Critical Mass Flow Research Articles

Alternative determination of critical mass flow rate for the photovoltaic solar thermal collector in forced fluid mode

From existing equations, which have been validated by experimental measurements in the literature, the photovoltaic (PV) cell efficiency for the photovoltaic solar thermal collector (PVT), cooled by forced fluid flow, is shown to be a function of the mass flow rate. This study shows, with calculus, that there is, in general, a critical mass flow rate which corresponds to the maximum PV cell efficiency. The derived new equations are applicable to laminar regime and transition or turbulent flow regimes. These equations can yield directly the critical mass flow rate, as compared with existing methods that use observation on the results obtained by repeated computational trials.

Modeling of critical filtration regimes of vapor-liquid flow

Critical flows are widely used in power engineering. Such flows are characterized by non-stationary processes, active vaporization due to a sharp drop in pressure when the mixture flows from a high-pressure medium to an atmospheric pressure medium, which especially necessitates the study of the parameters of such flows in emergency situations, such as an emergency depressurization of a pipeline or cooling system. Due to the presence of two phases and the transiency of the processes, it is necessary to develop methods for numerical simulation of this process. The energy apparatus with a granular layer adds an additional level of complexity to the study of critical flows, namely, the effect of granular backfill on the characteristics of a two-phase flow. A new model for numerical simulation of the critical outflow of a vapor-liquid flow from a channel with a granular backfill has been created. The values of the mass flow rate of the mixture, the effect of vapor content on the critical flow rate, and the effect of geometric parameters of the granular backfill on the critical mass flow rate are obtained. The calculated data were compared with the experiment, and new data were obtained in a wider range of mass vapor content compared to experimental study.

A New Homogeneous Non-Equilibrium Model to Compute Vapor-Liquid Two-Phase Critical Pressure Ratios of Multicomponent Hydrocarbon Mixtures

The critical pressure ratio (ηc) is an essential parameter for computing the vapor-liquid two-phase critical pressure and mass flow rate of multicomponent hydrocarbon mixtures flowing through valves and leakage orifices. The Homogeneous Non-Equilibrium Diener-Schmidt (HNE-DS) model widely used to calculate ηc assumes that the fluid's volume linearly changes with the pressure (using the Clausius-Clapeyron equation), which is not suitable for multicomponent gas mixtures. In this paper, a new Homogeneous Non-Equilibrium (new-HNE) model is proposed to calculate ηc of gas mixtures. Firstly, a new critical flow compressibility factor (ωc) is developed from its thermodynamic definition and the Peng-Robinson equation of state (EOS), overcoming the inherent limitations of the Clausius-Clapeyron equation. Then, ηc is correlated to the newly derived ωc by fitting experimental data at various pressures and gas mass fractions of both single-component and multicomponent gas mixtures, yielding the new HNE-DS model. Results show that, for the water-steam and air-water two-phase flow, the average relative deviations (ARD) between the calculated critical pressure ratios and experimental values are equal to 2.8% and 4.93%, respectively, which represents a significant improvement in comparison with the original HNE-DS model. Moreover, this new model is extended to the applications of Liquefied natural gas (LNG)/liquefied petroleum gas (LPG) fluids, and will further contribute to the calculation of the leakage mass flow rate of fluid flowing through the orifices/valves.

Three-dimensional numerical simulation of gas-liquid falling film flow characteristics on the airside of finned-tube heat exchanger with a typical large fin pitch

The closed-type heat-source tower (CTHST) heat pump system is a more promising alternative to the conventional air-source heat pump (ASHP) unit compared with the open-type heat-source tower (OTHST) heat pump system. However, the heat transfer efficiency of the CTHST is significantly lower than that of the OTHST, resulting from its indirect heat transfer way, liquid film break-up and high gas phase pressure drop. To provide a theoretical basis for the heat-mass transfer enhancement and structural optimization design of the high-performance CTHST, a three-dimensional (3D) model taking gas-liquid interfacial friction force into consideration was established in the present paper to study counter-current and co-current gas-liquid falling film flow characteristics on the airside of the finned-tube heat exchanger (FTHE) with a typical large fin pitch used in the CTHST. The predicting results of liquid film thickness based on the established model show good agreement with those of experiments in the reference, with a maximum deviation less than 5%, meaning that this model is reliable. Then the effects of contact angle, air flow direction, air Reg and liquid film Rel on liquid film characteristics were studied. The prediction correlation of average liquid film thickness was presented. The pressure drop characteristics of gas phase were analyzed in the co-current gas-liquid flow under three different liquid film Rel. Meanwhile, the change law of interfacial friction force with air Reg was revealed. The numerical results show that the critical mass flow rate of complete film flow on the finned-tube surface with contact angle of 30° is 0.06 kg/(m⋅s). The average liquid film thickness on the surface of the FTHE is obviously higher than that on the vertical plate. There is a close and positive quadratic curve relation between average interfacial friction force and air Reg. To obtain a complete film flow and small air pressure drop, the air Reg should be less than 2190.7 and 3286.0 in the counter-current and co-current gas-liquid falling film flow, respectively.

