Constant Pressure Mixing Research Articles

Compound-choking theory and artificial neural networks-based hybrid modeling for supersonic ejectors

As the core component of ejector refrigeration systems, the research of ejector mechanisms has always been a hot topic. Based on the compound-choking theory, this paper studies the relationship between the entrainment ratio and critical back pressure and designs a neural network-based online error compensation mechanism for supersonic ejectors. Firstly, a thermodynamic model of the ejector is developed by combining the ideal gas model, the compound-choking theory, and the constant-pressure mixing theory. Then, the thermodynamic relationship between the entrainment ratio and critical back pressure is derived by introducing the idea of a hypothetical mixing cross section. Compared with the existing results, our method is able to improve critical back pressure prediction accuracy by virtue of the actual entrainment ratio. Therefore, a new adaptive error compensation algorithm is proposed for supersonic ejectors based on neural networks. Thus, the proposed scheme can be regarded as a hybrid modeling method for supersonic ejectors, which combines thermodynamic laws and data-driven artificial intelligence algorithms. Experimental data from ejector refrigeration systems with R141b, R245fa, water vapor and R134a are used in this paper to verify the validity of the model. The simulation results show that our method can effectively predict the critical back pressure, and all the prediction errors are less than 10%.

Enhancing Energy Efficiency in Jet Ejectors: A Computational Fluid Dynamics Investigation

Abstract: This study investigates the analysis of the operating modes of two distinct jet ejector types, namely, Constant Rate of Momentum Change (CRMC), Constant Pressure Mixing (CPM). Computational Fluid Dynamics (CFD) was employed to thoroughly examine and evaluate their respective geometrical attributes. Through our comprehensive scrutiny, we ascertained the notably superior performance of CRMC ejectors. This superiority is primarily linked to the continuous presence of compression shock waves within the flow processes of CRMC, which consequently lead to comparable or even diminished critical condenser pressures. The core objective of this research is to advance the application of jet-ejector refrigeration technology, especially for the efficient harnessing of low-grade waste heat, thereby contributing to enhanced energy efficiency and sustainable cooling solutions. We concentrated on two operational modes, CRMC and CPM, and employed CFD to analyze the geometry of these ejectors. We found a particular configuration called RSO-2 that demonstrated exceptional performance after carrying out extensive experiments encompassing 53 different parameter combinations using the Taguchi Design of Experiments. With regard to the throat inlet, RSO-2 demonstrated an exceptional mass flow rate of 5.28E+05 J kg-1 and a Mach number of 1.5418 at the throat exit. Furthermore, a strong correlation was found between the diameter of the throat and the radius of the mixing chamber, as revealed by our thorough sensitivity analysis. This discovery offers important new information for the development of jet ejector designs.

Energy and exergy analysis in the ejector expansion refrigeration cycle under optimum conditions

Refrigeration systems progress in parallel with the development of technology and the ways of saving energy in refrigeration systems are being researched. The literature suggests that incorporating ejectors in refrigeration systems can boost the coefficient of performance (COP) of the system. By utilizing ejector expansion, it is possible to improve the performance of the vapor compression refrigeration cycle (VCRC) by recapturing the expansion work that is typically lost during the expansion valve process. The present study investigation aims to contribute to the field of refrigeration by exploring the optimum pressure drop for three commonly utilized refrigerants. Specifically, the study scrutinizes the performance of an ejector based refrigeration cycle that incorporates a constant pressure mixing ejector. Utilizing the energy and exergy analyses are conducted to assess the system's performance with R134a, R600a, and R290 refrigerants across five distinct evaporator temperatures, namely 0°C, -5°C, -10°C, -20°C, and -30°C. The study further determines the optimum pressure drops in the secondary nozzle and the ejector area ratio at a specified condenser temperature, and examines the resultant total exergy destruction and exergy efficiency of the system. For R290 refrigerant; performance improvement ratio, decrease in total exergy destruction and exergy efficiency improvement ratios were found as 1.23, 54.02% and 22.97%, respectively. As a result, R290 is the most appropriate refrigerant for ejector expansion refrigeration cycle (EERC) among the refrigerants investigated as a result of the energy and exergy analyses.

Optimization of Three Key Geometries of a Steam Ejector under Varied Primary Nozzle Geometries

In this paper, three key geometrical dimensions such as XL3 (constant pressure mixing chamber length), D5 (diameter of the throat of the ejector), and XL5 (length of the throat of the ejector) were separately or sequentially optimized under different lengths and angles of two sections of the primary nozzle. Furthermore, shock cluster number and shock chain length or area of low static pressure zone were used to analyze the effect of geometries on ejector performance, which is normally indicated by entrainment ratio (ER, or the ratio between the mass flow rate of secondary flow and the mass flow rate of primary flow). The results show that: (1) the improvement of ejector performance with only optimization of the primary nozzle is quite limited, in comparison, the impact of length and angle of nozzle diverging section on ejector performance is higher than that of converging section; (2) the relative sensitivity of ER to three key dimensions is much higher than that to the angles and lengths of the primary nozzle; (3) with the increase of XL3 and D5, ER needs a larger angle and smaller length of nozzle converging section; (4) the impact of key geometries on ejector performance can be analyzed with the help of shock cluster number and shock chain length or area of low static pressure zone.

An extended mechanism model of gaseous ejectors

An accurate and convenient theoretical model on ejector is valuable to the performance analysis and structure design. To address the problem, the paper develops an extended mechanism model with merely five parameters (four velocity coefficients and an area ratio characterizing the second limit state) under the hypothesis of ideal gas for gaseous ejectors to reveal the working characteristics. The paper discovers that the choking of the primary flow in the motive nozzle is a requisite of the double-choking theory and the physical realizable prerequisites are specifically proposed for the normal operation and performance analysis of the whole ejector. Model validation and performance comparison against existent models including the Sokolov-Zinger model, simplified constant-pressure mixing model, and compound-choking based real gas thermodynamic model have demonstrated its feasibility, compatibility and superiority. Moreover, the analytical whole-operating-condition characteristics coincide fairly well with the experimental data from added platform bench tests. The mean relative error (MRE) of the primary mass flowrates is −5.72% (±0.39%). The MREs of the entrainment ratios are 0.37% (±1.00%) while up to 5.05% (±12.58%) at the critical and subcritical modes, respectively. The research results can provide effective theoretical guidance on characteristic analysis and geometric design.

Performance investigation for CRMC and CPM ejectors applied in refrigeration under equivalent ejector geometry by CFD simulation

In this paper, one of the remaining questions for ejector design, “Does the constant rate of momentum change (CRMC) ejector provide better performance than the constant pressure mixing (CPM) ejector under identical ejector area ratio, ejector length, and operating conditions?”, has been answered. Two steam ejector designs operating with the various boiler and evaporator temperatures were simulated by the SST k-omega turbulence model. The present computational fluid dynamics (CFD) model produced a reasonable agreement with our previous published experimental data. The upstream operating conditions were simultaneously considered to assess the better performance ejector design with the help of the primary expansion coefficient. The predicted results revealed that the CRMC ejector showed an advantage in entrainment ratio and a disadvantage in critical condenser pressure. However, the ejector efficiency comparison confirmed that the CRMC ejector design provided better performance than the CPM ejector design for a primary expansion coefficient greater than unity. The maximum percentage improvement of ejector efficiency was 32.418%.

Transcritical carbon dioxide heat pump cycle: Validation and comparison of one-dimensional models of ejector with independent data sets

Two typical 1-D homogeneous equilibrium models from the literature (constant and variable pressure mixing models) were used to study the ejector expansion transcritical CO 2 heat pump cycle. A sensitivity analysis was performed to study the impact of the isentropic efficiency of the compressor and of each component of the ejector on the overall system performance. Two groups of independent experimental data from the literature were used to validate the two models. It was found that the cycle performance was more sensitive to the isentropic efficiency of the compressor than that of the individual components of the ejector. With appropriate input value of the compressor efficiency, both 1-D models accurately predicted the ejector outlet pressure and vapor quality. However, for the ejector entrainment ratio and cycle COP, the deviations were more than 50 %. These deviations can be significantly minimized to 10 % by eliminating the imbalance occurring in the system operation using a data post-processing method to correct the pseudo steady state in the real operation system. By comparing the simulation results of the two models, it has been shown that there is minor difference on the prediction accuracy. The research can serve as a practical reference for the operation of two-phase-flow ejector expansion transcritical heat pump cycle, and can also provide an insight and orientation for the subsequent optimization of 1-D ejector numerical models. • Two 1-D homogeneous equilibrium models of the ejector are experimental validated. • Neglecting the pressure variation during the mixing has no significant impact. • The liquid imbalance is a predominant source of the modeling deviation. • An innovative data post-processing method is proposed. • The system performance is more sensitive to the compressor isentropic efficiency.

Optimization of three key ejector geometries under fixed and varied operating conditions: A numerical study

In this paper, as for an ejector utilized in a carbon capture system, by using CFD simulation, its three key geometries such as length of constant-pressure mixing chamber (XL3), length and diameter of constant-area mixing chamber (XL5 and D5) were first optimized individually. Then, the relative sensitivity of ejector performance to the three geometries was identified. Next, the effect of six optimization sequences (S1: XL3 → D5 → XL5, S2: XL3 → XL5 → D5, S3: XL5 → D5 → XL3, S4: XL5 → XL3 → D5, S5: D5 → XL3 → XL5, S6: D5 → XL5 → XL3) of the three geometries on entrainment ratio (ER) was evaluated. And then, the ER under varied working conditions was analyzed. Finally, four typical working conditions were selected for doing re-optimization to check whether the ejector performance can be significantly improved and how big difference of the optimized geometries with re-optimization can be generated. The results showed that: (1) the relative sensitivity of ER to D5 is greater than XL3, and that to XL5 is the least; (2) Among six optimization sequences of three geometries, S2 offers the best ejector performance, both S5 and S6 generate the equal and lowest ER; (3) The change of ER with the primary flow pressure is largely related to the back pressure; (4) Re-optimization under four typical operating conditions can improve ejector performance by 4.3% ∼ 128.8%, and optimum D5 and XL3 increases evidently as compared to that without re-optimization. The research results would enhance the application of ejector in carbon capture and relevant chemical fields.

An improved 1-D thermodynamic modeling of small two-phase ejector for performance prediction and design

• An improved 1-D thermodynamic modeling of small two-phase ejector is presented. • The performances of the presented modeling are predicted. • The effects of the operating conditions and geometry parameters are analyzed. • The research results can provide theoretical direction about the ejector design. In this paper, an improved thermodynamic model for the design of a small two-phase ejector is proposed by using the constant-pressure mixing modeling method. Particularly, the mixing process modeling is associated with the area variation of the mixing section, where a corresponding area ratio of the mixing section entrance to exit is introduced. Meanwhile, the mixing pressure is determined by solving model equations under given operating conditions. Furthermore, the effects of the mixing area ratio, operating conditions, ejector components efficiencies on the ejector performance and geometry parameters are analyzed by the proposed model. The results show that the entrainment ratios increase from 0.47 to 1.14 as mixing area ratios range from 1.0 to 1.2 under the given conditions. The mixing area ratio has significant influences on the ejector performance at lower pressure lift ratio, higher primary fluid temperature and lower secondary fluid temperature. It can be concluded that the entrainment ratio, mixing pressure and mixing velocity of ejector could be improved with the mixing area ratio increasing. And it is further confirmed that the constant-pressure mixing ejector provides better performance than the constant-area mixing ejector under design operating conditions. The research results can provide theoretical guidance about the ejector design and performance predictions.

A comprehensive studies on constant area mixing (CAM) and constant pressure mixing (CPM) Ejectors: A review

Because of the attributes of no influencing elements, cost efficiency, increased dependability, and good efficiency, the applications of an add-on energy development ejector have great interest. This paper has discussed about design theories and methods of ejectors with various working fluids. The design methodology in the ejector fields observed constant area mixing (CAM) and constant pressure mixing (CPM). One of the alternatives is to utilize an ejector as an expansion mechanism. This review examines ejector development freezing systems using a combination ejector with constant pressure and constant area mixing as an expansion mechanism. That improves the efficiency and coefficient of performance and reduces power consumption.

