Thermodynamic and thermophysical effects enabling high-forced convection heat transfer coefficients in supercritical fluids

Abstract

The strong variation of thermophysical properties of working fluids operating in the vicinity of the critical point makes this thermodynamic domain attractive to several energy applications. Therefore, herein a two-dimensional numerical method is used to investigate the effect of local thermophysical property variations on the local and overall thermal performance of internal convective heat transfer in a pipe in 324 operational conditions. Focusing on carbon dioxide and water as heat transfer fluids, an association of the variation of key thermophysical properties with thermohydraulic performance metrics is proposed, namely: (a) the local and (b) mean convective heat transfer coefficient and (c) the maximal temperature obtained at the tube wall. It is shown that there is an optimal combination of parameters such as mass flow rate, operating pressure, wall heat flux, and inlet temperature that, when properly selected, allow for a minimal maximal wall temperature. As expected, optimality is strongly associated with the Widom—or pseudo critical—line that extends from the critical point. Interestingly, however, contrary to what is observed in constant-property fluids, high heat transfer coefficient or minimal maximum temperature lead to different sets of optimal operating conditions. This difference is explained by how thermophysical properties vary locally along heat exchangers, which significantly affects overall heat transfer.     

Cooling Augmentation with Microchanneled Structures

Experiments were conducted to investigate the heat transfer characteristics and cooling performance of subcooled liquid, water, flowing through rectangular cross-section microchanneled structures machined on a stainless steel plate. Heat transfer or flow mode transition was observed when the heating rate or wall temperature was increased. This transition was found to be suggestively induced by the variation in liquid thermophysical properties due to the significant rise of liquid temperature in the microstructures. The influence of such parameters as liquid velocity, subcooling, property variation, and microchannel geometric configuration on the heat transfer behavior, cooling performance and the heat transfer and liquid flow mode transition were also investigated. The experiments indicated that both slngle-phase forced convection and flow boiling characteristics were quite different from those in normal-sized tubes and the heat transfer was obviously intensified.     

Development of Heat Transfer Correlation for Supercritical Water in Vertical Upward Tubes

Supercritical water is widely used in many advanced single-phase thermosiphons due to its favorable heat and mass transfer characteristics and potentially high thermal efficiency. However, the heat transfer characteristics of supercritical water in the deterioration regime cannot be accurately predicted due to the absence of exact evaluation of the effect on steep variation in thermophysical properties near the pseudocritical point. The present paper focuses on the deterioration mode by analyzing the physical mechanism and constructing a new correlation. About 3,000 experimental data on supercritical water, including 40 deteriorated heat transfer cases from open literature, were collected. Quantitative assessment of heat transfer behavior was conducted based on existing test data and previous criteria gathered from extant literature. Based on experimental data evaluation and phenomenological analysis, an improved dimensionless correlation is proposed by introducing multi-dimensionless parameters, which can correct the deviation of heat transfer from its conventional behavior in the Dittus-Boelter equation. Comparisons of various heat transfer correlations with the selected test data show that the new correlation agrees better with the test data versus other correlations selected from the open literature.     

Convective Heat and Mass Transfer in Water at Super—Critical Pressures under Heating or Cooling Conditions in Vertical Tubes

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The Mean Temperature Difference Method for Micro Heat Exchanger Analysis Considering Property Variation

The influence of reducing dimensions to microscale on the performance parameters of parallel flow tubular micro heat exchanger is numerically analyzed considering the thermophysical property variation effect. Also, the improvement in convective heat transfer coefficient, at a given temperature, with the decrease in dimensions to microscale is investigated. In the micro heat exchanger, conventional method fails to give accurate performance analysis due to significant property variation. So, a new temperature difference, i.e. mean temperature difference correlation considering the property variation effect is derived. Operating conditions and geometric parameters are varied, keeping the inlet temperature of the both fluids and inlet velocity of the cold fluid fixed. The following performance parameters are evaluated: effectiveness, volumetric heat transfer coefficient, mean temperature difference, and log mean temperature difference. The reliability of the new mean temperature difference method is checked by calculating the percentage deviation between mean temperature difference and log mean temperature difference value for macroscale to microscale heat transfer. The results show that percentage deviation is maximum at microscale.     

