Numerical study of compressible convective heat transfer with variations in all fluid properties

The effects of property variations in single-phase laminar forced micro-convection with constant wall heat flux boundary condition are investigated in this work. The fully-developed flow through micro-sized circular (axisymmetric) geometry is numerically studied using two-dimensional continuum-based conservation equations. The non-dimensional governing equations show significance of momentum transport in radial direction due to μ(T) variation and energy transport by fluid conduction due to k(T) variation. For the case of heated air, variation in C_p(T) and k(T) causes increase in Nu. This is owing to: (i) reduction in T_w, (T_w ? T_m), and (?T/?r)_w and (ii) change in ?T_m/?z results in axial conduction along the flow. The effects of ρ(p,T) and μ(T) variation on convective-flow are indirect and lead to: (i) induce radial velocity which alters u(r) profile significantly and (ii) change in (?u/?r)_w along the flow. It is proposed that the deviation in convection with C_p(T), k(T) variation is significant through temperature field than ρ(p,T), μ(T) variation on velocity field. It is noted that Nu due to variation in properties differ from invariant properties (Nu = 48/11) for low subsonic flow.     

Geometric optimization of a convective T-shaped cavity on the basis of constructal theory

The aim of this paper is to optimize, by means of Bejan’s theory, the geometry of a T-shaped cavity that intrudes into a solid conducting wall. One direction in which the optimization of intrusion geometry can be pursued is that of increasing the complexity of the growing structures. When the heat generated by the volume is removed through one port, and when the smallest volume element size is fixed, the optimization of geometry generates a tree-shaped flow structure. The simplest tree-shaped structure is a ‘first construct’, or an optimized assembly of elemental volumes. The simplest first construct is the T-shaped tree here treated. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The structure has four degrees of freedom: L₀/L₁ (ratio between the lengths of the stem and bifurcated branches), H₁/L₁ (ratio between the thickness and length of the bifurcated branches), H₀/L₀ (ratio between the thickness and length of the stem) and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (?). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for the following values of the cavity volume fractions (after having fixed H/L = 1): ? = 0.05, 0.1, 0.2 and 0.3. The first optimization, referred to the degree of freedom L₀/L₁, highlighted one “intermediate” optimal shape, i.e., the best geometry was not obtained for the extremes values of L₀/L₁. As for the degree of freedom H₁/L₁, the optimal geometries were obtained for lowest ratio of H₁/L₁. Finally, when compared to the C-shaped cavity, i.e. the basic configuration, the T-shaped cavity performs approximately 45% better under the same thermal and geometric conditions.     

The hydrogen laminar jet

Numerical and asymptotic methods are used to investigate the structure of the hydrogen jet discharging into a quiescent air atmosphere. The analysis accounts in particular for the variation of the density and transport properties with composition. The Reynolds number of the flow R_j, based on the initial jet radius a, the density ρ_j and viscosity μ_j of the jet and the characteristic jet velocity u_j, is assumed to take moderately large values, so that the jet remains slender and stable, and can be correspondingly described by numerical integration of the continuity, momentum and species conservation equations written in the boundary-layer approximation. The solution for the velocity and composition in the jet development region of planar and round jets, corresponding to streamwise distances of order R_ja, is computed numerically, along with the solutions that emerge both in the near field and in the far field. The small value of the hydrogen-to-air molecular weight ratio is used to simplify the solution by considering the asymptotic limit of vanishing jet density. The development provides at leading-order explicit analytical expressions for the far-field velocity and hydrogen mass fraction that describe accurately the hydrogen jet near the axis. The information provided can be useful in particular to characterize hydrogen discharge processes from holes and cracks.     

Effects of agglomerate model parameters on transport characterization and performance of PEM fuel cells

A three-dimensional, non-isothermal and two-phase flow model for proton exchange membrane (PEM) fuel cells is developed. In the cathode catalyst layer, a spherical agglomerate model with consideration of catalyst layer structure and liquid water effect is applied to determine the electrochemical kinetics. The size and structure of the agglomerates are determined by the following parameters, i.e., the agglomerate radius (r_agg), the volume fraction of ionomer within the agglomerate (L_i,agg), and the thickness of the ionomer film over the agglomerate (δ_i). It is noted that a random combination of the three above parameters is widely used in agglomerate models by researchers. In this paper, the effects of r_agg and L_i,agg on the cell performance and local transport characteristics are numerically investigated by using the developed model with consideration of the relationships between agglomerate parameters. It is concluded that the cell performance is significantly improved by decreasing r_agg and increasing L_i,agg at medium and high current densities when the volume fractions of the solid phase (L_Pt/C) and ionomer phase (L_i) are maintained constant. In addition, the distributions of oxygen concentration, liquid water saturation, volumetric current density and effectiveness factor are also strongly influenced by the variation of the two parameters.     

Effects of fresh gas velocity and thermal expansion on the structure of a Bunsen flame tip

Numerical computations and order-of-magnitude estimates are used to describe the tip region of a Bunsen flame where the flame departs from a planar flame at an angle to the incoming fresh gas flow. A single irreversible Arrhenius reaction with high activation energy is assumed. The well-known linear relation between flame velocity and curvature is recovered in the thermodiffusive limit, when the thermal expansion of the gas is left out, for velocities of the fresh gas (U₀) only slightly larger than the velocity of a planar flame (U_L), provided this flame is stable. For large values of the velocity ratio U₀/U_L, the tip region becomes slender and the curvature of the reaction sheet at the tip increases proportionally to U₀/U_L. The thermal expansion of the gas across the flame reduces the aspect ratio of the tip region. A qualitative analysis of the structure of the tip region for very exothermic reactions shows that this region ceases to be slender when the burnt-to-fresh gas temperature ratio becomes of the order of the velocity ratio U₀/U_L. For even larger values of the temperature ratio, the tip region becomes a cap of characteristic size not very different from the thickness of a planar flame.     

Momentum and heat transfer in a turbulent cylinder wake behind a streamwise oscillating cylinder

The work aims to understand the effect of an oscillating circular cylinder on momentum and heat transport in the turbulent wake of a downstream identical cylinder, which is slightly heated. The oscillating amplitude, A, was 0.79d (d is the cylinder diameter) and the frequency was 0.17f_s for L/d = 2.5 and 0.24f_s for L/d = 4, where L and f_s are the cylinder centre-to-centre spacing and the frequency of vortex shedding from the downstream cylinder, respectively, at A = 0. The velocity and temperature fields were measured using a three-wire probe at 10d behind the stationary cylinder and a Reynolds number of 5920 based on d and the free-stream velocity. It is found that the upstream cylinder oscillation modifies the frequency of vortex shedding from the stationary cylinder, which is locked on with one harmonic of the oscillating frequency. This harmonic frequency is nearest to and below the natural vortex-shedding frequency. Furthermore, the wake response to the oscillation depends on L/d in terms of the cross-stream distributions of mean velocity, Reynolds stresses, temperature variance and heat fluxes; the turbulent Prandtl number decreases at L/d = 4 but increases at L/d = 2.5. The observations are linked to whether the flow regime experiences a change under the upstream cylinder oscillation.     

On the transition for a generalized Couette flow of a reactive third-grade fluid with viscous dissipation

We study the thermal transition of a reactive flow of a third-grade fluid with viscous heating and chemical reaction between two horizontal flat plates, where the top is moving with a uniform speed and the bottom plate is fixed in the presence of imposed pressure gradient. This study is a natural continuation of earlier work on rectilinear shear flows. The governing equations are non-dimensionalized and the resulting system of equations are not coupled. An approximate explicit solution is found for the flow velocity using homotopy-perturbation technique and the range of validity is determined. After the velocity is known, the heat transport may be analyzed. It is found that the temperature solution depends on the non-Newtonian material parameter of the fluid, Λ, viscous heating parameter, Γ, and an exponent, m. Attention is focused upon the disappearance of criticality of the solution set {β, δ, θ_max} for various values of Λ, Γ and m, and the numerical computations are presented graphically to show salient features of the solution set.     

An accurate numerical solution study of three-dimensional natural convection in a box

This paper describes the application of the finite difference method to the simulation of three-dimensional natural convection in a box. The velocity–vorticity formulation is employed to represent the mass, momentum, and energy conservations of the fluid medium. We employ a fractional time marching technique for solving seven field variables involving three velocity, three vorticity and one temperature components. By using the fast Fourier transform (FFT) and a tridiagonal matrix algorithm (TDMA), the velocity Poisson equations are advanced in space along with the continuity equation, thus solving efficiently and easily the diagonally dominant tridiagonal matrix equations. Both vorticity and energy equations are discretized through an explicit method (Adams–Bashforth central difference scheme) as a simplified numerical scheme for solving 3D problems, which otherwise requires enormous computational effort. A natural convection in a box for the Rayleigh number equal to 10⁴, 10⁵, 10⁶ and 10⁷ as well as As = L_x / L_z aspect ratios varying from 0.25 to 4 is investigated. It is shown that the benchmark results for temperature and flow fields could be obtained using the present algorithm.     

