Flashing Flow Research Articles

CFD-based shape optimization of flashing converging-diverging nozzles in pelton turbines for domestic carbon dioxide heat pumps including off-design conditions

A path to enhance the coefficient of performance (COP) of domestic heat pumps is to replace the throttling valve with a turboexpander. Designing this component requires addressing supersonic flashing flows localized within the nozzle. In particular, two-phase flows prevent the application of the method of characteristics to design efficient converging–diverging shapes. To overcome this issue, we propose a shape optimization combined with a homogeneous equilibrium flow model as a design tool. Kriging models are used as surrogates of the objective function and constraint to reduce the overall computational burden associated with shape optimization. The infilling criterion to improve surrogate accuracy involves the maximization of the constrained expected improvement. A multi-point optimization is formulated, including design and off-design conditions in both objective and constraint, for a total of four relevant operating conditions. The off-design conditions are derived from system analysis, accounting for variations in the evaporator temperature and outlet gas-cooler temperature. The optimized nozzle results in a COP improvement of 7.6%, compared to a 6.6% increase when replacing the throttling valve with a baseline geometry designed as recommended by the literature. The adoption of a multi-point optimization strategy ensures that this enhancement in design conditions is not offset by off-design performance decay, which is 0.3 percentage points over the three off-design conditions. Overall, replacing the throttling valve with the optimized expander leads to an average COP improvement of 8.6%.

Calibration and validation of a modified non-equilibrium boiling model for transcritical flashing flow in two-phase R744 nozzles

A modified homogeneous non-equilibrium boiling approach (HNB) was proposed for high-fidelity modelling of the trans-critical flashing process in two-phase R744 ejector nozzles. In the modified approach, the method of determining the metastable liquid saturation pressure was improved by integrating the metastable liquid enthalpy. Experimental tests were conducted on two different nozzles to calibrate the lumped accommodation coefficient in the modified HNB. The calibration dataset consisted of 30 trans-critical test points, with the motive inlet pressure ranging from 7.5 MPa to 11.5 MPa and temperature varying from 21 °C to 45 °C. It was demonstrated that the boiling coefficient was strongly related to nozzle inlet pressure and specific enthalpy. The coefficient was therefore fitted as a function of the operating condition. The modified HNB with the fitted function was then validated against another set of test data composed of 29 test points. The results demonstrated that the relative errors of the nozzle mass-flow rates were within 3 %. Finally, the modified HNB with the improved metastable liquid saturation pressure was compared and discussed with the existing HNB approach in the literature.

A flashing flow model for the rapid depressurization of [formula omitted] in a pipe accounting for bubble nucleation and growth

Flashing flow is encountered in many industrial systems involving nozzles, valves and decompression of vessels and pipes. In the context of CO2 capture and storage (CCS), the design of safe and efficient CO2 transportation systems requires accurate flashing models, e.g., for safety analysis of pipe fractures and to predict the mass flow through relief valves. We propose a homogeneous flashing model (HFM) for flashing flow accounting for the underlying physical phenomena of the phase change: bubble nucleation, coalescence, break-up and growth. Homogeneous nucleation is modeled using classical nucleation theory and heterogeneous nucleation is approximated with constant rates of bubble creation and mass transfer from liquid to vapor. The flashing flow model is fitted for CO2 pipe depressurization data at various initial conditions. We find that the same, constant model parameters can be applied for the whole set of depressurization cases considered, as opposed to the conventional homogeneous relaxation model which typically is tuned on a case-by-case basis. For depressurization paths where the fluid state passes close to the critical point, we demonstrate that an accurate description of the flashing process along the length of the pipe can only be achieved when both homogeneous and heterogeneous nucleation are accounted for.

Extension of the delayed equilibrium model to flashing flows of organic fluids in converging-diverging nozzles

Flashing flows of organic fluids find application in various energy systems, but the available modelling approaches rely on semi-empirical correlations calibrated for other fluids and operating conditions. This paper extends the state-of-the-art one-dimensional models developed for water to flashing of organic fluids, using R134a as a reference. First, the delayed equilibrium model combined with Grönnerud's friction correlation is identified as the most appropriate approach, reducing the error on mass flow rate with respect to experimental results from 48.3 %, obtained with the homogeneous equilibrium model, to 10.3 %. Then, the traditionally adopted incompressible flow assumption for the metastable liquid phase is replaced by a dedicated thermodynamic model, preventing the appearance of unphysical metastable phase temperatures. Moreover, the delayed equilibrium model is tailored to R134a by tuning the semi-empirical coefficients of the constitutive law. The proposed modifications to the state-of-the-art delayed equilibrium model result in an improvement in the prediction of the pressure profiles and the mass flow rate for flashing flows of R134a, with a decrease in the error on mass flow rate from 10.3 % to 6.1 % with respect to the original formulation.

