Thermodynamic Cycle Efficiency Research Articles

Proposal and comparison of two heat recovery measures for the coal-based Allam cycle: Double expansion and lower turbine backpressure

Improving the thermodynamic efficiency of the coal-fired semi-closed supercritical CO2 cycle (coal-based Allam cycle) can be achieved by implementing self-heat recuperative coal drying and recompression with more syngas heat integrated with the efficient power cycle. To prevent the heat exchanger from overtemperature during syngas heat recovery, two measures are considered: double expansion and lower turbine backpressure. For the double expansion, a portion of the recycle CO2 is fed into an expander and the exhaust is mixed with the flue gas in the main recuperator to raise the recycle flow rate. For the lower turbine backpressure, the turbine backpressure is decreased to reduce exhaust flue gas temperature. Thermodynamic analysis indicated that self-heat recuperative coal drying and recompression could enhance the net efficiency by 4.28 % points compared to the basic cycle, but the heat exchanger for raw syngas heat recovery faces overtemperature problem with the cold stream exceeding 777 °C. Both the measures proposed above can effectively reduce the temperature to 730–760 °C with slightly decreased efficiencies of 46.93 %∼47.68 % for double expansion and 47.12 %∼47.81 % for lower turbine backpressure. Furthermore, economic assessment shows that compared to the basic cycle, the cost of electricity decreases by 2.49 % and 5.04 % for the schemes with double expansion and lower turbine backpressure, respectively. Therefore, the proposed design with lower turbine backpressure demonstrates advantages in both thermodynamic and economic performance.

Part-load analysis and preliminary annual simulation of a constant inventory supercritical CO2 power plant for waste heat recovery in cement industry

The present work investigates the part-load performance of a MW-scale sCO2 power plant designed as waste heat recovery unit for an existing cement plant located in Czech Republic, in the framework of the H2020 funded project CO2OLHEAT. The study first presents the selected power plant configuration and then focuses on the evaluation of its part-load operation due to variation of flue gas mass flow rate and temperature. The range of flue gas conditions at the outlet of the upstream process is retrieved from a preliminary statistical analysis of historical trends obtained through the cement plant monitoring. The numerical model developed for this study aims at providing realistic results thanks to the adoption of turbomachinery performance maps provided by the turbomachinery manufacturer of the project. Moreover, heat exchangers have been modelled through a discretized approach which has been validated against manufacturer data, while piping inventory and pressure losses have been assessed through a preliminary sizing that considers the actual distances to be covered in the cement plant. Performance decay is estimated for the whole range of flue gas conditions, reporting the most significant power cycle parameters, and identifying the main causes of efficiency loss. The part-load analysis is carried out considering a constant CO2 inventory, in order to reduce the system complexity and capital cost and simplify plant operation. Results show that the operation entails minor variation of the compressors operative points in the whole range of operating conditions of the cement plant, avoiding the risk of anti-surge bypass activation. Moreover, the plant is able to work close to the nominal thermodynamic cycle efficiency (20.5 %–23.0 %) for most of the year and benefits from part-load operation in terms of overall performance. In the last part of the work, a preliminary techno-economic analysis of the plant is also presented to highlight the potential advantages of sCO2 technology for waste heat recovery applications. The results of the part-load performance of the plant are combined with the flue gases data obtained from the preliminary statistical analysis and the cement plant historical monitoring. An annual electricity production equal to 13′909.7 MWh is obtained, corresponding to 6560 equivalent hours and a system capacity factor of 74.9 %. The investment cost of each CO2OLHEAT plant component is estimated by means of cost correlations obtained from literature and the non-discounted payback time is computed as a function of the electricity selling price. The results show that, even considering electricity prices before 2022, the payback time of the CO2OLHEAT plant is estimated to be lower than 8 years, justifying the industrial interest in the proposed technology.

