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A theoretical analysis has been performed to study molecular and turbulent transport phenomena between subchannels of infinite bare rod arrays at laminar, transition and turbulent flow conditions. For this investigation, the theoretical approach of Ramm and Johannsen for predicting turbulent momentum and heat transfer in rod bundles has been extended to evaluate three-dimensional temperature fields. Results are presented enabling the prediction of the onset and growth of laminarization in typical subchannels of square and triangular rod arrays. These results are further applied to interpret the characteristic effects of variations in Reynolds number, Prandtl number or geometric spacing on integral exchange parameters as the thermal mixing flow rate and mixing length scale. These results are of particular significance relative to the explanation of recent data from tracer-type mixing experiments and also exhibit the importance of secondary flow effects on turbulent intersubchannel energy transport. In view of these findings, the physical relevance of current correlations derived from integral-type experiments to numerically predict exchange coefficients for use in lumped parameter subchannel analysis codes is discussed.

Stability and bifurcation of Couette flow between concentric rotating cylinders are investigated for the case when the ratios of their radii R and angular velocities Ω are nearly equal to unity. The limiting problem in the linear theory when R → 1 and Ω → 1 is the problem of convection stability in the layer [1]. We find that this is also correct in the case of a nonlinear problem. Below we show that solution of the problem of free convection yields the principal term of the expansion of the secondary flow (Taylor vortex) in the powers of a small parameter δ = R − 1. Therefore the results of [2, 3] can be used to provide, in the present case, a strict justification for the use of the Liapunov-Schmidt method to compute the Taylor vortices. The numerical results obtained for the critical Reynolds' number and the amplitude of the secondary flow provide a good illustration of the asymptotic passage as δ → 0.

TYPICAL SOLUTIONS FOR CONDUITS OF VARIOUS SHAPES ARE PRESENTED. FOR TURBULENT FLOW THE SOLUTION IS BASED ON THE VALIDITY OF THE USE OF AN EDDY VISCOSITY CONCEPT TO ACCOUNT FOR THE REYNOLDS STRESSES. THE SOLUTION PROCEDURE ALLOWS THE QUANTITATIVE ISOLATION OF THE EFFECTS OF SECONDARY FLOWS ON THE VELOCITY AND BOUNDARY SHEAR DISTRIBUTIONS. HOWEVER, THE EFFECT OF SECONDARY FLOWS HAS BEEN CONSIDERED HEREIN ONLY FOR A SQUARE DUCT BECAUSE OF THE PRESENT DEARTH OF KNOWLEDGE ABOUT THEIR DISTRIBUTION IN OTHER CONDUIT SHAPES. FOR THE SQUARE DUCT THE SOLUTION SHOWS THAT THE SECONDARY FLOW IS RESPONSIBLE FOR A 6 PERCENT INCREASE IN THE FRICTION FACTOR AND AN 11 PERCENT DECREASE IN THE MAXIMUM BOUNDARY SHEAR. THE INCLUSION OF THE SECONDARY FLOWS IN THE ANALYSIS ALLOWS SATISFACTORY AGREEMENT TO BE ACHIEVED BETWEEN THE CALCULATED AND EXPERIMENTAL VELOCITY AND BOUNDARY SHEAR DISTRIBUTIONS AND ILLUSTRATES THE LIMITATIONS THAT MUST ACCOMPANY ANY SOLUTION THAT IGNORES THE EFFECTS OF SECONDARY FLOWS. /ASCE/

It is shown that the effect of secondary flow on the separation of a three-dimensional boundary layer is determined by the parameters composed of coefficients at terms of second order of smallness in expansions of variables which define the external stream in the neighborhood of particular cross section of the boundary layer. Formulas are derived for appropriate parameters which must be additionally introduced in the separation criterion. When deriving separation criteria for plane and three-dimensional boundary layers it is customary to use a system of determining parameters which includes coefficients at terms of the first order of smallness in expansions of quantities which determine the external stream in the neighborhood of the separation point. Numerous experiments on the two-dimensional boundary layer show that in a wide class of cases, important from the practical point of view, the neglect of some second order terms is entirely justified. The effect of some second order parameters may become considerable in certain cases of three-dimensional boundary layer separation.

