scholarly journals Dynamic Model of a Transcritical CO2 Heat Pump for Residential Water Heating

2021 ◽  
Vol 13 (6) ◽  
pp. 3464
Author(s):  
Hélio A. G. Diniz ◽  
Tiago F. Paulino ◽  
Juan J. G. Pabon ◽  
Antônio A. T. Maia ◽  
Raphael N. Oliveira
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Mathematical Model ◽  
Steady State ◽  
Mass Flow Rate ◽  
Heat Pump ◽  
Mass Flow ◽  
Flow Rate ◽  
Outlet Temperature ◽  
Time Step

This paper presents a distributed mathematical model for a carbon dioxide direct expansion solar-assisted heat pump used to heat bath water. The main components are a gas cooler, a needle valve, an evaporator/collector, and a compressor. To develop the heat exchange models, mass, energy, and momentum balances were used. The model was validated for transient as well as steady state conditions using experimental data. A reasonably good agreement was observed between the predicted temperatures and experimental data. The simulations showed that the time step required to demonstrate the behavior of the heat pump in the transient regime is greater than the time step required for the steady state. The results obtained with the mathematical model revealed that a reduction in the water mass flow rate results in an increase in the water outlet temperature. In addition, when the carbon dioxide mass flow rate is reduced, the compressor inlet and outlet temperatures increase as well as the water outlet temperature.

scholarly journals Determination of cop maximum of cold water loop of heat pump heating system by means of numerical-graphical optimization procedure

2020 ◽  
pp. 104-104
Author(s):  
Zoltan Pek ◽  
Arpad Nyers ◽  
Jozsef Nyers
Keyword(s):  
Mathematical Model ◽  
Mass Flow Rate ◽  
Heat Pump ◽  
Mass Flow ◽  
Flow Rate ◽  
Water Mass ◽  
Cold Water ◽  
Energy Optimization ◽  
Heating System ◽  
Water Mass Flow Rate

The paper presents the energy optimization of the cold water loop of the heat pump heating system using analytical-numerical procedure. The aim of the study is obtain the maximum COP of the heating system by optimum of the wall water mass flow rate and well pump power. The objective function is the heating system's coefficient of performance (COP). All components of the heating system: evaporator, condenser, compressor, circulation pump and well pump are described by steady-state, lumped mathematical model. The model?s equations are coupled, non-linear, multivariable and algebraic the solution is feasible using an iterative numerical method. Matlab?s program with Gauss elimination and Newton linearization method is applied for solving the model. The obtained numerical data are presented in 3D graphics. The optimum value of the cold-well water mass flow rate is obtained from the graphics or by using a selection algorithm. The results of the study are the adequate mathematical model for energy optimization of the heating system, the numerical algorithm for solving the model and the ultimate goal to obtain the optimum of the power of well pump and compressor.

Flow Characteristics of Electronic Expansion Valves for Heat Pump System Using Carbon Dioxide as a Refrigerant

2010 ◽  
Author(s):  
Ook Joong Kim ◽  
Young-Ho Choi ◽  
Seok Ho Yoon
Keyword(s):  
Carbon Dioxide ◽  
Mass Flow Rate ◽  
Heat Pump ◽  
Mass Flow ◽  
Flow Rate ◽  
Flow Characteristics ◽  
Inlet Temperature ◽  
Pump System ◽  
Heat Pump System ◽  
Temperature And Pressure

An experimental study on the flow characteristics of electronic expansion valves (EEVs) for heat pump system using carbon dioxide as a refrigerant have been carried out in this study. Many researches and efforts have been made to replace chemical refrigerants like Chloro-Fluoro-Carbon (CFC) and Hydro-Chloro-Fluoro-Carbon (HCFC) with natural refrigerants such as carbon dioxide and apply natural refrigerants to chillers or heat pump systems. In this study, we focused on the development of EEV and 4-way valve among the important components of heat pump system using natural refrigerant. The mass flow rate was measured at various EEV inlet temperature and pressure conditions with respect to several EEV openings operated at a heat pump system which has about 10 kW of cooling capacity. The heat pump system consists of a reciprocating compressor, a gas cooler, an evaporator, an EEV, and a 4-way valve which was developed for this study. The inlet temperature and pressure of an EEV was varied from 5°C to 40°C and from 7 MPa to 10 MPa, respectively. The mass flow rate of carbon dioxide through the EEV ranged from 50 g/s to 120 g/s. The mass flow rate of carbon dioxide around the critical point was affected by the inlet temperature and pressure of EEV, valve opening, and density variation. An empirical mass flow rate correlation of carbon dioxide based on the Buckingham π-theorem was developed in this study, and this correlation predicted experimental data within an average absolute deviation of 4.2%. The correlation can be applied to predict the mass flow rate through EEV used in the heat pump system using carbon dioxide as a refrigerant. And the reliability test of developed 4-way valve was conducted. This 4-way valve showed stable operation in the high pressure condition.