h -ADAPTIVITY AND "HONEST" GFEM FOR ADVECTION-DOMINATED TRANSPORT

A standard two-dimensional Galerkin finite-element method (GFEM) code for coupled Navier-Stokes and energy equations is used with h -adaptive meshing based on a posteriori error estimation using the superconvergent patch recovery technique for solving a range of advection-dominated transport problems. It is demonstrated that such a method provides a highly effective, simple, and efficient way of dealing with the perennial problems in numerical modeling of advection-dominated transport, such as oscillations or wiggles with central difference-type discretizations (such as GFEM) and numerical ("false") diffusion when wiggle-suppressant schemes are used. Additionally, the auto-adaptive finite-element method provides a powerful means of achieving optimal solutions without having to predefine a mesh, which may be either inadequate or too expensive. A number of benchmark problems are presented as application examples for this method before solving a problem of natural convection in an air-filled cavity with various orientations, for which experimental results are available.     

Optimal monolithic configuration for heat integrated ethanol steam reformer

A design concept for optimal design of monolith catalyst is presented through modeling of transport–kinetic interactions in a monolith catalyst. We argue that reactors employing monolithic catalysts should be based on its optimal choice of geometry. In line with that argument, we present a thorough analysis of the geometrical parameters influencing the performance of non-isothermal reactor operation. In this study, an optimal monolith configuration is estimated to be a combination (d_h, t_w) of (0.9 mm, 0.2 mm) for a compact ethanol reformer to produce hydrogen for portable applications where maximum volumetric reactor activity exists. A three-dimensional modeling framework is developed for the resulting optimal monolithic catalyst design that couples the reforming section with a suitable heat source in a recuperative way. As a result, greater ethanol conversion is obtained from the monolith channels near the periphery of the block. The coupling with combustion could predict the formation of cold and hot spots inside the reactor, their nature being dependent on the flow configuration. Further, the effect of altering the feed inlet operating conditions over the variation of ethanol conversion and temperature inside the reactor is also analyzed. The increase in reforming inlet velocity decreases the outlet conversion and shifts the cold spot, forward and deeper in co-flow configuration. The decreasing inlet feed temperature enhances the transfer of heat, eliminating the cold spot.     

Effect of ignition position and inert gas on hydrogen/air explosions

The effects of inert gas (i.e., He, Ar, and N₂) and ignition position on flame dynamics in a half-open duct with an aspect-ratio of 10 are analyzed for hydrogen/air mixtures with constant laminar burning velocity S_L. The results indicate that hydrodynamic and thermo-diffusive instabilities dominate flame propagations with ignition at the right-half part of the duct, while Rayleigh–Taylor instability dominates with ignition at the left-half part of the duct. The flame-sound interaction results in the periodic pressure oscillations. Due to decreased instability, the He-diluted flame exhibits a weaker sensitivity of explosion parameters to the ignition position. The maximum pressure P_max is dominated by different mechanisms depending on the ignition position. Although constant S_L is used, P_max for the worst case with N₂ dilution is two times that with He dilution, demonstrating the considerable effect of flame instabilities. Finally, a chemical kinetic calculation is performed to clarify the flame stabilities.     

Aromatic amines as proton carriers for catalytic enhancement of hydrogen evolution reaction on copper in acid solutions

The catalytic effect of some aromatic amines towards hydrogen evolution reaction on copper in diluted sulfuric acid solution has been studied. Since amines facilitate the transport of protons from the solution bulk to the interface in the cathodic hydrogen evolution reaction, they are known as proton carriers. The catalytic effect of aniline, N-methylaniline, N-ethylaniline, N,N-dimethylaniline, N,N-diethylaniline, o-toluidine, m-toluidine and p-toluidine has been highlighted by linear sweep voltammetry. The kinetic parameters for the hydrogen evolution reaction (cathodic transfer coefficient 1-α and exchange current density i_o) in the presence of the studied aromatic amines were derived from the Tafel plots. It has been found that the catalytic effect of amines is active even at low concentration. Thus, in 0.5 mol L⁻¹ H₂SO₄ solution the exchange current density increases by two orders of magnitude, from 2.01⋅10⁻⁵ A m⁻² in the absence of aniline to 2.85⋅10⁻³ A m⁻² in the presence of 10⁻⁴ mol L⁻¹ aniline. The influence of amines concentration on the catalytic effect is described in detail for the case of m-toluidine. The results obtained by voltammetry have been compared with electrochemical impedance spectroscopy data. Furthermore, the kinetic parameters for the hydrogen evolution reaction have been determined as a function of temperature and amines concentration.     

