Steady-state Mass Flow Rate Research Articles

Steady state performance of molten salt natural circulation loop with different orientations of heater and cooler

Molten salts are proposed as a coolant and sensible heat storage medium for Solar Thermal Power Plant (STPP) as well as fuel and coolant for Molten Salt Reactor (MSR). The objective of the present study is to investigate the steady state behavior of molten salt in natural circulation flow condition along with effect of different orientations of heater and cooler on the steady state mass flow rate. For which a Molten Salt Natural Circulation Loop (MSNCL) has been setup with molten nitrate salt (mixture of Sodium Nitrate and Potassium Nitrate in 60:40 ratio by wt.) as working fluid. Steady state experiments in four different orientations of heater and cooler [Horizontal Heater Horizontal Cooler (HHHC), Horizontal Heater Vertical Cooler (HHVC), Vertical Heater Horizontal Cooler (VHHC) and Vertical Heater Vertical Cooler (VHVC)] have been performed and data generated are compared with the steady state correlations available in open literature which are derived considering either standard friction factor correlations or friction factor correlations deduced from their experiments and theoretical studies. Based on the deviations observed in the experimental values and correlation predictions, an improved formulation has been derived. The steady state formulation has been improved by incorporating Wall Thermal Inertia (WTI) effect and Heat Loss (HL) effect considering the importance of WTI & HL in dealing with high temperature molten salt loop. The improved formulation has been compared with the experimental results for different orientations of heater and cooler. Further, a new friction factor correlation has also been deduced from the experiments for vertical heater orientation. Description of MSNCL along with validation studies performed for different steady state correlation against experimental data generated in MSNCL, are reported in this paper.

Effect of geometrical and operating parameters on performance of a rectangular two-phase natural circulation loop

Natural Circulation Loops (NCLs) find application in a wide range of engineering devices and it is often necessary to predict and ensure the performance of such loops under various operating conditions. In this paper analytical expressions are presented in non-dimensional form for steady-state mass flow rate in typical rectangular, two-phase natural circulation loops having Vertical-Heater Vertical-Cooler (VHVC) and Vertical-Heater Horizontal-Cooler (VHHC) configurations. The normalized loop mass flow rates are expressed in terms of several geometrical and operating variables such as, normalized heat input, density ratio, volume/diameter of heater and cooler sections, aspect ratio of loop, inlet subcooling, fractional length of heater and cooler sections, two-phase friction multiplier and the loss coefficient at heater inlet. The analytical mass flow rate expressions are first validated using published data for various loops and shown to reasonably capture the gravity and friction dominated regimes in two-phase pipe flow. Parametric studies are then conducted to elucidate the effect of key variables on steady-state loop mass flow rates. For the chosen geometrical configuration of the loops, the possibility of existence of multiple steady-state solutions is checked for the entire range of values used in this study for each variable. The discussions in this paper are limited to explaining the influence of individual variables by comparing with a base case analysis.

Effect of heater and condenser orientations on fluid flow behaviour in a two-phase natural circulation loop

A Numerical investigation on the influence of heater and condenser orientation and its location on steady state performance of a Two Phase Natural Circulation Loop (TPNCL) is presented. In the present study, four possible orientations are considered in TPNCL namely, Vertical Heater and Vertical Condenser (VHVC), Vertical Heater and Horizontal Condenser (VHHC), Horizontal Heater and Horizontal Condenser (HHHC) and Horizontal Heater and Vertical Condenser (HHVC). An in house MATLAB code is developed to solve the systems of equations. Homogeneous equilibrium model (HEM) is used in two phase regions. It is observed that steady state mass flow rate of the loop is significantly influenced by the developed pressure gradient in the riser and downcomer sections, as well as available vapour quality in the riser section. Moreover, it is also noticed that condenser position and orientation significantly effects the thermo-hydraulic characteristic of loop compared with heater orientation.

