Numerical modeling of cryogenic chilldown process in terrestrial gravity and microgravity

In this paper, a numerical model is developed to predict the cryogenic chilldown process of a vertical tube for both terrestrial and microgravity conditions. The flow field is covered by four distinct regions, which are single-phase vapor region, dispersed flow region, inverted annular flow region, and single-phase liquid region. Heat transfer mechanisms are dictated by the flow patters. A two-fluid model is employed to analyze the dispersed flow region and the inverted annular film boiling region. Gravity effect on the chilldown process is also investigated. Model results indicate that film boiling heat transfer decreases with decreasing gravity level for the bottom flooding condition. The model results show a good agreement with the experimental data.     

Analytical considerations of flow boiling heat transfer in metal-foam filled tubes

Flow boiling in metal-foam filled tube was analytically investigated based on a modified microstructure model, an original boiling heat transfer model and fin analysis for metal foams. Microstructure model of metal foams was established, by which fiber diameter and surface area density were precisely predicted. The heat transfer model for flow boiling in metal foams was based on annular pattern, in which two phase fluid was composed by vapor region in the center of the tube and liquid region near the wall. However, it was assumed that nucleate boiling performed only in the liquid region. Fin analysis and heat transfer network for metal foams were integrated to obtain the convective heat transfer coefficient at interface. The analytical solution was verified by its good agreement with experimental data. The parametric study on heat transfer coefficient and boiling mechanism was also carried out.     

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.     

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.     

Effect of vapor flow on the wetting behavior of unstable evaporating menisci in heated capillary tubes

The wicking height of a heated, evaporating meniscus formed by surface-wetting liquid in a vertical capillary tube with dynamic flow has been investigated. Previous experimental results and analytical models for measuring/predicting wicking heights in capillaries are also reviewed. An analytical model is presented that accounts for both major and minor vapor pressure losses along the vertical capillary tube. It is shown that during thermo-mechanical instability, vapor/meniscus interaction can become more prevalent due to increased vapor generation/pressure near the meniscus free surface. A relatively simple procedure for estimating onset of meniscus instability is presented and, when used with the vapor Reynolds number, can estimate whether vapor pressure loss is significant. By comparing the current model with the available experimental data, it is shown that the wicking height of an unstable, evaporating meniscus of n-pentane in a vertical, glass capillary tube is better estimated by considering vapor flow pressure losses – providing a 40% improvement over previous models that neglect vapor flow. In addition to vapor flow pressure loss, the dynamic contact angle and thin film profile must also be calculated to ensure accurate prediction of wicking height. Although the proposed model shows improvement, it is prone to under-predicting the actual meniscus wicking height for stable, evaporating menisci at lower relative heat loads. The proposed model can be used for predicting wicking behavior of heated, vertically-aligned liquid columns in capillary structures – which is relevant to the design of miniature heat transfer equipment/media such as wicked heat pipes, micro-channels and sintered/porous surfaces.     

A theoretical study of free convection in turbulent film boiling on a horizontal elliptical tube

The present theoretical study investigates turbulent film boiling on an isothermal elliptical tube under quiescent liquid. The effect of radiation is included in the present analysis. The results of the boiling heat transfer under the turbulent vapor show both the temperature and velocity present the non-linear distribution. Besides, under the free convection turbulent film boiling with higher Rayleigh values, the elliptical tube can get a better heat transfer efficiency than a circular tube. However, when Rayleigh values are low, the eccentricity of an elliptical tube seldom influences the heat transfer. Finally, a comparison between the results of the present study and those reported in a previous theoretical and experimental data is provided.     

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).     

