An investigation on the component efficiencies of a small two-phase ejector

international journal of refrigeration 71 (2016) 26–38

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An investigation on the component efficiencies of a small two-phase ejector Xiao Wang, Jianlin Yu * Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

A R T I C L E

I N F O

A B S T R A C T

Article history:

This paper presents an investigation on the component efficiencies of a small two-phase

Received 6 May 2016

ejector. The experiments are firstly carried out to test the operation characteristics of a small

Received in revised form 8 August

two-phase ejector working with R600a. Combining the measured experimental data with

2016

an ejector model, a calculation method for the component efficiencies of the small two-

Accepted 12 August 2016

phase ejector including the motive nozzle, mixing chamber and diffuser is proposed. The

Available online 16 August 2016

results reveal that the ejector component efficiencies vary obviously with geometric parameters and operational conditions. The motive nozzle, mixing chamber and diffuser

Keywords:

efficiencies vary from 0.513 to 0.750, 0.492 to 0.755 and 0.610 to 0.734 under the studied con-

Component efficiencies

ditions, respectively. Moreover, three empirical correlations for the above mentioned component

Empirical correlations

efficiencies are summarized. The present study is hoped to be useful for the modeling and

Experiment

design of the two-phase ejector and contributes to the further researches on the variable

Two-phase ejector

characteristics of ejector component efficiencies. © 2016 Elsevier Ltd and IIR. All rights reserved.

Une étude de l’efficacité des composants d’un petit éjecteur diphasique Mots clés : Efficacités de composants ; Corrélations empiriques ; Expérience ; Éjecteur diphasique

1.

Introduction

With advantages of no moving parts, simple structure, long service life and low maintenance cost, applications of ejector in refrigeration systems have been widely studied. According to the functions of ejector in refrigeration systems, there are two main applications for the utilization of ejector, i.e. the ejector

refrigeration system and the ejector enhanced vapor compression refrigeration system. In a typical ejector refrigeration system such as the studies of Chandra and Ahmed (2014) and Bourhan et al. (2015), the ejectors were introduced to fulfill the function of the compressor and could be driven by low grade thermal energy or renewable energy. In the ejector enhanced vapor compression refrigeration systems such as those in the studies of Sag et al. (2015) and Lin et al. (2012a,2012b), the ejectors were

* Corresponding author. Department of Refrigeration & Cryogenic Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China. Fax: +86 29 82668725. E-mail address: [email protected] (J. Yu). http://dx.doi.org/10.1016/j.ijrefrig.2016.08.006 0140-7007/© 2016 Elsevier Ltd and IIR. All rights reserved.

international journal of refrigeration 71 (2016) 26–38

Nomenclature

A D h L  m NXP P q rp s t v w x

area [mm2] diameter [mm] specific enthalpy [ kJ kg −1 ] length [mm] mass flow rate [ kg h −1 ] nozzle exit position [mm] pressure [kPa] heating power [kW] pressure lift ratio of the ejector specific entropy [ kJ kg −1 K −1 ] temperature [°C] specific volume [ m3 kg −1 ] velocity [m s−1] quality

Greek letters η ejector efficiency μ entrainment ratio θ converging angle [°] Subscripts diffuser d m mixing chamber n nozzle p primary fluid s secondary fluid, isentropic process 1 inlet 2 outlet

used as expansion devices instead of the expansion valve or capillary tube to recover the expansion work and enhance the system performance. As summarized in the reviews of Sarkar (2012), Sumeru et al. (2012), Chen et al. (2015) and Besagni et al. (2016), more and more attentions have been drawn on the researches of refrigeration systems with the ejector in recent years, since the mentioned ejector applications in refrigeration systems perfectly meet the demands for environmentally friendly energy utilization and sustainable development. The working fluid flow in the ejector is very complicated and introduces irreversibilities due to the frictional effects, flow separation and interactions.The energy losses in the ejector are usually considered by introducing the ejector component efficiencies. Most studies of the ejector systems focused on the system performance characteristics under different ejector geometric parameters or operational conditions, and simply assumed the ejector component efficiencies as fixed values without considering the effects of the geometric parameters and operational conditions.Take the recently published papers for examples, when Xing et al. (2014) developed the mathematical model for a twostage transcritical CO2 heat pump cycle with double ejectors, the efficiencies of 0.85, 0.85 and 0.95 were assumed for the motive nozzle, mixing chamber and diffuser, respectively. Wang et al. (2015) gave the fixed motive nozzle efficiency of 0.90, mixing efficiency of 0.85 and diffuser efficiency of 0.80 in their study on a new ejector enhanced vapor injection heat pump cycle. In Saban and Tuncay’s (2015) study on the two-phase ejector

