applied sciences Article Numerical and One-Dimensional Studies of Supersonic Ejectors for Refrigeration Application: The Significance of Wall Pressure Variation in the Converging Mixing Section Eldwin Djajadiwinata 1 , Shereef Sadek 1, Shaker Alaqel 1 , Jamel Orfi 1,2 and Hany Al-Ansary 1,2,* 1 Mechanical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia; [email protected] (E.D.); [email protected] (S.S.); [email protected] (S.A.); orfi[email protected] (J.O.) 2 K.A.CARE Energy Research and Innovation Center at Riyadh, Riyadh 11451, Saudi Arabia * Correspondence: [email protected] Abstract: This paper studies the pressure variation that exists on the converging mixing section wall of a supersonic ejector for refrigeration application. The objective is to show that the ejector one- dimensional model can be improved by considering this wall’s pressure variation which is typically assumed constant. Computational Fluid Dynamics (CFD) simulations were used to obtain the pressure variation on the aforementioned wall. Four different ejectors were simulated. An ejector was obtained from a published experimental work and used to validate the CFD simulations. The other three ejectors were a modification of the first ejector and used for the parametric study. The secondary . mass flow rate, ms, was the main parameter to compare. The CFD validation results indicate that . the transition SST turbulence model is better than the k-omega SST model in predicting the ms. The Citation: Djajadiwinata, E.; Sadek, S.; results of the ejector one-dimensional model were compared before and after incorporating the wall Alaqel, S.; Orfi, J.; Al-Ansary, H. pressure variation. The comparison shows that the effect of the pressure variation is significant at Numerical and One-Dimensional certain operating conditions. Even around 2% change in the average pressure can give around 32% Studies of Supersonic Ejectors for . difference in the prediction of ms. For the least sensitive case, around 2% change in the average Refrigeration Application: The pressure can give around 7% difference in the prediction. Significance of Wall Pressure Variation in the Converging Mixing Section. Appl. Sci. 2021, 11, 3245. Keywords: ejector refrigeration; one-dimensional model; computational fluid dynamics (CFD); https://doi.org/10.3390/app11073245 transition SST turbulence model; converging mixing section; wall pressure variation Academic Editor: Szabolcs Varga Received: 16 March 2021 1. Introduction Accepted: 1 April 2021 Energy-saving topic gains more attention globally. This is a logical consequence of Published: 5 April 2021 the increase in people’s awareness all over the world regarding the limited fossil energy resources. It keeps depleting and eventually will become extinct. To solve this issue, many Publisher’s Note: MDPI stays neutral researchers have been searching for renewable energy resources as well as developing with regard to jurisdictional claims in efficient technologies to utilize that energy. These attempts have led researchers to various published maps and institutional affil- ideas such as an idea to use ejectors in refrigeration systems to compress the refrigerant. iations. Instead of using electricity, an ejector is able to utilize thermal energy to do the compression. An ejector is a device that entrains a fluid at low pressure (secondary flow) by ac- celerating another fluid at high pressure (primary flow) via a nozzle. Then, the primary and secondary flows mix inside the device and leave through an outlet at an intermediate Copyright: © 2021 by the authors. pressure. In an ejector refrigeration system, the secondary flow is the refrigerant leaving Licensee MDPI, Basel, Switzerland. the evaporator, and the ejector acts as a compressor through which this refrigerant is This article is an open access article compressed. A typical structure of an ejector can be seen in Figure1. In this work, the distributed under the terms and mixing section consists of a converging mixing section, also called constant pressure mixing conditions of the Creative Commons section, and a constant area mixing section, also called ejector throat (ET) (Figure1). Attribution (CC BY) license (https:// A supersonic ejector operation can be divided into three modes, i.e., critical (double- creativecommons.org/licenses/by/ choked) mode, sub-critical (single-choked) mode, and malfunction mode [1]. Figure2 4.0/). Appl. Sci. 2021, 11, 3245. https://doi.org/10.3390/app11073245 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 27 mixing section, and a constant area mixing section, also called ejector throat (ET) (Figure 1). Appl. Sci. 2021, 11, 3245 2 of 26 Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 27 shows various ejector operation modes at a fixed primary and secondary inlet pressures. The ejector is in a critical mode operation when the primary and secondary flows are both choked. This means that both mass flow rates are constant with respect to the change of Figure 1. Schematic