Parallel Flat Plates Research Articles

Simulation of a fluid flow and investigation of a permeability-porosity relationship in porous media with random circular obstacles using the curved boundary lattice Boltzmann method

In this paper, the fluid flow between two parallel flat plates filled with porous media was investigated numerically using the Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM). The obstacles representing porous media were considered as random, circular, rigid and granular ones with uniform diameters and without overlap. The fluid was supposed to be a single-phase viscous Newtonian fluid and the flow to be incompressible, steady and laminar. The uniform velocity profile was considered at the entrance of the canal and the no-slip condition was imposed at solid walls. For applying curved boundary conditions, the linear interpolation method ( $ \Delta$ fraction) was used in this work. The effect of varying the Reynolds number on the pressure gradient and the Darcy drag was studied. The porous medium was supposed to be isotropic and having scalar permeability. The dimensionless permeability was calculated as a function of the Knudsen number. Also, the dimensionless permeability versus porosity was investigated and the results were compared with the Clague equation for different materials. Because of rather low precision of the Clague equation at high porosities, an extension to the Clague equation was presented. The permeability-porosity relationship was surveyed and the corresponding curve was plotted in the LBM scale. It was seen from numerical results that the enhancement of the Knudsen number increases the dimensionless permeability. The change of streamlines tortuosity in terms of porosity was explored and the results were compared with the revised Bruggeman equation. The obtained results demonstrate that the Lattice Boltzmann Method is very useful in the challenging problems of fluid dynamics such as fluid flow simulation through porous media.

Rise velocities of single bubbles in a narrow channel between parallel flat plates

Effects of the bubble lateral motion and the liquid viscosity, μL, on the rise velocity, VB, and the drag coefficient of a single bubble in a narrow channel were investigated. The gap thickness of the channel was 3 mm. The bubble diameter, dB, was from 7 to 20 mm. Clean water and glycerol–water solutions were used for the liquid phase. The μL ranged from 0.9 to 65.7 mPa s. Air was used for the gas phase. The conclusions obtained are as follows: (1) the bubble motion transits from zigzagging to rectilinear as dB increases and the transition abruptly takes place at a certain critical dB, which decreases with increasing μL, (2) the abrupt transition causes a stepwise increase in VB, (3) the curvature of the bubble nose in the rectilinear regime strongly affects VB, resulting in unavoidable scatter in VB data in low viscosity systems due to large shape oscillation, and (4) Filella's VB correlation for air-water systems is deducible from the force balance and applicable to high viscosity systems, provided that the model coefficient is tuned for each μL, implying that the drag coefficient can be expressed in terms of the Morton number and the gap-to-bubble diameter ratio.

Experimental study on the conjugate heat transfer of double-wall turbine blade components with/without pins

The heat transfer and flow characteristics of double-wall turbine blade components with integrated impingement/effusion and impingement/pin/effusion cooling configurations are investigated experimentally. The measurements are conducted on layers of parallel flat plates, neglecting surface curvature effect, as an idealization of the actual turbine blade component. Non-dimensional aerodynamic and geometric parameters, excluding surface curvature, considered in the study are consistent with a typical double-wall structure of the turbine blade. The test plates are made of 304 stainless steel with a thermal conductivity of approximate 17 W/mK. The injection angle of effusion holes (α) is set at 30°, 45° and 60°, and blowing ratio (BR) changes within a range of BR = 0.25–1.0. Overall cooling effectiveness of the double-wall structure, taking convective heat transfer as well as the conduction effect into consideration, is measured using thermochromic liquid crystal technology. Effects of injection angle, blowing ratio and pin installations on the overall cooling performance and discharge coefficient of the double-wall structure are examined and analyzed. The test results show that overall cooling effectiveness is enhanced significantly as BR increases from 0.25 to 0.5, but changes little, up to 5.9% in limited regions, for BR ranging from 0.5 to 1.0. As the α increases, the double-wall cooling efficiency is reduced upstream, but is meanwhile enhanced downstream. Adding an array of cylindrical pins to the internal cooling structure leads to a considerable enhancement in the overall cooling effectiveness, while it causes the discharge coefficient to drop, to some extent.

