A generalized dimensionless local power-law correlation for refrigerant flow through adiabatic capillary tubes and short tube orifices

This paper presents a new method to obtain generalized dimensionless correlation of refrigerant mass flow rates through adiabatic capillary tubes and short tube orifices. The dimensionless Pi groups were derived from the homogeneous equilibrium model, which is available for different refrigerants entering adiabatic capillary tubes or short tube orifices as the subcooled liquid, two-phase mixture, or supercritical fluid. To mitigate the potential over-fitting risk in neural network, a new “local” power-law correlation reformed from the homogeneous equilibrium model was proposed and compared with the conventional “global” power-law correlation and recently developed neural network model. About 2000 sets of experimental mass flow rate data of R12, R22, R134a, R404A, R407C, R410A, R600a and CO₂ (R744) in the open literature covering capillary and short tube geometries, subcritical and supercritical inlet conditions were collected for the model development. The comparison between the recommended six-coefficient correlation and experimental data reports 0.80% average and 8.98% standard deviations, which is comparable with the previously developed neural network and much better than the “global” power-law correlation.     

A comparison of critical flow models for estimating two-phase flow of HCFC22 and HFC134a through short tube orifices

An experimental study to investigate the critical flow of refrigerants through short tube orifices has been performed by measuring the mass flowrates and pressure profiles along the short tube orifice. Eight critical flow models have been examined and their results compared with the experimental data for HCFC22 and HFC134a. These models include four homogeneous equilibrium models, two homogeneous frozen models, and two non-homogeneous equilibrium models. The data indicate that the flow was choked when downstream pressures were lower than the saturation pressure corresponding to the upstream temperature. The observed flows through short tube orifices included a lack of equilibrium due to short time of expansion and homogeneous mist flow at the exit plane. These flow trends would be more consistent with the basic assumptions of the homogeneous frozen models. Based on the comparison of the existing critical flow models and experimental data, the homogeneous frozen models showed the best agreement with the measured data except for exit qualities below 0.06.     

Two-fluid model of refrigerant two-phase flow through short tube orifice

Pronounced hydrodynamic and thermodynamic non-equilibrium exist in the flow of refrigerant through a short tube orifice under typical operating conditions. A non-equilibrium two-fluid model (TFM) for refrigerant two-phase critical flow inside the short tube orifice is developed. Both inter-phase velocity slip and inter-phase temperature difference are taken into account in the model. The mass flow rate, the two-phase velocity and temperature distributions in a short tube orifice are simulated. Comparisons among the experimental data of refrigerants R134a, R12, R22, R410A and R407C flowing through short tubes, the predictions by the TFM and by the homogeneous equilibrium model (HEM) show that the TFM gives acceptable predictions with the deviations of ±20%, while the HEM underestimates the flow rate by 20% or so.     

Experimental investigation of two-phase flow characteristics of HFC-134a through short-tube orifices

The two-phase flow characteristics of HFC-134a, including flow pattern, mass flow rate, pressure distribution and temperature distribution through short-tube orifices are experimentally investigated. Short tube diameters ranging between 0.605 and 1.2 mm with length-to-diameter ratios ranging between 8.3 and 33 are used in the experiments. The test runs are performed at upstream pressure ranging between 900 and 1300 kPa, downstream pressure ranging between 300 and 400 kPa, and degree of subcooling ranging between 1 and 12 °C. Two groups of short-tube orifices are used in the experiment. The first is used to visualise the flow pattern. The second is used to measure temperature and pressure distributions along the tube. The results from the present experiment show that metastable flow and choked flow phenomena exist inside the short-tube orifices over the whole range of experimental conditions. The metastable liquid flow region increases with increasing degree of subcooling and upstream pressure. The mass flow rate is directly proportional to upstream pressure and degree of subcooling. The results of pressure distribution inside the short-tube orifices indicate that accelerational pressure drop at the inlet and outlet has a significant effect on the total pressure drop across the short-tube orifice.     