Effects of various modeling assumptions on steady-state and transient performances of single-phase natural circulation loop

It is necessary to investigate the relative effect of various phenomena before neglecting the same for simulating the single-phase natural circulation loop to obtain an acceptable prediction. Hence, the present study focuses on the validation and effect of different assumptions related to Boussinesq approximation, property variation, bend effect, heat loss, axial fluid and wall conduction on the transient and steady-state characteristics. Effect of assumptions for different working fluids (water, brines and hybrid nanofluids), and assess the effect of different heat flux distributions, like uniform, linear, non-linear, sinusoidal and Gaussian, applied to heater are also explored. Mass flow rate (predicts heat transport capability), effectiveness (predicts heat transfer ability) and entropy generation rate (predicts irreversibility) are evaluated. The results disclose that the Boussinesq approximation with constant other properties under-predicts the steady-state mass flow rate and effectiveness and over-predicts the entropy generation rate. This assumption cannot be applied for all working fluids. The fluid and solid conduction is the crucial parameter for simulating transient characteristics. Gaussian heat flux distribution shows the highest mass flow rate and non-linear increasing heat flux shows the highest effectiveness and entropy generation rate. This study will help to consider reasonable assumptions for the numerical simulation.

Single-Phase Natural Circulation Loop Using Oils and Ternary Hybrid Nanofluids: Steady-State and Transient Thermo-Hydraulics

Abstract Steady-state and transient behaviors of single-phase natural circulation loop (SPNCL) are investigated using four thermal oils (Therminol VP1, Paratherm CR, Dowtherm A, and Dowtherm Q) and water-based ternary hybrid (various combinations of different nature and shaped nanoparticles: Al2O3, Cu, carbon nanotube (CNT) and graphene) nanofluids as loop fluid. The influences of nanoparticle volume concentration and loop height-to-width ratio on the mass flow rate and total entropy generation rate of SPNCL are investigated. Results disclose that ternary hybrid nanofluids enhance flow initiation, reduce fluctuation and are expected to attain a steady-state faster than water. Steady-state mass flow rate increases/decreases for ternary hybrid nanofluid depending on the shape of the nanoparticle, and the total entropy generation rate decreases as compared to water. Thermal oil shows a higher mass flow rate and total entropy generation rate as compared to water. Al2O3–Cu–CNT–water and Paratherm CR show the best result among all ternary hybrid nanofluids and thermal oils, respectively. The nanoparticle shape decides the optimum nanoparticle volume fraction. Increasing the height-to-width ratio decreases the total entropy generation and upsurges the mass flow rate at specified input power. The optimum height-to-width ratio depends on the loop fluid.

Numerical analyses of high temperature dense, granular flows coupled to high temperature flow property measurements for solar thermal energy storage

High temperature particle flow properties necessary to predict granular flow behavior for solar thermal energy storage applications were measured and calculated for Carbobead CP 30/60 up to 800 °C. The measured properties included elastic and shear moduli, particle–particle coefficients of static sliding and rolling friction, and particle–particle coefficients of restitution. Poisson’s ratio was calculated with elastic and shear moduli. The flow properties were used as inputs for a numerical model using the discrete element method to examine granular flows along an inclined plane at high temperature. The flow behavior was strongly influenced by the coefficients of static friction, which impacted the particle residence time, shear effects from the side walls, and particle flow mass flux. An 8.7%, 15.6%, and 8.5% increase and 37.9% decrease in steady state mass flow rate was observed for 200 °C, 400 °C, 600 °C, and 800 °C, respectively, when compared to room temperature simulations. A 52%, 59%, and 33% decrease in the time to reach steady state was observed for 200 °C, 400 °C, and 600 °C, respectively, while a 53% increase in time was observed for 800 °C. A significant delay in the flow development at 800 °C was observed due to significantly higher frictional forces.

Analysis of a single-phase natural circulation loop with hybrid-nanofluid

Abstract A rectangular single-phase natural circulation loop (NCL) has numerous industrial applications such as nuclear reactors, geothermal systems, solar water heating systems, gas turbine blade cooling, electrical machine rotor cooling, and electronic device cooling. To establish the heat transport capability of a NCL, it is important to realize the mass flow rate. Commonly, water has been considered as working fluid. In this paper, a hybrid nanofluid (Al2O3-Cu-water) is considered as working fluid. Firstly, the governing equations are written for the NCL. Then the dimensionless form of governing equations are solved. The influence of cooler length, heater length, tubes diameter, loop height, loop inclination angle, the concentration of nanoparticles, the power of the heater and the type of working fluid on the loop temperature distribution and loop mass flow rate are scrutinized. The results illustrate that the steady-state mass flow rate goes up with augmenting the heater power, the loop height, the loop diameter and the concentration of nanoparticles whereas it abates with rising the loop inclination angle. The results discovered that the steady-state mass flow augments 34.8% if the loop diameter increases 20% at ϕ = 2%. Also, the Reynolds number reaches a maximum value (Ress = 1303.5) at ϕ = 6% for hybrid nanofluid.

