Modified neural network correlation of refrigerant mass flow rates through adiabatic capillary and short tubes: Extension to CO2 transcritical flow

This paper presents a modified dimensionless neural network correlation of refrigerant mass flow rates through adiabatic capillary tubes and short tube orifices. In particular, CO₂ transcritical flow is taken into account. The definition of neural network input and output dimensionless parameters is grounded on the homogeneous equilibrium model and extended to supercritical inlet conditions. 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 are collected for neural network training and testing. The comparison between the trained neural network and experimental data reports 0.65% average and 8.2% standard deviations; 85% data fall into ±10% error band. Particularly for CO₂, the average and standard deviations are −2.5% and 6.0%, respectively. 90% data fall into ±10% error band.     

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.     

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.     

Mass flow rate of R-410A through short tubes working near the critical point

Experimental data were taken to examine R-410A mass flow rate characteristics through short tube restrictors at upstream pressures approaching the critical point. Four short tube restrictors were tested by varying upstream pressure from 2619 to 4551 kPa (corresponding to saturation temperature from 43.9 to 71.7 °C), upstream subcooling from 2.8 to 11.1 °C and downstream pressure from 772 to 1274 kPa. The experimental data were represented as a function of major operating parameters and short tube diameter. As compared to mass flow trends at typical upstream pressures, flow dependency on upstream subcooling was more significant at high upstream pressures due to a higher density change. Based on the database obtained from this study and literature, an empirical correlation was developed from a power law form of dimensionless parameters generated by the Buckingham Pi theorem. The post-predictions of the new correlation yielded average and mean deviations of 0.11 and 2.4%, respectively.     

Model-based neural network correlation for refrigerant mass flow rates through adiabatic capillary tubes

A capillary tube is a common expansion device widely used in small-scale refrigeration and air-conditioning systems. A generalized correlation of refrigerant mass flow rate through adiabatic capillary tubes covering both subcooled and two-phase inlet conditions is expected for multiple purposes. Based on the homogeneous equilibrium flow model, a new group of dimensionless parameters has been proposed. To express the nonlinear relationship between the mass flow rate and the associated parameters, the multi-layer perceptron neural network is employed as a universal function approximator. Simulated data from a validated homogeneous equilibrium model are used for the neural network training and testing. A 5-6-1 network trained with the simulated data of R600a and R407C shows good generality in predicting the simulated data of R12, R22, R134a, R290, R410A, and R404A. Also, the deviations between the trained neural network and the experimental data from the open literature fall into ±10%.     

Flow pattern, mass flow rate, pressure distribution, and temperature distribution of two-phase flow of HFC-134a inside short-tube orifices

New experimental data on the influence of short-tube orifice configuration, including diameter, length, length-to-diameter ratio (L/D), and orientation on the flow pattern, mass flow rate, and pressure distribution of HFC-134a inside the short-tube orifice are presented. Short-tube orifice diameters ranging between 0.605 and 1.2 mm with L/D ranging between 1.87 and 33 are used in the experiments. Three different forms of the metastable liquid flow, which are metastable liquid core flow, conical metastable liquid core flow, and full metastable liquid flow are visually observed. The short-tube orifice diameter has a significant effect on the increase in the flow rate. Conversely, the change in the orientation of the test section has no significant effect on the flow rate. The choke flow phenomenon disappears inside the short-tube orifice when L/D is less than 2.91. Based on the present data, a correlation for predicting the mass flow rate through short-tube orifices is proposed.     

Influences of miscible and immiscible oils on flow characteristics through capillary tube—part I: experimental study

A capillary tube is widely used as an expansion device for small refrigeration cycles. In a practical refrigeration cycle, some amount of refrigeration oil is discharged from a compressor and refrigerant/oil mixture flows through the capillary tube. This study investigated experimentally the influence of mixing of the refrigeration oil with the refrigerant on the flow through the capillary tube. The experiments are carried out with not only a miscible combination of refrigerant and oil but also an immiscible combination. In both cases, the mass flow rate through the capillary tube and temperature and pressure distributions along the tube are measured under several conditions of subcooled degree and oil concentration. In the case of miscible combination, the mass flow rate of refrigerant decreases with increasing the oil concentration because the viscosity of liquid phase increases by the mixing of viscous oil. Even in the case of the immiscible combination, the oil droplet is so small that it mixes homogeneously in the liquid phase in the capillary tube and the refrigerant mass flow rate decreases by the mixing of immiscible oil. There is no significant influence of the oil concentration on the underpressure, which means pressure difference between saturation pressure and flash inception pressure, in both miscible and immiscible combinations.     

