Numerical simulation of double-pipe condensers and evaporators

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behaviour of double-pipe heat exchangers (evaporators and condensers) has been carried out. The governing equations (continuity, momentum and energy) inside the internal tube and the annulus, together with the energy equation in the internal tube wall, external tube wall and insulation, are solved iteratively in a segregated manner. The discretized governing equations in the zones with fluid flow are efficiently coupled using an implicit step by step method. This formulation requires the use of empirical correlations for the evaluation of convective heat transfer, shear stress and void fraction. An implicit central difference numerical scheme and a line-by-line solver was used in the internal and external tube walls and insulation. A special treatment has been implemented in order to consider transitions (single-phase/two-phase, dry-out,…). All the flow variables (enthalpies, temperatures, pressures, mass fractions, velocities, heat fluxes,…) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretized. Different numerical aspects and comparisons with analytical and experimental results are presented in order to verify and validate the model.     

Numerical simulation of non-adiabatic capillary tubes considering metastable region. Part II: Experimental validation

A detailed one-dimensional steady and transient numerical simulation of the thermal and fluid-dynamic behavior of capillary tube–suction line heat exchangers considering metastable region and separated flow has been developed in Part I of this paper. The developed numerical model allows analysis of aspects such as geometry, type of fluid, critical or non-critical flow conditions and metastable region. The accuracy of the detailed simulation model is demonstrated in this part (Part II) of the paper by comparing simulation results with a wide range of steady state experimental data from the technical literature, which include the refrigerant mass flow rate, outlet suction line temperature, and temperature profile along concentric and lateral capillary tube–suction line heat exchangers. Of the 196 data points evaluated for mass flow rate 96.4% are within an error of ±15%, 81.1% are within ±10% with a mean deviation of ±6.3%. Of the 143 data points evaluated for outlet suction line temperature 89.5% are within an error of ±2 °C, with a mean deviation of ±0.98 °C.The numerical results obtained are used to understand the refrigerant flow behavior inside non-adiabatic capillary tubes. Some divergence problems in the numerical solution process is found to be the discontinuity in non-adiabatic capillary tube flow characteristics caused by re-condensation of the refrigerant within the heat exchanger zone; this aspect needs special attention while modeling the non-adiabatic capillary tube flow. Other important parameter to be evaluated experimentally with special care is the capillary tube internal diameter due to its strong influence on the refrigerant flow results (results of any study based on the nominal diameter are to be used with caution).     

A novel special distributed method for dynamic refrigeration system simulation

A novel dynamic mathematical model based on spatially distributed approach has been developed and validated in this paper. This model gives good agreement in predicting the system COP and other parameters. The validated model has been used to enhance the prediction of the micro variations of superheat and sub-cooling. The novel spatial distributed model for the condenser and evaporator in refrigeration system, calculates the two-phase region in gas and liquid field separately since the gas and liquid in the two-phase region have different velocities. Previous researchers have used a pre-defined function of the void fraction in their spatially distributed model, based on experimental results. This approach results in the separate solution of the mass and energy equations, and less calculation is required. However, it is recognized that the mass and energy equations should be coupled during solving for more accurate solution. Based on the energy and mass balance, the spatial distribution model constructed here solves the velocity, pressure, refrigerant temperature, and wall temperature functions in heat exchangers simultaneously. A novel iteration method is developed and reduces the intensive calculations required. Furthermore, the condenser and evaporator models have shown a parametric distribution along the heat exchanger surface, therefore, the spatial distribution parameters in the two heat exchangers can be visualised numerically with a two-phase moving interface clearly shown.     

A numerical simulation model for plate-type, roll-bond evaporators

This study presents a first-principles mathematical model developed to investigate the thermal behavior of a plate-type, roll-bond evaporator. The refrigerated cabinet was also taken into account in order to supply the proper boundary conditions to the evaporator model. The mathematical model was based on the mass, momentum and energy conservation principles applied to each of the following domains: (i) refrigerant flow through the evaporator channels; (ii) heat diffusion in the evaporator plate; and (iii) heat transmission to the refrigerated cabinet. Empirical correlations were also required to estimate the shear stresses, and the internal and external heat transfer rates. The governing partial differential equations were discretized through the finite-volume approach and the resulting set of algebraic equations was solved by successive iterations. Validation of the model against experimental steady-state data showed a reasonable level of agreement: the cabinet air temperature and the evaporator cooling capacity were predicted within error bands of ±1.5 °C and ±6%, respectively.     