Steady-State Energetic and Exergetic Performances of Single-Phase Natural Circulation Loop With Hybrid Nanofluids

Energy and exergy performances of natural circulation loop (NCL) with various water-based hybrid nanofluids (Al2O3 + TiO2, Al2O3 + CNT, Al2O3 + Ag, Al2O3 + Cu, Al2O3 + CuO, Al2O3 + graphene) with 1% volumetric concentration are compared in this study. New thermophysical property models have been proposed for hybrid nanofluids with different particle shapes and mixture ratio. Effects of power input, loop diameter, loop height, loop inclination and heater/cooler inclination on steady-state mass flow rate, effectiveness, and entropy generation are discussed as well. Results show that both the steady-state mass flow rate and energy–exergy performance are enhanced by using the hybrid nanofluids, except Al2O3 + graphene, which shows the performance decrement within the studied power range. Al2O3 + Ag hybrid nanofluid shows highest enhancement in mass flow rate of 4.8% compared to water. The shape of nanoparticle has shown a significant effect on steady-state performance; hybrid nanofluid having cylindrical and platelet shape nanoparticles yields lower mass flow rate than that of spherical shape. Mass flow rate increases with the increasing loop diameter and height, whereas decreases with the increasing loop and heater/cooler inclinations. Both effectiveness and entropy generation increase with the decreasing loop diameter and height, whereas increasing the loop and heater/cooler inclinations. This study reveals that the particle shape has a significant effect on the performance of hybrid nanofluids in NCL, and the use of hybrid nanofluid is more effective for higher power.

Integrated coordination scheduling framework of electricity-natural gas systems considering electricity transmission N\u2009\u2212\u20091 contingencies and gas dynamics

This paper discusses a security-constrained integrated coordination scheduling framework for an integrated electricity-natural gas system (IEGS), in which both tight interdependence between electricity and natural gas transmission networks and their distinct dynamic characteristics at different timescales are fully considered. The proposed framework includes two linear programming models. The first one focuses on hour-based steady-state coordinated economic scheduling on power outputs of electricity generators and mass flow rates of natural gas sources while considering electricity transmission N − 1 contingencies. Using the steady-state mass flow rate solutions of gas sources as the initial value, the second one studies second-based slow gas dynamics and optimizes pressures of gas sources to ensure that inlet gas pressure of gas-fired generator is within the required pressure range at any time between two consecutive steady-state scheduling. The proposed framework is validated via an IEGS consisting of an IEEE 24-bus electricity network and a 15-node 14-pipeline natural gas network coupled by gas-fired generators. Numerical results illustrate the effectiveness of the proposed framework in coordinating electricity and natural gas systems as well as achieving economic and reliable operation of IEGS.

Numerical investigation to study the effect of loop inclination angle on thermal performance of nanofluid-based single-phase natural circulation loop

ABSTRACTThe main objective of this paper is to numerically investigate the effect of inclination angle on thermal-hydraulic characteristics of a rectangular natural circulation loop (NCL). The density gradients generated due to simultaneous heating and cooling at heater and cooler sections, respectively, create buoyancy. Operating parameters that are varied in the present study are particle concentration, power input and inclination angle. The 3-D NCL model is developed and simulated using commercial software ANSYS-Fluent 14.5. The heat transfer behaviour of NCL is analysed after validation with the experimental results available in open literature. The results show that steady-state mass flow rate increases with particle concentration and decreases with loop inclination angle at a given power input. Rayleigh number and the average heat transfer coefficient are enhanced with particle concentration at a given power input, and these will have a marginal effect at lower inclinations for any particle concentration. The effectiveness variation is also analysed.

