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.     

A new turbulence model for porous media flows. Part II: Analysis and validation using microscopic simulations

A new model for turbulent flows in porous media developed in an accompanying paper [F.E. Teruel, Rizwan-uddin, A new turbulence model for porous media flows. Part I: Constitutive equations and model closure, Int. J. Heat Mass Transfer (2009), doi:10.1016/j.ijheatmasstransfer.2009.04.017.], in which new definitions of the macroscopic turbulence quantities are introduced, is analyzed and validated. The model is validated using a simple but often used porous medium consisting of a staggered arrangement of square cylinders. Theoretically predicted values of the newly defined turbulence variables, under fully developed conditions, are compared with corresponding variables used in existing turbulence models. Additionally, evolution of the macroscopic turbulence quantities obtained numerically using the model developed here are compared with reference results, obtained by averaging over space the microscopic level solution of the RANS equations. Comparison exercise for the 75% porosity case is carried out for a range of turbulence intensity at the entrance of the porous medium. Comparison of results shows very good agreement. The spatial evolution of the dispersive kinetic energy, which is included in the definition of the macroscopic turbulent kinetic energy introduced here, is computed using the microscopic solution. Its magnitude relative to the conventional turbulent kinetic energy shows the importance of this quantity in the representation of turbulence effects in porous media flows.     

A macroscopic turbulence model for flow in porous media suited for channel,pipe and rod bundle flows

In the literature, a macroscopic two-equation turbulence model is proposed for analyzing turbulent flows through porous media of particular morphologies (arrays of square or circular rods, packed spheres). This model has been adapted to longitudinal flows in channels, pipes and rod bundles, in order to be able to analyze turbulent flows within nuclear power reactor circuits and core using a macroscopic turbulence model. The additional source terms of the macroscopic k–ϵ equations, which appear as an output of the volume-averaging process, are modeled using the kinetic energy balance and physical considerations. The two unknown constants of the closure expression are determined from the spatial averaging of microscopic k–ϵ computations and from numerical and experimental results available in the literature. This present model has been first successfully evaluated in various simple geometries such as channel and pipe. Good agreement was also obtained between this present model and an experiment of decreasing turbulence inside a rod bundle.     

Turbulent flow over a layer of a highly permeable medium simulated with a diffusion-jump model for the interface

Flow over a finite porous medium is investigated using different interfacial conditions. In such configuration, a macroscopic interface is identified between the two media. In the first model, no diffusion-flux is considered when treating the statistical energy balance at the interface. The second approach assumes that diffusion fluxes of turbulent kinetic energy on both sides of the interface are unequal. Comparing these two models, this paper presents numerical solutions for such hybrid medium, considering here a channel partially filled with a porous layer through which fluid flows in turbulent regime. One unique set of transport equations is applied to both regions. Effects of Reynolds number, porosity, permeability and jump coefficient on mean and turbulence fields are investigated. Results indicate that depending on the value of the stress jump parameter, substantially dissimilar fields for the turbulence energy are obtained. Negative values for the stress jump parameter give results closer to experimental data for the turbulent kinetic energy at the interface.     

Modeling of turbulent heat transfer and thermal dispersion for flows in flat plate heat exchangers

In this paper, heat transfer and dispersion for both laminar and turbulent regimes in heat exchangers and nuclear cores are considered. Such hydraulic systems might be seen as spatially periodic porous media. The existence of a turbulent flow within a porous medium structure suggests the use of a spatial average operator, combined to a statistical average operator. Previous works [M.H.J. Pedras, M.J.S. De Lemos, Macroscopic turbulence modeling for incompressible flow through undeformable porous media, Int. J. Heat Mass Transfer 44 (2001) 1081–1093; F. Kuwahara, A. Nakayama, H. Koyama, A numerical study of thermal dispersion in porous medium, J. Heat Transfer 118 (1996) 756–761] have applied a double average procedure to the thermal balance equation, which led to a macroscopic turbulent transport and a subsequent macro-scale equation featuring dynamic dispersion. Considering the heat flux at the solid surfaces as a boundary condition for the fluid energy balance, the model proposed in this paper allows one to take into account this dispersion as the sum of two contributions. The first one is the classical dispersion due to velocity heterogeneities [G. Taylor, Dispersion of solute matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Lond. A 219 (1953) 186–203] and the second one is due to wall heat transfer. Applying Whitaker up-scaling method [S. Whitaker, Theory and applications of transport in porous media: the method of volume averaging, Kluwer Academic Publishers, 1999], a “closure problem” is then derived for a representative elementary volume, using the so-called Boussinesq approximation to account for small scale turbulence. The model is used to compute macro-scale heat transfer properties for turbulent flows inside a flat plate heat exchanger. It is shown that, for such flows, both dispersive fluxes strongly predominate over the macroscopic turbulent heat flux.     