A viscoelastic incompressible fluid, modeled by the White-Metzner equation, flows in a combined extruder. Approximate expressions are obtained for the secondary flows in the disk zone of the machine whose presence has been confirmed experimentally. By means of these expressions it is possible to determine the total shear deformation of an element of the melt as it passes through the extruder.

Flow and turbulence in a 50 Hz rotating-field MHD system are investigated using the hot-film constant-temperature anemometer. Factors affecting anemometer disturbances and response time are discussed. From measurements of the magnetic field at points within the liquid the distribution of MHD forces is estimated. The mean rotational velocity of the flow is of the expected order of magnitude but much less dependent on the axial co-ordinate than the corresponding MHD force. With the aid of a thermal transit-time anemometer, a weak secondary flow is detected. A note on scale-model studies of MHD systems envisaged in metallurgical applications of magnetohydrodynamics points out some basic difficulties in modelling large high-powered systems on a small scale.

A general characteristic of rapidly rotating fluids is that accurate experimental measurements can only be made of the main (azimuthal) flow. The secondary flow is then usually deduced from theory, although this is often incomplete in the boundary regions where the secondary flow is of most interest.In this paper we consider the case of source-sink flow between the porous walls of a rapidly rotating annular container and numerically integrate the full equations of motion in order to determine the complete structure of the secondary flow. The results are compared with the (approximate) analytic studies of Hide (1968) and Bennetts & Hocking (1973) to show the differences between the two approaches.A defect of many previous numerical papers has been the inability to check the solution in the nonlinear case. To overcome this, new experimental measurements of the azimuthal velocity profile for a Rossby number of 0·238 have been obtained and these are compared with the numerical results.

The presence of secondary vortex motions in the flow between eccentric rotating cylinders is shown to increase the power input requirements to the inner rotating cylinder at any eccentricity ratio. The effect of superimposing axial flow is to delay the onset of instability and hence decrease this power input to the system. An evaluation of the rotational power losses due to instability as compared with the pumping power required to introduce the necessary axial flow rates is carried out for three gap-radius ratios.

Rectilinear flow through pipes of non-circular cross section in the case of elastico- viscous liquids is not possible in general and some secondary flow in the cross section of the pipe is to be expected. The present paper contains a detailed theoretical and experimental study of the problem for pipes of square and rectangular cross section. Our main concern is the form that the secondary flows take and their influence on the flow rate through the pipe. The governing equations, which are non-linear partial differential equations, are solved numerically using finite difference methods used in conjuction with S.L.O.R. It is shown, that, for both the square and rectangular cross sections, there are eight vortices present. These have the same strength for the square cross section, but four of the eight become progressively weaker as the ratio of the sides of the rectangle is increased. The effect of a variable (shear-dependent) viscosity on the flow rate is found to be sub- stantial but the effect of the secondary flows on the flow rate is predicted to be small unless the fluid has some rather unusual properties The experimental results are in general agreement with the theoretical predictions.

The shapes of the entrance and exit slip-lines to the plastic flow zones in a metal-cutting process are obtained by strain etching the polished section of a partly formed chip, which was produced in an incremental cutting operation. The results are compared with the slip-line field solutions of Kudo, for cutting with chip curl. The shapes of the exit boundaries to the primary and secondary flow zones, which are situated in approximately non-hardening metal, show good general agreement with Kudo's perfect plasticity model.