Pressure drop and flashing mechanisms in refrigerant expansion devices

This paper examines a novel pressure drop mechanism as well as flow choking conditions that determine mass flow rate in refrigerant expansion devices. For this study, an ideal situation is considered where an expansion device such as a short tube orifice or a thermostatic expansion valve is modeled as an ideal isentropic nozzle. In addition, a liquid with a certain initial degree of superheat is first expanded in the converging nozzle down to the exit section without any phase transition. At the exit section where the metastable liquid jet flashes to produce a complex axisymmetric two-phase flow, a shock wave may terminate the overall expansion process. The model presented here is based on experimental observations in short nozzles, where the metastable liquid in the central core undergoes a sudden phase transition in the interfacial region, giving rise to a high-speed two-phase flow. A simple 1-D analysis of the radial evaporation wave based on the theory of discontinuities from gas dynamics leads to the Chapman–Jouguet (C-J) solution. Flow choking issues are examined and numerical examples are presented for three common refrigerants: R134a, R-22, and R-600a. Results suggest that the evaporation wave may be the flow controlling mechanism in these devices.     

基于VOF/PLIC界面追踪方法的RTM工艺充模过程数值模拟

针对基于Darcy定律的树脂传递模塑(RTM)工艺的充模过程数值模拟的局限性,将纤维预制体内的充填流动作为两相流(树脂相和空气相)处理,在动量方程中考虑了惯性项和粘性项,采用有限体积方法(FVM)离散控制方程,并与VOF/PLIC界面追踪方法相结合,发展了求解树脂在纤维预制体内非稳态流动问题的数值模拟方法.在此基础上开发了RTM工艺的充模过程数值模拟程序,其算例的数值模拟结果与解析解或实验结果吻合良好,验证了此数值模拟方法的有效性和可靠性.     

Two-dimensional turbulent film condensation of vapours flowing inside a vertical tube and between parallel plates: a numerical approach

Film condensation of vapour flowing inside a vertical tube and between parallel plates is treated. A methodology is presented to determine numerically the heat transfer coefficients, the film thickness and the pressure drop. The analysis is based on the resolution of the full coupled boundary layer equations of the liquid and vapour phases and does not neglect inertia and convection terms in the governing equations. Turbulence in the vapour and condensate film is taken into account using mixing length turbulence models. An explicit method and an implicit finite difference procedures are described. The calculated results for the condensation of steam in a 24 mm diameter tube are compared with those obtained from Chen's correlation. The heat flow rate for the condensation of R123 flowing between parallel plates obtained from numerical solution are compared with experimental values. The mean heat transfer coefficients for the condensation of vapour mixture R123/R134a are also presented.     

Dynamic behavior of a direct expansion evaporator under frosting condition. Part I. Distributed model

A general distributed model with two-phase flow for refrigerant coupled with a frost model is developed for studying the dynamic behavior of an evaporator. The equations are derived in non-steady-state manner for the refrigerant and a quasi-steady state model with permeation for the frost. The complex flow and geometry of the finned tube evaporator lead to uneven wall and air temperature distributions, which in turn affect the rate of frost growth and densification along the coil depth. Results include frost accumulation and its effect on energy transfer, air off-coil temperature, refrigerant liquid dry-out position and propagation of frost formation along the coil.     

CoilDesigner: a general-purpose simulation and design tool for air-to-refrigerant heat exchangers

A simulation and design tool to improve effectiveness and efficiency in design, and analysis of air to refrigerant heat exchangers, CoilDesigner, is introduced. A network viewpoint was adopted to establish the general-purpose solver and allow for analysis of arbitrary tube circuitry and mal-distribution of fluid flow inside the tube circuits. A segment-by-segment approach within each tube was implemented, to account for two-dimensional non-uniformity of air distribution across the heat exchanger, and heterogeneous refrigerant flow patterns through a tube. Coupled heat exchangers with multiple fluids inside different subsets of tubes can be modeled and analyzed simultaneously. A further sub-dividing-segment model was developed in order to address the significant change of properties and heat transfer coefficients in the single-phase and two-phase regime when a segment experiences flow regime change. Object-oriented programming techniques were applied in developing the program to facilitate a modular, highly flexible and customizable design platform and in building a graphic user-friendly interface. A wide variety of working fluids and correlations of heat transfer and pressure drop are available at the user's choice. The model prediction with CoilDesigner was verified against experimentally determined data collected from a number of sources.     