Numerical computation of macroscopic turbulence quantities in representative elementary volumes of the porous medium

In this study, fully developed macroscopic turbulence quantities—based on their definitions in some existing turbulence models for porous media as well as those based on definitions introduced in a recently developed model [F.E. Teruel, Rizwan-uddin, A new turbulence model for porous media flows. Part I: Constitutive equations and model closure, Int. J. Heat Mass Transfer (2009)]—are computed and analyzed for different Reynolds numbers as well as for different porosity levels. When computed based on the definition introduced in the new model, these numerically computed, pore-level turbulent quantities provide closure to the formulation. A large set of microscopic turbulent flow simulations of the REV of a porous medium, formed by staggered square cylinders, is carried out to achieve these tasks. For each Reynolds number selected, ten different porosities are simulated in the 5–95% range. The Reynolds number is varied from Re = 10³ to Re = 10⁵, covering four different cases of the turbulence flow regime. Numerical results obtained for the macroscopic turbulent kinetic energy based on the new definition show that the spatial dispersion of the mean flow is the main contributor to this quantity at low porosities. Additionally, it is found that for high porosities, the spatial average of the turbulent kinetic energy is the main contributor but the spatial dispersion of the mean flow cannot be neglected. The new definition of the macroscopic dissipation rate is found to asymptotically approach the volume average of this quantity at high Reynolds numbers. It is confirmed that microscopic numerical simulations are consistent with the macroscopic law that states that the macroscopic dissipation rate is determined by the pressure-drop through the REV.     

A new turbulence model for porous media flows. Part I: Constitutive equations and model closure

A new model for turbulent flows in porous media is developed. The spatial- and time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the k and ε type equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms as those found in the corresponding equations for clear flow, plus additional terms resulting from the interaction between solid walls in the porous media and the fluid characterize the model. These extra terms arise in a boundary integral form, facilitating their modeling. The model is closed by assuming the eddy viscosity approximation to be valid, and using simple models to represent the interaction between the walls in the porous media and the fluid.     

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.     

Large eddy simulation of turbulent flow in porous media

An LES (large eddy simulation) study was conducted using one of standard numerical models for a porous medium, namely, a flow through a periodic array of square cylinders. The LES results were processed to extract macroscopic results such as the macroscopic turbulent kinetic energy and the macroscopic pressure gradient. These macroscopic results are compared against those obtained using conventional models of turbulent kinetic energy and its dissipation rate, so as to examine the validity of extending the conventional two equation models of turbulence to the flow in porous media. The spectrum of turbulence was also examined to appreciate the onset of turbulence.     

Zone conditional assessment of flame-generated turbulence with DNS database of a turbulent premixed flame

Zone conditional two-fluid equations are derived and validated against a DNS database for a turbulent premixed flame. The conditional statistics of major flow variables are investigated to understand the mechanism of flame-generated turbulence. The flow field in the burned region shows substantially increased, highly anisotropic turbulence to conserve mass through a flamelet surface. The transverse component may be larger than the axial component for a distributed pdf of the flamelet orientation angle in the middle of the flame brush. The opposite occurs due to redistribution of turbulent kinetic energy and flamelet orientation mostly normal with respect to the mean flow at the end of the flame brush. The major source or sink terms of turbulent kinetic energy are the interfacial transfer by the mean reaction rate and the work terms induced by fluctuating pressure and velocity on the flame surface. Ad hoc modeling of some interfacial terms may be required for further application of the two-fluid model for modeling turbulence in turbulent premixed combustion simulations.     