This paper deals with the development of the flow in a curved tube near the inlet. The solution is obtained by the method of matched asymptotic expansions. Two inlet conditions are considered: (i) the condition of constant dynamic pressure at the entrance, which may be of practical interest in applications to blood flow in the aorta; and (ii) a uniform entry condition. It is shown that the geometry and the nature of the entry condition appreciably influence the initial development of the flow. The effect of the secondary flow due to the curvature on the wall shear is discussed and it is shown that the cross-over between shear maxima on the inside and the outside of the tube occurs at a downstream distance which is 1·9 times the radius of the tube for entry condition (i) while in the case of entry condition (ii) it is 0·95 times the radius, which is half the distance required in case (i). It is found that the pressure distribution is not significantly influenced by the secondary flow during the initial development of the motion. The analysis, which is developed for steady motion, can be extended to pulsatile flows, which are of greater physiological interest.

A numerical method for predicting three-dimensional, steady viscous flow in ducts is described. The method utilizes approximate governing equations which are applicable to flows having strong convection in one primary flow direction. The governing equations require a coordinate system as input to define primary and secondary flow directions, and an inviscid first approximation to static pressure gradients arising from curved flow geometries. The equations are parabolic and are solved by stepwise integration in the primary flow direction from prescribed upstream initial conditions. Specific details of the method are given by way of application to a special case chosen for its simplicity, that of laminar flow in the entrance region of straight rectangular ducts. A numerical method based on an alternating-direction implicit (ADI) scheme is described and used to compute solutions for flow in ducts having aspect ratios of 1:1 and 2:1; in one case, the effect of thermal convection caused by a transverse buoyancy force is also included. The computed solutions are found to be in good agreement with experimental velocity-profile and pressure-drop measurements. Extensions to treat more general geometries and to include compressibility effects and turbulent transport processes are possible and seem warranted by the present results.

This paper deals theoretically with the two-dimensional flow driven by a symmetrical Joukowski profile oscillating harmonically along its axis of symmetry in an unbounded viscous fluid otherwise at rest. Slow steady secondary flow which occurs outside the boundary layer around the profile is studied in detail. It is found that a uniform flow is induced at infinity owing to the asymmetry of the profile in the direction of oscillation.

The damping of axial instabilities by a variety of small-scale solid rocket nozzles has been determined experimentally under cold-flow conditions using the modified impedance tube technique. The dependence of the damping upon the cavity depth and the secondary flow rate issuing from the cavity of a submerged nozzle, the geometry of the convergent section of a single-ported nozzle, and the number of nozzles present in a multipleported nozzle cluster has been determined. Measured data indicate that in the case of the submerged nozzle the cavity depth surrounding the nozzle has a significant effect upon the nozzle admittance while the secondary flow rate issuing from the cavity has negligible effect on the admittance. Tests conducted with conical, equal-radii-ofcurvature and linear-velocity-profile nozzles showed that conical nozzles provide the most damping. Tests with multiple-ported nozzles indicated that quadruple-ported nozzles provide less damping for axial instabilities than single and dual-ported nozzles whose damping capabilities are approximately the same.

By considering the flow through a many-bladed cascade, a simple theory is developed for the effect of a change in axial velocity on the secondary flow at exit from a cascade. An expression is derived for the difference in the time taken for fluid particles to travel over the two surfaces of the blade and this is used, along with Kelvin's circulation theorem for incompressible flow, to obtain an equation for the distributed secondary vorticity. It is shown that for the row of inlet guide vanes tested by Gregory-Smith (1)†, the change of axial velocity across the blade row has a significant effect on the secondary vorticity.

Experiments were conducted to determine the film cooling effectiveness and convective heat transfer coefficient distributions on the endwall of a large-scale turbine vane passage. The vane test models employed simulated the passage geometry and upstream cooling slot geometry of a typical first-stage turbine. The test models were constructed of low thermal conductivity foam and foil heaters. The tests were conducted at a typical engine Reynolds number but at lower than typical Mach numbers. The film cooling effectiveness distribution for the entire endwall and the heat transfer distribution for the downstream one-half of the endwall were characterized by large gapwise variations which were attributed to a secondary flow vortex.Copyright © 1974 by ASME

By considering a many-bladed cascade, two simple theories are developed for secondary flow in cascades. Following the work of Hawthorne (1)†, three components of vorticity are identified at exit from the cascade. An expression is obtained for the difference in the time taken for fluid particles to travel over the two surfaces of the blade, and this is used to derive the governing equations for the distributed secondary, trailing filament and trailing shed vorticities. It is shown that, for a many-bladed cascade, the total secondary circulation in the downstream flow is zero. The calculation of secondary flow for a real cascade is discussed, and it is shown that earlier calculations of secondary flow at exit from cascades are consistent with this new approach.