Effect of Viscous Gas on Stability of the Electrified Liquid Sheet

An electrified liquid sheet was investigated by the linear analysis method. The sheet was injected into a dielectric viscous gas bounded by two horizontal parallel flat plates with a transverse electric field. To take into account the gas boundary layer thickness, the velocity profile of the liquid sheet must be considered and derived. By analyzing the liquid and gas domain, the relation between the growth rate and the wavenumbers for electrified liquid sheets was derived, and solved using the spectral method whose accuracy is higher than those of the finite element method and the finite difference method. Two modes, namely the sinuous mode and varicose mode were also investigated. The results revealed that the maximum growth rate of the sinuous disturbance wave is greater than that of the varicose one for the electrified liquid sheet. Moreover, the effects of the electrified Euler number and other parameters on the instability of the electrified liquid sheets have been tested. It is found that the growth rate is faster for an electrified liquid sheet than a non-electrified one. The electrical Euler number, the liquid Reynolds number, the Weber number and the momentum flux ratio can promote the breakup of a liquid sheet. However, the increase in the ratio l of the distance between the liquid sheet and flat plate to the liquid sheet thickness has an opposite influence with the other parameters.

Numerical simulation for flow shadowing and multiple reflections between two flat plates in the free-molecular regime

A free-molecular flow past two parallel circular flat plates is analyzed by the test particle Monte Carlo (TPMC) method. Flow shadowing and multiple reflections have a vital influence on aerodynamic coefficients of the two plates. At the pitch angle of 0[Formula: see text], lift coefficients of each plate do not equal to zero. Flow shadowing has a significant effect on the front side of the shaded plate while multiple reflections play a dominant role on the back side of the shading one. The area ratio of the two plates has an evident effect on flow shadowing and multiple reflections, and different area ratios lead to different pressure distributions on the front side of the shaded plate and the back side of the shading one.

Pulsatile electroosmotic flow in a microchannel with asymmetric wall zeta potentials and its effect on mass transport enhancement and mixing

In this work, we analyze theoretically the mass transport of a neutral solute in a pulsatile electroosmotic flow (PEOF), circulating in a parallel flat plate microchannel whose walls are characterized by asymmetric zeta potentials. The microchannel is connected to a two reservoirs having different concentrations. To analyze the mass transport in the PEOF, the Debye-Hückel approximation is assumed, and the electric potential in the Debye length is obtained from the Poisson-Boltzmann equation. Then, using the momentum and concentration equations, the flow and concentration fields are analytically determined for the periodic stage. Such field distributions depend principally on three dimensionless parameters: an angular Reynolds number, the Schmidt number, and the ratio between the half height of the channel and the Debye length. For obtaining insight on the physical aspects of the studied phenomenon, an asymptotic solution is additionally obtained in the limits of small and large values of the angular Reynolds number. Some important results derived from this analysis show the conditions for which the mass transport of a neutral solute can be enhanced and the circumstances whereby mixing of species is achieved.

Nanofluid flow and heat transfer in a microchannel with interfacial electrokinetic effects

The behaviour of microchannel flow of a nanofluid between two parallel flat plates in the presence of the electrical double layer (EDL) is investigated in this paper. The problem is formulated based on the Buongiorno nanofluid model with the electrical body force due to the EDL being considered in the momentum equation. As one of the highlights of the present investigation, the unphysical assumption introduced in previous studies often leading to the discontinuities of flow field that the electrostatic potential in the middle of the channel has to be equal to zero is eliminated. In addition, the inappropriate assumption that the pressure constant is treated as a known condition is also rectified. The new model is developed with the governing equations being reduced by a set of dimensionless quantities to a set of coupled ordinary differential equations. Based on the analytical approximations, the influences of various physical parameters on the flow field and temperature field, and the important physical quantities of practical interests are analysed and discussed in detail.

Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials

The pulsatile electroosmotic flow (PEOF) of a Maxwell fluid in a parallel flat plate microchannel with asymmetric wall zeta potentials is theoretically analyzed. By combining the linear Maxwell viscoelastic model, the Cauchy equation, and the electric field solution obtained from the linearized Poisson-Boltzmann equation, a hyperbolic partial differential equation is obtained to derive the flow field. The PEOF is controlled by the angular Reynolds number, the ratio of the zeta potentials of the microchannel walls, the electrokinetic parameter, and the elasticity number. The main results obtained from this analysis show strong oscillations in the velocity profiles when the values of the elasticity number and the angular Reynolds number increase due to the competition among the elastic, viscous, inertial, and electric forces in the flow.