27

air-conditioning system for buses, the nozzle, mixing and diffuser section efficiencies were taken as 0.90, 0.80 and 0.90. Khaled et al. (2014) assumed the values of 0.85, 0.97 and 0.70 for the nozzle, mixing and diffuser efficiencies in their research on modeling and numerical approach for the design and operation of two-phase ejectors. Chen et al. (2014) fixed the motive nozzle efficiency at 0.90, mixing efficiency at 0.85 and diffuser efficiency at 0.90 in their modeling study for determining the optimum performance and obtaining the design area ratio of the ejector in an ejector refrigeration system. In fact, the ejector component efficiencies are variable values with different ejector geometric parameters and operational conditions and have obvious influences on the performance of the ejector system. For examples, Aly et al. (1999) found that a fall in nozzle efficiency from 1 to 0.8 was predicted to result in a 25% increase in the steam to vapor ratio and the diffuser efficiency also had an effect on steam to vapor ratio. Chen et al. (2014) pointed out that the entrainment ratio largely increased with ejector component efficiencies. Deng et al. (2007) found that the COP of the transcritical CO2 refrigeration cycle with an ejector increased with the nozzle and diffuser efficiencies. Besagni et al. (2015a) performed a sensitivity analysis for the influences of the ejector component efficiencies and pointed out that a variation of ±0.05 in ejector component efficiency could lead to an appreciable effect of ±5% on the ejector modeling results. However, no information was given about the exact factors influencing the ejector component efficiencies in the mentioned studies. There are only a few reports in the opening literature focusing on the variable characteristics of the ejector component efficiencies. Huang et al. (1999) selected proper R141b ejector component efficiencies so that the experimentally measured performance data would fit best to the predicted model values. According to their study results, an equation for the mixing efficiency was preliminary given as a function of the ejector area ratio. Varga et al. (2009) used CFD (computational fluid dynamics) method to study the water ejector component efficiencies under different operational conditions.The results showed that the nozzle efficiency was only slightly affected by the nozzle diameter, and the suction efficiency was constant value when the ejector was operating below critical back pressure. The efficiencies of mixing and diffuser sections largely depended on operational conditions. Liu and Groll (2013) gave a comprehensive study on CO2 ejector component efficiencies under different operating conditions based on the ejector model and the measured experimental data. Three ejector component efficiency empirical correlations were established as the functions of ejector geometry, pressure ratio and entrainment ratio. Zheng et al. (2015,2016) modified Liu and Groll’s empirical correlations to be more practical and the modified empirical correlations only related to the pressure ratio and the diameter ratio. Besagni et al. (2014,2015b) used CFD approach to analyze the operation pressure influences on ideal gas ejector component efficiencies and proposed ejector component efficiencies correlations as functions of the inlet and outlet pressures of the ejector. These studies are far from enough due to the wide use of the ejector with different working fluids and applications. More comprehensive studies about the effects of geometric parameters and operational conditions on the variable characteristics of ejector component efficiencies are highly needed for the further development of the ejector systems.

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In this paper, performance of a small two-phase ejector working with R600a is firstly tested under different geometric parameters and operational conditions. The measured experimental data are introduced into the ejector model to determine the component efficiencies of the small two-phase ejector including the motive nozzle, mixing chamber and diffuser. The effects of the diameter ratio, the NXP (nozzle exit position), the pressure ratio and the primary fluid quality on the mentioned ejector component efficiencies are analyzed in detail. In addition, empirical correlations for the ejector component efficiencies are summarized as functions of the geometric parameters and operational conditions. The aim of this paper is to provide deep insights into the variable characteristics of ejector component efficiencies and it is hoped to be useful for the further ejector applications in refrigeration systems.

2.

Description of the experimental setup

In order to investigate the two-phase ejector performance with different geometric parameters, an ejector with converging motive nozzle is designed and tested. Fig. 1(a) shows the internal

geometric schematic of the tested ejector. The converging angles of the motive nozzle θ n and the constant-pressure mixing chamber θ m are 11° and 21°. The length of the mixing chamber throat and the diffuser Ld are 10 mm and 30 mm. The diameters of the motive nozzle inlet Dni , the secondary flow inlet Ds , the mixing chamber throat Dm and the diffuser exit Dd are 5 mm, 6 mm, 2 mm and 6.5 mm, respectively. The diameter of the motive nozzle throat Dn and the NXP are variable geometric parameters to be tested in this study. Four converging motive nozzles with different throat diameters Dn of 0.6 mm, 0.8 mm, 1.0 mm and 1.2 mm are alternative during the experiments. The NXP is adjusted by varying the thickness of the PTFE (poly tetra fluoro ethylene) gaskets between the motive nozzle and the suction chamber. Fig. 1(b) shows the general view of the tested ejector. The ejector is tested in the experimental setup charged with R600a. As shown in Fig. 2, besides the tested ejector, main equipment of the experimental setup includes a hermetic reciprocating compressor, an air-cooled condenser in which the rotation speed of the fan is adjustable, a SLHE (suction line heat exchanger), two evaporators, and a separator. Thus, the twophase fluid at the outlet of the high-temperature evaporator

Fig. 1 – (a) The internal geometric schematic of the tested ejector. (b) The general view of the tested ejector.

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Fig. 2 – The schematic diagram of the experimental setup.

flows into the tested ejector motive nozzle as the primary fluid, and the vapor fluid at the outlet of the low-temperature evaporator is sucked into the ejector as the secondary fluid. The mixed two-phase fluid coming from the ejector is separated in the separator. The saturated liquid fluid at the bottom of the separator flows into the low-temperature evaporator after being throttled down and the saturated vapor fluid is heated in the SLHX and then enters to the compressor. It should be noted that two needle valves are used as throttling devices since the pressure drop between the inlet and outlet of the needle valve can be continuously varied. The different primary fluid and secondary fluid pressures for the ejector can be obtained by adjusting the opening of the two needle valves. In addition, two silicone heating tapes are wrapped laterally with thermal insulation material to avoid lateral heat conduction and are used as heat sources for the two evaporators. Thus, the twophase ejector performance with different operational conditions can be also tested in this experimental setup. The determination of the ejector component efficiencies needs to know some specified parameters such as the flow rates and state parameters at the two inlets and one outlet of the ejector. The mass flow rates of the primary and the secondary fluids are very low due to the small dimensions of the experimental ejectors. However, the volume flow rates of the superheated vapors are relatively high and easy to measure. For this reason, two volume flowmeters are used to measure volume flow rates where the primary and the secondary fluids are under the state of superheated vapor. Combining with the measured data of temperatures and pressures, the mass flow rates could be calculated based on the volume flow rates. The primary fluid flow rate is measured by the flowmeter installed between the compressor suction inlet and the SLHX.

