Stagnation Point Region Research Articles

On the interaction of vortices with mixing layers

We describe the perturbations introduced by two counter-rotating vortices—in a two-dimensional configuration—or by a vortex ring—in an axisymmetric configuration—to the mixing layer between two counterflowing gaseous fuel and air streams of the same density. The analysis is confined to the near stagnation point region, where the strain rate of the unperturbed velocity field, A0, is uniform. We restrict our attention to cases where the typical distance 2r0 between the vortices—or the characteristic vortex ring radius r0—is large compared to both the thickness, δv, of the vorticity core and the thickness, δm∼(ν/A0)1/2, of the mixing layer. In addition, we consider that the ratio, Γ/ν, of the vortex circulation, Γ, to the kinematic viscosity, ν, is large compared to unity. Then, during the interaction time, A0−1, the viscous and diffusion effects are confined to the thin vorticity core and the thin mixing layer, which, when seen with the scale r0, appears as a passive interface between the two counterflowing streams when they have the same density. In this case, the analysis provides a simple procedure to describe the displacement and distortion of the interface, as well as the time evolution of the strain rate imposed on the mixing layer, which are needed to calculate the inner structure of the reacting mixing layer as well as the conditions for diffusion flame extinction and edge-flame propagation along the mixing layer. Although in the reacting case variable density effects due to heat release play an important role inside the mixing layer, in this paper the analysis of the inner structure is carried out using the constant density model, which provides good qualitative understanding of the mixing layer response.

The Effects of Nozzle Diameter on Impinging Jet Heat Transfer and Fluid Flow

Abstract The effects of nozzle diameter on heat transfer and fluid flow are investigated for a round turbulent jet impinging on a flat plate surface. The flow at the nozzle exit has a fully developed velocity profile. A uniform heat flux boundary is created at the plate surface by using gold film Intrex, and liquid crystals are used to measure the plate surface temperature. The experiments are performed for the jet Reynolds number (Re) of 23,000, with a dimensionless distance between the nozzle and plate surface L/d ranging from 2 to 14 and a nozzle diameter (d) ranging from 1.36 to 3.40 cm. The results show that the local Nusselt numbers increase with the increasing nozzle diameter in the stagnation point region corresponding to 0⩽r/d⩽0.5. This may be attributed to an increase in the jet momentum and turbulence intensity level with the larger nozzle diameter, which results in the heat transfer augmentation. In the mean time, the effect of the nozzle diameter on the local Nusselt numbers is negligibly small at the wall jet region corresponding to r/d>0.5.

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier–Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier–Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases.

Self-similar solution of the unsteady flow in the stagnation point region of a rotating sphere with a magnetic field

The unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid in the forward stagnation point region of a rotating sphere in the presence of a magnetic field are investigated in this study. The unsteadiness in the flow field is caused by the velocity at the edge of the boundary layer and the angular velocity of the rotating sphere, both varying continuously with time. The system of ordinary differential equations governing the flow is solved numerically. For some particular cases, an analytical solution is also obtained. It is found that the surface shear stresses in x- and y-directions and the surface heat transfer increase with the acceleration, the magnetic and the rotation parameters whether the magnetic field is fixed relative to the fluid or body, except that the surface shear stress in x-direction and the surface heat transfer decrease with increasing the magnetic parameter when the magnetic field is fixed relative to the body. For a certain value of the acceleration parameter, the surface shear stress in the x-direction vanishes while the surface shear stress in the y-direction and the surface heat transfer remain finite. Also, below a certain value of the acceleration parameter, reverse flow occurs in the x-component of the velocity profile.

External Heat Transfer Predictions in a Highly Loaded Transonic Linear Turbine Guide Vane Cascade Using an Upwind Biased Navier–Stokes Solver

External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds-averaged Navier–Stokes equations with algebraic (Arnone and Pacciani, 1998), one-equation (Spalart and Allmaras, 1994), and two-equation (low-Re k–ε, Biswas and Fukuyama, 1994) turbulence closures are solved with a fully implicit time-marching finite volume method. Comparisons with measurements (Arts et al., 1990; Arts, 1994) for a highly loaded transonic turbine nozzle guide vane cascade show good agreement in some cases, but also reveal problems with transition prediction and turbulence modeling. Special attention has been focused on the low-Re k–ε model concerning the influence of the inlet boundary condition for the ε-equation and problems in the stagnation point region.

