Modeling fluid and heat transport in the reactive, porous bed of downdraft (biomass) gasifier

A fluid flow and heat transfer model has been developed for the reactive, porous bed of the biomass gasifier to simulate pressure drop, temperature profile in the bed and flow rates. The conservation equations, momentum equation and energy equation are used to describe fluid and heat transport in porous gasifier bed. The model accounted for drag at wall, and the effect of radial as well as axial variation in bed porosity to predict pressure drop in bed. Heat transfer has been modeled using effective thermal conductivity approach. Model predictions are validated against the experiments, while effective thermal conductivity values are tested qualitatively using models available in literature. Parametric analysis has been carried out to investigate the effect of various parameters on bed temperature profile and pressure drop through the gasifier. The temperature profile is found to be very sensitive to gas flow rate, and heat generation in oxidation zone, while high bed temperature, gas flow rate and the reduction in feedstock particle size are found to cause a marked increase in pressure drop through the gasifier. The temperatures of the down stream zones are more sensitive to any change in heat generation in the bed as compared to upstream zone. Author recommends that the size of preheating zone may be extended up to pyrolysis zone in order to enhance preheating of input air, while thermal insulation should not be less than 15 cm.     

Heat Transfer and Gas Flow through Feed Stream within Horizontal Pipe

In the feeding process, the feed stream forms a moving packed bed of particle from the feedstock in the feed channel. When the feeding is at emergency interruption especially in the case of flooding and uncontrollable discharge, the hot gases from reactor would infiltrate into the feed stream. The high heat penetration into feed stream would affect the feeder performance. In this paper, transient thermal response of feed stream within horizontal pipe is described mathematically with a gas flow and heat transfer model. Influences of varied factors on the thermal penetration into feed stream are examined for different conditions. The temperature of the packed-bed particles and the gas velocity distribution curves are obtained for the feeding service at interruption and at normal operating conditions. The numerical results show that the thermal penetration to the packed-bed particles by the seepage flow fluid is high only in the position near the gas entrance. The thermal penetration depth tends to increase with the seepage flow velocity and decrease with feeding rate. There is no appreciable thermal penetration in the feed stream when the feeding service is at normal running. The operating conditions and the porosity of solid bed have importance effects on the gas velocity and temperature field in the thermal penetration zone. A test system is set up to determine the transient thermal response experimentally for the packed bed of particles within a horizontal pipe. The model results are found to compare favorably with the experimental data.     

Stability of Thermosolutal Natural Convection in Superposed Fluid and Porous Layers

This article deals with the onset of thermosolutal natural convection in horizontal superposed fluid and porous layers. A linear stability analysis is performed using the one-domain approach. As in the thermal convection case, the results show a bimodal nature of the marginal stability curves where each mode corresponds to a different convective instability. At small wave numbers, the convective flow occurs in the whole cavity (“porous mode”) while perturbations of large wave numbers lead to a convective flow mainly confined in the fluid layer (“fluid mode”). Furthermore, it is shown that the onset of thermosolutal natural convection is characterized by a multi-cellular flow in the fluid region for negative thermal Rayleigh numbers. For positive thermal Rayleigh numbers, the convective flow takes place both in the fluid and porous regions. The influence of the depth ratio and thermal diffusivity ratio is also investigated for a wide range of the thermal Rayleigh numbers.     

Convective heat transfer and fluid flow physics in some ribbed ducts using liquid crystal thermography and PIV measuring techniques

Enhancement of forced convection is important in several engineering applications. Surface modifications like rib-roughening are commonly used in applications such as compact heat exchangers and internal cooling of gas turbine blades and vanes. This paper gives a brief summary of convective heat transfer and fluid flow in some ribbed ducts using liquid crystal thermography and PIV measuring techniques. Details of the flow pattern and the influence of rib configuration and arrangement on the heat transfer are presented. Nevertheless, the understanding of the flow and thermal physics in ribbed ducts is not yet complete and further studies are needed.     

