Potential Flow Velocity Research Articles

Towed body measurements of flow noise from a turbulent boundary layer under sea conditions.

Results from an underwater experiment under sea conditions on flow noise beneath a flat-plate turbulent boundary layer are presented. The measurements were performed with a towed body at towing speeds U=2.3,…,6.1 m/s and depths h=-150,…,-100 m. Flow noise is measured with a linear array of equally spaced hydrophones (Δx=70 mm) that is orientated in streamwise direction and embedded within a laterally attached flat plate. In order to separate flow noise from ocean ambient noise and other acoustical noise sources wavenumber-frequency filtering is applied. The (nondimensionalized) spectral power density of flow noise Φ(ω) ⟨U∞⟩/ (⟨δ(∗)⟩ (1/2ρ ⟨U∞⟩)(2)) is found to scale like (ω⟨δ(∗)⟩/⟨U∞⟩)(-4.3) in a wide frequency range at higher towing speeds. Here, ω, ⟨δ(∗)⟩, and ⟨U∞⟩ denote frequency, boundary layer displacement thickness, and potential flow velocity in the array region, respectively. Potential flow velocity is estimated from numerical simulations around a symmetrical, two-dimensional body with a semi-elliptical nose. Evidence is given that a χ(2)-(Tsallis) superstatistics provides a reasonable representation of the probability distribution function of flow noise at higher towing speeds.

Unsteady MHD Forced Convective Heat and Mass Transfer Flow along a Wedge with Variable Electric Conductivity and Thermophoresis

Abstract In this paper the effects of thermophoresis on an unsteady magnetohydrodynamic (MHD) forced convective heat and mass transfer flow of viscous, incompressible and electrically conducting fluid over a wedge with variable electric conductivity have been investigated. The potential flow velocity has been taken as a function of the distance x and time t. The governing time dependent non-linear partial differential equations are transferred into locally similar ordinary differential equations and solve numerically by applying Nachtsheim- Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Steady solutions are compared with previously published works which show excellent agreement. The local similarity solutions for unsteady case are presented graphically for the velocity, temperature and concentration profiles in the boundary layer. The results show that skin friction coefficient, Nusselt number and Sherwood number are higher for the fluids of constant electric conductivity than those of the variable electric conductivity.

Calculation of radial forces in smooth shaft slot seals

A method based on determination of integral values of local pressure losses associated with potential flow velocity of a fluid in a smooth slot seal channel is proposed for calculating radial forces in slot seals in a case where the axes of the shaft and housing bushing of the seal assembly are eccentric. It differs from the well-known Lomakin calculation method based on differential calculation of local losses in terms of the flow rate of the fluid through the seal assembly. The proposed method can be used to simplify solution of the problem and to enhance the accuracy of calculations.

Parametric effects on the erosion–corrosion rate and mechanism of carbon steel pipes in oil sands slurry

In this paper, the parametric effects, including the sand concentration, slurry flow velocity and impact angle, on erosion–corrosion (E–C) of X65 steel in oil sands slurry were investigated using an impingement jet loop system by weight-loss test, polarization curve measurements and surface characterization. The mechanism of the steel E–C was determined. It was found that erosion components, including pure erosion and corrosion-enhanced erosion, are the dominant contributors to E–C of the steel, while the contribution of corrosion components is slight. With the increase of the sand concentration and slurry flow velocity, the E–C rate of the steel increases. However, an increasing impact angle would decrease the E–C rate of the steel in oil sands slurry. When the potential of the steel is relatively negative, erosion is dominant, especially at high flow velocities. At positive potentials, corrosion of steel is important in E–C process, especially at low flow velocities. An E–C map is built to illustrate mechanistically the E–C process depending on the steel potential and slurry flow velocity.

Non-Newtonian flow in microporous structures under the electroviscous effect

Single phase non-Newtonian microporous flow combined with the electroviscous effect is investigated in the pore-scale under conditions of various rheological properties and electrokinetic parameters. The lattice Boltzmann method is employed to solve both the electric potential field and flow velocity field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends on both the fluid rheological behavior and pore surface area ratio significantly. For the shear thinning fluid with power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electrovicous effect plays a more important role compared to the Newtonian fluid and shear thickening fluid. The high pore surface area ratio in the porous structure increases the electroviscous force and the induced flow resistance becomes important even to the flow of Newtonian and shear thickening fluids.