Development of flow and heat transfer of a viscous fluid in the stagnation-point region of a three-dimensional body with a magnetic field

The development of flow and heat transfer of a viscous electrically conducting fluid in the stagnation point region of a three-dimensional body with an applied magnetic field is studied when the external stream is set into an impulsive motion from rest and at the same time the surface temperature is suddenly raised from that of the surrounding fluid. This analysis includes both short time solution (Rayleigh-type of solution) and the steady-state solution as time tends to infinity (Falkner-Skan type of solution). The unsteady three-dimensional boundary layer equations represented by a system of parabolic partial differential equations are solved numerically using an implicit finite-difference scheme. For certain particular cases analytical solutions are obtained. In the absence of the magnetic field, the reverse flow occurs in the transverse component of the velocity in a certain portion of the saddle-point region (−1≦c<−0.4, wherec=b/a is the ratio of the velocity gradients in they- andx-directions at the edge of the boundary layer). The magnetic field delays or prevents the reverse flow. The surface shear stresses in the principal and transverse directions and the surface heat transfer increase with the magnetic field both in nodal point (0≦c≦1) and saddle point (−1≦c<0) regions. For a fixed magnetic field, the surface shear stress inx-direction and the surface heat transfer increase with time in nodal and saddle point regions, but the surface shear stress in the transverse direction increases with time for 0<c≦1 and decreases with increasing time for −1≦c<0.

Technical NoteTurbulent heat transfer from a convex hemispherical surface to a round impinging jet

As an effective method to enhance heat and mass transfer, impinging jets have been widely used in a variety of engineering applications such as cooling of hot steel plates, tempering of glass, drying of papers and textiles, cooling of turbine blades and electronic components, and manufacturing of TFT-LCD plate. Numerous studies of the heat transfer and flow characteristics for the jet impingement on surfaces have been reported. These studies have dealt with the effects of Reynolds number, nozzle-to-surface distance, nozzle geometry, jet orientation, multiple jets, cross flow, and impinging surface shape on the resulting flow and heat transfer. Several review and summary papers on the impinging jet heat transfer have been published by Martin [1], Jambunathan et al. [2], and Viskanta [3]. Although many different jet characteristics have been considered, a great majority of impinging jet studies in the past were on the flat surface. However, many engineering applications of jet impingement cooling on curved surfaces may be encountered. A few papers have studied the impinging jet heat transfer from the curved surface. Chupp et al. [4]studied the heat transfer characteristics with an array of round jets impinging on a concave surface. Thomann [5]and Hrycak [6]reported the total heat transfer on the concave surface is higher than on the flat surface due to larger surface area especially for small nozzle-to-surface distances. For a highly concave surface, the optimum distance is less than for the equivalent flat surface case. With decreasing surface curvature and increasing nozzle-to-surface distance, the heat transfer characteristics approach those for the flat surface. Gau and Chung [7]investigatged the effects of surface curvature on the slot jet impingement heat transfer along semi-cylindrical concave and convex surfaces. They observed a series of three-dimensional counterrotating vortices near the stagnation point region on the convex surface. And they also found Taylor–Görtler vortices initiated along the concave surface. Yang et al. [8]investigated jet impingement cooling on the semi-cylindrical concave surface with two different nozzles (round edged nozzle and rectangular edged nozzle) . In the present study, the local Nusselt numbers are measured for an air jet issuing from a long straight pipe and impinging perpendicular on the convex hemispherical surface. The experiments are made for Re = 11 000–87 000, L⧹ d = 2–10, and D⧹ d = 10.6. An electrically heated gold film Intrex (a very thin gold-coated polyester substrate sheet) is used to create a uniform heat flux on the convex surface. The temperature on the surface is measured using a thermochromic liquid crystal and a digital color image processing system.

Unsteady free convection flow in the stagnation-point region of a three-dimensional body

The unsteady free convection flow in the stagnation-point region of a heated three-dimensional body placed in an ambient fluid is studied under boundary layer approximations. We have considered the case where there is an initial steady state that is perturbed by a step-change in the wall temperature. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using a finite difference scheme. The presented results show the temporal development of the momentum and thermal boundary layer characteristics.

Unsteady free convection flow in the stagnation-point region of a rotating sphere

The unsteady free convection boundary-layer flow in the forward stagnation-point region of a sphere, which is rotating with time-dependent angular velocity in an ambient fluid, has been studied. Both constant wall temperature and constant heat flux conditions have been considered. The non-linear coupled parabolic partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The skin friction and the heat transfer are enhanced by the buoyancy force. The effect of the buoyancy force is found to be more pronounced for smaller Prandtl numbers than for larger Prandtl numbers. For a given buoyancy force, the heat transfer increases with an increase in Prandtl number, but the skin friction decreases.

