Short Tube Orifices Research Articles

Experimental investigation of stepped short tube orifice as expansion device in domestic air conditioning/heat pump system

A stepped short tube orifice (SSTO) consisting of two serial-connected short tube orifices with different diameters was recently proposed as an inexpensive expansion device in air conditioning/heat pump system. In this study, a split air conditioner/heat pump employing stepped short tube orifices was investigated experimentally to further evaluate the performance of the SSTO air conditioner/heat pump system. At first, the mass flow rate of refrigerant (R-22) through stepped short tube orifices and an original expansion device were studied in both cooling and heating flow directions to verify the throttling capacity difference of these two type of expansion devices. Then, the influence of geometric sizes of SSTOs, refrigerant charge amount and environment temperature on the performance of the SSTO air conditioner/heat pump were examined. Besides, the performance of the SSTO systems also compared with that of the original system with capillary tube under nominal and varying conditions. The results show that 18# SSTO system performed the best COP among all the five SSTO systems and one original system in nominal cooling and heating conditions, though the heating capacity of the 18# SSTO system was slightly inferior to that of the original system due to the insufficient throttling capacity of 18# SSTO in heating mode.

Experimental investigation of mass flow rate difference between forward flow and reverse flow of sub-cooled R-22 through stepped short tube orifices

An expansion device of two capillary tubes with a by-pass check valve is popularly used in domestic heat pump systems. In order to reduce the manufacturing cost and improve reliability of the heat pump systems, a stepped short tube orifice consisting of two serial-connected short tube orifices with different diameters is employed as an alternative. The effects of upstream pressure, downstream pressure, upstream degree of sub-cooling and the geometric sizes of stepped short tube orifices on mass flow rate difference between forward flow and reverse flow of R-22 through stepped short tube orifices were investigated in this study. The results showed that there was a distinguishing mass flow rate difference between forward flow and reverse flow of R-22 through stepped short tube orifices under upstream pressure ranged from 1460kPa to 1940kPa, downstream pressure ranged from 420kPa to 680kPa and degree of sub-cooling ranged from 2 to 12°C. The mass flow rate difference is about 10kg/h between forward flow and reverse flow of R-22 through the stepped short tube orifice with sizes of D1=0.8mm, D2=1.0mm, L1=3mm, L2=6.5mm at the upstream pressure of 1940kPa, downstream pressure of 500kPa and the degree of sub-cooling ranging between 2°C and 12°C.

A new method for calculating the sonic conductance of airflow through a short-tube orifice

In this study, we proposed a method for calculating the sonic conductance of a short-tube orifice. First, we derived a formula for calculating the sonic conductance based on a continuity equation, a momentum equation and the definition of flow-rate characteristics. The flow-rate characteristics of different orifices were then measured using the upstream constant-pressure test method in ISO 6358. Based on these test data, the theoretical formula was simplified using the least squares fitting method, the accuracy of which was verified experimentally. Finally, the effects of the diameter ratio, the length-to-diameter ratio and the critical pressure ratio were analysed with reference to engineering applications, and a simplified formula was derived. We conclude that the influence of the diameter ratio is greater than that of the length-to-diameter ratio. When the length-to-diameter ratio is <5, its effect can be neglected. The critical pressure ratio has little effect on the sonic conductance of a short-tube orifice, and it can be set to 0.5 when calculating the sonic conductance in engineering applications. The formula proposed in this study is highly accurate with a mean error of <3%.

Experimental investigation on pressure drop characteristic of R410A through short tube orifices

The pressure drop characteristic experiments of R410A through short tube orifices (diameter ranged from 0.7 to 1mm, and length ranged from 5 to 15mm) were performed under specific condensing pressure, evaporating pressure and sub-cooling degree conditions. A quadratic regression semi-empirical benchmark model was established based on the impedance calculation method. According to the benchmark model, the pressure drop characteristic experiments were performed under condensing pressures ranged from 2500 to 3100kPa, evaporating pressures ranged from 900 to 1200kPa and sub-cooling degrees ranged from 3 to 9°C. A semi-empirical universal model of pressure drop characteristic of R410A through short tube orifices is developed. The model can cover the test range of working conditions and refrigerant mass flow rate. The model is used to predict the pressure drop of R410A through two kinds of the short tube orifices under a variety of working conditions, and the deviation between the predicted value and the measured value is within ±10%. The experimental results of air conditioner matching validation experiments show that the air conditioning system don’t need to adjust with the short tube orifices replace the capillary tubes.