Surrogate model‐based strategy for cryogenic cavitation model validation and sensitivity evaluation

The study of cavitation dynamics in cryogenic environment has critical implications for the performance and safety of liquid rocket engines, but there is no established method to estimate cavitation‐induced loads. To help develop such a computational capability, we employ a multiple‐surrogate model‐based approach to aid in the model validation and calibration process of a transport‐based, homogeneous cryogenic cavitation model. We assess the role of empirical parameters in the cavitation model and uncertainties in material properties via global sensitivity analysis coupled with multiple surrogates including polynomial response surface, radial basis neural network, kriging, and a predicted residual sum of squares‐based weighted average surrogate model. The global sensitivity analysis results indicate that the performance of cavitation model is more sensitive to the changes in model parameters than to uncertainties in material properties. Although the impact of uncertainty in temperature‐dependent vapor pressure on the predictions seems significant, uncertainty in latent heat influences only temperature field. The influence of wall heat transfer on pressure load is insignificant. We find that slower onset of vapor condensation leads to deviation of the predictions from the experiments. The recalibrated model parameters rectify the importance of evaporation source terms, resulting in significant improvements in pressure predictions. The model parameters need to be adjusted for different fluids, but for a given fluid, they help capture the essential fluid physics with different geometry and operating conditions. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Experimental study of heat transfer in a HVMLI cryogenic tank after SCLIV

One of the worst accidents that may occur in a high-vacuum-multilayer-insulation (HVMLI) cryogenic tank is a sudden, catastrophic loss of insulating vacuum (SCLIV). The influence of SCLIV on the heat transfer characteristics in a HVMLI cryogenic tank has been researched experimentally in this paper. A test rig was built up and experiments were conducted using LN₂ as the test medium. Some important phenomena and heat transfer characteristics in a vacuum-lost LN₂ HVMLI cryogenic tank have been obtained. The effects of the insulation layer numbers and the initial liquid level on venting rate and heat flux leaking into the cryogenic liquid as well as the temperatures of wall and liquid have been analyzed and discussed for a LN₂ HVMLI cryogenic tank after SCLIV in this paper.     

Effect of acoustic cavitation on boiling heat transfer

Boiling heat transfer on a horizontal circular copper tube in an acoustical field is investigated experimentally and the relation between the liquid cavitation, the boiling and the micro bubble radii are analyzed theoretically. The results show that cavitation bubbles have an important influence on the nucleation, growth and collapse of vapor embryo within cavities on the heat transfer surface and that the enhancement of boiling heat transfer by acoustic cavitation mainly depends on whether the vapor embryo is activated by the cavitation bubbles to initiate boiling.     

On the calculation of wall temperatures in the post dryout heat transfer region

A non-equilibrium post dryout heat transfer model for calculating the wall temperature distribution in vertical upflows is presented in this study. The model is based upon the three path heat transfer formulation developed by MIT researchers (Laverty & Rohsenow 1964, Forslund & Rohsenow 1968, Hynek et al. 1969 and Plummer et al. 1974) that involves heat transfer from wall to vapor, from wall to droplets in contact with the wall and from vapor to liquid droplets in the vapor core. Downstream gradients for the bulk vapor temperature, vapor quality, droplet size and vapor velocities are identical to those used by Hynek et al. (1969) and Plummer et al. (1974). Conditions at the dryout location are calculated using a modified version of a technique developed by Hynek et al. (1969).A procedure for determining an average droplet diameter based on a size distribution is introduced. Migration of droplets through the boundary layer and droplet deposition flux are predicted with the model of Gani? & Rohsenow (1979). Heat transfer from the wall to the impinging liquid droplets is calculated with a correlation by Holman & McGinnis (1969). Mechanisms contributing to wall to droplet heat transfer are identified as (a) droplet-wall contact, (b) intensive droplet evaporation inside the boundary layer, and (c) destruction of the boundary layer due to droplet migration to, and rebound from, the hot surface. The significance of the average droplet size and size distribution is demonstrated through its control over the free stream evaporation and droplet deposition rates.Predicted uniform heat flux wall temperature profiles for water, nitrogen and freon 12 are in good agreement with the data of Era et al. (1966), Bennett et al. (1967), Forslund & Rohsenow (1968), Ling et al. (1971), Groeneveld (1972) and Janssen & Kervinen (1975).     

