A CFD-based investigation of the energy performance of two-phase R744 ejectors to recover the expansion work in refrigeration systems: An irreversibility analysisUne étude basée sur la mécanique des fluides numérique de la performance énergétique d’éjecteurs diphasiques au R744 pour récupérer le travail de détente dans des systèmes frigorifiques : une analyse de l'irréversibilité
Introduction
Two-phase ejectors for expansion work recovery have garnered significant attention from the scientific community in recent decades, specifically in the field of R744 refrigeration, where they constitute an attractive alternative for expansion devices in the classic vapour compression systems, primarily due to the possible reduction of the compressor work, Elbel (2011). In addition, the ejector's simplicity (i.e., it has no moving parts) compared to expanders, its low cost and its reasonable efficiency make its use additionally beneficial. Fig. 1 represents the most common option of the ejector cycle used for small capacity refrigeration and heat pumping systems. Nevertheless, the proper design of a two-phase ejector requires a detailed analysis of the flow conditions inside the ejector passages and various parameters of the overall ejector performance.
The overall ejector energy performance is often assessed using a universally accepted approach: a dimensionless factor called the ejector efficiency, ηEJ, is commonly used to reflect the total irreversibility of all changes that occur inside the ejector passages, e.g., see Elbel and Hrnjak, 2008, Elbel, 2011, and Lucas and Koehler (2012).
This factor, expressing the efficiency of expansion work recovery, is defined as the ratio of the expansion work rate recovered by the ejector to the maximum possible expansion work rate, i.e., the recovery potential that is available in the primary stream. The recovered amount of the expansion work rate is defined as the product of the suction mass flow rate, , and the specific enthalpy difference , which is identified by the beginning and ending points of an imaginary, isentropic compression from the evaporation pressure to the diffuser outlet pressure. This compression work is assumed to be removed from the compressor's duty and replaced with the ejector operation. Conversely, the maximum possible recovery potential of the expansion work rate is defined as the product of the motive mass flow rate, , and the specific enthalpy difference , which is identified by the points that end two theoretical, isenthalpic, and isentropic expansion lines from the motive stream to the diffuser outlet pressure.
Unfortunately, the evaluation approach for the separately considered individual sections of the ejector has been a subject of debate. Such analysis is crucial to properly identify and comprehend any encountered flow irreversibility and may suggest potential remedies, particularly in terms of geometric modifications. Although the spectrum of the utilised evaluation parameters is broad, their values often reveal only partial information about the size of the local irreversibility and its contribution to the total ejector efficiency. Furthermore, the underlying methodology is based on numerical simulations instead of experimental work. This approach yields results that depend on the accuracy of the models and are vulnerable to inappropriate assumptions.
Varga et al. (2009) reviewed the available definitions of local ejector efficiencies and numerically determined their values for a steam ejector using an axi-symmetric CFD model. The authors used a classic concept of isentropic efficiency, ηs, for the single-stream passages (motive nozzle, suction nozzle) and the diffuser. Four different approaches were employed to include the irreversibility that is associated with the mixer: (i) entrainment efficiency (defined as a fraction of the kinetic energy in the motive fluid transmitted to the mixture), (ii) mixing efficiency ηMIX (defined as the momentum transfer efficiency), (iii) mixing loss friction factor (defined in the form of the Darcy–Weisbach equation), and (iv) isentropic expansion efficiency (defined as a squared ratio of the diameters of the primary flow at the cross section, where the secondary fluid is choked; the numerator represents an ideal case, and the denominator represents the actual case). The values computed for different operating conditions fell within the following ranges:
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0.92–0.95 for the isentropic efficiency of the motive nozzle,
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0.83–0.91 for the isentropic efficiency of the suction nozzle,
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0.65–0.83 for the entrainment efficiency of the mixer,
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0.82–0.93 for the mixing efficiency of the mixer,
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0.033–0.104 for the mixing loss friction factor of the mixer,
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0.66–0.94 for the isentropic expansion efficiency of the mixer, and
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0.5–0.9 for the isentropic efficiency of the diffuser.
Nevertheless, the authors did not indicate the most representative definition of the mixer performance, and they did not elaborate on the contribution manner of the individual efficiencies to the total irreversibility.