The secondary fluid flow rate is measured by the flowmeter installed between the ejector suction nozzle and the low temperature evaporator. Both of the two flowmeters are target flowmeters calibrated for R600a with accuracies of ±0.5% of the reading value. Temperatures of the refrigerant along the refrigeration loop are obtained by the calibrated T-type thermocouples with the maximum error of ±0.1 °C. Pressures are acquired continuously through pressure transducers with the ±0.1% accuracies of the full scale. The heating powers of silicone heating tapes are measured by the digital multimeters with accuracies of 0.2% of the reading value. The mass flow rate calculated from the measured data shows an acceptable uncertainty of 2.3%. All experimental data including temperature, pressure, heating power and flow rate should be stable for at least 30 minutes before acquired, and data are acquired and stored in an Excel file automatically through a data acquisition system. Based on the experimental setup, 12 ejectors with different geometric parameters listed in Table 1 are tested under 5 different pressure ratios of the primary fluid and secondary fluid Pp1/Ps1.

Table 1 – Tested ejectors with different Dn/Dm and NXP. Ejector E1 E2 E3 E4 E5 E6

Dn/Dm

NXP

Ejector

Dn/Dm

NXP

0.3 0.3 0.3 0.4 0.4 0.4

2 mm 6 mm 10 mm 2 mm 6 mm 10 mm

E7 E8 E9 E10 E11 E12

0.5 0.5 0.5 0.6 0.6 0.6

2 mm 6 mm 10 mm 2 mm 6 mm 10 mm

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3.

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xp1 = x ( Pp1, hp1 ) ,

Description of the modeling

In order to determine the ejector component efficiencies, mathematical models of the two-phase ejector components are presented using a one-dimensional model based on mass, momentum and energy balances. The constant pressure mixing methodology of modeling the ejector is carried out (He et al., 2009; Liu et al., 2012; Yari and Mahmoudi, 2011). In order to simplify the modeling progress, the homogeneous flow model is also used for the two-phase ejector. Furthermore, the following assumptions are considered: (1) the flow is steady and the inner walls of the ejector are assumed to be adiabatic; (2) the pressure drop in the suction nozzle is given as a constant value of 2 kPa, which would obtain the optimum COP of the cycle (Ersoy and Bilir, 2012; Li et al., 2014a, 2014b); (3) the energy losses in the ejector are considered by introducing the component efficiencies of the motive nozzle, mixing chamber and diffuser; (4) the inlet and outlet velocities of working fluids in the ejector are neglected; (5) the flow in the converging motive nozzle will not exceed sound speed (Liu and Groll, 2013). With the above assumptions, the following equations can be obtained in terms of the mass, momentum and energy conservation:

∑ (ρ Aw)

in

= ∑ ( ρ Aw)out

∑ ( PA + ρ Aw ) 2

⎡

⎛

∑ ⎣⎢ρ Aw ⎜⎝ h + 3.1.

in

= ∑ ( PA + ρ Aw2 )out

w2 ⎞ ⎤ w2 ⎞ ⎤ ⎡ ⎛ = ∑ ⎢ ρAw ⎜ h + ⎟ ⎟ ⎝ 2 ⎠ ⎦⎥ in 2 ⎠ ⎥⎦out ⎣

(1)

(2)

(3)

Motive nozzle

Based on the nozzle throat area At, the given pressure drop in the suction nozzle ΔP and the experimentally measured data of the motive nozzle inlet pressure Pp1, the mass flow rate of the primary fluid mp,test and the heating power of the high temperature silicone heating tape, the following equations are solved for the motive nozzle throat mass flow rate mp,cal with an initial assumed motive nozzle efficiency ηn. The inlet specific enthalpy of the primary fluid can be obtained according to the energy conservation in the hightemperature evaporator:

hp1 = hhi + qer

sp1 = s ( Pp1, hp1 )

(5)

The exit pressure and specific enthalpy through an isentropic expansion process in the nozzle can be calculated as:

hp2s = h ( Pp2, sp1 )

Pp2 = Ps1 − ΔP,

(6)

The actual flow in the ejector nozzle is a non-isentropic expansion progress and introduces irreversibility results from frictional effects, flow separation and internal heat transfer. The nozzle efficiency ηn is defined as:

ηn =

hp1 − hp 2 hp1 − hp 2 s

(7)

The actual exit specific enthalpy and volume of the primary fluid in the nozzle can be obtained as:

hp2 = (1 − ηn ) hp1 + ηn hp2s,

vp2 = v ( Pp2, hp2 )

(8)

From the energy conservation, the velocity of primary fluid leaving the nozzle can be found as:

wp2 = 2ηn (hp1 − hp2s )

(9)

By giving the nozzle throat area, the mass flow rate through the nozzle throat can be calculated by:

mp,cal = w p2 An vp2

3.2.