The structure and flame propagation regimes in turbulent hydrogen jets

Experiments on flame propagation regimes in a turbulent hydrogen jet with velocity and hydrogen concentration gradients have been performed. Horizontal stationary hydrogen jets released at normal and cryogenic temperatures of 290, 80 and 35 K with different nozzle diameters and mass flow rates have been investigated. Sampling probe method and laser PIV techniques have been used to evaluate the distribution of hydrogen concentration and flow velocity. High-speed photography combined with a Background Oriented Schlieren (BOS) system was used for the visual observation of the turbulent flame propagation. In order to investigate different flame propagation regimes the ignition position was changed along the jet axis. It was found that the flame propagates in both directions, up- and downstream of the jet flow if hydrogen concentration is >11%, whereas in case [H₂] < 11%, the flame propagates only downstream. This means that at normal temperature the flame is able to accelerate effectively only if the expansion ratio σ of the H₂-air mixture is higher than a critical value σ* = 3.75 defined for a closed geometry.     

Magnetic field effects on g-jitter induced flow and solute transport

Numerical modeling and analyses are presented of magnetic damping of g-jitter driven fluid flow and its effect on the solutal striation in a simplified Bridgman-Stockbarger crystal growth system under microgravity. The model development is based on the finite element solution of the momentum, energy and solute transport equations under g-jitter conditions in the presence of an external magnetic field. The numerical model is verified by comparison with analytical solutions obtained for a simple parallel plate channel flow driven by g-jitter in a transverse magnetic field. Simulations are carried out to study the behavior of convective flow and solutal transport induced by the combined g-jitter and magnetohydrodynamic forces. Both the idealized single frequency g-jitter force and the real g-jitter perturbation taken during space flight are considered. Results indicate that an applied magnetic field can effectively damp the velocity caused by g-jitter and help to reduce the time variation of solute redistribution. A stronger applied field is more effective in suppressing the convective flows and hence reducing concentration variation. It is found that g-jitter driven flows have the same oscillation period as the driving force with or without the applied field. However, an applied magnetic field shortens the transient period over which the flow field evolves into a quasi-steady state time harmonic oscillation after g-jitter sets in. The flow intensity increases with an increase in g-jitter magnitude but decreases with an increase in the applied field strength. The reduced convection in the liquid pool by the applied magnetic field results in a reduction of the concentration oscillation. The magnetic field is very useful in suppressing the spiking velocities that are induced by the spikes in the real g-jitter data. The damping effect is more pronounced if the magnetic field is switched on before the onset of g-jitter disturbances.     

Transient phenomenological modeling of photoelectrochemical cells for water splitting - Application to undoped hematite electrodes

A phenomenological model is proposed for a better understanding of the basic mechanisms of photoelectrochemical (PEC) cells. The main assumptions of the one-dimensional transient phenomenological model are: i) bulk recombination of the conduction band electrons with holes in the valence band; ii) the mobile charge transport takes place via diffusion, which arises from the concentration profiles, and migration, caused by a macroscopic electric field; iii) negligible effects of microscopic electric fields in the cell and screening effects, as well as negligible Helmholtz and diffuse layers. For modeling purposes, the photoanode was assumed to be a homogeneous nanocrystalline hematite structure, with thickness L, porosity ?_p and tortuosity τ. The TCO/semiconductor interface was modeled as an ideal ohmic contact, while the electrolyte/platinized TCO interface was described by a Butler-Volmer approach. An alkaline electrolyte solution was used, allowing the transport of the ionic species from the counter-electrode to the photoanode. The continuity and transport governing equations are defined for the mobile species involved: electrons in the conduction band of the semiconductor, holes in the valence band and hydroxyl ions in the electrolyte. Simulated I-V characteristics were computed and the corresponding results compared with the experimental values. The simulated results were in straight agreement with the experimental data.     

Effect of rotating cylinder on heat transfer in a square enclosure filled with nanofluids

Convective heat transfer in a differentially heated square enclosure with an inner rotating cylinder is studied theoretically. The free space between the cylinder and the enclosure walls is filled with water–Ag, water–Cu, water–Al₂O₃ or water–TiO₂ nanofluids. The governing equations are formulated for velocity, pressure and temperature formulation and are modeled in COMSOL, a partial differential equation (PDE) solver based on the Galerkin finite element method (GFEM). The governing parameters considered are the solid volume fraction, 0.0 ? ? ? 0.05, the cylinder radius, 0 ? R ? 0.3 and the angular rotational velocity, ?1000 ? Ω ? 1000. The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the strength of the flow circulation is much stronger for a higher nanoparticle concentration, a better thermal conductivity value and a smaller cylinder with a faster, negative rotation. The maximum heat transfer are obtained at a high nanoparticle concentration with a good conductivity value, a slow positive rotation and a moderate cylinder size located in the center of the enclosure.     