The stability of buoyancy-driven convection in a slot, slightly tilted with respect to the horizontal, is investigated analytically on the basis of linear theory. For mathematical simplicity, the boundaries are assumed free and isothermal. It is shown that the Rayleigh number and the wave number at the critical point have the same values as for an exactly horizontal slot, however, the predicted motion, rather than being indeterminate, is one of longitudinal rolls with their axes aligned in the direction of the mean flow. This is in contrast to the analogous problem of convection in a vertical slot in which the secondary flow pattern is known to consist of transverse rolls, i.e. rolls with their axes normal to the mean motion.

The nonlinear problem of two-dimensional motion of an unbounded incompressible viscous fluid under the action of a spatially periodic force is considered in a finite-dimensional approximation. When the number of finite-amplitude perturbation harmonics is restricted, a stationary solution is found to exist, corresponding to a secondary flow. This solution is however unstable with respect to smaller perturbations. Equations expressing the total contribution of the most unstable harmonics are derived and are found to have no stationary solutions. Papers [4 – 7] propose a relatively simple approximate procedure of computing secondary equilibrium flows for the purpose of describing the first stage of formation of the finite-amplitude perturbations according to the scheme given in [1] (also see [2 and 3]). In this procedure the Reynolds stresses governed by the finiteamplitude perturbations are balanced against the dissipation and the mean flow. The problem of the secondary flows, stationary or periodic, arising when the laminar flows of a viscous incompressible fluid become unstable, is considered in [8 – 13]. The concept of mechanical hydrodynamic systems embracing finite-dimensional approximations to the equations of hydrodynamics, is introduced in [14]. In [15] a mechanical model is constructed in the form of chains of simplest systems. This model imitates the cascade mechanism of the energy transfer in a developed turbulent flow and serves as an illustration of a possible simplest realisation of the Landau scheme. Below an equilibrium mode of a secondary flow is studied in a finite-dimensional approximation for a two-dimensional case.

When a thin film of viscous fluid is produced by passing it through a small gap between a roller or spreader and a flat plate, it often presents a waved, or ribbed, surface. An analysis is given here in terms of lubrication theory to show why in many cases flow leading to a uniform film is unstable. Account is taken of surface tension which proves to be a stabilizing factor. The most unstable values of the wave-number, n (characterizing the disturbance), are calculated as functions of the dimensionless variable T/μU0, and of the geometry of the system; T is the surface tension, μ the viscosity and U0 a representative velocity of the fluid. For the particular case of a spreader in the form of a wide-angled wedge, these predictions are compared with experimental observations. Agreement is obtained for values of T/μU0 between about 10 and 0.1, but for smaller values of T/μU0 it is clear that other considerations, involving only viscous and pressure forces, determine the nature of the secondary flow.

Keller and Rubinow(l) have considered the force on a spinning sphere which is moving through an incompressible viscous fluid by employing the method of matched asymptotic expansions to describe the asymmetric flow. Childress(2) has investigated the motion of a sphere moving through a rotating fluid and calculated a correction to the drag coefficient. Brenner(3) has also obtained some general results for the drag and couple on an obstacle which is moving through the fluid. The present paper is concerned with a similar problem, namely the axially symmetric flow past a rotating sphere due to a uniform stream of infinity. It is shown that leading terms for the flow consist of a linear superposition of a primary Stokes flow past a non-rotating sphere together with an antisymmetric secondary flow in the azimuthal plane induced by the spinning sphere. For a3n2 > 6Uv, where n is the angular velocity of the sphere, U the speed of the uniform stream, and a the radius of the sphere, there is in the azimuthal plane a region of reversed flow attached to the rear portion of the sphere. The structure of the vortex is described and is shown to be confined to the rear portion of the sphere. A similar phenomenon occurs for a sphere rotating about an axis oblique to the direction of the uniform stream but the analysis will be given in a separate paper.