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time.

Electrostatic effects in inertial impactors

A focusing impactor is used to study the influence of particle charge q on the capture efficiency versus Stokes number curve η( S). For highly charged particles, image attraction to the collector leads to considerable particle capture even at S = 0. This produces long subcritical tails in the η( S) curve (poor sizing resolution) and reduces the value S ∗ of S at which ν = 1 2 . A similar behavior, now due to Brownian motion, arises for singly charged ultrafine particles, with a negligible influence of the image force. Both types of tails are reduced or eliminated by a repulsive electric field E between the collector and the nozzle, though at the price of increasing S ∗ . For repelling fields E large enough for the subcritical tails to disappear, S ∗ is a function only of the ratio ZE/U between the electrical and hydrodynamic velocities of the particles. The functional dependences S ∗(ZE/U) is characterized experimentally for a nearly incompressible thin-plate orifice nozzle flow at Reynolds number Re = 68. Calibration aerosols include singly or doubly charged oil droplets with diameters between 16 and 155 nm. Also polystyrene latex spheres (PSL) 74 nm in diameter generated from a water suspension by electrospray, whose charge q was narrowly controlled in the range 540 > q e > 390 with a differential mobility analyzer. The analysis of the rate of deposition in the stagnation point region in the limit S = 0 predicts the repulsive fields required to offset the tails, in fair agreement with those observed both for singly and doubly charged as well as highly charged particles. The conclusion is reached that impactors whose detector is an electrometer can attain rather high resolutions in all the range of sizes and charges explored.

A numerical study of vorticity layers in a two-dimensional stratified shear flow

A numerical study is conducted to find out the conditions of occurrence of a secondary Kelvin-Helmholtz instability in the thin layers (referred to as baroclinic layers) that form in a stably-stratified shear layer. For this purpose, three high resolution calculations of a moderately stratified shear layer have been carried out, at a fixed Reynolds number. The wavelength of the initial perturbation is progressively increased, starting from the fundamental wavelength predicted by linear stability theory up to twice this fundamental wavelength. The baroclinic layer of the flow is shown to lengthen and destabilize progressively from one calculation to the other, eventually bearing a secondary Kelvin-Helmholtz instability. The structure and dynamics of the baroclinic layers of the three calculations are examined in the frame of a theoretical model proposed by Corcos and Sherman ([1]). An excellent agreement with the predictions of this model have been found. We next show that the stability of the layer is controlled by the large-scale Kelvin-Helmholtz vortex, via the strain field that it induces in the stagnation point region of the layer. A consequence of this study is that secondary Kelvin-Helmholtz instabilities are fostered by the pairing of primary Kelvin-Helmholtz vortices in a strongly-stratified shear layer.

Forced convection film boiling in the stagnation region of a molten drop and its application to vapour explosions

This work was undertaken as part of an investigation into the heat transfer mechanism related to thermal explosion. The theoretical model of forced convection film boiling in the stagnation point region of an axi-symmetrical molten drop is presented. The model is particularly relevant to the coarse pre-mixing stage of vapour explosion: it takes account of the fact that, at this stage, the hot substance is molten. Stagnation point momentum (Falkner-Skan) and energy equations, for cold and hot liquids and for the vapour layer, were solved numerically, with a wide range of boundary-matching conditions at the interfaces. The model presented, by covering a wide range of the conditions and parameters, is more general than the cases discussed in other publications. For this reason the results can be applied not only to the coarse pre-mixing stage of vapour explosion, but also to other situations, where three-phase forced convection occurs on an axi-symmetrical body.

Evaluation of the Stagnation Point Region Overshoot

Stagnation point region overshoot is the augmentation of total heat transfer owing to the presence of insulation at the stagnation point region of an otherwise isothermal body. Evidence summarized by the present work indicates that this paradoxical event can be made to occur. The overshoot is due to the singularly high temperature gradient that is impressed upon the boundary layer just as it arrives at the leading edge of the heated surface after passing over the insulated central portion. The evidence comprises experimental results based on the mass-heat analog using sublimation of naphthalene and on theoretical boundary layer calculations using a method of local similarity. In the experiments, the insulated surfaces were simulated with inert wax, and isothermal regions with active naphthalene. The surfaces were circular disks facing uniform airstreams. The finding was that the total rate of mass transfer would be as much as 10 percent greater than that of a fully active disk if the radius of the central inert region were half the radius of the disk. Put another way, if only the 30-percent annulus at the outer edge of the disk were active, it would transfer mass at the same rate as the completely active disk under the same circumstances of flow. Corresponding results are expected from analogically heated disks operating with Prandtl number near unity and disk Reynolds number ranging from 5000 to 250,000.