Discrete Element Model Calibration Using Multi-Responses and Simulation of Corn Flow in a Commercial Grain Auger

Abstract. Grain augers are primary grain conveying equipment in agriculture. Quantitative prediction of dynamic grain flow in grain augers using discrete element modeling (DEM) has potential to support simulation-based engineering design of grain handling equipment. The objective of this study was to develop a DEM corn model using a multi-response calibration methodology and validation of combine-harvested corn flow in a commercial grain auger. Using a Latin hypercube design of experiment (DOE) sampling from four particle interaction DEM parameters values, 27 DEM simulations were generated for four DEM corn shape approximations (1-sphere, 2-spheres, 5-spheres, and 13-spheres) to create virtual DEM experiments of bucket-discharged and anchor-lifted angle of repose (AOR) tests. A surface meta-model was developed using the DEM interaction parameters as predictor variables, and normalized AOR expressed as a mean square error (MSE), i.e., the sum of square differences between DEM simulations and laboratory-measured AOR. Analysis of the MSE percentiles with lower error differences between DEM simulations and laboratory AOR and the computational effort required per simulation (h per simulation) showed that the 2-spheres DEM model had better performance than the 1-sphere, 5-spheres, and 13-spheres models. Using the best stepwise linear regression models of bucket AOR MSE (R2 of 0.9423 and RMSE of 94.56) and anchor AOR MSE (R2 of 0.5412 and RMSE of 78.02) and a surface profiler optimization technique, an optimized 2-spheres DEM corn model was generated. The DEM predicted AOR with relative errors of 8.5% for bucket AOR and 7.0% for anchor AOR. A DEM grain auger simulation used as a validation step also showed good agreement with the laboratory-measured steady-state mass flow rate (kg s-1) and static AOR (degrees) of corn piled on a flat surface, with DEM prediction relative error ranging from 2.8% to 9.6% and from 8.55% to 1.26%, respectively. Keywords: Corn, DEM, Discharge angle of repose, Discrete element modeling, Grain auger, Lift angle of repose.

Steady-state performances and scaling analyses for an open flashing-driven natural circulation system

Simulating investigations are carried out to study the steady-state performances, the pressure resistance distributions and the scaling methods of the single-phase and flashing-induced two-phase flow in the open natural circulation system, which is designed for the passive containment cooling system. The results show that the steady-state mass flow rate changes with the heat transfer regularly both in the single-phase and flashing-induced two-phase flow under a certain inlet subcooling. From the sensitivity analysis, it can be found that the riser height only has impact on the single-phase flow but has little influence on the flashing-driven two-phase flow. Both increasing the diameters of the riser and downcomer can enhance the flow and heat transfer in sing-phase and two-phase flow when keeping the structure of the heat exchanger unchanged, but the influence degree for each flow type is different. The flow resistance distributions of the loops under different flow modes have been studied to provide the foundation for improving the heat transfer capacity by choosing the structural parameters reasonably. The pressure resistance distribution of the steady single-phase flow only relates to the geometrical, but the pressure resistance distribution of the two-phase flow relates both to the pipe diameters and to the external conditions. The acceleration pressure resistance in the riser section is the main resistance under the higher-quality two-phase conditions. Therefore, the influence of the riser diameter on the flashing-induced two-phase flow is far greater than that of downcomer diameter and the most effective method to improve the two-phase flow and heat transfer is to increase the diameter of the riser. Finally, the scaling analysis is performed for the penetration and economy considerations after selecting the optimal dimensions. The scaling of the cold and hot sections is considered separately to insure the driven force of the system unchanged, and different scaling criterions are given for the single-phase and flashing-induced two-phase flow according to the analyses of the pressure resistance distributions. The results show that the scaling criterion of the two-phase flow can deal with the scaling problem accurately both in the single-phase and two-phase flow. However, the scaling criterion of the single-phase flow only can solve the single-phase scaling problem, but it will overestimate the operating results in the scaling model.

Effect of Pressure on Steady State and Heat Transfer Characteristics in Supercritical CO2 Natural Circulation Loop

A 2D axi-symmetric CFD code (NAFA-LOOP) has been developed for studying the heat transfer and steady state characteristics of supercritical CO2 natural circulation loop (SPNCL). NAFA-Loop is derived from the pipe flow solver (NAFA) which was developed earlier to study the heat transfer characteristics of supercritical fluid pipe flow. The code is validated at supercritical condition with experimental results. Effect of pressure on heat transfer and steady state characteristics has been studied by keeping all the operating parameters such as secondary side coolant flow rate and secondary side coolant inlet temperature constant except the pressure. And the heater power is varied from 200W to 3000W for each pressure. As increasing the pressure, the steady state mass flow rate increases because of increase in the density difference in loop (driving force). But the maximum value of heat transfer coefficient decreases as increasing the pressure.

