Homogeneous Flow Model Research Articles

Flow of Neon-Nitrogen-Hydrocarbon mixture through adiabatic capillary tube at cryogenic temperatures

Capillary tubes are widely used in J-T refrigerators owing to their simplicity, easy operation, and zero maintenance. J-T refrigerators are mainly used for domestic and commercial refrigeration and air conditioning and hence the study on flow through capillary tubes is highly focused on conventional refrigerants at relatively higher temperatures. The present work is an extension of previous work done by the authors and focuses on the flow of refrigerant mixtures consisting of neon, nitrogen, and hydrocarbons at cryogenic temperatures for the capillary tube of a J-T cryocooler. The mass flow rate through the capillary tube is studied experimentally by changing refrigerant mixture composition and inlet temperature to the capillary tube. A mathematical model is developed based on a length feedback loop to predict the mass flow rate through the capillary tubes using the homogenous flow model. The model is found to predict mass flow rate through the capillary tube with an average error of 10 % for almost all the experimental values.

Investigation on the Influence of Entrained Air to Internal Flow of Centrifugal Pumps under Cavitation Condition

The introduction of air is often used in engineering to delay the occurrence of cavitation. A steady simulation on a single-stage and single-suction centrifugal pump was used to study the influence of the air on the internal flow under cavitation condition at 1% inlet void fraction. Steady simulation based on SST k-ω turbulence model and Rayleigh-Plesset cavitation model included in Ansys CFX 17.0 were processed to obtain vapor volume fraction, gas volume fraction and the turbulent energy of the impeller under the condition of natural cavitation and cavitation with entrained air. A homogeneous two-phase flow model was adopted to describe the air-water mixed flow. The experimental cavitation performance curve provides boundary condition support for the numerical simulation. In conclusion, it shows that the head of the pump keeps steady after 1% air entrained like natural cavitation. Then it goes worse when the cavitation number decreases but with lower NPSHr which means cavitation performance is improved by 1% air entrained. It indicated that the entrained air changes the distribution of the vapor in the passage of the impeller. However, the descent of the pressure over a certain value will also do harm to the internal flow of the model pump whether it is ventilating or not. The internal flow of the pump will be seriously damaged and even be blocked completely due to more and more vapor generated causing a dramatic decline of the head.

Simulations of water-vapor two-phase flows with non-condensable gas using a Noble-Able-Chemkin stiffened gas equation of state

In order to simulate some accidental scenarii which might affect a pressurized water reactor, a homogeneous two-phase water-vapor flow model taking into account non-condensable gas is considered. The liquid phase and the gaseous phase are assumed to be immiscible, but the gaseous phase is composed of two miscible components. Due to these hybrid hypotheses of miscibility, the configurations with at least one missing field are carefully examined. A semi-analytical equation of state is chosen for the liquid water, which is an extension of the Noble-Able stiffened gas equation of state. Its accuracy is assessed with respect to the reference equation of state IAPWS. The homogeneous model is first verified thanks to Riemann problems. Then, some simulations aiming at reproducing SUPERCANON experiment are presented. The amount of air dissolved in liquid water is shown to have a strong influence on numerical results, in particular on the sound speed. Some out of thermodynamical equilibrium simulations are also presented, using two time scales describing the return towards equilibrium.

An optimized volume of fluid method for modelling three-dimensional debris flows. Implementation in OpenFOAM, validation, and application in the Aiwa Watershed, Beijing

Debris flows are a common type of geological hazard. They move down slopes at rapid speeds, causing severe damage to buildings and humans. It is of great significance to study the development and movement characteristics of debris flows. In this study, we developed a numerical method of simulating the movement of debris flows. The phase fraction was used to represent the contents of the debris flow components. The Herschel–Bulkley–Papanastasiou model was used to simulate the movement of the fine particle–water mixture in the debris flow, and the pressure-dependent Coulomb viscoplastic model was used to describe the movement of the gravel-size particles. The interface between the debris flow and the air was obtained using the volume of fluid method. The above models were implanted in OpenFOAM. Finally, indoor experimental data were used to verify the numerical method developed in this study, and the experimental and simulation results were found to be in good agreement. The proposed method was then applied to debris flow prediction in the Aiwa Watershed, Beijing. The homogeneous flow model developed in this study can significantly reduce the number of calculations required and can be used for the three-dimensional simulation of large-scale debris flows.