Flux-splitting finite volume method for turbine flow and heat transfer analysis

A novel numerical method was developed to deal with the flow and heat transfer in a turbine cascade at both design and off-design conditions. The Navier–Stokes equations are discretized and integrated in a coupled manner. In the present method a time-marching scheme was employed along with the time-integration approach. The flux terms are discretized based on a cell finite volume formulation as well as a flux-difference splitting. The flux-difference splitting makes the scheme rapid convergence and the finite volume technique ensure the governing equations for the conservation of mass, momentum and energy. A hybrid difference scheme for quasi-three-dimensional procedure based on the discretized and integrated Navier–Stokes equations was incorporated in the code. The numerical method possesses the positive features of the explicit and implicit algorithms which provide a rapid convergence process and have a less stability constraint. The computed results were compared with other numerical studies and experimental data. The comparisons showed fairly good agreement with experiments.     

Optimal shape of the multi-passage branching system in a single-phase parallel-flow heat exchanger

A numerical simulation is performed to examine the heat and fluid flow characteristics of the branching system in a single-phase parallel-flow heat exchanger (PFHE) and to obtain its optimal shape. The relative importance of the design parameters [injection angle of the working fluid (Θ), inlet shape and location (Y_c), and height of the protruding flat tube (Y_b)] is determined to decide the optimization sequence. The optimal geometric parameters are obtained as follows: Θ=−21°, Type A, Y_c=0 and Y_b=0. The heat transfer rate of the optimum model compared to that of the reference model is increased by about 55%. The optimal values of the parameters can be applicable to the Reynolds number ranging from 5000 to 20,000.     

考虑亚稳态影响的非绝热毛细管数学模型及数值计算

根据两相流动的均相流动模型，考虑亚稳态的影响，建立了非绝热毛细管的数学模型，在此基础上进行数值计算，并将结果与实验文献进行了比较。     

Wall and fluid inlet temperature effect on heat transfer in incompressible laminar oscillating flows

This paper deals with the problem of oscillating flows occurring in devices such as Stirling or thermoacoustic engines and refrigerators. Since the global governing equations cannot be solved, the authors propose to introduce a few simplifications; the most simplifying reduction is that the fluid is assumed to be incompressible. However, specific attention is paid to describing the flow characteristics that's why the Lagrangian formalism which allows the individual study of each fluid particle is adopted. Thereby each particle contribution to global thermal effects can be evaluated and the gas temperature profiles along the exchanger can be computed. Various situations are presented including the case of a non-uniform temperature at the wall and a phase lag between pressure and temperature at the fluid entrance. The efficiency of the wall to fluid thermal exchange is analyzed. The authors show that this exchange depends upon two important parameters: the geometric ratio between the exchanger length and the particle oscillating displacement, and a thermal parameter “β”, governing the temperature profiles and related to the Prandtl number, the operating frequency and the phase lag between the instantaneous heat flux and the wall to fluid temperature difference.     

Heat transfer in the evaporator of an advanced two-phase thermosyphon loop

As heat generation from electronic components increase and the limit of air-cooling is reached, the interest for using liquid cooling for high heat flux applications has risen. Thermosyphon cooling is an alternative liquid cooling technique, in which heat is transferred as heat of vaporization from evaporator to condenser with a relatively small temperature difference.The effect of fluid properties, the structure of wall surfaces, and the effect of system pressure was investigated and reported previously by the author. In this paper, the influence of heat flux, system pressure, mass flow rate, vapor fraction, diameter of evaporator channel and tubing distance between evaporator and condenser on the heat transfer coefficient of an advanced two-phase thermosyphon loop is reported. The tested evaporators were made from small blocks of copper with 7, 5, 4, 3 and 2 vertical channels with the diameters of 1.1, 1.5, 1.9, 2.5, and 3.5 mm, respectively and the length of 14.6 mm. Tests were done with isobutane at heat fluxes ranging between 28.3 and 311.5 kW/m².     

Modeling of a domestic frost-free refrigerator

In the present study, a comprehensive thermo-fluidic model is developed for a domestic frost-free refrigerator. The governing equations, coupled with pertinent boundary conditions, are solved by employing a conservative control volume formulation, in the environment of a three-dimensional unstructured mesh. Experiments are also conducted to validate the results predicted by the present computational model. It is found that the computational and experimental results qualitatively agree with each other, although certain discrepancies can be observed in terms of the exact numerical values obtained. For the freezer compartment, the computationally predicted temperatures are somewhat higher than the experimental ones, whereas for the refrigerating compartment, the computed temperatures are lower than the corresponding experimental observations. The difference between experimental and computational results may be attributed to the lack of precise data on the airflow rates and the unaccounted heat transfer rates through the door gaskets and the compressor. From the heat transfer and fluid flow analysis, certain modifications in the design are also suggested, so as to improve the performance of the refrigerator.     

