A numerical model for ammonia–water absorption into a constrained microscale film

A one-dimensional, steady state model for absorption of ammonia vapor into a constrained microscale film is presented. A weak solution of ammonia–water flows in a microchannel into which ammonia vapor bubbles are injected in cross flow from a porous wall. A counter flowing coolant solution removes the heat generated due to absorption from the opposite wall. The 1-D, steady state species and energy transport equations are solved to yield, along the length of the channel, concentration and temperature profiles of the solution stream and the temperature profile of the coolant fluid stream. The model is validated from experimental measurements of global parameters. A parametric study of fluid and geometrical parameters based on the validated model is presented. Results show that a balance between the residence time within the absorber and the absorption time scales, by way of adjusting the mass flow rates of the vapor and weak solution, is needed to ensure complete absorption. A lower coolant inlet temperature significantly enhances absorption rate by increasing the local concentration difference between the saturation and bulk values. The absorption rate is more sensitive to the liquid–vapor interfacial area than to the heat transfer area between the solution and the coolant.     

Numerical study of liquid film cooling in a rocket combustion chamber

A numerical study is reported to investigate the liquid film cooling in a rocket combustion chamber. Mass, momentum and heat transfer characteristics through the interface are considered in detail. A marching procedure is employed for solution of the respective governing equations for the liquid film and gas stream together. The standard turbulence k–ε model is used to simulate the turbulence gas flow and a modified van Driest model is adopted to simulate the turbulent liquid film flow. Radiation of gas stream is also considered and simulated with the flux model. Downstream of the liquid film the gaseous film cooling is numerically studied simultaneously. Results are presented for a mixed gases–water system under different condition. Various effects on the liquid film length are examined in detail. There is a good agreement between the numerical prediction and experimental result on the liquid film length.     

Prediction of film cooling with a liquid coolant

A numerical method of analysing film cooling with a liquid coolant is presented. The model assumes a turbulent boundary-layer flow for the hot gas stream and a Couette flow in the liquid coolant film. A marching procedure is employed for solution of the equations of mass, momentum, enthalpy and species conservation. Numerical results for an air-water system are presented. The effects of flow conditions on the film cooling mechanism are discussed. An increase in free-stream temperature, free-stream velocity or coolant temperature causes reduction in the film-cooled length while an increase in coolant flow rate causes a proportionate increase in the film-cooled length. The comparison with the limited experimental data indicates that the observed trends are well predicted. However, more detailed data are required to validate and refine the prediction procedure particularly with regard to the flow within and on surface of the coolant film.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

The numerical computation of the evaporative cooling of falling water film in turbulent mixed convection inside a vertical tube

An analysis has been developed for studying the evaporative cooling of liquid film falling inside a vertical insulated tube in turbulent gas stream is presented. Heat and mass transfer characteristics in air–water system are mainly considered. A low Reynolds number turbulence model of Launder and Sharma is used to simulate the turbulent gas stream and a modified Van Driest model suggested by Yih and Liu is adopted to simulate the turbulent liquid film. The model predictions are first compared with available experimental data for the purpose of validating the model. Parametric computations were performed to investigate the effects of Reynolds number, inlet liquid temperature and inlet liquid mass flow rate on the liquid film cooling mechanism. Results show that significant liquid cooling results for the system with a higher gas flow Reynolds number Re, a lower liquid flow rate Γ₀ or a higher inlet liquid temperature T_L0.     