Assessment of thermo-fluid analogies for different flow configurations: the effect of Prandtl number, and laminar-to-turbulent flow regimes

The differential equations of momentum and heat transfer are similar to each other based on some assumptions, leading to exact analogous equations. These analogies have since been the focus of attention and their applicability is explored in many fields and flow types. In some cases, these analogies hold valid even if the theoretical foundation is not available for such conditions. The Reynolds and Chilton-Colburn analogy are the focus of the current work, with four types of flow situations including, Couette flow, tube flow, parallel plate and flow over a flat surface. The numerical results show the best match for parallel flow and flat plate, while Couette flow resulted in large differences (by a factor up to 3.3).

Dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a microchannel with a slowly varying wall zeta potential

The dispersion coefficient of a passive solute in a steady-state pure electro-osmotic flow (EOF) of a viscoelastic liquid, whose rheological behaviour follows the simplified Phan-Thien–Tanner (sPTT) model, along a parallel flat plate microchannel, is studied. The walls of the microchannel are assumed to have modulated and low $\unicode[STIX]{x1D701}$ potentials, which vary slowly in the axial direction in a sinusoidal manner. The flow field required to obtain the dispersion coefficient was solved using the lubrication approximation theory (LAT). The solution of the electric potential is based on the Debye–Hückel approximation for a symmetric $(z:z)$ electrolyte. The viscoelasticity of the fluid is observed to notably amplify the axial distribution of the effective dispersion coefficients due to the variation in the $\unicode[STIX]{x1D701}$ potentials of the walls. The problem was formulated for two cases: when the Debye layer thickness (EDL) was on the order of unity (thick EDL) and in the limit where the thickness of the EDL was very small compared with the height of the microchannel (thin EDL limit). Due to the coupling between the nonlinear governing equations and the sPTT fluid model, they were replaced by their approximate linearized forms and solved in the limit of $\unicode[STIX]{x1D700}\ll 1$ using the regular perturbation technique. Here $\unicode[STIX]{x1D700}$ is the amplitude of the sinusoidal function of the $\unicode[STIX]{x1D701}$ potentials. Additionally, the numerical solution of the simplified governing equations was also obtained for $\unicode[STIX]{x1D700}=O(1)$ and compared with the approximate solution, showing excellent agreement for $0\leqslant \unicode[STIX]{x1D700}\leqslant 0.3$. Note that the dispersion coefficient primarily depends on the Deborah number, on the ratio of the half-height of the microchannel to the Debye length, and on the assumed variation in the $\unicode[STIX]{x1D701}$ potentials of the walls.

Experimental Characterization of Meso-Micro Fractals from Nanoparticle Seeded Resin in Lifting Plate Hele-Shaw Cell

Various processes are developed to fabricate meso and micro size fractal structures for wide variety of engineering applications. Various types of fluid flows are studied and are deployed to develop meso and micro fractal structures. Lift Plate Hele-Shaw fluid flow also termed as Saffman-Taylor instability is one of the fluid phenomenon’s which can be easily used to fabricate such structures. In this process, fractals are formed by capturing the fluid droplet between thin gaps of two flat parallel plates and moving the upper plate in controlled manner. The formation of the fractal depends on process parameters; viz velocity of plate, fluid property and gap between the plates. This paper presents the exhaustive characterization of fluid composed of photopolymer seeded with the nanopowder in lifting plate Hele-Shaw cell. The prepared resin is mixture of monomer Hexanediol Diacrylate (HDDA) and photoinitiator Benzoyl Ethyl Ether (BEE) seeded with ceramic nanopowder. The fractal growth is observed from the prepared resin under lifting plate Hele Shaw cell through designed of experiments. The parameters; fluid separation velocity and gap between the plates are varied through developed system and effect of viscosity is observed by varying the loading of the ceramic nanopowder. The exhaustive characterization of the process has presented the effect of parameters and its interactions on the formation of the fractal. Further the fractal growth is presented in the dimensionless manner for its generalization. The experimental characterization has given a generalised methodology for the formation of controlled fractals or to mimic various meso and micro fractals available in the nature.

