External Stream Research Articles

SECOND-ORDER EFFECTS IN A LAMINAR AXISYMMETRIC PLUME SUBJECTED TO AN EXTERNAL COFLOWING UNIFORM STREAM

Asymptotic solutions are found for the steady laminar mixed convective flow of a Boussinesq fluid above a point heat source sited in an aligned uniform coflowing stream. The equations are first developed in vorticity-temperature form and then analysed in inner and outer regions using matched asymptotic expansions. Attention is restricted to the case of unit Prandt1 number and consideration is given to the effects of varying the strength of the external stream. When this is zero, analytical solutions are available for the zeroth-order shear-layer flow thus providing useful checks on the numerical procedure employed for non-zero strengths. The higher-order correction, which is of higher order than for the two-dimensional line-source problem, is found up to arbitrary multiples of the leading-edge shift eigensolution. The analysis facilitates the investigation of the non-parallel flow stability of this problem and this will be reported elsewhere.

The Turbulent Premixed Boundary Layer with Variable Enthalpy

Abstract A previous analysis of the turbulent boundary layer which arises from the injection of premixed reactants into a stream of combustion products is extended to the case of variable enthalpy. The variation in enthalpy can be due either to losses or gains in heat in the product stream or to differences in the stoichiometry of reactants and products and leads to a temperature in the external stream different from the adiabatic equilibrium temperature of the injected reactants. The thermochemistry of the system is described by a multivariate probability density function involving two scalars, the progress variable and an enthalpy variable. Three different forms of the probability density function of the distributed enthalpy within products are considered. An extension to incorporate the pdf of the velocity components and those scalars permits description of the aerothermochemistry of the system. Similarity solutions of the complete set of equations for first and second moment quantities permits the eff...

An Automatic Generation of FORTRAN Code for the Finite Difference Method

It is, in general, a tedious and mistake-prone task for us to prepare a FORTRAN program which solves differential equations by means of the finite difference method. To avoid this procedure, the authors have developed a LISP program which generates the necessary FORTRAN code. The practical utility of the present LISP program is amply demonstrated by using this program for ordinary and partial differential equations. As an example, the authors solve the boundary layer equations which govern the flow on a rotating cone in a linearly retarded external axial stream. It is shown that as the effect of rotation grows, the flow ceases to separate from the wall, and then the axial, circumferential wall shear stresses and the local Nusselt number increase.

Analysis of turbulent underexpanded jets. I - Parabolized Navier-Stokes model, SCIPVIS

A new computational model (SCIPVIS) is described which predicts the multiple-cell wave/shock structure in underexpanded or overexpanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet-mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility-corrected two-equation turbulence models. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial-marching solution can be obtained. The features of SCIPVIS are reviewed, and calculations are described exhibiting the influence of turbulence modelling, jet temperature, and flight velocity on the jet shock structure.

THE EFFECT OF FREE STREAM CONCENTRATION ON HEAT AND BINARY MASS TRANSFER WITH THERMODYNAMIC COUPLING IN CONVECTION ON A ROTATING DISC†

Simultaneous heat and mass transfer, which arises from injecting a gas (helium or hydrogen) from or through the solid surface into a flowing external stream, has been studied for a rotating disc geometry. The effects of concentration levels of the injected gas in the external stream on the thermodynamic coupling in the presence of centrifugal force have been investigated over a wide range of Tw/Te. Boundary layer equations for heat and mass transfer were solved numerically. Exact and linearized approximate solutions were obtained. The results have shown that the thermal diffusion effect on mass transfer becomes increasingly important as the free stream concentration increases and as Tw/Te departs from unity. The diffusion thermo effect on heat transfer was found to be the most important when the free stream concentration is zero and as Tw/Te approaches unity.

Single-sided ventilation — Part I. The flow between a cavity and external air stream

This paper considers in detail particular flows of the kind which give rise to single-sided ventilation. It presents an experimental study of turbulent flow in a square cavity, with particular reference to the shear layer between cavity and external flows. Hot-wire measurements were carried out in a cubical cavity placed beneath the floor of the test section of the boundary-layer tunnel. Results are presented for zero, positive and negative external pressure gradients, and include time-mean velocity, as well as turbulence intensities, kinetic energy, and shear stress. Flow visualization conducted in a smoke tunnel reveals the behaviour in the shear layer and within the cavity. Predictions of two-dimensional flow fields have been undertaken using a finite-difference scheme and a two-equation model of turbulence. Comparisons with measurements show good agreement in regions where the comparison is valid, and reference to the flow-visualization studies reveals that the essential features of the entire flow field are reproduced by the analytical model.