Comparison between homogeneous and separated flow models of isobutane flowing through adiabatic capillary tubes

Capillary tubes have been widely used as expansion devices in small-scale refrigeration and heat-pump systems. However, adiabatic flow through a capillary tube is extremely complicated, despite its simple geometry. This work presents a comparative study on the homogenous flow model and separated flow model, which were used to simulate the flow of isobutene (R600a) through adiabatic capillary tubes. The influence of different combinations of friction factor and two-phase viscosity correlations, and the effect of metastable flow on the flow characteristics were investigated. The predicted mass flow rate was lower when the separated flow model was used. The separated flow model performed better in predicting a mass flow rate over 2 kg·h<sup>−1</sup>. The Colebrook friction factor correlation combined with the Dukler or McAdams viscosity correlation yielded smaller deviations of 5.43%, 5.49% and 5.44%, 5.43% when ignoring and considering the metastable flow, respectively. Additionally, the homogenous flow model adopting the Bittle and Pate friction factor and Dukler viscosity correlations achieved the highest accuracy with a mass flow rate under 2 kg·h<sup>−1</sup>. The mean error was 4.12% in the case without metastable flow, and 3.37% in the case with metastable flow.

Experimental investigation on flow condensation pressure drop of steam in a horizontal tube

The pressure drop characteristics of pure steam condensation are studied in a horizontal tube with an inside diameter of 38 mm and a length of 3.4 m. The mass flux ranges from 3-7.5 kg/(m2s). The saturation temperatures of the inlet steam are 50?, 60?, and 70?. The temperature difference between the inlet steam and the inlet cooling water is from 3-7?. The influences of mass flux, total heat transfer temperature difference and inlet saturation temperature total pressure drop are investigated. The new correlation is proposed to calculate the total pressure drop of pure steam flow in a horizontal tube. The Dukler correlations based on the homogeneous flow model are good predictors for calculating the frictional pressure drop in this work.

A Nonhomogeneous Bulk Flow Model for Gas in Liquid Flow Annular Seals: An Effort to Produce Engineering Results

Abstract Seals in multiple-phase rotordynamic pumps must operate without compromising system efficiency and stability. Both field operation and laboratory experiments show that seals supplied with a gas in liquid mixture (bubbly flow) can produce rotordynamic instability and excessive rotor vibrations. This paper advances a nonhomogeneous bulk flow model (NHBFM) for the prediction of the leakage and dynamic force coefficients of uniform clearance annular seals lubricated with gas in liquid mixtures. Compared to a homogeneous bulk flow model (HBFM), the current model includes diffusion coefficients in the momentum transport equations and a field equation for the transport of the gas volume fraction (GVF). Published experimental leakage and dynamic force coefficients for two seals supplied with an air in oil mixture whose GVF varies from 0% (pure liquid) to 20% serve to validate the novel model as well as to benchmark it against predictions from a HBFM. The first seal withstands a large pressure drop (∼38 bar) and the shaft speed equals 7.5 krpm. The second seal restricts a small pressure drop (1.6 bar) as the shaft turns at 3.5 krpm. The first seal is typical as a balance piston whereas the second seal is found as a neck-ring seal in an impeller. For the high pressure seal and inlet GVF = 0.1, the flow is mostly homogeneous as the maximum diffusion velocity at the seal exit plane is just ∼0.1% of the liquid flow velocity. Thus, both the NHBFM and HBFM predict similar flow fields, leakage (mass flow rate), and drag torque. The difference between the predicted leakage and measurement is less than 5%. The NHBFM direct stiffness (K) agrees with the experimental results and reduces faster with inlet GVF than the HBFM K. Both direct damping (C) and cross-coupled stiffness (k) increase with inlet GVF < 0.1. Compared to the test data, the two models generally under predict C and k by ∼25%. Both models deliver a whirl frequency ratio (fw) ∼ 0.3 for the pure liquid seal, hence closely matching the test data. fw raises to ∼0.35 as the GVF approaches 0.1. For the low-pressure seal, the flow is laminar; the experimental results and both NHBFM and HBFM predict a null direct stiffness (K). At an inlet GVF = 0.2, the NHBFM predicted added mass (M) is ∼30% below the experimental result while the HBFM predicts a null M. C and k predicted by both models are within the uncertainty of the experimental results. For operation with either a pure liquid or a mixture (GVF = 0.2), both models deliver fw = 0.5 and equal to the experimental finding. The comparisons of predictions against experimental data demonstrate that the NHBFM offers a marked improvement, in particular for the direct stiffness (K). The predictions reveal that the fluid flow maintains the homogeneous character known at the inlet condition.

