Optimization of heat transfer coefficient correlation at supercritical pressure using genetic algorithms

The paper presents a new heat transfer correlation of water at supercritical pressure after review on existing heat transfer correlations. The new correlation is optimized by genetic algorithms based on existing test data. Based on current results, we conclude that genetic algorithms are effective to search a global optimized correlation but it is important to carefully select representative and authentic test data to reach an optimized solution and special attention needs to be paid on the deteriorated heat transfer region in the design of supercritical water reactor because it can not be predicted well by any correlations reviewed. Supported by the National Basic Research Program of China (973 Program No. 2007CB209800) and Atomic Energy of Canada Limited.     

Sensitivity analysis of freestream turbulence parameters on stagnation region heat transfer using a neural network

A neural network has been used to predict stagnation region heat transfer in the presence of freestream turbulence. The neural network was trained using data from an experimental study to investigate the influence of freestream turbulence on stagnation region heat transfer. The integral length scale, Reynolds number, all three components of velocity fluctuations and the vorticity field were used to characterize the freestream turbulence. The neural network is able to predict 50% of the test data within ±1%, while the maximum error of any data point is under 3%. A sensitivity analysis of the freestream turbulence parameters on stagnation region heat transfer was performed using the trained neural network. The integral length scale is found to have the least influence on the stagnation line heat transfer, while the normal and spanwise turbulence intensities have the highest influence.     

高精度迎风紧致差分格式与热流计算研究的注记

利用高精度差分格式求解了可压缩 N-S方程球头热流问题。分析了不同差分格式在对球头粘性绕流热流计算中存在的问题 ,并分析了相应的网格雷诺数。在利用高精度迎风紧致 [1 ] 格式求解粘性绕流热流问题时 ,采用 Steger-Warming[2 ]的通量分裂技术将守恒型方程中的流通向量分裂成两部分 ,在此基础上据风向构造逼近于无粘项的高精度迎风格式。对方程中的粘性部分采用中心差分格式。数值结果表明 :高精度差分格式能在较大的网格雷诺数下较好地计算球头驻点热流     

Experimental study on forced convective heat transfer of flowing gaseous solid suspension at high temperature

The results of an experimental study of the forced convective heat transfer to helium-graphite suspension at high temperatures up to 1173K are presented. Entering gas Reynolds number ranges from 1.0 x 10⁴ to 2.0 x 10⁴ and the particle loading ratio reaches about 4. The ratio of the Nusselt number of the suspension to that of gas alone increases considerably in a range of high loading ratios as the wall temperature increases. Subsequently, two kinds of turbulence promoters (200 and 400 mm pitch twisted tapes) are inserted in the flowing gaseous solid suspensions to make use of the large inertia forces of particles. The current results show that the local heat fluxes with use of the tapes increase significantly with the rise in the wall temperature owing to the radiative effect of the particulate phase.     

Experimental verification of heat transfer coefficient for nucleate boiling at sub-atmospheric pressure and small heat fluxes

In this paper we study the influence of sub-atmospheric pressure on nucleate boiling. Sixteen correlations for pool boiling available in literature are gathered and evaluated. Analysis is performed in the pressure range 1–10 kPa and for heat flux densities 10–45 kW/m². Superheats are set between 6.2 and 28.7 K. The results of calculations were compared with experimental values for the same parameters. The experiments were conducted using isolated glass cylinder and water boiling above the copper plate. Results show that low pressure adjust the character of boiling curve—the curve flattened and the natural convection region of boiling is shifted towards higher wall temperature superheats due to the influence of low pressure on the bubble creation and process of its departure. In result, 8 of 16 analyzed correlations were determined as completely invalid in subatmospheric conditions and the remaining set of equations was compared to experimental results. Experimentally obtained values of heat transfer coefficients are between 1 and 2 kW/m²K. With mean absolute deviation (MAD) we have found that the most accurate approximation of heat transfer coefficient is obtained using Mostinski reduced pressure correlation (0.13–0.35 MAD) and Labuntsov correlation (0.12–0.89 MAD).     