垂直窄缝通道内环状流沸腾传热特性

本研究基于液膜和蒸汽的质量、动量和能量方程,建立了均匀热流垂直窄缝通道内环状流沸腾传热模型,通过相关文献估算环状流起始点处液膜厚度,利用有限差分法对环状流模型方程组进行数值求解,得到沿流道环状流区域的液膜厚度,并进一步预测了局部沸腾传热系数,结果表明:环状流区域的局部沸腾传热系数随质量流量和干度的增加而增加,与Kenning关联式对比,模型预测沸腾传热系数较关联式计算值偏低。将不同工况下的226组两相环状流实验数据与模型预测结果进行对比,平均绝对误差为18.2%。     

Effects of Non-Darcian and Inlet Conditions on the Forced Convection Along a Vertical Plate With Film Evaporation

The present study analyzes theoretically the non-Darcian effects and inlet conditions of forced convection flow with liquid film evaporation in a porous medium. The physical scheme includes a liquid–air streams combined system; the liquid film falls down along the plate and is exposed to a cocurrent forced moist air stream. The axial momentum, energy, and concentration equations for the air and water flows are developed based on the steady two-dimensional (2-D) laminar boundary layer model. The non-Darcian convective, boundary, and inertia effects are considered to describe the momentum characteristics of a porous medium. The paper clearly describes the temperature and mass concentration variations at the liquid–air interface and provides the heat and mass transfer distributions along the heated plate. Then, the paper further evaluates the non-Darcian effects and inlet conditions on the heat transfer and evaporating rate of liquid film evaporation. The numerical results show that latent heat transfer plays the dominant heat transfer role. Carrying out a parametric analysis indicates that higher air Reynolds number, higher wetted wall temperature, and lower moist air relative humidity will produce a better evaporating rate and heat transfer rate. In addition, a non-Darcy model should be adopted in the present study. The maximum error for predictions of heat and mass transfer performance will be 21% when the Darcy model is used.     

Extensive study on laminar free film condensation from vapor–gas mixture

The dimensionless velocity component method was successfully applied in a depth investigation of laminar free film condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the film condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the film condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for condensation was proposed, and evaluated for the film condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the film condensation from the vapor–gas mixture were achieved.The laminar free film condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the film condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the film condensation from the vapor–gas mixture.     

The convective drying of liquid films on slender wires

We solve numerically the balance equations of mass and thermal energy for drying liquid films of binary solutions on cylindrical substrates to simulate the drying process of liquid coatings on round metal wires, which are used for electrical insulation in magnet wire technology. The liquid phase diffusion coefficient and the solvent activity are treated as concentration and temperature dependent. The evaporation rate of the solvent across the shrinking liquid–gas interface is determined using the film theory, accounting for the thermodynamic state of the ambient medium and the convective flow situation. The quality of the coatings is assessed by the temporal evolution of radial profiles of the solute mass fraction and by detecting boiling, which leads to the formation of vapour bubbles in the liquid films and is undesired. A guideline for uniform drying at various drying conditions is presented. The simulation model is applied to the test system PVA-water.     

A model of liquid film breakdown formed due to impingement of a two-phase jet on a horizontal surface

The present work aims to provide an explanation to the phenomenon of breakdown of the thin liquid film created by impinging two-phase, liquid–gas jet. Existing in the literature models describe merely the breakdown of single phase liquid films. The model presented here is based on examination of mass and energy equations under the applied criterion of the minimum of total energy. That allows to determine the minimum thickness of isothermal, thin liquid film created by impinging two-phase jet on a solid surface. The mechanical energy of the system consists of kinetic energy of liquid film and surface energy of all physical surfaces consisting for the control surface. An analytical expression for the minimum thickness of such liquid film is derived. The liquid film thickness at the breakdown is a function of the contact angle and shear stresses on the liquid–gas interface. Some comparisons with the experimental data are shown exhibiting a good performance of the postulated model.     

Optimal distribution of cooling during gas compression

This paper describes the optimization of the distribution of heat transfer (cooling) during the process of gas compression. The coolant is a stream of cold liquid. There is a fundamental tradeoff between the savings in compressor power, which are due to distributed cooling, and the pumping power required to circulate the coolant. The tradeoff is revealed on the basis of a combined model of multi-stage gas compression, resistance to fluid flow, and area-constrained counter- or co-current heat exchange between the gaseous stream and the liquid stream. The results are illustrated for the compressor of an actual ammonia refrigeration plant, for which the distributed-cooling design is highly recommended because the compressor discharge temperature in such units is high. It is shown that there is an optimal coolant (water) flow rate such that the total power requirement is minimized. The optimized distribution of gas compression and cooling is robust with respect to the selection of the water flow rate.     