The effect of the velocity distribution at the inlet to blade cascades on the kinetic energy of secondary flows is treated on the basis of a simple mathematical model of an ideal fluid flow. The kinetic energy of secondary flow in reaction turbine blades is found to be very small, compared with that in impulse and compressor blades. The influence of blade spacing is also considered. By comparison with experimental data and with practical experience, the present results demonstrate the importance of separation of the three-dimensional, viscous fluid flow in blade cascades of finite length.

Hydraulic transport of solid materials through pipe bends was investigated experimentally. Four kinds of 90° pipe bends of which the radii of curvature were 0, 12, 24 and 48cm, were made of polyacrylate pipe. The pressure drops were measured over sections of about 5 m, each including a pipe bend. The solid particles used in this experiment were glass beads (0.5-2.0mm diameter) and polystyrene particles (1.0mm diameter). The behavior of particles in pipe bends was found to be very much complicated by the effect of gravitational and centrifugal forces and the secondary flow of fluid. The results of the pressure-drop measurement were as follows, a) The horizontal pipe Bend : In the case of polystyrene particles, even though delivered particle concentration exceeded about 20%, the effect of particle concentration mc on the pressure drop did not appear to be the same as in the case of a straight pipeline. On the other hand, in the case of glass particles the additional pressure drop, which was nearly constant regardless of flow rate, increased with increasing particle concentration except where R=0 and 12cm. Moreover, the additional pressure drop was correlated by the dimensionless term Um2/gR (ρs/ρw-1) and mc. b) The vertical pipe bend : It was found from experiment that both polystyrene and glass particles showed additional pressure drop, which was nearly constant regardless of the flow rate, similar to the case of horizontal pipe bends.

A numerical simulation of the turbulent mass diffusion process from an elevated, continuous point source over a wind-disturbed water surface is described. The diffusion equation, with models for turbulent diffusivities, in the boundary layer over water waves was solved with a successive-over-relaxation finite difference scheme. In the numerical computation, measured quantities of flow conditions such as mean velocities, turbulent intensities and boundary layer thickness were used. To improve computational efficiency, a variable grid system was used. The grid system was designed to expand with the spread of the diffusing plume. The water surface was viewed, in the mean, as a flat surface with influences of the wavy surface implicitly incorporated into the turbulent diffusivities. The diffusivities are functions of the turbulent intensities, the boundary layer thickness, and the scale of the phenomenon. The numerical solutions were compared with experimental results of particle concentration measurements obtained with an optical system ( Liu and Karaki , 1972a) in a wind-water tunnel at Colorado State University. With the net mean convection properly corrected for the effects of the particle fall velocity, streamline displacements in a developing boundary layer, and secondary flow (in the experimental facility), general agreements were observed between numerical solutions and corresponding experimental results.

A theoretical and experimental investigation is made of supersonic ejectors with mixing at constant cross-section. In the theoretical part formulae are derived treating the essential points of the behaviour of such an ejector. The theory is mainly based upon one-dimensional flow of a perfect gas; some extensions are included concerning the influence of friction and mixing profile.

In this paper the condition for the existence of a secondary flow in a straight non-circular pipe is determined according to the modified vorticity transfer theory, with Goldstein's assumed form for the tensorIt is shown that a secondary motion arises if the mixture length is not constant on the curves along which | gradu| is constant,ubeing the velocity parallel to the pipe axis.In problems of turbulent flow treated by means of the modified vorticity transfer theory, the quantitywhereis the mean value of the square of the velocity fluctuation andpthe mean pressure, plays a part analogous to the pressure in laminar flow. In two-dimensional flow through a channel the theory shows the existence of a gradient ofacross the channel from the central plane to each wall. Qualitative arguments such as are used to explain the existence of a secondary flow for laminar motion in a curved pipe are applied here to show that a secondary flow is to be expected near the short sides in the turbulent flow through a straight rectangular pipe of large length/breadth ratio.The equations to determine the secondary flow through an almost circular elliptic pipe are discussed, the mixture length being assumed constant on ellipses similar to and concentric with the pipe section. For a first approximation the problem is reduced to the numerical solution of three simultaneous ordinary linear differential equations.