A generalized correlation for refrigerant mass flow rate through adiabatic capillary tubes

A capillary tube is a common expansion device used in small sized refrigeration and air-conditioning systems. A generalized correlation for refrigerant flow rate in adiabatic capillary tubes is developed by implementing dimensionless parameters based on extensive experimental data for R-22, R-290, and R-407C measured in this study. Dimensionless parameters are derived from the Buckingham Pi theorem, considering the effects of tube inlet conditions, capillary tube geometry, and refrigerant properties on mass flow rate. The generalized correlation yields good agreement with the present data for R-22, R-290, and R-407C with average and standard deviations of 0.9 and 5.0%, respectively. Approximately 97% of the present data are correlated within a relative deviation of ±10%. Further assessments of the correlation are made by comparing the predictions with measured data for R-12, R-134a, R-152a, R-410A, and R-600a in the open literature. The correlation predicts the data for those five refrigerants with average and standard deviations of −0.73 and 6.16%, respectively.     

Numerical simulation and experimental analysis of refrigerants flow through adiabatic helical capillary tube

In the present study, two-phase refrigerant flow is simulated using drift flux model for straight and helical capillary tubes. The conservation equations of mass, energy and momentum are solved using the 4th order Runge–Kutta method. This model is validated by previously published experimental and numerical results and also by experimental results presented in this work. The effect of various parameters such as inlet pressure, inlet temperature, sub-cooling degree, and geometric dimensions are studied. The results of the present study show that for the same length and under similar conditions, mass flux through helical capillary tube with coil diameter of 40 mm are about 11% less than that through the straight tube, where the helical tube length is about 14% shorter than the straight one for the same refrigerant mass flux.     

Transient flow of rarefied gas through a short tube

A transient rarefied gas flow through a short tube is studied on the basis of the direct simulation Monte Carlo method. The mass flow rates through both inlet and outlet cross sections are calculated as a function of the time in the free-molecular, transitional and hydrodynamic regimes with respect to the gas rarefaction. Two values of the pressure ratio, i.e. 0.1 and 0.5, and two values of the aspect ratio, i.e. 1 and 5, are considered. A characteristic time equal to that needed to cross the tube radius with the most probable molecular speed is defined. A typical interval of time to establish the steady flow rates was calculated. It was found that this time is about ten and forty characteristic times for the shorter and longer tubes, respectively. The flow field for the longer tube is analyzed in details.     

Gravitational flow of superfluid helium through small orifices

We present data on the flow of superfluid helium through channels of diameters 2.5 and 5.0 µm. Three modes of flow are observed: (1) flow that can be identified with the thermal nucleation of vorticity, (2) flow described by z (t – t ₀), where z is the gravitational head andt the time, and (3) flow described by (z)^1/2 (t – t ₀). Associated with the third mode, flows appear with a critical velocity close to that of the Feynman prediction for small channels.Research supported in part by a grant from the National Science Foundation and in part by the U.S. Atomic Energy Commission.     

A generalized equation for the surface tension of refrigerants

This work presents a literature survey of the available data of the experimental surface tension data for refrigerants. The experimental data were collected for the following pure fluids: R11, R12, R13, R13B1, R14, R21, R22, R23, R32, R113, R114, R115, R123, R123a, R124, R125, R134, R134a, R141b, R143a, R152a, R218, R225ca, R225cb, R227ea, R236ea, R236fa, R245ca, R245fa, R365mfc, R846, and R1234yf. Experimental data were regressed with the most reliable semi-empirical correlating methods based on the corresponding state theory existing in the literature.To minimize the deviation between the predicted data and the experimental data and to find the optimal equation for data representation, a design of experiment procedure coupled with the Yates algorithm and the steepest ascent method was adopted. Finally, the influence of the dipole moment on the refrigerant surface tension prediction was discussed and a new equation to represent the surface tension of refrigerants was presented.     

Experimental investigation of contraction in single- and two-phase flow through sharp-edged short orifice

The flow contraction through sharp-edged short orifices respectively the narrowest flow cross-section or the vena contracta has been measured for water, air and air/water mixture. The results demonstrate that the contraction in the case of subcritical single-phase flow is restricted to values between 0.62 and one, while in the two-phase flow it is limited to very narrow ranges of air mass flow qualities where the flow regime is specified as bubbly or spray.     

Viscous fluid flow through a pipe with orifices

An approximate solution is obtained to the problem of fluid flow through a pipe with orifices, in close agreement with the solution obtained numerically.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 4, pp. 766–768, April, 1973.     

