Generalized method of pressure drop and tube length calculation with boiling and condensing refrigerants within the entire zone of saturation

A simple and universal method of pressure drop and horizontal tube length calculation with boiling and condensing refrigerants within the entire saturation zone ranging from critical point down to the lowest temperatures, is proposed. The method can be applied for the calculation ofevaporators and condensers operating in conventional and non-conventional refrigeration, air conditioning and heat pump system, as well as in similar cases. By introducing a two-phase flow factor, β, and a liquid/vapour gradient ratio, θ, the correlation given by Müller-Steinhagen and Heck can be rearranged to a siple dimensionless form which leads to a family of universal curves that enable any dry-saturated vapour flow gradient to be transformed into an actual two-phase flow gradient, or vice versa, at any temperature and liquid/vapour mixture quality within the entire saturation zone of refrigerants. Determination of θ is a key factor in the accuracy of the calculation. Appropriate correlations and diagrams for predicting τ are presented in terms of corresponding states principle. Some practical advice and numerical examples of evaporators and condensers calculation are given.     

Condensing two-phase pressure drop and heat transfer coefficient of propane in a horizontal multiport mini-channel tube: Experimental measurements

This article reports the condensing flow heat transfer coefficient and pressure drop results of propane (R290) flowing through a square section horizontal multiport mini-channel tube made of aluminium having an internal diameter of 1.16 mm and a condensing length of 259 mm. Pressure drop and two phase flow experiments were performed at saturation temperatures of 30, 40 and 50 °C. Heat flux was varied from 15.76 to 32.25 kWm⁻² and mass velocity varied from 175 to 350 kg m⁻² s⁻¹. The results show that the two-phase friction pressure gradient increases with the increase of mass velocity and vapour quality and with the decrease of saturation temperature. The heat transfer coefficients showed to increase with increases of vapour quality and mass velocity while increases of saturation temperature were observed to reduce heat transfer coefficient. The two phase frictional pressure drop correlations of Sun and Mishima and Agarwal and Garimella, and the two-phase flow heat transfer correlations of Koyama et al. and Wang et al. predicted well the experimental results.     

Control of a weakly perturbed Lagrangian system with a guaranteed escape rate

This paper considers a problem of controlling a weakly perturbed Lagrangian system so as to keep it within a reference domain on a pregiven time interval. Escape from this domain is associated with failure of the system. The criterion of interest is the rate of escape, and the task is to design a controller ensuring a noise-independent escape rate (in the small noise limit) of the controlled system. We treat this problem in the context of control against large deviations in weakly perturbed dissipative systems. As this paper demonstrates, for Lagrangian systems, in contrast to the great majority of large deviation problems, an explicit logarithmic asymptotic of the escape rate can be found. An explicit formula allows us to define the parameters of a regulator guaranteeing weak dependence of the escape rate on the noise strength. The regulator consists of two units, nonlinear velocity feedback with the parameters depending on the noise strength and state feedback, independent of noise. The first unit stabilizes the system and ensures a noise-independent asymptotics of the logarithmic escape rate; the second unit is designed to modify the exit location on the boundary of the reference domain. Applications of these results to stabilization and tracking models illustrate the theory.     

Visualization and void fraction measurement of decompressed boiling flow in a capillary tube

A capillary tube is often used as a throttle for a refrigerating cycle. Subcooled refrigerant usually flows from a condenser into the capillary tube. Then, the refrigerant is decompressed along the capillary tube. When the static pressure falls below the saturation pressure for the liquid temperature, spontaneous boiling occurs. A vapor-liquid two-phase mixture is discharged from the tube. In designing a capillary tube, it is necessary to calculate the flow rate for given boundary conditions on pressure and temperature at the inlet and exit. Since total pressure loss is dominated by frictional and acceleration losses during two-phase flow, it is first necessary to specify the boiling inception point. However, there will be a delay in boiling inception during decompressed flow. This study aimed to clarify the boiling inception point and two-phase flow characteristics of refrigerant in a capillary tube. Refrigerant flows in a coiled copper capillary tube were visualized by neutron radiography. The one-dimensional distribution of volumetric average void fraction was measured from radiographs through image processing. From the void fraction distribution, the boiling inception point was determined. Moreover, a simplified CT method was successfully applied to a radiograph for cross-sectional measurements. The experimental results show the flow pattern transition from intermittent flow to annular flow that occurred at a void fraction of about 0.45.     

Flow in a laminar boundary layer under intensive injection and radiant heat exchange

An asymptotic solution has been obtained for the system of boundary layer equations with intense injection of a foreign absorbing substance for optically thick and thin boundary layers taking account of the influence of a magnetic field. Analytical formulas are presented which permit computation of the temperature, concentration, and heat flux profiles.     