The effect of combustion on a laminar boundary layer, formed near the surface of a flat plate, was studied analytically and experimentally. The fuel is ethyl alcohol, and it is evaporated from the surface of the flat plate in the air stream and burned in the laminar boundary layer. In an analytical calculation of the temperature profile in the boundary layer, the exact values of physical properties were used, and thermal cracking of the fuel was assumed. The calculated result shows that the temperature profile is almost linear from the surface of the plate to the reaction plane, and that a singular point exists between the plate and the reaction plane, where the inclination of the temperature curve changes peculiarly. This point is caused by thermal cracking of the fuel. Secondary flow due to natural convection was avoided by setting the flat plate horizontally in a wind tunnel. Then, the temperature and the concentration profile in the boundary layer were measured. From this measurement of the temperature, it was shown that there was a singular point on the temperature profile in the same position as the calculated result, and that the agreement of the analysis and experiment is good. It is concluded that, if the exact values of the physical properties are used and thermal cracking of the fuel is considered, the laminar boundary layer with combustion is analyzed.

Performance characteristics and interaction between primary and secondary fluid flow streams of supersonic ejector systems

A visualization study of the flow through a three ft dia model of a four bladed inducer, which is operated in air at a flow coefficient of 0.065, is reported in this paper. The flow near the blade surfaces, inside the rotating passages, downstream and upstream of the inducer is visualized by means of smoke, tufts, ammonia filament, and lampblack techniques. Flow is found to be highly three dimensional, with appreciable radial velocity throughout the entire passage. The secondary flows observed near the hub and annulus walls agree with qualitative predictions obtained from the inviscid secondary flow theory. Based on these investigations, methods of modeling the flow are discussed.

A fully developed laminar flow field and temperature field in a pipe rapidly rotating around a perpendicular axis are analyzed theoretically, by assuming velocity and temperature boundary layers along the pipe wall. The resistance coefficient and the Nusselt number are obtained in the region of large values of ( N / χ ). The parameter N is the product of Re and \ gw, where \ gw is the ratio of Coriolis force to viscous force, and χ represents the effect of Coriolis force caused by the secondary flow. It is shown that the resistance coefficient and the Nusselt number increase remarkably, due to a secondary flow driven by Coriolis force. It is also shown by analyzing the two wall temperature conditions, i.e. the constant wall temperature gradient and the uniform wall temperature, that the Nusselt number is almost the same for both these conditions.

An analytical model has been developed to predict the flow behavior within axisymmetric single-nozzle ejectors employing variable-area mixing tubes. The primary flow may be supersonic or subsonic and may have a different stagnation temperature than the subsonic secondary flow. Tests were performed on an ejector with an 800 deg F supersonic (M = 2.72) primary jet to evaluate the analytical model. Measured velocity profiles, temperature profiles, and wall static pressure distributions are presented and compared to the analytical predictions. Agreement is generally good.

A theory for the development of the axial and peripheral velocity profiles in the early stages of an axial-flow compressor is presented. The theory assumes the existence of a stall-zone in the corner formed by the convex surface of each blade and the annulus wall. The extent along each blade of this stall-zone is assumed to be related to the theoretical annulus boundary layer thickness; equations are derived for predicting its growth through the blade roots and tips. The conditions at the blade ends are determined from the theory of a two-dimensional stalled cascade and the outlet angle variation is determined by momentum mixing. Actuator disc theory is then used to find the resulting flow. The predictions of this method are compared both with experimental results obtained from a three-stage compressor and with the predictions of secondary flow theory in which both loss and blade row entry velocity profile are taken from experiment. Somewhat better agreement between the stall-zone theory and experiment is found and to make the theory useful for designers the determination of a single parameter from experiment is indicated.

