Determination of the constants of electrochemical reactions and the ion mobility coefficients in weakly conducting liquids from an analysis of the current—voltage characteristics

The problem is considered of the passage of a direct current through a solution of a weak electrolyte in a two-dimensional cell. Allowance is made for the electrochemical reactions of dissociation and reconbination which take place in the electrolyte when the rate of dissociation of the molecules is regarded as dependent on the electric field intensity [1–3]. For electrolytes whose recombination coefficient is of the order of magnitude of the Langevin coefficient, theoretical current—voltage characteristics are given for the limiting cases of large and small values of the characteristic times for the ion concentrations to be changed by electrochemical reactions and the transport of ions by the electric field. A method of determining the dissociation rate, the recombination coefficient, and the ion mobility coefficients is proposed on the basis of comparison of the theoretical and experimental current—voltage characteristics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 113–120, November–December, 1984.     

Ionization and Recombination Kinetics in a Plasma Accelerator Channel

A number of theoretical approaches to the investigation of ionizing gas flows are analyzed and compared with reference to a plasma accelerator channel. The transition from a weakly ionized gas to a plasma is considered within the framework of the complete system of equations. The ionizing gas flow model is based on the magnetogasdynamic equations of a continuum and the equation of ionization and recombination kinetics. The corresponding coefficients are determined both within the framework of the standard theory and within a modified diffusion approximation, including possible variations. In addition, for comparison purposes some results of numerical experiments on the ionization process under conditions of local thermodynamic equilibrium are given.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

Simulation of the Action of a Permeable Barrier on an Ideal Incompressible Channel Flow

Plane ideal incompressible flow in a rectangular channel partitioned by a thin permeable barrier (lattice) is considered. In flowing through the lattice the stream suddenly (jumpwise) changes direction and loses energy. The flow is assumed to be vortical; the vorticity is discontinuous on the lattice. A mathematical formulation of the problem for the stream function is proposed in the form of a nonlinear elliptic equation with coefficients discontinuous on the lattice line. A numerical solution is constructed using the finite-element iteration method. The results of the numerical simulation show how the flow velocity profile in the channel can be controlled by means of permeable barriers.     

Fluid flow and heat transfer in a two-dimensional wavy channel

A numerical study is presented for the laminar fully developed flow and heat transfer in a two-dimensional wavy channel. The effects of the geometry, Reynolds and Prandtl number on the flow field and heat transfer are investigated. The channel is characterized by a wavy wall, heated at uniform heat flux, and an opposite wall, being plane and adiabatic. The extent of the wall waviness and the distance between the channel walls are found to significantly affect the streamlines contours as well as the heat transfer coefficients. Comparisons with the straight channel, in the same flow rate and heat transfer conditions, have been performed. Pressure drop of the wavy channel is found to be always larger than the value characteristic of a straight channel, while heat transfer performance decreases or increases depending on the values of the parameters (geometry, Reynolds and Prandtl numbers).     

One-dimensional flows of a nonequilibrium plasma with variable degree of ionization in the absence of currents

The one-dimensional flows of an inviscid plasma not in thermal equilibrium and with a variable degree of ionization are investigated in the absence of currents. A criterion showing when the ordinary equations of gasdynamics may be used to describe these flows is given. An expression is found for the velocity of sound in such a plasma. Under certain conditions it passes into Newton's formula for isothermal sound. The condition fulfilled in the critical cross section of the channel is found. It is established that the flow of a weakly ionized plasma occurs at constant electron temperature. A detailed investigation is made of the possible types of flow in a cylindrical channel.A criterion is given which shows when the model of a plasma in thermal equilibrium may be applied, and also relationships which permit complete calculation of the flow of such a plasma in a channel of variable cross section.Generally speaking, the flow of a plasma with no currents present differs from the flow of a nonionized gas. This difference is related to the processes of ionization and recombination taking place in the plasma. The electrons usually play the main part in these processes, and so the average energies (temperatures) of electrons and heavy particles (atoms and ions) may differ. If the inelastic collision frequency in the plasma is small compared with the elastic collision frequency, then the temperature difference between the electron component and the heavy component of the plasma may be considerable. The simplest cases of one-dimensional plasma flows are considered with account for ionization and recombination processes and in the absence of thermal equilibrium among the components.The author is grateful to M. N, Kogan for discussing the paper.     