Experimental two-phase heat transfer coefficient and frictional pressure drop inside mini-channels during condensation with R1234yf and R134a

The present paper reports condensing two-phase flow pressure drop gradient and heat transfer coefficient (HTC) inside a mini-channel multiport tube with R1234yf and R134a. Several models available in the literature are used to compare predictions of these two fluids. Experimental data are analysed to get the influence of saturation temperature, mass flux, vapour quality and fluid properties. HTC values of R1234yf seem to be lower than R134a under similar conditions. Two-phase flow pressure drops are also lower in the case of the new refrigerant R1234yf.     

In-tube condensation of mixture of R134a and ester oil: empirical correlations

This paper presents a comparative study of the condensation heat transfer coefficients in a smooth tube when operating with pure refrigerant R134a and its mixture with lubricant Castrol “icematic sw”. The lubricant is synthetic polyol ester based oil commonly used in lubricating the compressors. Two concentrations of R134a-oil mixtures of 2% and 5% oil (by mass) were analysed for a range of saturation temperatures of refrigerant R134a between 35 °C and 45 °C. The mass flow rate of the refrigerant and the mixtures was carefully maintained at 1 g/s, with a vapour quality varying between 1.0 and 0. The effects of vapour quality, flow rate, saturation temperature and temperature difference between saturation and tube wall on the heat transfer coefficient are investigated by analysing the experimental data. The experimental results were then compared with predictions from earlier models [Int J Heat Mass Transfer (1979), 185; 6th Int Heat Transfer Congress 3 (1974) 309; Int J Refrig 18 (1995) 524; Trans ASME 120 (1998) 193]. Finally two new empirical models were developed to predict the two-phase condensation heat transfer coefficient for pure refrigerant R134a and a mixture of refrigerant R134a with Castrol “icematic sw”.     

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.     

钢铁工业中的自由边值问题

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture.The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region. overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin "intermediate region" at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

Free Boundary Problems in the Steel Industry

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture. The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig .iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin “intermediate region“ at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

Estimation of the thermal diffusivity profile in functionally gradient materials with the stepwise heating method

Temperature response in a functionally gradient material (FGM) which is subjected to stepwise heating is investigated, to estimate the profile of the thermal diffusivity from the temperature response at the rear surface of the FGM. Emphasis is placed on a distribution parameter which gives the profiles of the thermophysical properties when an exact analytical solution exists for the temperature response in the FGM. An explicit expression to determine the distribution parameter is obtained as a function of the thermophysical properties at the rear surface. This explicit expression can represent the dependence of the temperature response on the thermophysical properties within 5% in comparison to the exact solution. It is expected that this identification can provide useful insight into the estimation of thermophysical properties in FGMs. The usefulness of this relation is also examined by comparing given and estimated profiles for the thermal diffusivity. Fair agreement is demonstrated as far as the trend and the approximate magnitude are concerned.     

Forced convection of a temperature-sensitive ferrofluid in presence of magnetic field of electrical current-carrying wire: A two-phase approach

This research examines laminar forced convection of a temperature-sensitive magnetic nanofluid flowing within a horizontal tube through the two-phase mixture model. The ferrofluid flowing in the tube is exposed to the magnetic field generated by electrical current-carrying wire(s) along the tube, and the effect of such magnetic field is studied on heat and mass transfer phenomena. It is observed that due to the dependency of magnetization on temperature, the cold fluid flowing at the central regions of the tube is attracted more significantly towards the source of the magnetic field, which results in creation of secondary flow. Such mixing in the flow, subsequently, disturbs the thermal and hydrodynamic boundary layers, especially at the vicinity of the magnetic field source, leading to better heat transfer rate and also higher pressure drop. Furthermore, increasing the strength of the magnetic field leads to greater enhancement in heat transfer, while increasing the Reynolds number decreases the effectiveness of the magnetic field on the ferrofluid flow and heat transfer. Moreover, placing two wires above and under the tube can enhance the heat transfer even more significantly, such that the average convective heat transfer coefficient in this case is about 34.5% higher than that of the case without magnetic field.     

An efficient method for nonlinear analysis of layered shells

Finite element formulation based on explicit through-thickness integration scheme assumes importance when applied to multilayered shells, as it is numerically accurate and computationally efficient. Explicit integration becomes possible on assuming the variation of the inverse Jacobian through the thickness. The element stiffness matrices are discussed for (i) large rotation, and (ii) small rotation. Relative efficiencies of the explicit through-thickness integration schemes are compared with that of the conventional formulation involving numerical integration in three directions in each layer and summation over the layers. The small rotation formulation assuming linear variation of the Jacobian inverse across the thickness and based on further approximation regarding certain submatrices is seen to be computationally efficient. The geometric nonlinear behaviours of laminated composite cylindrical panels subjected to external pressure are discussed. The parameters considered are: number of layers, symmetric/antisymmetric, cross-ply/angleply, boundary conditions and central angle. The strength of shallow panels with longitudinal edges hinged and curved edges free is controlled by the limit point load, while for deep panels it is controlled by the bifurcation load. The boundary conditions have significant influence on load carrying capacities. A list of symbols is given at the end of the paper     

The effect of external convection on freezing in steady turbulent flow in a tube

An analysis is presented of the turbulent flow heat transfer and frozen deposit which occur in a tube that is cooled convectively on its external boundary sufficiently to create an internal frozen layer. The effects of Biot number, Prandtl number and inlet and outside temperatures on the initial freeze-free zone within the tube are shown. Additionally, the thickness profile of the freeze layer and the overall heat transfer rate which occur at steady state are determined and illustrated for a variety of representative cases.     