of a typical ejector. ejector outlet pressure, P4. The secondary flow is choked because it accelerates until it mixing section, andreaches a constant sonic speedarea throughmixing ase hypotheticalction, also converging called ejector annular throat duct formed(ET) (Figure by the outer 1). A supersonic ejector operation can be divided into three modes, i.e., critical (double-choked)boundary of the mode, primary sub-critical flow jet (singl ande-choked) the wall ofmode, the ejector and malfunction [2]. mode [1]. Figure 2 shows various ejector operation modes at a fixed primary and secondary inlet pressures. The ejector is in a critical mode operation when the primary and secondary flows are both choked. This means that both mass flow rates are constant with respect to the change of ejector outlet pressure, . The secondary flow is choked because it accelerates until it reaches sonic speed through a hypothetical converging annular duct formed by the outer boundary of the primary flow jet and the wall of the ejector [2]. As we increase the outlet pressure, the secondary flow will not be choked anymore (only the primary flow is choked). This pressure threshold is referred to as critical pressure, . Beyond this pressure, the ejector will enter the sub-critical mode operation within which an increase in will decrease the secondary mass flow rate but has no effect on the primary mass flow rate. As the outlet pressure is increased further, it reaches a pressure, , at which the ejector starts to malfunction. There will be no secondary flow or, even, reverse flow through the secondary inlet will occur. In practice, an ejector is usually required to Figure 1. Schematic of a typical ejector. Figure 1. Schematic operateof a typical in the ejector.critical mode/condition, and hence, it is also called the on-design condition. A supersonic ejector operation can beSub-critical divided into three modes, i.e., critical mode (double-choked) mode, sub-criticalCritical mode (single-choked) mode, Malfunction and malfunction mode [1]. Figure 2 shows various ejector operation modes at a fixed primary and secondary inlet pressures. The ejector is in a critical mode operation when the primary and secondary flows are both choked. This means that both mass flow rates are constant with respect to the change of ejector outlet pressure, . The secondary flow is choked because it accelerates until it reaches sonic speed through a hypothetical converging annular duct formed by the outer boundary of the primary flow jet and the wall of the ejector [2]. As we increase the outlet pressure, the secondary flow will not be choked anymore (only the primary flowEntrainmentER ratio, is choked). This pressure threshold is referred to as critical pressure, . Beyond this pressure, the ejector will enter the sub-critical mode operation within which an increase in will decrease the secondary mass flow rate but has no Outlet pressure, effect on the primary mass flow rate. Figure 2. Various ejector operation modes at a fixed primary and secondary inlet pressures. Entrain- As the outlet Figurepressure 2. Various is increasejector operationed further, modes at ait fixe reachesd primary a and pressure, secondary inlet pressures., at which the ment ratio (the y-axis) is the ratio of secondary to primary mass flow rates. ejector starts to malfunction.Entrainment ratio (theThere y-axis) will is the beratio noof secondary secondary to primary flow mass or,flow even,rates. reverse flow through the secondaryAs inlet we increasewill occur. the outlet In pr pressure,actice, thean secondaryejector is flow usually will notrequired be choked to any- operate in the criticalmore mode/condition, (only the primary and flow henc is choked).e, it is Thisalso pressure called the threshold on-design is referred condition. to as critical pressure, Pcrit. Beyond this pressure, the ejector will enter the sub-critical mode operation within which an increase in P4 will decrease the secondary mass flow rate but has no effect on the primary massSub-critical flow rate. As the outlet pressuremode is increased further, it reaches a pressure, Pmal, at which the Criticalejector mode starts to malfunction. There will Malfunction be no secondary flow or, even, reverse flow through the secondary inlet will occur. In practice, an ejector is usually required to operate in the critical mode/condition, and hence, it is also called the on-design condition. Designing an ejector is an important task so that the system utilizing this device is not only able to operate functionally, but also efficiently. To know/predict the performance of an ejector, analytical and computational fluid dynamics (CFD) models are usually used before experiment. The one-dimensional analytical model has an advantage over the CFD for its simplicity and quick result. It does not require the time-consuming generation of the discretized EntrainmentER ratio, Outlet pressure, Figure 2. Various ejector operation modes at a fixed primary and secondary inlet pressures.