Non-uniform Velocity Profile Research Articles

The Role of Longitudinal Waves in Quartz Crystal Microbalance Applications in Liquids

The generation of shear waves in liquids by the quartz crystal microbalance (QCM) is evident from the influence of liquid properties on the QCM frequency and electrical characteristics. With the exception of a few reports, contributions from longitudonal waves that arise from nonuniform velocity profiles along the shear direction or nonideal contributions from crystal longtudinal and flexure modes have been largely ignored. The presence of these longitudinal components is demonstrated by the influence of a glass plate, fixed Gel to the QCM surface at a remote distance, on the QCM resonant frequency and electrical impedance characteristics. In agreement with a previous report, these effects can be observed even when the glass plate is positioned >1 cm away from the QCM, substantially longer than the shear wave decay length. Longitudinal standing waves are evident from the periodicity of the resonant frequency, inductance, capacitance, and resistance as the distance between the QCM and the glass plate. The wavelength of the standing waves agrees with that expected for the resonant frequency of the QCM and the fluid medium. The amplitude of the standing waves depends strongly upon the quartz crystal contour, as evident from extremely large frequency excursions observed for plano-convex crystals in witch energy trapping in the center of the resonator is greater than that for plano-plano crystals. Impedance analysis indicates that the frequency excursions are primarily a consequence of changes in the capacitance of the quartz crystals that result from a decrease in the compliance of the quartz resonator due to pressure exerted by the longitudinal waves. Standing waves resulting from reflection from the fluid-air interface are also observed, although the amplitude of the standing waves is smaller than the amplitude observed with the glass reflector plate owing to the larger reflection coefficient for the latter. However, the frequency excursions that result from small changes in the height of the fluid-air interface are substantial relative to frequency changes measured in typical QCM experiments. These results demonstrate that it is important to design QCM experiments to avoid contributions from longitudinal waves

Effects of the propagation velocity of a surface depolarization wave on the extracellular potential of an excitable cell.

Extracellular electric fields have been proposed as a mechanism for electrical coupling between excitable cells. This study deals with the extracellular potential produced by an isolated excitable spherical cell due to a traveling depolarization wave on the cell's surface. Both uniform and nonuniform propagation velocity profiles are considered. Using boundary element methods, the extracellular potential was computed. The polarity of the extracellular potential was found to be space-dependent. The peak extracellular potential increased when a) the propagation velocity decreased, b) the rise time of the depolarization decreased, and c) the extracellular resistivity increased.

NUMERICAL SIMULATION OF INTERMITTENT AND CONTINUOUS DEEP-BED DRYING OF BIOLOGICAL MATERIALS

Abstract This paper presents a simulation study of dryers. A two-dimensional deep-bed drying model, which incorporates modifications in existing one-dimensional models, has been developed and has the capability of handling both non-uniform velocity profiles and material properties dependence on temperature and moisture content. A corn drying system was simulated in order to analyze its temporal and spatial drying behavior. Both intermittent and continuous drying were simulated. The results showed that continuous drying is more efficient than intermittent drying with respect to drying time. However, intermittent drying led to more uniform temperature and moisture distributions, which improve grain quality. The model can be easily extended to three-dimensional drying analysis.

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.

Flooding and Flow Reversal in Annular Two-Phase Flows

A two-fluid model for annular two-phase flow is presented, which incorporates realistic phase interaction terms corresponding to turbulence in the gas phase, interphase pressure differences, and profile effects (nonuniform velocity profiles); this model avoids the conundrum of illposedness associated with the simplest averaged model [D. A. Drew, Continuum modelling of two-phase flows, in Theory of Dispersed Flow, R. E. Meyer, ed., Academic Press, New York, 1983]. In this paper it is shown that an appropriately scaled form of this model is capable of significant (asymptotic) simplification and in its reduced form is able to predict the phenomena of flooding and flow reversal in annular flow, both qualitatively and quantitatively.

Non‐uniform motion and extended media effects on the mutual coherence function: An analytic solution for spaced frequency, position, and time

An analytical expression for the two‐frequency, two‐position, two‐time mutual coherence function applicable to propagation through thick random media with nonuniform electron density and plasma velocity is derived using the phase‐screen/diffraction method (PDM). In this method the ionization is collapsed to a number of thin screens and diffraction is developed in the free space between. The resulting mutual coherence function converges rapidly to the continuum result as the number of screens representing the medium is increased. The effects of multiple scatter occurring over long distances and varying plasma velocity over the propagation path are shown to be important in HF propagation. Scattering functions (delay‐Doppler power spectra) obtained as Fourier transforms of the PDM mutual coherence function are compared to scattering functions measured by an HF channel probe. Nonuniform velocity profiles are shown to account for the variety of delay‐Doppler couplings observed.