Modelling of liquid oxygen and nitrogen injection under flashing conditions

The present numerical investigation of two-phase flashing flows examines the injection of liquid oxygen and liquid nitrogen into near-vacuum conditions prevailing in the upper-stage boosters of rocket engines. The predictive capability of a pressure-based solver and a density-based solver, each employing distinct approaches related to the imposed phase-change rate and thermodynamics closure, has been comparatively evaluated. Regarding the pressure-based solver, the departure from thermodynamic equilibrium during phase-change has been taken into account via the implementation of a bubble-dynamics model employing the Hertz-Knudsen equation. In contrast, the density-based solver relies on the adoption of thermodynamic equilibrium while real-fluid thermodynamic properties are assumed by loading tabulated values to the solver. Each thermodynamic property value was calculated in advance by solving the Helmholtz Equation of State (EoS) for a wide range of density and internal energy conditions. Numerical findings have been compared against experimental data available in the literature. The comparison demonstrates the capability of both methodologies in capturing the evolution of cryogenic flashing flow expansion, phase-change, and spray formation. The salient features identified in the numerical results, i.e., the expansion sphere immediately downstream of the injector exit, the bell-shaped topology of the spray, as well as the dependency of the spray cone angle on superheat, are in agreement with experimental measurements. Especially the density-based approach has been proven highly accurate with respect to the steady expanding flow described by a level of superheat in the range of 3 to 245, while also being independent of any parameter tuning.

Numerical Simulation of Flashing Flows in a Converging–Diverging Nozzle with Interfacial Area Transport Equation

Flashing flows of initially sub-cooled water in a converging–diverging nozzle is investigated numerically in the framework of the two-fluid model (TFM). The thermal non-equilibrium effect of phase change is considered by an interfacial heat transfer model, while the pressure jump across the interface is ignored. The bubble size distribution induced by nucleation, bubble growth/shrinkage, coalescence, and breakup is described based on the interfacial area transport equation (IATE) and constant bubble number density model (CBND), respectively. The results are compared with the experimental data. Satisfactory prediction of the axial pressure distribution along the nozzle as well as the flashing inception, is achieved by the TFM-IATE coupling method. It was also found that the vapor production in the diverging section was overpredicted, and the radial gas volume fraction distribution deviated from the experiment. The radial diameter profiles exhibit opposite patterns at the nozzle throat and near the outlet, and similar trends can be observed for the superheated degree. A poly-disperse method is suggested to be introduced to describe the evolution of interfacial area concentration.

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.

Numerical investigation on the performance of transcritical CO2 two-phase ejector with a novel non-equilibrium CFD model

Flashing flow in the transcritical CO2 ejector was simulated using a novel non-equilibrium evaporation-cavitation CFD model. The novel model was verified using the experimental results of three ejectors with nozzle diverging angles (NDAs) of 0°, 2.00° and 6.70°. Furthermore, the effects of dimensions of mixing chamber and diffuser on the ejector performance were disclosed. The results suggested that prediction errors of secondary flow mass flow rate using the proposed model were less than 9%, and the maximum error of primary flow mass flow rate was within the range of 15%, which was much smaller than that of −34.55% predicted by homogenous equilibrium model. The results also showed that the mass transfer rates increased with increasing NDAs, and the maximum mass transfer rate of evaporation was approximately 3–13 times that of cavitation as the NDAs increased from 0° to 6.70°, proving evaporation dominates the flashing process in the CO2 ejector. Besides, the results showed that the entrainment ratio increased first and then decreased with increasing the mixing chamber width, mixing chamber length and diffuser angle, and the entrainment ratio was improved by 36.55%. This study is helpful to understand flashing mechanisms inside the CO2 ejector and improve the ejector performance.