Heat transfer and flow temperature measurements in a rotating triangular channel with various rib arrangements

In the present study, the regionally-averaged heat transfer coefficients and flow temperature distributions were measured in an equilateral triangular channel with three different rib arrangements (α = 45, 90 and 135°). To measure regionally-averaged heat transfer coefficients in the channel, two rows of copper blocks and a single heater were installed on two ribbed walls. The fluid temperature distributions were obtained using a thermocouple-array. The rotation number ranged from 0.0 to 0.1 with a fixed Reynolds number of 10,000. For the 90° ribs, the heat transfer coefficients on the pressure side surface were increased significantly with rotation, while the suction side surface had lower heat transfer coefficients than the stationary channel. For the angled ribs, rib-induced secondary flow dominated the heat transfer characteristics and high heat transfer rates were observed on the regions near the inner wall for the 45° angled ribs and near the leading edge for the 135° angled ribs.     

Flow of a dual-temperature plasma in the channel of a disk-magnetohydrodynamic generator,taking account of nonequilibrium ionization and recombination reactions

The establishment of a supersonic one-dimensional flow of a dual-temperature, partially ionized plasma is investigated in the channel of a disk-MHD generator, taking account of nonequilibrium ionization and recombination reactions. A detailed formulation of the problem is given in [1]; flows are considered in the absence of ionization and recombination reactions and in the case of equilibrium reactions.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–142, November–December, 1972.     

The analysis of the channel flow sensitivity to the parameters of the k–ε method

This paper deals with the problem of using sensitivity analysis for fluid mechanics solutions to the constants of the standard k–ε method for 2D, incompressible and steady flows. The problem is described and analysed on the basis of a channel flow. Sensitivity coefficients of the following properties were determined: a pressure, two components of a velocity, a turbulence kinetic energy, a dissipation rate of turbulence kinetic energy and a turbulence dynamic viscosity. The calculated property values depend on five model constants that are parameters of the sensitivity analysis in this paper. Sensitivity coefficients are derivatives of the above properties, for individual parameters. In this paper these coefficients are determined using a finite difference approximation to the sensitivities coefficients. The author of this paper compares three models of the boundary layer with regard to the sensitivity of properties to the parameters. Irrespective of the boundary layer model used here, the analysis of sensitivity coefficients for the channel flow properties shows that the most sensitive property is the turbulence dissipation rate. Next properties of consequence, although of significantly smaller values of sensitivity coefficients, are the turbulence viscosity and the turbulence kinetic energy. All flow properties are mostly sensitive to the C_µ parameter. One of the final conclusions in this paper is that the analysis of sensitivity coefficient fields allows the reliable checking of results and indicates those areas most prone to calculation difficulties. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow of Particulate-Fluid Suspension in a Channel with Porous Walls

The problem of the dispersed particulate-fluid two-phase flow in a channel with permeable walls under the effect of the Beavers and Joseph slip boundary condition is concerned in this paper. The analytical solution has been derived for the longitude pressure difference, stream functions, and the velocity distribution with the perturbation method based on a small width to length ratio of the channel. The graphical results for pressure, velocity, and stream function are presented and the effects of geometrical coefficients, the slip parameter and the volume fraction density on the pressure variation, the streamline structure and the velocity distribution are evaluated numerically and discussed. It is shown that the sinusoidal channel, accompanied by a higher friction factor, has higher pressure drop than that of the parallel-plate channel under fully developed flow conditions due to the wall-induced curvature effect. The increment of the channel’s width to the length ratio will remarkably increase the flow rate because of the enlargement of the flow area in the channel. At low Reynolds number ranging from 0 to 65, the fluids move forward smoothly following the shape of the channel. Moreover, the slip boundary condition will notably increase the fluid velocity and the decrease of the slip parameter leads to the increment of the velocity magnitude across the channel. The fluid-phase axial velocity decreases with the increment of the volume fraction density.     

Two-dimensional wall temperature measurements and heat transfer enhancement for top-heated horizontal channels with flow boiling

Two-dimensional (circumferential and axial) wall temperature distributions were measured for top-heated coolant channels with internal geometries that include smooth walls, spiral fins and both twisted tape and spiral fins. Freon-71 was the working fluid. The flow regimes studied were single-phase, subcooled flow boiling, and stratified flow boiling. The inside diameter of all test sections was near 10.0 mm. Circumferentially averaged heat transfer coefficients at several axial locations were obtained for selected coolant channels for a volumetric flow rate of 4.738 x 10⁻⁵m³/s, 0.19 MPa (absolute) exit pressure, and 22.2°C inlet subcooling. Overall (averaged over the entire channel) heat transfer coefficients were compared for the various channel geometries. This comparison showed that the channel with large-pitch spiral fins had higher heat transfer coefficients at all power levels. However, the results appear to indicate that if the twist ratio (ratio of the twisted tape period to the inside diameter) is decreased, the configuration employing both fins and a twisted tape will have had greater enhancements.     