Characteristics of direct injection combustion fuelled by natural gas–hydrogen mixtures using a constant volume vessel

The effects of hydrogen addition and turbulence intensity on the natural gas–air turbulent combustion were studied experimentally using a constant volume vessel. Turbulence was generated by injecting the high-pressure fuel into the vessel. Flame propagation images and combustion characteristics via pressure-derived parameters were analyzed at various hydrogen volumetric fractions (from 0% to 40%) and the overall equivalence ratios of 0.6, 0.8 and 1.0. The results showed that the turbulent combustion rate increased remarkably with the increase of hydrogen fraction in fuel blends when hydrogen fraction is over 11%. Combustion rate was increased remarkably with the introduction of turbulence in the bomb and decreased with the decrease of turbulence intensity. The lean flammability limit of natural gas–air turbulent combustion can be extended with increasing hydrogen fraction addition. Maximum pressure and maximum rate of pressure rise increased while combustion duration decreased monotonically with the increase of hydrogen fraction in fuel blends. The sensitivity of natural gas/hydrogen hybrid fuel to the variation of turbulence intensity was decreased while increasing the hydrogen addition. Maximum pressure and maximum rate of pressure rise increased while combustion duration decreased with the increase of turbulent intensity at stoichiometric and lean-burn conditions. However, slight influence on combustion characteristics was presented with variation of hydrogen fraction at the stoichiometric equivalence ratio with and without the turbulence in the bomb.     

Depth-averaged turbulent heat and fluid flow in a vegetated porous medium

In this article, the latest developments of porous media science are used in order to simulate heat and fluid flow in a non-flexible vegetated porous media. Vegetation porosity and density at the domain interior are redefined. The same strategy is then applied in order to define the boundary porosity near the bed and water surface. Regarding the vegetation arrangement in natural streams and flumes, three different models are suggested for calculating the porosity near other boundaries. The microscopic time-mean secondary force in momentum equations is modified for a vegetated porous media and its macroscopic form is derived. A dissipation source term is derived and, it is added to vorticity equation in order to take account of vegetation damping effect on secondary flows. The effect of this dissipation source term on the absolute magnitude of vorticity and velocity field is then investigated. Application of a high Reynolds number turbulence model to turbulent flow in partially vegetated open channels is numerically examined. A model is suggested for taking account of vegetation material on heat flux through walls in a vegetated porous media. The thermal diffusion due to the porosity gradient is modeled and, the contribution of this porosity-induced heat flux on temperature field is investigated. The effect of laminar thermal dispersion on temperature field is also investigated at low stem Reynolds number.     

Two-dimensional simulation of turbulent flow and transfer through stacked spheres

We propose a one-equation model for two-dimensional turbulent flow through porous media. The momentum equation is derived from the space averaging of Navier-Stokes equations, leading to the so-called Darcy-Forchheimer equations. In the turbulent kinetic energy transport equation, the production term is assumed to be proportional to the cube of velocity. The dissipation term is not estimated with a transport equation, it is explicitly given by a law involving turbulent kinetic energy and velocity. The model requires only four experimentally determined parameters. The local Nusselt number was correlated to local Reynolds number, and to local turbulence intensity. Good agreement between the simulated and the experimental local Nusselt number is obtained.     

Turbulent kinetic energy distribution across the interface between a porous medium and a clear region

For hybrid media, involving both a porous substrate and an unobstructed flow region, difficulties arise due to the proper mathematical treatment given at the macroscopic interface. The literature proposes a jump condition in which shear stresses on both sides of the interface are not of the same value. This paper presents numerical solutions for such hybrid medium, considering here a channel partially filled with a porous layer through which an incompressible fluid flows in turbulent regime. Here, diffusion fluxes of both momentum and turbulent kinetic energy across the interface present a discontinuity in their values, which is based on a certain jump coefficient. Effects of such parameter on mean and turbulence fields around the interface region are numerically investigated. Results indicate that depending on the value of the stress jump parameter, a substantially different structure for the turbulent field is obtained.     

Computational analysis of fuel saving by using porous-end configuration for a PEM fuel cell

In the present study, a novel porous-end PEMFC inspired by the characteristics of open-end and dead-end PEMFCs is proposed for fuel saving. For this purpose, a porous media region with a certain thickness is added to the outlet region of the anode channel of an open-end PEMFC. The effect of porous media thickness at the anode channel on the current density and hydrogen mass flow was numerically analyzed. Results indicate that in comparison to the base model PEMFC, the presence of porous media at the end of the anode channel of porous-end PEMFC leads to an increase in the pressure and a decrease in the velocity magnitude in the anode channel. Results illustrate that the porous-end PEMFC with t = 1 mm thickness can be an adequate choice to gain an optimum design for the porous-end configuration. This conclusion becomes more highlighted when the results give the 66.17% reduction in fuel consumption.     