Convective heat transfer to water near the critical region in a horizontal square duct

Numerical analysis has been carried out to investigate forced convective heat transfer to water near the critical region in a horizontal square duct. Near the critical point convective heat transfer in the duct is strongly coupled with large variation of thermophysical properties such as density and specific heat. Buoyancy force parameter has also severe variation with fluid temperature and pressure in the duct. There is flow acceleration along the horizontal duct resulted from fluid density decrease due to the heat transfer from the wall. Local heat transfer coefficient has large variation along the inner surface of the duct section and it depends on pressure. Nusselt number on the center of the bottom surface also has a peak where bulk fluid temperature is higher than the pseudocritical temperature and the peak decreases with the increase of pressure. Flow characteristics of velocity, temperature, and local heat transfer coefficient with water properties are presented and analyzed. Nusselt number distributions are also compared with other correlations for various pressures in the duct.     

Local Convective Heat Transfer from a Horizontal Tube in an Acoustic Cavitation Field

An experiment has been carried out to investigate the local convective heat transfer from a horizontal circular copper tube in an acoustic cavitation field. The effects of acoustical parameters (including sound source intensity, the vibrator location and sound distance), fluid temperature and thermophysical properties of working fluid on heat transfer enhancement were studied, as well as the variation of heat transfer rate with sound source intensity at constant heat flux. Results show that convection heat transfer was remarkably enhanced due to disturbance and impingement by cavitation bubble. Among these cases tested, the maximum augmentation ratio of 3.95 was reached for acetone with a cluster of cavitation bubbles impinging perpendicularly on the tube surface.     

Influence of thermophysical properties on two-phase flow convective boiling of refrigerant mixtures

In this paper, an analytical study on the influence of thermophysical properties on heat transfer characteristics of two-phase flow boiling of some refrigerant mixtures in air/refrigerant horizontal enhanced surface tubing is presented.Correlations were proposed to predict the thermophysical properties of refrigerant mixtures such as thermal conductivity and viscosity as well as their impact on the heat transfer characteristics such as average heat transfer coefficients, and pressure drops of R-507, R-404A, R-410A, and R-407C in two-phase flow boiling inside enhanced surface tubing. In addition, it was found that the refrigerant mixture's pressure drop is a weak function of the mixture's composition.It was also evident that the proposed improved correlations for predicting the thermophysical properties were applicable to the entire heat and mass flux, investigated in the present study. The deviation between the experimental and predicted value using new and improved correlations for the heat transfer coefficient and pressure drop were <±20 %, for the majority of data.     

Predictions of In-Tube Cooling Heat Transfer Coefficients and Pressure Drops of CO2 and Lubricating Oil Mixture at Supercritical Pressures

The in-tube cooling heat transfer and flow characteristics of supercritical pressure CO₂ mixed with small amounts of lubricating oil differ from those for pure CO₂ due to the entrainment of the lubricating oil as well as the sharp property variations of the supercritical CO₂ working fluid. In-tube gas cooling flow and heat transfer models were developed in this study for CO₂ with entrained polyol ester type lubricating oil in a CO₂ gas cooler at supercritical pressures. A “thermodynamic approach,” which treats the CO₂–oil mixture as a homogenous mixture was used with the heat transfer coefficients and frictional pressure drops evaluated based on the thermophysical properties of the CO₂–oil mixture. Thermophysical property variation correction terms as a function of the wall temperature and the oil concentration were included in the models. The frictional pressure drop correlation predicts more than 90% of the experimentally measured data within ±10%, while the heat transfer coefficient correlation predicts more than 90% of the experimentally measured data within ±20%.     

Treatment of Transport at the Interface Between Multilayers via the Lattice Boltzmann Method

The lattice Boltzmann method (LBM) has reached maturity in many aspects for modeling incompressible, laminar flow and heat and mass transfer. However, many issues still need to be clarified. One of those is how to deal with Neumann boundary conditions (heat, momentum, and mass fluxes) at the interface between layers of different thermophysical properties, which is the topic of this work. In this work, we try to illustrate modeling of transient and steady-state heat transfer through multilayers, ensuring continuity of the flux, temperature, momentum, velocity, or species concentration at the interface, which is not a trivial issue in any of the numerical methods. Satisfying continuity conditions at the interface using the LBM needs special treatment, because the relaxation time depends on the thermophysical properties. In this work, methods to solve this issue are introduced for solving 1-D and 2-D, unsteady heat diffusion problems However, the methods can be equally applied for multilayer immiscible fluid flow and mass transfer problems. The predictions of the LBM are compared with those of the finite-volume method (FVM).     