(10)

Suction nozzle

The pressure drop in the suction nozzle is so small compared with that in the motive nozzle that the frictional loss in the suction nozzle can be neglected. The secondary fluid through the suction nozzle is regarded as the isentropic expansion progress. Similar to the calculation progress of the flow in the motive nozzle, the inlet pressure and temperature of the superheated secondary fluid can be measured and the other state parameters can be obtained as:

hs1 = h ( Ps1, Ts1 ) ,

ss1 = s ( Ps1, Ts1 )

(11)

The exit pressure and specific enthalpy of the secondary fluid flow through the suction nozzle can be expressed as:

Ps2 = Ps1 − ΔP,

hs2 = h ( Ps2, ss1 )

(12)

The velocity of secondary fluid leaving the suction nozzle can be obtained according to the energy conservation:

ws2 = 2 (hs2 − hs1 )

(13)

(4)

3.3. where hhi is the specific enthalpy at the inlet of the hightemperature evaporator; qer is the heating power of the high temperature silicone heating tape. The quality and specific entropy of the two-phase primary fluid can be found as:

Mixing chamber

Based on the mixing chamber throat area Am, the measured data of the mass flow rate of the two fluids mp,test and ms,test and the calculation results of the motive and suction nozzle models, the following equations are solved for the mass flow

international journal of refrigeration 71 (2016) 26–38

rate through the mixing chamber throat mm,cal with an initial assumed mixing efficiency ηm. The momentum conservation in the mixing chamber can be expressed as:

mpwp2 + ms ws2 = (mp + ms ) wm 2s

2 wm 2 2 wm 2s

(15)

The entrainment ratio is an important parameter for evaluating the ejector performance and defined as:

μ=

s m p m

(16)

Combining the above equations, the actual velocity of the mixed fluid can be expressed as:

wm 2 =

wp2 + μws2 ηm 1+μ

(17)

Based on the energy conservation equation for the mixing chamber, the specific enthalpy and volume of the mixed fluid can be expressed as:

hm 2 =

2 hp1 + μhs1 wm 2 , − 1+μ 2

vm 2 = v ( Pm 2, hm 2 )

(18)

Under the given mixing chamber throat area, the mass flow rate through the mixing chamber throat can be calculated by:

mm,cal = w m 2 Am vm 2

3.4.

(19)

Diffuser

Based on the measured data of the diffuser outlet pressure Pd2 and the calculation results of the mixing chamber model, the following equations are solved for the quality of the diffuser outlet fluid xd2 with an initial assumed diffuser efficiency ηd. The specific entropy of the two-phase mixed fluid in the mixing chamber can be found as:

sm 2 = s ( Pm 2, vm 2 )

(22)

The actual specific enthalpy and quality of the diffuser outlet fluid can be obtained as:

hd2 = hm 2 + (hd2s − hm 2 ) ηd,

xd2 = x ( Pd2, hd2 )

(23)

The fundamental relationship between the entrainment ratio of the ejector, μ , and the quality of the diffuser outlet fluid xd2 must satisfy a mass balance for the steady-state operation of the cycle (Neal and Stefan, 2013; Sarkar, 2010; Yari, 2009):

1 + μ = 1 xd 2

(24)

Thus, the calculation of the ejector component efficiencies can be performed based on the above equations. The calculation program is written in Fortran Language where the refrigerant thermodynamic properties are calculated by using NIST database and subroutines (Lemmon et al., 2007). Specified parameters of the pressure, temperature, ejector area, heating power and mass flow rates are measured during the experiment. The outline of the iteration calculation procedure for the determination of ejector component efficiencies is shown in Fig. 3. As shown in Fig. 3, the motive nozzle efficiency ηn is adjusted until the measured primary fluid mass flow rate mp,test is equal to the calculated mass flow rate through the motive nozzle throat mp,cal. It should be pointed out that the primary flow at nozzle outlet is checked to make sure that the flow speed is less than sound speed (Liu and Groll, 2013). The mixing efficiency ηm is adjusted until the measured total mass flow rate ms,test + mp,test is equal to the calculated mass flow rate through the mixing chamber throat mm,cal. It should be noted that the tested two-phase ejectors work under the condition of the design criteria for the steady-state operation calculation of the two-phase ejector used as an expander in the refrigeration cycle. The diffuser outlet quality xd2 could be obtained from the experimentally measured mass flow rate ratio (i.e. ejector entrainment ratio μ ) according to Eq. (24). Thus, the diffuser efficiency ηd is adjusted until the ejector entrainment ratio μ and the diffuser outlet quality xd2 satisfy the given balance in Eq. (24) under the measured diffuser outlet pressure Pd2. The tolerance of 0.1% is used for convergence in the iteration calculation for each ejector component efficiency, which may give acceptable uncertainties for the proposed ejector component efficiencies below 5.3%.

4.

