The combustion of large particles of char in bubbling fluidized beds: The dependence of Sherwood number and the rate of burning on particle diameter

Particles of char derived from a variety of fuels (e.g., biomass, sewage sludge, coal, or graphite), with diameters in excess of , burn in fluidized bed combustors containing smaller particles of, e.g., sand, such that the rate is controlled by the diffusion both of O₂ to the burning solid and of the products CO and CO₂ away from it into the particulate phase. It is therefore important to characterize these mass transfer processes accurately. Measurements of the burning rate of char particles made from sewage sludge suggest that the Sherwood number, Sh, increases linearly with the diameter of the fuel particle, dchar (for ). This linear dependence of Sh on dchar is expected from the basic equation Sh=2εmf(1+dchar/2δdiff)/τ, provided the thickness of the boundary layer for mass transfer, δdiff, is constant in the region of interest (). Such a dependence is not seen in the empirical equations currently used and based on the Frössling expression. It is found here that for chars made from sewage sludge (for ), the thickness of the boundary layer for mass transfer in a fluidized bed, δdiff, is less than that predicted by empirical correlations based on the Frössling expression. In fact, δdiff is not more than the diameter of the fluidized sand particles. Finally, the experiments in this study indicate that models based on surface renewal theory should be rejected for a fluidized bed, because they give unrealistically short contact times for packets of fluidized particles at the surface of a burning sphere. The result is the new correlation

     

Subcooled flow boiling heat transfer in narrow passages

Subcooled flow boiling heat transfer coefficients for refrigerants R11 and HCFC123 in smooth copper tubes of small diameter have been investigated experimentally. The parameter ranges examined are: tube diameters of 0.92 and 1.95 mm; heat fluxes 11-170 kW m⁻²; mass fluxes 110-1840 kg m⁻² s⁻¹. The range of liquid Reynolds numbers encompassed by the data set is 450 to 12,000.The data in the subcooled and saturated regions are well represented by the simple addition of convective and nucleate boiling heat transfer contributions

     

Downward flame spread over a thick PMMA slab in an opposed flow environment: experiment and modeling

This work investigates experimentally and theoretically the downward spread of a flame over a thick polymethylmethacrylate (PMMA) slab with an opposed flow of air. Simulation results, using an unsteady combustion model with mixed convection, indicate that the ignition delay time increases with a decreasing opposed-flow temperature or increasing velocity. The ignition delay time is nearly constant at a low opposed flow velocity, i.e., . Experiments were conducted at three different opposed flow temperatures and velocities, namely, , and 353 K and , respectively. Measurements included the flame-spread rate and temperature distributions, using thermocouples and laser-holographic interferometry. The qualitative trends of the flame-spread rate and thermal boundary layer thickness, as obtained experimentally and from numerical predictions, were identical. For a quantitative comparison, the predicted and experimental flame-spread rates correlated well with each other, except at the lowest velocity . The discrepancies between the measured and predicted thermal boundary layer thicknesses decreased with an increasing flow velocity. The quantitative agreement with a high velocity indicates that the spread of an opposed flame is mainly controlled by the flame front, whereas the discrepancies at low flow rates demonstrate the importance of radiation, the finite length of the fuel, and also three-dimensional effects, which were not considered in the model. The temperature profiles around the flame front measured by interferometric photographs indicate a recirculation flow there, as predicted by the simulation.     

An experimental investigation of critical flow rates of subcooled water through short pipes with small diameters

Critical two-phase flow rates of subcooled water through short pipes (L < 400 mm) with small diameters (D < 7.15 mm) have been experimentally investigated for wide ranges of subcooling (0 ∼ 199 °C) and pressure (0.5 ∼ 2.0 MPa). To examine the effects of various parameters (i.e., the location of flashing inception, the degree of subcooling, the stagnation temperature and pressure, and the pipe size) on the critical two-phase flow rates of subcooled water through short pipes with small diameters, a total of 135 runs were made for various combinations of test parameters using four different test sections. Experimental results that show effects of various parameters on subcooled critical two-phase flow rates are presented in the form of graphs such as the dimensionless mass flux () versus the dimensionless subcooling () curve. An empirical correlation expressed in terms of a dimensionless subcooling () is also obtained for subcooled two-phase flow rates through present test sections. Comparisons between the mass fluxes calculated by present correlation and a total of 679 selected experimental data points of 9 different investigators show that the agreement is fairly good except for very low subcooling data obtained from small (less than 10) orifices.     