Liu and Groll (2013) presented a method to determine the internal-ejector component efficiencies by combining zero-dimensional modelling with measurements performed for a R744 ejector refrigeration cycle. Measured and simulation data were used to determine the isentropic efficiencies of the motive nozzle, the suction nozzles, and the mixing section efficiency. The authors used the same definition of isentropic efficiency for the motive nozzle and the suction nozzle as Varga et al. (2009), but they introduced a slightly modified concept of the mixing efficiency, ηMIX, which was based on a momentum conservation equation that included the effects of pressure lift over the mixer. However, the use of this modified definition of ηMIX may be limited for two reasons. Firstly, its values only have a physical meaning for constant-diameter channels since a varying diameter yields significant reaction forces that act on a converging passage of the mixer inlet, which influences these values. Secondly, its values reflect only the irreversibilities that result from the friction between the fluid and the wall and neglect the irreversibilities generated in the fluid core. For relatively high mass flow rates that pass through the unit cross section area of the mixer (mixer mass flux) at various operating conditions, i.e., between 12,000 kg s−1 m−2 and 25,000 kg s−1 m−2, the reported values of the motive nozzle, the suction nozzle, and the mixer efficiencies ranged from 0.50 to 0.93, 0.37 to 0.90, and 0.50 to 1.00, respectively. Based on these results, empirical correlations were established and incorporated into a CO2 air conditioning system model to estimate the ejector component efficiencies for different ejector geometries and operating conditions. The authors claimed that all three efficiencies were determined with an acceptable uncertainty (less than 6% of the computed value), but they did not elaborate on the effect of the model's assumptions on the efficiency values, given that the registered trends were ambiguous and not supported by any physical interpretation. Moreover, the effects of the individual efficiencies on the overall ejector efficiency were not examined.
In the previous studies, a significant dependence of the ejector performance on several geometric and operation parameters was experimentally and theoretically demonstrated, among which the ratio of the throat diameter to the mixer diameter or the corresponding mixer mass flux was considered the most substantial, e.g., Elbel and Hrnjak, 2008, Elbel, 2011, Banasiak et al., 2012. However, those studies did not analyse the local irreversibilities and their contributions to the overall performance. Therefore, this paper focused on the numerical analysis of local- and global-flow irreversibilities for three different levels of the mixer mass flux. These three levels represent three dissimilar flow patterns to enhance our former studies of the approach applied by Varga et al. (2009) and Liu and Groll (2013). Therefore, a previously developed CFD tool by Smolka et al. (2013) was used. Furthermore, an original approach was proposed to assess the contribution of the local effects to the overall irreversibility based on the increase in entropy. Finally, a numerical sensitivity analysis of the influence of the selected geometric parameters on the ejector performance was performed to demonstrate the practicality of the proposed method.
Section snippets
Simulation tool – extended validation
All simulations were performed with a mathematical model of the compressible transonic single- and two-phase flow of a real fluid, which is discussed in detail in one of the authors' former publications, Smolka et al. (2013). In the proposed approach, a classic temperature-based energy equation was replaced with an enthalpy-based formulation, in which the specific enthalpy was an independent variable instead of the temperature. A thermodynamic and mechanical equilibrium between the gaseous
Irreversibility analysis
After the model was validated, the flow irreversibilities for the three investigated cases were analysed. This analysis was based on close examination of the flow variable profiles, as well as on the energy and the entropy balances formulated for individual ejector passages.
Geometry case studies
Because of the highest registered values of ζEJ, Case 1 was selected for further geometry studies. Each analysed geometric parameter was varied twice, i.e., increased and decreased by a constant difference and compared to the original design presented in Table 1, whereas the remaining the geometry remained unchanged. Based on the previous experiences with the ejector performance sensitivity to various geometry parameters (Banasiak et al. (2012)), the mixer diameter was varied by ±0.25 mm,
Conclusions
A CFD-based investigation of flow irreversibilities in two-phase R744 ejectors was presented in this paper. The authors used the previously developed CFD tool to analyse the location and the origin of entropy increase for three distinct flow patterns, which were invoked by three different levels of mass flux that passed through the mixer. The latter variable was determined to be the key parameter that influenced the ejector performance because both high and low values of the mass flux
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