Homogeneous Two-phase Flow Model Research Articles

Critical Heat Flux Condition and Post-Critical Heat Flux Heat Transfer of Carbon Dioxide at High Reduced Pressures in a Microchannel

Abstract Flow boiling heat transfer around the critical heat flux (CHF) condition at high reduced pressures of carbon dioxide in a 296-μm hydraulic diameter microchannel was experimentally studied. The CHF conditions for developing flow and fully developed flow were measured and compared to established correlations. The post-CHF heat transfer coefficient was obtained for l/d of 3.2, 7.4, and 11.6 for inlet Reynolds numbers, based on the homogeneous two-phase flow model, ranging from 6622 to 32,248. The critical heat flux conditions seemed to peak around a reduced pressure of about 0.5 and gradually decreased with reduced pressure. However, the typical rapid increase in the surface temperature following the CHF condition decreased with increasing pressure, and the post-CHF heat transfer coefficient was appreciably high (up to about 50 kW/m2K) at high reduced pressures. The enhancement in the heat transfer coefficient and CHF condition near the inlet were quantified. The experimental results were compared to established CHF correlations and heat transfer coefficient correlations with some limited success. Thus, the Katto CHF correlation (Katto and Ohno, 1984, “An Improved Version of the Generalized Correlation of Critical Heat Flux for the Forced Convective Boiling in Uniformly Heated Vertical Tubes,” Int. J. Heat Mass Transfer, 27(9), pp. 1641–1648) and the Bishop correlation (Bishop et al., 1964, “Forced-Convection Heat Transfer to Water at Near-Critical Temperatures and Supercritical Pressures,” Westinghouse Electric Corp, Atomic Power Division, Pittsburgh, PA.) for the post-CHF heat transfer coefficient were adjusted to better predict the experimental results. Additionally, an enhancement factor was derived to predict the increase in the heat transfer coefficient in the developing region.

Two-phase flow, pressure drop, and Joule-Thomson effect in a micro-orifice with trans critical carbon dioxide flow

Two-phase flow, pressure drop, and Joule-Thomson coefficient (JTh) of sub- and super- critical carbon dioxide expanding through a 81 µm orifice embedded inside a 300 µm microchannel was experimentally studied. It was demonstrated and validated that a flow of CO2 in a micro-orifice can support the thermodynamic conditions that are ripe for the JTh effect to be significant. The inlet pressure, temperature, and mass flux were independently varied between 5.6 MPa and 10.2 MPa, 293 K and 314 K, and 47,277 kg/m2s and 162,101 kg/m2s, respectively. The measured pressure drop and Joule-Thomson coefficient ranged from 0.1 MPa to 5 MPa and from 0 K/MPa to 10 K/MPa, respectively. Pressure drop results were compared with the homogenous two-phase flow model, the separated two-phase flow model, the capillary tube model, and an empirical fit equation that resulted in mean average errors of 0.84 MPa, 1.4 MPa, 0.7 MPa, and 0.75 MPa, respectively.

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.

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.

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.

A coupled neutronic/thermal–hydraulic module for the transient analysis of VVER-1000 reactor during reactivity insertion accidents

For the safety analysis of nuclear power plants, it is essential to provide a simple and fast model to investigate the time-dependent behavior of reactor cores. Most research papers in this field have generally been limited to use coupling techniques between existing codes. In this paper, an integrated module called CMS (nuclear reactor Core Modular Simulator) is proposed to simulate the transient thermo-neutronic behavior of a VVER-1000 reactor core during reactivity insertion accidents. CMS contains three modules: a neutronic module based on the point kinetic equations, a thermal-hydraulic module based on the time-dependent single heated channel approximation and a reactivity calculation one. A two-stage fourth order implicit Runge-Kutta method was used for solving the point kinetics equations and the homogeneous two-phase flow model was considered for the thermal-hydraulic part. To verify the proposed module, two reactivity insertion accidents of the Bushehr VVER-1000 reactor, a design basis accident and an anticipated operational occurrence, have been simulated and the obtained results have been compared with its final safety analysis report showing a good agreement.

