Laminar Boundary Layer Model Research Articles

Magnetic diffusion of time distributed-order Maxwell fluid in boundary layer under the action of induced magnetic field

Hydrogel has been widely used in energy storage devices and flexible electronic equipment. To promote its applications, a laminar boundary layer model is proposed to analyze the velocity and temperature distributions in the mold. Based on the time distributed-order Maxwell and Cattaneo constitutive relations, the research establishes governing equations of unsteady two-dimensional incompressible viscoelastic electrically conducting hydrogel taking into account the induced magnetic field. When the magnetic Reynolds number is large enough, it is necessary to consider the magnetic diffusion in the boundary layer. The effects of thermal radiation and velocity slip are also considered at the same time. The Gauss quadrature rule is used to approximate the distributed-order integral, and then the numerical solution of the model is obtained by using the finite difference method and the L1-algorithm. The analytical solution is constructed to verify the effectiveness of the numerical solution. The results show that the fluid velocity decreases with the increment of magnetic parameter, while the induced magnetic field increases. The boundary layer thickness of velocity, induced magnetic field, and thermal becomes thinner with the enlargement of velocity and temperature relaxation time parameters. Moreover, the distributed-order and the fractional constitutive models are compared through different weight coefficients, and it is found that the fractional constitutive model obtains larger velocity and temperature distributions.

Dynamics of the jet wiping process via integral models

Abstract

Self-powered microfluidic pump using evaporation from diatom biosilica thin films

In recent years, researchers have successfully applied diatom biosilica to molecular detection platforms including Surface-Enhanced Raman Scattering (SERS) optofluidic sensors that are currently capable of detecting a variety of biological and chemical molecules at concentrations as low as 10−10 M. This study investigates the feasibility of an SERS device that couples the sensing and pumping capabilities of diatom biosilica thin films by determining flow rate limitations and stability. In this paper, we quantify the ability of porous diatom biosilica thin films to continuously pump deionized (DI) water from a reservoir via wicking flow by utilizing the strong capillary forces of the porous film coupled with evaporation. Our microfluidic device is comprised of a narrow horizontal reservoir fixed to a horizontal capillary whose end contacts a diatom biosilica film. Flow rates were controlled by altering the size and/or temperature of the biosilica porous film, determined by tracking the liquid meniscus displacement in the reservoir, and correlated with a modified laminar boundary-layer model. System stability was observed by tracking flow rates over the course of a given experiment, image analysis of the meniscus contacting the film, and a flow duration study. We found that for untreated DI water bubbles begin to form in the capillary tube at temperatures above 40 °C, but degassed water remains stable at temperatures of 90 °C and below. The pumping capabilities of the films ranged from 0.11 to 10.46 µL/min, matched theoretical predictions, demonstrated stable flow trends, and maintained flow for over 48 h.

Boundary layer control by a fish: Unsteady laminar boundary layers of rainbow trout swimming in turbulent flows.

ABSTRACTThe boundary layers of rainbow trout, Oncorhynchus mykiss [0.231±0.016 m total body length (L) (mean±s.d.); N=6], swimming at 1.6±0.09 L s−1 (N=6) in an experimental flow channel (Reynolds number, Re=4×105) with medium turbulence (5.6% intensity) were examined using the particle image velocimetry technique. The tangential flow velocity distributions in the pectoral and pelvic surface regions (arc length from the rostrum, lx=71±8 mm, N=3, and lx=110±13 mm, N=4, respectively) were approximated by a laminar boundary layer model, the Falkner−Skan equation. The flow regime over the pectoral and pelvic surfaces was regarded as a laminar flow, which could create less skin-friction drag than would be the case with turbulent flow. Flow separation was postponed until vortex shedding occurred over the posterior surface (lx=163±22 mm, N=3). The ratio of the body-wave velocity to the swimming speed was in the order of 1.2. This was consistent with the condition of the boundary layer laminarization that had been confirmed earlier using a mechanical model. These findings suggest an energy-efficient swimming strategy for rainbow trout in a turbulent environment.

Development of a laminar boundary layer model for curved wall jets

The paper addresses the issue of thin jets subjected to the Coanda effect and in particular the boundary layer modeling. An existing semi-empirical Coanda effect mathematical model is modified, with a more complex boundary layer model, in order to allow the estimative calculation of the detachment point and of other parameters such as friction coefficients, wall shear stress and the momentum and displacement integral thicknesses. The method used is analytical, based on the Rodman-Wood-Roberts model and the Pohlhausen boundary layer method. The work is significant for the pre-design calculations as well as for a quick checking of RANS CFD simulation results.

