Generalized correlation of refrigerant mass flow rate through adiabatic capillary tubes using artificial neural network

A capillary tube is a common expansion device widely used in small-scale refrigeration and air-conditioning systems. Generalized correlation method for refrigerant flow rate through adiabatic capillary tubes is developed by combining dimensional analysis and artificial neural network (ANN). Dimensional analysis is utilized to provide the generalized dimensionless parameters and reduce the number of input parameters, while a three-layer feedforward ANN is served as a universal approximator of the nonlinear multi-input and single-output function. For ANN training and test, measured data for R12, R134a, R22, R290, R407C, R410A, and R600a in the open literature are employed. The trained ANN with just one hidden neuron is good enough for the training data with average and standard deviations of 0.4 and 6.6%, respectively. By comparison, for two test data sets, the trained ANN gives two different results. It is well interpreted by evaluating the outlier with a homogeneous equilibrium model.     

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%.     

A generalized correlation for the characteristics of adiabatic capillary tubes

The capillary tube is often served as an expansion device in small refrigeration and air-conditioning systems. In this paper, a generalized correlation for predicting the refrigerant mass flow rate through the adiabatic capillary tube is developed with approximate analytic solutions based on the extensive data for R12, R22, R134a, R290, R600a, R410A, R407C, and R404A, in which a homogeneous equilibrium model for two-phase flow is employed, and there is a subcooled liquid or saturated two-phase mixture at the inlet of the capillary tubes. The collected database about capillary tubes covers the inner diameter from 0.5 mm to 2 mm, the tube length from 0.5 m to 5 m, the condensing temperature from 20 °C to 60 °C, the subcooling from 0 °C to 20 °C, and the quality from 0 to 0.3 at the inlet. Assessments for the correlation are made with some experimental data for R12, R22, R134a, R290, R407C, R410A, and R404A obtained from the open literature and some existing correlations based on the experimental database also. The present correlation yields an average deviation of −0.83% and a standard deviation of 9.02% from the database.     

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.     

Experimentation and modeling of refrigerant flow through coiled capillary tubes

Air-conditioners use spirally coiled capillary tubes as an expansion device to enhance compactness of the unit. However, most empirical correlations for predicting refrigerant flow rate through capillary tubes were developed for straight capillary tubes without consideration of coiled effects. The objectives of this study are to investigate the flow characteristics of the coiled capillary tubes and to develop a generalized correlation for the mass flow rate through the coiled capillary tubes. The mass flow rate of R22 through the coiled capillary tubes and straight capillary tubes was measured for various operating conditions and tube geometries. The mass flow rates of the coiled capillary tubes decreased by 5–16% more than those of the straight capillary tubes at the same operating conditions. A generalized correlation for predicting refrigerant mass flow rate through coiled capillary tubes was developed by introducing the parameter of capillary equivalent length. The present correlation showed good predictions with the present database for R22, R407C and R410A in the straight and coiled capillary tubes, yielding average and standard deviations of 0.24% and 4.4%, respectively.     

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.     

Experimental investigation of the performance of R22, R407C and R410A in several capillary tubes for air-conditioners

The objective of this study is to present test results and to develop a dimensionless correlation on the basis of the experimental data of adiabatic capillary tubes for R22 and its alternatives, R407C (R32/125/134a, 23/25/52 wt.%) and R410A (R32/125, 50/50 wt.%). Several capillary tubes with different length and inner diameter were selected as test sections. Mass flow rate through the capillary tube was measured for several condensing temperatures and various degrees of subcooling at the inlet of each capillary tube. Experimental conditions for the condensing temperatures were selected as 40, 45 and 50°C, and the degrees of subcooling were adjusted to 1.5, 5 and 10°C. Mass flow rates of R407C and R410A were compared with those of R22 for the same test conditions. The results for straight capillary tubes were also compared with those of coiled capillary tubes. A new correlation based on Buckingham π theorem to predict the mass flow rate through the capillary tubes was presented based on extensive experimental data for R22, R407C and R410A. Dimensionless parameters were chosen considering the effects of tube geometry, capillary tube inlet conditions, and refrigerant properties. Dimensionless correlation predicted experimental data within relative deviations ranging from −12% to +12% for every test condition for R22, R407C and R410A. The predictions by the developed correlation were in good agreement with the results in the open literature.     

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.