Multi-round optimization of an ejector with different mixing chamber geometries at various liquid volume fractions of inlet fluids

• Two inlet fluids of the ejector have four liquid volume fraction combinations. • Multi-round optimization with six sequences of three geometries is conducted. • Optimal three geometries and ER under six optimization sequences are obtained. • Recommended sequence for each liquid volume fraction combination is presented. • Ultimate optimal three parameters and ER largely depend on inlet fluid states. The performance of the ejector relies on the geometrical parameters and the fluid phase state. Although the optimization of geometries of the ejector has been conducted in previous studies, the influence of different optimization sequence of geometric parameters was ignored in previous literatures. To close the knowledge gap, the goal of this paper is to investigate whether different optimization sequences affect the ejector performance and whether the ejector performance is the same under different optimization sequences after multiple rounds of optimization. Therefore, three geometrical parameters, namely the constant-pressure mixing chamber length (L pm ), the constant-area mixing chamber length (L am ) and diameter (D am ), are selected for the optimization study; besides, multi-round optimization with six optimization sequences of these three parameters is conducted by CFD simulations under four different combinations of primary flow liquid volume fraction (LVF 1 ) and secondary flow liquid volume fraction (LVF 2 ) (LVF 1 = 0 plus LVF 2 = 0, LVF 1 = 0 plus LVF 2 = 0.06, LVF 1 = 0.06 plus LVF 2 = 0, LVF 1 = 0.06 plus LVF 2 = 0.06) for the first time. The results showed that: (1) for each LVF combination, the three optimal parameters and corresponding maximum ER produced by one round optimization of six different optimization sequences are evidently different; (2) after multiple rounds of optimization, for LVF 1 = 0 plus LVF 2 = 0 or LVF 1 = 0.06 plus LVF 2 = 0.06, ultimate optimal geometrical parameters and maximum ER are the same with each other for six optimization sequences, however, for LVF 1 = 0 plus LVF 2 = 0.06 or LVF 1 = 0.06 plus LVF 2 = 0, each of them still has two different ultimate maximum ER; (4) for those four combinations, different sequence takes different optimization rounds, recommended sequences are D am → L am → L pm (S6), L pm → L am → D am (S1) or L pm → D am → L am (S2), and L am → L pm → D am (S3) and D am → L am → L pm , respectively; and (5) the ultimate optimal parameters and maximum ER in four combinations differ significantly because they are largely dependent on the inlet fluid states.

Study on the Expansion of Primary Flow for the Mixing Uniformity in the Two-Phase Ejector

The expansion of primary flow in the suction chamber of the CO2 two-phase ejector is investigated and its influences on the mixing characteristics are analyzed. An ejector model is developed, by constructing differential equations for mass, momentum and energy then get the governing equation. In the suction chamber, the expansion of primary flow and the compression of secondary flow are modeled along the flow path. Based on the constant-pressure mixing theory, the pressure equilibrium positions of two stream (namely at the inlet and inside of mixing chamber, respectively) are considered. The mass and energy transfer in the mixing chamber were analyzed by using the double-flow model formulation. The ejector performance parameters are obtained for the different operation conditions, and the distributions of temperature and velocity of two streams in the mixing chamber are presented. The simulation results showed the influence of primary flow expansion on the pressure lift ratio was relatively obvious, and the larger expansion distance was helpful to improve the mixing efficiency and decrease the thermodynamic entropy change during the mixing. Moreover, the temperature of secondary flow for lower primary flow pressure presented larger descent rates at the initial of mixing. This work is helpful for the improvement of ejector theoretical model and the optimization design.

Optimization on key geometries of a highly coupled two-stage ejector

In this paper, an ejector-based multi-evaporator refrigeration system is proposed, in which, the refrigerant mixture coming from the exit of the first-stage enters into the second-stage primary nozzle and entrains its secondary flow refrigerant, thus, the two stages of the ejector are highly coupled. In this case, the primary nozzle throat diameter of the second-stage (PNTD2) plays a key role in affecting and improving both-stage performance. By using Computational Fluid Dynamics (CFD) simulation, key geometries of both stages such as: area ratio (AR), nozzle exit position (NXP), and the angle of constant-pressure mixing chamber (θ) are optimized with varied PNTD2. When PNTD2 increases from 4.1 mm to 5.3 mm, the simulation results show that: (1) Optimum AR of first-stage increases from 2.9 to 5.9, optimum NXP of first-stage rises from 8 mm to 14 mm, and optimum θ of first-stage improves from 7.5° to 15.5°, however, optimal AR of second-stage decreases from 10.5 to 6.9, optimal θ of second-stage decreases from 15.7° to 13.7°, and optimal NXP of second-stage keeps a constant value of 28 mm; (2) AR is the most sensitive one to influence each stage performance, which is followed by NXP, and the least one is θ; and (3) AR and NXP give an evident performance influence to the local stage but a negligible influence to the other stage. The novelty of this work is to investigate the effect of key geometries on a highly coupled two-stage ejector.

Effect of mixing chamber length on ejector performance with fixed/varied area ratio under three operating conditions in refrigerated trucks

In this paper, an ejector-based multi-evaporator refrigeration system is proposed to provide three switchable operating modes of refrigerated trucks, namely, refrigerating – freezing (R-F), air-conditioning – freezing (A-F) and air-conditioning – refrigerating (A-R) modes. Under these three operating modes, CFD simulations are conducted to evaluate the optimum ejector constant-pressure mixing chamber length (Lpm) and constant-area mixing chamber length (Lam) as well as the sum of these two lengths (Lpam) with fixed and varied ejector area ratio (AR, which is expressed as ratio of the cross-sectional area of constant-area mixing chamber to primary nozzle outlet area). The results show that: (1) optimization of Lpm and Lam has small effect on ejector entrainment ratio (ER, which is defined as the ratio of secondary mass flow rate to primary mass flow rate) with fixed AR of 3 under three operating modes, and the maximum increment of ER are 0.0752, 0.0884 and 0.0205 for R-F, A-F and A-R mode, respectively; (2) under varied AR, when optimizing Lpm and Lam, the increment of ejector ER is 1.615, 2.249 and 0.021 for R-F, A-F and A-R modes, respectively; (3) the optimal Lpm and Lpam of the ejector increase first and then decrease with the increase of AR, however, the optimal Lam is irregular with the increase of AR; (4) compared with Lpm and Lam, the effect of AR on ejector performance is the most prominent when AR gets larger. The novelty of this study is that the relations between the optimal mixing chamber length and varied AR are identified.

Performance evaluation of a modified R290 dual-evaporator refrigeration cycle using two-phase ejector as expansion device

This paper presents a modified dual-evaporator ejector expansion refrigeration cycle (MDEEC) in which a two-phase ejector is used as the expansion device to recover the expansion work. Based on constant-pressure mixing theory, a thermodynamic model is developed to investigate the effects of various parameters on the system performance. Also a comparative study of the modified cycle with a conventional one (CDVCC) and a previous ejector cycle (COSEC) is conducted in terms of energy and exergy analysis. The results show that COP of the modified cycle is improved by about 10% and the exergy destruction of expansion device is reduced by more than 90% compared with the COSEC. At the operating condition of Tc = 45 °C and Te2 = 5 °C, the COP and exergy efficiency of the MDEEC can reach 6.515 and 0.3184, respectively, which are 42.6% and 36.7% higher than those of the CDVCC. It is also revealed the performance improvements become more significant at higher condensing temperatures or lower evaporating temperatures. Finally, the effects of the ejector components efficiency and the performance under off-design conditions are discussed.

A theoretical study on a novel combined organic Rankine cycle and ejector heat pump

A novel combined organic Rankine cycle and ejector heat pump is proposed, which combines the organic Rankine cycle and ejector heat pump, and could produce both power output and heat output simultaneously. An ejector is installed on the turbine inlet side to increase the total heat exchange amount of the combined cycle by utilizing the injection capability of the high-pressure primary fluid. Using the heat exchange capacity of the cold source to adjust the matching problem between the primary fluid heat source and secondary fluid heat source. The constant pressure mixing model is used to model the ejector, and a new solution method of the model is proposed. Through the parametric analysis, the results show that the heat exchange of secondary fluid and turbine intake pressure have significant effects on the thermal efficiency and heat recovery capacity. By comparing with the basic organic Rankine cycle, the maximum net power output of the novel combined cycle can be increased by 10.78%, and the maximum heat recovery capacity can be increased by 19.04%.