A comprehensive modeling of choked two-phase flow through short-tube orifices with application to alternative refrigerants HFO-1234yf and HFO-1234ze

Due to the evaporating two-phase flow and the choked-flow condition, numerical analysis of flow through short-tube orifices is a complicated procedure. A comprehensive method for analyzing such flows is the two-fluid model, which does not assume equilibrium between phases. However, in all previous applications of this model, two-phase flow calculations at the entrance and vena contracta regions were eliminated. In this investigation, two additional steps were introduced to improve the accuracy of computations: (1) applying a comprehensive two-fluid model, including the effect of various two-phase flow patterns and the metastability of liquid phase; and (2) performing a two-phase analysis of the evaporating flow through the entrance and vena contracta, which involves simulation of this region as a contraction from the up-stream to the throat, and an expansion from the throat to downstream. Results showed more compatibility with experimental data in comparison with those of previous investigations for predicting the critical flow condition of common refrigerants HFC-134a, HCFC-22, and HFC-410a through short-tube orifices. In addition, the developed numerical scheme was utilized in order to develop selection charts for short-tube orifices based on the common refrigerant HFC-134a and the alternative newly released hydrofluoroolefin refrigerants HFO-1234yf and HFO-1234ze.

Performance comparison of air-source heat pump water heater with different expansion devices

Air source heat pump water heater (ASHPWH) is designed to work under wide operating conditions. Therefore, both the system and components require higher reliability and stability than ordinary heat pump air-conditioning systems. In this paper, a quasi-steady-state system model of ASHPWH using electronic expansion valve (EEV), capillary tube or short tube orifice as expansion device is developed and validated by a prototype using R134a and scroll compressor, by which the system performance is evaluated and compared at varying water temperature and different ambient temperature. Flow characteristics of those three expansion devices in ASHPWH are comparatively analyzed. Results show that the EEV throttling system performs best. Compared with capillary tube, flow characteristics of short tube orifice are closer to that of EEV and therefore more suitable for ASHPWH. Reliability concern of liquid carryover to the compressor in the system using short tube orifice is investigated as well. Higher superheat or less system refrigerant charge could help mitigate the risk.

Numerical simulation and validation of a stepped capillary tube using as throttling device in residential heat pump systems

A stepped capillary tube is a new design proposed by Zhao et al. that consist of two serial-connected capillary tubes with different diameter as an alternative in order to reduce the manufacturing cost of the typical assembly of two capillary tubes and a by-pass check valve widely used to achieve different mass flow rates in residential heat pump systems.In previous works, one-dimensional numerical modeling of fluid-flow inside capillary tubes and short tube orifices were performed, and successfully validated against a wide range of mass flow rate measurements reported for different refrigerant and mixtures. In this article, the model is applied to stepped capillary tubes (expansion devices). Governing equations (continuity, momentum, energy, and entropy) for describing the fluid flow have been solved by using a fully implicit step-by-step method. A numerical treatment has been codified for considering thermodynamic and flow transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). Sudden contraction and enlargement were also considered. A comparison and validation analyses of the simulation results were carried out by using mass flow rate experimental data (No = 30), which have been recently reported in the literature for R-22. Linear relationships between mass flow rate (predicted) and experimental mass flow rate data were statistically demonstrated. Average deviation error of ±3.2% was consistently computed between numerical model and experimental data, which demonstrates the good capability of the model developed for predicting the fluid flow processes.These results demonstrate a new and robust application of the model developed to predict reliably the mass flow rate through stepped capillary tubes, which enable this tool to be reliably used for the design of this kind of systems.

Numerical Modeling of Supercritical CO2 Leaks and its Subsequent Dispersion in the Ambient Air

An integrated 3D CFD based model to calculate the leak rates of supercritical CO2 from high pressure tanks and pipelines and its subsequent atmospheric dispersion is developed. The first component of the model takes into account the transition flow of supercritical CO2 under the action of large pressure changes through small flow passages such as orifices and leaks in high pressure pipe walls. It considers steep changes in transport and thermodynamic properties using appropriate equations of state for the wide range of pressures involved. The second component of the model calculates the large scale dispersion through the ambient air. This model includes consideration of the formation of dry ice due to sudden expansion and subsequent sublimation of dry ice due to entrainment of relatively hot ambient air. It also takes into account the effects of surrounding wind field using an atmospheric boundary layer model. The first model is validated by comparing the computed mass flow rates with the experimental data for transition flow through short-tube orifices and then for a high pressure tank of CO2 emptied through a small orifice. The second model is validated by comparing the temperature and volume fractions of CO2 at different points in the downstream of the jet during dispersion with the measurements in the latter experiment.