Computational study of two-phase flashing flow in a calcite scaled geothermal wellbore

This work presents a computational study to understand different heat transfer and phase transition processes of two-phase flow in a geothermal wellbore. The simulation uses a six-equation model with mass, momentum, and energy balance equations for the liquid and vapour phase, which is available in Ansys Fluent. The model considers the effect of phase transition due to flashing, caused by thermal non-equilibrium at the liquid-vapour interface. Two wellbore scenarios, one with a constant inner diameter and the other a variable inner diameter along the flow direction due to calcite scaling, were simulated using the model. Comparison of the simulation results with measured pressure log data shows good agreement. Simulation studies for the fluid flow in a wellbore with variable diameter occurring due to calcite scaling shows higher mass transfer rate and wall normal bubble flux in the region of scaling, resulting in higher chances of mineral precipitation and deposition in the same region.

Flashing flow in the rotating curved channels with variable cross-section of a two-phase flow turbine

The rotating flash flow has rarely been studied, although its characteristics affect significantly the performance of the two-phase flow turbine. In this paper, through analyzing the flashing flow obtained by CFD methods, which is validated with the experimental data, the relationships of average flow parameters under various rotational speeds were studied theoretically and numerically using the flow equations established on the Frenet coordinate system. The ratio of the mass flow rate under various rotational speeds was formalized and found to be dependent on the rotational speed and thermophysical properties. The generation and development of vapour were revealed and correlated to the geometry of the channel. The secondary flow in the flashing rotating channel was discussed and found to rotate in opposite directions upstream/downstream of the throat. The flashing induced near the throat had the effect on flow homogenizing in the normal direction of the cross-section. The analysis could be further applied to the analogy of the secondary flow between the rotating single-phase flow and the rotating flashing flow.

Investigation of Flashing Flow in a Siphon to Extract Condensate in Paper Dryer Application

Abstract The paper industry uses steam to dry paper web through cylinder dryers. As steam condenses inside the dryer, the condensate is removed by means of either a stationary or a rotary siphon. However, during the siphoning process for transporting the condensate, flashing of the condensate occurs, which could cause backflow or discontinuity in the siphoning process. To resolve this flashing issue, two approaches have been employed: (a) increasing the amount of steam supplied to the cylinder to “blow-through” the stalled condensate–steam mixture and (b) reducing the back pressure by inducing “suction” through a thermocompressor from downstream. The objective of this study is to investigate and improve understanding of the flashing phenomena during condensate transport through the siphon and piping system in order to develop means to reduce the excessive steam consumption during the paper drying process. A computational fluid dynamics (CFD) simulation is performed that uses the Eulerian–Eulerian multiphase method. The steady-state case is first solved to obtain the flow field without flashing. Then, the transient method is initiated by employing evaporation and condensation model. The results show that reduction of local pressure triggers flashing; however, flashing in turn reduces local temperature and subsequently induces condensation, resulting in an alternating flashing and condensation behavior. To maintain continuity of the siphon flow, the inlet pressure fluctuates corresponding to the variation of total vapor volume ratio inside the siphon. The results will be used to modify the current siphon system design and operating practices to reduce the steam consumption.

A developed analytical model for the pressurizer unit in nuclear power plants

ABSTRACT The pressure control in the pressurized water reactor (PWR) primary loop is key to secure the safe operation. The pressurizer (PZR) unit is responsible for attaining this task. Thus, the PZR unit’s modeling is an important issue for the tracking control purpose and performance analysis concerning the turbine load. This paper develops a mathematical model to accurately predict the PZR unit pressure in the normal and load power changes. The model is a non-equilibrium three region model developed based on the thermodynamics of mass and energy for the water and steam in the PZR. The variations of the pressure and the temperature due to thermodynamic variables (enthalpy, density) and the mechanical work effect are considered in the developed model. The model also addresses other thermodynamic processes such as bulk flashing, spray condensation, interface condensation, wall condensation, and rainout flow. The inlet and outlet flow rates of the primary circuit (PC) and the average temperature and the hot leg temperature are included in the developed model. Based on data generated from the VVER-1200 simulator, parameter estimation, verification, and validation of the developed model through load power changes are achieved. Besides, a comparison with other models given in literature has been performed. This comparison indicated that the developed model is more sensitive against the minimum variation of PZR dynamics. Finally, a closed-loop PZR pressure control system, including a conventional Proportional Integral Derivative (PID) controller, was designed to test the control purpose’s developed model. The simulation results over typical load change transients have been demonstrated the feasibility, effectiveness, and accuracy of the developed nonlinear model of PZR for dynamic modeling and control purposes.

