Heat Exchange and Friction Analysis in Noble Gas Mixtures for Closed Gas Turbines

The types of heat exchange surfaces used in closed gas turbines for space applications and their conversion version (ground application) as autonomous long-resource power plants of low power (less than 10 kW) are considered. The data of the works currently known in Russia and abroad on the developed turbulent flow in the tube when using gas mixtures with abnormally low Prandtl numbers (0.2) have been analyzed. Recommendations on the application of the analytical relations of Kays, Petukhov and Popov for the calculation of the Nusselt number in pipes are given. The influence of non-isothermal flow and initial pipe section on friction as well as the working body Prandtl number on heat exchange and friction for highly compact plate and fin heat exchange surfaces with staggered arrangement of ribs are analyzed. It is revealed that the relations obtained for the air model are inapplicable for working bodies with Prandtl numbers different from the air Prandtl number. The necessity of further experimental and analytical investigations of heat exchange and friction in tubes under transient flow regime and in highly compact finned surfaces with staggered ribs is confirmed

Numerical Study of Free Convection inside the Differentially Heated Cavity incorporating Variable Property Al2O3-H2O Nanofluid

This paper investigates free convection in a partially heated square cavity filled with alumina-water nanofluid. The investigation is carried out at the three-volume fraction of nanoparticles (0, 0.03, 0.05), two Prandtl numbers (2.66, 6), and constant Grashof number (105) with three shapes of insulating obstacles (Square, Circular, and Rectangular). The results show that the nanofluid volume fraction and Prandtl number significantly enhance the heat transfer. The user-defined function (UDF) is developed and computed to investigate the effect of nanoparticle diameter and its temperature-dependent viscosity on convection. The average Nusselt number (Nu) increased with the temperature-dependent viscosity model and by increasing the percentage concentration of the nanoparticles. For all obstacle shapes, the thermal performance improved with increase in the nano-particle diameter.

Bounds for rotating Rayleigh–Bénard convection at large Prandtl number

Bounds are derived for rotating Rayleigh–Bénard convection with free slip boundaries as a function of the Rayleigh, Taylor and Prandtl numbers ${\textit {Ra}}$ , ${\textit {Ta}}$ and ${\textit {Pr}}$ . At infinite ${\textit {Pr}}$ and ${\textit {Ta}} > 130$ , the Nusselt number ${\textit {Nu}}$ obeys ${\textit {Nu}} \leqslant \frac {7}{36} \left ({4}/{{\rm \pi} ^2} \right )^{1/3} {\textit {Ra}} {\textit {Ta}}^{-1/3}$ , whereas the kinetic energy density $E_{kin}$ obeys $E_{kin} \leqslant ({7}/{72 {\rm \pi}}) \left ({4}/{{\rm \pi} } \right )^{1/3} {\textit {Ra}}^2 {\textit {Ta}}^{-2/3}$ in the frame of reference in which the total momentum is zero, and $E_{kin} \leqslant ({1}/{2{\rm \pi} ^2})({{\textit {Ra}}^2}/{{\textit {Ta}}})({\textit {Nu}}-1)$ . These three bounds are derived from the momentum equation and the maximum principle for temperature and are extended to general ${\textit {Pr}}$ . The extension to finite ${\textit {Pr}}$ is based on the fact that the maximal velocity in rotating convection at infinite ${\textit {Pr}}$ is bound by $1.23 {\textit {Ra}} {\textit {Ta}}^{-1/3}$ .

Boundary layers in turbulent vertical convection at high Prandtl number

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$ . This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$ , the heat flux is found to scale linearly with the friction velocity $V_\ast$ . Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

Gravity-driven film flow down a uniformly heated smoothly corrugated rigid substrate

Gravity induced film flow over a rigid smoothly corrugated substrate heated uniformly from below, is explored. This is achieved by reducing the governing equations of motion and energy conservation to a manageable form within the mathematical framework of the well-known long-wave approximation; leading to an asymptotic model of reduced dimensionality. A key feature of the approach and to solving the problem of interest, is proof that the leading approximation of the temperature field inside the film must be nonlinear to accurately resolve the thermodynamics beyond the trivial case of ‘a flat film flowing down a planar uniformly heated incline.’ Superior predictions are obtained compared with earlier work and reinforced via a series of corresponding solutions to the full governing equations using a purpose written finite element analogue, enabling comparisons to be made between free-surface disturbance and temperature predictions, as well as the streamline pattern and temperature contours inside the film. In particular, the free-surface temperature is captured extremely well at moderate Prandtl numbers. The stability characteristics of the problem are examined using Floquet theory, with the interaction between the substrate topography and thermo-capillary instability modes investigated as a set of neutral stability curves. Although there are no relevant experimental data currently available for the heated film problem, recent existing predictions and experimental data concerning the behaviour of corresponding isothermal flow cases are taken as a reference point from which to explore the effect of both heating and cooling.

Nusselt number correlation for turbulent heat transfer of helium–xenon gas mixtures

A gas-cooled nuclear reactor combined with a Brayton cycle shows promise as a technology for high-power space nuclear power systems. Generally, a helium–xenon gas mixture with a molecular weight of 14.5–40.0 g/mol is adopted as the working fluid to reduce the mass and volume of the turbomachinery. The Prandtl number for helium–xenon mixtures with this recommended mixing ratio may be as low as 0.2. As the convective heat transfer is closely related to the Prandtl number, different heat transfer correlations are often needed for fluids with various Prandtl numbers. Previous studies have established heat transfer correlations for fluids with medium–high Prandtl numbers (such as air and water) and extremely low-Prandtl fluids (such as liquid metals); however, these correlations cannot be directly recommended for such helium–xenon mixtures without verification. This study initially assessed the applicability of existing Nusselt number correlations, finding that the selected correlations are unsuitable for helium–xenon mixtures. To establish a more general heat transfer correlation, a theoretical derivation was conducted using the turbulent boundary layer theory. Numerical simulations of turbulent heat transfer for helium–xenon mixtures were carried out using Ansys Fluent. Based on simulated results, the parameters in the derived heat transfer correlation are determined. It is found that calculations using the new correlation were in good agreement with the experimental data, verifying its applicability to the turbulent heat transfer for helium–xenon mixtures. The effect of variable gas properties on turbulent heat transfer was also analyzed, and a modified heat transfer correlation with the temperature ratio was established. Based on the working conditions adopted in this study, the numerical error of the property-variable heat transfer correlation was almost within 10%.

Numerical simulation of coupled diffuse radiation and natural convection in a cubic cavity heated from bottom

We present, a three-dimensional numerical simulation of coupled natural convection with diffuse radiation in a cubic cavity whose all four vertical walls are isothermal, the bottom wall is convectively heated and the top wall is insulated. All walls are treated as black, diffuse and opaque for radiation. The simulations are carried out for the fixed Rayleigh (Ra=105) and Prandtl numbers (Pr=0.71) for a transparent and participating medium. The flow visualization technique Q-criteria has been used for analysis of the flow structure. The isothermal surfaces inside the cavity form vertical co-axially convergent-divergent three-dimensional open and closed nozzles, while inside the cavity Q-criteria reveals the formation of Jellyfish like flow structure. The cavity contains four conical vortices whereas each vortex is occupied in tetrahedron space.

Numerical Solution of Natural Convection on a Vertical Stretching Surface with Suction and Blowing

In this paper, the natural convective heat transfer from a stretching sheet oriented vertically involving surface mass transfer is of primary focus. A similarity solution in three dimensions is described for energy and momentum. The transformed equations are answered by using MATLAB in-built numerical programmer solver bvp4c. For a range of Prandtl numbers and surface mass transfer rates, friction factor and Nusselt numbers are tabulated. The heat transfer mechanism is observed to influence surface mass transfer. Heat transfer rate increases and thermal boundary layer thickness decreases with an increase of Prandtl values. In addition, the current results are compared with the previously published results and initiate to be a successful agreement.In this paper, the natural convective heat transfer from a stretching sheet oriented vertically involving surface mass transfer is of primary focus. A similarity solution in three dimensions is described for energy and momentum. The transformed equations are answered by using MATLAB in-built numerical programmer solver bvp4c. For a range of Prandtl numbers and surface mass transfer rates, friction factor and Nusselt numbers are tabulated. The heat transfer mechanism is observed to influence surface mass transfer. Heat transfer rate increases and thermal boundary layer thickness decreases with an increase of Prandtl values. In addition, the current results are compared with the previously published results and initiate to be a successful agreement.