Results and discussion

(20)

The exit specific enthalpy through an isentropic compression process in the diffuser can be found as:

hd2s = h ( Pd2, sm 2 )

hd2s − hm 2 hd2 − hm 2

(14)

where wm2s is velocity of the mixed fluid through an ideal mixing process in the mixing chamber The flow in the mixing chamber and the diffuser is very complicated, involving strong flow interactions, shear forces, turbulent mixing and even vortices. The mixing efficiency ηm is defined as a kinetic energy ratio between the actual and ideal velocities of the mixed fluid:

ηm =

ηd =

31

(21)

The actual flow in the diffuser is a non-isentropic compression and the irreversibility losses are taken into account by using the isentropic efficiency of the diffuser ηd:

Combining the experimental data with the proposed models, ejector component efficiencies of the motive nozzle, mixing chamber and diffuser are obtained with the mentioned 60 experimental operation data points. In the following discussion, the effects of the geometric parameters and operational conditions on the motive nozzle, mixing chamber and diffuser efficiencies are analyzed in detail. Furthermore, the empirical correlations of the three ejector component efficiencies are proposed and validated.

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Fig. 4 – Motive nozzle efficiencies determined from all experimental data points.

Fig. 3 – The calculation procedure for determining ejector component efficiencies.

4.1.

the motive nozzle efficiency. The motive nozzle efficiency obviously increases when the diameter ratio increases from 0.4 to 0.5, while the motive nozzle efficiency shows a relatively slight increase when the diameter ratio further increases to 0.6. Fig. 6 shows the motive nozzle efficiency variation with diameter ratio under different pressure ratios and NXPs. It is seen that motive nozzle efficiency increases with diameter ratio and the increasing rate is decreasing. For the fixed pressure ratio of 4 and the NXP of 6 mm, as the diameter ratio increases from 0.3 to 0.5, the motive nozzle efficiency shows a significant increase from 0.518 to 0.620. After that, the motive nozzle efficiency slightly increases to 0.623 when the diameter ratio increases from 0.5 to 0.6. It is also seen that the motive nozzle efficiency is more sensitive to the pressure ratio than the NXP. For the considered operation conditions with fixed NXP of 6 mm, the average motive nozzle efficiencies are 0.696, 0.658 and 0.589 for pressure ratios of 2, 3 and 4. While for the considered

Motive nozzle efficiency

Fig. 4 displays the all 60 motive nozzle efficiencies determined from the experimental data points. The results show that the motive nozzle efficiencies vary from 0.513 to 0.750 with different geometric parameters and operational conditions. To be specific, the motive nozzle efficiency of ejector E1 can be as low as 0.513 with the pressure ratio of 4. While the motive nozzle efficiency of ejector E12 reaches 0.750 with the pressure ratio of 2. The pressure ratio, diameter ratio and NXP may have influences on the motive nozzle efficiency. The effects of the mentioned parameters are further analyzed in detail with typical cases. Fig. 5 displays the motive nozzle efficiency variation with pressure ratio for different ejector geometric parameters. It can be observed from Fig. 5 that the motive nozzle efficiency decreases with the pressure ratio. Take the geometric parameter with diameter ratio of 0.4 and NXP of 6 mm for example. As the pressure ratio increases from 2.0 to 4.0, the motive nozzle efficiency decreases from 0.705 to 0.595. Moreover, results also indicate that the diameter ratio also has certain influence on

Fig. 5 – The motive nozzle efficiency variation with pressure ratio.

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33

Fig. 6 – The motive nozzle efficiency variation with diameter ratio.

operation conditions with fixed pressure ratios, the motive nozzle efficiencies are almost the same for different NXPs. Fig. 7 displays the motive nozzle efficiency variation with NXP under different pressure ratios and diameter ratios. It is confirmed that the motive nozzle efficiency is not sensitive to the NXP. When the NXP increases from 2 mm to 10 mm, the motive nozzle efficiencies with diameter ratio of 0.5 range from 0.723 to 0.732, 0.690 to 0.694 and 0.620 to 0.626 for pressure ratios of 2, 3 and 4, respectively. This means the motive nozzle efficiency dependency on the NXP is very small at the NXP range of 2 mm to 10 mm, where the motive nozzle efficiency variation is less than 0.01. In consideration of the characteristic that the two phase fluid is used as the primary fluid in the motive nozzle, the quality xp1 is an important factor to the ejector performance and the motive nozzle efficiency which should also be investigated. It should be pointed out that the value of the primary fluid quality is not the controlled factor during the test and is calculated during data reduction progress. Fig. 8(a) shows the effects of the primary fluid quality on the ejector E8 performance of

Fig. 8 – (a) The effects of the primary fluid quality on the ejector performance. (b) The motive nozzle efficiency variation with primary fluid quality.

pressure lift ratio and entrainment ratio. The pressure lift ratio obviously increases with the primary fluid quality, while the entrainment ratio shows the opposite tendency. Fig. 8(b) shows the motive nozzle efficiency variation with quality for different ejector geometric parameters. As shown in Fig. 8(b), the motive nozzle efficiency obviously increases with the primary fluid quality. In general, four factors including pressure ratio, diameter ratio, NXP and primary fluid quality are investigated for their effects on the motive nozzle efficiency. The results indicate that the pressure ratio, diameter ratio and primary fluid quality are the main determining factors of the motive nozzle efficiency and the NXP has slight influence on the motive nozzle efficiency.

4.2.

Fig. 7 – The motive nozzle efficiency variation with NXP.