Heat transfer and pressure drop for boiling nitrogen flowing in a horizontal tube: 2. Pressure drop

The pressure drop of boiling two-phase nitrogen flow in a smooth horizontal tube has been studied experimentally. The results show in principle the well-known dependence of the local pressure drop from the vapour quality, the mass flow rate, and the heat flux.A comparison of the measured frictional pressure drop shows a sufficient agreement with predicted values using published correlations. The accelerational pressure gradient can also be predicted taking into account a suitable void fraction relationship.     

Crack arrest model for a piezoelectric plate — A generalised Dugdale model

The constant search for new materials has provided impetus to research in piezoelectric materials. An anti-plane problem for a cracked unbounded two-dimensional poled piezoelectric plate has been investigated. The crack rims open on account of shear mechanical forces applied at the remote boundary and in-plane electric displacement field prescribed at the infinite boundary. Thus the crack yields both mechanically and electrically. Consequently, a plastic zone and a saturation zone protrude ahead of each tip of the crack. These developed zones are in turn closed by applying yield point shear stress at the rims of plastic zone and normal closing saturation limit displacement on the rims of saturation zones. Two cases are investigated when (i) the developed saturation zone length exceeds that of the developed plastic zone, and (ii) saturation zone length is smaller than that of the plastic zone. Fourier integral transform method is used in each case to obtain the length of plastic zone and saturation zone. Closed form analytic expressions are obtained in each case. Crack opening displacement and potential drop across the rims of the crack are also obtained. The effect of mechanical loads on crack closure in the presence of electric field is investigated and vice-versa. Also energy release rate expressions are obtained for both the cases.     

Boundary layer structure at the exit of a cascade of parallel thin plates

The laminar flow near the exit from a cascade of parallel thin plates is investigated. The transition from the Poiseuille flow developed between two parallel plates to a uniform flow in the wake is carried out in two stages using an analytical approach for large Reynolds numbers. The first stage involves the study of the regular disturbances in the wake, where the equations of motion are reduced to the Prandtl equations. The numerical solution of these equations and their asymptotic treatment in the near wake are carried out. Comparison of the results shows that the asymptotic approach enables an improved solution near the exit, where singular disturbances arise. The second stage requires study of this singular region, by introducing boundary layers surrounding the trailing edges. This study treats the interactions induced upstream of the trailing edges and acts to ensure the asymptotic matching of the Poiseuille flow upstream with the asymptotic solution of the near wake downstream.     

Modelling the bleed port of a thermostatic expansion valve

This article presents a model to predict refrigerant flow rate through the bleed port of a thermostatic expansion valve using a separated flow model. Four types of inlet/outlet conditions: liquid/liquid; liquid/two-phase; two-phase/two-phase; and vapour/vapour are studied. Refrigerant flow rate predictions of the model are compared to measured data. The results of this comparison show that the model is within ±20% for 95% of the experimental data corresponding to either an inlet fluid in a sub-cooled or a two-phase state. When the inlet fluid is in a vapour state, the model is able to predict 96% of the experimental data within ±16%.     

Effect of wear of the atomic-absorption spectrometer graphite furnace on the analytical zone temperature

One mechanism of increase in the heating temperature of the analytical zone of the graphite tube furnace of the atomic-absorption spectrometer as a result of wear is discussed. The influence of the furnace profile on its heating temperature is shown, and the calculated heating temperature of the standard tube is compared to the temperature in the special case where the cross-section area of the analytical zone of the furnace is reduced by half. Experimental proofs of a given temperature excess, as well as of a relation between the change in the tube profile and the decrease in its mass, are given. The dependence of temperature on the furnace mass and the number of measurements has been investigated. The necessity of taking into account the increase in the heating temperature of the furnace in the wear process has been considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 1, pp. 149–155, January–February, 2007.     

The mechanism of increase of the thickness of the zone of thermal effect during pulse-periodic treatment of a target by an electron beam

Based on the results of numerical simulation of temperature fields, the reasons for the growth of the layer thickness of the zone of thermal effect in a target of 45 steel during pulse-periodic stimulation by a low-energy high-current electron beam in the mode of initial melting are analyzed. It is concluded that the growth of thickness of these layers is primarily caused by the spread of the beam energy density from pulse to pulse and by the presence of individual pulses with a higher-than-average value of energy density. It is shown that the variation of the thermal properties of steel, which occurs during irradiation due to the carbon saturation of the surface region of the target, results in the increase of the thickness of only those layers of the zone of thermal effect which are formed in the region of former melt. The dependence of the target temperature on the number of irradiation pulses is measured and calculated numerically. It is demonstrated that the increase of the target temperature has no noticeable effect on the growth of the thickness of the zone of thermal effect