Heat transfer and two-phase flow characteristics of refrigerants flowing under varied heat flux in a double-pipe evaporator

A mathematical model based on the annular flow pattern is developed to simulate the evaporation of refrigerants flowing under varied heat flux in a double tube evaporator. The finite difference form of governing equations of this present model is derived from the conservation of mass, energy and momentum. The experimental set-up is designed and constructed to provide the experimental data for verifying the simulation results. The test section is a 2.5 m long counterflow double tube heat exchanger with a refrigerant flowing in the inner tube and heating water flowing in the annulus. The inner tube is made from smooth horizontal copper tubing of 9.53 mm outer diameter and 7.1 mm inner diameter. The agreement of the model with the experimental data is satisfactory. The present model can be used to investigate the axial distributions of the temperature, heat transfer coefficient and pressure drop of various refrigerants. Moreover, the evaporation rate or the other relevant parameters that is difficult to measure in the experiment are predicted and presented here. The results from the present mathematical model show that the saturation pressure and temperature of refrigerant decrease along the tube due to the tube wall friction and the flow acceleration of refrigerant. The liquid heat transfer coefficient increases with the axial length due to reducing the thickness of the liquid refrigerant film. Due to increase of the liquid heat transfer coefficient, increasing wall heat flux is obtained.Finally, the evaporation rate of refrigerant increases with increasing wall heat flux.     

An investigation of a model of the flow pattern transition mechanism in relation to the identification of annular flow of R134a in a vertical tube using various void fraction models and flow regime maps

In the present study, new experimental data are presented for literature on the prediction of film thickness and identification of flow regime during the co-current downward condensation in a vertical smooth copper tube having an inner diameter of 8.1 mm and a length of 500 mm. R134a and water are used as working fluids in the tube side and annular side of a double tube heat exchanger, respectively. Condensation experiments are done at mass fluxes of 300 and 515 kg m^?2 s^?1. The condensing temperatures are between 40 and 50 °C; heat fluxes are between 12.65 and 66.61 kW m^?2. The average experimental heat transfer coefficient of the refrigerant HFC-134a is calculated by applying an energy balance based on the energy transferred from the test section. A mathematical model by Barnea et al. based on the momentum balance of liquid and vapor phases is used to determine the condensation film thickness of R134a. The comparative film thickness values are determined indirectly using relevant measured data together with various void fraction models and correlations reported in the open literature. The effects of heat flux, mass flux, and condensation temperature on the film thickness and condensation heat transfer coefficient are also discussed for the laminar and turbulent flow conditions. There is a good agreement between the film thickness results obtained from the theoretical model and those obtained from six of 35 void fraction models in the high mass flux region of R134a. In spite of their different valid conditions, six well-known flow regime maps from the literature are found to be predictive for the annular flow conditions in the test tube in spite of their different operating conditions.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

Experimental research on transient critical heat flux in vertical tube under oscillatory flow condition

The transient critical heat flux (CHF) experiments with forced sinusoidal inlet flow oscillation (oscillation period in 1–11 s, normalized amplitude of inlet flow oscillation in 0–3.0) were conducted in a vertical tube under low pressure condition. To analyze the triggering mechanism and aftermath of periodic dryout, the wall temperature fluctuation characteristics at the onset of periodic dryout and during post-periodic dryout were investigated. Under inlet flow oscillation condition, periodic dryout would be triggered at the wave trough of liquid film oscillation as wall heat flux far below the stable-flow CHF. The transient periodic dryout would give rise to temperature fluctuations on the tube wall, the amplitude of which increased with oscillation period and heat flux. The large wall temperature fluctuation during long-playing periodic dryout could significantly pre-trigger continuous dryout. The changing trends of the periodic dryout heat flux show a reasonable agreement with Okawa’s theoretical model, in which the liquid film oscillation was supposed be weakened by the axial mixing of liquid film. Moreover, the droplet entrainment at the oscillatory interface also has noticeable influence on the oscillation characteristics of liquid film. Based on the analysis of parameter effects on periodic dryout, a semi-empirical correlation was proposed to predict the periodic dryout heat flux under inlet flow oscillation condition.     