Investigation of the diffuser flow quality in an icing research windtunnel

In this paper, the flow in the diffuser section of the Icing Research Tunnel at the NASA Lewis Research Center is both numerically and experimentally investigated. To accomplish the numerical portion of the work, and existing computer code is utilised. The code, known as PARC3D, is based on the Beam-Warming algorithm applied to the strong conservation law form of the complete Navier-Stokes equations. Following a brief description of the diffuser geometry, the measured flow characteristics are described. A brief discussion of the code work is also provided. The flow measurements show a highly nonuniform velocity profile across the diffuser exit with boundary-layer growth more prevalent near the centres of the walls rather than in the corners of the diffuser. Predicted velocity profiles at the centreline are similar to those measured; however, the code did not accurately predict the boundary-layer behaviour near the corners.

Flow regimes in wide-angle screened diffusers

The results of an experimental investigation into the use of screens and perforated plates to control the velocity profile emerging from wide-angle diffusers are reported. Tests were undertaken using two screens in diffusers of area ratio 10 and included angles of 45° and 60°. Without the use of screens to control the flow, highly non-uniform velocity profiles occur. Depending upon the porosity of the screens and their location within the diffuser, three principal types of exit velocity profile were found. These included (i) a regime characterized by high-velocity wall layers together with a depleted core region; and (ii) a regime involving a high-velocity region occupying a cruciform flow pattern, together with low-velocity corner regions. However, the most important finding of the work was that, with appropriate choice of porosity and location of the two screens, mean velocity profiles could be achieved which avoided flow separation and displayed a high degree of flow uniformity. These results extend significantly the range of area ratios in which two screens are sufficient to ensure uniformity of the velocity profile at the exit plane of wide-angle diffusers.

Local Convective Heat Transfer From a Heated Surface to a Planar Jet of Water With a Nonuniform Velocity Profile

Experiments have been conducted on a planar, free surface jet of water to investigate the effects of a nonuniform velocity profile on the local convection coefficient for a uniform heat flux surface. Heat transfer coefficient distributions were measured for heat fluxes ranging from 0.24 to 1.47 MW/m2 and for Reynolds numbers (based on the average nozzle velocity and nozzle width) from 15,000 to 54,000. This range of flow conditions yielded turbulent velocity profiles similar to those of channel flow. Results have been obtained for both single-phase convection and nucleate boiling. Relative to results for a uniform velocity profile, the nonuniform profile was found to enhance heat transfer significantly. However, enhancement is attributed primarily to increased levels of turbulence and only secondarily to changes in the velocity profile.

Flow velocity profile via time-domain correlation: error analysis and computer simulation

An ultrasonic human-blood-flow velocity profile measurement method using time-domain correlation of consecutive echo pairs has been developed. The time shift between a pair of range gated echoes is estimated by searching for the shift that results in the maximum correlation. The time shift indicates the distance a group of scatterers has moved, from which flow velocity is estimated. The basis for the computer simulations and error analyses of the scheme includes a band-passed white Gaussian noise signal model for an echo from a scattering medium, the estimate of flow velocity from both a single scatterer and multiple scatterers, and a derived precision estimation. The error analysis via computer simulation includes an evaluation of errors associated with the correlation method. For a uniform flow velocity profile, beamwidth modulation represents the greatest error source. However, for a nonuniform flow velocity profile, the jitter caused by a small flow velocity gradient can exceed the other error sources. A detailed computer simulation evaluated the interdependencies of window length, beam width, vessel diameter, and viewing angle on the estimation of flow velocity.

Velocity and concentration measurements in multiphase flows by NMR

A nuclear magnetic resonance technique for the quantitative and noninvasive determination of flow-induced structure of a multiphase system is introduced and illustrated. It is a three-dimensional Fourier transform method in which a slice perpendicular to the flow is selected, frequency encoding is performed in the flow direction, and phase encoding is performed in the other two mutually orthogonal directions. Spatially resolved concentration and velocity profiles are extracted from this complete set of data. In particular, the nonuniform velocity and concentration profiles which result from a suspension of negatively buoyant particles flowing in a straight circular pipe are obtained. The average velocity range studied was between 1.6 and 31 cm/s and the average solid phase concentration was 10% by volume. The method is applicable to a wider range of these parameters, including much higher solid concentrations. Thus, we have been able to characterize a system which is difficult or impossible to study by other methods.