Convective heat transfer and second law analysis of non-Newtonian fluid flows with variable thermophysical properties in circular channels

This study presents an analytical solution, for fully developed non-Newtonian fluid flows in circular channels under isoflux thermal boundary conditions based on perturbation techniques. Since the physical properties are generally a function of temperature and may not be assumed constant under certain circumstances, the change in viscosity and thermal conductivity with temperature was taken into account. Viscous dissipation term was also included in the performed analysis. In this study, first closed form expressions for velocity, temperature distributions, and Nusselt numbers corresponding to constant thermophysical properties were given in terms of governing parameters. Then, numerical calculation was performed to obtain the values of Nusselt number and global entropy generation for variable thermophysical properties. The results revealed that neglecting the property variation significantly affects heat transfer characteristics and entropy generation, in which the deviation from the constant physical property assumption may reach up to about 32.6%.     

Effects of superheat and temperature-dependent thermophysical properties on evaporating thin liquid films in microchannels

A model based on the augmented Young–Laplace equation and the Clausius–Clapeyron equation was developed to describe the extended evaporating meniscus in a microchannel. The effects of the adsorbed film thickness, channel height and temperature-dependent thermophysical properties of the fluid are included in the model at wall superheats up to 50 K. The liquid flow is coupled with the vapor flow to obtain the mass transport across the liquid–vapor interface. The results show that the constant thermophysical property model greatly overestimates the liquid pressure difference and the total thin film heat transfer rate at higher superheats compared with the variable thermophysical property model. The adsorbed film thickness, which is controlled by the disjoining pressure limit, reaches a minimum near about 20 K superheat for water. The maximum film curvature and liquid pressure difference then decrease at superheats larger than 20 K. The effects of the capillary pressure limit produced by the channel height can be reduced by increasing the superheat.     

Mechanisms proposed through experimental investigations on thermophysical properties and forced convective heat transfer characteristics of various nanofluids – A review

Experimental investigations on thermophysical properties and forced convective heat transfer characteristics of various nanofluids are reviewed and the mechanisms proposed for the alteration in their values or characteristics due to the addition of nanoparticles are summarized in this review. A comprehensive review on the experimental works on specific application of nanofluids is also presented. As the literature in this area is spread over a span of two decades, this review could be useful for researchers to have an accurate screening of wide range of experimental investigations on thermophysical properties, forced convective heat transfer characteristics, the mechanisms involved and applications of various nanofluids.     

Effect of Relative Humidity on the Prediction of Natural Convection Heat Transfer Coefficients

Results of an investigation into the sensitivity of natural convection heat transfer correlations with respect to relative humidity are presented. Given the relatively small values of natural convection heat transfer coefficients, small changes in the thermophysical properties can have a significant impact on the values predicted by theoretical/empirical correlations. In this study, the thermophysical properties are assumed to be those of a dry air and water vapor mixture. The mole fractions are determined as a function of relative humidity. Several widely used natural convection heat transfer correlations have been examined to determine the impact of varying the relative humidity on the predicted Nusselt number. The results show a general trend of an increasing Nusselt number with relative humidity. The results presented in this paper provide an engineering tool for obtaining accurate values of natural convection heat transfer coefficients for a moist air environment using only the thermophysical properties of dry air.     

Heat transfer to sub-cooled binary solution in horizontal tube

Predicted heat transfer coefficients (HTC) are widely used for calculations of various heat and mass transfer processes. Various empirical and semi-empirical models of non-dimensional groups are used for calculating the heat transfer coefficients. These groups depend on the fluid and flow properties. The common accuracy of the predicted heat transfer coefficient is usually about ±25%; however, the accuracy is failing by the lack of mechanistic model for convective heat transfer and by the inaccurate predictions of the fluid properties. This work is aimed to improve the heat transfer coefficient prediction by reducing the deviations which associated with the fluid properties. When the fluid is a mixture of miscible fluids the predictions of the fluid properties are very rough and therefore the prediction of the heat transfer coefficient is more complicated.In the present study the heat transfer coefficient of sub-cooled organic mixture chlorodifluoromethane (R22)–dimethylacetamide (DMAC) was measured experimentally. In order to compare the experimental value with the predicted one, thermophysical properties of the solution, such as density, viscosity, heat capacity and thermal conductivity have to be known. Since the thermal conductivity of the solution (R22–DMAC) was the only unknown property, various correlations and mixing rules were tested, and the most appropriate was chosen. Based on this method for evaluating the solution’s properties the predicted HTC obtained with an error range of 15%.     