Underpressure of vaporization of refrigerant R-134a through a diabatic capillary tube

Experimental test results with R-134a have demonstrated the phenomenon of metastable flow through a diabatic capillary tube, and showed that the metastable flow of the refrigerant exists when the heat transfer is weak between the capillary tube and the suction line flows. Using homogeneous nucleation theory, a correlation predicting the underpressure of vaporization (a characteristic quantity for the metastable flow) for a diabatic capillary tube has been developed based on the experimental results.     

Friction factor correlation and pressure loss of single-phase flow inside herringbone microfin tubes

Pressure drop of single-phase turbulent flow inside herringbone microfin tubes of different fin dimensions has been measured experimentally to develop a general correlation of single-phase friction factor for the herringbone tubes. Water has been used as a working fluid and the mass flow rate has been varied from 0.03 to 0.2 kg/s, where the Reynolds number range is 10⁴ to 6.5 × 10⁴. Comparison of experimental data of the herringbone microfin tubes with those of helical microfin and smooth tubes shows that pressure drop of the herringbone tube is significantly higher than the helical and smooth tubes depending on the fin geometric parameters and mass velocity of the working fluid. Through semi-analytical approach and using the present experimental data, a new correlation of single-phase friction factor for the herringbone microfin tubes has been proposed incorporating the effects of fin geometric parameters. The proposed correlation can predict the experimental data within ±10%.     

Analysis of refrigerant flow and deformation for a flexible short-tube using a finite element model

A finite element model was used to simulate single-phase flow of R-22 through flexible short-tubes. The numerical model included the fluid-structure interaction between the refrigerant and the deformation of the short-tube as upstream pressure was varied. The finite element model was developed using a commercially available finite element package. Short-tubes with moduli of elasticity ranging from 5513 to 9889 kPa were studied. Four upstream and downstream pressures were applied and the upstream subcooling was held at a constant value of 16.7 °C. Mass flow rates from the numerical model were compared to available published experimental results. The study showed that upon deformation the short-tube resembled the shape of a converging-diverging nozzle. Both tube inlet and outlet had a chamfered-like shape after deformation which reduced the pressure drop at the tube inlet. The smaller the modulus of the tube, the larger the chamfered-like angle at the inlet and the higher the pressure drop along the tube due to the higher tube contraction. The results illustrated that as the upstream pressure was increased by 45%, there was almost a 60% decrease in the flow area. The more flexible (5513 kPa) short-tube restricted the mass flow rate more than the most rigid (9889 kPa) short-tube used in this study. The mass flow rates estimated with the finite element model were as much as 14% higher than those from experimental results reported in the literature.     

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.     

A visual study of R-404A/oil flow through adiabatic capillary tubes

The present study explores the potential of using visualization techniques to investigate refrigerant/oil flow through adiabatic capillary tubes. A literature review shows that these techniques have been used before for capillary tube investigations, but none of these studies focused on the refrigerant/oil phenomena. Therefore, the main objective is to investigate the flow of a refrigerant/oil mixture through a glass capillary tube, with special emphasis on the behavior of the vaporization point. The test fluids are R-404A (a near azeotropic blend) and a polyolester-type oil. Experimental data cover oil concentrations ranging from 5.6 to 6.9% (by mass), degrees of subcooling ranging from 6.2 to 21.5 °C (11.2 F to 38.7 F), and a condensing pressure of 1825 kPa (250 psig). The results show trends of mass flow rate, and give some useful insights about the location of the vaporization point for various oil concentrations and operating conditions.     