On two-compartment population balance modeling of spray fluidized bed agglomeration

The present work focuses on the modeling and analysis of a spray fluidized bed granulation (SFBG) process based upon the concept that particles are communicating between the two compartments at some steady state mass flow rate. A numerical technique for solving the proposed two-compartment model (2CM) is developed and validated against some newly derived analytical solutions. Moreover, the inverse technique for extracting the rate constant of one-compartment model (1CM) is extended to 2CM. A correlation of aggregation rate constant of 2CM with the rate constant of conventional 1CM under some restrictions is investigated and it is found that the 1CM cannot be used, in general, to predict results of 2CM. Furthermore, it is observed that the existence of two zones in SFBG is responsible to certain extent for time dependent behaviour of aggregation rate constant. Finally, influence of compartment sizes and particles residence times on particle size distribution is investigated.

Application of Data Reconciliation and Gross Error Detection to Nuclear Material Accounting for Spent Fuel Reprocessing

Data reconciliation and gross error detection are applied to nuclear material accounting of spent fuel reprocessing in order to demonstrate their usefulness for verification activities in a safeguards system. In a simple flowsheet of the Purex process including dissolution, co-decontamination, and uranium-plutonium partition processes, the measurements of the steady-state mass flow rate, which include artificial random errors imitating measurement errors and/or process disturbances, are reconciled by a least-squares method with linear constraints of mass balance equations. The reconciled measurements satisfy the mass balance equations and their random errors are reduced. By use of another set of measurements, which includes both random and systematic errors, the gross error detection with χ2 test statistic is tested in order to find the systematic errors, which can correspond to the failure of measurement devices and the loss of nuclear materials. The systematic error is successfully detected with a given confidence limit.

Evolutionary design of reactor vessel assembly for liquid metal cooled battery

The Battery Omnibus Reactor Integral System (BORIS) is being developed as a multipurpose integral fast reactor at the Seoul National University. This paper focuses on developing design methodology for optimizing geometry of the liquid metal cooled reactor vessel assembly. The key design parameters and constraints are chosen considering technical specifications such as thermal limits and manufacturing difficulties. The evolution strategy is adopted in optimizing the geometry. Two objective functions are selected based upon economic and thermohydraulic reasons. Optimization is carried out in the following steps. First, selected design values are supplied to the momentum integral model code to evaluate steady-state mass flow rate and coolant temperature distribution of the reactor vessel assembly utilizing the thermodynamic boundary condition on heat exchanger calculated by the thermodynamics code. Second, the objective function values are calculated and compared against the previous results. The steps are repeated until an optimum value is obtained. Results of the improved design of the reactor vessel assembly are presented and their characteristics are discussed.

Application of Data Reconciliation and Gross Error Detection to Nuclear Material Accounting for Spent Fuel Reprocessing

Data reconciliation and gross error detection are applied to nuclear material accounting of spent fuel reprocessing in order to demonstrate their usefulness for verification activities in a safeguards system. In a simple flowsheet of the Purex process including dissolution, co-decontamination, and uranium-plutonium partition processes, the measurements of the steady-state mass flow rate, which include artificial random errors imitating measurement errors and/or process disturbances, are reconciled by a least-squares method with linear constraints of mass balance equations. The reconciled measurements satisfy the mass balance equations and their random errors are reduced. By use of another set of measurements, which includes both random and systematic errors, the gross error detection with χ2 test statistic is tested in order to find the systematic errors, which can correspond to the failure of measurement devices and the loss of nuclear materials. The systematic error is successfully detected with a given confidence limit.

