Ejectors for Efficient Refrigeration: Design, Applications and Computational Fluid Dynamics

By Giuseppe Grazzini, Adriano Milazzo and Federico Mazzelli

Encompassing both practical applications and recent research developments, this book takes the reader from fundamental physics, through cutting-edge new designs of ejectors for refrigeration. The authors’ unique vision marries successful design, system optimization, and operation experience with insights on the application of cutting-edge Computational Fluid Dynamics (CFD) models. This robust treatment leads the way forward in developing improved ejector technologies. The book covers ejectors used for heat powered refrigeration and for expansion work recovery in compression refrigerators, with special emphasis on two-phase flows of “natural” fluids within the ejector, i.e. steam and carbon dioxide. It features worked examples, detailed research results, and analysis tools. 

• Language: English
• Publisher: Springer
• Release date: Mar 21, 2018
• ISBN: 9783319752440

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© Springer International Publishing AG, part of Springer Nature 2018

Giuseppe Grazzini, Adriano Milazzo and Federico MazzelliEjectors for Efficient Refrigerationhttps://doi.org/10.1007/978-3-319-75244-0_1

1. Introduction

Giuseppe Grazzini¹ , Adriano Milazzo¹ and Federico Mazzelli¹

(1)

Department of Industrial Engineering, University of Florence, Florence, Italy

Keywords

EjectorsInjectorsTwo-phase ejectorsEjector applicationsEjector chillers

1.1 Working Principle of Ejectors

The basic scheme of an ejector is shown in Fig. 1.1. The shape and proportioning of the parts are purely indicative. The motive (or primary) fluid is fed through a nozzle which, in most cases, is shaped as a converging/diverging duct in order to accommodate a supersonic flow at the exit. The entrained (or secondary) fluid is fed through the annular space that surrounds the primary nozzle. In this way, at the nozzle exit the two streams come in touch. Their velocities are highly different, and hence a transfer of momentum accelerates the secondary and decelerates the primary flow. We may imagine that a central core of primary flow and a lateral shell of secondary flow remain substantially unaffected, while the mixing takes place in an intermediate zone shaped as a cylindrical wedge, where turbulent shear stress produces a velocity distribution that grows steeply toward the ejector axis. Actually, if the primary flow is supersonic, a sequence of oblique shocks will form along the mixing zone, undergoing multiple reflections.

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Fig. 1.1

Schematic section of a supersonic ejector

In modern applications, the secondary flow normally accelerates up to sonic speed, and hence the whole mixed stream is supersonic . This mixed stream must be decelerated in order to convert its kinetic energy and finally reach the exit pressure, intermediate between the high value featured by the motive fluid at inlet and the low value (suction pressure) of the entrained flow. This happens in a supersonic diffuser which follows the mixing zone and features a convergent-divergent or cylindrical-divergent shape.

It may be worth to point out that, from a functional point of view, the ejector substitutes the much more complex assembly shown in Fig. 1.2. The ejector eliminates the transmission of mechanical work from the expansion to the compression via the connecting shaft. Flow energy is transmitted directly from the two flows, avoiding rotating blades, bearings, lubrication, etc.

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Fig. 1.2

Functionally equivalent assembly

Obviously, the direct interaction between streams at different velocities introduces some limitations and specific losses. For example, the transition between super- and subsonic flow should ideally occur at the diffuser throat, and the velocity should decrease continuously. This ideal condition happens for a single combination of inlet/exit conditions and is hence practically unfeasible. In practice, the supersonic flow decelerates to subsonic velocity through a second shock train.

For stable operation the shock should take place downstream of the diffuser throat. In this condition, the ejector flow rates are insensitive to any increase in the discharge pressure. When discharge pressure increases , the shock moves toward the inlet side of the ejector, and, as it reaches the throat, the ejector experiences its most efficient working condition.

However, any further small increase in the discharge pressure causes the flow to become subsonic in the throat, and hence the flow rate becomes dependent on the discharge pressure. In this condition the ejector becomes unstable, i.e., an increase in the discharge pressure produces a steep decrease in the ejector performance which, in most applications, is unacceptable. Many ejectors feature a cylindrical zone upstream of the conical diffuser. They work in a stable condition as far as the shock occurs within this cylindrical zone.