A uniformly valid series solution to the unsteady stagnation-point flow towards an impulsively stretching surface

The paper studies the problem of the unsteady two-dimensional stagnation-point flow of an incompressible viscous fluid over a flat deformable sheet. The flow is started impulsively from rest and the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. An analytical series solution is obtained by means of the homotopy analysis method (HAM). Also, the homotopy-Pade technique is employed. An explicit formula for the local friction coefficient is provided. The present formula, different from the perturbation solution, is accurate and uniformly valid for all dimensionless time in the whole spatial region and for all possible values of physical parameter λ, defined as the ratio of the potential flow velocity to the sheet sudden stretching velocity. Numerical tests are done to verify the present formula for its validity and accuracy.

Analytical study of heat transfer from circular cylinder in liquid metals

In this study the influence of a thin hydrodynamic boundary layer on the heat transfer from a single circular cylinder in liquid metals having low Prandtl number (0.004–0.03) is investigated under isothermal and isoflux boundary conditions. Two separate analytical heat transfer models, viscous and inviscid, are developed to clarify the discrepancy between previous results. For both models, integral approach of the boundary layer analysis is employed to derive closed form expressions for the calculation of the average heat transfer coefficients. For an inviscid model, the energy equation is solved using potential flow velocity only whereas for a viscous model, a fourth-order velocity profile is used in the hydrodynamic boundary layer and potential flow velocity is used outside the boundary layer. The third-order temperature profile is used inside the thermal boundary layer for both models. It is shown that the inviscid model gives higher heat transfer coefficients whereas viscous flow model gives heat transfer results in a fairly good agreement with the previous experimental/numerical results.

Fluid Flow And Heat Transfer from a Cylinder Between Parallel Planes

An integral approach is employed to investigate the effects of blockage on fluid flow and heat transfer from a circular cylinder confined between parallel planes. The integral form of the boundary-layer momentum equation is solved using the modified von Karman-Pohlhausen method, which uses a fourth-order velocity profile inside the hydrodynamic boundary layer. The potential flow velocity, outside the boundary layer, is obtained by the method of images. A third-order temperature profile is used in the thermal boundary layer to solve the energy integral equation for isothermal and isoflux boundary conditions. Closed-form solutions are obtained for the fluid flow and heat transfer from the cylinder with blockage ratio and Reynolds and Prandtl numbers as parameters. It is shown that the blockage ratio controls the fluid flow and the transfer of heat from the cylinder and delays the separation. The results for both thermal boundary conditions are found to be in a good agreement with experimental/numerical data for a single circular cylinder in a channel.

Electrostatic potential and plasma flow near the edge of a divertor tokamak

Explicit expressions are given to determine the electrostatic potential and ion parallel flow velocity in the region of an axisymmetric low collisionality tokamak with moderately large ion flow, electrostatic potential, and safety factor Q.

On the Persistence of Small Regions of Vorticity in the Protoplanetary Nebula

The fate of small regions of vorticity in a barotropic model of the protoplanetary nebula is investigated over thousands of years using a finite difference model. It is found that the coherence time for a small island of vorticity depends on its size, strength, orientation, and radial location in the nebula. Anticyclonic vorticity retains its coherence for longer times than cyclonic vorticity due to favorable interactions with the Keplerian shear flow. Rossby waves are generated as a result of mean vorticity gradients across the disk. The two-dimensional nebula evolves from discrete vortices into an axisymmetric flow consisting of small-amplitude vortex sheets at the radial locations of the initial vorticity. These vortex sheets induce an additional small, potential flow velocity superimposed on the Keplerian rotation curve.

COMBINED EFFECT OF SUCTION AND PRESSURE GRADIENT ON SEPARATION OF SUPERSONIC BOUNDARY LAYER

The effect of pressure gradient on separation of supersonic compressible boundary layer is studied at two different Mach numbers of 5.0 and 6.0. Moreover, the study of constant suction effect at different locations is performed for flow at Mach number 5.0. The non-similar boundary layer equations for steady compressible flow have been solved with a potential flow velocity distribution corresponding to power law edge Mach number variation. In this study, the changes in Prandtl number and the specific heat with temperature are considered. The resulting conclusion show that the higher adverse pressure gradient is less affected by a constant suction than the lower one.