Free convection on a vertical plate with uniform and constant heat flux in a thermally stratified micropolar fluid

This paper analyzes flow and heat transfer characteristics of the free convection on a vertical plate with uniform and constant heat flux in a thermally stratified micropolar fluid. The dimensionless forms of boundary layer equations and their associated boundary conditions have been derived and the numerical results have been obtained using the method of cubic spline collocation with a finite difference scheme. The effects of the micropolar and stratification parameters on the dimensionless wall temperature, skin friction parameter and wall couple stress are discussed.     

Stability of a vertical liquid film with consideration of the marangoni effect and heat exchange with the environment

The stability of a free vertical liquid film under the combined action of gravity and thermocapillary forces has been studied. An exact solution of the Navier-Stokes and thermal conductivity equations is obtained for the case of plane steady flow with constant film thickness. It is shown that if the free surfaces of the film are perfectly heat insulated, the liquid flow rate through the cross section of the layer is zero. It is found that to close the model with consideration of the heat exchange with the environment, it is necessary to specify the liquid flow rate and the derivative of the temperature with respect to the longitudinal coordinate or the flow rate and the film thickness. The stability of the solution with constant film thickness at small wave numbers is studied. A solution of the spectral problem for perturbations in the form of damped oscillations is obtained.     

管内定型流传热过程的有效能损失

对管道内充分发展对流传热过程的有效能损失进行了分析．根据定型流状态下定热流与定壁温换热条件的特点,经代数推演,得到了这两种条件下的表征换热状态、流动功耗以及黏性变化的无量纲形式的有效能损失关系式,适用于不同截面形状的管道内的层流与湍流工况下的有效能分析．     

Evaporation of laminar,falling liquid film on a horizontal cylinder

An analytical study of falling film evaporation on a horizontal tube is accomplished for the case of constant heat flux condition imposed at the wall. The process of evaporation from the liquid film interface is conjugated to thermal conduction in the wall of the tube around its periphery. In addition, the flow of the film is considered to be thermally developing throughout its travel around the tube. Influence of various governing parameters on local and average heat transfer coefficient is presented. The theoretical investigation is compared with the available experimental data. The agreement is found to be satisfactory.     

Two-phase annular flow and evaporative heat transfer in a microchannel

A physical and mathematical model has been developed to predict the two-phase flow and heat transfer in a microchannel with evaporative heat transfer. Sample solutions to the model were obtained for both constant wall temperature and constant wall heat flux conditions. Results are provided for evaporation rate, liquid film thickness, liquid and vapor phase pressure and temperature distributions. In addition to the sample calculations that were used to illustrate the transport characteristics, computations based on the current model were performed to generate results for comparisons with the experimental results of Qu and Mudawar (2004) where two different mass flow rates of the working fluid were used in the experiment. The comparisons of total pressure drops with the experimental data of Qu and Mudawar (2004) cover the wall heat flux range of 142.71-240 W/cm² with a total channel mass flux of 400.1 kg/m² s and also the wall heat flu range of 99.54-204.39 W/cm² with total channel mass flux of 401.9 kg/m² s. The calculated results from the current model match closely with those of Qu and Mudawar (2004).     

Natural convection flow over a vertical frustum of a cone for constant wall heat flux

Laminar natural convection flow and heat transfer over a vertical frustum of a cone has been studied. The governing boundary layer equations are solved using local non-similarity method for constant wall heat flux. The local similarity and the local non-similarity two and three-equation models are constructed and the resulting equations are solved numerically. Results obtained from two and three-equation models are in good agreement. The numerical values of the flow and temperature functions required to calculate the surface skin friction and heat transfer rate are reported for various values of Prandtl numbers.     