Numerical Simulation of Cavitation and Damping Force Characteristics for a High-Speed Supercavitation Vehicle

In this study, an attempt has been made to investigate the supercavitation and hydrodynamic characteristics of high-speed vehicles. A homogeneous equilibrium flow model and a Schnerr–Sauer model based on the Reynolds-averaged Navier–Stokes method are used. Grid-independent inspection and comparison with experimental data in the literature have been carried out to verify the accuracy of numerical methods. The effect of the navigation speed and angle of attack on the cavitation morphology and dynamic characteristics has been investigated. It has been demonstrated that the angle of attack has a remarkable influence on the wet surface and hydrodynamic force, whereas navigation speed has little effect on the position force of the vehicle under the circumstance of no wet surface. The hydrodynamic force changes periodically with the swing of the vehicle, but its maximum is greater than that for the direct navigation state at the same attack angle. Moreover, the damping effect obviously affects the hydrodynamic force amplitude and movement trend.

Study of Thermodynamic Effect on the Mechanism of Flashing Flow Under Pressurized Hot Water by a Homogeneous Model

Abstract The flashing flow in a Moby_Dick converging-diverging nozzle under pressurized hot water from 460.5 to 483.5 K is simulated using a homogeneous compressible water-vapor two-phase flow model. The kinematic and thermodynamic mass transfer are accessed using the cavitation model based on the Hertz–Knudsen–Langmuir equation. Our simplified thermodynamic model is coupled with the governing equations to capture the phase-change heat transfer. This numerical method proved its reliability through a comparison with available experimental data of flow parameters inside the nozzle. Consequently, the present numerical method shows good potential for simulating the flashing flow under pressurized hot water conditions. The satisfying prediction of averaged flow parameters with a slight improvement compared to reference numerical data is reproduced. The results confirm a noticeable impact of the thermodynamic effect on the mechanism of flashing flow, resulting in a considerable decrease in the flow temperature and the saturated vapor pressure. The flashing nonequilibrium is significantly decreased, forcing the flashing flow to be classified as the usual cavitation behavior and better suited to homogeneous model. While the temperature drop is highly dependent on evaporation, the thermodynamic suppression is influenced by the condensation. The suppression effect, unobserved in water at a lower temperature in previous studies, is noticeable for the pressurized hot water flow characterized by the cavitation mechanism. The vapor void fraction decreased considerably in the radial and axial directions as the water temperature rose to 483.5 K in this study.