Water hammer with non-equilibrium gas release

Water hammer transient with gaseous cavitation in a pipe shows that the amplitude of the first pressure surge, caused by the closure of the fast valve, is approximate to the Joukowsky pressure rise in liquid, while subsequent pressure surges are strongly influenced by the presence of air in the mixture with liquid water. These conditions are described and numerically simulated with the homogeneous two-phase flow model and a non-equilibrium model of air mass transfer between dispersed air bubbles and continuous liquid water. It is found that the generation of air bubbles is intensive when the rarefaction wave decreases pressure below the pressure of gas saturation in water for the first time after the Joukowsky pressure peak, while, later on, the mass transfer rate, due to air degassing and absorption, is much smaller. A numerically predicted pressure transient is validated by the comparison with available measured data, and an excellent agreement is achieved.

Research on axis orbit of the journal bearing lubricated with oil and refrigerant mixtures in a twin-screw refrigeration compressor

In twin-screw refrigeration compressor for high pressure applications, journal bearing has been a preferred option to bear larger and larger radial force. Hence, the stability of rotor-journal bearing system is worth investigating to ensure the reliability of a twin-screw refrigeration compressor, which can be reflected on axis orbit. This paper presents a homogeneous two-phase flow model to calculate the axis orbit of journal bearing used in a twin-screw compressor, considering gas-induced force, unbalanced force and gravitational force. In order to compute gas-induced force acting on bearings by FEM, the p-V indicator diagram is measured experimentally. In addition, axial orbit under different evaporating temperature and different built-in volume ratio was investigated experimentally. Meanwhile it verifies that the proposed two-phase flow model has a good agreement in terms of orbit shape with the experimental result. Moreover, the effects of refrigerant mass fraction at supply groove and structural parameters are analyzed theoretically.

Estimation of performance of a J-T refrigerators operating with nitrogen-hydrocarbon mixtures and a coiled tubes-in-tube heat exchanger

The exergy efficiency of Joule-Thomson (J-T) refrigerators operating with mixtures (MRC systems) strongly depends on the choice of refrigerant mixture and the performance of the heat exchanger used. Helically coiled, multiple tubes-in-tube heat exchangers with an effectiveness of over 96% are widely used in these types of systems. All the current studies focus only on the different heat transfer correlations and the uncertainty in predicting performance of the heat exchanger alone. The main focus of this work is to estimate the uncertainty in cooling capacity when the homogenous model is used by comparing the theoretical and experimental studies. The comparisons have been extended to some two-phase models present in the literature as well.Experiments have been carried out on a J-T refrigerator at a fixed heat load of 10 W with different nitrogen-hydrocarbon mixtures in the evaporator temperature range of 100–120 K. Different heat transfer models have been used to predict the temperature profiles as well as the cooling capacity of the refrigerator. The results show that the homogenous two-phase flow model is probably the most suitable model for rating the cooling capacity of a J-T refrigerator operating with nitrogen-hydrocarbon mixtures.

Numerical simulation of external inertia and compressibility effects on the dynamic instabilities of two-phase boiling flows in horizontal parallel channels

Density wave oscillations and pressure drop oscillations are investigated numerically in two horizontal parallel channels using lumped parameter model assuming a homogeneous two-phase flow model. In this study the effects of external parameters, such as fluid inertia and compressible gases on the stability margins and transient behaviors of parallel channels system are analyzed. The results show, that the fluid inertia and compressible gases have high impact on the stability margins of two parallel channels; in fact, increasing the inlet inertia and outlet compressibility will increase the system stability while increasing the outlet inertia and inlet compressibility decrease its stability.

Effect of inertia and compressibility on the pressure drop oscillations of two-phase boiling flows in horizontal parallel channels

In this study, a mathematical model is developed to study Pressure drop oscillations (PDOs) in two horizontal parallel channels using lumped parameter model assuming a homogeneous two-phase flow model. This model investigates the effect of external parameters, such as fluid inertia and compressible gases, on the stability margins of PDOs. Results show that the fluid inertia and compressible gases have high impact on the stability margins of two parallel channels; in fact, increasing the inlet inertia and outlet compressibility increases system stability, while increasing the outlet inertia and inlet compressibility decreases system stability. Thus, increasing the sub-cooling number and inlet resistance coefficient improves stability behavior.