Critical two-phase stratified flow during horizontal condensation

A theoretical investigation is made for two-phase, stratified, condensing flow between two parallel horizontal plates. From this investigation a correlation predicting critical flows during condensation is developed. According to this correlation it is shown that critical flow conditions are strongly dependent on the condensing mass flux, quality, void fraction and fluid properties. It is also shown that the inviscid Kelvin-Helmholtz theory is in error in predicting critical flow conditions because it ignores the effect of viscosity.     

Experimental study of turbulent single-phase flow and heat transfer inside a micro-finned tube

Single-phase heat transfer and pressure drop characteristics of a commercially available internally micro-finned tube with a nominal outside diameter of 7.94 mm were studied. Experiments were conducted in a double pipe heat exchanger with water as the cooling as well as the heating fluid for six sets of runs. The pressure drop data were collected under isothermal conditions. Data were taken for turbulent flow with 3300 ≤ Re ≤ 22,500 and 2.9 ≤ Pr ≤ 4.7. The heat transfer data were correlated by a Dittus–Boelter type correlation, while the pressure drop data were correlated by a Blasius type correlation. The correlation predicted values for both the Nusselt number and the friction factors were compared with other studies. It was found that the Nusselt numbers obtained from the present correlation fall in the middle region between the Copetti et al. and the Gnielinski smooth tube correlation predicted Nusselt number values. For pressure drop results, the present correlation predicted friction factors values were nearly double that of the Blasius smooth tube correlation predicted friction factors. It was also found that the rough tube Gnielinski and Haaland correlations can be used as a good approximation to predict the finned tube Nusselt number and ffriction factor, respectively, in the tested Reynolds number range.     

Research on the air pressure drop in plate finned tube heat exchangers

In order to establish a reliable procedure for estimation of air pressure drop, experiments on plate finned tube heat exchangers have been conducted, as well as the research on the open literature. The procedure of Kays and London was tested against the experimental data and significant level of uncertainty was found. Using own experimental data, as well as previously published data of Kays and London, new correlation for estimation of air pressure drop has been established. Statistical parameters of new correlation enable the conclusion that it can be used for wide range of Reynolds numbers.     

Measurement and prediction of evaporator shell-side pressure drop

The pressure drop across a heat exchanger is an important parameter, along with the heat transfer capacity. In fact, the operating cost throughout the life of the exchanger depends on the pressure losses. Therefore, it is important to be able to predict pressure drop accurately as it is to predict heat transfer.A new data set of shell-side pressure drop measurements taken during isothermal flow of brines in shell and tube evaporators was collected in the Alfa Laval laboratory. It covers several different configurations of industrial shell and tube evaporators and a wide range of operating conditions, with cross flow Reynolds number ranging from 170 to 33,000.The database is compared against two predictive procedures available in the literature for computing shell-side pressure drop, showing that no method is accurate enough for design purpose.As a further step, a new suggested procedure is presented, which extends the Wills and Johnston [Wills MJN, Johnston D. A new and accurate hand calculation method for shellside pressure drop and flow distribution. 22nd National Heat Transfer Conference, HTD N. 36. New York: ASME; 1984, p. 67–79] method to the low Reynolds number range and improve its capability to predict experimental data.     

Two-phase flow regimes in round, square and rectangular tubes during condensation of refrigerant R134a

An experimental investigation of two-phase flow mechanisms during condensation of refrigerant R134a in six small diameter round (4.91 mm), square (D_h=4 mm, α=1), and rectangular (4×6 and 6×4 mm: D_h=4.8 mm, α=0.67 and 1.5; 2×4 and 4×2 mm: D_h=2.67 mm, α =0.5 and 2) was conducted. Unique experimental techniques and test sections were developed to enable the documentation of the flow mechanisms during phase change. For each tube under consideration, flow mechanisms were recorded over the entire range of qualities for five different refrigerant mass fluxes between 150 and 750 kg m⁻² s⁻¹. The flow mechanisms were categorized into four different flow regimes: intermittent flow, wavy flow, annular flow, and dispersed flow. In addition, the large amount of data enabled the delineation of several different flow patterns within each flow regime, which provides a clearer understanding of the different modes of two-phase flow. Transition lines between the respective flow patterns and regimes on these maps were established based on the experimental data. It was found that for similar hydraulic diameters, flow regime transitions are not very strongly dependent on tube shape or aspect ratio. These maps and the transition lines can be used to predict the particular flow pattern or regime that will be established for a given mass flux, quality and tube geometry.     