Onset of flow instability in a heated capillary tube

We study the stability of flow in a heated capillary tube with an evaporating meniscus. The behavior of the vapor/liquid system, which undergoes small perturbations, is analyzed by linear approximation, in the frame of a one-dimensional model of capillary flow, with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes, on the flow stability is studied. The velocity, pressure and temperature oscillations in a capillary tube with a constant wall heat flux or a constant wall temperature are determined. A scenario of a possible process at small and moderate Peclet numbers corresponding to the flow in capillaries is considered. The boundaries of stability, subdividing the domains of stable and unstable flows, are outlined, and the values of geometrical and operating parameters corresponding to the transition from stable to unstable flow are estimated. It is shown that the stable capillary flow occurs at relatively small wall heat fluxes, whereas at high ones, the flow is unstable, with continuously growing velocity, pressure and temperature oscillations.     

下降液膜层流换热发展段中的积分分析

对等温竖直壁面上层流液膜发展段的流动换热进行了理论分析 ,用积分法得到并求解了速度和温度边界层的积分方程式 ,求得了发展段的流动和换热特性的变化规律 ,讨论了进口流态和普朗特数对换热的影响。     

Thermo-mechanical modeling of turbulent heat transfer in gas–solid flows including particle collisions

A thermo-mechanical turbulence model is developed and used for predicting heat transfer in a gas–solid flow through a vertical pipe with constant wall heat flux. The new four-way interaction model makes use of the thermal k_θ–τ_θ equations, in addition to the hydrodynamic k–τ transport, and accounts for the particle–particle and particle–wall collisions through a Eulerian/Lagrangian formulation. The simulation results indicate that the level of thermal turbulence intensity and the heat transfer are strongly affected by the particle collisions. Inter-particle collisions attenuate the thermal turbulence intensity near the wall but somewhat amplify the temperature fluctuations in the pipe core region. The hydrodynamic-to-thermal times-scale ratio and the turbulent Prandtl number in the region near the wall increase due to the inter-particle collisions. The results also show that the use of a constant or the single-phase gas turbulent Prandtl number produces error in the thermal eddy diffusivity and thermal turbulent intensity fields. Simulation results also indicate that the inter-particle contact heat conduction during collision has no significant effect in the range of Reynolds number and particle diameter studied.     

Forced convective film condensation inside vertical tubes

A theoretical study of forced convective film condensation inside vertical tubes is presented. We propose a unified procedure for predicting the pressure gradient and condensation heat transfer coefficient of a vapor flowing turbulently in the core and associated with laminar or turbulent film on the tube wall. The analysis for the vapor flows is performed under the condition that the velocity profiles are locally self-similar. The laminar and turbulent film models equate the gravity, pressure and viscous forces, and consider the effect of interfacial shear. The transition from laminar to turbulent film depends not only on the liquid Reynolds number but also on the interfacial shear stress. In this work we also proposed a new eddy viscosity model which is divided into three regions: the inner region in liquid condensate near the wall; the interface region including both liquid and vapor; and the outer region for the vapor core. Comparisons of the theory with some published experimental data showed good agreement.     

A Local Thermal Non-Equilibrium Analysis of Fully Developed Forced Convective Flow in a Tube Filled with a Porous Medium

A local thermal non-equilibrium model has been considered for the case of thermally fully developed flow within a constant heat flux tube filled with a porous medium. Exact temperature profiles for the fluid and solid phases are found after combining the two individual energy equations and then transforming them into a single ordinary differential equation with respect to the temperature difference between the solid phase and the wall subject to constant heat flux. The exact solutions for the case of metal-foam and air combination reveal that the local thermal equilibrium assumption may fail for the case of constant heat flux wall. The Nusselt number is presented as a function of the Peclet number, which shows a significant increase due to both high stagnant thermal conductivity and thermal dispersion resulting from the presence of the metal-foam.     