scholarly journals Development of circuit model with natural circulation of coolant under conditions of ship motion

Vestnik IGEU ◽  
2021 ◽  
pp. 19-26
Author(s):  
A.M. Samoilov ◽  
A.A. Sataev ◽  
A.A. Blokhin ◽  
V.V. Ivanov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Nuclear Power ◽  
Natural Circulation ◽  
Ship Motion ◽  
Nuclear Power Installation ◽  
Testing Bench

Safety is the key requirement to any nuclear power installation. Various factors affect safety during operation of the nuclear power installation. These factors are difficult to study due to the high economic costs. This problem can be solved by developing prototype models to conduct the research of many complex processes. Dynamic impact on the ship installation is one of these processes. The most significant impact is the impact on the natural circulation of the coolant, that is one of the basic emergency safety systems. Also, it is a promising way to ensure movement in the main circulation circuit. The purpose of this paper is to assess the influence of external dynamic forces on the processes of natural circulation. For the study a testing bench has been developed that simulates one of the circulation loops of the reactor unit. The basic method to obtain experimental data is temperature sounding of the specific sections of the circulation route. A mathematical model has been developed that describes this process. The model is based on the equations of momentum conservation and heat balance. In accordance with the experimental data, the calculation of natural circulation for static and dynamic modes has been carried out. A mathematical model to describe this process has been developed. A comparative analysis of the results of calculating the static and dynamic modes has been carried out. It is founded out that the decrease of mass flow rate is about 10 % as compared with the static regime. It confirms the qualitative effect of ship motion on natural circulation. The practical significance of the research is the development of a model under conditions of ship motion, as well as verification of the model at the testing bench. The results show a significant effect of ship motion on the mass flow rate of the coolant in the case of natural circulation. Thus, to ensure the required safety of ship installations, it is recommended to conduct a study of natural circulation in accordance with the developed model under conditions of maximum possible ship motion.

Numerical Simulation of the Performance of an Axial Compressor Operating With Supercritical Carbon Dioxide

2018 ◽  
Author(s):  
Jinlan Gou ◽  
Wei Wang ◽  
Can Ma ◽  
Yong Li ◽  
Yuansheng Lin ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Numerical Simulation ◽  
Supercritical Carbon Dioxide ◽  
Critical Point ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Axial Compressor ◽  
Brayton Cycle ◽  
Supercritical Carbon

Using supercritical carbon dioxide (SCO2) as the working fluid of a closed Brayton cycle gas turbine is widely recognized nowadays, because of its compact layout and high efficiency for modest turbine inlet temperature. It is an attractive option for geothermal, nuclear and solar energy conversion. Compressor is one of the key components for the supercritical carbon dioxide Brayton cycle. With established or developing small power supercritical carbon dioxide test loop, centrifugal compressor with small mass flow rate is mainly investigated and manufactured in the literature; however, nuclear energy conversion contains more power, and axial compressor is preferred to provide SCO2 compression with larger mass flow rate which is less studied in the literature. The performance of the axial supercritical carbon dioxide compressor is investigated in the current work. An axial supercritical carbon dioxide compressor with mass flow rate of 1000kg/s is designed. The thermodynamic region of the carbon dioxide is slightly above the vapor-liquid critical point with inlet total temperature 310K and total pressure 9MPa. Numerical simulation is then conducted to assess this axial compressor with look-up table adopted to handle the nonlinear variation property of supercritical carbon dioxide near the critical point. The results show that the performance of the design point of the designed axial compressor matches the primary target. Small corner separation occurs near the hub, and the flow motion of the tip leakage fluid is similar with the well-studied air compressor. Violent property variation near the critical point creates troubles for convergence near the stall condition, and the stall mechanism predictions are more difficult for the axial supercritical carbon dioxide compressor.

scholarly journals Solar Field Output Temperature Optimization Using a MILP Algorithm and a 0D Model in the Case of a Hybrid Concentrated Solar Thermal Power Plant for SHIP Applications

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3731
Author(s):  
Simon Kamerling ◽  
Valéry Vuillerme ◽  
Sylvain Rodat
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Solar Thermal ◽  
Outlet Temperature ◽  
Field Mass ◽  
Heat Demand ◽  
Process Heat ◽  
Solar Field ◽  
Control Trajectory