Laminar mixed convection in power law fluids in continuous flow electrophoresis systems

Laminar mixed convection in a power law fluid flowing between vertical parallel plates is considered. Heat is generated in the fluid by a non-uniform volumetric heat source and the plates are assumed to be adiabatic. The boundary-layer equations are solved using a finite-difference numerical technique. A knowledge of the resulting flow field is of interest in the study of continuous flow electrophoresis systems. Results are presented which show that flow redevelopments due to buoyancy effects occur as well as mixing due to a non-uniform velocity profile. It is shown that the use of pseudoplastic non-Newtonian fluids and the proper geometry and flow rates, can effectively prevent flow redevelopments and velocity profile dispersion under conditions for which they would otherwise occur.

Comparison of Three MHD Flow Control Methods for Self-Cooled Liquid Metal Blankets

The heat deposition in a blanket is concentrated near the first wall. Uniform liquid-metal velocity in a self-cooled blanket is unattractive, because it leads to low mixed-mean temperature rise through the blanket and reduced power conversion efficiency. The objective of MHD flow control is to use the electromagnetic forces to produce a non-uniform velocity distribution which gives a uniform temperature distribution over the thickness of the blanket. Three methods of MHD flow control are presented here and the MHD pressure drops corresponding to the three methods are compared. One of the methods, although successful at achieving nonuniform velocity profiles, permits a large circulation of electric current which produces a high pressure drop. The analytical results do not indicate a clear choice between the other two methods. The analytical results do point to possible difference in heat transfer performance with the two methods.

A two-dimensional analysis of laser heat addition in a constant absorptivity gas

The two-dimensional equations of motion describing the interaction between a laser beam and a flowing gas are considered. An implicit numerical scheme is used to solve these equations for unchoked flow through a converging-diverging nozzle. Separate grids are used for the fluid dynamics and the radiation equations. The ef- fects of beam focusing and cross-beam intensity profiles are included. The calculations are based upon real gas properties for all quantities except the gas absorptivity, which is taken as a constant. The solutions contain the expected hot central core region with cool gas near the walls. This results in steep temperature gradients in both the streamwise and cross-stream directions. The absorption zone acts as a blockage in the nozzle causing a nonuniform velocity profile at the inlet and an overall decrease in mass flow. The absorption region also forces the streamlines to move away from the axis of symmetry, although this effect is not strong. ASER thermal propulsion promises to deliver higher specific impulse from a rocket nozzle than can be at- tained with conventional chemical propellants. The laser thruster derives its energy by absorbing an incoming beam of electromagnetic radiation, rather than from the combustion process which is utilized in a conventional system. Because its energy supply is external to the working fluid, the heat added per unit mass in the laser engine is not rigidly limited. Instead, the temperature rise and hence, the specific impluse, depends upon the details of the radiation/gasdynamic in- teraction. This interaction is highly complex and strongly nonlinear. Improved understanding is required if this poten- tially attractive concept is to be developed. Experimental studies must certainly be undertaken (Refs. 1 and 2 describe experiments currently under way), but analytical results are also necessary to guide and interpret the experimental studies and to scale laboratory results to full-scale applications. The general picture of a laser thruster is similar to that depicted in Fig. 1. Both the laser beam and the cool unheated gas enter the nozzle from the upstream end. As the gas flows toward the throat, it is heated by absorption of ra- diant energy, causing it to accelerate. The converging nozzle walls also aid in accelerating the gas. For the space propul- sion application, the nozzle remains choked at all times and the flow becomes supersonic downstream of the throat. Although the mixing and recombination phenomena which take place in the supersonic portion of the nozzle are of im- portance to propulsive performance, they do not affect the absorption process and are considered to be secondary in the present discussion. In an attempt to focus on the radia- tion/gasdynamic interaction, the present analysis considers the unchoked nozzle where the Mach number remains sub- sonic throughout. The unchoked nozzle flowfield contains the essential physics of the absorption process and provides considerable insight into this complex interaction. The exten- sion to choked throat conditions is straightforwa rd and re- quires no additional computational advances. In a practical laser thruster, the absorption heating will probably be restricted to the region near the centerline of the nozzle, leaving a cool, unheated layer of gas near the wall3'4

Unsteady-state motion of a polydisperse gas suspension in a cocurrent-flow reactor