An attic-interior infiltration and interzone transport model of a house

A detailed model is developed for predicting the ventilation rates of the indoor, conditioned zone of a house and the attic zone. The complete set of algorithms is presented in a form for direct incorporation in a two zone ventilation model. One of the important predictions from this model is the leakage flow rate between the indoor and attic zones. Ventilation rates are predicted from a steady state mass flow rate balance for each zone where all individual flow rates through leakage sites are based on a power law expression for flow rate versus pressure difference. The envelope leakage includes distributed leakage associated with background leakage, localized leakage associated with vents and flues, and active fan ventilation. The predicted ventilation rates agree quite well with field measurements of ventilation rates in houses and attics with different leakage configurations, without the use of any empirically adjusted parameters or constants.

High‐Pressure Annular Seal Leakage and Rotordynamics with Application to Turbomachinery

The paper presents theoretical investigations that deal with the steady state mass flow rate, labyrinth seal-influence coefficients, and unbalance response of a cryogenic turbopump. A numerical method for calculating the leakage flow rates, stiffness, and damping coefficients of liquid hydrogen‐ lubricated seals is presented. Rotation and seal surface roughness effects are also included for leakage and dynamic force calculation. A finite element solution of a Reynolds equation is obtained for steady state as well as dynamic pressure distributions produced by a small amplitude whirl of the seal journal center (a first order perturbation solution). Film rupture is taken into account with the boundary to the ruptured film zone determined by an iterative procedure. A brief procedure is presented for modeling of the rotor/seals system. This work extends the previous theory for plain centered seals to large eccentricities using a perturbation analysis, which includes surface roughness effects. Investigations have been carried out for seal breadth-to-diameter ratio (BDR) of 0.25 to 0.5. The performance of a convergent and three-stepped seal is estimated. Numerical data for these seals for an eccentricity ratio up to 0.8 has been obtained.

Extended Insight into the Metastable Liquid Region Behavior in an Adiabatic Capillary Tube

Over the past decade, the development of theoretical models used to simulate capillary tube performance has steadily progressed. Currently, the major obstacle to improving performance model accuracy is the inability to accurately predict the onset of vaporization (flash point) and thereby the metastable liquid region length. It has been demonstrated that neglecting this region's effect on the overall flow resistance can lead to an underprediction by 5 to 25% of the actual mass flow rate through a capillary tube. Before an accurate metastable liquid region model can be developed, however, a more thorough understanding of the region behavior is necessary. In response, an experimental study has been completed with R-134a using a single adiabatic capillary tube. Testing was undertaken to determine if the metastable liquid region effect on steady-state mass flow rate measurements was repeatable and dependent on controllable test parameters, as had been suggested in a recent study. The experimental parameters were: steady-state inlet subcool level (three levels), the direction of approach to the steady-state inlet temperature (increasing or decreasing temperature), and the forced inlet temperature response rate used in attaining the steady-state flow condition. The resulting general data trend demonstrated increasing scatter in repeated flow rate measurements as the inlet subcool level decreased. Further, there appeared to be some dependence of the flow rate data on the experimental procedure used in setting the inlet condition. However, even under controlled test conditions the dependence was not always repeatable. Using a theoretical flow model, it was shown that most of the data scatter among repeated measurements was caused by variation in the flash point location and thereby the metastable liquid region length. These results precipitated a second experimental phase designed to determine if the flash point location could be controlled. If so, the scatter in measured mass flow rate data for a common inlet condition would be reduced. Two modifications were made to the capillary tube. First, a thin wire was run through its entire length and the original test matrix repeated. The overall measured flow rate levels were lower due to the decrease in flow area caused by the wire. But in comparison to the measurements without the wire, the proportional range of data scatter was cut in half. The second modification was made by drilling five 0.020 in. (0.51 mm) diameter holes through the tube wall, which were spaced at 5 in. (127 mm) toward the end of the tube. Each hole was sealed along the outer tube surface, thus creating a series of wall cavities acting as potential nucleation sites. The overall measured flow rate levels were reduced by roughly 13% in comparison to the original unmodified tube. But more interestingly, the range of data scatter was reduced by nearly an order of magnitude. In conclusion, it was proven that the data scatter in repeated measurements of mass flow rate was caused by variation in the flash point location. It was then demonstrated that the variation in the flash point location could be controlled. Once controlled, an accurate prediction of the metastable liquid region length is potentially possible, which will in turn improve the accuracy of theoretical flow models used to simulate capillary tube performance.