Multiple-scale modelling of acoustic sources in low Mach-number flow

The main difficulty in the calculation of sound generated by fluid flow at low Mach numbers is the occurrence of different scales. The fluid flow is characterized by small spatial structures containing a large amount of energy that may propagate with a small convective velocity, such as small vortices in a turbulent flow. The radiated acoustic waves have small amplitudes and carry a small amount of energy, but have a long wavelength due to their fast propagation velocity. In this paper a perturbation method is used to calculate noise generation and propagation in combination with fluid flow based on the incompressible equations. The idea for the numerical modelling is to introduce a fine grid for the resolution of the fluid flow that is embedded into a larger acoustical domain with a coarse grid adapted to the long wavelength acoustics. To get an appropriate restriction of the acoustic source terms from the fine CFD-grid to the coarse CAA-grid, a multi-scale expansion with one time and two space scales is introduced. To cite this article: C.-D. Munz et al., C. R. Mecanique 333 (2005).     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

The characteristics of gas–solid flow and wall heat transfer in a fluidized bed reactor

Numerical study using computational fluid dynamics has been carried out to investigate the heat transfer characteristics of a laboratory fluidized bed reactor. The fluidized bed reactor of vTI (Johann Heinrich von Thünen-Institute)-Institute of Wood Technology and Wood Biology is modeled. For the simulation of multiphase flow and thermal fields, an Eulerian–Eulerian approach is applied. The flow and thermal characteristics of the reactor are fully investigated for the wide range of superficial gas velocities and two different particle diameters. In particular, the contributions of the gas bubble and emulsion phase flows on the wall heat transfer are scrutinized. From the predicted results, it is fully elucidated that particular near-wall bubble motions mainly govern the wall heat transfer.     

Tracking of coherent thermal structures on a heated wall.

The temporal evolution of a thermal pattern observed on a heated wall by infrared camera is correlated with the propagation velocity of the thermal perturbations calculated by DNS. In the experiment the propagation velocity was measured by using PIV-based analysis of infrared images of the thermal pattern on the wall. To verify the experimental technique of image analysis, a sequence of synthetic images, simulating thermal patterns on the wall, was generated from the DNS solution, and the convective velocity was evaluated. It was found that the convective velocity of thermal structures obtained by PIV-based analysis of the experimental and synthetic images was in relatively good agreement with that calculated from the DNS solution. The present study confirmed that for a high Prandtl number fluid (water) the propagation velocity of the thermal perturbations is only about half of the convective velocity of the velocity perturbations. It was also found that the convection velocity observed for hot spots is distinctly lower than that for the cold spots.     

Propagation of a pressure wave in two-phase flow with very high void fraction

An experimental and theoretical study of a finite amplitude pressure wave propagating through a two-phase media of about 0.9999–0.99999 void fraction is performed. This two-phase media consists of many parallel liquid films in a gas. The films are perpendicular to the wave propagation direction and result in a two-phase fluid of extremely high void fraction. Experiments are done in a vertical shock tube and show that the shock wave is broken down into an initial sharply rising wave and a second gradually rising wave. The velocity of the first wave agrees well with the theoretical prediction assuming an adiabatic thermal equilibrium change, which approaches the gas sonic velocity in the two-phase flow in the low void fraction region. The second wave is caused by the complex reflection and destruction of the waves.     

Particle convective heat transfer near the wall in a supercritical water fluidized bed by single particle model coupled with CFD-DEM

Supercritical water fluidized bed (SCWFB) is a promising reactor to gasify biomass or coal. Its optimization design is closely related to wall-to-bed heat transfer, where particle convective heat transfer plays an important role. This paper evaluates the particle convective heat transfer coefficient (h_pc) at the wall in SCWFB using the single particle model. The critical parameters in the single particle model which is difficult to get experimentally are obtained by the computational fluid dynamics-discrete element method (CFD-DEM). The contact statistics related to particle-to-wall heat transfer, such as contact number and contact distance, are also presented. The results show that particle residence time (τ), as the key parameter to evaluate h_pc, is found to decrease with rising velocity, while increase with larger thermal boundary layer thickness. τ follows a gamma function initially adopted in the gas–solid fluidized bed, making it possible to evaluate h_pc in SCWFB by a simplified single particle model. The theoretical predicted h_pc tends to increase with rising thermal gradient thickness at a lower velocity (1.5 U_mf), while first decreases and then increases at higher velocity (1.75 and 2 U_mf). h_pc occupies 30%–57% of the overall wall-to-bed heat transfer coefficient for a particle diameter of 0.25 mm. The results are helpful to predict the overall wall-to-bed heat transfer coefficient in SCWFB combined with a reasonable fluid convective heat transfer model from a theoretical perspective.     