Experimental Performance of a Two-Phase Ejector: Nozzle Geometry and Subcooling Effects

This paper presents the results of an experimental study on a two-phase ejector. The main objective is to assess the effects of the nozzle’s divergent and the throat diameter on performance under various working conditions. Under the same conditions, ejector operation with a convergent nozzle, results in higher critical primary mass flow rate and lower critical pressure than with a convergent-divergent nozzle version. Experiments show as well that the flow expansion is higher in the convergent-divergent nozzle. The throat diameter turns out to have an important impact only on the amount of the critical mass flow rate. The nozzle geometry has no impact on its optimal position in the ejector. Globally, the ejector with the convergent-divergent nozzle provides a higher entrainment ratio, due to a reduced primary mass flow rate and an increased secondary flow induction. Tests also show that the ejector with a lower throat diameter provides a higher entrainment ratio, due to better suction with less primary flow. Unlike the convergent-divergent nozzle, the convergent nozzle permits an entrainment ratio almost insensitive to a wide range of primary inlet sub-cooling levels. Primary and secondary mass flow rates increase proportionally with the subcooling level and result in a quasi-constant entrainment ratio.

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.

Energy, economic and environmental evaluation of a novel combined cooling and power system characterized by temperature and humidity independent control

A novel combined cooling and power system with independent control of temperature and humidity was presented to meet the energy supply demand in buildings. The energy, economic and environmental characteristics of the organic Rankine cycle powered two-stage vapor compression cycle with sixteen organic working fluids were discussed at variable geothermal fluid temperature. The results showed that organic Rankine cycle powered two-stage vapor compression cycle had certain advantages in improving refrigeration performance. Taking the critical mass flow rate as the boundary, the cooling and electricity output of the system could be controlled by adjusting the mass flow rate of refrigeration device. As far as the output power of the system was concerned, R1234yf, R134a, R600a, R600, R123 and R601 were suitable for different temperature ranges of geothermal fluids, while in terms of refrigeration performance, R1234ze, R245fa, R123, and R601 were respectively suitable for different geothermal fluid temperatures. The system with N-heptane had the optimal techno-economic performance, which electricity production cost decreases from 0.1543 $/kWh to 0.0484 $/kWh. Therefore, the novel combined cooling and power system can meet the seasonal cooling and electricity demand of the building and maximize the use of dry hot rock resources.

Dynamic thermal analysis of a residential ground-source heat pump

We present the dynamic thermal analysis of a residential ground-source heat pump (GSHP) with the following objectives: (1) to present a comprehensive GSHP model accounting for the dynamic behavior of a vapor compression unit, lumped serviced space, and the ground heat exchanger (GHE); (2) to identify a set of GHE temperature, mass flow rate, and evaporator area fraction (α) improving the time-averaged coefficient of performance (COP‾) while retaining thermal comfort in the serviced space; and (3) to propose a GHE design satisfying the desired design and operating conditions determined in (2). For a 4-ton residential GSHP considered herein, we verified the existence of a critical GHE mass flow rate of 1kg/s after which the COP‾ hardly varied. Furthermore, we observed a design trade-off between cooling and heating modes wherein a smaller α was preferred in cooling mode while the heating mode favored a higher α. Cooling COP‾ was sensitivity to both α and GHE temperature (TB), whereas that in heating mode was insensitive to TB as long as both α and Lt were sufficiently high. The optimal α impartial to both modes was 0.29 and the peak COP‾=5.49 and 3.6 in cooling and heating mode, respectively.