Feasibility of solar-driven trilateral-like organic Rankine cycle with radial-inflow turboexpander

Low-temperature solar collectors coupled with thermal energy storage can enable stable and carbon-free energy production. This work proposes a fully integrated organic Rankine cycle (ORC) with solar field and thermocline direct energy storage. The organic fluid remains liquid inside the solar field and the thermal energy storage, leading to a trilateral-like thermodynamic cycle. As opposed to other trilateral (flash) cycles, the proposed system distinguishes itself by including a turboexpander to deal with two-phase expansion, leading to higher conversion efficiency. In particular, with the same turbine efficiency, the proposed cycle outperforms alternative integrated ORC-solar field configurations by 1.5–3.8 percentage points in thermodynamic cycle efficiency for maximum temperatures between 400–600K. The equivalent electric energy density also increases by 30% to 60%. The problem of the two-phase turbine is tackled by relying on a recently proposed radial-inflow turbine concept. The centripetal stator leverages the retrograde shape of the saturation curve to achieve a complete liquid-to-vapor expansion. As a result, the rotor can handle dry organic vapors without experiencing mechanical damage or additional losses from two-phase interactions. Preliminary turbine designs, obtained through optimization of a validated meanline method, consistently yield isentropic total-to-static efficiencies exceeding 85%, confirming the potential of the proposed system.

Isothermal turbines − New challenges. Numerical and experimental investigations into isothermal expansion in turbine power plants

The efficiency of power plants with steam or gas turbines depends on the efficiencies of a thermodynamic cycle and devices implementing this cycle. In the case of high power outputs, we cannot expect a significant increase in the efficiency of individual devices. Therefore, what remains is to increase the efficiency of the implemented thermodynamic cycle − the complex Rankine cycle in the case of steam turbines or the extended Brayton cycle in gas turbine units. The efficiencies of these cycles depend on the hot reservoir temperatures, limited by the materials used. The solution seems to be the thermodynamic cycles with the highest efficiency within given temperature limits, the „generalized Carnot cycles”. About gas turbines, such a cycle is the Ericsson cycle. The most difficult element of this cycle is carrying out high-temperature expansion. So far, there is no literature data on a technical device implementing this process. In this article, we present a method for designing turbine nozzles for isothermal expansion and the results of experimental tests of the first isothermal turbine. In the case of gas microturbines with a regenerator, isothermal expansion can increase efficiency from 24% to 28% up to 36%. An increase in efficiency of several to a dozen percentage points is expected for Organic Rankine Cycle (ORC) turbines. Due to such significant increases in energy generation efficiency, an isothermal turbine may become a future solution for energy systems.

Primary investigation on Ram-Rotor Detonation Engine

The study presents a new type of detonation engine called the Ram-Rotor Detonation Engine (RRDE), which overcomes some of the drawbacks of conventional detonation engines such as pulsed detonation engines, oblique detonation engines, and rotating detonation engines. The RRDE organizes the processes of reactant compression, detonation combustion, and burned gas expansion in a single rotor, allowing it to achieve an ideal detonation cycle under a wide range of inlet Mach numbers, thus significantly improving the total pressure gain of the propulsion system. The feasibility and performance of RRDE are discussed through theoretical analysis and numerical simulations. The theoretical analysis indicates that the performance of the RRDE is mainly related to the inlet velocity, the rotor rim velocity, and the equivalence ratio of reactant. Increasing the inlet velocity leads to a decrease in the total pressure gain of the RRDE. Once the inlet velocity exceeds the critical value, the engine cannot achieve positive total pressure gain. Increasing the rim velocity can improve the total pressure gain and the thermodynamic cycle efficiency of RRDE. Increasing the equivalence ratio can also improve the thermodynamic cycle efficiency and enhance the total pressure gain at lower inlet velocities. While at higher inlet velocities, increasing the equivalence ratio may reduce the total pressure gain. Numerical simulations are also performed to analyze the detailed flow field structure in RRDE and its variations with the inlet parameters. The simulation results demonstrate that the detonation wave can stably stand in the RRDE and can adapt to the change of the inlet equivalence ratio within a certain range. This study provides the preliminary theoretical basis and design reference for the RRDE.

Design and simulation of an efficient gas-liquid separation device for component regulation of zeotropic mixtures

ABSTRACT Improving the overall energy efficiency of thermodynamic cycles relies heavily on the replacement of traditional pure fluids with zeotropic mixtures. The selection of the optimal components within the zeotropic mixture depends on the specific operating conditions of the thermodynamic cycle. Therefore, significant enhancements in performance can be achieved across varying operating conditions by effectively controlling the composition of zeotropic mixtures in the cycle. According to the gas-liquid equilibrium characteristics of the zeotropic mixtures, the adjustment of the medium components and the boundary conditions can be realized if the components can be adjusted through the gas-liquid separation. In this study, a novel device is proposed for automatically regulating the speed of gas-liquid separation in order to separate the components of the zeotropic mixtures. The CFD simulation was utilized to analyze the structural parameters and boundary conditions that impact the efficiency of gas-liquid separation. The results indicate that the adjustable mass flow range of the optimal structure is broadened by 5.5 times compared to conventional gas-liquid separation devices, ranging from 0 kg/s to 0.15 kg/s. Additionally, within this range, the gas-liquid separation efficiency exceeds 95%, representing a 10% improvement over traditional phase separators.