Numerical prediction on the erosion in the hearth of a blast furnace during tapping process

The erosion caused by mass transfer in hearth is the most important factor for determining blast furnace campaign life. To support a helpful insight information of mass transfer for the hearth of the No. 2 blast furnace at CSC (China Steel Corporation), a numerical model including the mass transfer of carbon in thermal convective flow from a blast furnace hearth has been developed during the steady tapping process (based on a uninterrupted tapping process assumption). The three dimensional Navier–Stokes equation combined with the transport equations of energy and species with conjugate heat transfer and physical dissolution source is solved by the finite control volume scheme subjected to the segregated iterate under propriety boundary conditions. The results showed the concentration distribution of carbon expressed in terms of mass flux for analyzing the erosion of carbon brick in the blast furnace hearth with the different conditions including the status of dead-man, production of liquid iron, carbon concentration at the inlet, and porosity distribution in coke zone during tapping process at steady state. The result is useful to mitigate the erosion caused by mass transfer, and prolong the life span of the blast furnace.     

Entropy generation on MHD flow of a Casson fluid over a curved stretching surface with exponential space-dependent heat source and nonlinear thermal radiation

The present model concentrates on entropy generation on a steady incompressible flow of a Casson liquid past a permeable stretching curve surface through chemical reaction and magnetic field effects. The exponential space-dependent heat source cum heat and mass convective boundary conditions are accounted for. The resulting nonlinear boundary layer model is simplified by the transformation of similarity. Chebyshev spectral technique is involved for obtaining numerical results of the converted system of the mathematical models. Behavior of the determining thermo-physical parameters on the profiles of velocity, temperature, concentration, skin friction, heat, mass transfer rate, rate of entropy generation, and finally the Bejan number are presented. The major point of the present investigation show that the curvature term weakens the mass transfer profile as the fluid temperature reduces all over the diffusion regime. A decrease in heat generation strengthens the species molecular bond, which prevents free Casson particle diffusion. Furthermore, the mass transfer field diminishes in suction and injection flow medium.     

On modelling the multidimensional coupled fluid flow and heat or mass transport in porous media

We consider the solution of coupled fluid flow and heat or mass transport in porous media. The aim of this work is to appraise mathematical assumptions used to decrease the CPU cost of the solution of these strongly non-linear coupled equations. This purpose is reached with a reduced model for which the term in the mass balance equation is neglected. Indeed, we show that this assumption allows an important reduction of computer time compared to the standard model. Moreover, contrarily to the Boussinesq approximation, no significant differences are found between the reduced and the standard model.Model validation is carried out with a numerical code based on mixed and discontinuous finite elements. First, the Elder and the modified Evans and Raffensperger problems are simulated to test the different assumptions. Second, a simulation of two kinds of laboratory experiment is run without any calibration. For both computations, very similar results are obtained between the complete and the reduced fluid mass balance equations. Both models give numerical results in good agreement with the laboratory layered porous medium experiments. However, these models give less satisfactory results for the salt-pool problem.     

Natural convective heat transfer from isothermal cuboids

The paper presents results of theoretical and experimental investigations of the convective heat transfer from isothermal cuboid. The analytical solution was performed taking into account complete boundary layer length and the manner of its propagation around isothermal cuboid. It arises at horizontal bottom surface and grows on vertical lateral surface of the block. After changing its direction, the boundary layer occurs above horizontal surface faced up and next it is transformed into buoyant convective plume. To verify obtained theoretical solution the experimental study has been performed. The experiment was carried out for three possible positions of the same tested cuboid.As the characteristic linear dimension in Nusselt-Rayleigh theoretical and experimental correlations we proposed the ratio of six volumes to the cuboids surface area, for the analogy to the same ratio using as the characteristic dimension for the sphere, which is equal to the sphere’s diameter. It allowed performing the experimental results independently from the orientation of the block. The Rayleigh numbers based on this characteristic length ranged from 10⁵ to 10⁷. The Nusselt number describing intensity of convective heat transfer from the cuboid can be expressed by: Nu=XRa^1/5+YRa^1/4, where X and Y are coefficients dependent on the cuboid’s dimensions. For the range of provided experiment the experimental Nusselt-Rayleigh relation can be presented in the form: