This paper provides a literature review on ejectors and their applications in refrigeration. A number of studies are grouped and discussed in several topics, i.e. background and theory of ejector and jet refrigeration cycle, performance characteristics, working fluid and improvement of jet refrigerator. Moreover, other applications of an ejector in other types of refrigeration system are also described.

Ejectors: applications in refrigeration technology

In ejector refrigeration systems, the performance of the ejector is critical to the performance, capability, size and cost of the whole system. Construction of mathematical models has been used as an effective method for analyzing the performance of the ejector as well as the whole refrigeration system. These models can also be used to guide system operation, interpret experimental results and assist in system design and optimization. The overall objective of this paper is to provide a review of various researches of the mathematical model on the hydrodynamic and thermodynamic character within the ejector. The paper first briefly describes ejector including fundamental principle, flowing and mixing mechanism and the method of model establishment. Then various models consisting of ideal assumptions, governing equations, auxiliary conditions, solution methods and main results are presented. The models can be classified into two main categories: (i) steady thermodynamic models which can be further subdivided into single-phase flow model and two-phase flow model and (ii) dynamic models which are also subdivided according to the flowing phases considered. It has been shown that the dynamic models have higher prediction precision and give more information compared with the steady thermodynamic models. In addition, the simplified empirical and semi-empirical models based on measured data are briefly discussed. This review is useful for understanding the evolution process and the current status of the mathematical models on ejector and highlighting the key aspects of model improvement such as the mixing mechanism, the capture of the shock wave, etc.

Progress of mathematical modeling on ejectors

Ejector efficiencies for the primary nozzle, suction, mixing and diffuser were determined for the first time, according to their definitions, using an axi-symmetric CFD model. Water was considered as working fluid and the operating conditions were selected in a range that would be suitable for an air-conditioner powered by solar thermal energy. Ejector performance was estimated for different nozzle throat to constant section area ratios. The results indicated the existence of an optimal ratio, depending on operating conditions. Ejector efficiencies were calculated for different operating conditions. It was found that while nozzle efficiency can be considered as constant, the efficiencies related to the suction, mixing and diffuser sections of the ejector depend on operating conditions.

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Numerical assessment of steam ejector efficiencies using CFD

Steam jet ejectors are an essential part in refrigeration and air conditioning, desalination, petroleum refining, petrochemical and chemical industries. The ejectors form an integral part of distillation columns, condensers and other heat exchange processes. In this study, semi-empirical models are developed for design and rating of steam jet ejectors. The model gives the entrainment ratio as a function of the expansion ratio and the pressures of the entrained vapor, motive steam and compressed vapor. Also, correlations are developed for the motive steam pressure at the nozzle exit as a function of the evaporator and condenser pressures and the area ratios as a function of the entrainment ratio and the stream pressures. This allows for full design of the ejector, where defining the ejector load and the pressures of the motive steam, evaporator and condenser gives the entrainment ratio, the motive steam pressure at the nozzle outlet and the cross section areas of the diffuser and the nozzle. The developed correlations are based on large database that includes manufacturer design data and experimental data. The model includes correlations for the choked flow with compression ratios above 1.8. In addition, a correlation is provided for the non-choked flow with compression ratios below 1.8. The values of the coefficient of determination ( R 2 ) are 0.85 and 0.78 for the choked and non-choked flow correlations, respectively. As for the correlations for the motive steam pressure at the nozzle outlet and the area ratios, all have R 2 values above 0.99.

Evaluation of steam jet ejectors

A number of factors influence the performance of an ejector. In this work, three geometrical factors – the area ratio between the nozzle and constant area section ( r A ), nozzle exit position (NXP) and constant area section length ( L m ) – were considered. The theoretical analysis was carried out by a CFD model of a steam ejector using FLUENT. The results indicated the existence of an optimal area ratio, depending on operating conditions. Therefore, a new feature, a spindle in the primary nozzle is suggested to fine tune the primary flow rate depending on operating conditions. The location of NXP influenced both entrainment ratio ( λ ) and critical back pressure ( p c,crit ), showing an optimum at 60 mm from the inlet plane of the ejector mixing section. L m had little influence on λ ; however, longer constant area sections resulted in higher p c,crit . For an optimal design, a value of L m  = 155 mm was identified.

Influence of geometrical factors on steam ejector performance – A numerical assessment

Modelling and simulation of steam jet ejectors

The present study considers the dynamic behaviour of the pressurised water reactor safety features, represented by the integrity of the fuel cladding, under some transient cases. A cosine-shaped heating through the fuel is taken with the corresponding coolant lumps, to simulate realistic cases encountered in nuclear reactors. A mathematical model was developed for the Westinghouse 3411 MWth pressurised water reactor, as an example of a familiar design with predominantly published data design. The model consists of two parts. The first part is concerned with the dynamics of the primary side of the reactor, which is described in this paper. The second part is concerned with the secondary side of the plant, which is described elsewhere in this issue. To study the dynamics of the reactor, a model of 17 lumped parameters was used, consisting of first-order differential equations deduced from the first principles considering six groups of delayed neutrons. A computer program was developed using the Runge-Kutta method to solve these equations and to predict the behaviour of the state variables with time. Two case studies were considered as examples for normal transients. The first case study, which represents Part 1 of this study, considers the effect of primary side transient on the system as the reactivity changes. Reactor reactivity changes, including movements of the reactor control rods, which are taken as an example for the effect of the reactor primary side conditions. These reactivity changes vary from 0.0005 up to 0.003, both for positive and negative reactivity. The results of the developed model, which describe the dynamic response of the reactor primary circuit, have been analysed and verified with the relevant models. These results indicate that the reactor components and the integrity of the fuel cladding were attained during different step changes of reactivity.

M.M. Shamloul

Papers

Modelling and simulation of steam jet ejectors

Dynamics of reverse osmosis in a standalone cogenerative nuclear reactor (Part I: reactivity changes)