A SIMPLIFIED ANALYTICAL MODEL OF STIRLING ENGINE EFFICIENCY CALCULATION. A THEORETICAL ANALYSIS OF WORKING GAS

The indicated power and thermal efficiency are the most important features of the Stirling engine. In the most general way, the efficiency depends on a set of parameters, such as the ratio between the volumes and temperatures of the working gas in the hot and cold compartment, the adiabatic function and energy losses due to friction processes between engine components. Stirling engines can use mono, bi or polyatomic molecules such as helium, hydrogen or carbon dioxide as working gases. The first part of the contribution is dedicated verification and completion of our results obtained on the basis of the technical design data of the Genoa03 Stirling engine. These were determined based on an analytical model of the thermal efficiency of a simplified thermodynamic cycle described in the pressure-volume diagram by two adiabatic transformations and two isochoric transformations. The input data used are those used by our αSETS calculation code. The second part of the article is dedicated to the analytical elaboration of the adiabatic function of the working gas for the case of a mixture consisting of two or three types of working gases at different molar ratios. The adiabatic functions are used to estimate thermal efficiency. It has been shown that a mixture of two or three types of gas does not improve the thermal efficiency of the Stirling engine compared to the use of one-component gas. The results of these models related to the Beale relationship can be used successfully in the design process of Stirling engines

Progress in design and experimental activities for the development of an advanced breeding blanket

There is no doubt about the interest of achieving as fast as possible the capability to build and operate high performance reactors that finally allow fusion competing in the electricity market. An advanced breeding blanket based on the Dual Coolant Lithium Lead concept with single module segment architecture, designed for the European DEMO, is certainly aligned with such objective. This work describes some recent outcomes of the efforts carried out in the framework of the Prospective R&D Work Package in EUROfusion to develop this line. The evolution of the design has been guided by strategies aimed to achieve an equilibrium between tritium breeding & shielding requirements and mechanical integrity. To enhance the thermodynamic cycle efficiency and reduce the recirculation power by minimizing pressure losses in both the breeding zone and the first wall have been complementary guidelines. Specific models have been created to characterize phenomena like heat transfer and tritium permeation in the breeder channels. The experimental activities, which in general have produced promising results, have consisted in the characterization of different ceramic materials (carbides and oxides) in terms of functional properties at high temperature (as-received and irradiated/implanted samples) and compatibility with PbLi.

Breaking the limitation of thermodynamic cycle efficiency of the plasma synthetic jet actuator: Noble gases

The low thermodynamic cycle efficiency of the plasma synthetic jet actuator (PSJA) limits its application in flow control of supersonic aircraft. To improve the thermodynamic cycle efficiency of the PSJA, the energy conversion process of the PSJA under single discharge has been investigated by thermodynamic theory analysis and numerical simulation. The relations between thermodynamic cycle efficiency, specific heat ratio of gas medium, non-dimensional energy deposition and heating efficiency are established by theoretical deduction. Employing the three-dimensional nonconstant electrode center energy deposition model, energy conversion processes in the PSJA with six different gas mediums have been investigated. The simulation results show that the thermodynamic cycle efficiency of the PSJA with noble gas medium can exceed 3.2 %, which is 1.92 times of the PSJA with air medium due to their low volume specific heat. The maximum jet x-velocity of helium can reach 493.11 m/s, which is 3.3 times higher than that of air. Consequently, noble gases prove to be effective in improving the thermodynamic cycle efficiency of the PSJA and enhancing the strength of the synthetic jet. The advancement in the performance of the PSJA contributes to their enhanced capabilities in the field of active flow control.