Vortex Structures in the Wake of the Flat Parallel Plates with Periodic Disturbance

Vortex Structures in the Wake of the Flat Parallel Plates with Periodic Disturbance

Experimental study of a method of reducing the drag of a circular cylinder by installing a flat plate

The article describes experimental investigation of a method of reducing the drag of a circular cylinder. We consider installation of a flat plate parallel to the flow before the cylinder. The results for the cylinder drag coefficient depending on various locations of the flat plate relative to the cylinder are presented. The following geometric characteristics are studied: the reference chord of the plate and the angle of the plates position with respect to the cylinder. It was found that the drag coefficient depends on the location of the plate relative to the cylinder. The article presents experimental results that were obtained in the wind tunnel of Samara University. The locations of the plate relative to the cylinder that provide the lowest value of the drag coefficient are identified.

Experimental study of the possibility of reducing the resistance and unevenness of output field of velocities in flat diffuser channels with large opening angles

In modern combined cycle gas turbines (CCGT), when designing the reducers from the output diffuser of a gas turbine to a boiler-utilizer, wide-angle diffusers are used, in which practically from the input a flow separation and transition to jet stream regime occurs. In such channels, the energy loss in the field of velocities sharply rise and the field of velocities in the output from them is characterized by considerable unevenness that worsens the heat transfer process in the first by motion tube bundles of the boiler-utilizer. The results of experimental research of the method for reducing the energy loss and alignment of the field of velocities at the output from a flat asymmetrical diffuser channel with one deflecting wall with the opening angle of 40° by means of placing inside the channel the flat plate parallel to the deflecting wall are presented in the paper. It is revealed that, at this placement of the plate in the channel, it has a chance to reduce the energy loss by 20%, considerably align the output field of velocities, and decrease the dynamic loads on the walls in the output cross-section. The studied method of resistance reduction and alignment of the fields of velocities in the flat diffuser channels was used for optimization of the reducer from the output diffuser of the gas turbine to the boiler-utilizer of CCGT of PGU-450T type of Kaliningrad Thermal Power Plant-2. The obtained results are evidence that the configuration of the reducer installed in the PGU-450T of Kaliningrad Thermal Power Plant-2 is not optimal. It follows also from the obtained data that working-off the reducer should be necessarily conducted by the test results of the channel consisting of the model of reducer with the model of boiler-utilizer installed behind it. Application of the method of alignment of output field of velocities and reducing the resistance in the wide-angle diffusers investigated in the work made it possible—when using the known model of diffusion reducer for PGU-450T, which is bad from the standpoint of aerodynamics— to reduce the value of the coefficient of the total loss by almost 20% as compared with the model of real reducer of PGU-450T.

Hydrodynamic dispersion in a combined magnetohydrodynamic- electroosmotic-driven flow through a microchannel with slowly varying wall zeta potentials

The effective dispersion coefficient of a neutral solute in the combined electroosmotic (EO) and magnetohydrodynamic (MHD)-driven flow of a Newtonian fluid through a parallel flat plate microchannel is studied. The walls of the microchannel are assumed to have modulated and low zeta potentials that vary slowly in the axial direction in a sinusoidal manner. The flow field required to obtain the dispersion coefficient is solved using the lubrication approximation theory. The solution of the electrical potential is based on the Debye-Hückel approximation for a symmetric (Z:Z) electrolyte solution. The EO and MHD effects, together with the variations in the zeta potentials of the walls, are observed to notably modify the axial distribution of the effective dispersion coefficient. The problem is formulated for two cases of the zeta potential function. Note that the dispersion coefficient primarily depends on the Hartmann number, on the ratio of the half height of the microchannel to the Debye length, and on the assumed variation in the zeta potentials of the walls.

Influence of an effective Prandtl number model on squeezed flow of γAl2O3-H2O and γAl2O3-C2H6O2 nanofluids

The flow squeezed between parallel flat plates that placed horizontally in nonporous media is of great interest because of its uses in many industries and engineering side as well. In the light of this fact, we have considered the flow of nanofluids between two plates. The dimensional flow is successfully reduced into a set of self-similar form with the help of feasible similarity variables. In the next step, the system is solved analytically (Homotopy Analysis method) and to ensure the analytical computation, numerical solutions (by means of Runge-Kutta method) are also performed. Influences of the effective Prandtl number are investigated on thermal filed and local rate of heat transfer along with ingrained physical quantities. Under certain assumptions, present results are compared with already existing ones in the literature and found to be agree well. The major outcomes of the presented letter are described in the last section.