Shock waves in microchannels

AbstractA fully instrumented microscale shock tube, believed to be the smallest to date, has been fabricated and tested. This facility is used to study the transmission of a shock wave, produced in a large (37 mm) shock tube, into a 34 $\mathrm{\mu} \mathrm{m} $hydraulic diameter and 2 mm long microchannel. Pressure microsensors of a novel design, with gigahertz bandwidth, are used to obtain pressure–time histories of the microchannel shock wave at five axial stations. In all cases the transmitted shock wave is found to be weaker than the incident shock wave, and is observed to decay both in pressure and velocity as it propagates down the microchannel. These results are compared with various analytical and numerical models, and the best agreement is obtained with a Navier–Stokes computational fluid dynamics computation, which assumes a no-slip isothermal wall boundary condition; good agreement is also obtained with a simple shock tube laminar boundary layer model. It is also found that the flow developing within the microchannel is highly dependent on conditions at the microchannel entrance, which control the mass flux entering into the device. Regardless of the micrometre dimensions of the present facility, shock wave propagation in a microchannel of that scale exhibits a behaviour similar to that observed in large-scale facilities operated at low pressures, and the shock attenuation can be explained in terms of accepted laminar boundary models.

Effects of Non-Darcian and Inlet Conditions on the Forced Convection Along a Vertical Plate With Film Evaporation

The present study analyzes theoretically the non-Darcian effects and inlet conditions of forced convection flow with liquid film evaporation in a porous medium. The physical scheme includes a liquid–air streams combined system; the liquid film falls down along the plate and is exposed to a cocurrent forced moist air stream. The axial momentum, energy, and concentration equations for the air and water flows are developed based on the steady two-dimensional (2-D) laminar boundary layer model. The non-Darcian convective, boundary, and inertia effects are considered to describe the momentum characteristics of a porous medium. The paper clearly describes the temperature and mass concentration variations at the liquid–air interface and provides the heat and mass transfer distributions along the heated plate. Then, the paper further evaluates the non-Darcian effects and inlet conditions on the heat transfer and evaporating rate of liquid film evaporation. The numerical results show that latent heat transfer plays the dominant heat transfer role. Carrying out a parametric analysis indicates that higher air Reynolds number, higher wetted wall temperature, and lower moist air relative humidity will produce a better evaporating rate and heat transfer rate. In addition, a non-Darcy model should be adopted in the present study. The maximum error for predictions of heat and mass transfer performance will be 21% when the Darcy model is used.

Hydrodynamics and heat exchange in water suntraps

Heat exchange in water suntraps (WS) is discussed. It is shown that the heat exchange and the hydrodynamic characteristics of the flow in the initial sections of the heat removal channels of the WS can be calculated with the help of the laminar boundary layer model, using the assumptions adopted in boundary layer theory.

Nonsimilar, laminar, steady, electrically-conducting forced convection liquid metal boundary layer flow with induced magnetic field effects

A nonsimilar steady laminar boundary layer model is described for the hydromagnetic convection flow of a Newtonian, electrically-conducting liquid metal past a translating, non-conducting plate with a magnetic field aligned with the plate direction. The non-dimensional boundary layer equations are solved with the Sparrow–Quack–Boerner local nonsimilarity method (LNM). An increase in magnetic Prandtl number ( Pr m ) is found to strongly enhance wall heat transfer rate ( Nu x Re x − 1 / 2 ), velocity ( f ′ ) and induced magnetic field function ( g), but exerts negligible influence on the temperature ( θ) in the boundary layer. A rise in magnetic force number ( β) increases velocity, f ′ , shear stress function, f ″ , and wall heat transfer gradient, i.e. Nu x Re x − 1 / 2 , but reduces magnetic field function, g and temperature, θ. Increasing ordinary Prandtl number ( Pr), decreases temperature, θ, but increases wall heat transfer rate ( Nu x Re x − 1 / 2 ). An increase in wall to free stream velocity ratio parameter, ζ, increases flow velocity, f ′ , and induced magnetic field gradient, g ′ for small ξ but reduces g ′ for larger ξ, and also boosts the wall temperature gradient, Nu x Re x − 1 / 2 . The model has potential applications in astronautical magneto-thermo-aerodynamics, nuclear reactor channel flow control with magnetic fields and MHD (magnetohydrodynamic) energy generators.

Prediction of Mean Droplet Size of Sprays Issued from Wall Impingement Injector

The purpose of this study is to make a numerical model that predicts the spray characteristics of a wall impingement injector. The film flow on the wall was analyzed theoretically using the laminar boundary-layer model. The biquadratic velocity profile was employed for the laminar boundary layer. The thickness of the liquid film on the wall was measured by an automatic thickness measurement system, which was newly developed for the present study and is based on the contact needle method. From the measurements, the film thickness decreased first toward the periphery, and then increased along the line that was perpendicular to the liquid injection direction. The theoretical analysis of the film thickness on the wall agreed well with the measurements. The sizes of the droplets from the newly developed wall impingement injector were predicted by using the proposed theoretical analysis of a film flow and the existing liquid-film breakup model. From the measurements from the phase Doppler particle analyzer, the mean droplet size decreased once toward the spray periphery and then increased. This trend of the droplet size was coincident to that of the liquid-film thickness at the edge of the wall. The mean droplet size decreased as the liquid injection pressure increased. The predictions of the droplet size agreed well with the measurements.

