Joseph C. Mollendorf

A new density relation for pure and saline water

Abstract An equation has been developed for the density of pure and saline water. It contains only one term in temperature, as an expansion around the temperature at the density extremum. The salinity and pressure effects appear in the equation in an ordered way. The density variation is fitted in the temperature, salinity and pressure ranges to 20°C, 40%, and 1000 bars abs. The most accurate form is in agreement with the pure water correlation of Fine and Millero ( Journal of Chemical Physics , 59 , 5529–5536, 1973) to an r.m.s. difference of 3.5 ppm. For saline water it agrees to 10.4 ppm with the data of Chen and Millero ( Deep-Sea Research , 23 , 595–612, 1976). The overall r.m.s. difference, for both pure and saline water, is 9.0 ppm. Inferences concerning the inherent accuracy of the data arise from the comparisons. Our results also suggest the pressure effect on the extremum temperature, for both pure and saline water. The equation is also separately fitted to the 1-atm correlation of Fofonoff and Bryden ( Journal of Marine Research , 33 , 69–82, 1975) to 2.5 ppm, over the salinity range from 8 to 40%, and from 0 to 20°C.

Buoyancy-induced flows in water under conditions in which density extrema may arise

The temperature dependence of the density of both pure and saline water, even to very high salinity and pressure levels, decreases at decreasing temperature toward an extremum. The nature of this variation precludes approximating the buoyancy-force density difference linearly with a temperature difference. This peculiar density variation of water has very significant effects, even at environmental temperature levels. A new equation has appeared which relates density to temperature, salinity and pressure with very high accuracy. Its form is especially suited to the analysis of convective motions. We consider here vertical boundary-layer flows. Analysis of flows arising from thermal buoyancy and from combined buoyancy effects shows the simplicity of the formulation. Relatively few new parameters arise. Extensive calculations for thermally buoyant flows show the large magnitude of the effects of the complicated density variation on transport. Buoyancy-force reversals and convective inversions are predicted. The latter are in close agreement with past experiments. A new Grashof number arises which is an accurate indication of the actual local flow vigour. The effects of specific temperature conditions are given in detail. The appreciable effect of the Prandtl number is calculated. Transport parameters are given for salinities and pressures up to 40 p.p.t. and 1000 bars, respectively.

Variable viscosity effects in several natural convection flows

Abstract A regular perturbation analysis is presented for three laminar natural convection flows in liquids with temperature dependent viscosity: a freely-rising plane plume, the flow above a horizontal line source on an adiabatic surface (a plane wall plume) and the flow adjacent to a vertical uniform flux surface. While these flows have well-known power-law similarity solutions when the fluid viscosity is taken to be constant, they are non-similar when the viscosity is considered to be a function of temperature. A single similar flow, that adjacent to a vertical isothermal surface, is also analyzed for comparison in order to estimate the extent of validity of the perturbation analysis. The formulation used here provides a unified treatment of variable viscosity effects on these four flows. With the exception of water, the major temperature variation of the fluid properties of common liquids is seen to be in the absolute viscosity. This has been previously recognized and utilized for other flows and is the basis for the applicability of the present analysis. Computed first-order perturbation quantities are presented for all four flows. Several interesting variable viscosity trends on flow and transport are suggested by the present results. These modifications to a constant viscosity formulation are seen to be significant even within the necessarily limited range of a first-order perturbation analysis. Heat transfer results for the isothermal and uniform heat flux surfaces are in very close agreement with the corresponding data and correlations of previous investigations. The present results also place some previous conclusions regarding plume flows in clearer perspective.

Thermodynamic and transport properties of pure and saline water

Publisher Summary This chapter presents a complete collection of the thermodynamic and transport properties of seawater. The chapter reviews the available fundamental data and correlations of both the molecular transport and thermodynamic properties of saline water for a wide range of temperature (t), salinity (s), and pressure (p). The purpose is to establish a database that could be used to achieve systemic representations of, as many as possible, the basic properties required in many areas of analysis and in calculations concerning terrestrial surface-water transport processes and circulations. The properties calculated using a density relation are coefficient of thermal expansion, coefficient of saline expansion, change in specific heat, change in enthalpy, and change in entropy. The results for the change in specific heat along with other previously reported data of other properties are used to calculate the Prandtl number. The Schmidt number is compiled solely from previously reported measurements. However, except at low temperatures and pressures, good agreement can be seen in the comparison of thermal expansion results.

Thermal Conductivity and Compressive Strain of Aerogel Insulation Blankets Under Applied Hydrostatic Pressure

1 Background Silica aerogels are among the best solid thermal insulating materials 1. Aerogels are formed by sol-gel processes and dried by supercritical extraction 2,3. This process leaves a porous medium which has pore sizes of approximately 10 nm which is about eight times smaller than the mean free path of air 4. The porosity can be as high as 90% 5,6. The overall effective thermal conductivity can be as low as 0.013 W / m K for aerogels with a density of 120 kg/ m 3 1.

Buoyancy force reversals in vertical natural convection flows in cold water

Calculated numerical results are presented for laminar buoyancy-induced flows driven by thermal transport to or from a vertical isothermal surface in cold pure and saline water wherein a density extremum arises. The present calculations specifically explore the consequences of temperature conditions wherein the buoyancy force reverses across the thermal region owing to the presence of a density extremum within the region. Such conditions commonly occur in terrestrial waters and in technological processes utilizing cold water. The linear approximation of density dependence on temperature, used in conventional analysis, is here replaced by a very accurate non-linear density equation of state for both pure and saline water. This permits an accurate treatment of such flows for bounding temperatures up to 20 °C at ambient salinity and pressure levels from 0 to 40 p.p.t. and 1 to 1000 bars, respectively. The results may be applied to the melting or slow freezing of a vertical ice surface in pure water as well as to a heated or cooled vertical isothermal surface in pure or saline water. For example, buoyancy force reversals arise for a vertical ice surface at 0 °C melting in fresh water between 4 °C and 8 °C at atmospheric pressure. Temperature conditions for which buoyancy force reversals occur are of special interest because of the resulting anomalous flow behaviour and low surface heat-transfer rates. The transition from conditions with no buoyancy-force reversal to those resulting in a large buoyancy-force reversal is accompanied by as much as 50% decrease in surface heat transfer. This produces a corresponding trend in the melt rate of a vertical ice surface in pure water. Sufficiently strong buoyancy force reversals are found to cause local flow reversal either at the edge of the flow layer or near the surface. Conditions are determined for which flow reversals occur at each of these locations. These local flow reversals are the precursors of convective inversion, that is, of the reversal of the net flow direction with changing ambient medium temperature. Limits on conditions for convective inversion are determined. Calculated transport is compared with previous experimental results, with good agreement throughout the several regions of such complicated flows. The calculations indicate that such flows are relatively very weak. However, their form may lead to early laminar instability.

THERMAL BUOYANCY IN ROUND LAMINAR VERTICAL JETS

Abstract A perturbation analysis is performed which includes the effect of a small amount of thermal buoyancy on the velocity and temperature fields of a round, laminar, vertical jet. A numerical solution of the resulting perturbation equations shows that the predominant effect of positive thermal buoyancy is to increase the axial velocity component of the jet. The magnitude of the effect is shown to increase for decreasing Prandtl numbers. Other details of buoyancy effects on the flow and temperature fields are presented and discussed. It is expected that buoyancy effects may have a large influence on laminar stability.

Application of theoretical principles to swimsuit drag reduction

This study investigated the basic fluid mechanics associated with the hydrodynamic drag of a human. The components of drag (frictionDSF, pressureDP and waveDW) on a human swimmer were analysed by applying classical fluid dynamic fundamentals. General methods of reducing drag were considered and the most probable method identified, applied and tested on swimsuit hydrodynamic drag. This study employed turbulators, either one (upper back) or three (across the upper back, the chest and across the buttocks), that were compared to an identical full body suit with no turbulators. Male and female elite competitive swimmers (n = 7 each) were towed in an annular pool to determine passive drag at speeds from 0.4 to 2.2 m s−1. The total drag was reduced by 11–12% by one turbulator and 13–16% by three turbulators. The total drag was decomposed intoDSF, DP andDW to determine the mechanisms responsible for the reduced total drag by the turbulators. The presence of the turbulators did not significantly increase friction or wave drag; however, flow was attached to the body as there was a significant reduction in pressure drag (19–41%), with the greatest reduction being for three turbulators (chest, back, buttocks). This study demonstrated the importance of pressure drag in determining total drag at high human swimming speeds, and that drag reducing technology can significantly reduce it, in this case by appropriately sized and placed turbulators.

Thermal conductivity and compressive strain of foam neoprene insulation under hydrostatic pressure

The purpose of this study was to show that the thermal properties of foam neoprene under hydrostatic pressure cannot be predicted by theoretical means, and that uni-axial pressure cannot simulate hydrostatic compression. The thermal conductivity and compressive strain of foam neoprene were measured under hydrostatic pressure. In parallel, uni-axial compressive strain data were collected. The experimental set-up and data were put into perspective with past published studies. It was shown that uni-axial compression yielded strains 20–25% greater than did hydrostatic compression. This suggests the need for direct hydrostatic pressure measurement. For comparison to hydrostatic experimental data, a series of thermal conductivity theories of two phase composites based on particulate phase geometry were utilized. Due to their dependence on the porosity and constituent thermal conductivities, a model to predict porosity under hydrostatic pressure was used and an empirical correlation was derived to calculate the thermal conductivity of pure neoprene rubber from experimental data. It was shown that, although some agreement between experimental data and thermal conductivity theories was present, no particular theory can be used because they all fail to model the complex structure of the pores. It was therefore concluded that an experimental programme, such as reported here, is necessary for direct measurement.

Developing flow and transport above a suddenly heated horizontal surface in water

Abstract The results of this experimental investigation are observations and conclusions, determined by transport measurements and flow visualization, regarding the development of convection above an instrumented, horizontal surface (with side walls) in an extensive water ambient subjected to a step in electrical energy generation. The initial mode of heat transfer was concluded to be conduction, since the measured plate surface temperature closely agreed with one-dimensional transient conduction theory. Departures from the theoretical conduction solution were an indication of the onset of convective motion. When the heated layer became sufficiently thick, a wave-like instability was observed, followed by fluid motion, with nearlyspherically-shaped ‘heat bubbles’ (thermals) rising randomly, increasing in size, with some assuming a mushroom shape and breaking away from the bulk of the heated fluid. Thereafter, both the local and spatially averaged plate surface temperatures were seen to be time dependent. Another observation was the presence of wispy, swaying ‘convection columns’ which meandered to-and-fro on the surface. The first visual convective instability was seen to precede the departure of the measured surface temperature from the conduction solution. As the low ambient temperature range was approached, the density extremum effect reduced Nu Ra − 1 3 by as much as about 50%. It is concluded that transport above a heated, horizontal surface in an extensive water ambient is inherently time dependent; initially largely because of‘heat bubbles’ breaking away from the conduction layer, and later because of the continual movement of ‘convection columns’.