It has been found experimentally that the turbulent pipe flow through a mitred, right-angle bend produces a downstream secondary circulation which does not conform to the twin-circulatory flow usually to be found in pipe bends. The secondary flow is dominated by a single circulation about the axis in either a clockwise or an anticlockwise sense, between which it switches abruptly at a low, random frequency. The phenomenon is explained in terms of the asymmetry of the inner wall separation and the turbulent axial circulation generated in the upstream flow.

From the observation and the theoretical consideration on the deformation of chip during orthogonal cutting, followings were found on the curl of chip :(1) Owing to the secondary flow due to the tool-chip friction, the part of chip adjacent to the tool face behaved as if there was a built-up edge, which had a cylindrically curved face and curled the chip.(2) The radius of curvature of chip ρ0 was given approximately by the following equation :ρ0=m3/6Anwhere m is the length of tool-chip contact and An is an area which is given by the deformation of chip due to the secondary flow.(3) An effective cutting fluid decreased the length of tool-chip contact, and this was seemed to be the main reason for the decrease in the radius of curvature of chip.(4) For the large depth of cut, the first rake face of double rake tool was covered with a built-up edge, which had a cylindrically curved face and curled the chip. For the small depth of cut, straight or even counterwisely curled chip was born by the same tool.

32 Wood, A. D., Springfield, J. F., and Pallone, A. J., "Chemical and Vibrational Relaxation of an Inviscid Hypersonic Flow," AIAA Journal, Vol. 2, No. 10, Oct. 1964, pp. 1697-1705. 33 Waldman, G. D., "Inviscid Supersonic Stability Problems," Tech. Memo, Avco Space Systems Div. (to be published). 34 Kang, S. W., Rae, W. J., and Dunn, M. G., "Effects of Mass Injection on Compressible, Three-Dimensional Laminar Boundary Layers with Small Secondary Flow," Rept. AI-2187-A-Z, Aug. 1966, Cornell Aeronautical Lab. 35 Eichelbrenner, E. S., "Separation, Reattachment and Stall in Three-Dimensional Laminar and Turbulent Boundary Layers," American Society of Mechanical Engineers Symposium on Separated Flows, Philadelphia, Pa., May 18-20, 1964. 36 Zakkay, V., "Pressure and Laminar Heat Transfer Results in Three-Dimensional Hypersonic Flow," Wright Air Development Center TN 58-182, ASTIA Doc. 155679, Sept. 1958, Dept. of Aeronautical Engineering and Applied Mechanics, Polytechnic Institute of Brooklyn. 37 Cleary, J. W., "Effects of Angle of Attack and Nose Bluntness on the Hypersonic Flow Over Cones," Paper 66-414, June 1966, AIAA; also TN D-2969, NASA. 38 Cooke, J. C. and Jones, O. K., "The Boundary Layer on a Townend Surface," Aero. Quarterly, Vol. 16, May 1965, pp. 145-158.

Upstream injection of small gas bubbles causes increases of up to 50 per cent in heat-transfer coefficient for water flowing upward in a channel of rectangular cross-section. The increase depends on gas flow rate and liquid phase Reynolds number but not on heat flux, indicating that thermocapillary flows do not contribute to the heat transfer. A possible mechanism for the increase is secondary flow production by the interaction of bubbles with the shear flow near the wall.

A device similar to a hot wire anemometer has been developed in which the wire is replaced with a thermistor. Niiler has presented a theory of the response of the anemometer to velocity gradients. Experimental calibration curves are presented here to show that Niiler's model explains the operational characteristics quite satisfactorily. The associated electronic circuitry is described and the design considerations which determine the magnitudes of the various adjustable parameters are discussed. This anemometer has been used to detect the onset of the various modes of secondary flow, the amplitude of the disturbances, their wavelengths, and their drift velocities. Both velocity and temperature fields may be measured.