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.

Modelling of fluid flow through short tube orifices under metastable conditions: A new numerical validation approach for evaluating the mass flow rate with refrigerant mixtures (HFC-407C and HFC-410A)

In a previous work, one-dimensional numerical modelling of fluid-flow inside short tube orifices was performed, and successfully validated against a wide range of mass flow rate measurements reported for the refrigerant HFC-134a. Governing equations of continuity, momentum, energy and entropy were solved for describing the fluid flow under a wide variety of thermodynamic transitions (e.g., subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region), including sudden contraction and enlargement. In this new study, a comprehensive comparison analysis between numerical simulation data and experimental measurements obtained for HFC-407C and HFC-410A refrigerants (No = 241) to extend the applicability of the same mathematical model was carried out. Using a widespread statistical analysis, based on weighted linear regressions with an outlier detection/rejection module at 95% of confidence level, the prediction performance of the mathematical model was again assessed. Linear regressions between predicted mass flow rate data and experimental measurements were computed, and used them as a statistical comparison criterion. A statistical comparison between predicted simulation results and mass flow rate experimental data are reported. Average deviation errors of ±11.1% (for the refrigerant HFC-407C) and ±7.3% (for refrigerant HFC-410A) were found between numerical model and experimental data. These results demonstrate a new and robust application of the model to predict reliably the mass flow rate through short tube orifices under metastable conditions, which enable this tool to be reliably used for the design of short tube orifices.

Numerical simulation and validation of HFC-134a fluid flow through short-tube orifices considering metastable conditions

One-dimensional numerical modelling of the fluid-flow behaviour inside short-tube orifices (expansion devices) has been carried out. Governing equations (continuity, momentum, energy, and entropy) for describing the fluid flow have been solved by using a fully implicit step-by-step method. A numerical treatment has been codified for considering thermodynamic and flow transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). Sudden contraction and enlargement at inlet and outlet sections were also considered. Fluid-flow variables (e.g., enthalpies, temperatures, pressures, mass fractions, and heat fluxes) and thermophysical and transport properties of fluid were numerically evaluated at each grid point in a discretized domain. The physical model used for solving the fluid-flow problem enabled an analysis of geometry, fluid type, critical and non-critical flow conditions, metastable regions, and transient effects to be performed. A comparison and validation analyses of the simulation results were carried out by using a wide range of mass flow rate experimental data (No = 634), which have been reported in the literature for the refrigerant 134a. Using a comprehensive statistical analysis, based on weighted linear regressions with an outlier detection/rejection algorithm at 95% of confidence level, the prediction performance of the numerical model was evaluated. Linear relationships between mass flow rate (predicted) and experimental mass flow rate data were statistically demonstrated. A global statistical evaluation of deviation errors between mass flow rate experimental data and predicted simulation results was also calculated. Average deviation error of ±8.9% was consistently computed between numerical model and experimental data, which demonstrates the good capability of the model developed for predicting the fluid-flow processes.

Numerical simulation of refrigerants flowing through short-tube orifices during flashing process

A numerical simulation for calculating the flashing flow characteristics of refrigerants inside short-tube orifices is presented. The refrigerant flow behaviors along short-tube orifices are separated into three sections: subcooled liquid region, metastable liquid region, and two-phase region. Annular two-phase flow pattern is developed from the mass, energy, and momentum equation. The present simulation is corroborated by comparison with the experimental data. The selection charts are also presented to estimate the refrigerant mass flow rate along short-tube orifices in practical applications.

Characteristics of R-123 two-phase flow through micro-scale short tube orifice for design of a small cooling system

We present a new discharge coefficient correction method for the orifice equation for R-123 two-phase flows. In this method, an evaporator is mounted after the orifice as a vapor refrigeration cycle, and the evaporator is used to measure the quality of downstream flow through the orifice. Quality is estimated from the measured temperature and pressure of the evaporator inlet and outlet, respectively, instead of by direct measurement of quality. The condition of upstream flow of the orifice is the liquid state at 3 bar and 60 °C. The liquid flow is changed to two-phase flow after passing through the orifice. Orifice diameters of 300, 350, 400, and 450 μm are used for the experiment, and the results are analyzed. Experiments are conducted for various conditions of flow rate between 20 and 70 ml/min and for cooling loads of 60, 80, and 100 W. The results show that the quality of flow downstream from the orifice can be calculated using the enthalpy difference between the inlet and outlet of the evaporator. An equation to determine the discharge coefficient is formulated as a function of quality. We expect that these results can be used to help design a small cooling system.