Experimental study of in-tube cooling heat transfer and pressure drop characteristics of R134a at supercritical pressures

The in-tube cooling flow and heat transfer characteristics of R134a at supercritical pressures are measured experimentally for various pressures and mass fluxes in a horizontal tube. The tube is made of stainless steel with an inner diameter of 4.01 mm. Experiments are conducted for mass fluxes from 70 kg/m² s to 405 kg/m² s and pressures from 4.5 MPa to 5.5 MPa. The inlet refrigerant temperature is from 80 °C to 140 °C. The results show that the refrigerant temperature, the mass flux and the pressure all significantly affect the flow and heat transfer characteristics of R134a at supercritical pressures. The experimentally measured frictional pressure drop and heat transfer coefficient are compared with predicted results from several existing correlations. The comparisons show that the predicted frictional pressure drop using Petrov and Popov’s correlation accounting for the density and viscosity variations agree well with the measured data. Gnielinski’s correlation for the heat transfer coefficient agrees best with the measured data with deviations not exceeding 25%, while correlations based on supercritical CO₂ heat transfer data overcorrect for the influence of the thermophysical property variations resulting in larger deviations. A new empirical correlation is developed based on the measured results by modifying Gnielinski’s equation with thermophysical property terms including both the property variations from the inlet to the outlet of the entire test section and from the bulk to the wall. Most of the experimental data is predicted by the new correlation within a range of 15%.     

Experimental study of free convective heat transfer in a liquid-saturated porous bed at high Rayleigh number

Experiments have been performed to investigate the heat transfer of a horizontal porous bed saturated by liquid heated from below. Attention was especially focussed on the heat-transfer characteristics at the high Rayleigh number where the observed data deviate to a great extent from the linear dependence of the Nusselt number on the Rayleigh number predicted by the previous investigators. The porous bed was made up of packed spherical glass beads with diameter ranging from 3.02 mm to 16.4 mm, while the depth of the bed was varied from 16.4 mm to 103.0 mm. Distilled water, ethylalcohol, fluorocarbon R-11 and transformer oil as testing liquids were used. The results revealed that the effects of particle diameter, depth of bed, and the Prandtl number on the heat-transfer characteristics at the high Rayleigh number are unexpectively large. It was also elucidated that the heat-transfer data which do not exhibit linear dependence of Nu on Ra with Pr_m ranging from 1.1 to 7.3 can well be correlated by the following equations: Nu= 0.10Pr_m ^0.132(d/H)^–0.655Ra^0.5 200 < Ra < 1400 Nu=0.88 Pr^0.132(d/H)^–0.655Ra^0.2 1400 < Ra < 40000

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Experimentelle Untersuchung des Wärmeübergangs bei freier Konvektion in einem flüssigkeits-gesättigten porösen Bett bei hohen Rayleigh-Zahlen

Zusammenfassung Die Versuche betrachten den Wärmeübergang in einem waagerechten porösen Bett, das mit Flüssigkeit gesättigt war und von unten beheizt wurde. Insbesondere wurde der Bereich hoher Rayleigh-Zahlen untersucht, wo die beobachteten Daten stark von der linearen Abhängigkeit der Nusselt-Zahl von der Rayleigh-Zahl abwichen, wie sie in der älteren Literatur behauptet wurde. Das poröse Bett bestand aus Glasperlen mit Durchmessern von 3,02 mm bis 16,4 mm bei einer Tiefe von 16,4 mm bis 103,0 mm. Destilliertes Wasser, Äthylalkohol, Fluorkohlenstoff R-11 und Transformatorenöl wurden verwendet. Die Versuche zeigen, daß die Einflüsse des Teilchendurchmessers, der Tiefe des Betts und der Prandtl-Zahl unerwartet hoch sind. Die Wärmeübergangsdaten, die keine lineare Abhängigkeit zwischen Nu und Ra im Bereich von Pr_m =1,1 bis 7,3 aufwiesen, ließen sich durch folgende Beziehungen wiedergeben: Nu=0,10 Pr_m ^0,132(d/H)^–0,655Ra^0.5 200 < Ra < 1400 Nu=0,88 Pr_m ^0,132(d/H)^0,655Ra^0.2 1400 < Ra < 40000.