Experimental and theoretical investigations on reverse flow characteristics in vertically inverted U-tube steam generator under transient condition

Under natural circulation conditions, the primary circuit of a steam generator (SG) has a tendency to occur flow instabilities. These instabilities due to reverse flow in some vertically inverted U-tubes will increase the flow resistance coefficient and reduce the natural circulation ability in the primary system. To address the lack of existing research on transient reversed flow, in the present work, the reverse flow characteristics in the U-tubes of vertically inverted U-tube steam generator (UTSG) are investigated experimentally and theoretically. By gradually rising the inlet plenum mass flow of steam generator simulator at a constant fluid temperature, the reverse flow characteristics are observed in a thermal hydraulic test facility. Based on the experiment, the flow and heat transfer model in U-tubes are established to study the effects of change rate of mass flow and flow distribution on the reverse flow inside the UTSG. The experimental and theoretical results demonstrate that during the transient process, some U-tubes get reverse flow with the continuous decrease of mass flow and the reverse flow U-tubes also have a significant impact on other U-tubes, which results in a maximum temperature drop of about 35%. With the decrease of mass flow in U-tubes, the critical mass flow of the UTSG will increase and the reverse flow will occur more easily during the transient process. The results can provide a basis for avoiding the occurrence of reverse flow in actual SGs and improving the ability of natural circulation.

3D thermal-hydraulic analysis of a symmetric wavy parabolic trough absorber pipe

We analyzed a symmetric wavy parabolic trough absorber pipe using an experimentally validated 3D FEM coupled to a semi-analytical optical model. The proposed absorber design was assessed based on the first and second law efficiency as well as the performance evaluation criteria (PEC), which accounted for both heat transfer enhancement and pressure drop relative to a conventional design, as we varied the wave amplitude, periodicity length, and fluid mass flow rate. Significant improvement in the first law efficiency was observed with the proposed design, especially at high mass flow rates due to the accelerated flow across the pipe throat which in turn enhanced the mixing. The second law efficiency variation shifted from an increasing to a decreasing trend with respect to the wave amplitude as the mass flow rate increased, and the exergy destruction due to pressure drop became evident accordingly. The PEC verified the superior performance of the proposed absorber design over the traditional straight pipe as its peak value was approximately 1.25. We also determined critical wave amplitude, periodicity length, and mass flow rate below which the PEC was less than unity due to an escalated pressure drop that offset the heat transfer enhancement.

Effect of blockage ratio on the existence of multiple waves in rotating detonation engine

The effect of blockage ratio on the existence of multiple waves in rotating detonation engine was investigated through experimental approach. It has been shown experimentally that four typical detonation propagation modes (single wave, hybrid mode of single wave and double waves, double waves, longitudinal pulsed detonation) were obtained by varying blockage ratios and air mass flow rates at the global equivalence ratio of around 1.60. The results show that the increase of blockage ratio reduces the critical mass flow rate for the occurrence of multiple waves. The occurrence of multiple waves experiences coexistence of single wave and two co-rotating detonation waves, and steady two co-rotating detonation waves. The increase of blockage ratio intensifies the effect of reflected oblique shock waves on fresh reactants and elevates average pressure in the combustor, which play important role in the occurrence of multiple waves. Moreover, the increase of blockage ratio elevates the pre-combustion pressure. The high pre-combustion pressure resulting from high blockage ratio leads to the existence of volumetric explosion immediately after ignition, which extends the formation time of rotating detonation wave. Further increasing of blockage ratio triggers the longitudinal pulsed detonation (LPD), and the highly decreased injection pressure ratio is considered to be the main reason for the occurrence of LPD.

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.