Homogeneous two-phase flow models and accurate steam-water table look-up method for fast transient simulations

The accurate simulation of fast steam-water transients requires precise algorithms for calculating fluid properties. The system of the governing flow equations must be closed with an Equation of State (EoS) to calculate the pressure as a function of the system conservative variables. For water, accurate analytical EoS for this purpose are not available yet. The aim of this paper is to show an efficient and very accurate algorithm to calculate water properties when the independent variables of the EoS are the density and the specific internal energy. Our algorithm uses a new table look-up method with bicubic interpolation based on the IAPWS-IF97 EoS formulation, and it is able to account for metastable states. The liquid metastability domain is extended until the spinodal curve, here determined and compared with other formulations.The EoS algorithm is coupled to two classical homogeneous two-phase flow models, namely the Homogeneous Equilibrium Model (HEM) and the Homogeneous Relaxation Model (HRM). HEM and HRM are used to simulate fast depressurization, waterhammer and steam explosion problems. Comparison of the numerical results with available experimental data shows the good performance of the proposed algorithms.

Dynamic flow behavior during fuel-offloaded process in control valve for unit pump fuel system

As an important part of high-pressure fuel systems, the control valve adjusts the pressure by regulating the fuel delivery quantity and the withdrawal of fuel. This study presents both experimental and numerical investigations into the flow characteristics within the control valve of a diesel unit pump fuel system (UPS). To observe the fuel flow within the control valve, an optical test rig based on a baseline UPS is built. Further, numerical simulations based on Computational Fluid Dynamics (CFD) method are conducted based on the homogenous two-phase unsteady flow model using dynamic mesh. The results show that during the valve opening period cavitation occurs, directly affecting the fuel-offloading process of the high-pressure fuel line and delaying the time for injector needle seating to cut off fuel injection. There are two cavitation regions: the conical region and the downstream of the conical region. Due to great pressure differential between the inlet and outlet of the control valve, the cavitation in the conical region induces choking flow. Once choking flow occurs, the mass flow rate maintains stable even as the pressure differential continues rising, but the discharge coefficient (Cd) declines. This choking flow increases the time delay of stop fuel injection.

Long time stability of a classical efficient scheme for an incompressible two-phase flow model

In this article we consider the implicit Euler scheme for a homogeneous two-phase flow model in a two-dimensional domain and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.

EMPIRICAL CORRELATIONS FOR SIZING ADIABATIC CAPILLARY TUBES USING CONVENTIONAL REFRIGERANTS AND THEIR ALTERNATIVES

This paper presents new empirical correlations developed by using conventional and alternative refrigerants for determining the size of adiabatic capillary tubes used in small vapor compression refrigeration systems. A homogenous two-phase flow model based on the principal equations of conservation of mass, momentum, and energy has been developed. Colebrook's and Churchill's formulations were used to determine the single-phase friction factor. Also, the two-phase viscosity models of Cicchitti et al. (1960), Dukler et al. (1964), McAdam et al. (1942), and Lin et al. (1991) were used to determine the two-phase viscosity factor. The developed numerical model that takes account of a metastable process to enhance the model was validated by using experimental data from the literature with an average error of 1.75%. This developed model that had not been employed previously by researchers was used to study the effects of relevant parameters on the capillary tube length. From these effects, empirical correlations of the capillary tube length with these dependent variables have been developed. Comparing the empirical models with experimental data from the literature showed a reasonable agreement with an average error of 3.45%. Though the empirical model developed in this study covers a large set of refrigerants, it should be used with caution by considering the range of operating conditions covered.