Mixing efficiency

Fig. 9 displays all the 60 mixing efficiencies determined from the experimental data points. The results show that the mixing efficiencies vary from 0.492 to 0.755 for the considered operation conditions. The ejector E9 with the pressure ratio of 4 has the lowest mixing efficiency of 0.492, while the ejector E1 with

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international journal of refrigeration 71 (2016) 26–38

Fig. 9 – Mixing efficiencies determined from all experimental data points.

the pressure ratio of 4 has the highest mixing efficiency of 0.755. Similar to the discussion above, the effects of the pressure ratio, diameter ratio and NXP on the mixing efficiency are further analyzed in detail with typical cases. The mixing efficiency variation with pressure ratio for different ejector geometric parameters is shown in Fig. 10. It can be found from Fig. 10 that when the pressure ratio is under 3.0, the mixing efficiency increases with the pressure ratio but the increasing rate is decreasing. When the pressure ratio is over 3.0, the mixing efficiency slightly varies and even slightly decreases with the increase of the pressure ratio. Using the ejector with diameter ratio of 0.5 and NXP of 6 mm, the mixing efficiency significantly increases from 0.527 to 0.728 when the pressure ratio increases from 2.0 to 3.0, while with the further increase of pressure ratio from 3.0 to 4.0, the mixing efficiency shows a slight decrease from 0.728 to 0.719. The results also show that the diameter ratio and the NXP have certain influences on the mixing efficiency.

Fig. 10 – The mixing efficiency variation with pressure ratio.

Fig. 11 – The mixing efficiency variation with diameter ratio.

Fig. 11 presents the mixing efficiency variation with diameter ratio under different pressure ratios and NXPs. It is seen that mixing efficiency decreases with the diameter ratio. Take the operation condition with pressure ratio of 2 and NXP of 6 mm for example. When the diameter ratio increases from 0.3 to 0.6, the mixing efficiency shows a decrease from 0.610 to 0.514. It is also found that the mixing efficiency is very sensitive to the pressure ratio, especially with low pressure ratio. For the tested operation conditions with fixed NXP of 6 mm, the average motive mixing efficiencies are 0.565, 0.714 and 0.723 for pressure ratios of 2, 3 and 4, while the NXP has relatively small influence on the mixing efficiency since the average mixing efficiencies with fixed pressure ratio of 3 are 0.731, 0.714 and 0.711 for different NXPs of 2 mm, 6 mm and 10 mm. The variation of the mixing efficiency with the NXP under different pressure ratios and diameter ratios is presented in Fig. 12. It can be seen that when the NXP is less than 6 mm, the mixing efficiency slowly decreases with the NXP. When the NXP is over 6 mm, the ejector efficiency slightly changes with the NXP. The mixing efficiency with the fixed pressure ratio of

Fig. 12 – The mixing efficiency variation with NXP.

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35

Fig. 13 – Diffuser efficiencies determined from all experimental data points.

Fig. 14 – The diffuser efficiency variation with pressure ratio.

3 and diameter ratio of 0.4 decreases from 0.738 to 0.718 as the NXP increases from 2 mm to 6 mm. After that a further increase in NXP results to the slight increase of the mixing efficiency from 0.718 to 0.721. The results indicate that the mixing efficiency dependency on the NXP is relatively small compared with pressure ratio and diameter ratio.

ratio increases from 0.3 to 0.6, the diffuser efficiency slightly increases from 0.700 to 0.715. Furthermore, the results also indicate that the diffuser efficiency dependency on the NXP is relatively small compared with pressure ratio. For the particular range of operation condition, the average diffuser efficiencies with the same NXP of 6 mm are 0.707, 0.665 and 0.629 for pressure ratios of 2, 3 and 4, respectively, while the average diffuser efficiencies with the same pressure ratio of 3 are 0.680, 0.665 and 0.651 for NXPs of 2 mm, 6 mm and 10 mm, respectively. Fig. 16 shows the variation of the diffuser efficiency with the NXP for different pressure ratios and diameter ratios. As shown in Fig. 16, the diffuser efficiency shows a nearly linear decrease with NXP. And the diffuser efficiency dependency on the NXP is larger than the diameter ratio while smaller than the pressure ratio. For example, with the pressure ratio of 2 and the diameter ratio of 0.5, the diffuser efficiency decreases from 0.726 to 0.688 when the NXP increases from 2 mm to 10 mm. With the fixed pressure ratio of 3, the average diffuser

4.3.

Diffuser efficiency

Fig. 13 displays all the 60 diffuser efficiencies determined from the experimental data points. Compared to the motive nozzle efficiency and mixing efficiency, the diffuser efficiency variation range is relatively small for the same tested operation conditions. The ejector E3 with the pressure ratio of 4 has the lowest diffuser efficiency of 0.610, while the ejector E10 with the pressure ratio of 2 has the highest mixing efficiency of 0.734. In the following discussion, the effects of the pressure ratio, diameter ratio and NXP on the diffuser efficiency are analyzed under typical operation conditions. Fig. 14 presents the diffuser efficiency variation with the pressure ratio for different ejector geometric parameters. It is observed that the diffuser efficiency shows a nearly linear decrease with the pressure ratio. For the ejector with the diameter ratio 0.4 and NXP of 6 mm, the diffuser efficiency decreases from 0.705 to 0.595 when the pressure ratio increases from 2.0 to 4.0. In addition, both of the diameter ratio and NXP have influence on the diffuser efficiency, but the diffuser efficiency is more sensitive to the NXP. Under the tested conditions, the average diffuser efficiencies with the same NXP of 6 mm are 0.673, 0.680 and 0.685 for diameter ratios of 0.4, 0.5 and 0.6, respectively, while the average diffuser efficiencies with the same diameter ratio of 0.5 are 0.699, 0.680 and 0.662 for NXPs of 2 mm, 6 mm and 10 mm, respectively. Fig. 15 displays the diffuser efficiency variation with the diameter ratio under different pressure ratios and NXPs. As mentioned above, the diffuser efficiency is not so sensitive to the diameter ratio and shows the slow increase tendency with the diameter ratio. Take the operation condition with pressure ratio of 2 and NXP of 6 mm for example. As the diameter

Fig. 15 – The diffuser efficiency variation with diameter ratio.