Numerical simulation of non-adiabatic capillary tubes. Special emphasis on the near-saturation zone

The aim of this article is to present a distributed numerical model that simulates the thermal and fluid-dynamic phenomena inside non-adiabatic capillary tubes. The resolution approach is based on a two-phase flow model where the fluid domain is discretized in a one-dimensional way, and the governing equations (continuity, momentum, and energy) are solved by means of a step-by-step algorithm. The model explained herein consists of an improved and extended version of previous works (Escanes et al., 1995; García-Valladares et al., 2002a,b; Ablanque et al., 2010) including two additional features. On the one hand, it allows the simulation of the two typical geometric arrangements found in capillary-tube/suction-line heat exchangers (i.e. concentric and lateral). On the other hand, it has an enhanced capability to address the convergence difficulties found in distributed models at the near-saturation zone. This document presents the major numerical adaptations done to the model, a comprehensive validation of the two geometric configurations, the model performance when tackling the aforementioned numerical difficulties and finally, some numerical studies.     

A generalized moving-boundary model for transient simulation of dry-expansion evaporators under larger disturbances

A generalized model based on the moving-boundary approach is developed to describe the transient behavior of dry-expansion evaporators in the vapor-compression refrigeration system. To improve the robustness of the traditional moving-boundary model under larger disturbances, the time-variant mean void fraction is employed instead of the constant. Numerical integration is applied to get the mean properties in the two-phase region and the superheated region. The interface wall temperature between the two-phase and the superheated regions is also evaluated by a new weighted mean. Qualitative case study shows that the present model can well predict the transient behaviors of evaporators under larger disturbances and keep the robustness whenever superheated region appears or disappears.     

Evolutionary design of dynamic neural networks for evaporator control

This paper presents a novel neural network (NN) to control an ammonia refrigerant evaporator. Inspired by the latest findings on the biological neuron, a dynamic synaptic unit (DSU) is proposed to enhance the information processing capacity of artificial neurons. Treating the dynamic synaptic activity after the nonlinear somatic activity helps to capture the dynamics demarcated by the Gaussian activation pertaining to the input space. This practice leads to a remarkable reduction in curse of dimensionality. The proposed NN architecture has been compared with two other conventional architectures; one with dynamic neural units (DNUs) and the other with nonlinear static functions as perceptrons. The objective is to control evaporator heat flow rate and secondary fluid outlet temperature while keeping the degree of refrigerant superheat in the range 4–7 K at the evaporator outlet by manipulating refrigerant and evaporator secondary fluid flow rates. The drawbacks of conventional approaches to this problem are discussed, and how the novel method can overcome them are presented. An evolutionary approach is adopted to optimize the parameters of the NN controllers. Then evaporator process model is accomplished as a combination of governing equations and a sub NN resulting in a simple and sufficiently accurate model. The effectiveness of the proposed dynamic NN controller for the evaporator system model is validated using experimental data from the ammonia refrigeration plant.     

Coupled heat and mass transfer during nonisothermal absorption by falling droplet with internal circulation

We considered mass and heat transfer during nonisothermal absorption of a gas by a falling droplet with internal circulation. Gas phase is assumed to be free of inert admixtures and mass transfer is liquid phase controlled. Mass flux is directed from a gaseous phase to a droplet, and the interfacial shear stress causes a fluid flow inside the droplet. Droplet deformation under the influence of interface shear stress is neglected. Absorbate accumulation and temperature increase in the bulk of liquid phase are taken into account. The problem is solved in the approximations of a thin concentration and temperature boundary layers in the liquid phase. The thermodynamic parameters of the system are assumed constant. The system of transient partial parabolic differential equations of convective diffusion and energy balance with time-dependent boundary conditions is solved by combining the similarity transformation method with Duhamel's theorem, and the solution is obtained in a form of Volterra integral equation of the second kind which is solved numerically. Theoretical results are compared with available experimental data for water vapor absorption by falling droplets of aqueous solution of LiBr.     

A study on numerical simulations and experiments for mass transfer in bubble mode absorber of ammonia and water

An absorber is a major component in the absorption refrigeration systems, and its performance greatly affects the overall system performance. In this study, both the numerical and experimental analyses in the absorption process of a bubble mode absorber were performed. Gas was injected into the bottom of the absorber at a constant solution flow rate. The region of gas absorption was estimated by both numerical and experimental analyses. A higher gas flow rate increases the region of gas absorption. As the temperature and concentration of the input solution decrease, the region of gas absorption decreases. In addition, the absorption performance of the countercurrent flow was superior to that of cocurrent. Mathematical modeling equations were derived from the material balance for the gas and liquid phases based on neglecting the heat and mass transfer of water from liquid to gas phase. A comparison of the model simulation and experimental results shows similar values. This means that this numerical model can be applied for design of a bubble mode absorber.