A set of nondimensional parameters may be introduced:

Entrainment ratio

$$ \omega ={\dot{m}}_s/{\dot{m}}_p $$

, i.e., ratio between the secondary ( $$ {\dot{m}}_s $$ ) and the primary ( $$ {\dot{m}}_p $$ ) mass flow rates

Compression ratio ζ = PC/PE, i.e., ratio between the discharge (PC) and entrained fluid (PE) pressures

Expansion ratio θ = PG/PE, i.e., ratio between the motive (PG) and entrained fluid (PE) pressures

The aforementioned behavior may be described in terms of entrainment ratio as shown in Fig. 1.3. For a given combination of primary and secondary conditions, the line representing ω as a function of the discharge pressure P C has a first horizontal part on the left and a second sharply decreasing part on the right. The dividing point corresponds to the critical discharge pressure P crit (or maximum discharge pressure) that is commonly taken as the limit operating condition. This critical point conjugates the maximum entrainment ratio with the maximum compression ratio ζ crit.

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Fig. 1.3

Map of the operation for a supersonic ejector

When the entrained fluid pressure is lowered, e.g., from P E-3 to P E-1 at constant primary fluid pressure P G-1, the operating curve moves left and downward, i.e., both ζ crit and ω decrease.

When the motive fluid pressure is raised, e.g., from P G-1 to P G-2 at constant entrained fluid pressure (θ increases), ω is lowered but ζ crit increases.

Another fundamental parameter is the area ratio between primary nozzle and mixer/diffuser throat flow sections. In supersonic conditions, these sections limit the two flow rates and hence the entrainment ratio. We may hence introduce a ratio ξ = d/D between the nozzle throat diameter d and the diffuser throat diameter D. As this ratio increases, the motive flow increases and, as a rule, the compression ratio grows. Correspondingly the entrainment ratio decreases, because the entrained flow remains constant or even decreases, as an increased portion of the diffuser throat section is occupied by the primary flow.

1.1.1 Ejectors as Components of Refrigeration Systems

An ejector may be used as a fluid-driven compressor in a refrigeration system. The motive fluid can be heated up in a generator, where it boils at constant pressure. The entrained fluid is vaporized at low pressure in an evaporator, in order to extract the cooling load from a cold source. The mixed fluid at discharge is condensed and, once in the liquid state, is divided into two flows: the first goes to the evaporator through an expansion valve, and the second is pumped back at suitable pressure toward the generator (Fig. 1.4).

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Fig. 1.4

Basic scheme of ejector-based refrigeration system

The ideal thermodynamic cycle , shown in Fig. 1.5 for steam on a pressure/enthalpy diagram, is actually comprised of two cycles sharing the condensation C-A: the motive cycle has a practically vertical left side (the pump absorbs very little work in the case of water) and then has a constant pressure heating, vaporization, and superheating (if present) up to point G. From this point, the vapor expands in the primary nozzle and mixes with the vapor exiting from the evaporator at state E. In this simplified representation, the mixing process is assumed at constant pressure, slightly below the evaporator exit pressure . Actually, in the real process, the expansion of the entrained fluid before mixing is scarcely significant, and the mixing pressure is hardly distinguishable on the diagram from the evaporator pressure. The mixed fluid is then compressed in the diffuser up to the condenser pressure and is discharged at state C. The entrained fluid exiting from the condenser in state A is expanded through a valve, and the process is assumed isoenthalpic.

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Fig. 1.5

Ideal thermodynamic cycle of refrigeration system using a steam ejector

The cycle efficiency may be calculated as a ratio between useful effect and input power:

$$ \mathrm{COP}=\frac{{\dot{Q}}_{\mathrm{f}}}{{\dot{Q}}_m+{\dot{W}}_{\mathrm{pump}}}=\omega \frac{h_{\mathrm{E}}-{h}_{\mathrm{A}}}{h_{\mathrm{G}}-{h}_{\mathrm{A}}} $$

(1.1)

where $$ {\dot{Q}}_f $$ is the cooling power, $$ {\dot{Q}}_m $$ the motive heat power, and $$ {\dot{W}}_{\mathrm{pump}} $$ the generator feed pump power.

The last part of Eq. 1.1 contains the entrainment ratio and a further ratio between the enthalpy differences (h E − h A) and (h G − h A) that depends on the fluid and operating conditions . Therefore, the global performance for fixed fluid and working conditions depend on the ejector entrainment ratio. This latter may be evaluated from an energy balance on the ejector and turns out to be

$$ \omega =\frac{h_{\mathrm{G}}-{h}_{\mathrm{C}}}{h_{\mathrm{C}}-{h}_{\mathrm{E}}} $$

(1.2)

i.e., the ratio between motive (h G − h C) and compression (h C − h E) enthalpy differences. Ejector losses increase the enthalpy at condenser entrance h C, decreasing numerator and increasing denominator in Eq. 1.2.

