A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids

Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations.

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

Heat transfer and skin-friction in channel with flow behind a cylinder

The paper presents the results of an experimental study of the parameters of the boundary layer, distribution of static pressure, heat transfer and friction coefficients of smooth surface located in the wake behind the cylinder in the channel. Cylinders of various diameters were placed in a slotted channel with a height of 30 mm on its axis. In all experiments, the flow velocity at the inlet was 50 m/s. The cylinder was made unheated. The friction coefficients of the smooth model were determined both from the velocity profile in the boundary layer and by direct weighing of the model on a one-component strain-gage balance. The local values of the heat transfer coefficients were determined by transient heat-transfer method using a thermal imager. The values of the heat transfer and friction coefficients in the wake behind the cylinder, referred to the values on the smooth wall in the undisturbed flow, varied in the range 1.15–1.65 and 1.3–1.75, respectively. The value of the Reynolds analogy factor for all cylinder diameters turned out to be less than unity.

The Heat Transfer Coefficient Predictions in Engineering Applications

Most engineering applications have boundary layers; the convective transport of mass, momentum and heat normally occurs through a thin boundary layer close to the wall. It is essential to predict the boundary layer heat transfer phenomenon on the surface of various engineering machines through calculations. The experimental, analogy and numerical methods are the three main methods used to obtain convective heat transfer coefficient. The Reynolds analogy provides a useful method to estimate the heat transfer rate with known surface friction. In the Reynolds analogy, the heat transfer coefficient is independent of the temperature ratio between the wall and the fluid. Other methods also ignore the effect of the temperature ratio. This paper summarizes the methods of predicting heat transfer coefficients in engineering applications. The effects of the temperature ratio between the wall and the fluid on the heat transfer coefficient predictions are studied by summarizing the researches. Through the summary, it can be found that the heat transfer coefficients do show a dependence on the temperature ratio. And these effects are more obvious in turbulent flow and pointing out that the inaccuracy in the determination of the heat transfer coefficient and proposing that the conjugate heat transfer analysis is the future direction of development.

Heat transfer and skin-friction in a nonequilibrium adverse pressure gradient

The paper presents the results of an experimental study of influence of a weak and moderate nonequilibrium adverse pressure gradient (APG) on the parameters of the dynamic and thermal boundary layers. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re **=5500. The section of the channel with APG was a slotted channel with an opening angle of the upper wall of 0-14°. The values of the relative (referred to the parameters in a zero pressure gradient flow at the same Re **) friction and heat transfer coefficients, as well as the Reynolds analogy factor depending on the longitudinal pressure gradient, are obtained. The values of the relative friction coefficient decreased to cf/cf0 =0.7 and those of the heat transfer to St/St0=0.9. A maximum value of the Reynolds analogy factor (St/St0)/(cf/cf0 )=1.16 was reached for the pressure gradient parameter β=2.9. The ratio of the heat transfer and drag coefficients of the dimpled to smooth surfaces remained approximately constant regardless of the presence or magnitude of a adverse pressure gradient.

Generalized Reynolds Analogy: An Engineering Prospective of Thermo-Fluid Physics for Heat Exchanger Design