Mixed convective heat transfer characteristics and mechanisms in structured packed beds

The structured packed bed is considered a promising reactor owing to its low pressure drop and good heat transfer performance. In the heat transfer process of thermal storage in packed beds, natural convection plays an important role. To obtain the mixed convective heat transfer characteristics and mechanisms in packed beds, numerical simulations and coupling analyses were carried out in this study on the unsteady process of fluid flow and heat transfer. A three-dimensional model of the flow channel in the packed bed was established, and the Navier–Stokes equations and Laminar model were adopted for the computations. The effects of the driving force on fluid flow around a particle were studied in detail. The differences in velocity and density distributions under different flow directions due to effect of the aiding flow or opposing flow were intuitively demonstrated and quantitatively analyzed. It was found that the driving force strengthens the fluid flow near the particle surface when aiding flow occurs and inhibits the fluid flow when opposing flow occurs. The boundary layer structure was changed by the natural convection, which in turn influences the field synergy angle. For the aiding flow, the coordination between the velocity and density fields is higher than that for the opposing flow. By analysis the effects of physical parameters on mixed convective heat transfer, it is indicated that with an increase in the fluid-solid temperature difference or the particle diameter, or a decrease in the fluid temperature, the strengthening or inhibiting effect of natural convection on the heat transfer became more significant.     

Numerical investigation of unsteady shock waves in vapor-gas-droplet mixtures

The results of mathematical modeling of the evolution of unsteady shock waves in two-phase mixtures of inert gas, vapor and suspended liquid droplets with allowance for dynamic, thermal and mass phase interaction processes are presented. The influence of interphase mass transfer effects (droplet breakdown and evaporation, vapor condensation) on the structure of unsteady shock waves in vapor-gas-droplet mixtures is analyzed. The important influence of phase mass transfer and, in particular, droplet breakdown as a result of surface layer stripping by the gas flow on the distribution of the parameters of the carrier and dispersed components of the mixture behind the shock front is demonstrated. The effect of the principal governing parameters of the two-phase mixture on the unsteady shock wave propagation process is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 67–75, July–August, 1992.     

Wave propagation through mangrove forests in the presence of a viscoelastic bed

The influence of viscoelastic ocean beds on the characteristics of surface waves passing through mangrove forests is analyzed under the assumption of linearized water wave theory in two dimensions. The trunks of the mangroves are assumed to be in the upper-layer inviscid fluid domain, whilst the roots are inside the viscoelastic bed. The associated equation of motion is obtained by coupling the Voigt’s model for flow within the viscoelastic medium with the equation of motion in the presence of mangroves. The modified dynamic conditions are coupled with the kinematic conditions to obtain the boundary condition at the free surface and the interface of the two fluids consisting of the upper layer inviscid fluid and the viscoelastic fluid bed. To understand the effects of bed viscosity as well as elasticity on energy dissipation, the complex dispersion relation associated with the plane progressive wave is derived and analyzed. Effect of physical parameters associated with mangroves and viscoelastic bed on wave motion in surface and internal modes are computed and analyzed to understand their roles in attenuating wave effects. The present model will be useful in the better understanding of wave propagation through mangroves in the coastal zone having muddy seabed.     