Flow boiling visualization in a vertical circular minichannel at high vapor quality

This paper reports on an experimental study of saturated flow boiling of R134a inside a circular vertical quartz tube coated with a transparent heater. The inner diameter of the tube was 1.33 mm and the heated length 235.5 mm. The flow pattern at high vapor qualities and the dryout of the liquid film were studied using a high speed CCD camera at the mass fluxes 47.4 and 124.4 kg/m² s in up flow at 6.425 bar. The heat fluxes ranged from 5 to 13.6 kW/m² for the lower mass flux and from 20 to 32.4 kW/m² for the higher mass flux.

The behavior of the flow close to dryout was found to be different at low and high mass flux. At low mass flux the location of the liquid front fluctuated with waves passing high up in the tube. In between the waves, a thin film was formed, slowly evaporating without breaking up.

At high mass flux the location of the liquid front was more stable. In this case the liquid film was seen to break up into liquid streams and dry zones on the tube wall.     

Analysis of laminar flow forced convection heat transfer in the entrance region of a circular pipe

A numerical solution, for incompressible, steady-state, laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux and constant wall temperature. The development of velocity profile is obtained from Sparrow's entrance region solution. This velocity distribution is used in solving the energy equation numerically to obtain temperature profiles. Variation of the heat transfer coefficient for these two different boundary conditions for the early stages of boundary layer formation on the pipe wall is obtained. Local Nusselt numbers are calculated and the results are compared with those given byUlrichson andSchmitz. The effect of the thermal boundary conditions is studied by comparing the uniform wall heat flux results with uniform wall temperature.     

Primary instabilities of liquid film flow sheared by turbulent gas stream

Evolution of excited waves on a viscous liquid film has been investigated experimentally for the annular gas–liquid flow in a vertical tube. For the first time the dispersion relations are obtained experimentally for linear waves on liquid film surface in the presence of turbulent gas flow. Both cocurrent and countercurrent flow regimes are investigated. As an example of comparison with theory, the experimental data are compared to the results of calculations based on the Benjamin quasi-laminar model for turbulent gas flow. The calculation results are found to be in good agreement with experiments for moderate values of film Reynolds number.     

Numerical simulation of flow boiling for organic fluid with high saturation temperature in vertical porous coated tube

A semi-analytical model is developed for the prediction of flow boiling heat transfer inside vertical porous coated tubes. The model assumes that the forced convection and nucleate boiling coexist together in the annular flow regime. Conservations of mass, momentum, and energy are used to solve for the liquid film thickness and temperature. The heat flux due to nucleate boiling consists of those inside and outside micro-tunnels. To close the equations, a detailed analysis of various forces acting on the bubble is presented to predict its mean departure diameter. The active nucleation site density of porous layer is determined from the pool boiling correlation by introducing suppression factor. The flow boiling heat transfer coefficients of organic fluid (cumene) with high saturation temperature in a vertical flame-spraying porous coated tube are studied numerically. It is shown that the present model can predict most of the experimental values within ±20%. The numerical results also indicate that the nucleate boiling contribution to the overall heat transfer coefficient decreases from 50% to 15% with vapor quality increasing from 0.1 to 0.5.     

Pure steam condensation model with laminar film in a vertical tube

A new physical model for calculating the liquid film thickness and condensation heat transfer coefficient in a vertical condenser tube is proposed by considering the effects of gravity, liquid viscosity, and vapor flow in the core region of the flow. To estimate the velocity profile in the liquid film, the liquid film was assumed to be in Couette flow forced by the interfacial velocity at the liquid–vapor interface. For simplifying the calculation procedures, the interfacial velocity was estimated by introducing an empirical power-law velocity profile. The resulting film thickness and heat transfer coefficient from the model were compared with the experimental data and the results obtained from the other condensation models. The results demonstrated that the proposed model described the liquid film thinning effect by the vapor shear flow and predicted the condensation heat transfer coefficient from experiments reasonably well.