Experimental and numerical investigation of convection heat transfer of CO2 at supercritical pressures in a vertical mini-tube

Convection heat transfer of CO₂ at supercritical pressures in a 0.27 mm diameter vertical mini-tube was investigated experimentally and numerically for inlet Reynolds numbers exceeding 4.0 × 10³. The tests investigated the effects of heat flux, flow direction, buoyancy and flow acceleration on the convection heat transfer. The experimental results indicate that the flow direction, buoyancy and flow acceleration have little influence on the local wall temperature, with no deterioration of the convection heat transfer observed in either flow direction for the studied conditions. The heat transfer coefficient initially increases with increasing heat flux and then decreases with further increases in the heat flux for both upward and downward flows. These phenomena are due to the variation of the thermophysical properties, especially c_p. The numerical results correspond well with the experimental data using several turbulence models, especially the Realizable k–ε turbulence model.     

Numerical investigation on conjugate heat transfer to supercritical CO2 in membrane helical coiled tube heat exchangers

ABSTRACT

Conjugate heat transfer to supercritical CO₂ in membrane helical coiled tube heat exchangers has been numerically investigated in the present study. The purpose is to provide detailed information on the conjugate heat transfer behavior for a better understanding of the abnormal heat transfer mechanism of supercritical fluid. It could be concluded that the supercritical fluid mass flux and vertical/horizontal placement would significantly affect the abnormal heat transfer phenomenon in the tube side. The flow field of supercritical fluid is affected by both the buoyancy and centrifugal force in the conjugate heat transfer process. The local wall temperature and heat transfer coefficient in the tube side would rise and fall periodically for the horizontal heat exchanger, but this phenomenon will gradually disappear with the increase of the mass flow rate or fluid temperature in the tube side. The dual effects of buoyancy force and centrifugal force lead to the deflection of the second flow direction for the vertical placement, which further results in the heat transfer deterioration region on the top-generatrix wall for the downward flow being larger than that for the upward flow.     

Numerical investigation on heat transfer of supercritical water in a roughened tube

ABSTRACT

The turbulent mixed convection heat transfer of supercritical water flowing in a vertical tube roughened by V-shaped grooves has been numerically investigated in this paper. The turbulent supercritical water flow characteristics within different grooves are obtained using a validated low-Reynolds number κ-ε turbulence model. The effects of groove angle, groove depth, groove pitch-to-depth ratio, and thermophysical properties on turbulent flow and heat transfer of supercritical water are discussed. The results show that a groove angle γ = 120° presents the best heat transfer performance among the three groove angles. The lower groove depth and higher groove pitch-to-depth ratio suppress the enhancement of heat transfer. Heat transfer performance is significantly decreased due to the strong buoyancy force at T_b = 650.6 K, and heat transfer deterioration occurs in the roughened tube with γ = 120°, e = 0.5 mm, and p/e = 8 in the present simulation. The results also show that the rapid variation in the supercritical water property in the region near the pseudo-critical temperature results in a significant enhancement of heat transfer performance.     

Turbulent convective heat transfer of methane at supercritical pressure in a helical coiled tube

The heat transfer of methane at supercritical pressure in a helically coiled tube was numerically investigated using the Reynolds Stress Model under constant wall temperature. The effects of mass flux (G), inlet pressure (P_in) and buoyancy force on the heat transfer behaviors were discussed in detail. Results show that the light fluid with higher temperature appears near the inner wall of the helically coiled tube. When the bulk temperature is less than or approach to the pseudocritical temperature (T _pc ), the combined effects of buoyancy force and centrifugal force make heavy fluid with lower temperature appear near the outer-right of the helically coiled tube. Beyond the T _pc , the heavy fluid with lower temperature moves from the outer-right region to the outer region owing to the centrifugal force. The buoyancy force caused by density variation, which can be characterized by Gr/Re² and Gr/Re^2.7, enhances the heat transfer coefficient (h) when the bulk temperature is less than or near the T _pc , and the h experiences oscillation due to the buoyancy force. The oscillation is reduced progressively with the increase of G. Moreover, h reaches its peak value near the T _pc . Higher G could improve the heat transfer performance in the whole temperature range. The peak value of h depends on P_in. A new correlation was proposed for methane at supercritical pressure convective heat transfer in the helical tube, which shows a good agreement with the present simulated results.     