CFD investigation on reverse flow characteristics in U-tubes under two-phase natural circulation

During the small break loss of coolant accident (SBLOCA) in a pressurized water reactor (PWR), single and two-phase natural circulations (NCs) as well as reflux condensation can be the three major flow modes in the primary side to remove the residual core heat. The performance of U-tube steam generators (UTSGs) during the accident is of great significance for the reactor safety and integrity. However, flow behaviors in UTSG parallel U-tubes are considerably complicated and the reverse flow phenomenon may occur during both the single and two-phase NCs. Despite the rich researches on the phenomenon occurring under the single-phase NC, studies concerning that under the two-phase NC are still quite scarce. In this paper, the vapor-liquid two-phase flow condensed in the U-tube is numerically simulated using the computational fluid dynamics (CFD) method. The distribution of vapor volume fraction αg in the U-tube is investigated and analyzed. It is shown that a negative slope region obviously exists in the curve of pressure drop versus mass flow rate, and two-phase flow excursion can occur if the mass flow rate reduces to a critical value, namely the critical mass flow rate Mc. Afterwards, some influence factors on αg and Mc are numerically studied, which include the inlet vapor volume fraction, the bubble diameter, the inlet slip ratio, the U-tube wall temperature and the primary side pressure. The results can provide references for the long-term core cooling during a SBLOCA and the optimization design of SGs.

Improved Pyrolysis Model of Polymer Materials under Windy Conditions

The polymer materials are widely used in various occasions, of which polymethyl methacrylate(PMMA) is used in architectural transparent roofs, telephone booths, stairs, and their fire risk is getting more and more attention. The ignition conditions （critical surface temperatures and critical mass flow rates） of polymer materials have extensively researched, but their internal heat transfer studies have been relatively rare, especially in wind environments. Considering that internal heat transfer research is important for the heat transfer of multi-layer materials, the study of heat transfer inside materials is also worthy of attention. In this work, we found that in-depth absorption theory is more suitable for solid pyrolysis models under wind conditions. An absorption coefficient depends with temperature are assumed, and it fits better than the constant absorption coefficient. In addition, this work made some improvements to the ignition model by employing the theory of in-depth absorption.

Whole wellbore liquid loading recognition model for gas wells

Liquid loading is a serious issue in the production of gas wells. In order to recognize liquid loading, the flow regime and the transition criteria of the gas-liquid two-phase in the wellbore were obtained by theoretical analysis. The prediction correlation for the size of the entrained droplet was given for every flow pattern. Based on the force balance condition of the largest droplet in the gas core, the dimensionless critical gas mass flow rate was defined to recognize liquid loading along the whole wellbore. The influence of different factors on liquid loading was analyzed by an example. The results show that there are three kinds of flow regime in the wellbore, which are co-current annular flow with disturbance wave torn off, co-current annular flow with bag breakup and churn-annular flow with wave under-cut. The maximum size of the droplet in the gas core depends on the droplet breakup process under co-current annular flow and droplet entrainment process under churn-annular flow. The dimensionless critical gas mass flow rate decreases with the increase of gas flow rate and the decrease of tube diameter, which reduces the possibility of liquid loading. Liquid loading can be avoided by the decrease of surface tension. The viscosities of the gas and liquid phases have slight influence on the dimensionless critical gas mass flow rate.

Impact of Shear History on Powder Flow Characterization Using a Ring Shear Tester

In this study, we have investigated the impact of repeated shear displacement on powder flow properties. We show that when multiple yield loci are obtained using the same bulk solid specimen by stepping through different stress levels (i.e., stress walk [SW]), the shear deformation of the powder in a rotational shear cell, that is, Schulze Ring Shear Tester, is maximized, reducing the powder shear strength. This approach is material and time sparing; however, it imprecisely predicts better powder flowability. The magnitude of the change in the unconfined yield strength, σc, due to this prolonged shear displacement appears to be material-dependent, being less impactful for free-flowing powders. Using the SW and the individual yield loci-generated flow properties, we have demonstrated that in hopper design, the shear displacement effect impacts the computed critical arching diameter more than the critical mass flow angle. This knowledge of powder flow properties highlights limitations associated with the SW. An exponential function was found to describe the relationship between the change in σc at the highest major principal stress and the density weighted flowability, ffρ, with an R2 of 0.98. Such a model could be a valuable tool for correcting shear strength results obtained from SW, saving time, and material.