Empirical Correlations for Sizing Adiabatic Capillary Tube Using LPG as Refrigerant in Split-Type Air-Conditioner

This paper presents correlations for sizing adiabatic capillary tubes which serves as an expansion device in split-type air-conditioner with LPG, novel hydrocarbon (HC) mixtures of butane (HC600) and propane (HC290) as refrigerant. A homogenous two-phase flow model developed by the authors and also experimental investigation of the Liquified Petroluem Gas (LPG) refrigerant flow in adiabatic capillary tubes were used in this study. The theoretical model was used to assess various percentage compositions of these HC mixtures and validated with the experimental data. For each HC refrigerant mixture, correlations for sizing adiabatic capillary tube which contains the relevant factors, viz. capillary tube inner diameter, inlet pressure, refrigerant mass flow rate, capillary tube surface roughness and capillary tube inlet subcooling was developed. The proposed correlations were compared with the authors measured data and found to be in good agreement. Further validation was made by comparing the mass flow rates predictions of the correlations with experimental data of previous studies and found that these correlations are consistent. The correlations can be used in small vapour compression refrigeration systems working with the HC refrigerant mixtures for practical design and optimization.

Time-domain linear and non-linear studies on density wave oscillations

Density wave oscillations (DWOs) are investigated in this paper as the most representative instabilities encountered in the boiling systems. This dynamic type instability mode constitutes an issue of paramount interest for the design of industrial systems and equipments, such as steam generators and boiling water nuclear reactor cores.Suited analytical and numerical modelling tools are useful for grasping the fundamental features of this oscillation mode and for predicting the instability threshold dependence on the main system parameters. A theoretical lumped parameter model – moving boundary type – was developed, based on the integration of mass, energy and momentum 1D equations. Homogeneous two-phase flow model has been assumed within the boiling region. Theoretical predictions on DWOs have permitted to investigate the delay propagation phenomena that, in respect of the constant-pressure-drop boundary condition across the channel, trigger the development of self-sustained flow rate oscillations. Instability threshold calculation has permitted to draw stability maps (Npch−Nsub stability plane), representing e.g. the parametric effect of the inlet subcooling on the instability inception. Several sensitivity studies have permitted finally to identify in the proper simulation of two-phase frictional pressure drops the most critical issue for a correct prediction of the phenomenon.Theoretical calculations from analytical model were then successfully compared with numerical results obtained with the RELAP5 thermal-hydraulic code and the COMSOL multiphysics code. In addition to homogeneous flow model, a drift-flux model for the two-phase flow was also implemented with the latter approach.Topological characterization of DWO instability phenomena was completed by means of a linear stability analysis leading to the definition of the system eigenvalues, both dealing with the analytical model equations and with the thermal-hydraulic model developed in COMSOL. Linear analysis showed to be a quick and powerful tool generally for instability studies and in particular when addressing the influence of the two-phase friction models.

Pullback attractors for a non-autonomous homogeneous two-phase flow model

This article studies the pullback asymptotic behavior of solutions for a non-autonomous homogeneous two-phase flow model in a two-dimensional domain. We prove the existence of pullback attractors AV in V (the velocity has the H1-regularity) and AY in Y (the velocity has the L2-regularity). Then we verify the regularity of the pullback attractors by proving that AV=AY, which implies the pullback asymptotic smoothing effect of the model in the sense that the solutions eventually become more regular than the initial data. The method used in this article is similar to the one used in Zhao and Zhou (2007) [42] in the case of the non-autonomous incompressible non-Newtonian fluid in a two-dimensional domain. Let us mention that the nonlinearity involved in the model considered in this article is stronger than the one in the two-dimensional non-Newtonian flow studied in Zhao and Zhou (2007) [42].

Averaging of an homogeneous two-phase flow model with oscillating external forces

In this article, we consider a non-autonomous diffuse interfacemodel for an isothermal incompressible two-phase flow in atwo-dimensional bounded domain. We assume that the external forceis singularly oscillating and depends on a small parameter $ \epsilon. $We prove the existence of the uniform global attractor $A^{\epsilon}. $Furthermore, using the method of [13] in the case of thetwo-dimensional Navier-Stokes systems, we study the convergence of$A^{\epsilon} $ as $ \epsilon $ goes to zero. Let us mention that thenonlinearity involved in the model considered in this article isslightly stronger than the one in the two-dimensional Navier-Stokessystem studied in [13].