A momentum integral model for prediction of steady operation and flooding in thermosyphons

An analytical momentum integral model is developed for the prediction of the steady operation of closed two-phase thermosyphons over a wide range of temperatures, pressures and heat inputs. Using a new proposed velocity distribution for the flow of the liquid film, differential equations for mass, momentum, and energy balances have been solved simultaneously to obtain the continuous solution for the thickness of the liquid film, mass flow rate, and heat transfer along the length of the condenser. The interfacial shear due to phase-change at the liquid–vapor interface, as well as acceleration of the condensate film in the momentum balance equation, has been taken into account. The current model uses minimal number of semi-empirical correlations for interfacial shear and heat transfer coefficient and utilizes self-consistent assumptions. The current model is able to accurately predict the essential performance parameters of the system including local and overall mass flow and heat transfer rates through the length of the condenser for a wide range of low to medium heat inputs, up to the flooding limit. Despite the simplicity of the model in comparison to previous studies, the predictions for local mass flow rates and heat fluxes are in excellent agreement with available experimental data.     

Effects of film evaporation on laminar mixed convection heat and mass transfer in a vertical channel

A numerical study of finite liquid film evaporation on laminar mixed convection heat and mass transfer in a vertical parallel plate channel is presented. The influences of the inlet liquid mass flow rate and the imposed wall heat flux on the film vaporization and the associated heat and mass transfer characteristics were examined for air-water and air-ethanol systems. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made by Tsay and Yan (Wärme- und Stoffübertragung 26, 23–31 (1990)) is only valid for a system with a small liquid mass flow rate. Additionally, it is found that the heat transfer between the interface and gas stream is dominated by the transport of latent heat associated with film evaporation. The magnitude of the evaporative latent heat flux may be five times greater than that of sensible heat flux.     

Two-phase modelling of laminar film condensation from vapour–gas mixtures in declining parallel-plate channels

A two-phase model is presented that analyzes laminar film condensation from mixtures of a vapour and a non-condensing gas in parallel-plate channels. The channel is declining (inclined downward from the horizontal) and has an isothermal cooled bottom plate and an insulated upper plate. The model uses a finite volume method to solve the complete two-phase boundary-layer equations including inertia forces, energy convection, interfacial shear, and axial pressure change. Results are presented for steam–air mixtures in terms of axial variation of film thickness and local Nusselt number for various Froude numbers, inlet Reynolds numbers, inlet gas mass fractions, and inlet temperature differences. Profiles of axial velocity, temperature, and gas mass fraction are also presented. Increasing the angle of declination (decreasing the Froude number) produces thinner, faster moving films. The change in local Nusselt number with Froude number was not as substantial as the change in film thickness. The detrimental effect of the noncondensable gas on the heat transfer rate was observed to be more pronounced at higher Froude numbers. An exact analytical solution for the liquid and mixture axial velocity profiles under end of condensation conditions is also presented and compared with the numerical results.     

Numerical solution of film condensation from turbulent flow of vapor–gas mixtures in vertical tubes

A complete two-phase model is presented for film condensation from turbulent downward flow of vapor–gas mixtures in a vertical tube. The model solves the complete parabolic governing equations in both phases including a model for turbulence in each phase, with no need for additional correlation equations for interfacial heat and mass transfer. A finite volume method is used to form the discretized mean flow equations for conservation of mass, momentum, and energy. A fully coupled solution approach is used with a mesh that automatically adapts to the changing film thickness. The results of using three turbulence models involving combinations of mixing length and k–ε models in the film and mixture regions are compared. This new model is extensively compared with previous numerical and experimental studies. In the experimental comparisons, it was found that a model consisting of a k–ε turbulence model for both the film and the mixture flows produced the best agreement. Results are also presented for a parametric study of condensation from steam-air mixtures. The effects of changes to the inlet Reynolds number, the inlet gas mass fraction, and the inlet-to-wall temperature difference on the film thickness and heat transfer are presented and discussed. Local profiles of axial velocity, temperature, and gas mass fraction are also presented.     