Using solar power for industrial process heat is an increasing trend to fight against climate change thanks to renewable heat. Process heat demand and solar flux can both present intermittency issues in industrial systems, therefore solar systems with storage introduce a degree of freedom on which optimization, on a mathematical basis, can be performed. As the efficiency of solar thermal receivers varies as a function of temperature and solar flux, it seems natural to consider an optimization on the operating temperature of the solar field. In this paper, a Mixed Integer Linear Programming (MILP) algorithm is developed to optimize the operating temperature in a system consisting of a concentrated solar thermal field with storage, hybridized with a boiler. The MILP algorithm optimizes the control trajectory on a time horizon of 48 h in order to minimize boiler use. Objective function corresponds to the boiler use, for completion of the heat from the solar field, whereas the linear constraints are a simplified representation of the system. The solar field mass flow rate is the optimization variable which is directly linked to the outlet temperature of the solar field. The control trajectory consists of the solar field mass flow rate and outlet temperature, along with the auxiliary mass flow rate going directly to the boiler. The control trajectory is then injected in a 0D model of the plant which performs more detailed calculations. For the purpose of the study, a Linear Fresnel system is investigated, with generic heat demand curves and constant temperature demand. The value of the developed algorithm is compared with two other control approaches: one operating at the nominal solar field output temperature, and the other one operating at the actual demand mass flow rate. Finally, a case study and a sensitivity analysis are presented. The MILP’s control shows to be more performant, up to a relative increase of the annual solar fraction of 4% at 350 °C process temperature. Novelty of this work resides in the MILP optimization of temperature levels presenting high non-linearities, applied to a solar thermal system with storage for process heat applications.

Experimental Investigation on Flow Characteristic of Stepped Capillary Tube for Heat Pump Type Air Conditioner with R410A

2014 ◽  
Vol 960-961 ◽  
pp. 643-647
Author(s):  
Yan Sheng Xu
Keyword(s):  
Mass Flow Rate ◽  
Heat Pump ◽  
Mass Flow ◽  
Flow Rate ◽  
Capillary Tube ◽  
Coefficient Of Performance ◽  
Tube Length ◽  
Air Conditioner ◽  
Capillary Tubes ◽  
Tube Assembly

A stepped capillary tube consisting of two serially connected capillary tubes with different diameters is invented to replace the conventional expansion device. The mass flow rate of refrigerant R410A in stepped capillary tubes with different size were tested. The model of stepped capillary tube is proposed, and its numerical algorithm for tube length and mass flow rate is developed. The experimental results show that the performance comparing between stepped capillary tube system and capillary tube assembly system, the cooling capacity is reduced by 0.3%, the energy efficiency ratio (EER) is equal to each other, the heating capacity is increased by 0.3%, the coefficient of performance (COP) is decreased by 0.3%. That is to say, the performance index of the two kinds of throttle mechanism is almost identical. It indicates that the stepped capillary tube can replace the capillary tube assembly in the R410A heat pump type air conditioner absolutely. The model is validated with experimental data, and the results show that the model can be used for sizing and rating stepped capillary tube.

Pitfalls for Accurate Steady-State Port Flow Simulations

2012 ◽  
Author(s):  
Xiaofeng Yang ◽  
Zhaohui Chen ◽  
Tang-Wei Kuo
Keyword(s):  
Steady State ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Measured Data ◽  
Steady State Flow ◽  
Bench Tests ◽  
Flow Simulations ◽  
Mesh Topology ◽  
State Flow

Steady-state port flow simulations were carried out with a commercial three dimensional (3D) Computational Fluid Dynamics (CFD) code using Cartesian mesh with cut cells to study the prediction accuracy. The accuracy is assessed by comparing predicted and measured mass-flow rate and swirl and tumble torques at various valve lifts using different boundary condition setup and mesh topology relative to port orientation. The measured data is taken from standard steady-state flow bench tests of a production intake port. The predicted mass-flow rates agree to within 1% with the measured data between the intermediate and high valve lifts. At low valve lifts, slight over prediction in mass-flow rate can be observed. The predicted swirl and tumble torques are within 25% of the flow bench measurements. Several meshing parameters were examined in this study. These include: inlet plenum shape and outlet plenum/extension size, embedded sphere with varying minimum mesh size, finer meshes on port and valve surface, orientation of valve and port centerline relative to the mesh lines. For all model orientations examined, only the mesh topology with the valve axis aligned closely with the mesh lines can capture the mass-flow rate drop for very high valve lifts due to flow separation. This study further demonstrated that it is possible to perform 3D CFD flow analyses to adequately simulate steady-state flow bench tests.

