J.D. Jackson

Studies of mixed convection in vertical tubes

Abstract The early study of convective heat transfer considered the branches of forced and free convection independently with only passing reference to their possible interaction. In fact the two are extreme cases of the general condition of “mixed” or “combined” forced and free convection where both mechanisms operate simultaneously. The present contribution aims to provide an up-to-date review of those works concerned with mixed convection heat transfer in vertical tubes. The review is divided into two sections, the first dealing with laminar flow, and the second with turbulent flow; further subdivisions are made according to whether the work is theoretical or experimental. Comparisons between theory and experiment are made where possible, expressions defining the conditions for onset of buoyancy effects are presented and equations for determining heat transfer are given. The paper ends with some general comments and recommendations. The survey is restricted to fluids of moderate Prandtl number; mixed convection in liquid metals can display very different characteristics which will be discussed in a future paper.

A study of turbulence under conditions of transient flow in a pipe

A detailed investigation of fully developed transient flow in a pipe has been undertaken using water as the working fluid. Linearly increasing or decreasing excursions of flow rate were imposed between steady initial and final values. A three-beam, two-component laser Doppler anemometer was used to make simultaneous measurements of either axial and radial, or axial and circumferential, components of local velocity. Values of ensemble-averaged mean velocity, root-mean-square velocity fluctuation and turbulent shear stress were found from the measurements. Being the first really detailed study of ramp-type transient turbulent flow, the present investigation has yielded new information and valuable insight into certain fundamental aspects of turbulence dynamics. Some striking features are evident in the response of the turbulence field to the imposed excursions of flow rate. Three different delays have been identified: a delay in the response of turbulence production; a delay in turbulence energy redistribution among its three components; and a delay associated with the propagation of turbulence radially. The last of these is the most pronounced under the conditions of the present study. A dimensionless delay parameter τ + [= √2τ U τ0 / D ] is proposed to describe it. The first response of turbulence is found to occur in the region near the wall where turbulence production peaks. The axial component of turbulence responds earlier than the other two components and builds up faster. The response propagates towards the centre of the pipe through the action of turbulent diffusion at a speed which depends on the Reynolds number at the start of the excursion. In the core region, the three components of turbulence energy respond in a similar manner. Turbulence intensity is reduced in the case of accelerating flow and increased in decelerating flow. This is mainly as a result of the delayed response of turbulence. A dimensionless ramp rate parameter γ[= (d U b /d t ) (1/ U b 0 )( D / U τ0 ] is proposed, which determines the extent to which the turbulence energy differs from that of pseudo-steady flow as a result of the delay in the propagation of turbulence.

Vertical tube air flows in the turbulent mixed convection regime calculated using a low-Reynolds-number k ~ ϵ model

Abstract Heat transfer to fluids flowing in vertical tubes under conditions of combined forced and free (‘mixed’) turbulent convection can exhibit marked departures from the case of purely forced convection. Significant impairment or enhancement of heat transfer can occur, depending upon flow orientation and the degree of buoyancy influence. A second important phenomenon arising in the ascending flow configuration is the occurrence of very long thermal-hydraulic development lengths. Calculations performed using a formulation of the Launder and Sharma low-Reynolds-number k ~ ϵ turbulence model for developing flow in a tube show close agreement with a range of experimental heat transfer data and flow profile measurements for air, major discrepancies occurring only in strongly buoyancy-influenced descending flow.

A study of squeezing flow

The problem of the squeezing of a film of liquid between two parallel surfaces is considered. Approximate expressions are deduced for the instantaneous distribution of velocity within the fluid and the reaction on the surfaces. These are obtained by an approximate iterative solution of the continuity and momentum equations. The radial pressure distribution in a squeezed film is found to be due partly to the action of viscosity and partly to inertia effects. The latter cause the relationship between the reaction on the surfaces and their relative velocity to be non-linear. This effect is significant for conditions where the Reynolds number based upon the distance between the surfaces and their relative velocity is greater than unity. The results obtained should be of interest in connection with the study of the performance of transiently loaded bearings in reciprocating engines, and a possible application in the field of chemical engineering might arise in connection with the phenomenon of adhesion.

Simulation of mixed convection heat transfer to carbon dioxide at supercritical pressure

Abstract Computational simulations of turbulent mixed convection heat transfer experiments using carbon dioxide at supercritical pressure have been performed by solving the Reynolds averaged transport equations using an elliptic formulation. A number of two-equation low Reynolds number turbulence models have been used and the results have been compared directly with the experimental data. It has been shown that most of the models were to some extent able to reproduce the effects of the very strong influences of buoyancy on heat transfer in these experiments. However, the performance of the models varied significantly from one to another in terms of the predicted onset of such effects.