Conical flows in the neighborhood of breaks in the edges of surfaces separating cocurrent supersonic streams of perfect gas

An investigation is made into the conical flows which occur when a perfect (inviscid and nonheat conducting) gas flows over the “terminal” edges of surfaces with breaks separating an “external” and an “internal” flow with velocity vectors parallel to the line of intersection of the surfaces. Such flows are observed, in particular, in the neighborhood of breaks in the outlet edge of a nozzle of rectangular cross section with a “straight” or “skewed” exit plane under conditions of underexpanded flow of a supersonic jet into a cocurrent supersonic stream. By means of a linear analysis flow patterns corresponding to various flow interaction regimes and edge geometries are constructed and a law of similarity is formulated. The validity of the results thus obtained is confirmed by examples of the numerical solution of the complete nonlinear system of Euler equations. In this connection, within the framework of the approach outlined in [1], as a rule, together with the shocks and characteristic surfaces bounding the conical flow in question, the shear discontinuity separating the external and internal streams is constructed.

A Method of Approximate Dimensionless Correlations for Convective Heat Transfer Between a Cavity Wall Surface and the External Main Stream

A Method of Approximate Dimensionless Correlations for Convective Heat Transfer Between a Cavity Wall Surface and the External Main Stream

Urethral resistance? Urodynamic concepts of physiological and pathological bladder outlet function during voiding

Keywords: urethral resistance; pressure/flow relation; external stream velocity; flow rate controlling zone; flow rate/volume relation; bladder outlet obstruction; voiding efficiency

Single-sided ventilation — Part II. further considerations

This paper extends an earlier report of measurements and computer predictions of flows in a cubical cavity exposed on one side to the scavenging effect of an external stream. Further measurements and photographs are presented; they are consistent with each other and with the predictions of the computational model. Specifically, comparisons are made between measured and predicted mean velocities and turbulent shear stresses, and photographs are used to elucidate features of the shear layers generated by accelerating and decelerating external flows. The computer model is used to deduce approximate relations between internal turbulent activity (measured by mean velocity, turbulence energy and shear stress) and external velocity, percentage ‘window’ opening and relative position of the plane walls upstream and downstream of the cavity.

Interactive Phenomena in Supersonic Jet Mixing Problems, Part 11: Numerical Studies

Applications of the numerical techniques discussed in Part I of this article are presented. Fundamental wave/shear-layer interaction calculations are performed exhibiting the waves produced by high-speed turbulent mixing processes and the interactions of an expansion fan and shock wave with a developing shear layer. Calculations for an underexpanded supersonic jet into a supersonic external stream at different velocity ratios are presented which delineate betweeen weakly interactive and strongly interactive processes in the jet near field. Calculations for the multiple-cell shock structure of an underexpanded jet into still air exhibit the damping of wave intensities by the turbulence and compare quite favorably with available data.

Computation of base flow characteristics with uniform blowing

Blowing at bluff body base was considered under different conditions and for small amount of blowing this problem was solved using dividing streamline model [1]. The effect of supersonic blowing on the flow characteristics of the external supersonic stream was studied in [2–4]. The procedure and results of the solution to the problem of subsonic blowing of a homogeneous fluid at the base of a body in supersonic flow are discussed in this paper. Analysis of experimental results (see, e.g., [5]) shows that within a certain range of blowing rate the pressure distribution along the viscous region differs very little from the pressure in the free stream ahead of the base section. In this range the flow in the blown subsonic jet and in the mixing zones can be described approximately by slender channel flow. This approximation is used in the computation of nozzle flows with smooth wall inclination [6, 7]. On the other hand, boundary layer equations are used to compute separated stationary flows with developed recirculation regions [8] in order to describe the flow at the throat of the wake. The presence of blowing has significant effect on the flow structure in the base region. An increasing blowing rate reduces the size of the recirculation region [9] and increases base pressure. This leads to a widening of the flow region at the throat, usually described by boundary-layer approximations. At a certain blowing rate the recirculation region completely disappears which makes it possible to use boundary-layer equations to describe the flow in the entire viscous region in the immediate neighborhood of the base section.

On the aerodynamics of natural ventilators

The performance of natural ventilators subjected to the action of a free stream are experimentally investigated by using the method of Baturin. To analyse experimental data a mathematical model of the extraction characteristics is introduced. The model has been obtained from considerations of natural ventilator behaviour under extreme conditions within the normal operating range (zero external free stream and zero mass flow through the ventilator) and includes a correction term which accounts for the interference between the external wind and the flow through the ventilator. In this model ventilator performances are explained in terms of only four parameters which in turn are easily calculated from experimental results. Finally, the steps followed to enhance the performance of an existing ventilator are shown as an illustration of the use of the model here presented.