Daily thermodynamic analysis of a solar dish-driven reheating organic Rankine cycle

Solar concentrating systems can play a critical role in the future for designing sustainable cities. The goal of this investigation is the energy analysis of a solar-driven power plant based on the solar dish collector, storage thermal tank and a reheating organic Rankine cycle. The present thermodynamic cycle is a more efficient choice compared to other similar designs due to the existence of a double expansion with an intermediate reheating. Also, the use of the solar dish collector enables efficient operation in medium and high temperatures. More specifically, this investigation is performed on dynamic conditions aiming to determine the unit?s performance on a usual summer day. The analysis is done with a dynamic model based on mathematical formulas which are inserted into Engineering Equation Solver. The simulation results proved that a collecting area of 500 m2 (50 modules) coupled with a storage tank of 5 m3 volume that feeds an Organic Rankine Cycle of 50 kWel nominal power leads to daily electricity production of 577 kWhel. The system efficiency is found to be 12.6%, the thermodynamic cycle efficiency 20.8% and the solar field thermal efficiency 60.8%. Therefore, it is obvious that the suggested unit leads to satisfying results, and it is a promising one for the design of sustainable renewably driven units in the future.

Теоретическая оценка эффективности применения одноступенчатых длинноходовых поршневых компрессоров в холодильной технике и системах сжижения углеводородов

The analysis of the main modern technologies for obtaining low temperatures and liquefying hydrocarbons using compressor equipment is presented and the most significant results of research in the field of low-flow compressors based on low-speed, long-stroke piston stages are presented. A method for calculating an ideal vapor-compression refrigeration cycle is presented, adapted to the object under consideration, taking into account the possibility of implementing quasi-isothermal compression. A comparative computational analysis of temperature conditions and thermodynamic efficiency of a two-stage refrigeration cycle and single-stage refrigeration cycles is carried out during adiabatic and quasi-isothermal compression processes in the boiling temperature range 278 K ... 198 K. It is shown that in terms of the discharge temperature and coefficient of performance, a single-stage vaporcompression ammonia refrigeration machine based on a low-speed quasi-isothermal stage is comparable to a similar two-stage machine based on adiabatic stages. This allows, in relation to actual objects — small refrigeration machines and installations, to predict both the energy and technical advantages of using a single-stage scheme based on low-speed, long-stroke piston compressors. In addition, it has been shown that the effective use of such a compressor is also possible in hydrocarbon liquefaction systems, while ensuring their safe temperature conditions in a wide range of atmospheric temperatures.

Thermal conductivity measurements for n-nonane and n-undecane at elevated temperature and pressure

Hydrocarbons have wide applications in various industrial processes, and the knowledge of thermophysical properties is the foundation for their utilization. As an important thermophysical property, the thermal conductivity of fluids is vital in the evaluation of energy conversion quality, like heat transfer enhancement, thermodynamic cycle efficiency evaluation, etc. Therefore, obtaining accurate experimental data is of great importance for the utilization of hydrocarbons. Here, the thermal conductivities of liquid n-nonane and n-undecane were investigated using the transient hot-wire method (combined expanded uncertainty is 2.0 %) with a wide temperature and pressure range from 293.15 to 523.15 K and 0.1 to 15.0 MPa. For the convenience of engineering applications, a polynomial as a function of temperature and pressure was proposed to correlate the experimental data, the average absolute deviations between experimental data and fitted data are 0.29 % for n-nonane and 0.35 % for n-undecane, which indicates that the polynomial describes the experimental data well in the measured region. Meanwhile, the available literary data were collected and compared with our results, and good agreement was found between literary data and our results. This work is not only helpful for the industrial applications of hydrocarbons but also helps to understand the internal mechanism of the thermal conductivity of hydrocarbons.

Magnetocaloric effect in the Laves phases RCo2 (R = Er, Ho, Dy, and Tb) in high magnetic fields

The heavy rare-earth-based Laves phases are well-studied intermetallic materials that stand out for their remarkably high magnetocaloric effects, particularly at cryogenic temperatures. In this study, we present the findings of our comprehensive investigation of cobalt Laves phases RCo2 with R standing for erbium, holmium, dysprosium, and terbium. This includes the determination of the magnetocaloric effect by indirect methods using calorimetric and magnetization data. Furthermore, for the first time in these materials, we directly measured the adiabatic temperature change at high magnetic fields up to 20 T. The largest ΔTad value of 17 K, we obtained for ErCo2. Because the order of the transition significantly impacts the efficiency of thermodynamic cycles, we have also focused on determining the transition order in these materials. This was done through the application of established methods and a recently proposed quantitative criterion including the value of the local exponent n. Further, we compare our results with other materials using a straightforward material-based figure of merit - the temperature-averaged entropy change (TEC). Our results demonstrate the great potential of these materials for applications such as for magnetic hydrogen liquefaction.