Effect of an acoustic wave on mean-flow stability

The interaction between an acoustic wave and a mean flow near the surface of a bluff body will be discussed. The base flow solution will be presented. A nonlinear analysis will be used to find the region of validity of the linear stability solution. Nonlinear effects will be shown to stabilize disturbances outside the stagnation point region.

Combustion of a carbon surface in a stagnation point flow field part II: Ignition and quench phenomena

This paper presents results of a theoretical investigation of the combustion of a carbon surface in an oxidizing cross flow in the stagnation point region. A preceeding study by the authors, which has mainly been concerned with the influence of the free stream parameters on the rate of combustion, is extended to the investigation of ignition and quench phenomena leading to discontinuous behavior of the steady state solutions. With respect to experimental studies of the stagnation point combustion of carbon, which are based on different mechanisms of controlling the combustion process, two of these mechanisms are distinguished in this paper. On the one hand an externally generated heat flux to the surface may control the process, and on the other hand the surface temperature may be the controlling or independent variable. The ignition and quench behavior strongly depends upon these controlling mechanisms. In the first case up to five steady state solutions may be obtained corresponding to different heterogeneously or homogeneously ignited or quenched states. If the surface temperature is the controlling parameter no heterogeneous ignition or quenching occurs. Then only up to three steady state solutions are possible, which correspond to an ignited or quenched homogeneous reaction. The sensitivity of the ignition and quench behavior to variations in the free stream parameters and in the heterogeneous reaction rate data is investigated with respect to both controlling mechanisms. Emphasis is put on the influence of the Boudouard reaction rate data, which are rather uncertain.

Diffusion flame extinction at small stretch rates: The mechanism of radiative loss

A theoretical analysis of diffusion flame extinction in the stagnation point region of a condensed fuel has been made including radiative heat loss from the fuel surface. In addition to the blowoff limit normally found when flame stretch rate is large, an extinction limit has been identified when the flame stretch rate becomes sufficiently small. This limit occurs as a result of flame temperature reduction when the rate of radiative loss becomes substantial compared with the rate of combustion heat release. A flammability map using oxygen mass fraction and stretch rate as coordinates shows that the extinction boundary consists of a blowoff and a radiative extinction branch. The merging point of the two branches defines a fundamental low oxygen flammability limit.

The influence of liquid viscosity and system pressure on stagnation point vapour thickness during forced-convection film boiling

The theoretical model of forced-convection film boiling in the stagnation point region of an axisymmetrical particle is demonstrated. Due to the ‘lubrication effect’ of the laminar vapour flow around the hot particle the liquid flow is slightly perturbed from the frictionless flow. This perturbation depends upon particle surface, free-stream and saturation temperatures. The effect of vapour velocity from the interface, towards the hot surface, on the heat flux conducted from the particle is taken into account. An attempt has been made to include the influence of the system pressure on the phenomenon—so the presented model can be utilized in the description of the coarse premixing phase during vapour (thermal) explosion. The applicability of the model to the calculation of vapour layer thickness in the stagnation point of the sphere and also of heat fluxes at the interface and at the hot surface (the important parameters which influence stability and film boiling collapse) is shown.

A direct method for studying particle deposition onto solid surfaces

An experimental technique has been developed to study the deposition of colloidal particles under well controlled hydrodynamic conditions. The deposition process is observed under a microscope and recorded on video tape for further analysis. Fluid flow conditions in the experimental set-up were determined by numerical solution of the Navier-Stokes equations. Mass transfer equations were solved numerically (taking into account hydrodynamic, gravitational, electric double layer, and dispersion forces) for the stagnation point region. Also, some analytical solutions are presented. Deposition has been studied of 0.5μm polystyrene latex particles on cover glass slides used as collectors. From an analysis of the shape of the coating density vs. time curves and independently from the distribution of the particles on collector surfaces, it was found that one particle is able to block an area of about 20 to 30 times its geometrical cross-section. The initial flux of particles to the collector for a given salt concentration was found to depend strongly on the method of cleaning the collector surface. In general the flux and the escape of particles to and from the collector surface are sensitive to the interaction energy at small separations. The direct method of observing particle deposition and detachment could lead to important insights into the nature of particle-wall interactions at near contact.