Investigation on reverse flow phenomena in UTSGs under two-phase natural circulation with low steam quality

The reverse flow phenomenon is disadvantageous for the normal operation and the reactor safety, which can occur in some tubes of an inverted U-tube steam generator (UTSG) under both single and two-phase natural circulations (NCs). Despite the rich studies of reverse flow behavior under the single-phase NC, special and in-depth investigations concerning that under the two-phase NC are far from enough. Using the system analysis code RELAP5/MOD3.3, the reverse flow phenomenon in a UTSG under the two-phase NC with low steam quality is simulated and analyzed in this paper. The effects of secondary side temperature and inlet mass quality on this phenomenon are also studied. Based on the theoretical model for calculating the two-phase flow and heat transfer characteristics in the U-tubes, the mechanism explanations of the simulation results are given. The conclusions show that the reverse flow firstly occurs in the longest U-tube. The mass flow rates in the normal flow U-tubes will increase and the inlet temperatures of these U-tubes will decrease when the reverse flow appears. With the increase of secondary side temperature or the decrease of inlet mass quality, both the critical mass flow rate (CMFR) of steam generators (SGs) and the CMFR of U-tubes will decrease, thus the reverse flow can be effectively reduced. The reverse flow phenomenon under the two-phase NC will be more easily to occur compared with that under the single-phase NC.

Mechanisms performance and pressure dependence of hydrogen/air burner-stabilized flames

The kinetic mechanism of hydrogen combustion is the most investigated combustion system. This is due to extreme importance of the mechanism for combustion processes, i.e. it is present as a sub-mechanism in all mechanisms for hydrocarbon combustion systems. Therefore, detailed aspects of hydrogen flames are still under active investigations, e.g. under elevated pressure, under conditions of different heat losses intensities and local equivalence ratios etc. For this purpose, the burner stabilized flame configuration is an efficient tool to study different aspects of chemical kinetics by varying the stand-off distance, pressure, temperature of the burner and mixture compositions. In the present work, a flat porous plug burner flame configuration is revisited. A hydrogen/air combustion system is considered with detailed molecular transport including thermo-diffusion and with 8 different chemical reaction mechanisms. Detailed numerical investigations are performed to single out the role of chemical kinetics on the loss of stability and on the dynamics of the flame oscillations. As a main outcome, it was found/demonstrated that the results of critical values, e.g. critical mass flow rate, weighted frequency of oscillations and blow-off velocity, with increasing the pressure scatter almost randomly. Thus, these parameters can be considered as independent and can be used to improve and to validate the mechanisms of chemical kinetics for the unsteady dynamics.

Numerical Simulation of Supercritical Carbon Dioxide Critical Flow in the Nozzle Tube

The supercritical carbon dioxide (S-CO2) Brayton gas turbine cycle has been studied as an efficient and cost-effective option for advanced power systems. One major safety issue for any power cycle is a pipe break and the associated discharge of the working fluid and subsequent decrease in system pressure. In this paper, an S-CO2 critical flow in the nozzle tube is analyzed numerically with fluent 15.0. The Redlich–Kwong real gas equation is selected to calculate carbon dioxide density and the standard k-epsilon turbulence model is selected. Experimental data are used as a benchmark to examine the capability of the current approach. Compared with experimental data, the simulation results overestimate the critical mass flux; the error range is between 15% and 25%. The simulation results show that as L/D increases, critical mass flow decreases. As stagnation temperature increases, critical mass flow decreases. The complex thermal hydraulic behavior in the nozzle tubes is analyzed. Three flow patterns in the nozzle tube during transient critical flow are obtained and discussed. From inlet to outlet of the tube, CO2 may undergo the following phases in turn: (1) supercritical phase; (2) supercritical phase—gas phase; (3) supercritical phase—gas phase—liquid phase. The simulation results are also helpful for further experimental and theoretical research.

저급탄 건조공정이 결합된 석탄화력 발전플랜트의 성능해석

Low rank coals are cheaper than high rank coals but are seldom used as fuel for coal fired power plants directly because they have several adverse effects including a lower plant efficiency due to the large energy loss by the latent heat of water content. In this study, the combination of the coal drying technology with the coal power plant was analyzed as a way to enhance the usefulness of the low rank coal. In the combined system, some of the extracted steam for feed water heating was used for coal drying. The influences of steam extraction location and amount of drying coal on the power plant performance were investigated. It was found that the system power was nearly insensitive to the mass flow rate of the drying coal until a certain point but then it began to decrease over the critical mass flow rate. The thermal efficiency decreased with increasing mass flow rate but the rate of decrease slightly is reduced over the critical value. In addition, we researched the influence of coal drying strategy on the power plant performance.