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。     

Experimental and numerical study of convection heat transfer of CO2 at super-critical pressures during cooling in small vertical tube

Convection heat transfer of CO₂ at super-critical pressures during cooling in a vertical small tube with inner diameter of 2.00 mm was investigated experimentally and numerically. The local heat transfer coefficients were determined through a combination of experimental measurements and numerical simulations. This study investigated the effects of pressure, cooling water mass flow rate, CO₂ mass flow rate, CO₂ inlet temperature, flow direction, properties variation and buoyancy on convection heat transfer in small tube. The results show that the local heat transfer coefficients vary significantly along the tube when the CO₂ bulk temperatures are in the near-critical region. The increase of specific heat and turbulence kinetic energy due to the density variation leads to the increase of the local heat transfer coefficients for upward flow. The buoyancy effect induced by density variation leads to a different variation trend of the local heat transfer coefficients along the tube for upward and downward flows. The numerical simulations were conducted using several k–ε turbulence models including the RNG k–ε model with a two-layer near wall treatment and three low-Reynolds number eddy viscosity turbulence models. The simulations using the low-Reynolds number k–ε model due to Yang–Shih has been found to be able to reproduce the general features exhibited in the experiments, although with a relatively large overestimation of measured wall temperatures. A better understanding of the mechanism of properties variation and buoyancy effects on convection heat transfer of CO₂ at super-critical pressures in a vertical small tube during cooling has been developed based on the information generated by the simulation on the detailed flow and turbulence fields.     

Effect of curvature ratios on the heat transfer and flow developments in the horizontal spirally coiled tubes

Effect of curvature ratios on the heat transfer and flow developments in the horizontal spirally coiled tubes are investigated. The spirally coiled tube is fabricated by bending a 8.00 mm diameter straight copper tube into a spiral-coil of five turns. The spirally coiled tube with three different curvature ratios of 0.02, 0.04, 0.05 under constant wall temperature are tested. Cold water entering the innermost turn flows along the spiral tube and flows out at the outermost turn. The turbulent flow and heat transfer developments are simulated by using the k–ε standard turbulence model. A finite volume method with an unstructured nonuniform grid system is employed for solving the model. The simulated results are validated by comparing with the present experiment. The predicted results for the convective heat transfer and flow characteristics are reasonable agreement with the experiments. The centrifugal force has significant effect on the enhancements of heat transfer and pressure drop. In addition, due to this force, the heat transfer and pressure drop obtained from the spirally coiled tube are higher than those from the straight tube.     

Laminar mixed convection boundary layers induced by a linearly stretching permeable surface

The boundary layer flow on a linearly moving permeable vertical surface is studied when the buoyancy force assists or opposes the flow. Similarity and local similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as Prandtl number Pr, injection parameter d, and the mixed convection parameter λ=Gr_x/Re_x², which determine the velocity and temperature distributions, the heat transfer coefficient, and the shear stress at the surface are studied. The heat transfer coefficient increases as λ assisting the flow for all d for uniformly or linearly heated surface and as Pr increases it becomes almost independent of λ. However, as the temperature inversely proportional to the distance up the surface, the buoyancy has no effects on the heat transfer coefficient. Critical buoyancy parameter values are obtained for vanished shear stress and for predominate natural convection. Critical values are also presented for predominate buoyancy shear stress at the surface for assisting or opposing flow. A closed form analytical solution is also presented as a special case of the energy equation.     

Optimization of high-pressure shell-and-tube heat exchanger for syngas cooling in an IGCC

This work investigates the flow field and the heat transfer characteristics of a shell-and-tube heat exchanger for the cooling of syngas. Finite volume method based on FLUENT software was used and the RNG k–ε turbulence model was adopted for modeling turbulent flow. The porosity rate, the distribution of the resistance and the distribution of the heat source are introduced to FLUENT by coupling the user defined function. The pressure drop, the temperature distribution and the variation of local heat transfer are studied under the effects of the syngas components and the operating pressure, and the effect of the arrangement of the baffles on the heat transfer is studied. The results show that higher operation pressure can improve the heat transfer, however brings bigger pressure drop. The components of the syngas significantly affect the pressure drop and the heat transfer. The arrangement of the baffles influences the fluid flow.     