Enhancement of heat transfer due to bubbles passing through a narrow vertical rectangular channel (Change in heat transfer along flow)

The objective of this paper is to make clear how heat transfer coefficient changes along the flow with the passing bubbles through a narrow vertical rectangular channel (20 mm wide, 2 mm deep and 450 mm long). The experiments were done using subcooled water of 80, 60, and 40 K at atmospheric pressure in which the air bubbles were injected into the channel at a designated period from 0.125 to 1.0 s and their length was controlled to be equal to 0.03, 0.02, and 0.01 m. The experiment shows that the heat transfer coefficients decrease along the flow and then reach a constant value beyond a certain distance from the leading edge of the heated surface where the flow becomes fully developed in both the velocity and the thermal conditions. Under the fully developed conditions, the heat transfer coefficients are predicted well by the existing theoretical analysis in which both the convective term and evaporation on the interface are ignored.     

Two dimensional analytical solution for a partially vegetated compound channel flow

The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region＇s differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.     

Analysis of two-phase flow magnetohydrodynamic generator performance in terms of flow and electrical conductivity distribution parameters

A general method is presented for analyzing two-phase flow in magnetohydrodynamic generators. The method utilizes the time and flow-area-averaged kinematic, dynamic and electromagnetic quantities, and develops prediction capabilities of the generator performance parameters in terms of two fundamental physical parameters. These parameters are the flow and the electrical conductivity-flow distribution coefficients. The flow coefficient takes into consideration flow and relative velocity distribution, and the electrical conductivity-flow coefficient expresses the distribution of electrical conductivity with flow at any cross-sectional area of the generator duct.

The flow and electrical conductivity-fiow distribution coefficients depend primarily on the two-phase flow regime and on the ratio of volumetric flow rates of the two phases in the duct. This conclusion has been established by examining the experimental data. Examination of the experimental data has also revealed the values of these coefficients for bubbly and churn-turbulent flow regimes for the wide range of ratios of volumetric flow rates. The analysis develops expressions for two-phase MHD generator load factor, electromagnetic pressure distribution across and along the generator channel, the distribution of the electromagnetic fields and interaction parameter.     

高温非平衡流动中的氧分子振动态精细分析

高超声速流动在头激波压缩后常处于高 温条件下的热化学非平衡状态. 本文采用态-态方法和双温度模型计算分析了一维正激波后和高超声速钝体绕流驻点线上的氧气热化学非平衡流动. 态-态方法将氧气的每个振动能级当成独立的组分,通过耦合 Euler 方程或驻点线上的降维 Navier-Stokes 方程,数值求解得 到了高温流动中的精细热化学非平衡状态. 而双温度模型假设氧气的振动能级服从 Boltzmann 分布,通过求解振动能方程得到振动温度. 一维正激波后热化学松弛过程的计算结果表明,态-态计算预测的温度分布和氧原子浓度分布较好地吻合了文 献中的实验结果,而经典的双温度模型的预测结果误差较大,且不同双温度模型的计算结果比较发散. 态-态方法详细地给出了所有振动能级的变化过程. 无论是正激波还是脱体激波后的流场,都是高振动能级首先得到激发;但是数密度大的低振动能级先达到热平衡,而高能级 分子要经过很长距离后才能达到热平衡. 在驻点附近,复合反应生成的氧气分子处于高振动能级,导致高振动能级分子数密度显著高于平衡分布. 计算还发现,经典双温度模型的离解反应速率明显偏离态-态计算结果,无法准确体现振动离解耦合效应对离解反应 速率的影响,但是 Park 双温度模型将离解失去的振动能取为 0.3$\sim 高超声速流动在头激波压缩后常处于高 温条件下的热化学非平衡状态. 本文采用态-态方法和双温度模型计算分析了一维正激波后和高超声速钝体绕流驻点线上的氧气热化学非平衡流动. 态-态方法将氧气的每个振动能级当成独立的组分,通过耦合 Euler 方程或驻点线上的降维 Navier-Stokes 方程,数值求解得 到了高温流动中的精细热化学非平衡状态. 而双温度模型假设氧气的振动能级服从 Boltzmann 分布,通过求解振动能方程得到振动温度. 一维正激波后热化学松弛过程的计算结果表明,态-态计算预测的温度分布和氧原子浓度分布较好地吻合了文 献中的实验结果,而经典的双温度模型的预测结果误差较大,且不同双温度模型的计算结果比较发散. 态-态方法详细地给出了所有振动能级的变化过程. 无论是正激波还是脱体激波后的流场,都是高振动能级首先得到激发;但是数密度大的低振动能级先达到热平衡,而高能级 分子要经过很长距离后才能达到热平衡. 在驻点附近,复合反应生成的氧气分子处于高振动能级,导致高振动能级分子数密度显著高于平衡分布. 计算还发现,经典双温度模型的离解反应速率明显偏离态-态计算结果,无法准确体现振动离解耦合效应对离解反应 速率的影响,但是 Park 双温度模型将离解失去的振动能取为 0.3$\sim $0.5 倍分子离解能是比较合理的.     