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Fig. 16 – The diffuser efficiency variation with NXP.

efficiencies are 0.664, 0.670 and 0.673 for diameter ratios of 0.4, 0.5 and 0.6, respectively, while with the fixed diameter ratio of 0.5, the average diffuser efficiencies are 0.708, 0.670 and 0.635 for pressure ratios of 2, 3 and 4, respectively.

4.4. Empirical correlations of the ejector component efficiencies Combining the measured experimental data with the proposed ejector model, three empirical correlations for the motive nozzle, mixing chamber and diffuser efficiencies are summarized as Eq. (25) to Eq. (27) based on the determined ejector component efficiencies as shown in Fig. 4, Fig. 9 and Fig. 13. As analyzed above, the motive nozzle efficiency dependency on the NXP is so small that the motive nozzle efficiency variation is less than 0.01 during the variation of the NXP. On the contrary, the primary fluid quality has obvious influence on the motive nozzle efficiency. Thus the motive nozzle efficiency correlation is developed as a function of the pressure ratio, diameter ratio and primary fluid quality. With regard to the mixing chamber and diffuser efficiencies, the pressure ratio, diameter ratio and NXP are selected as the determining factors for these two component efficiencies. Taking account of the correlation and the complexity of the equations, higherdegree polynomials are chosen as the particular form for the empirical correlations. It should be pointed out that the three proposed ejector component efficiency empirical correlations can be used with refrigerant R600a under the following operation conditions:

0.6 mm ≤ Dn ≤ 1.2 mm,

2

Pp1 Pp1 D 2 ηn = −0.01615 ⎛⎜ ⎞⎟ + 0.06925 − 1.32811 ⎛⎜ n ⎞⎟ ⎝ Ps1 ⎠ ⎝ Dm ⎠ Ps1 Dn 2 + 1.40543 − 1.25177xp1 + 1.54065xp1 − 0.16937 Dm

Pp1 4 Pp1 3 Pp1 2 ηm = −0.50685 ⎛⎜ ⎞⎟ + 5.91466 ⎛⎜ ⎞⎟ − 25.43486 ⎛⎜ ⎞⎟ ⎝ Ps1 ⎠ ⎝ Ps1 ⎠ ⎝ Ps1 ⎠ + 47.90428

Pp1 D 4 D 3 + 12.50076 ⎛⎜ n ⎞⎟ − 17.06804 ⎛⎜ n ⎞⎟ ⎠ ⎝ ⎝ Ps1 Dm Dm ⎠

D 2 D + 7.52924 ⎛⎜ n ⎞⎟ − 1.29759 n ⎝ Dm ⎠ Dm − 0.00016NXP2 − 0.0018NXP − 32.60023 Pp1 2 Pp1 D 2 ηd = 0.00482 ⎛⎜ ⎞⎟ − 0.06947 + 0.08833 ⎛⎜ n ⎞⎟ ⎝ Ps1 ⎠ ⎝ Dm ⎠ Ps1 Dn 2 − 0.04263 + 0.00013NXP − 0.00744NXP + 0.87024 Dm

100 kPa ≤ Pp1 ≤ 200 kPa, 50 kPa ≤ Ps1 ≤ 70 kPa, 2 mm ≤ NXP ≤ 10 mm, 0.313 ≤ xp1 ≤ 0.531, Dm = 2 mm

Fig. 17 – (a) Comparison between the calculated and tested pressure lift ratios. (b) Comparison between the calculated and tested entrainment ratios.

(25)

(26)

(27)

The three empirical correlations show acceptable accuracies in predicting the corresponding component efficiency with the coefficients of determination (R2) of 98.8%, 96.7%, 98.0% and the average relative errors of 1.03%, 1.86% and 1.35% for the motive nozzle, mixing chamber and diffuser efficiencies, respectively. Instead of using the assumed fixed values of the three component

international journal of refrigeration 71 (2016) 26–38

efficiencies, the established ejector component efficiency empirical correlations are supposed to improve the accuracy of the mathematical models in predicting the performance of ejector enhanced refrigeration cycles under certain operation conditions. In order to validate the feasibility of the ejector component efficiency empirical correlations, the ejector performance under the mentioned 60 experimental operation conditions are simulated using the previously developed cycle model (Wang et al., 2014). It should be pointed out that the simulation conditions (such as the condensing temperature, the subcooling degree in the condenser, the compressor suction temperature, etc.) should be adjusted to match the experimental operation conditions in the simulation progress. Fig. 17(a) and (b) shows the comparisons of the calculated and tested pressure lift ratio and entrainment ratio. As shown in Fig. 17(a) and (b), the calculated results based on the simulation model combined with the empirical correlations agree well with the tested results from the experiment, showing the maximum errors of ±7% and ±12% for the pressure lift ratio and the entrainment ratio. It should be noted that the efficiencies obtained from our study cannot be directly used to larger ejectors or other applications with different working fluids because the ejector geometry and refrigerant thermodynamic properties usually have effects on these efficiencies. But the calculation method proposed in the present paper could be used for estimating the ejector component efficiencies with larger geometry or different working fluids under their application conditions.