Characterization of the Pressure Drop during Condensation in Channels of Multi-Channel Cylinder Dryer Using Homogeneous and Separated Flow Models

The condensation resistance characteristics of steam flow in horizontal rectangular channels of multi-channel cylinder dryer (MCD) is a very important factor that affects the heat transfer, while it is not very clear due to the limited studies. In this paper, the frictional resistance characteristics of the two-phase flow (steam and water) in the rectangular small channels of MCD were investigated with deionized water as the working fluid, and the calculation models, homogeneous and separated flow models, of the two-phase flow pressure drop in the channel were verified and evaluated. It showed that the main part of the total pressure drop was the frictional pressure drop, which means that the calculation of frictional pressure drop was the key to the calculation of the pressure drop of the two-phase flow in the channel. Meanwhile, it was found that the homogeneous model was not suitable for the calculation of the frictional pressure drop and the separated flow model was completely in line with the experimental data. In this study, the converted coefficient of complete steam/liquid phase were concerned to calculate the frictional resistance using five separated flow models. It was found that the Chisholm B model showed better accuracy than prior correlations, which was greatly consistent with experimental data, and the average absolute percentage deviation (MAPE) was 24.9%.

A comparative study of flow characteristics of adiabatic spiral and helical capillary tube in a CO2 transcritical system

Flow characteristics of an adiabatic spiral and a helical capillary tube in a CO2 transcritical system are numerically simulated. A homogeneous two-phase flow model is developed using the mass, energy and momentum conservation equations, taking into consideration the helical and spiral coiling effects of the capillary tubes. Friction factor and viscosity correlations are used from the available literature. Results are compared with conventional subcritical refrigerant R22. Reduction in a mass flow rate of refrigerant is more pronounced in the spiral capillary tube than helical capillary tube effect; about 18% and 11% with CO2 and R22, respectively. Length requirement with a spiral capillary tube is relatively less compared to other chosen configurations for the given mass flow rate and operating conditions.

Numerical Simulation of Heat Transfer in Laminar Natural Convection of Mixed Newtonian-Non-Newtonian and Pure Non-Newtonian Nanofluids in a Square Enclosure

Abstract This paper presents a steady-state heat transfer model for the natural convection of mixed Newtonian-Non-Newtonian (Alumina-water) and pure non-Newtonian (Alumina-0.5 wt% Carboxymethyl Cellulose (CMC)/water) nanofluids in a square enclosure with adiabatic horizontal walls and isothermal vertical walls, the left wall being hot and the right wall cold. In the first case, the nanofluid changes its Newtonian character to non-Newtonian past 2.78% volume fraction of the nanoparticles. In the second case, the base fluid itself is non-Newtonian and the nanofluid behaves as a pure non-Newtonian fluid. The power-law viscosity model has been adopted for the non-Newtonian nanofluids. A finite-difference based numerical study with the Stream function-Vorticity-Temperature formulation has been carried out. The homogeneous flow model has been used for modeling the nanofluids. The present results have been extensively validated with earlier works. In Case I, the results indicate that Alumina-water nanofluid shows 4% enhancement in heat transfer at 2.78% nanoparticle concentration. Following that there is a sharp decline in heat transfer with respect to that in base fluid for nanoparticle volume fractions equal to and greater than 3%. In Case II, Alumina-CMC/water nanofluid shows 17% deterioration in heat transfer with respect to that in base fluid at 1.5% nanoparticle concentration. An enhancement in heat transfer is observed for increase in hot wall temperature at a fixed volume fraction of nanoparticles, for both types of nanofluid.

Development of a two-fluid based thermal-hydraulic subchannel analysis code with high-resolution numerical method

The SACOS code is thermal-hydraulic subchannel analysis code designed to meet steady-state conditions and operational transients in different types of reactor cores. It uses a homogeneous flow or drift-flux model to simulate single-phase and two-phase flow characteristics. In order to achieve a more refined two-phase flow modeling for LWR cores, a new eight-equation two-fluid based analysis module of SACOS is developed in this study. The phasic equations for mass continuity, momentum, and energy are spatially discretized by the finite volume method (FVM) with a staggered grid structure. To reduce numerical diffusion and improve numerical accuracy, the high-resolution scheme with nonlinear flux limiter is implemented. The code assessment is performed with linear advection flow problem and the preliminary code validation is presented by comparing with the experimental results of Weiss 14 × 14 blockage test, CNEN 4 × 4 mixing test, Studsvik 3 × 3 mixing test, and ISPRA 4 × 4 mixing test covering single/two-phase and unheated/heated conditions. The application of SACOS implies that the code can be used to model and perform assembly-level core safety analysis with visualization capabilities for hexagonal and rectangular geometry.

