial deviations about mean values. Turbulent transport is accounted for via a macroscopic version of the k–ε model. Variation of the cavity Nusselt and Sherwood numbers due to changes on N, where N is the ratio of solute to thermal Grashof numbers, is presented. Results indicate that for adding cases, mass and heat transfer across the cavity are enhanced faster than for cases with opposing temperature and concentration gradients. For the conditions here investigated, the use a turbulence model gave results for Nu and Sh that were nearly double when compared with laminar results for the same conditions.     

Combined radiation and convection heat transfer in a porous channel bounded by isothermal parallel plates

Combined radiation and convection heat transfer in a porous medium confined between gray isothermal parallel plates is investigated. The medium is absorbing, emitting and scattering. Cases of boundaries at temperatures higher or lower than the medium are considered. In the porous medium, the boundary effect on the fully developed laminar velocity field as proposed by Kaviany is accounted for. For various values of the extinction coefficient, the scattering albedo, the conduction-radiation parameter and the boundary emissivity, Nusselt number, temperature and heat flux distributions are found for the range of values including the extreme limits of the porous medium shape parameter (PMSP), γ=(W²φ/K)^1/2, where W is the channel width, φ the porosity and K the permeability. For the lower limiting value of the PMSP γ, the effect of the porous medium is negligible and the situation approaches that of Poiseuille flow. For this limiting case, results from the present work are compared with those available in the literature. For medium to high values of the PMSP γ, for the purpose of comparison, some results are presented in tabular form. Radiation is found to have a significant effect on various parameters studied. The discrete transfer method was used for the solution of the radiative part of the energy equation. An iterative finite difference scheme was used to solve the energy equation.     

Use of porous baffles to enhance heat transfer in a rectangular channel

An experimental investigation was carried out to measure module average heat transfer coefficients in uniformly heated rectangular channel with wall mounted porous baffles. Baffles were mounted alternatively on top and bottom of the walls. Heat transfer coefficients and pressure loss for periodically fully developed flow and heat transfer were obtained for different types of porous medium (10, 20, and 40 pores per inch (PPI)) with two window cut ratios (B_h/D_h=1/3 and 2/3) and two baffle thickness to channel hydraulic diameter ratios (B_t/D_h=1/3 and 1/12). Reynolds number (Re) was varied from 20,000 to 50,000. To compare the effect of foam metal baffle, the data for conventional solid-type baffle were obtained for (B_t/D_h=1/3). The maximum uncertainties associated with module Nusselt number and friction factor were 5.8% and 4.3% respectively. The experimental procedure was validated by comparing the data for the straight channel with no baffles (B_h/D_h=0) with those in the literature [Publications in Engineering, vol. 2, University of California, Berkeley, 1930, p. 443; Int. Chem. Eng. 16 (1976) 359]. The use of porous baffles resulted in heat transfer enhancement as high as 300% compared to heat transfer in straight channel with no baffles. However, the heat transfer enhancement per unit increase in pumping power was less than one for the range of parameters studied in this work. Correlation equations were developed for heat transfer enhancement ratio and heat transfer enhancement per unit increase in pumping power in terms of Reynolds number.     

Laminar heat transfer in a porous channel simulated with a two-energy equation model

Laminar heat transfer in a porous channel is numerically simulated with a two-energy equation model for conduction and convection. Macroscopic equations for continuity, momentum and energy transport for the fluid and solid phases are presented. The numerical methodology employed is based on the control volume approach with a boundary-fitted non-orthogonal coordinate system. Fully developed forced convection in a porous channel bounded by parallel plates is considered. Solutions for Nusselt numbers along the channel are presented for laminar flows. Results simulate the effects Reynolds number Re, porosity, particle size and solid-to-fluid thermal conductivity ratio on Nusselt sumber, Nu, which is defined for both the solid and fluid phases. High Re, low porosities, low particle diameters and low thermal conductivity ratios promote thermal equilibrium between phases leading to higher values of Nu.     

Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium

This paper describes the heat transfer analysis with thermal radiation on the two-dimensional magnetohydrodynamic (MHD) flow in a channel with porous walls. The upper-convected Maxwell (UCM) fluid fills the porous space between the channel walls. The corresponding boundary layer equations are transformed into ordinary differential equations by means of similarity transformations. The resulting problems are solved by employing homotopy analysis method (HAM). Convergence of the derived series solutions is ensured. The effects of embedded parameters on the dimensionless velocity components and temperature are examined through plots. The variation of local Nusselt number is also analyzed.     

Viscoelastic effects on the oscillatory flow in a fluid-saturated porous layer

The oscillating flow of the viscoelastic fluid-saturated porous layer has been useful in many areas, including the petroleum, chemical, and bioengineering industries. It is studied using the modified Darcy-Oldroyd-B model in this article. The exact solution is obtained utilizing a simpler and more reasonable method. According to this velocity solution, the time-velocity profile of one kind of viscoelastic fluid is analyzed. From the analysis, it was found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Further, velocity, temperature, shear stress, and the rate of heat transfer are exponential solutions that are obtained and analyzed for different values of known physical parameters. Finally, we recognize that the relaxation and retardation parameters in this model act in the opposite manner.     

Micropolar flow in a porous channel with high mass transfer

In this research the injective micropolar flow in a porous channel is investigated. The flow is driven by suction or injection on the channel walls, and the micropolar model is used to describe the working fluid. This problem is mapped into the system of nonlinear coupled differential equations by using Berman's similarity transformation. These are solved for large mass transfer via Optimal Homotopy Asymptotic Method (OHAM). Also the numerical method is used for the validity of this analytical method and excellent agreement is observed between the solutions obtained from OHAM and numerical results. Trusting this validity, effects of some other parameters are discussed.     

Bounds on natural convective heat transfer in a porous layer with fixed heat flux

Using the background field variational method, bounds on natural convective heat transfer in a porous layer heated from below with fixed heat flux are derived from the primitive equations. The enhancement of heat transfer beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the non-dimensional forcing scale set by the ‘effective’ Rayleigh number (Rˆ) according to Nu ≤ 0.354Rˆ^1/2 and in terms of the conventional Rayleigh number (Ra) defined by the temperature drop across the layer according to Nu ≤ 0.125Ra. It is presented that fixing the heat flux at the boundaries does not change the linear dependence between Nusselt number and Rayleigh number at high Rayleigh number region.     

Natural convection boundary layer flow over a truncated cone in a porous medium saturated by a nanofluid

This work studies the natural convection boundary layer flow over a truncated cone embedded in a porous medium saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A suitable coordinate transformation is performed, and the obtained nonsimilar equations are solved by the cubic spline collocation method. The effect of the Brownian motion parameter and thermophoresis parameter on the temperature, nanoparticle volume fraction and velocity profiles are discussed. The effects of the thermophoresis parameter, Brownian parameter, Lewis number, and buoyancy ratio on the local Nusselt number have been studied. Results show that an increase in the thermophoresis parameter or the Brownian parameter tends to decrease the local Nusselt number. Moreover, the local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased.     

Extended Oberbeck-Boussinesq approximation study of convective instabilities in a porous layer with horizontal flow and bottom heating

A study of the onset of convective instabilities in a porous layer with a horizontal basic flow is performed by including the effects of viscous dissipation and pressure work in the energy balance. Firstly, the so-called extended Oberbeck-Boussinesq approximation, i.e. the model based on the enthalpy formulation of the energy balance, is adopted. Then, the results for the marginal stability condition are compared with those obtained by the so-called Chandrasekhar approximation, i.e. the model based on the internal-energy formulation of the energy balance. It is shown that a marked discrepancy occurs between the two approaches, that becomes specially evident for high values of the Gebhart number. According to the extended Oberbeck-Boussinesq approximation, the effects of the viscous dissipation and of the pressure work result in a stabilization of the basic flow. On the contrary, the Chandrasekhar approximation predicts a destabilization of the basic flow induced by the viscous dissipation. The destabilization can be so intense that the onset of convective rolls may occur even in the absence of a boundary temperature difference, i.e. with a vanishing Darcy-Rayleigh number.     