Thermo-economic analysis of the impact of the interaction between two neighboring dry cooling towers on power generation of dual thermal power units and the energy-efficient operation strategy

Thermo-hydraulic behavior of the dry cooling tower and thermodynamic performance of the power unit was coupled by a well-developed computational framework. The interaction between two neighboring towers was detected through a numerical model under variable working conditions, and the impact of cooling performance variation of each tower on cycle efficiency of the corresponding unit was quantified by a thermo-economic model. Results showed that tower interaction mostly impacts heat rejections of radiators at the neighboring halves of both towers. A higher unit load ensures both towers better cooling performances subject to crosswind. The unfavorable wind-effect on cooling behavior of the upstream tower mitigates with increasing wind attack angle, while that on the downstream tower varies little initially and drops sharply as wind attack angle approaching 90°. For each unit, thermodynamic cycle efficiency is more sensitive to crosswind under a higher unit load. Cycle efficiency grows with unit load at low wind speeds, but generally increases and then decreases with unit load at medium–high wind speeds. Dual units should operate at the same load to maximize operational energy efficiency. Otherwise, the unit corresponding to the upstream tower should follow higher and lower load commands under small-medium and large wind attack angles, respectively.

Development of a Semi-Empirical Model for Estimating the Efficiency of Thermodynamic Power Cycles

Power plants constitute the main sources of electricity production, and the calculation of their efficiency is a critical factor that is needed in energy studies. The efficiency improvement of power plants through the optimization of the cycle is a critical means of reducing fuel consumption and leading to more sustainable designs. The goal of the present work is the development of semi-empirical models for estimating the thermodynamic efficiency of power cycles. The developed model uses only the lower and the high operating temperature levels, which makes it flexible and easily applicable. The final expression is found by using the literature data for different power cycles, named as: organic Rankine cycles, water-steam Rankine cycles, gas turbines, combined cycles and Stirling engines. According to the results, the real operation of the different cases was found to be a bit lower compared to the respective endoreversible cycle. Specifically, the present global model indicates that the thermodynamic efficiency is a function of the temperature ratio (low cycle temperature to high cycle temperature). The suggested equation can be exploited as a quick and accurate tool for calculating the thermodynamic efficiency of power plants by using the operating temperature levels. Moreover, separate equations are provided for all of the examined thermodynamic cycles.

Dynamic Investigation of a Solar-Driven Brayton Cycle with Supercritical CO2

The exploitation of solar irradiation is a critical weapon for facing the energy crisis and critical environmental problems. One of the most emerging solar technologies is the use of solar towers (or central receiver systems) coupled with high-performance thermodynamic cycles. In this direction, the present investigation examines a solar tower coupled to a closed-loop Brayton cycle which operates with supercritical CO2 (sCO2) as the working medium. The system also includes a storage system with two molten salt tanks for enabling proper thermal storage. The sCO2 is an efficient fluid that presents significant advancements, mainly reduced compression work when it is compressed close to the critical point region. The novelty of the present work is based on the detailed dynamic investigation of the studied configuration for the year period using adjustable time step and its sizing for achieving a continuous operation, something that makes possible the establishment of this renewable technology as a reliable one. The analysis is conducted with a developed model in the Modelica programming language by also using the Dymola solver. According to the simulation results, the yearly solar thermal efficiency is 50.7%, the yearly thermodynamic cycle efficiency is 42.9% and the yearly total system efficiency is 18.0%.

Thermodynamic investigation of a solar-driven organic Rankine cycle with partial evaporation

The partial evaporation organic Rankine cycle (PE-ORC) is an emerging technology for the efficient exploitation of low-temperature heat sources. The purpose of the present study is the energy and thermodynamic analysis of a solar-fed PE-ORC with a solar field of evacuated flat plate collectors coupled to a sensible storage tank. The studied PE-ORC operates with the environmentally friendly working fluid R1233zd(E) with variable evaporation percentage in the expander inlet. The thermodynamic investigation is done with a validated model in Engineering Equation Solver, and the transient analysis is performed with the TRNSYS tool by coupling it with the thermodynamic model. According to the dynamic analysis, the annual electrical yield is found at 6243 kWh, while the maximum obtained value is found at 3.81 kW. Moreover, the annual mean solar field efficiency was calculated at 45.0%, the annual mean thermodynamic cycle efficiency at 8.71% and the annual mean system efficiency at 3.68%.