Numerical prediction of transient hydraulic loads acting on PWR steam generator tubes and supports during blowdown following a feedwater line break

This paper presents a numerical prediction of the transient hydraulic loads acting on the tubes and external supports of a pressurized water reactor (PWR) steam generator (SG) during blowdown following a sudden feedwater line break (FWLB). A simplified SG model was used to easily demonstrate the prediction. The blowdown discharge flow was treated as a flashing flow to realistically simulate the transient flow fields inside the SG and the connected broken feedwater pipe. The effects of the SG initial pressure or the broken feedwater pipe length on the intensities or magnitudes of transient hydraulic loads were investigated. Then predictions of the decompression pressure wave-induced impulsive pressure differential loads on SG tubes and the transient blowdown loads on SG external supports were demonstrated and the general aspects of transient responses of such transient hydraulic loads to the FWLB were discussed.

Numerical and experimental analysis of flashing cryogenic nitrogen

The development of new upper orbit thrusters using cryogenic propellants requires an improved understanding of the dynamics of oxidizer and fuel injection at near vacuum conditions before ignition. Due to the low ambient pressure, the propellants enter a superheated state and flash evaporation occurs. Flash boiling of cryogenic liquid nitrogen is studied experimentally on the newly developed test bench at DLR Lampoldshausen and numerically with a newly developed OpenFOAM© solver. Here, a one-fluid approach is selected where phase properties, such as density, enthalpy and saturation conditions are determined with the thermodynamic library CoolProp and tabulated before runtime. The phase change is modeled by the homogeneous relaxation model. For highly superheated jets the flow becomes supersonic and forms a shock after the injector outlet. The solver is validated with the aid of flashing acetone spray experiments where the shock structures are more clearly visible. The results show that the developed solver is capable to predict the all important gas dynamics by matching shock structure and spray angle to the experiment. The experiments using cryogenic liquid, however, do not reveal any shock structures but regions with low negative axial velocities can be identified on the jet centerline. A comparison with the simulations now demonstrates that shocks continue to persist but the respective shadowgraph signals may be obscured in these flows. The joint experimental and numerical study thus provides a consistent understanding of the observed flow features that govern the fluid dynamics and jet breakup of cryogenic flashing flows.

Development of Delayed Equilibrium Model for CO2 convergent-divergent nozzle transonic flashing flow

The one-dimensional implementation of the Delayed Equilibrium Model (DEM) is known as a relatively simple yet accurate approach for prediction of critical mass flow rate, pressure and void fraction distributions for two-phase water transonic flows in ducts of variable geometry. However, the direct application of DEM equipped with original saturation index evolution law and Lockhart-Martinelli approach (the original setup) is incapable of accurate prediction of CO2 transonic flow. Moreover, the Darcy friction factor approach has a significant impact on the simulation results. Consequently, this paper presents a new law of the saturation index evolution and a new frictional pressure gradient approach for CO2 transonic two-phase flows together with experimental validation and discussion of obtained data. A comparative analysis of the developed DEM setup and the referential Homogeneous Equilibrium Model revealed that application of the proposed approaches decreases the mean maximal discrepancy between experimental and calculated static pressure values by a factor of app. 2, with simultaneous decrease of the standard deviation by a factor of app. 4. That proves that both the frictional pressure gradient approach and the proper introduction of the thermal non-equilibrium effects are substantial for accurate modelling of the flashing process in CO2 flows.

Experimental and theoretical study on fluid-structure interaction and non-equilibrium of the flow through micro cracks

To figure out the flow characteristics through cracks with narrow and short passage, experimental and theoretical studies were conducted in this study. The leakage flow phenomena such as crack opening enlargement, partial flashing and actual flow region were discovered during the test. The mechanism models were proposed according to the test results. Mechanical model on the COD (crack opening displacement) variation was presented considering the fluid-structure interaction; the entrance resistant coefficient model for cracks was raised, which elaborates the dependence of entrance resistance on stagnation condition and crack opening; non-equilibrium model based on flashing fraction and flashing inception was put forward, taking partial flashing and choking into account; for circumferential crack, flow region was suggested, which increases with stagnation temperature. The above models have been validated and evaluated by the experimental results of this study and from literature. It was proved that, by considering the detailed flow phenomenon and characteristics for cracks with extreme narrow and short passage, these mechanism models significantly improve the prediction accuracy. This study provides a large enhancement on the understanding and prediction of choked flow though micro cracks.