Effect of air mass fraction on transient pressure and structural integrity assessment in a relatively long cast iron pipe

A numerical model was developed to study transient flow in air–liquid mixtures in quasi-rigid pipes. Hydraulic transient was generated in a relatively long cast iron pipe by the fast closure of the downstream valve. The presented model is based on the homogeneous flow model approach which considers the two-phase flow as a mixture without the assumption of a non-interface exchange. The method of characteristics was used to solve the set of partial differential equations. To validate the numerical model, experimental data from literature were used. The pressure wave propagation was analyzed through the pipe to understand the behavior of the air–liquid mixture under pressure disturbances. The value of the air mass fraction was also varied to discuss its effect on transient pressure. Obtained results revealed that the increase of the air mass fraction in the operating liquid may contribute to decreasing the maximum transient pressure. Based on the thin-walled hollow cylinder assumptions, the maximum stresses in the pipes were calculated for different values of the air mass fraction. Obtained results were used to conduct a structural integrity analysis of the cast iron pipe with a semi-elliptical crack. A Failure Assessment Diagram (FAD) was obtained based on the SINTAP method to calculate the safety factor for different values of the air mass fraction. It has been observed that the safety factor varies with the presence of the gaseous phase in the operating fluid.

Experimental and Numerical Investigation on Flow Boiling in a Small Semi-circular Channel of Plate Once-Through Steam Generator

The heat transfer coefficients of flow boiling in a small semi-circular channel of plate once-through steam generator were tested by experimental method in this paper. Based on the experimental data, the numerical simulation of flow boiling in the semi-circular channel was carried out using STAR-CCM + software. The numerical models are the homogenous flow model, the Rohsenow model and the two-fluid model. The heat transfer coefficients of homogenous flow model are lower than the experimental results. The heat transfer coefficients of Rohsenow model and experiment are in good agreement.

Investigation of transfer line cool-down transients using equilibrium two-phase models

Optimization of the transfer line cool-down process is essential for propellant loading as well as thermal management in space flights. Hence, selection of an appropriate numerical model for the investigation of the same has significant industrial application. So, in this work, the predictability of cool-down transients by homogeneous and slip flow models are studied by simulating experimental work reported in the literature. By investigating the thermal and pressure transients in the wall material and fluid flow path respectively, the predictive capability of the above models is discussed in detail.

전기자동차 모터 유냉식 방열성능 향상을 위한 열전달 해석 및 최적화

This paper presents the heat transfer analysis of the electric vehicle motor and optimization of an operating parameter for improving the performance of the motor with an oil cooling system. The homogeneous multi-phase flow model in commercial software, ANSYS CFX, is applied to solve the flow of mixture, including oil and air. We mainly focus on the influence of operating (oil level) and driving conditions (roll and pitch angles) on the cooling system. Several CFD simulations are performed with various input parameters (oil level, roll, and pitch angles) generated from the Latin Hypercube Sampling method. Based on the CFD results, we built a Polynomial Chaos Expansions based surrogate model to predict the temperature distribution, maximum temperature, and torque loss, which respond to the input parameters. Sensitivity analysis indicates that the oil level significantly affects system performance (maximum temperature and torque loss). Finally, the optimal range of oil level is estimated, considering the maximum allowable temperature of the motor.