节流短管流量特性试验研究

通过试验研究R22流过节流短管的流动特性,分析影响节流短管中制冷剂流量的几个重要因素;上游压力、下游压力、上游过冷度和短管直径。试验结果表明,当节流短管的下游压力小于上游温度所对应的饱和压力时,制冷剂出现壅塞现象,此时制冷剂流量不再受下游压力变化的影响;上游压力、上游过冷度、短管直径对制冷剂流量的影响较大。     

Thermodynamic properties for the alternative refrigerants

Models commonly used to calculate the thermodynamic properties of refrigerants are summarized. For pure refrigerants, the virial, cubic, Martin-Hou, Benedict-Webb-Rubin, and Helmholtz energy equations of state and the extended corresponding states model are discussed. High-accuracy formulations for 16 refrigerants are recommended. These models may be extended to mixtures through the use of mixing rules applied either to the parameters of the equation of state or to some property of the mixture components. Mixtures of a specific composition may also be modeled as a pseudo-pure fluid. Five mixture models, employing four distinct approaches, have been compared by a group working under the auspices of the International Energy Agency. These comparisons show all five models to be very capable in representing mixture properties. No single model was best in all aspects, but based on its combination of excellent accuracy and great generality, we recommend the mixture Helmholtz energy model as the best available.Experimental data are essential to both fit the adjustable parameters in property models and to assess their accuracy. We present a survey of the data available for mixtures of the HFC refrigerants R32, R125, R143a, R134a, and R152a and for mixtures of the natural refrigerants propane, butane, isobutane, and carbon dioxide. More than 60 data references are identified. Further data needs include caloric data for additional mixtures, comprehensive pressure-density-temperature data for additional mixture compositions, and improved accuracy for vapor-liquid equilibria data.     

An NTU- model for alternative refrigerants

This paper presents a steady state simulation model to predict the performance of alternative refrigerants in vapour compression refrigeration/heat pump systems. The model is based on the NTU- method in analysing the heat exchangers following an elemental approach. The model extends its applicability to new refrigerants including hydrocarbons and uses a large database of REFPROP package for refrigerant properties. The main inputs to the model include the physical details of the heat exchangers, compressor efficiency, mass flow rates of heat transfer fluids and their inlet temperatures to the evaporator and the condenser, the pressure drops across the heat exchangers and the capacity of either the evaporator or condenser (in kW). The model results are validated with a wide range of experimental data of HCFC22 and propane (HC290) on a heat pump test facility for a number of parameters, e.g. coefficient of performance, condenser capacity, mass flow rate of the refrigerant and compressor discharge temperature. Although the model is currently tested for pure refrigerants using compact brazed plate (counter flow type) heat exchangers, it can also be applied to mixture of refrigerants as well as to other types of heat exchangers.

Résumé

Dans cet article, on présente un modèle de simulation de régime permanent pour prédire la performance des frigorigènes de remplacement dans les systèmes frigorifiques ou les pompes à chaleur à compression de vapeur. Fondé sur la méthode NTU- utilisée pour analyser les échangeurs de chaleur, ce modèle emploie une approche élémentaire. Ce modèle étend la méthode aux nouveaux frigorigènes, y compris deees hydrocarbures, et utilise une base de données étendue, celle de REFPROP, pour les propriétés des frigorigènes. Les principaux paramètres du modèle comprennent des détails physiques sur les échangeurs de chaleur, le rendement des compresseurs, et les débits massiques des fluides de transfert de chaleur et leurs températures à l'entrée de l'évaporateur ou du condenseur, la chute de pression à travers les échangeurs de chaleur et la puissance soit de l'évaporateur, soit du condenseur (exprimés en kW). Les résultats obtensus en utilisant ce modèle sont validés pour une large gamme de données expérimentales obtenus avec le HCFC22 et avec le propane (le HC290) sur un banc d'essai de pompe à chaleur et pour un certain nombre de paramètres, par exemple le coefficient de performance, la puissance du compresseur, le débit massique du frigorigène et la température du frigorigène à la sortie du compresseur. En ce moment, le comportement des frigorigènes purs utilisés dans des échangeurs de chaleur compacts à plaques brasées (de type contre-courant) est en train d'être étudié; le modèle peut également être appliqué aux mélanges de frigorigènes et à d'autres types d'échangeurs de chaleur.     