Synthesis of unvoiced speech sounds using an aeroacoustic source model

An aeroacoustics-based method for synthesizing unvoiced speech sounds is presented. The source model is that of Howe (1975) for sound generated by flow of vorticity through a nonuniform duct. In this formulation three quantities must be known: the potential flow velocity, which changes according to the duct shape, the vorticity, and the velocity induced by vorticity in the flow and its images in the duct walls. The potential flow velocity magnitude is found using a transmission-line representation of the vocal tract, and the direction is found using a panel method. A model for the generation and evolution of vorticity has been developed in which the vortex shedding frequency is a random variable, and the vortex convects at a constant speed and direction. The computational model was used to simulate three cases: (1) a jet flowing through a pipe constriction, (2) a fricative sound (/s/), and (3) a VCV combination (/a s a/). Simulation results are presented and compared to experimental data, in terms of spectra and listening tests.

Deep circulation of groundwater in overpressured subglacial aquifers and its geological consequences

It is generally assumed that meltwater from the base of ice sheets is discharged in a relatively thin subglacial zone. Whereas this may be true for ice sheets resting on impermeable beds, many ice sheets, such as the glacial period ice sheets of North America and Europe, flowed over extensive aquifers. A theory is developed which suggests that high rates of meltwater discharge into these aquifers would have completely reorganised their flow fields, producing intergrated patterns of glacially pressurised flow controlled by the continental-scale form of the ice sheet surface rather than the small-scale topographic basins which determine modern aquifer extent. The theory is applied to the aquifers which underlay the Saalian ice sheet in The Netherlands, where it is shown that potential gradients and groundwater flow velocities would have developed which were two orders of magnitude greater than modern values and that the dominant flow vectors would have been normal to those of the modern flow. Thus, glacial/interglacial cycling in areas which have suffered periodic glaciation during the late Cenozoic may have experienced alternating phases of greater and lesser flow energy. It represents another example of climatically-driven cyclical change in the earth. Under highly energised glacial conditions, potential gradients much larger than modern values may have produced many common features of sediment disruption, such as diapirs, liquifaction structures and pipes, and forms such as glacial ‘doughnuts’ and pock marks, which have hitherto been explained by other processes. Deep and penetrative flushing of aquifers by glacial meltwater may have left a distinctive geochemical signal in them which may be used to test the theory. Gases such as methane, generated at shallow depth, may have been trapped beneath the glacial ‘cap-rock’, and may also have played an important role in these processes.

Effect of pressure gradient on the stability of compressible boundary layers

An investigation into the influence of pressure gradient (wall shaping) on the stability of compressible boundary layers is presented. The steady, compressible, nonsimilar boundary-layer equations are solved with a potential flow velocity distribution corresponding to a power law edge Mach number distribution. The stability of the mean flow is investigated using the small-disturbance compressible linear stability theory. The results indicate that two-dimensional second-mode (Mack) waves can be stabilised with pressure gradient. However, the effectiveness of the pressure gradient on the natural laminar flow control of two-dimensional second-mode waves decreases at hypersonic speeds. The maximum growth rate varies almost linearly with the pressure gradient level. The effect of pressure gradients on stabilising three-dimensional first-mode waves is much larger than their effect on stabilising two-dimensional first-mode waves.

An Inverse Method for the Design of Bodies of Revolution by Boundary Integral Modelling

A surface vorticity boundary integral method is presented for the design of bodies of revolution in axisymmetric flow. The analysis finds the desired body shape to deliver a prescribed surface potential flow velocity or pressure distribution. To achieve this the body surface is simulated by a flexible vorticity sheet of prescribed strength. Starting from an arbitrary first guess for the body shape, normally an ellipsoid, the flexible vortex sheet is successively realigned with its own self-induced flow field during an iterative process which converges accurately onto the desired shape. A well-proven analysis method is also presented for back-checking the final design.

Experimental and numerical investigation of soot deposition in laminar stagnation point boundary layers

Soot deposition from a hot gas flow to a cooled solid wall is investigated numerically and experimentally for laminar stagnation point flows. Numerical predictions of soot deposition are made by solving the coupled momentum, energy, and soot transport equations, which include the effects of variable transport properties and thermophoretic transport (i.e. mass transport down a temperature gradient) of soot particles. The results of the numerical computations indicate that the deposition rate, expressed in terms of the deposition velocity, increase with an increasing potential flow velocity gradient and decrease as the wall temperature approaches the freestream temperature. In addition, an insitu laser diagnostic technique is developed which provides simultaneous measurement of the soot deposit thickness and freestream soot concentration. The technique uses two laser beams (488 and 632 nm wavelength) coincident at a point adjacent to the deposition surface to measure the thickness of the deposit and the light extinction by airborne soot particles. Comparison of the experimental results to the numerical model indicates a critical velocity gradient beyond which the “sticking” fraction for the soot significantly decreases. This velocity gradient, which corresponds to maximum deposition, has been found to be approximately 2000 sec −1 for soot produced from fuel rich air/ethylene mixtures.