Numerical simulation of the modulated flow pattern for vertical upflows by the phase separation concept

The multiphase heat transfer could be enhanced by creating thin liquid film on the wall. The phase separation concept is called due to the separated flow paths of liquid and gas over the tube cross section to yield thin liquid film. Our proposed heat transfer tube consists of an annular region close to the wall and a core region, interfaced by a suspending mesh cylinder in the tube. The heat transfer tube is a multiscale system with micron scale of mesh pores, miniature scale of annular region and macroscale of tube diameter and length. Great effort has been made to link from micron scale to macroscale. The Volume of Fluid (VOF) method simulates air/water two-phase flow for vertical upflow. The three-dimensional system was successfully converted to a two-dimensional one by using three equivalent criteria for mesh pores. The non-uniform base grid generation and dynamic grid adaption method capture the bubble interface. The numerical results successfully reproduce our experimental results. The numerical findings identify the following mechanisms for the enhanced heat transfer: (a) counter-current flow exists with upward flow in the annular region and downward flow in the core region; (b) void fractions are exact zero in the core region and higher in the annular region; (c) the liquid film thicknesses are decreased to 1/6–1/3 of those in the bare tube section; (d) the gas–liquid mixture travels much faster in the annular region than in the bare tube; (e) three-levels of liquid circulation exists: meter-scale bulk liquid circulation, moderate-scale liquid circulation around a single-elongated-ring-slug-bubble, and microliquid circulation following the ring-slug-bubble tails. These liquid circulations promote the fluid mixing over the whole tube length and within the radial direction. The modulated parameters of void fractions, velocities and liquid film thicknesses in the annular region and three-levels of liquid circulation are greatly beneficial for the multiphase heat transfer enhancement.     

爆震室壁面条件对脉冲爆震发动机爆震性能的影响

在爆震室内快速形成稳定传播的爆轰波是脉冲爆震发动机的关键．本文利用有限速率化学反应模型,考虑粘性、热对流,基于N-S方程对氢气与空气/氧气为反应混合物的爆震发动机爆震室内流场进行计算．从流场压力、速度、涡量、湍流动能等方面研究爆震室壁面条件对燃烧爆轰性能的影响,分析流场爆轰波压力与流场湍动能的关系,讨论可燃气体燃烧转爆轰的机理．结果表明：爆震室内燃烧爆轰机理受到化学反应能量释放、壁面摩擦效应、壁面与外界热交换的影响．在文中讨论的范围内,相比于半圆形和三角形的爆震室装置,矩形的爆震室增强装置能在更短的时间内得到较高的爆轰波压力和湍动能峰值．壁面粗糙层高度（粗糙度）影响爆震室的燃烧爆轰性质．当壁面粗糙度为0.15mm时,粗糙度对爆轰的激励作用大于抑制作用,能较快形成稳定的爆轰波,且推力为35.5N;随着壁面对流换热系数的增大,爆震室壁面的散热加剧．当壁面对流换热系数大于临界值2.6W/(m2·K)时,爆震室内不能形成稳定的爆震波．     

Determination of heat transfer coefficients on the surfaces of plastic tubes

 The paper discusses the statistical steady heat and momentum transfer problem in the inlet section of the plastic tubes. The modified two equation k–ɛ turbulent model utilizing variability of turbulent Prandtl number, Pr_t, was used for the analysis. Considering the thermophysical anisotropy of the tube material, a balance of local temperatures and local heat fluxes on the boundary between the fluid and the tube wall was assumed (conjugate heat transfer problem). The thermal boundary condition on the external surface of the tube (temperature) measured in the experiment was taken into account. The boundary problem described was solved by the control volume method. The values of the parameters of Pr and Re obtained from the experiments were included in the numerical calculations. Based on the results obtained, profiles of mean fluid temperatures, local Nusselt numbers on the internal and external surface of the tube, and profiles of temperatures on the internal surface of the tube and inside of the tube wall were determined. The analysis shows that changes in Pr_tand turbulence intensity, Tu, influence the local values of Nusselt numbers, and it also shows that the results for the local Nusselt numbers inside the tube obtained from numerical calculations are of great accuracy in comparison with results published in the available literature. Received on 11 June 2001     