Surface effects in rarefied gas dynamics: an analysis based on the Cercignani–Lampis boundary condition

The flow of a rarefied gas, in a plane channel, is investigated, with special attention to the gas–surface interaction, modeled by the Cercignani–Lampis kernel that is defined in terms of normal and tangential accommodation coefficients. An analytical version of the discrete-ordinates method is used to solve, in an unified approach, the Poiseuille flow, thermal-creep flow and Couette flow problems with kinetic equations defined in terms of the BGK model. Numerical results for the velocity and heat-flow profiles and flow rates are reported, for a wide range of the accommodation coefficients and the Knudsen number.     

Modeling of the transient processes in the channels of an EHD pump

The nonstationary process of development of weakly conducting electrohydrodynamic flow in the channel of an EHD pump with plane permeable electrodes, between which a potential difference is created from an external source, is considered in the hydraulic approximation within the framework of the model proposed in [1, 2]. It is shown that the efficiency of the EHD device can be improved if in the fluid the spatial process of ion formation is retarded, while the recombination process is intense. The effect of the flow velocity on the formation of a space charge region in the interelectrode gap is investigated. On a certain range of the problem parameters the flow induced in the channel substantially modifies the space charge distribution as a result of the blowoff of narrow diffusion electrode ion layers. This creates a nonmonotonic dependence of the fluid velocity on the applied potential difference.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 30–41, May–June, 1994.     

Heat transfer characteristics of developing gaseous slip-flow in rectangular microchannels with variable physical properties

The effects of variable physical properties on the flow and heat transfer characteristics of simultaneously developing slip-flow in rectangular microchannels with constant wall temperature are numerically investigated. A colocated finite-volume method is used in order to solve the mass, momentum and energy equations in their most general form. Various channel aspect ratios are studied at different Knudsen numbers. Simulations indicate that the constant physical property assumption can result in under/over-prediction of the local friction and heat transfer coefficients depending on the problem configuration. Density and thermo-physical property variations have significant effects on predicting flow and heat transfer characteristics in the developing and fully-developed regions. The degree of discrepancy varies for different cases depending on Knudsen number, aspect ratio and the temperature difference between the channel inlet and the wall. The results suggest that even low temperature differences can alter the friction and heat transfer coefficients considerably.     

Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

Three-dimensional incompressible Reynolds-averaged Navier–Stokes (RANS) computations are performed for water flow past an actuator disk model (representing a tidal turbine) placed in a rectangular channel of various blockages and aspect ratios. The study focuses on the effects of turbulent mixing behind the disk, as well as on the effects of channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.     

Numerical study of the unsteady flow and heat transfer in channels with periodically mounted square bars

 Numerical investigations of unsteady laminar flow and heat transfer in a channel of height H with periodically mounted square bars of height d = 0.2H arranged side by side to the approaching flow have been conducted for different transverse separation distances of the bars. Five cases with transverse separation distance of 0, 0.5, 1, 1.5 and 2d for a Reynolds number of 300 in a channel with a periodicity length of 2H were studied. The unsteady Navier–Stokes equations and the energy equation have been solved by a finite volume code with staggered grids combined with the SIMPLEC algorithm and a fine grid resolution. Due to the arrangement of bars detached from the channel walls the flow is unsteady with vortex shedding from the bars. The amplitude and mean values of the drag coefficients, skin friction coefficients, friction factor and Nusselt numbers have a strong dependence of the transverse separation distance of the bars. Received on 28 January 2000