This article presents a system of equations for determining the velocity field of polydisperse gas and of the individual fractions of the polydisperse material as a function of channel height and radius, with allowance for changes in the regime of flow around the particles. The proposed method is based on a procedure developed previously for the calculation of the unsteady-state motion of a two-phase system with a polydisperse solid phase and with a nonuniform velocity profile of the carrier medium. The initial distribution of disperse-phase concentrations across the section of the channel is assumed to be uniform and equal to the concentration of particles in the fluidized bed. It is determined that the velocity profile of the single-phase flow differs from the steady-state profile, the actual profile being determined in particular by the design of the gas distributor. The velocity profile of the carrier medium depends on the distribution of disperse-phase concentration with respect to cross section and height of the channel. In the process of motion, there is a redistribution of particles of different sizes relative to the cross section of the channel, and this determines a change in structure of the flow of the polydisperse gas suspension.

Dynamics of Vertical Annular Liquid Jets

A theoretical model is developed to determine the flow characteristics for vertical liquid jets of annular cross section. The fully implicit numerical marching integration procedure is based on the parabolic flow theory of Patankar and Spalding. The method is more accurate and general than previous analytical models, since it accounts for all significant forces acting upon the jet and for complex boundary conditions, such as an ambient pressure difference across the jet or a non-uniform velocity profile at the inlet. Comparison of the results with existing experimental data indicates reasonable agreement, and the predictions correspond closely to those of the earlier theories for simplified flow cases.

Modeling and Experimental Determination of the Axisymmetric Flow in a Diesel Engine Cylinder

Internal air motion in a Detroit Diesel 6V-92 two-stroke engine cylinder was determined by an idealized axisymmetric finite difference model under steady flow conditions. This model was used to compute axial and tangential velocities with entrance angles of 25 and 40 deg. Laser Doppler anemometer measurements were made in one plane for comparison under steady flow bench test conditions using actual engine hardware. Calculations and measurements showed that the swirl induced by the angled inlet flow was responsible for the nonuniform axial velocity profiles. These profiles exhibited large peaks in the midradius region (between cylinder center and wall). Increasing the inlet angle from 25 to 40 deg sharpened the axial velocity peak and shifted it toward the cylinder wall. The measurements indicated nearly isotropic turbulence across the measurement plane. A better understanding of the relationship between design and internal flow is expected to lead to improved combustion, scavenging tradeoffs.

An analytical solution for dispersion in packed beds with low bed-to-particle diameter ratios

An analytic solution to the unsteady advective-diffusion equation is obtained which correctly describes the dispersion from an instantaneous point source in a flow field having a velocity distribution generally found in packed beds of low bed-to-particle diameter ratios. The non-uniform but symmetrical velocity profile shows a great influence on the local distribution of concentrations, C(τ,ϱ,ξ), but this effect disappears when only C m (τ,ξ), known as the breakthrough curve, is of interest. The effective dispersion coefficient ( K 2(τ) - (1/ Pe 2)) approaches a constant of 1/1196 for the particular velocity profile used as τ → ∞; it reduces itself to 1/192 as expected or laminar flow in empty tubes.

Gravity flow of coarse cohesionless granular materials in conical hoppers

This paper is concerned with the flow of cohesionless granular materials in conical hoppers. The granules are considered to be coarse such that the effects of interstitial fluid can be neglected. Two analytical approaches based upon the method of integral relations are presented. In the first the detailed variations of shear and normal stresses over the cross-section of the hopper are considered. The second is a very simple analysis which makes use of a mean normal stress averaged over the cross-section. The two analyses yield predictions for the flow rate which are almost identical. After the inclusion of an empirical correction factor to account for non-uniform exit velocity profiles and bulk density reductions near the outlet, the flow rate predictions and their variations with internal and wall friction angles and with hopper wall slope are found to agree well with experimental measurements.

The microinstabilities of a high-β plasma flow with a non-uniform velocity profile

The microinstabilities of a high-pressure plasma moving along a magnetic field with a non-uniform velocity profile are investigated. A similar problem was studied earlier by Dobrowolny on the basis of hydromagnetic equations with an oblique viscosity tensor. The present paper, unlike Dobrowolny's work, gives a kinetic analysis. Perturbations with transverse wavelength both larger and smaller than the ion Larmor radius are considered. The analysis indicates that there is a large family of microinstabilities of the ‘drift’ type whose mechanism differs from the classical Kelvin–Helmholtz instability.