Thwaites' Method In Laminar Boundary Layer

Thwaites' method can be applied to find the boundary layer characteristics for either similar or nonsimilar flow for a variety of boundaries ranging from a simple flat plate (Blasius's Solution(1)) to a symmetrical airfoil. The flow properties to be determined include potential flow velocity distribution, displacement thickness, momentum thickness and coefficient of friction. Furthermore,the location of flow separation is readily obtainable from the numeric value of local coefficient of friction. Thwaites' Method is able to provide satisfactory approximate solution to different types of simple boundary as long as the flow is laminar and not separated. For a complex curvature such a an airfoil Thwaite' Method is yet to be tested. In this context, we will look into the applicability of Thwaites' Method for a particular symmetrical airfoil, NACA 0012.

Presheath profiles in simulated tokamak edge plasmas

Steady state magnetized plasmas produced by the PISCES experiment are used to study plasma-wall interaction phenomena relevant to confinement devices such as tokamaks. An experimental investigation of the presheath region that extends from a wall surface into “simulated tokamak” edge plasmas along magnetic field lines is reported. Diagnostics especially developed for this work include a fast-scanning multiple Langmuir/Emissive/Mach probe system and a CID camera imaging system. Measurements of density, electron temperature, floating potential, space potential, and bulk plasma flow velocities have been obtained in plasmas with densities ranging from 10 12 to 10 13 cm −3, electron temperatures from 5 to 15 eV. and axial magnetic fields of 0.2 to 1.4 kG. Plasma density profiles along the magnetic field typically show a characteristic factor of 2 decrease towards the wall surface. A plasma potential variation in the near presheath zone of order 0.5 T e is measured, consistent with the bulk plasma flow approaching the ion sound speed near the wall surface, as inferred from a simple “free fall” model. A Boltzmann model for the presheath density profile accuracy tracks the density profile measured both by the Mach probe and by spectroscopic means. Flow profiles are used as a consistency check on various magnetized Mach probe theories. Results suggest that cross-field transport of parallel momentum through viscosity is relatively unimportant in PISCES plasmas and thus may be unimportant in tokamak boundary layer plasmas. Discharges with non-thermal electrons display axial profiles of space potential and floating potential which indicate a “hotter” electron distribution function near the wall surface, consistent with “colder” electrons being reflected by the presheath potential drop.

Curvature and pressure-gradient effects on a small-defect wake

A fully developed two-dimensional turbulent wake was deflected by an airfoil-like thin plate placed at small angles in the external flow. The response of the mean-flow and turbulence properties of the wake to the ‘mild’ pressure gradient and the ‘mild’ streamline curvature caused by the deflection is studied. Owing to the small defect velocity, the extra strain rates are large compared with the main shear strain and the Reynolds stresses are strongly influenced by both the pressure gradient and the streamline curvature. The defect velocity relative to an appropriately chosen ‘potential-flow velocity’, and the mean vorticity, however, are not as strongly influenced by the curvature. Changes in the magnitudes of the Reynolds-stress components are much larger than would be caused by the simple rotation of coordinates aligned with the wake path. Most turbulence-model parameters are influenced significantly, while some pure turbulence parameters, such as the Taylor microscale, are relatively uninfluenced. The rapid and lagged responses are apparent and the terms in the transport equation for turbulent kinetic energy indicate that the response of the production terms is almost instantaneous, while the diffusion and dissipation terms are delayed.

HEAT AND MASS TRANSFER AT AN UPSTREAM-FACING BLUNT FACE SITUATED IN A UNIFORM ONCOMING FLOW

A numerical investigation was performed to determine the heat /mass transfer from upstream-facing blunt faces of axisymmetric and plane two-dimensional bodies, which are situated such that a uniform flow approaches normal to the respective blunt faces. Face-average and stagnation-point Nusselt and Sherwood numbers, velocity and temperature profiles, and streamline maps are presented over the Reynolds number range from 5 × 103 to5 × 104. Average Nusselt number predictions for Pr = 0.7 (heat transfer in air) and average Sherwood numbers for Sc = 2.5 (naphthalene sublimation in air) agreed well with experiment. These results are well represented by a 0.5-power Reynolds number and 0.4-power Prandtl number fit. Stagnation-point Nusselt and Sherwood number predictions showed excellent agreement with boundary layer results using experimentally measured pressure distributions as input. Boundary layer results based on potential flow velocities as input overpredicted both the present numerical results and experimen...