Wave mode analysis of a turbine guide vane-integrated rotating detonation combustor based on instantaneous frequency identification

Owing to the pressure gain combustion characteristics, the gas turbine can enhance the system thermodynamic cycle efficiency by integrating a rotating detonation combustor (RDC). In this study, an experimental model of a hydrogen/air RDC with a variant installation of turbine guide vanes (TGVs) was developed. A mathematical model was proposed to identify the rotating detonation wave (RDW) propagation direction. The accuracy of the calculated RDW instantaneous velocity was improved, and the range of velocity fluctuations narrowed from 200 to 1700 m s−1 to 800–1600 m s−1. The impact of TGV installation on the rotating detonation characteristics was investigated. Both the RDW frequency and static pressure increased by installing the TGV at the combustor outlet. The propagation direction of the initial detonation wave induced the RDW to propagate along the same direction. TGV installation reduced the discrepancy in the RDW velocity between two opposite directions as well as the propagation direction changing frequency, while the inverse TGV installation achieved better optimization. The high-frequency pressure oscillations attenuated at the downstream of the TGV, and the amplitude varied depending on the TGV installation options. The static pressure decreased by 14%–16% in both TGV installation options when the combustion flow travelled through the TGV.

An Overview of Real Gas Brayton Power Cycles: Working Fluids Selection and Thermodynamic Implications

This paper discusses and reviews the main real gas effects on the thermodynamic performance of closed Brayton cycles. Cycles with carbon dioxide as working fluids are taken as a reference and a comparison of the thermodynamic cycle efficiencies that are made with other possible working fluids (pure fluids and fluid mixtures). We fixed the reduced operating conditions, in optimal conditions, so that all working fluids had the same thermodynamic global performances. Therefore, the choice of the working fluid becomes important for adapting the cycle to the different technological requirements. The positive effects of the real gas properties in supercritical cycles were approximately maximal at reduced minimum cycle temperatures of about 1.01 to 1.05, with maximum to minimum cycle temperatures of about 2.2. The use of mixtures furthers widens the application of the field of closed Brayton cycles, thereby allowing a continuous variation in the critical temperature of the resulting working fluid and, in some cases, also making it possible to take the condensation with a significant further increase in the thermodynamic cycle efficiency. The paper also demonstrates the thermodynamic convenience of resorting to mixtures of carbon dioxide and inert gases. Extensive measurements of vapour–liquid equilibria and analysis of the thermal stability and material compatibility are essential for a practical and full use of the real gas Brayton cycles.

Comparison analysis of density wave oscillation type two-phase flow instability of superheated and saturated boiling tubes

Most of previous conclusions about two-phase flow instability come from saturated two-phase flow boiling tubes (SatTFB). Superheated two-phase flow boiling tubes (SupTFB) can generate superheated steam, which will make the thermodynamic cycle efficiency higher and the steam generator or system simpler. However, there is no systematic mathematical analysis about the difference between the two-phase flow instabilities of SatTFB and SupTFB. Algebraic criteria composed of dimensionless numbers are deduced to easily determine their flow instability boundary. Different from six dimensionless numbers used in SatTFB, SupTFB have one more dimensionless number. It is superheated number or two-phase number. The verified model is applied to investigate the parameters’ effects and the transient characteristics of density wave oscillation (DWO) type two-phase flow instability. The effects of Froude number and friction number for SupTFB are the same as that for SatTFB. When system pressure is low, only the case with high inlet resistance coefficients can be stable in SupTFB. Thus for SupTFB at low system pressures, they become stable when increasing the inverse of Froude number (or inclination angle) or decreasing friction number, which do not have the nonmonotonic phenomenon as the SatTFB. For the added superheated steam region, increasing its friction number makes SupTFB unstable. The reasonable application range of the figure expressed by subcooling number and phase change number is the same for both SatTFB and SupTFB when analyzing parameters’ effects. Different from increasing continually for SatTFB, the ratio between oscillation period and transit time for the SupTFB first increases with subcooling numbers and then keeps unchanged at high subcooling numbers.