Performance improvement of ejector expansion refrigeration cycles employing a booster compressor using different refrigerants: Thermodynamic analysis and optimization

A novel ejector-expansion refrigeration cycle (EERC) is proposed, analyzed and optimized in this paper. Assuming a constant-pressure mixing model for ejector simulation, a detailed and comprehensive thermodynamic analysis, based on the first and second laws, is conducted and the system performance is investigated for six proper refrigerants. The proposed system is then optimized considering the exergy efficiency as the objective function and a comparison is made with the standard EERC and conventional vapor compression refrigeration system at the optimized conditions. The results indicated that, among the six investigated refrigerants, R1234ze is the best one for which the proposed system has 5.7% and 15.5% higher exergy efficiency values than the standard EERC and conventional vapor compression refrigeration cycle, respectively, at condensing temperature of 40 ∘C and evaporation temperature of 5 ∘C. Also, it is concluded that for higher condensing and lower evaporating temperatures the value of performance improvement is higher.

Impact of the mixing theories on the performance of ejector expansion refrigeration cycles for environmentally-friendly refrigerants

Ejector expansion refrigeration cycle was investigated theoretically to compare the constant pressure mixing and constant area mixing ejector theories making use of thermodynamic models. Performance improvement was presented according to optimum and constant value pressure drop assumptions in order to simulate the design and off-design conditions, respectively. The agreement between the results with respect to both pressure drop assumptions is better at higher condenser and lower evaporator temperatures for each ejector mixing theory. Optimum area ratio (ϕopt) is less for constant area mixing approach since the ratio of the secondary flow velocity to the primary flow is higher for this ejector theory at each operation point. Although a group of low-global-warming-potential refrigerants were compared in terms of the performance and expansion losses, deep investigations were presented for R1234yf in main and sometimes R1234ze(E). Finally, when compared to other ejector sections, the mixing section efficiency has the most critical effect on the optimum performance improvement ratio of R1234yf with reference to constant pressure mixing assumption.

Thermodynamic modeling and sensitivity analysis of ejector in refrigeration system

This paper focuses on the problems of thermodynamic modeling and sensitivity analysis of the ejector in refrigeration. Firstly, a new thermodynamic model is proposed based on the assumptions of constant pressure mixing and constant area mixing. The proposed model contains fewer parameters and simpler structure compared with the traditional ejector models. Later, the sensitivity analysis of the ejector is carried out based on the adjoint sensitivity method. Three different sensitivity coefficients are given to reveal the relation between design parameters and ejector performance. The result shows that geometric parameters have the most influences on the entrainment ratio of the ejector. For the ejector using R600a, the sensitivity coefficients of entrainment ratio to At and Am are -2.43% and 2.40% respectively.

Effects of component polytropic efficiencies on the dimensions of monophasic ejectors

An inappropriate choice of isentropic efficiencies for the sizing of the component parts of monophasic ejectors is one of the greatest sources of error in their design. The present study shows that the replacement of isentropic efficiencies with polytropic efficiencies within 1D ejector models provides more accurate results. Polytropic efficiencies access more precisely the effects of the pressure ratio variation on the irreversibilities of the acceleration and deceleration processes. It is demonstrated that the deviation in the constant area duct length, calculated by using an isentropic efficiency from the real length is three times greater than the one calculated by using a polytropic efficiency. The polytropic efficiencies are extracted from the CFD modeling of two types of ejectors, a constant area mixing (CAM) ejector and a constant pressure mixing (CPM) ejector. A 1D thermodynamic model for CAM and CPM ejectors, based on the polytropic efficiency concept, is proposed and validated against experimental data. Parametric studies based on this model were completed. They reveal that the variation in polytropic efficiency of the primary nozzle has the most important impact on the constant area duct length. New empirical correlations to estimate the polytropic efficiencies are also provided.