Turbulence modeling of atmospheric boundary layer flow over complex terrain: a comparison of models at wind tunnel and full scale

The aim of this work is to evaluate the performance of two popular k ? ? turbulence closure schemes for atmospheric boundary layer (ABL) flow over hills and valleys and to investigate the effect of using ABL‐modified model constants. The standard k ? ? and the RNG k ? ? models are used to simulate flow over the two‐dimensional analytical shapes from the RUSHIL and RUSHVAL wind tunnel experiments. Furthermore, the mean turbulent flow over the real complex terrain of Blashaval hill is simulated and the results verified with a data set of full‐scale measurements. In general, all models yield similar results. However, use of ABL‐modified constants in both models tends to decrease the predicted velocity and increase the predicted turbulent kinetic energy. Copyright © 2010 John Wiley & Sons, Ltd.     

Thermal instability in a porous medium layer saturated by a nanofluid

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The analysis reveals that for a typical nanofluid (with large Lewis number) the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles, the contribution of nanoparticles to the thermal energy equation being a second-order effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution.     

Thermal management in PEMFCs: The respective effects of porous media in the gas flow channel

This study aims to evaluate the convective heat transfer enhancement of the proton exchange membrane fuel cells (PEMFC) numerically. As the higher heat transfer surfaces lead to higher heat transfer rates, a flat plate porous layer is utilized in the gas flow channel (GFC). This enhancement in heat transfer stems from the corresponding modification in the temperature and velocity profiles. The influencing parameters on these profiles are the thickness, permeability, and porosity of the GFC porous layer. After performing the simulations, the results indicate that convective heat transfer has a direct relationship with GFC porous layer's thickness and permeability. However, lower values of porosity lead to the higher Nusselt numbers. Previous investigations have also mentioned the positive impact of the microporous layer (MPL) on the water management of these fuel cells. Therefore, six different sizes of MPL and the gas diffusion layer (GDL) are utilized to evaluate their impacts on the thermal management. Results indicate that although these sizes have negligible effects on the heat transfer, Nu increases by enhancing the total size of MPL and GDL. The results also show that thicker MPLs lead to higher heat transfer rates. The evaluation of the friction factor also indicates the adverse effect of the GFC porous layer, although this undesirable effect is negligible. Finally, all the simulated values are utilized to train an artificial neural network (ANN) model with high precision. This ANN model can produce more data for sensitivity analysis and presenting respective 3D diagrams of the influencing parameters on heat transfer.     

Couple stress effects on the MHD oscillatory flow in a fluid-saturated porous layer

In this paper, the oscillatory flow of hydromagnetic couple stress fluid-saturated porous layer with inhomogeneous wall temperatures is studied. The flow is modeled using the modified Darcy equation. The fluid is subjected to a transverse magnetic field and the velocity slip at the lower plate is taken into deliberation. The governing coupled partial differential equations of the flow are transformed to coupled ordinary differential equations and are solved analytically. The impact of the physical parameters such as the Grashof number, Prandtl number, Darcy number, Hartmann number, and couple stress parameters on velocity profiles, temperature, rate of heat transfer, and skin friction are emphasized. The velocity field increased as either the Grashof number, the Darcy number, the suction/injection parameter, and Prandtl number increased nevertheless reverse growth can be seen by increasing the Hartmann number and the couple stress parameter. The temperature field in the channel increases with increasing the suction/injection parameter and Prandtl number but a conflicting development can be seen with increasing the oscillation amplitude. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate.