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Heat Transfer and Energy Dissipation
Published in G. I. Kelbaliyev, D. B. Tagiyev, S. R. Rasulov, Transport Phenomena in Dispersed Media, 2020
G. I. Kelbaliyev, D. B. Tagiyev, S. R. Rasulov
These numbers take into account the influence of the physical properties of the coolant and the features of the hydromechanics of its movement on the intensity of heat transfer. The physicochemical properties of the liquid (gas) entering into these equations must be taken at the determining temperature. Many factorial equations of convective heat transfer include a factor (Pr/Prw)0.25,where Prw is the value of the number calculated at the wall temperature. For gases Pr/Prw=1 with both heating and cooling, since for gases the number is approximately constant, independent of temperature and pressure. At present, there are a lot of formulas in the literature for calculating heat transfer coefficients, both for forced and for natural convection. Below are some of the criteria equations used in practical heat transfer calculations for forced (laminar and turbulent flows) and natural convection. The heat transfer in the turbulent flow is mainly determined by the intensity of the movement of chaotically pulsating volumes of liquid. The difficulty in analyzing turbulent heat exchange is that the intensity of turbulent exchange depends on the distance to the solid wall. It is generally recognized that a purely turbulent heat transfer prevails far from the solid wall, whereas in the immediate vicinity of the wall, the molecular nature of the heat transfer is paramount. The ratio of turbulent heat transfer coefficients is determined by the numerical value of the turbulent Prandtl number. According to many experimental data, PrT it can have values from 0.5 to 1 and remain constant or vary in the transverse direction of the turbulent flow. For practical calculations of the heat transfer intensity in turbulent flow, the relationships correlating the experimental results are applied.
Comparison of turbulent Prandtl number correction models for the Stanton evaluation over rough surfaces
Published in International Journal of Computational Fluid Dynamics, 2020
Two models were implemented in SU2 to correct the predicted heat flux over rough surfaces. The models were based on a corrected turbulent Prandtl number near the wall. The first model was developed and calibrated by Aupoix; the second one was based on a temperature shift model initially developed for the integral boundary layer prediction to predict heat transfer over a rough surface. By integrating the equation for the normalised temperature , the model use the effective turbulent Prandtl number equation to obtain a two parameters Prandtl correction model. The Aupoix Prandtl correction and the 2PP correction models were successfully implemented and validated against literature results. The turbulent Prandtl number correction models reduce the magnitude of the heat transfer, and results are closer to experiments. For most of the cases presented here, the discrepancies between the 2PP and the Aupoix Prandtl correction model are small, of the order of the typical experimental uncertainties on heat transfer measurements. In the worst cases, the discrepancy can reach a maximum of for flow around an iced aerofoil. Further work will consist in analysing this effect on ice shape predictions.
Numerical Study of Compressible Wall-Bounded Turbulence – the Effect of Thermal Wall Conditions on the Turbulent Prandtl Number in the Low-Supersonic Regime
Published in International Journal of Computational Fluid Dynamics, 2022
David J. Lusher, Gary N. Coleman
The objective of this study is to determine the behaviour of the turbulent Prandtl number within a subspace of compressible wall-bounded turbulence via Direct Numerical Simulation (DNS). The turbulent Prandtl number, defined by analogy of the molecular Prandtl number as the ratio of momentum to thermal eddy diffusivities in eddy-viscosity models (Cebeci and Bradshaw 1984), is widely used to model heat transfer in turbulent flows. Accurate prediction and modelling of for turbulent wall-bounded shear flows has long been the subject of analytical, numerical, and experimental investigations, due to its importance in a wide range of engineering applications (Cebeci 1973; Reynolds 1975). Kays' remarks in 1994 (Kays 1994) regarding the relevance of , and the eddy-diffusivity assumption upon which it is based, remain in force – given the continuing need for a simple model that ‘is capable of accurately predicting behaviour in a great variety of situations – in fact in most engineering boundary layer problems that one is likely to encounter’. More recently, Churchill (2002) noted that the turbulent Prandtl number ‘remains to this day incompletely defined either experimentally or theoretically’. In addition to wall-bounded engineering flows, is also of importance in atmospheric boundary layers for weather and climate prediction, where it is necessary to understand its role to distinguish between active and passive scalars (Li 2019).
Calibration of the Reynolds Stress Model for the Simulation of Gas Flows in Corrugated Tubes
Published in Heat Transfer Engineering, 2018
Steven Mac Nelly, Willi Nieratschker, Marc Nadler, Kevin Einsle, Antonio Delgado
The turbulent Prandtl number increases the effective thermal conductivity λeff by the effect of turbulent flow conditions. The turbulent viscosity can be adjusted as well. In case of the RSM-ω, the turbulent viscosity is used for determining the turbulent diffusion Dt, ij and the effective thermal conductivity λeff.