竖直平面激波与水平热层作用后流场的理论计算方法研究

围绕竖直平面激波与固壁附近水平热层作用问题，提出了流动进入准自相似阶段后固壁附近流场参量的理论计算方法。与已有的Mirels方法相比，本文的方法在下列三个方面进行了改进:（1）舍弃“热层内激波速度与入射激波速度相等”的假定，分析了热层内激波的传播过程，并基于几何激波动力学理论计算热层内激波强度；（2）假定在与入射激波后流体而非入射激波阵面固连的坐标系中，波后流体在定常等熵波作用下，形成沿固壁运动的“活塞”，驱动其前方的热层气体运动；（3）“活塞”内流体与其毗邻的热层气体满足压力和速度连续，不再引入速度比例系数。利用改进后的方法，对于马赫数为2.00的竖直平面激波，在不同热层密度条件下进行计算。本文方法得到的热层内激波强度以及物质界面处的压力、速度和密度等参量，与数值模拟结果偏差均小于10%，优于Shreffler和Mirels计算方法。对于马赫数为1.36的竖直平面激波，当其传播速度小于热层内气体声速时，Shreffler和Mirels计算方法不再适用，而本文中提出的方法得到的计算结果与数值模拟结果和已有实验数据基本吻合，最大偏差约20%。上述结果表明，本文中提出的理论计算方法提高了现有方法的合理性，扩大了适用范围。     

气液两相流压力波传播速度研究

将双流体模型用于绝热无相的管道气液两相流,依据小扰动线化分析原理,导出了压力波波数Ｋ方程通过对不同空隙率下肉体上压力波小随角频率变化的计算,研究了虚拟质量力和狭义相间阻力对压力波波速及其人色散性的影响。对泡状流和弹状流压力波波速的计算结果与前人的测量结果作了比较,两者符合良好。     

Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid

The problem of the stabilization of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid is solved using both asymptotic and numerical methods. The analytical solution describes the structure of the main convective cells, including thin meridional jets flowing along the surface and plumes spreading from the flow convergence regions above the upper and lower poles of the sphere which gradually return the fluid particles to the neutral buoyancy horizon. The total width of the flows adjacent to the surface exceeds the thickness of the salinity deficit layer or the density boundary layer. The numerical solution of the complete problem in the nonlinear formulation describes the main convective cells and two systems of unsteady integral waves formed in the vicinity of the sphere poles. At large times, out of the entire system of internal waves only those nearest to the neighborhood of their horizon of formation remain clearly defined. The calculated flow patterns are in agreement with each other and the data of shadow visualization of the stratified fluid structure near a submerged obstacle at rest.     

On the propagation waves in the theory of thermoelasticity with microtemperatures

The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasi-thermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.     

Generation of linear and nonlinear waves in numerical wave tank using clustering technique-volume of fluid method

A two-dimensional(2D) numerical model is developed for the wave simulation and propagation in a wave flume.The fluid flow is assumed to be viscous and incompressible,and the Navier-Stokes and continuity equations are used as the governing equations.The standard k-ε model is used to model the turbulent flow.The NavierStokes equations are discretized using the staggered grid finite difference method and solved by the simplified marker and cell(SMAC) method.Waves are generated and propagated using a piston type wave maker.An open boundary condition is used at the end of the numerical flume.Some standard tests,such as the lid-driven cavity,the constant unidirectional velocity field,the shearing flow,and the dam-break on the dry bed,are performed to valid the model.To demonstrate the capability and accuracy of the present method,the results of generated waves are compared with available wave theories.Finally,the clustering technique(CT) is used for the mesh generation,and the best condition is suggested.     

Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition

The steady laminar boundary layer flow over a moving plate in a moving fluid with convective surface boundary condition and in the presence of thermal radiation is investigated in this paper. Under certain conditions, the present problem reduces to the classical Blasius and Sakiadis problems. The effects of radiation and convective parameters on the thermal field are thoroughly examined and discussed. Dual solutions are found to exist when the plate and the fluid move in the opposite directions.     

Impact of thermal radiation on MHD slip flow over a flat plate with variable fluid properties

The influence of partial slip, thermal radiation and temperature dependent fluid properties on the hydro-magnetic fluid flow and heat transfer over a flat plate with convective surface heat flux at the boundary and non-uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature respectively. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into similarity non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The numerical values obtained within the boundary layer for the dimensionless velocity, temperature, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed from the physical point of view.