Controlled Heat Transfer in a Laminar Boundary Layer along the Penetrable Surface of a Blunt Body

The problem on the determination of distributed forced injection from the surface of a blunt body subjected to flow for attaining preassigned characteristics of heat transfer is treated within the framework of the model of laminar boundary layer.

A field study of the wind effects on the performance of an unglazed transpired solar collector

An experimental study was carried out on a working unglazed transpired solar collector (UTSC) to determine what effects ambient wind has on its performance. The monitoring system included instruments to measure temperatures, collector outlet flow rates, solar radiation, wind speed, and wind direction; as well as an ultrasonic anemometer placed near the centre of the collector. Efficiency was defined as the fraction of incident solar heat flux that went to preheating the transpired air. Our observations indicate a high degree of turbulence near the wall which feeds the near wall region. This is supported by observations of efficiency which decrease monotonically with increasing turbulence intensities. It was also observed that peak efficiencies did not occur at the lowest wind speeds. Both these findings seem to contradict existing laminar boundary layer models for UTSC performance.

Film boiling heat transfer from a vertical cylinder in forced flow of liquids under saturated and subcooled conditions at pressures

Forced convection film boiling heat transfer on a vertical 3-mm diameter and 180-mm length platinum test cylinder located in the center of the 40-mm inner diameter test channel was measured. Saturated water, and saturated and subcooled R113 were used as the test liquids that flowed upward along the cylinder in the test channel. Flow velocities ranged from 0 to 3 m s −1, pressures from 102 to 490 kPa, and liquid subcoolings for R113 from 0 to 60 K. The heat transfer coefficients for a certain pressure and liquid subcooling are almost independent of flow velocity and of a vertical position on the cylinder for the flow velocities lower than ≈1 m s −1 (the first range), and they become higher for the velocities higher than ≈1 m s −1 (the second range). Slight dependence on a vertical position being nearly proportional to z −1/4, where z is the height from the leading edge of the test cylinder, exists for the flow velocities in the second range. The heat transfer coefficients at each velocity in the first and second ranges are higher for higher pressure and liquid subcooling. Correlation for the forced convection film boiling heat transfer with radiation contribution on a vertical cylinder was derived by modifying an approximate analytical solution for a two-phase laminar boundary layer model to agree better with the experimental data. It was confirmed that the experimental data of film boiling heat transfer coefficients in water and R113 were described by the correlation within ±20% difference.

Symmetries and Heir Equations for the Laminar Boundary Layer Model

Iterations of the nonclassical symmetries method applied to both the Prandtl equation and Prandtl system give rise to new nonlinear equations, which inherit the Lie symmetry algebra of the original Prandtl equation (system). Invariant solutions of these heir equations supply new solutions of the original equation (system).

Modeling heterogeneous/homogeneous reactions and transport coupling for catalytic combustion of methyl chloride over a Mn-based catalyst

The effect of boundary-layer flow and heterogeneous/homogeneous reaction chemistry in determiningproduct selectivity for catalytically promoted oxidation of ultralean CH 3 Cl over a Mn-based catalyst was investigated numerically. This work has relevance to modeling of more general catalytic combustion systems in defining the importance of transport and chemistry interactions. In this study, we find that the presence of Mn-based catalyst can significantly decrease the temperature necessary to achieve a given conversion of CH 3 Cl. The numerical study of the experiment used plug-flow, lumped-parameter transport, and laminar-flow models with detailed gas-phase chemistry. These flow models coupled with gas-phase reaction mechanisms from the literature and an experimentally determined surface reaction rate were used to illustrate heterogeneous/homogeneous reaction coupling and how it is influenced by transport. Kinetic modeling shows that the heterogeneous and homogeneous interaction occurs through CH 3 Cl decomposition on the surface that initiates gas-phase reaction. For the slower velocity, there is small difference in plug-flow model and detailed laminar boundary-layer model predictions. The difference in prediction between flow models becomes larger at the high velocity, with shorter residence time, where the higher surface temperature needed for equivalent conversion causes surface reaction products to be converted before they can be transported to the bulk. The important parameter for modeling heterogeneous/homogeneous interactions is the Damköhler number with respect to gas-phase consumption of species produced by surface reaction.