Fracture initiation at the root of a blunt flaw: description in terms of Kr–Lr failure assessment curves

In assessing the effect of a defect on the integrity of an engineering structure, considerable use is now being made of failure assessment diagrams. Recent work, focused on the effects of a sharp crack, has highlighted the geometry dependence of the failure assessment curve when it is expressed in terms of normalised stress intensity (K_r) and normalised limit load (L_r) parameters. This article extends the earlier work, in that it quantifies the geometry dependence of the failure assessment curve for the case of a blunt flaw, with K_r now being defined in terms of an effective K parameter, as if the flaw were a sharp crack.     

A stochastic geometry based model for total triple phase boundary length in composite cathodes for solid oxide fuel cells

An analytical equation is derived for total triple phase boundary length per unit volume (L_TPB) in an isotropic uniform random microstructure of LSM/YSZ composite cathode. The equation is applicable to YSZ and LSM particles of any convex shapes and size distributions. The equation explicitly relates L_TPB to the shapes, mean sizes, coefficient of variation (a measure of the spread in a size distribution) and skewness of YSZ and LSM particle populations, and volume fractions of YSZ, LSM, and porosity. The equation is verified using available experimental data, and compared with the results of earlier simulations and models. The parametric analysis reveals that (1) non-equiaxed plate-like, flake-like, and needle-like YSZ and LSM particle shapes can yield substantially higher L_TPB; (2) mono-sized YSZ and LSM powders lead to higher L_TPB as compared to the powders having size distributions with large coefficient of variation; (3) L_TPB is inversely proportional to the mean sizes of YSZ and LSM particles; (4) high value of L_TPB is obtained at the lowest porosity volume fraction that permits sufficient connectivity of the pores for gas permeability; and (5) L_TPB is not sensitive to the relative proportion of YSZ and LSM phases in the regime of interest in composite cathode applications.     

Experimental parametric equation for the prediction of valve coefficient (Cv) for choke valve trims

The calculation of nominal choke valve size determines the effective capacity for an oil and gas production system. The degree of restriction for the controlling area in the valve is a function of the surrounding geometry. In an orifice plate this is known as the “velocity of approach” and can be used to determine the meter coefficient (C_m). This paper presents a technique for choke valves, based on the meter velocity of approach parameter, which can be used to predict the Valve Coefficient (C_v) for new trim designs. The prediction method uses a data trend based on a number of flow tests conducted on various trim characteristics. The resultant parametric equation is used to predict the C_v of a new trim geometry. The method relies on experimental data determined per IEC 60534-2-3, with calculations per IEC 60534-2-1. This paper further investigates the effect of varying upstream geometry on C_v for a 4″ nominal valve.     

Bio-hydrogen production from acid hydrolyzed waste ground wheat by dark fermentation

Waste ground wheat was subjected to acid hydrolysis (pH = 3.0) at 90 °C for 15 min using an autoclave. The sugar solution obtained from acid hydrolysis was subjected to dark fermentation for hydrogen gas production after neutralization. In the first set of experiments, initial total sugar concentration was varied between 3.9 and 27.5 g L⁻¹ at constant biomass (cell) concentration of 1.3 g L⁻¹. Biomass concentration was varied between 0.28 g L⁻¹ and 1.38 g L⁻¹ at initial total sugar concentration of 7.2 ± 0.2 g L⁻¹ in the second set of experiments. The highest hydrogen yield (1.46 mol H₂ mol⁻¹ glucose) and the specific formation rate (83.6 ml H₂ g⁻¹ cell h⁻¹) were obtained with 10 g L⁻¹ initial total sugar concentration. Biomass (cell) concentration affected the specific hydrogen production rate yielding the highest rate (1221 ml H₂ g⁻¹ cell h⁻¹) and the yield at the lowest (0.28 g L⁻¹) initial biomass concentration. The most suitable X_o/S_o ratio, maximizing the yield and specific rate of hydrogen gas formation was X_o/S_o = 0.037. Dark fermentation of acid hydrolyzed ground wheat was found to be more beneficial as compared to simultaneous bacterial hydrolysis and fermentation.