Turbulent heat transfer characteristics of supercritical n‐decane in a vertical tube under various operating pressures

To explore the effect of the operating pressure on the flow and thermal characteristics in a vertical tube with supercritical n‐decane, the inner wall temperature along the streamwise direction, the applicability of empirical correlations and buoyancy criteria are studied firstly. The mechanisms in views of density distribution, velocity field, turbulence intensity, the thickness of the thermal boundary layer, and secondary flow are then analyzed. It is observed that the buoyancy is helpful for the phenomenon of heat transfer deterioration at lower operating pressures but higher operating pressures can diminish this tendency. According to this reason, the empirical correlation proposed by Bae and Kim is suitable for the higher operating pressures but cannot well predict the occurrence of heat transfer deterioration. However, it can be evaluated by the buoyancy criterion Gr/Re² = 0.01 qualitatively. The decrease of turbulence intensity, the thickened thermal boundary layer, and secondary flow generation make contributions to the heat transfer deterioration in particular. Similarly, this situation can be diminished and even removed by the higher operating pressures.     

Mixed convection about a rotating sphereConvection mixte autour d'une sphere tournanteMischkonvektion an einer rotierenden kugelCмeшaHHaя кoHвeкция oкoлo вpaщaющeйCя Cфepы

The paper presents a theoretical analysis of flow and heat transfer characteristics of the effects of buoyancy force on laminar boundary layer over a rotating sphere in forced flow under two kinds of heating conditions: uniform wall temperature and uniform surface heat flux. By applying appropriate coordinate transformations and using Merk's types of series, the governing momentum and energy equations are reduced to a set of coupled ordinary differential equations, which depend on wedge, rotation and buoyancy parameters. Numerical computations are carried out for Prandtl numbers 0.7,1.0 and for various values of buoyancy and rotation parameters. For aiding flow, it is found that both the friction factor and the local Nusselt number increase with increasing buoyancy force. The local free stream velocity increases with buoyancy which, in turn, affects the friction coefficient and Nusselt number. The coupling between rotation and buoyancy results in increased overshooting of the velocity profiles in the vicinity of the rotating sphere. For an equivalent buoyancy effect, heating by uniform surface heat flux yields larger local Nusselt number than heating by uniform wall temperature. The ratio Nu_UHF/Nu_UWT is higher for the rotating sphere (as compared to a nonrotating case) and further the ratio increases as the sphere spins faster. The effect of free stream, rotation and buoyancy on the eruption of flow is examined and also a suggestion for further investigation is made.     

Analysis of wind flow around a parabolic collector (2) heat transfer from receiver tube

Parabolic collectors of commercial solar thermal power plants are subject to variable convection heat transfer from the receiver tube. In the present study heat transfer from a receiver tube of the parabolic trough collector of the 250 kW solar power plants in Shiraz, Iran, is studied taking into account the effects of variation of collector angel of attack, wind velocity and its distribution with respect to height from the ground.The governing equations for the two-dimensional steady state wind flow include continuity, momentum and energy equations and RNG-based k–ε model for turbulence scheme. Finite volume discretization method is used to solve the governing equations with wall function boundary condition and the SIMPLE approach is employed to iterate for the pressure correction and convergence of the velocity field. The momentum equation contains buoyancy force when the buoyancy effect is high and force convection effect is low.Computation is carried out for various wind velocities and different collector orientations with respect to wind direction. For solution of the energy equation, temperature of the receiver tube is taken as 350 K and ambient temperature is assumed to be 300 K. Various recirculation and temperature fields were observed around the receiver tube for different flow conditions. Effect of collector orientation on the average Nu number for the receiver tube was found negligible when the wind speed is low (Re⩽4.5×10⁵ based on the collector aperture). But when the wind velocity is high (Re>4.5×10⁵), the collector effect on the variation of Nu around the glass cover of the absorber tube is considerable.     

Three-dimensional CFD analysis for simulating the greenhouse effect in solar chimney power plants using a two-band radiation model

The greenhouse effect in the solar collector has a fundamental role to produce the upward buoyancy force in solar chimney power plant systems. This study underlines the importance of the greenhouse effect on the buoyancy-driven flow and heat transfer characteristics through the system. For this purpose, a three-dimensional unsteady model with the RNG k–ε turbulence closure was developed, using computational fluid dynamics techniques. In this model, to solve the radiative transfer equation the discrete ordinates (DO) radiation model was implemented, using a two-band radiation model. To simulate radiation effects from the sun's rays, the solar ray tracing algorithm was coupled to the calculation via a source term in the energy equation. Simulations were carried out for a system with the geometry parameters of the Manzanares power plant. The effects of the solar insolation and pressure drop across the turbine on the flow and heat transfer of the system were considered. Based on the numerical results, temperature profile of the ground surface, thermal collector efficiency and power output were calculated and the results were validated by comparing with experimental data of this prototype power plant. Furthermore, enthalpy rise through the collector and energy loss from the chimney outlet between 1-band and two-band radiation model were compared. The analysis showed that simulating the greenhouse effect has an important role to accurately predict the characteristics of the flow and heat transfer in solar chimney power plant systems.     