A mathematical model of an adiabatic helical capillary tube used for R1234yf and R600a refrigerants

This paper presents a mathematical model to simulate the effect of the coiling diameter, subcooling degree and internal diameter on the characteristics flow of the refrigerants R1234yf and R600a, flowing through an adiabatic helical capillary tube. The homogeneous flow model was developed in the two-phase region based on the fundamentals of conservation of mass, momentum and fluid energy in the capillary tube. To validate this model, a comparison with numerical data on helical capillary tubes obtained by previous investigators has been made. It was reported that the coiling diameter, the inner diameter and inlet temperature of the capillary tube significantly influence on the pressure drop and quality and temperature distribution of the refrigerants R1234yf and R600a flowing inside the adiabatic helical tube. To validate this model, a comparison with numerical data on helical capillary tubes obtained by previous investigators has been made. Finally, the outcomes obtained from the present model exhibit satisfactory agreement with the available numerical data of helical capillary tubes.

Constraining a Flow Model with Field Measurements to Assess Water Transit Time Through a Vadose Zone

AbstractThe modeling of thick vadose zones is particularly challenging because of difficulties in collecting a variety of measured sediment properties, which are required for parameterizing the model. Some models rely on synthetic data, whereas others are simplified by running as homogeneous sediment domains and relying on a single set of sediment properties. Few studies have simulated flow processes through a thick vadose zone using real and comprehensive data sets comprising multiple measurements. Here, we develop a flow model for a 7‐m‐thick vadose zone. This model, combining the numerical codes CTRAN/W with SEEP/W, includes the measured sediment hydraulic properties of the investigated vadose zone and incorporates the actual climate and subsurface conditions of the study site (precipitations, water‐table elevations, and stable isotope data). The model is calibrated by fitting the simulated and measured vertical profiles of water content. Our flow model calculates a transit time of 1 year for the travel of water through the 7‐m vadose zone; this estimate matches stable isotope‐based results obtained previously for this site. A homogeneous sediment domain flow model, which considers only a single set of sediment properties, produces a transit time that is approximately half the duration of that of the heterogeneous flow model. This difference highlights the importance of assuming heterogeneous material within models of thick vadose zones and testifies to the advantage gained when using real sediment hydraulic properties to parametrize a flow model.

Numerical simulation of Electrokinetically Driven Peristaltic Pumping of Silver-Water Nanofluids in an asymmetric microchannel

This article intends to focus on the theoretical and numerical investigation of the peristaltic pumping of water-based silver nanofluid in the presence of electroosmotic forces. The investigation is carried out in an asymmetric microchannel subject to the influence of mixed convection and viscous dissipation. No-slip boundary conditions for velocity, temperature, and nanoparticle volume fraction are imposed on channel walls. The lubrication approach is utilized to simplify the normalized constitutive equations. The distribution of electric potential in the electric double layer is characterized by Poisson-Boltzmann ionic distribution which is further linearized by Debye-Hückel approximation. Nanofluid properties are predicted by a combination of the Buongiorno two-phase mixture model and homogeneous flow model. Additionally, the effective thermal conductivity and dynamic viscosity of silver-water nanofluid are characterized by the Corcione model. Silver nanoparticles of 20nm diameter are utilized in this suspension. The transformed set of nonlinear and coupled equations is numerically executed for axial velocity, temperature, and nanoparticle volume fraction by employing the mathematical software Maple 17. Pumping and trapping phenomena are also investigated. A comparison between the thermal conductivity of nanofluid predicted by the Corcione model and the Maxwell model is further presented. The influence of various flow parameters is outlined through graphical results. It has been observed that the thermal conductivity of silver-water nanofluid enhances with increasing nanoparticle volume fraction and temperature but decreases for larger sized nanoparticles. Moreover, the heat transfer rate rises significantly when smaller silver nanoparticles are suspended in water. Furthermore, the temperature of nanofluid is directly related to the Debye length parameter and the Helmholtz- Smoluchowski velocity parameter.