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Nomenclature Cp_f specific heat of liquid - d diameter of spherical particles - g gravitational acceleration - H depth of porous bed - k permeability of porous bed - Nu Nusselt number for porous bed, defined in Eq.(4) - Pr_m modified Prandtl number for porous bed, as defined in Eq. (3) - q rate of heat transfer per unit cross-sectional area of porous bed - Ra Rayleigh number for porous bed, as defined in Eq.(1) - T_c temperature of cold wall - T_h temperature of hot wall - T temperature of environment Greek symbols coefficient of volumetric expansion of liquid - temperature difference between hot wall and cold wall - porosity of porous bed - _m modified thermal diffusivity for porous bed - _f thermal conductivity of liquid - _m modified thermal conductivity for porous bed - _f kinematic viscosity of liquid - _f density of liquid     

Efficiency analysis of organic Rankine cycle with internal heat exchanger using neural network

In this study, artificial neural network (ANN) has been used for efficiency analysis of the organic Rankine cycle with internal heat exchanger (IHEORC) using refrigerants R410a, R407c which do not damage to ozone layer. It is well known that the evaporator temperature, condenser temperature, subcooling temperature and superheating temperature affect the thermal efficiency of IHEORC. In this study, thermal efficiency is estimated depending on the above temperatures. The results of ANN are compared with actual results. The coefficient of determination values obtained when the test set were used to the networks were 0.99946 and 0.999943 for the R410a and R407c respectively which is very satisfactory.     

Numerical simulation of coupled heat and mass transfer in wood dried at high temperature

The mutual effect between heat and mass transfer is investigated for wood dried at high temperature. A numerical model of coupled heat and mass transfer under the effect of the pressure gradient is presented. Based on the macroscopic viewpoint of continuum mechanics, the mathematical model with three independent variables (temperature, moisture content and gas pressure) is constructed. Mass transfer in the pores involves a diffusional flow driven by the gradient of moisture content, convectional flow of gaseous mixture governed by the gradient of gas pressure, the Soret effect and phase change of water. Energy gain or loss due to phase change of water is taken as the heat source. Numerical methods, the finite element method and the finite difference method are used to discretize the spatial and time dimension, respectively. A direct iteration method to solve the nonlinear problem without direct evaluation of the tangential matrix is introduced. The local convergence condition based on the contraction–mapping principle is discussed. The mathematical model is applied to a 3-D wood board dried at high temperature with the Neumann boundary conditions for both temperature and moisture content, and the Dirichlet boundary conditions for gas pressure.     

Experimental study of nucleate boiling heat transfer under low gravity conditions using TLCs for high resolution temperature measurements

Heat transfer in nucleate boiling is strongly influenced by a very small circular area in the vicinity of the three phase contact line where a thin liquid film approaches the heated wall. This area is characterised by high evaporation rates which trigger a local temperature drop in the wall. The wall temperature drop can be computed using an existing nucleate boiling model. To verify the complex model and the underlying assumptions, an experiment was designed with an artificial nucleation site in a thin electrically heated wall featuring a two-dimensional, high resolution temperature measurement technique using unencapsulated thermochromic liquid crystals and a high speed colour camera. The shape of the bubble is observed simultaneously with a second high speed camera. Experiments were conducted in a low gravity environment of a parabolic flight, causing larger bubble departure diameters than in normal gravity environments. Thus, it was possible to measure the evolution of the predicted temperature drop in a transient boiling process.     

Bodies of revolution with minimal drag coefficient and low heat transfer at high supersonic speeds

On the basis of modified Newtonian theory and the theory of selfsimilar hypersonic flows we study the form of the optimal contour of a body of revolution with minimal drag coefficient at hypersonic speeds. It is shown that bodies of optimal form also have a small heat transfer coefficient, much smaller than for a conical body. It is established experimentally that the optimal properties of these bodies of revolution are also retained for moderate supersonic flight speeds.In concluslion the author wishes to thank V. V. Sychev for valuable discussions of this problem.     