Investigation of MHD Go-water nanofluid flow and heat transfer in a porous channel in the presence of thermal radiation effect

In this paper, flow and heat transfer of MHD Go-water nanofluid between two parallel flat plates in the presence of thermal radiation are studied. One of plates is externally heated and cooled by coolant injection through the other plate, which also expands or contracts with time. A similarity transformation is used to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The obtained non-linear ordinary differential equations are solved by Duan–Rach Approach (DRA). This method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of various parameters such as the Reynolds number, the expansion ratio, the magnetic parameter, the power law index, the solid volume fraction and the radiation parameter are investigated on the velocity and temperature. Furthermore, the value of the Nusselt number is calculated and presented through figures. The results indicate that the temperature profile and the Nusselt number have a direct relationship with the solid volume fraction and have an inverse relationship with the radiation parameter. In addition, the limiting cases are gained and found to be in an excellent agreement with the previous works.

HEAT AND MASS TRANSFER OF MHD VISCO-ELASTIC OSCILLATORY FLOW THROUGH AN INCLINED CHANNEL WITH HEAT GENERATION/ ABSORPTION IN PRESENCE OF CHEMICAL REACTION

The purpose of this work is to investigate the unsteady hydromagnetic oscillatory flow of a fluid through an inclined channel between two parallel flat plates under the influence of magnetic field and first-order chemical reaction with heat transfer including heat generating sources or heat absorbing sinks, while one of these two plates is adiabatic. The fluid is assumed to be visco-elastic (second-order), incompressible and electrically conducting. The magnetic field is applied transversely to the direction of the flow. The resulting problem has been solved and the graphs for velocity profile, temperature profile, concentration profile and shear stress are plotted and discussed. The analysis of the obtained results showed that the flow field is appreciably influenced by the material parameter of the second-order fluid and the flow parameters involved in the problems.

Electrical capacitance as a proxy measurement of miscanthus bulk density, and the influence of moisture content and particle size

This research aimed at measuring the electrical capacitance of miscanthus biomass as a potential proxy measure of bulk density. The experimental arrangement allowed for continuous variation of bulk density through compression, whereas moisture content was varied at two levels, being air-dried (<5%) and oven dried (14.5%), and particle size was varied by using material that passed milling screen aperture sizes of 6.35, 9.53, 12.7, and 25.4mm. A chamber was constructed containing the biomass, which was compressed using a hydraulic cylinder, causing the biomass bulk density to increase during the experiment. During the compression, the pressure applied vertically onto the biomass was inferred from the measured fluid pressure in the hydraulic cylinder. In addition, the displacement of the cylinder was measured using a linear encoder, allowing for instantaneous bulk density calculations.Two capacitors, each comprising dual parallel flat copper plates, were fitted inside the chamber, where the biomass under compression acted as the dielectric medium. The conjecture was made that the force with which the biomass is pushed against the capacitor plates would highly influence the measured capacitance value, and therefore, one capacitor was placed in a longitudinal direction to capture vertical forces, and a second in the lateral direction to capture transverse forces.The results showed a quasi-linear relationship between capacitance and bulk density. A proportional relationship was found between electrical capacitance and moisture content as well as between electrical capacitance and particle size. A comparison between vertical capacitance versus bulk density and the applied pressure versus bulk density showed that they are independent measurements. Therefore, the initial conjecture being that the force with which the biomass is pushed against the capacitance plates would have a large effect on the capacitance was deemed false; instead, the internal reorganization of biomass particles seems responsible for the variation in capacitance as observed.The results imply that electrical capacitance may serve as a proxy for the measurement of miscanthus bulk density, but since moisture content and particle size have a marked effect on the capacitance, they must be determined separately or calibrated for. Currently, to determine the instantaneous moisture content of field crops, capacitor plates are already an integral part of yield monitoring systems. However, the method as investigated, adds the potential simultaneous measurement of the instantaneous bulk density of a biomass flow.

Finite Element Solution of an Unsteady MHD Flow through Porous Medium between Two Parallel Flat Plates

Finite element solution of unsteady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible viscous fluid past through porous medium between two parallel plates is presented in the presence of a transverse magnetic field and Hall effect. The results obtained from some test cases are then compared with previous published work using the finite difference method (FDM). Numerical examples show that the finite element method (FEM) gives more accurate results in comparison with the finite difference method (FDM).