A laminar boundary layer model of heat transfer due to a nonuniform planar jet impinging on a moving plate

A theoretical model is developed of planar jet impingement heat transfer on a moving plate. Boundary layer equations in their integral forms are used in order to include, both near and away from the stagnation line, the effects of surface motion directed perpendicular to the jet plane, an arbitrary surface temperature variation, and nonuniform jet discharge velocity profiles. The validity and accuracy of the approximate solution is assessed by comparison to an exact solution restricted to regions near the stagnation line. Results indicate that the influence of a nonuniform jet discharge velocity decreases with distance from the stagnation line. Surface motion affects heat transfer at regions away from the stagnation line, but has little influence near the stagnation line when the surface temperature is constant.

Computational study of incipient leading-edge separation on a supersonic delta wing

A computational study on a 65 deg delta wing at a freestream Mach number of 1.60 has been conducted by obtaining conical Reynolds-averaged, Navier-Stokes solutions on a parametric series of geometries that varied in leading-edge radius and/or circular-arc camber. The computational results showed that increasing leadingedge radius or camber delay the onset of leading-edge separation on the leeside of a delta wing at a specific angle of attack. The Reynolds number was varied from 1 x 106-5 x 10 6 for a turbulent boundary layer and was shown to have a minor effect on the effectiveness of leading-edge radius and/or camber in delaying the onset of leading-edge separation. Both laminar and turbulent boundary-layer models were investigated at a Reynolds number of 1 x 10 6, and the predicted flow pattern was found to change from attached flow for the turbulent boundary-layer model to separated flow for the laminar boundary-layer model.

Fire Plume Along Vertical Surfaces: Effect of Finite-Rate Chemical Reactions

Fire plume along a vertical wall is analyzed using a laminar boundary layer model, including finite-rate, gas-phase chemical kinetics. The chemical reactions include two semiglobal steps: In the first, fuel is oxidized to form carbon monoxide and water vapor, and in the second, carbon monoxide is oxidized to form carbon dioxide. Several important nondimensional kinetic parameters are identified and a parametric study is given. The computed results indicate that by slowing down the relative kinetic rates in the gas-phase reactions, the total surface heat transfer rate and the preheating distance are decreased. Furthermore, slowing down the kinetics also increases the amount of unreacted combustibles that escape from the flame.

Real Gas Laminar Boundary-Layer Separation Prediction Methodology

AREAL gas laminar boundary-layer separation methodology has been developed to predict Space Shuttle Orbiter control surface effectiveness during atmospheric entry. The methodology is based on the LeesKlineberg moment integral theory. A real gas laminar boundary-layer model, having a binary atomic diffusion of frozen gas composition, is assumed. A brief discussion of theory and sample results are presented herein. A set of boundary-layer profile parameters which are required for this theory is given in the full paper. Contents The aerodynamic control surface effectiveness of the Space Shuttle Orbiter (SSO) during re-entry is strongly affected by the laminar flow separation induced by the compressively deflected surface. The SSO re-entry hypersonic control surface effectiveness (HCSE) estimates were initially based primarily on wind-tunnel test data. Extrapolation of test data to higher elevon/body flap deflections revealed that a potential control reversal phenomena may exist. However, the quality of test data was such that a definite control reversal trend could not be established. A methodology for predicting the supersonic/hypersonic laminar boundary-layer separation for the ideal gas case has been developed and presented in Ref. 1. During re-entry, in the flight regime where aerodynamic forces become significant, inviscid air on the windward side of the SSO can be fully dissociated by compression heating. However, since the outer surface skin temperature of the SSO thermal protection system (TPS) will not exceed 2000 K, the neighboring dissociated air will recombine fully. Therefore, a dissociation-recombination cycle of the reacting gas is expected to be produced within the boundary layer, the contribution of which to the laminar flow separation mechanism is presently unknown. Theory for Real Gas Flow Separation Prediction The real gas flow separation prediction methodology, which is suitable for design applications, is derived from the ideal gas Lees-Klineberg Moment Integral Theory.2 Since the analysis of multispecies gas having a finite reaction rate is too complex and not suitable for the integral theory method, an idealized binary reacting gas (molecule-atom of one species of gas) has been selected to represent the approximate behavior of a real gas. The binary-single-species reaction assumption is valid, because in the flight regime considered, one species of molecule is reacting while the others are in an equilibrium

A Boundary-Layer Theory for Transient Viscous Losses in Turbulent Flow

A laminar boundary-layer model is proposed to account for viscous losses during the transient turbulent flow of a liquid in a tube. In this model, inviscid slug flow is assumed for the core and all viscous effects are assumed to occur in the boundary layer. The transient boundary-layer velocity distribution is determined as a function of a prescribed variation in core velocity and the associated pressure gradient. Both analytical and numerical solutions are presented. This transient flow information is used to calculate local and integrated energy dissipation rates which are then combined, with one-dimensional energy analyses. The result is a prediction of the decrease in pressure-wave magnitude due to viscous dissipation, and a comparison is made with experimental data for rapid flow extinction. Good agreement between the observed and predicted results is obtained.