Numerical study on the thermal-hydraulic characteristics of the choked flow through micro cracks for various conditions

It’s of great significant to figure out the detailed mechanisms of the leak flow through micro-crack. Three-dimensional numerical simulation provides a visual and effective access to elaborate the complex leak phenomena and characteristics by taking advantages of full-size crack passages modeling. In this study, three-dimensional numerical simulation was developed by establishing geometrical and thermal-hydraulic models. The crack morphologies (COD, crack length, crack depth and cross section) were simulated, and various thermal-hydraulic conditions (liquid, superheated vapor, supercritical fluid and multiphase) were considered. The numerical method was validated by the experimental results both from this study and literatures. What’s more, the leak flow phenomena such as flow pattern, compression, flashing and choking were obtained based on the validated numerical simulation. Influences of crack morphologies and thermal-hydraulic parameters on flow characteristics were analyzed. The flow mechanisms of flashing, phase interaction and critical flow were elaborated using the three-dimensional numerical method. This study gives a comprehensive and thoughtful investigation on the choked flow through micro-crack, revealing the detailed thermal-hydraulic phenomena and mechanisms of the flow through micro cracks for various crack morphologies and conditions. Therefore, this study provides an effective approach and a theoretical foundation for understanding the choked flow mechanisms through cracks.

Prediction of critical mass rate of flashing carbon dioxide flow in convergent-divergent nozzle

The prediction of a critical mass flow rate of flashing flow is of crucial importance for many applications in chemical and processing apparatus. One of the most prosperous application is the two-phase ejector as a device with flashing liquid phase as a motive fluid and vapour phase as a secondary fluid. In that case the prediction of critical flashing flow mass flow rate is necessary. A new generalised procedure of the transonic trajectory determination that uses enhanced Possible-Impossible Flow algorithm is proposed. The procedure is much faster than the commonly used Newton Critical Point (NCP) approach. The approach was applied in modelling of carbon dioxide transonic two-phase flow through the convergent-divergent nozzle by means of Homogeneous Equilibrium Model (HEM) and Delayed Equilibrium Model (DEM). These models were used to simulate flows that were experimentally and theoretically investigated in literature. The application of DEM model for determination of the supersonic trajectory part for CO2 flow is a novel contribution provided in the paper. The comparison with literature experimental data revealed that the original closure equations developed for water are improper for CO2 transonic flows, thus the adjusting attempts were demonstrated. It was revealed that the applied Darcy friction factor determination approach significantly influences on the results. Moreover, an effective DEM adjustment is impossible until Lockhart–Martinelli approach is utilised. It was shown that for CO2 case Darcy friction factor calculated by means of Friedel approach is more appropriate than the one calculated by means of the commonly used Lockhart–Martinelli approach. Nevertheless, it was demonstrated that using a frictionless approach would still give better results while adjusting DEM to better approximate the experimental pressure distributions.

Analysis of Xenon Flashing during On-orbit Refueling Process

On-orbit Refueling of liquid xenon can prolong life of the electric propulsion system. Subcooled liquid xenon easily evaporates to form two-phase flow owing to reduction in pressure against continuing refueling. This paper investigates the steady flashing flow characteristics of xenon during the process of on-orbit refueling based on one-dimensional homogenous equilibrium model. Two phases are seen homogeneously without the discrepancy of pressure, temperature and velocity between liquid and vapor. One-dimensional fluid equations are discrete by the finite difference method. Distributions of pressure, dryness, void fraction, temperature and velocity are calculated in the condition of given inlet pressure, subcooling and mass flux. Effect of heat flux on two-phase flow is obtained. The results can help us better understand two-phase flow characteristics of xenon during the process of on-orbit refueling and design on-orbit refueling system of liquid xenon.

CFD analysis of the flashing flow characteristics of subcritical refrigerant R134a through converging-diverging nozzles

A CFD-based numerical analysis of the choking flashing flow characteristics in R134a converging-diverging nozzles is presented in this paper. The CFD results are validated with available experimental data of R134a converging-diverging nozzles. After that, the critical mass flux and effects of geometric dimensions on the performance of converging-diverging nozzles are investigated. Furthermore, the calculated critical mass fluxes are compared to that of the classical models. Results show that the metastable state in R134a converging-diverging nozzle is weaker than that of water at the same operating parameters and a higher choking correction factor of R134a compared to that of water is obtained. The optimum ratio of nozzle exit diameter to the throat diameter of 2.4 is recommended among the studied nozzle geometry dimensions. Effect of the divergent length on the nozzle flow characteristics is relatively smaller than that of the nozzle exit diameter.