Performance characteristics of HFC-134a and HFC-410A refrigeration system using a short-tube orifice as an expansion device

In the present article, the effect of heat source temperature, heat sink temperature, short-tube orifice diameter and short-tube orifice length on the performance characteristics of HFC-140A and HFC-134a refrigeration system using a short-tube orifice as expansion device, i.e., mass flow rate, cooling capacity, compressor pressure ratio, power consumption, and second law efficiency are experimentally studied. The short-tube orifices diameters ranging from 0.849 to 1.085 mm with length ranging from 10 to 20 mm are used in this examination. The test run are done at heat source temperature ranging between 16.5 and 18.5°C, and heat sink temperature ranging between 30 and 35°C. The results show that the tendency of second law efficiency is increased as the short-tube orifice diameter and heat source temperature are enhanced, but it is decreased by increasing the short-tube orifice length and heat sink temperature. Under the similar conditions, the mass flow rate, cooling capacity, and compressor power consumption obtained from HFC-410A are higher than those obtained from HFC-134a.

Choked flow mechanism of HFC-134a flowing through short-tube orifices

This paper is a continuation of the author’s previous work. New experimental data on the occurrence of choked flow phenomenon and mass flow rate of HFC-134a inside short-tube orifices under choked flow condition are presented. Short-tube orifices diameters ranging from 0.406mm to 0.686mm with lengths ranging from 1mm to 3mm which can be applied to a miniature vapour-compression refrigeration system are examined. The experimental results indicated that the occurrence of choked flow phenomena inside short-tube orifices is different from that obtained from short-tube orifice diameters of greater than 1mm, which are typically used in air-conditioner. The beginning of choked flow is dependent on the downstream pressure, degree of subcooling, and length-to-diameter ratio. Under choked flow condition, the mass flow rate is greatly varied with the short-tube orifice dimension, but it is slightly affected by the operating conditions. A correlation of mass flow rate through short-tube orifices is proposed in terms of the dimensionless parameters. The predicted results show good agreement with experimental data with a mean deviation of 4.69%.

Numerical Modeling of Refrigerants Flowing through Short Tube Orifices

A numerical model is developed for predicting the mass flow rates of a refrigerant flowing through short tube orifices under various working conditions. The numerical model is theoretically based and not refrigerant-oriented though the majority of past works are based on semi-empirical correlations. The metastable state flow is considered in the numerical model, and the critical flow condition at the outlet is directly obtained by using the analytical two-phase critical model. The comparison between the predicted mass flow rates and the experiment data obtained from literatures shows that the mean absolute deviations (MADs) for R-410A, R-407C, and R-134a are 6.91%, 5.33%, and 7.09%, respectively. The accuracy of this numerical model provides the basis for a more detailed and theoretical analyses of refrigerant flowing characteristics in short tube orifices, such as the determination of flow regimes and variation of inception of vaporization. Also, the effects of working conditions such as upstream pressure and inlet subcooling degree on the mass flow rates are theoretically studied using the developed numerical modeling technique, which shows exact trends as experiment data.

Flow mechanisms of HFC-410A inside short-tube orifices during flashing process

New experimental data of HFC-410A flow mechanisms, including pressure and temperature distributions, flow pattern, and mass flow rate inside a short-tube orifice are studied. Different short-tube orifice lengths of 10 mm, 15 mm, and 20 mm, with short-tube orifice diameters ranging from 0.849 to 1.096 mm were manufactured for this experiment. The test runs are done at upstream pressures ranging from 2100 to 2600 kPa, and with a degree of subcooling between 4 and 12 °C. The results show that the refrigerant flow mechanisms in the entrance region and inside a short-tube orifice agree with incompressible flow theory, but the refrigerant flow mechanisms in the exit region are similar to choked flow in a theoretical compressible flow. The temperature distribution inside a short-tube orifice is directly related to the pressure distribution. The mass flow rate is directly proportional to the upstream pressure and degree of subcooling, whereas it is strongly affected by the short-tube diameter. The downstream pressure has insignificant effects on the mass flow rate and pressure distribution inside a short-tube orifice. However, the downstream pressure has a slight effect on the temperature distribution inside a short-tube orifice.

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.

Modified neural network correlation of refrigerant mass flow rates through adiabatic capillary and short tubes: Extension to CO 2 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, CO 2 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 CO 2 (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 CO 2, the average and standard deviations are −2.5% and 6.0%, respectively. 90% data fall into ±10% error band.

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.