In practical interest of Reynolds analogy for power and process industries, in a unified system approach an engineering prospective of thermo-fluid physics has been proposed by developing a theory of basic heat exchanger design and analysis. Needless to mention of excellent books on heat exchangers, this paper focuses on the novelty of heat exchanger, which in author’s view depends upon the possibility of energy exchange between two fluid streams at different temperatures. Since operation cannot be random, the principal act of design is to engineer a product such that it operates in specified manner to perform its desired function of de-energizing one stream by virtue of energizing the other. With law of the integral as the guiding principle of physics, it shall be made clear that energy exchange in the form of heat must be accompanied by energy transfer such that heat exchanger must operate due to simultaneous process of cooling and heating of the fluid streams with an intervening medium. To unlock the secret of steady operation a fundamental postulate concerning thermodynamic behavior of the system has been made by invoking zeroth law of thermodynamics. Remarkably, it lends itself a necessary and sufficient condition concerning proportionality between heat-flux and required temperature difference to yield fluids unique thermal response in relation to the heat transfer surface temperature. Consequently, far-reaching physical implications of the constant of proportionality on system design can be clearly exposed of with due consideration to Eulerian descriptions of conservation principles according to Newton’s mechanical theory. Consistently enough, because of thermal non-equilibrium, effectiveness of system design and off design performance warrants a fundamental theorem like one suggested by Reynolds concerning augmentation of thermal diffusion due to fluid motion. Accordingly, flow rates become critical operating parameters for thermal performance and pressure drop requirements. Furthermore, and most importantly, in support of the theorem an order magnitude analysis appears to be in order, to show the dependence of flow resistance and hence, system thermal response on fluid flow behavior in terms of non-dimensional parameters. As a result, it is made clear that development of design correlations for friction factor and non-dimensional heat transfer coefficient in terms of both Reynolds number and Prandtl number is an integral part of heat exchanger design process by gathering experimental data. Finally, generalized mathematical statement of Reynolds analogy has been obtained relating Stanton number with friction factor, which reduces to our familiar expression for Prandtl number of unity.

Improvement of Condensation Model With the Presence of Non-Condensable Gas for Thermal-Hydraulic Analysis in Containment

Steam condensation plays a key role in prediction of the pressure behavior and hydrogen distribution in the containment during a hypothetical loss-of-coolant accident or a severe accident in a light water nuclear reactor. The objective of this study is to evaluate and improve the condensation model in GASFLOW code. Reynolds analogy coupled with wall function and Chilton-Colburn empirical analogy is used to model heat and mass transfer in GASFLOW, which has requirements for dimensional distance of the first cell near the wall and some deficiencies in description of heat and mass transfer process in the stagnant zone. Based on the evaluation of original condensation, the results shows good agreement with COPAIN experiment cases where the mass fraction of air ranges from 76.7 to 86.4%. However, with the changes in geometry of the facility and the presence of helium, the original model has a large deviation in the prediction of pressure, temperature and gas distribution compared with MISTRA ISP47 (OECD International Standard Problem No. 47) experiment data. This work proposes a modified condensation model which uses McAdams correlation and Schlichting correlation with a weight factor to calculate natural, forced, or mixed convection heat transfer coefficient, and adopts Chilton-Colburn empirical analogy to model mass transfer. The modified model has no requirement for the dimensionless distance near the wall in heat and mass transfer calculation and improves the prediction performance of heat transfer in stagnant zone. The prediction result of the modified model shows good agreements with MISTRA ISP47 problem, and the error of it compared with COPAIN experiment data is within 25% which is the same as that predicted by the original model.

Experimental and Numerical Investigation of Flow and Heat Transfer in Stationary Two-Pass Rectangular Duct (AR = 1:2) with Continuous and Broken V- shaped ribs

The combined experimental and Large Eddy Simulations (LES) were performed in the stationary two-pass duct of aspect ratio (AR) 1:2. The experiments were conducted with three different rib arrangements, namely 60° V, 60° V-IV, and broken 60° V-IV ribs, and analysis was carried out with Reynolds numbers of 45,000, 60,000, and 75,000. The infrared thermography (IRT) technique is employed to obtain the local temperature distribution on heated smooth and ribbed surfaces. In all ribbed cases, the copper ribs are glued to the heated surface with a fixed rib height-to-hydraulic diameter (e / Dh) ratio is 0.125 and the rib pitch-to-height ratio (P / e) is 10 and 5 for continuous and broken ribs, respectively. In addition, LES turbulence model was adopted for carrying out simulation to understand the flow and heat transfer behavior in ducts populated with all three V-shaped ribs. The comparison of the time-averaged thermal fields generated using computations has been made with experimentally measured Nusselt numbers, friction factors, thermal performance factor (TPF), and Reynolds analogy performance parameter (RAPP) for all cases. The overall thermal performance factor was found to be quantitatively within 8.0 - 10.66% between experimental and numerical results. Among all the cases, the 60° V-IV ribbed duct provides the best TPF and RAPP than the other two ribbed ducts, whereas the smooth duct shows poor TPF.