An investigation of laminar radial flow between two parallel discs

Experiments have been carried out to test recent theoretical predictions of the pressure distribution for laminar flow between parallel discs, including inertia effects. The experimental investigation covered the condition where the inertia effects were always completely dominant over the central region of the discs in contrast to other recent experimental work on the problem where the central injection diameter was considerably larger. The present experiments subject the theories to a stringent test, due to the dominance of the inertia effects, and it is found that the inertia effects predicted by the various theoretical analyses are significantly smaller than those shown by the experimental results. It is suggested that the theoretical approach requires further development before it will cover the conditions where the central injection diameter is small.

The pressure distribution in a hydrostatic thrust bearing

Abstract An expression is obtained for the pressure distribution in a hydrostatic thrust bearing using an existing series expansion solution for radial flow between parallel planes. It is shown that the same result can be obtained by a simple uni-directional flow analysis. The present results are compared with those of earlier investigations in which inertia effects were either neglected or represented approximately by a momentum integral method.

Combined heat and mass transfer in a uniformly heated vertical tube with water film cooling

A computational study is reported of buoyancy-influenced forced upward turbulent flow of air and water vapour in the range of Reynolds number from 4600 to 13 800 within a long uniformly heated vertical tube in the presence of a falling film of water on the inside wall. Procedures have been successfully developed which enable this complex problem to be simulated using turbulence modelling and an elliptical computational scheme. Simulations have been made for a range of conditions and detailed comparisons are made with experiments. Useful progress has been made in understanding the fluid dynamics and thermal physics involved. Within the first 20 diameters, the effects of the re-organisation of the flow and turbulence field dominate. Within this region, turbulence entering with the imposed flow decays away, a new turbulence structure is generated in the wall region and this propagates into the core further downstream. The sensible Nusselt number in this region is generally lower than it is in the upper section of the tube. Both the mean and the turbulent fields are affected by buoyancy under certain conditions. In extreme cases, the flow is laminarised and heat transfer considerably impaired. Two very different modes of heat transfer were identified. When the cooling water is supplied at relatively high temperature, the system operates in the evaporation mode. Energy supplied by the wall is mainly absorbed by evaporation of water from the film. The water temperature and the conditions of the flow are important factors controlling the effectiveness of heat transfer under such conditions. In contrast, when the temperature at which the water is supplied is relatively low the system operates in the direct film cooling mode. Convection of heat by the flowing water film becomes the main mechanism for heat removal from the tube.

Heat Transfer to Air, Carbon Dioxide and Helium Flowing through Smooth Circular Tubes under Conditions of Large Surface/Gas Temperature Ratio

In this paper, experiments are described on the transfer of heat from a heated tube to a gas flowing through it. Three gases were used: air, helium and carbon dioxide. The difference in temperature between the tube and the gases was large and the main objective of the work was to study the effects of radial variations of the gas properties with temperature. The conditions under which the experiments were performed were (1) essentially fully developed velocity and temperature profiles, (2) approximately uniform wall heat flux and (3) low subsonic turbulent flow.Some analysis has been developed to cover the present experimental work. Predicted Nusselt number-Reynolds number relations for the constant properties case are found to be in reasonable agreement with the experimental data for Reynolds numbers above about 10 000, provided the ratio of eddy diffusivities is assumed to vary from about 1·0 at Re = 104 to about 1·2 at Re = 105. The effects of variations of surface/gas temperature ratio, predicted by th...

An experimental investigation of buoyancy-opposed wall jet flow

Abstract An experimental study is reported of the flow and thermal fields produced by injecting a plane jet of warm water down one wall of a vertical passage of rectangular cross section into a slowly moving upward stream of cooler water. Flow visualisation and particle image velocimetry techniques were used to obtain pictures of the flow. This was found to be turbulent and non-steady under certain conditions. Detailed measurements of local mean velocity, turbulence quantities and temperature were made using a laser Doppler anemometry system and a traversable rake of thermocouples. In the regions where the warm water encountered the cooler water the variation of temperature with time was highly intermittent. As Richardson number was increased, the influence of the buoyancy, opposing the flow, had the effect of stabilising it and restricting the downward penetration of the jet and its lateral spread. In the case of the experiments with the higher values of Richardson number a very concentrated shear layer was formed at the interface between the two flow streams. The turbulence was strongly modified in this region, its intensity peaked and the turbulent shear stress changed sign.