A simplified numerical approach to hydrogen and hydrocarbon combustion in single and double-layer porous burners

Motivated by the fuel hydrogen applications in porous combustors, as well as hydrogen production in syngas porous devices, this work shows a simplified one-dimensional, steady state heat and mass transfer model for stabilized premixed flames in porous inert media. Single-layer and double-layer porous burner are studied. The model has three conservation equations, describing the heat transfer in the solid and fluid phases and the mass transfer in the reacting flow. The model considers a plug flow and is solved numerically by using the finite volume method. The results are compared with benchmark data, depicting the superadiabatic flames and the heat recirculation process. A parametric analysis of the model reveals the effects of the porous media properties and the Lewis and Peclet numbers on the heat and mass transfer processes. Furthermore, the effects of the flame stand-off parameter in double layer porous burner are also analyzed. The results have considered the values of the dimensionless parameters based on reference data for hydrogen/air and methane/air combustion in porous burners built with SiC and Al₂O₃.     

多孔介质发动机流动与燃烧特性的大涡模拟初探

对多孔介质发动机的燃烧特性采用大涡模拟进行了初步分析.首先计算了考虑多孔介质随机结构特性的定容燃烧室内气体燃料喷射过程,并与自由空间中的喷射过程进行了对比.然后采用大涡模型对两种结构形式的多孔介质发动机的燃烧过程进行了初步的计算分析.多孔介质的存在增强了湍流涡团的小尺度结构,明显改变了燃料的空间分布,而采用大涡模拟(L...     

Numerical simulations of non-premixed turbulent combustion of CH4–H2 mixtures using the PDF approach

The present work is devoted to the study of non-premixed turbulent combustion with the PDF approach using three turbulence models: k-? model, modified k-? model and RSM model. A detailed kinetic mechanism is used in the numerical simulations. The three turbulence models are compared and evaluated with the experimental data and the numerical results of the literature. The evaluation concludes that the modified k-? is the most appropriate for simulating this kind of flame. A study of the effect of hydrogen addition on methane combustion is performed. Hydrogen addition causes the elevation of combustion temperature, the decreasing of CO and CO₂ mass fractions but leads to the increase of NO mass fraction.     

Heat- mass transfer and flow characteristics of two-phase countercurrent annular flow in a vertical pipe

Experimental and theoretical results on flow, heat and mass transfer characteristics for the countercurrent flow of air and water in a vertical circular pipe are compared. An experimental setup was designed and constructed. Hot water is introduced through a porous section at the upper end of a test section and flows downward as a thin liquid film on the pipe wall while the air flows countercurrently. The air and water flow rates used in this study are those before the flooding is reached. A developed mathematical model is separated into three parts: A high Reynolds number turbulence model, in which the local state of turbulence characteristics consists of the turbulent kinetic energy (k) and its dissipation rate (ϵ).The transport equations for both k and s are solved simultaneously with the momentum equation to determine the kinetic turbulence viscosity, the pressure drop, interfacial shear stress and then the friction factor at the film/core interface; Heat and mass transfer models are proposed in order to estimate the distribution of the temperature and the mass fraction of water vapor in gas core. The results from the model are compared with the present experimental ones. It can be shown from the present study that the influence of the interfacial wave phenomena is significant to the pressure loss, and the heat and mass transfer rate in the gas phase.     

Turbulent flow in a channel occupied by a porous layer considering the stress jump at the interface

For hybrid media, involving both a porous structure and a clear flow region, difficulties arise due to the proper mathematical treatment given at the interface. The literature proposes a jump condition in which shear stresses on both sides of the interface are not of the same value. This paper presents numerical solutions for such hybrid medium, considering here a channel partially filled with a porous layer through which fluid flows in turbulent regime. One unique set of transport equations is applied to both regions. Effects of Reynolds number, porosity, permeability and jump coefficient on mean and turbulence fields are investigated. Results indicate that depending on the value of the stress jump parameters, a substantially different structure for the turbulent field is obtained.