As a heat-powered refrigeration system, the machine sketched in Fig. 1.4 may be used in addition to a heat engine for combined heating, cooling, and power generation. For example, it may complement a district heating system in order to guarantee air conditioning in summer or produce refrigeration in civil or industrial environments from any form of waste heat. Alternatively, it may be used for solar cooling in conjunction with solar thermal panels having a suitably high temperature or use other forms of renewable energy.

1.2 Historical Background

An early application of a rudimentary jet device may be seen in the blast pipe found in the smokebox (the volume at the end of the boiler where smoke and ash are collected before going toward the chimney) since the very first steam locomotives (Fig. 1.6). This device directs exhaust steam from the cylinders through a nozzle at the bottom of the chimney, in order to reduce the flue gas pressure and increase the draught on the fire. The blast pipe significantly increased the locomotive power and produced the familiar intermittent flow of smoke from the chimney, synchronous with the alternate motion of the pistons.

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Fig. 1.6

Blast pipe in a steam locomotive

The French inventor Henri Giffard, as a locomotive engineer, was familiar with the blast pipe. When he attempted to apply a steam engine to a dirigible, Giffard deserved a simple, light, and reliable means to pump water in the boiler. Mechanical feed pumps were heavy and complex. Since 1850 he understood the basic principle of the steam injector, writing down a momentum equation which is basically still valid (Kranakis 1982). The attempt to build a steam-powered flying vehicle was unsuccessful, but the injector survived and was patented in 1858, gaining immediate success.

In contrast to pumps, the injector was small and efficient, had no moving parts (which eliminated a major source of friction), needed no oiling, and even served to preheat the feedwater. Injectors had an additional advantage with regard to locomotive boilers because they would operate when the locomotive was at rest.

Because of its simplicity and efficiency, the injector made traditional pumps virtually obsolete. By 1860 several French railroad lines were regularly outfitting their locomotives with injectors, and they were also in use by the French Navy. At the London Exhibition of 1862, nearly one-third of the locomotives were equipped solely with injectors. Injectors were manufactured in America since 1860, and a year later nearly 1200 had been sold in the USA alone. At the turn of the century, the number had risen to over a half million. By that time, many locomotive engineers had never seen one of the older feed pumps.

Figure 1.7 shows a very refined construction , with a non-return valve at the water discharge port and an overflow exit that are necessary when the ejector is started. A further refinement is the needle that varies the nozzle exit section. Unfortunately, the properties of expanding steam were not completely known in that period, and hence the need for a convergent-divergent nozzle was not realized. By the way, the modeling of an expanding flow of metastable, condensing steam is still quite troublesome nowadays.

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Fig. 1.7

Giffard’s injector (Routledge 1876)

It’s worth to note that the injector , having a compression ratio equal to the expansion ratio, gives a first proof of the importance of a correct energy balance in the evaluation of these devices. The high enthalpy of the steam coming from the boiler is transformed in kinetic energy within the nozzle and, once transferred to the feed water flow, may overcome a relatively high discharge pressure. This was very surprising for the engineers of the middle nineteenth century and stimulated a lively discussion (Kranakis 1982), eventually promoting a widespread comprehension and acceptance of the newly born first law of thermodynamics .

The same principle successfully demonstrated by the injector was easily transferred to the steam ejector (Fig. 1.8) used on early locomotives as a vacuum pump for the brake circuit (Encyclopædia Britannica 1911). In this case, the large availability of steam and the simplicity and ruggedness of ejectors offered a convenient technical solution to the urgent need of a reliable braking system (the vacuum brake was the first intrinsically safe method because it automatically stops the train whenever the circuit is accidentally opened to atmosphere). The vacuum brake had major success in the UK, where it survived until the 1970s.

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Fig. 1.8

Vacuum brake for trains – the ejector is on the upper left corner (Encyclopædia Britannica 1911)

Another fundamental field of usage for ejectors was soon found in steam power plants, where incondensable gases had to be evacuated from the condenser and steam at various pressure levels was available along the expansion. An ejector was used for this purpose by Sir Charles Parson in 1901 (Chunnanond and Aphornratana 2004). Again, a steam ejector was cheaper and more reliable than any other kind of vacuum pump.