Measurement and correlation of volumetric heat transfer coefficients of cellular ceramics

The volumetric heat transfer coefficients (h_v) between cellular ceramics and a stream of air were measured using the single-blow transient experimental technique in conjunction with an inverse analysis. Test specimen made of mullite, YZA, SiC, cordierite and cordierite with LS-2 coating was studied. The number of pores per centimeter (PPC) ranged from 4 to 26 and the specimen thickness ranged from 6 to 12 mm. Based on the experimental data, the volumetric heat transfer coefficients were generalized by developing Nusselt number vs. Reynolds number correlations of the form Nu_v=C Re^m for the materials studied. The effects of pore length-scale and specimen thickness on the volumetric heat transfer coefficients are presented and discussed.     

A new procedure for the prediction of forced convection heat transfer at near- and supercritical pressure

Based on heat transfer experiments with tubes of different inside geometry, correlations for forced convection heat transfer at near- and supercritical pressure are presented. They are of the Dittus-Boelter typeNu=CRe ^m Pr ⁿ and over the whole enthalpy range. The simple form is made possible by a new method of determining a representative specific heat capacity. At five reference temperatures heat capacities are computed with semi-empirical equations. The two highest values closest to the (pseudo-)critical state are then sorted out, because they are not relevant for turbulent flow. The average of the remaining three values represents a reasonable characteristic heat capacity. Comparisons to measurements show the very good accuracy of the new correlations. The procedure can be recommended whenever strong dependencies of fluid properties on temperature or even singularities occur.     

Topology optimization of conjugate heat transfer systems: A competition between heat transfer enhancement and pressure drop reduction

Topology optimization method is developed for a multi-objective function combining pressure drop reduction and thermal power maximization (incompressible flows at low to moderate Reynolds numbers). Innovative optimal designs are obtained, discussed and presented on a Pareto-frontier. The numerical developments (continuous adjoint technique) have been conducted inside an open source CFD platform via the finite volume method. Comparisons have been presented with an optimal design obtained by a Lattice Boltzmann Method from the literature. Finally, this contribution presents and discuss several detailed numerical vitrification steps which are essential to be conducted in topology optimization method when applied with multi-objective functions.     

Comparisons of the heat transfer and pressure drop of the microchannel and minichannel heat exchangers

The present study investigated the comparisons of the heat transfer and pressure drop of the microchannel and minichannel heat exchangers, both numerically and experimentally. The results obtained from this study indicated that the heat transfer rate obtained from microchannel heat exchanger was higher than those obtained from the minichannel heat exchangers; however, the pressure drops obtained from the microchannel heat exchanger were also higher than those obtained from the minichannel heat exchangers. As a result, the microchannel heat exchanger should be selected for the systems where high heat transfer rates are needed. In addition, at the same average velocity of water in the channels used in this study, the effectiveness obtained from the microchannel heat exchanger was 1.2–1.53 times of that obtained from the minichannel heat exchanger. Furthermore, the results obtained from the experiments were in good agreement with those obtained from the design theory and the numerical analyses.     

Prediction of mass transfer coefficient in rotating bed contactor (Higee) using artificial neural network

The feasibility of drastically reducing the contactor size in mass transfer processes utilizing centrifugal field has generated a lot of interest in rotating packed bed (Higee). Various investigators have proposed correlations to predict mass transfer coefficients in Higee, but, none of the correlations was more than 20–30% accurate. In this work, artificial neural network (ANN) is employed for predicting mass transfer coefficient data. Results show that ANN provides better estimation of mass transfer coefficient with accuracy 5–15%.     

Energy correlation of heat transfer and enhancement efficiency in decaying swirl flow

 This paper presents the experimental results of the energy and enhancement efficiency characteristics of a decaying swirl flow generated by different radial guide-vane swirl generators. Energy and enhancement efficiency correlation equations were obtained for three types of swirl generator, which had differed from each other by the design of the deflecting element; swirl generator with conical deflecting element, with spherical deflecting element, and with no deflecting element. The enhancement efficiencies varied between 0.86–1.31 depending upon swirl intensity, Reynolds number and type of swirl generator. It was found that the enhancement efficiency increased with increasing vane angle, and decreased with increasing Reynolds number for all types of swirl generator. By comparing heat transfer enhancement efficiencies of each swirl generator, swirl generator with no deflecting element was found to have the highest heat transfer enhancement efficiency. Received on 20 June 2000 / Published online: 29 November 2001