A numerical study on heat transfer of the nanofluid flow inside helical tube through the two-phase method

In this study, a new numerical investigation was carried out to study the heat transfer characteristics of nanofluid flow inside a copper helical tube under constant heat flux. A nanofluid with different particle weight concentrations of 0.5%, 1.0%, and 2.0% was used. The effects of different parameters such as Reynolds number, nanofluid particle concentration, and constant heat fluxes (1500 and 3800?W/m²) on heat transfer coefficient were studied. For validation, Nusselt number and convection heat transfer coefficient obtained from the numerical model was compared with the experimental results. Also, to verify the accuracy of the method, grid independency was studied for each heat flux. The observations showed that the heat transfer coefficient increased by using nanofluid instead of base fluid. In addition, the convection heat transfer coefficient performance improved by increasing the nanoparticles’ concentration. The results from the numerical simulation compared with the experimental data showed that this new numerical method has high accuracy and could correctly predict the heat transfer behavior of nanofluids with different weight particle concentrations under constant heat flux.     

Oscillating two-phase flow in an elastic tube

Summary Analytical expressions of dust and fluid velocities have been obtained for small amplitude waves having large wave length. Equations giving the wave-velocity and its damping factor have been derived. Corresponding graphs for various values of dust parameters and elasticity of the wall of the thin walled tube have been drawn. It is found that both the wave-velocity and its damping factor decrease with the increase in mass-concentration of dust and also they increase with the increase in Poisson's ratio of the wall of the tube.

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Schwingende Zweiphasenströmung in einem elastischen Rohr

Zusammenfassung Analytische Ausdrücke der Staub- und Flüssigkeitsgesch windigkeiten werden für kleine Amplituden von Wellen mit großer Wellenlänge erhalten. Gleichungen für die Geschwindigkeit der Welle und ihr Dämpfungsverhalten werden hergeleitet und zugehörige Diagramme für verschiedene Werte des Staubparameters und der Wandelastizität des dünnwandigen Rohres erhalten. Es wird gefunden, daß sowohl die Wellengeschwindigkeit als auch der Dämpfungsfaktor mit zumehmender Massenkonzentration des Staubs abnehmen und daß sie mit der Poissonzahl der Rohrwand zunehmen.

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With 3 Figures

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On leave from Bolpur College, Bolpur, West Bengal, India.     

Saturated liquid viscosity correlations for alternative refrigerants

This article presents dimensionless equations for the temperature dependence of the saturated liquid viscosity of R32, R123 R124, R125, R134a. R141b. and R152a valid over a temperature range of engineering interest. The correlation has the form _n ^D =A +BT, where _D is the dimensionless fluidity (l _D) andT _D is a dimensionless temperature.n. A. andB are evaluated for each of the above refrigerants based on a least-squares fit to experimental data. This equation is found to provide an improved fit over those existing in the literature up toT _D=0.8.     

A new correlation for the viscosity of gaseous fluorocarbon refrigerants

A new generalized correlation is presented for the low-pressure gaseous viscosity of fluorocarbon refrigerants. The following empirical equation is obtained based on the most reliable experimental data for 16 fluorocarbons: $$\eta \xi = \left( {0.5124T_r - 0.0517} \right)^{0.82} Z_c ^{ - 0.81}$$ where η is the viscosity in μPa·s and ξ is the viscosity parameter defined using the critical temperature T _c in K, the critical pressure P _c in MPa, and the molar mass M in g·mol^?1 as follows: $$\xi = T_c ^{1/6} M^{ - 1/2} P_c ^{ - 2/3}$$ The applicable ranges are 0.6<T _r<1.8 and 0.253<Z _c<0.282. The availability of the correlating equation for both pure fluorocarbons and their mixtures has been investigated based on the experimental data of these authors and those in the literature. It is found that the present correlation is useful for the prediction of the viscosity of pure fluorocarbons and their binary mixtures at atmospheric pressure with mean deviations less than 1.6%.     

毛细管内R410A两相流摩擦因子关联式研究

准确预测毛细管内两相流制冷剂的压降是提高毛细管分流精度的基础,而高精度的毛细管内制冷剂两相流摩擦因子关联式又是准确预测毛细管压降的关键。本文拟合得到毛细管内R410A两相流摩擦因子关联式,并给出基于近似积分的毛细管压降计算模型。试验验证表明:基于Blasius公式拟合的毛细管内R410A两相流摩擦因子关联式的平均预测误差为±5.3%,95%的数据点的预测误差在±20%以内,而基于本文提出的毛细管内R410A两相流摩擦因子关联式的压降计算结果与试验数据的误差在±12%以内,平均误差在±5%以内,相比Blasius公式具有更高的计算精度。