超临界CO2倾斜螺旋槽管内冷却换热特性研究

为了提高气体冷却器内换热效率,对不同倾斜角下(-90°,-45°,0°,45°,90°)螺旋槽管内超临界CO2冷却对流换热特性进行了数值模拟,分析了各槽管内的湍动能和速度分布随倾斜角的变化趋势,并研究了不同螺旋角下倾斜角对换热特性的影响。结果表明:浮升力沿流动方向分量和垂直于流动方向分量对流动特性的影响并不相同;在类气区,流体速度对流动特性起主要作用,且换热系数随倾斜角的减小而增大;在类液区,流动特性的主要影响因素是速度梯度,此时换热系数随倾斜角的变化与类气区相反;螺旋角越大即螺旋程度越小,当流体倾斜向上流动时浮升力效应越为显著;当螺旋角为 0.70 rad时,最优倾斜角度为-45°,当螺旋角为0.94 rad时,最优倾斜角为45°。     

超临界压力下航空煤油在竖直管内的传热研究

对竖直上升管内超临界压力下航空煤油的传热特性进行了实验研究。分析了不同质量流量、热流密度、压力和进口温度对超临界压力下航空煤油传热特性的影响。实验结果表明,提高质量流量或进口温度均使煤油传热效果变好。而热流密度对流体传热的影响主要在于改变了流体和壁面温度,热流密度越大,传热系数越高。压力对煤油传热影响不大,一般情况下,提高压力会恶化传热。超临界状态下,煤油物性变化很大,因此对煤油的传输和热力学性质的准确计算是研究超临界压力下传热现象的关键。利用拓展的对比态法来计算煤油的密度和传输特性,如黏度、热导率等。给出了煤油在超临界压力下的传热关联式,其计算值和实验值吻合良好。     

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%.     

Numerical study of laminar mixed convection of a nanofluid in horizontal curved tubes

Fully developed laminar mixed convection of a nanofluid consisting of water and Al₂O₃ in a horizontal curved tube have been studied numerically. Three-dimensional elliptic governing equations have been used. Simultaneous effects of the buoyancy force, centrifugal force and nanoparticles concentration has been presented and discussed. The nanoparticles volume fraction does not have a direct effect on the secondary flow, axial velocity and the skin friction coefficient. However, its effect on the entire fluid temperature could affect the hydrodynamic parameters when the order of magnitude of the buoyancy force becomes significant compared to the centrifugal force. For a given Reynold number, buoyancy force has a negative effect on the Nusselt number while the nanoparticles concentration has a positive effect on the heat transfer enhancement and also on the skin friction reduction.     

粗糙圆管内超临界航空煤油湍流换热特性分析

给出了国产航空煤油RP-3的三组分热物性替代燃料模型。采用k-ε湍流模型结合增强壁面处理的方法对超临界压力下航空煤油RP-3在圆形粗糙冷却通道中的流动与换热过程进行数值研究。分析了粗糙元形状、高度以及间高比等因素对其超临界流动和传热特性的影响规律,探究了人为粗糙度强化超临界航空煤油换热的机理。结果表明,人为设置粗糙元能使壁面附近产生局部回流区和旋涡结构,强化煤油与受热壁面间的对流换热。通过合理布置粗糙元结构,能大幅降低圆形冷却通道的壁面温度,有效抑制航空煤油的超临界传热恶化现象的发生。     

Analysis of turbulent flow and heat transfer over a double forward facing step with obstacles

A numerical study has been conducted to analyze the turbulent forced convection heat transfer for double forward facing step flow with obstacles. Obstacles have rectangular cross-sectional area with different aspect ratio that is located before each step. The numerical solutions of continuity, momentum and energy equations were solved by using a commercial code which uses finite volume techniques. The effect of turbulence was modeled by using a k–ε model. The effects of step height, obstacle aspect ratio and Reynolds number on the flow and heat transfer are investigated. The obtained results show that the rate of heat transfer is enhanced as aspect ratio of obstacle increases and this trend is affected by the step height. Also the results verified that the pressure drop decreases as obstacle aspect ratio increases.