Receiver Outlet Temperature Control for Falling Particle Receiver Applications

2021 ◽  
Author(s):  
Nathan Schroeder ◽  
Henk Laubscher ◽  
Brantley Mills ◽  
Clifford K. Ho
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Temperature Rise ◽  
Pid Controller ◽  
Input Parameter ◽  
Slide Gate ◽  
Process Variable ◽  
Test Facility ◽  
Outlet Temperature

Abstract Falling particle receivers (FPRs) are being studied in concentrating solar power applications to enable high temperatures for supercritical CO2 (sCO2) Brayton power cycles. The falling particles are introduced into the cavity receiver via a linear actuated slide gate and irradiated by concentrated sunlight. The thickness of the particle curtain associated with the slide-gate opening dimension dictates the mass flow rate of the particle curtain. A thicker, higher mass flow rate, particle curtain would typically be associated with a smaller temperature rise through the receiver, and a thinner, lower mass flow rate, particle curtain would result in a larger temperature rise. Using the receiver outlet temperature as the process variable and the linear actuated slide gate as the input parameter a proportional, integral, and derivative (PID) controller was implemented to control the temperature of the particles leaving the receiver. The PID parameters were tuned to respond in a quick and stable manner. The PID controlled slide gate was tested using the 1 MW receiver at the National Solar Thermal Test Facility (NSTTF). The receiver outlet temperature was ramped from ambient to 800°C then maintained at the setpoint temperature. After reaching a steady-state, perturbations of 15%–20% of the initial power were applied by removing heliostats to simulate passing clouds. The PID controller reacted to the change in the input power by adjusting the mass flow rate through the receiver to maintain a constant receiver outlet temperature. A goal of ±2σ ≤ 10°C in the outlet temperature for the 5 minutes following the perturbation was achieved.

Adiabatic Capillary Tube Model for a Carbon Dioxide Transcritical Cycle

2015 ◽  
Vol 23 (02) ◽  
pp. 1550011 ◽  
Author(s):  
R. O. Nunes ◽  
R. N. Faria ◽  
N. Bouzidi ◽  
L. Machado ◽  
R. N. N. Koury
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Mathematical Model ◽  
Mass Flow ◽  
Flow Condition ◽  
Capillary Tube ◽  
Tube Model ◽  
Minimum Diameter ◽  
Conservation Of Energy ◽  
Capillary Tube Model

This paper presents a mathematical model for a capillary tube using CO 2 as fluid in steady flow transcritical cycle. The capillary tube is divided into N volumes controls and the model is based on applying the equations of conservation of energy, mass and momentum in the fluid in each of these volumes controls. The model calculates the mass flow of the CO 2 in the capillary tube as a function of CO 2 pressures at the inlet and outlet of the capillary and the temperature of CO 2 at the input of this device. The capillary tube is considered to be adiabatic, and the limit of operation due to blocked flow condition is also considered in the model. The validation of the model was performed with experimental data and the results showed that the model is capable of predicting the mass flow in the capillary tube with errors less than 10%. The model was also used to determine the minimum diameter of the capillary tube for various conditions of CO 2 transcritical cycle.

An Experimental Study of the Flow of R-407C in an Adiabatic Spiral Capillary Tube

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
M. K. Mittal ◽  
R. Kumar ◽  
A. Gupta
Keyword(s):  
Experimental Data ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Capillary Tube ◽  
Flow Characteristics ◽  
Flow Rates ◽  
Tube Test ◽  
Mass Flow Rates ◽  
R 134A

The objective of this study is to investigate the effect of coiling on the flow characteristics of R-407C in an adiabatic spiral capillary tube. The characteristic coiling parameter for a spiral capillary tube is the coil pitch; hence, the effect of the coil pitch on the mass flow rate of R-407C was studied on several capillary tube test sections. It was observed that the coiling of the capillary tube significantly reduced the mass flow rate of R-407C in the adiabatic spiral capillary tube. In order to quantify the effect of coiling, the experiments were also conducted for straight a capillary tube, and it was observed that the coiling of the capillary tube reduced the mass flow rate in the spiral tube in the range of 9–18% as compared with that in the straight capillary tube. A generalized nondimensional correlation for the prediction of the mass flow rates of various refrigerants was developed for the straight capillary tube on the basis of the experimental data of R-407C of the present study, and the data of R-134a, R-22, and R-410A measured by other researchers. Additionally, a refrigerant-specific correlation for the spiral capillary was also proposed on the basis of the experimental data of R-407C of the present study.

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