The influence of binary mixture thermophysical properties in the analysis of heat and mass transfer processes in solar distillation systems

Although a substantial amount of research work has already been devoted to various aspects of modeling the convective and mass transport processes in solar distillation systems, it appears that the role of thermophysical and transport properties of the working medium and their effect on the thermal behavior and performance analysis of such systems has been left almost completely unnoticed. The working medium in these systems, which is a binary mixture of water vapor and dry air in equilibrium, appears to exhibit a completely different set of properties than dry air, especially at saturation conditions and at the higher region of the solar still operational temperature range. An analysis is presented aiming to signify the effect of binary mixture thermophysical properties on the transport processes and the associated quantities and evaluate the thermophysical properties of the working medium in these systems, based on contemporary data for dry air and water vapor. The derived results, in the form of convenient algebraic correlations, are employed to investigate the effect of using the appropriate thermophysical properties on the calculation of the convective heat and mass transfer, as well as the distillate mass flow rates. According to the results from the present investigation, although the use of improper dry air data leads to a significant overestimation of the convective heat transfer coefficient, the errors associated with the use of improper dry air properties is a moderate overestimation of distillate output which is estimated to be up to 10% for maximum average still temperatures of 100 °C.     

矩形冷却通道内超临界RP-3航空煤油对流传热数值研究

对超临界压力下RP-3航空煤油在内截面宽为4mm、高为4mm、固体壁面厚为1mm、加热段长度为500mm的水平矩形冷却通道内的对流传热特性进行了数值模拟研究。分析了通道内速度场的分布规律,讨论了热流密度、压力、进口温度对传热的影响。计算结果表明:当主流温度处于拟临界温度附近时,流体物性参数变化剧烈,导致传热系数降低,传热出现恶化。在超临界压力下,较低的热流密度、增大压力、降低进口流体温度或提高质量流速均有利于改善冷却通道内的传热性能。     

Study of turbulent heat transfer of aviation kerosene flows in a curved pipe at supercritical pressure

The flow and heat transfer characteristics of China No. 3 aviation kerosene in a heated curved tube under supercritical pressure are numerically investigated by a finite volume method. A two-layer turbulence model, consisting of the RNG k–ε two-equation model and the Wolfstein one-equation model, is used for the simulation of turbulence. A 10-species kerosene surrogate model and the NIST Supertrapp software are applied to obtain the thermophysical and transport properties of the kerosene at various temperature under a supercritical pressure of 4 MPa. The large variation of thermophysical properties of the kerosene at the supercritical pressure make the flow and heat transfer more complicated, especially under the effects of buoyancy and centrifugal force. The centrifugal force enhances the heat transfer, but also increases the friction factors. The rise of the velocity caused by the variation of the density does not enhance the effects of the centrifugal force when the curvature ratios are less than 0.05. On the contrary, the variation of the density increases the effects of the buoyancy.     

超临界碳氢燃料对流换热特性解析

选用10组分模型替代碳氢燃料,对其在临界点附近的物理特性进行详细分析描述。根据超临界碳氢燃料热物性变化及其在管道内的对流换热特征,基于边界层理论,建立其在换热管中对流换热边界层分析模型和微分方程式,采用理论分析方法给出多项式和正弦速度分布式下常物性和变物性时的温度分布函数表达式。给出的计算公式为超燃冲压发动机的冷却计算提供指导。     

Physical Effects of Variable Thermophysical Fluid Properties on Flow and Thermal Development in Micro-Channel

Micro-scale cooling is an efficient and effective cooling technique to achieve the goal of higher heat removal capabilities. The present research focuses to find the physical effects of fluid property variations on flow and thermal development in micro-channel. The effects of temperature-dependent density, viscosity, and thermal conductivity variations on single-phase laminar forced convection are numerically investigated. The problem is especially simulated for hydrodynamically and thermally developing water flow in micro-channel with no-slip, no-temperature jump, and constant wall heat flux boundary conditions. It is observed that the density variation induces radially inward flow due to continuity, which sharpens the axial velocity profile and decreases Nusselt number compared to constant property solution. The axial velocity profile significantly alters due to viscosity variation. This alteration varies along the micro-flow and it induces radially flow due to flow continuity. The reducing rate of Nusselt number for viscosity variation is substantially lower than constant property solution due to a significant flattening effect of the axial velocity profile, which augments the Nusselt number. Thermal-conductivity variation across the flow induces radial conduction, which enhances convection compared to constant property solution. Additionally, the effects of thermophysical fluid property variations on static gauge pressure drop are also investigated.