A study of steady laminar diffusion flame over methanol pool surface

A numerical study of laminar, boundary layer type diffusion flames established over a liquid fuel pool, under the influence of forced air flow parallel to the pool surface, has been carried out. Burning of a confined methanol pool at atmospheric pressure and under normal gravity conditions is investigated. A numerical model, which solves transient, two-dimensional, mass, momentum, species and energy conservation equations, has been employed to predict the flame characteristics. The gas-phase alone is solved in a decoupled manner using appropriate interface boundary conditions, without considering the effects of liquid-phase transport on the combustion process. A single-step global reaction for methanol–air oxidation, considering carbon-dioxide dissociation, is employed to model the chemical kinetics. An optically thin radiation model has also been incorporated to account for thermal radiation losses by absorbing species in a non-luminous flame. At the outset, the model is validated against the experimental results available in literature. Thereafter, it has been used to investigate the influence of free stream air velocity on fuel mass burning rate, flame stand-off distance, temperature and flow fields. The study brings out the variation in the structure of confined laminar boundary layer type diffusion flames over methanol pool for several air velocities under normal gravity environment.     

Shear-driven flows of locally heated liquid films

This paper considers the flow of a liquid film sheared by gas flow in a channel with a heater placed at the bottom wall. A one-sided 2D model is considered for weakly heated films. The heat and mass transfer problem is also investigated in the framework of a two-sided model. The exact solution to the problem of heat transfer is obtained for a linear velocity profile. The double effect of Marangoni forces is demonstrated by the formation of a liquid bump in the vicinity of the heater’s upper edge and film thinning in the vicinity of the lower edge. The criterion determining the occurrence of “ripples” on the film surface upstream from the bump is found. Numerical analysis reveals that evaporation dramatically changes the temperature distribution, and hence, thermocapillary forces on the gas–liquid interface. All transport phenomena (convection to liquid and gas, evaporation) are found to be important for relatively thin films, and the thermal entry length is a determining factor for heaters of finite length. The thermal entry length depends on film thickness, which can be regulated by gas flow rate or channel height. The influence of the convective heat transfer mechanism is much more prominent for relatively high values of the liquid Reynolds number. The liquid–gas interface Biot number is shown to be a sectional-hyperbolic function of a longitudinal axis variable. Some qualitative and quantitative comparisons with experimental results are presented.     

Numerical Study of Film and Regenerative Cooling in a Thrust Chamber at High Pressure

Numerical study of coupled heat transfer of gas flow with film cooling, chamber wall conduction, and regeneration coolant cooling in the thrust chamber of a liquid rocket engine was performed. A one-dimensional model was adopted for regeneration cooling to couple two-dimensional model simulation in the thrust camber. Numerical results show that the method adopted can simulate the gas flow field well, and can calculate the heat flux through the wall, the wall temperature, and the temperature increase of the coolant quickly. In addition, liquid film cooling can reduce the wall temperature greatly, and decrease the heat flux transferred from the hot gas to the chamber wall.     

Y型喷嘴内部气液两相流动及液膜雾化的数学模型

根据前人实验观察结果所得的流动结构,从气液两相各的质量,动量、能量平衡及其相互作用方程的构造入手,包括混合孔内油流端部界上的正应力传递,两相平行界面上的剪应力作功传热等,建立了Ｙ型喷嘴内部流动过程的数学模型,进而,依据不稳定表面波理论及空气动力破碎理论,分别对Ｙ型喷嘴出口油膜的初级破碎及二次雾化过程作了进一步的模化,建立了一套较为完整的Ｙ型喷嘴性能预测及设计优化的数学方法,经检验,实际使用效果良好