Non-dimensional numbers associated with the evaporation from a capillary porous medium / Nombres sans dimensions associés à l'évaporation au sein d'un milieu poreux

ABSTRACT The different factors that produce evaporation of moisture from a capillary porous medium are being investigated. Thermodynamic measurements of the porous medium-air-water system and a mathematical model have permitted the establishment of some correlations between the principal non-dimensional numbers associated with heat and mass transfer between the evaporating water in the porous medium and the external gas stream. These correlations lead to the prediction of some important parameters such as the depth of the surface of vaporization and the exchange coefficients of the heat and mass transfer during the evaporation from a capillary porous medium.

An internal recycle mixer for solvent extraction. Mass transfer characterization with liquid surfactant membranes

A novel internal recycle mixing device, in which the solvent-to-feed ratio may be enhanced without the introduction of an external recycle stream, is proposed. The device was tested on, and found to be effective for, the extraction of ammonia from water using a liquid surfactant membrane (LM) system. A detailed model of the mass transfer processes occurring within the system is presented and used to develop an equation suitable for th sizing of LM contactors. This equation accounts for the effect of the internal reagent on the overall mass transfer rate. The experimental data are in favorable agreement with the model predictions.

Calculation of three-dimensional boundary layer on a triangular plate of finite length in a hypersonic stream

The results are given of the calculation of a three-dimensional boundary layer on a triangular plate of finite length in a regime of strong viscous interaction with an external hypersonic stream for both symmetric flow as well as in the presence of an angle of slip. The influence of the change in the pressure on the trailing edge of the plate on the boundary layer characteristics is investigated.

Take-off ground roll of propeller driven aircraft

using a heater-burner to simulate the engine exhaust, seemed to indicate that the two-dimensional CD nozzle with exit aspect ratios less than 10 would not produce less IR signature than the equivalent axisymmetric nozzle (see Fig. 67 of Ref. 5). The effect of the engine swirl is expected to be more important when external streams are present, since in such cases external mixing due to shear is otherwise reduced because of the lowered velocity differences between the plume and external stream. In conclusion, a simple modeling technique has been developed to provide economical yet adequate prediction of two-dimensional-nozzle plume properties for IR signature analysis. Successful models were developed for ADEN, twodimensional CD, and two-dimensional plug nozzles with and without bypass flow and/or engine swirl. A 10-deg engine swirl was found to reduce the predicted plume temperature dramatically. Therefore the inherent engine swirl, though undesirable from the performance point of view, appears to be highly effective in reducing the IR signature of a twodimensional-nozzle plume.

Deformation of a drop in a viscous stream and conditions of existence of its equilibrium form

The difference method is used for obtaining a solution of the problem of unsteady motion of a drop in a stream, taking into account its deformation under conditions of axial symmetry. The fluid inside and outside the drop is assumed viscous and incompressible. The stable forms of drop are represented for various Reynolds and Weber numbers of external stream. By analyzing the conditions for normal stresses at the drop boundary, the critical Weber number was obtained, which establishes the conditions of existence of equilibrium form of the drop.

The investigation of a compressible laminar boundary layer past an elliptical cone

The self-similar boundary layer on a sharp circular cone was calculated first by Vvedenskaya[1]. The boundary layer equations were solved in a plane containing an outflow line which lies in this case in the symmetry plane at the leeward side, and after that a solution was constructed by using a marching method along a circumferential coordinate. The calculation results for the boundary layer on an elliptic cone were presented in Bashkin's papers [2–4]. However, only the middle angles of attack (30–50°) were considered. where the outflow line of an external stream is located in the windward symmetry plane, and the flow pattern in the boundary layer is analogous to that of the circular cone. In the present the laminar boundary layer on an elliptic cone is studied for a wide range of angles of attack. The boundary layer has been calculated at small incidence when the outflow of an external flow were located out of the symmetry plane. In this case the equations are solved first in the plane containing the outflow line and then the solutions were constructed by a marching method along a circumferentialcoordinate to the windward and leeward symmetry planes. The distribution of the skin-friction coefficients and the Stanton's numbers on a cone surface was given. The similarity solution of a set of boundary layer equations was obtained for thin cones at large incidence when the stream on the windward side of the cone was directed to the cone nose. The calculations of the laminar boundary layer at hypersonic velocities were carried out to include the real equilibrium properties of the air.

Smoke Visualization of Boundary-Layer Transition on a Spinning Axisymmetric Body

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