Experimental study of melting ice cylinders in a warm air cross-flow

An experimental study is reported which investigates the melting of ice cylinders transverse to a warm humid flow, under controlled conditions in an air-conditioned wind tunnel. This work was initiated prior to a more general study of warm air defrosting of a complete heat pump evaporator. Tests were conducted with air at various temperatures, relative humidities and velocities. Similarly, the temperature of the core tube, on which the ice cylinders were mounted, was varied by alteration of the water-glycol mixture flowing through it. Two diameters of ice cylinder, 20 and 27 mm, were used. For core temperatures below the melting point of ice, the melting rate was shown to be a strong function of air humidity and temperature. With the core temperature above 0°C, the melting process was dominated by this factor so that air conditions were relatively unimportant.     

An experimental study on heat transfer and pressure drop characteristics of carbon dioxide during gas cooling process in a horizontal tube

The heat transfer coefficient and pressure drop during gas cooling process of CO₂ (R744) in a horizontal tube were investigated experimentally. The experiments are conducted without oil in the refrigerant loop. The main components of the refrigerant loop are a receiver, a variable-speed pump, a mass flow meter, a pre-heater and a gas cooler (test section). The water loop consists of a variable speed pump, an isothermal tank, and a flow meter. The refrigerant, circulated by the variable-speed pump, condenses in the inner tube while water flows in the annulus. The gas cooler of tube diameter is 6000 mm in length, and it is divided into 12 subsections.The pressure drop of CO₂ in the gas cooler shows a relatively good agreement with those predicted by Blasius's correlation. The local heat transfer coefficient of CO₂ agrees well with the correlation by Bringer–Smith. However, at the region near Pseudo-critical temperature, the experiments indicate higher values than the Bringer–Smith correlation. Based on the experimental data presented in this paper, a new correlation to predict the heat transfer coefficient of supercritical CO₂ during in-tube cooling has been developed. The majority of the experimental values are within 18% of the values predicted by the new correlation.     

Heat transfer, pressure drop, and flow pattern recognition during condensation inside smooth, helical micro-fin, and herringbone tubes

This paper presents a study of flow regimes, pressure drops, and heat transfer coefficients during refrigerant condensation inside a smooth, an 18° helical micro-fin, and a herringbone tubes. Experimental work was conducted for condensing refrigerants R-22, R-407C, and R-134a at an average saturation temperature of 40 °C with mass fluxes ranging from 400 to 800 kg m⁻² s⁻¹, and with vapour qualities ranging from 0.85 to 0.95 at condenser inlet and from 0.05 to 0.15 at condenser outlet. These test conditions represent annular and intermittent (slug and plug) flow conditions. Results showed that transition from annular flow to intermittent flow, on average for the three refrigerants, occurred at a vapour quality of 0.49 for the smooth tube, 0.29 for the helical micro-fin tube, and 0.26 for the herringbone tube. These transition vapour qualities were also reflected in the pressure gradients, with the herringbone tube having the highest pressure gradient. The pressure gradients encountered in the herringbone tube were about 79% higher than that of the smooth tube and about 27% higher than that of the helical micro-fin tube. A widely used pressure drop correlation for condensation in helical micro-fin tubes was modified for the case of the herringbone tube. The modified correlation predicted the data within a 1% error with an absolute deviation of 7%. Heat transfer enhancement factors for the herringbone tube against the smooth tube were on average 70% higher while against the helical micro-fin tube it was 40% higher. A correlation for predicting heat transfer coefficients inside a helical micro-fin tube was modified for the herringbone tube. On average the correlation predicted the data to within 4% with an average standard deviation of 8%.