Volume of fluid approach of boiling flows in concentrated solar plants

The Computational Fluid Dynamics (CFD) model proposed in this paper allows the flow patterns that evolve during progressive boiling inside large scale horizontal tubes to be simulated from the initial vapor generation stage to large vapor slugs. The volume of fluid (VOF) model was employed in combination with relatively simple hypothesis. The aim of the present work is to improve the design of receiver tubes at concentrated solar power plants with direct steam generation by simulating the evolution of flow regimes within these tubes. Despite numerous studies conducted in the past years on convective boiling, only a few made use of the VOF model to simulate large flow regime transitions. This work presents a preliminary and relatively qualitative approach to address this problem. Heat and mass transfer at the tube inner wall and at the liquid-gas interface were solved with the additional transport of two scalars. One accounts for the enthalpy field and the other represents the dispersed vapor phase of the liquid. This new phase was created at the wall surface of the liquid phase and rises up to the liquid-vapor interface. Different phenomena linked to the boiling process were taken into account: vapor creation at the wall, its transport, recondensation and the creation of large structures. This model was validated with boiling flow in a bent tube at different mass flow rates and heat fluxes, which allowed us to observe the evolution of two-phase flow patterns. Finally, numerical simulation of direct steam generation inside a concentrated solar plant receiver clearly showed the apparition and evolution of various two-phase flow patterns.     

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.     

Experimental study of jet structure and pressurisation upon liquid nitrogen injection into water

The rapid phase change and heat transfer obtained by direct contact heat exchange between a cryogen and water can generate high rates of pressurisation, which is of interest to a number of applications. A visualization study of liquid nitrogen injection into water is conducted in this work, with synchronized pressure and temperature measurement, to obtain insight into this complex phenomenon. High speed imaging reveals a four-stage evolution of liquid nitrogen jet structure upon injection into water, with a thick vapour blanket forming around a liquid nitrogen core and break-up brought on predominantly through impact with the vessel wall. Maximum pressurisation rate occurs in the third stage of injection due to a combination of heat and mass transfer. Pressurisation rates in excess of 350 bar/s are recorded and found to vary proportionally with injection pressure. The scenario of gaseous nitrogen injection is also investigated, and compared with liquid nitrogen injection. A clear advantage of liquid nitrogen injection is elucidated from the point of heat transfer and pressurisation, and implications for use in a cryogenic engine are discussed.     

Investigation on Heat and Mass Transfer in a Evaporator of a Capillary-Pumped Loop with the Lattice Boltzmann Method: Pore Scale Simulation

A two-dimensional transient numerical model based on the lattice Boltzmann method (LBM) for the global evaporator of a capillary-pumped loop (CPL) is proposed to describe heat and mass transfer with evaporation in the porous wick, heat conduction in the cover plate, and heat transfer in the vapor groove. To indicate the stochastic phase distribution characteristics of most porous wick, the quartet structure generation set (QSGS) is introduced for generating more realistic microstructures of porous media. By using the present lattice Boltzmann algorithm along with the porous structure, the heat and mass transfer of an evaporator on pore scale can be predicted without resorting to any empirical parameters determined case by case. The energy equations for entire evaporator are solved as a conjugate problem, which are solved by means of a spatially varying relaxation time in the lattice Boltzmann model and the liquid flow is driven via the interfacial mass flux. A convective boundary condition considering the latent heat during the evaporation on the interface is introduced into the lattice Boltzmann model based on the nonequilibrium extrapolation rule. Especially, the bounce-back rule and the equilibrium rule of the LBM are, respectively, introduced to deal with the momentum boundary conditions inside the porous wick and on the evaporation interface in order to ensure the stability and the efficiency of the LBM model. Numerical results corresponding to different working conditions and different working fluids are presented, which provide guidance for the evaporator design of a CPL system.     

Strömungs- und Wärmeübergangsverhalten von flüssigem Quecksilber bei Benetzung und Nichtbenetzung

In wetted and nonwetted tubes the hydrodynamics and heat transfer of liquid metal flow were investigated. Mercury was used as test fluid. For the laminar flow no hydraulics anomalies were indicated. In the case of the wetted tube a steady change of diameter and an increase of the surface roughness were observed. This is due to the formation and removing of a viscous amalgam layer at the tube wall. In the laminar region heat transfer measurements show very good agreement with theory. In the turbulent region the experimental results are comparable with heat transfer coefficients valid for the nonwetted tube published in literature. The influence of different surface contact conditions to heat transfer can be excluded. A thermal contact resistance could not be found.