Coming to the main topic of this book, we must finally mention the Machines frigorifiques à vapeur d’eau et à éjecteur invented by Maurice Leblanc (1911). The idea of using an ejector to produce a low-pressure reservoir wherein water could be evaporated and subtract heat at low temperature is even older, but the commonly cited reference year for this invention is 1910. The system is also known as Westinghouse-Leblanc due to the rapid commercialization in the USA and was very successful in this period, especially for use on ships. This is not surprising, as the ejector refrigerator must get rid of a substantial amount of heat (sum of the cooling load and motive heat) and is very sensitive to the heat sink temperature. Therefore, the availability of cool seawater was undoubtedly a key for success in this application. Simplicity and ruggedness were also very convenient for ship operators. Many different refrigeration cycles had already been used for both refrigeration and air conditioning purposes. However, the steam jet refrigerator had the advantage that it could run using exhaust steam from any source (steam engines, industrial or chemical processes, etc.). Hence, from 1910 to the early 1930s, steam jet refrigeration systems were successful in factories, for air conditioning of large buildings and on trains (Stoecker 1958; Arora 2003).

Despite this promising start, the use of supersonic ejectors for refrigeration applications almost disappeared when the first synthetic refrigerants were introduced during the 1930s. These gases could overcome the problems that hampered the large-scale commercialization of vapor compression systems . Furthermore, steam was losing its importance as heating fluid, while all buildings hosting refrigerators or air conditioners were served by the electric energy network. Therefore, however scarcely efficient and reliable initially, electrically operated compressors became increasingly common and soon virtually unrivalled. Steam ejector chillers survived (and are still in use) in those industrial plants where steam is available at low cost.

Much later, new perspectives opened for ejector chillers . In the 1970s, two events, the oil crisis and the stratospheric ozone depletion, suddenly interrupted the apparently unlimited growth of the conventional refrigeration market. On one side the consolidated working fluids were questioned and eventually phased out in a relatively short period. On the other hand, refrigeration and air conditioning were recognized as an important item in the inventory of electricity end users. This stimulated a renewed interest toward heat-powered refrigeration systems and environmentally safe working fluids. A significant amount of literature was published along the 1980s and the 1990s, reporting a number of thermodynamic analysis and various experimental results.

Unfortunately for ejector chillers , by that time absorption systems were ready to dominate the market of heat-powered refrigeration. Since their invention in 1858 by Ferdinand Carré, absorption machines enjoyed a strong research effort, and now, specially thanks to the good performance at low heat source temperature offered by lithium bromide systems , they are mass produced and leave few chances to competitors.

A possible breakthrough for ejector refrigeration systems was sought in the use of alternative working fluid. If steam is not provided and the heat source has a relatively low temperature, the circuit may be filled with any suitable refrigerant. The quest for alternatives started since the 1990s (Dorantes and Lallemand 1995) and is still open. Many authors propose synthetic refrigerants with the aim of overcoming the indisputable drawbacks of steam , i.e.:

The high triple-point temperature that impedes to work below 0 °C

The very low pressure at evaporator and condenser that poses sealing problems

The high specific volume at low pressure that increases the system volume and cost

The problem of condensation along the expansion that complicates the analysis and the design of the ejector

On the other hand, steam has various advantages; it is available everywhere at very low cost, is absolutely safe for the environment and operators, and requires a low pressure at generator.

In this last decade, another promising use of ejectors within refrigeration systems has emerged. Instead of trying to replace the mechanical compressor , the ejector can be used to complement it, working on the expansion side of the cycle. In this case, the motive fluid is the high-pressure liquid coming from the condenser, and the entrained fluid is the low-pressure vapor coming from the evaporator. The mixed flow, after pressure recovery, is sent to an intermediate pressure reservoir , e.g., a liquid separator that feeds the expansion valve (and hence the evaporator) and the compressor. With respect to other proposed means for expansion work recovery, the ejector has the advantage to have no moving parts. This idea dates back to the patent (Fig. 1.9) of Norman H. Gay (1931) but has known a rapidly increasing interest since the rebirth of carbon dioxide refrigeration systems in the 1990s, due to the high incidence of the expansion loss in CO2 inverse cycles .

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Fig. 1.9

Ejector for expansion work recovery (Gay 1931)

1.3 Applications

As pointed out, ejectors may have a number of applications and are referred to by different names. A classification may be found, e.g., in Sokolov and Zinger (1989):

1.

Ejectors using motive and entrained fluid in the same phase

2.

Ejectors using motive and entrained fluid in different phases but having no phase change within their bodies

3.

Ejectors using motive and entrained fluid in different phases and featuring a phase change

Clearly, the difficulty of analysis increases from case 1 to 3. For example, an ejector used in a heat-powered chiller featuring a working fluid that does not condense along the expansion belongs to the first category, while an ejector used for expansion