4.5.

Comparison with the literature

A comparison of ejector component efficiencies studies presented by Varga et al. (2009), Liu and Groll (2013), Besagni et al. (2014, 2015b) and the current study are summarized in Table 2. More detailed information for their result discussions and ejector component efficiency empirical correlations can be

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found in the original references. As summarized in Table 2, although the working fluids and conditions for the mentioned studies are quite different from our study, some agreements could be found for supporting our findings. For example, the ηn variation with Dn/Dm and Pp1/Ps1, the ηm variation with Dn/Dm found in our study agree well with Liu and Groll (2013). The variation tendency of ηd with Dn/Dm in our study is also found by Varga et al. (2009).

5.

Conclusions

This paper presents an investigation on the component efficiencies of a small two-phase ejector combining the measured experimental data with the ejector model. The performance of a small two-phase ejector working with R600a is experimentally tested for 60 experimental operation conditions with different geometric parameters (D m = 2 mm, 2 mm ≤ NXP ≤ 10 mm, 0.6 mm ≤ D n ≤ 1.2 mm) and operational conditions (100 kPa ≤ Pp1 ≤ 200 kPa, 50 kPa ≤ Ps1 ≤ 70 kPa, 0.313 ≤ xp1 ≤ 0.531). The measured data are introduced into the ejector model and the component efficiencies of the small two-phase ejector are obtained and analyzed. The results indicate that the efficiencies of the motive nozzle, mixing chamber and diffuser vary from 0.513 to 0.750, 0.492 to 0.755 and 0.610 to 0.734 under the tested conditions, respectively. The motive nozzle efficiency increases with the diameter ratio and the primary fluid quality decreases with the pressure ratio.The mixing efficiency increases with the pressure ratio, decreases with the diameter ratio and the NXP. The diffuser efficiency increases with the diameter ratio, decreases with the pressure ratio and the NXP. Furthermore, three empirical correlations with the coefficients of determination (R2) of 98.8%, 96.7% and 98.0% for the motive nozzle, mixing chamber and diffuser efficiencies are summarized as functions of the geometric parameters (NXP,

Table 2 – Comparison of ejector component efficiencies studies. References and method Varga et al. (2009), CFD

Liu and Groll (2013), Ejector model combined with experimental data

Besagni et al. (2014); Besagni et al. (2015b), CFD Current study, ejector model combined with experimental data

Working fluid and conditions

Results and conclusions

Water Single-phase supersonic ejector, Tc = 25–40 °C, Dn = 10.6–14.8 mm, rA = (Dn /Dm)2 = 13.5–26.4 CO2 Two-phase subsonic ejector, Pp1 = 8–14 MPa, Ps1 = 2.5–5 MPa, Tp1 = 40–60°C, Ts1 = 15–26°C, mp = 0.1–0.25 g s−1, ms = 0.05–0.07 g s−1, Dn = 1.8–2.7 mm, Dm = 4 mm Ideal gas Single-phase subsonic ejector, φp =Pp1/Pd2 =1.07–41.79, φs =Ps1/Pd2 =0.91–2.58, fixed ejector geometry R600a Two-phase subsonic ejector, Pp1 = 100–200 kPa, Ps1 = 50–70 kPa, xp1 = 0.313–0.531, NXP = 2–10 mm, Dn = 0.6–1.2 mm, Dm = 2 mm

ηn (0.92–0.95) increases with Dn and is slightly affected by Tc; ηs (~0.90) is constant in critical condition and drops in subcritical operation; ηm obviously varies with Tc and rA and the variation depends on the definition of ηm; ηd (0.50–0.85) increases with Tc and rA. ηn (0.50–0.93) increases with Dn/Dm, decreases with Pp1/Ps1; ηs (0.37–0.90) increases with Pp1/Ps1 and mp/ms, and it is relatively high with small Dn/Dm and NXP; ηm (0.50–1.00) increases with mp/ms, and it is relatively high with small Dn/Dm.

ηn (0.50–0.95) increases with φp until reaching a constant value of 0.95; ηs (0.10–0.65) increases with φs and the non-optimized geometry causes the low values; ηm (0.65–0.85) is a function of both φp and φs. ηn (0.513–0.750) increases with Dn/Dm and xp1, decreases with Pp1/Ps1; ηm (0.492–0.755) increases with Pp1/Ps1, decreases with Dn/Dm and NXP; ηd (0.610–0.734) increases with the Dn/Dm, decreases with Pp1/Ps1 and NXP.

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Dn/Dm) and operational conditions (Pp1/Ps1, xp1). The simulation results based on the previously developed NERC (novel ejector enhanced refrigeration cycle) model combined with the summarized empirical correlations agree well with the tested results from the experiment, showing the maximum errors of ±7% and ±12% for the pressure lift ratio and the entrainment ratio. The aim of this study is to provide useful guidelines for the variable characteristics of ejector component efficiencies and it is hoped to further relevant researches on the modeling and design of the two-phase ejector.

Acknowledgements This study is financially supported by the National Natural Science Foundation of China (NSFC) under the grant No. 50876081. The authors would like to thank NSFC for the sponsorship.

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