advancesinorcexpanderdesign -...

1

Advances in ORC expander design

Vincent Lemort and Sylvain Quoilin

Laboratoire de Thermodynamique, Université de Liège, Belgium

INTERNATIONAL SYMPOSIUM ON ADVANCED WASTE HEAT VALORISATION TECHNOLOGIES

13-‐14 September 2012, Kortrijk, Belgium

2

IntroducWon Early years of posi3ve displacement machines

The posi)ve displacement machine is not a new idea…

o  1588: vane-‐type water pump by Ramelli o  1636: gear water pump in/by Pappenheim o  1765: James Wa`s steam engine o  1799: Murdoch steam engine, should

deliver ½ HP but too many leakages o  …

« There is much fric3on in this kind of engine, much leakage, and but a small power realised in propor3on to the size of the machine… » (Bourne, 1858)

Source: Museum of retrotechnology

Wood 3p seals Steam supply

Steam exhasut

1799: Murdoch steam engine

Today: gear pump

3

IntroducWon

o  Today, regain of interest for small and medium scale expanders

Ø  RefrigeraWon (expansion valve replacement)

Ø  StaWonary power producWon (steam cycles, ORC)

Ø  Heat recovery on engines

o  Purpose of this presentaWon: ü  Describe technical constraints inherent to the design of posiWve displacement

machines (piston, screw and scroll)

ü  Present some modeling techniques

ü  Discuss about the selecWon of expansion machines

ü  Stress some relevant R&D trends related to posiWve displacement machines in order to improve the energy performance of both the expander and the ORC system

4

Technical constraints Losses in posi3ve displacement expanders

o  Supply/discharge pressure losses, under-‐over expansion, leakages, heat transfer, (clearance volume), mechanical losses

The Japan Society of Mechanical Engineers

NII-Electronic Library Service

Scroll (Yanagisawa et al., 2001)

Screw (Kaneko and Hirayama, 1985)

Piston (Doyle et al., 1970)

5

Technical constraints Capacity



displacement

6


4

Figure 2 – Principle diagram for a bottoming or waste heat recovery cycle. Waste heat from the exhaust of an internal combustion engine is used to generate additional mechanical power via an external combustion engine (i.e. via a heat recovery steam generator and a steam engine system). The total power of this subsystem exceeds the power generated by the ICE.

2.2 Expander types

To convert heat to mechanical work some type of expander has to be utilized. Different

kinds of expanders are suitable concerning efficiency and mechanical aspects, depending

on the application, i.e. power range. Generally there is a characteristic optimum

peripheral velocity (tip speed) u (or mean piston velocity for reciprocating machines), for

every type of positive displacement machine, determined by their inherent leakage and

throttling losses [7]. This optimal tip speed is fairly independent of the machine size and

virtually constant for a uniform specific type of machine. Also for turbo (dynamic)

machines there is a fairly size independent optimum tip speed, in this case primarily

determined by vane geometry (the “specific speed” parameter for turbo machines) [4].

Thus, from the kinematic relation nDu �� S , the optimal shaft speed n becomes

dependent of the machine size (rotor diameter) D (Figure 3).

Figure 3 – Optimal shaft speed and volume flow relations for positive displacement and turbo machines. Power scale valid for air compression duty (after [4]). As seen, the closest match on shaft speed in applications such as the automotive application corresponds to the optimal shaft speed of piston machines.

o  A category of machine is characterized by an opWmal Wp speed (m/s) fairly independent of its size (Persson, 1990).

o  Turbines operate at larger Wp speed than displacement machines.

Approximate range of chiller cooling capacity range by compressor type (ASHRAE, 2008)

Source: Grip, 2009

7


Piston expanders o  Currently used for small-‐scale CHP and waste heat

recovery on ICE (niche market tech.) o  Axial expanders: compact, low vibraWons (MAC) o  Displacement: approx 1.25 to 75 l/s

Source: Amovis, 2012

Screw expanders o  From 20 kWe to 1 MWe (In comp: 200W-‐2/3 MWe) o  Displacement: approx 25 to 1100 l/s o  Few records on micro-‐screw expanders (volumetric

perf.!) o  Mainly twin-‐screw (except BEP, Wang et al., 2011) o  Only rotaWng elements: high rota)onal speeds

(21,000 rpm recorded) Pumps, Compressors and Process Components 2012 121

CompressorsScrew expander

Due to the liquid to be expected inside the expansion machine, screw expan-ders the functional principle and de-scribing parameters of which will be presented in the following, are parti-cularly suitable for these applications. With the help of basic design variants, the properties of these fluid energy machines are demonstrated and the systematic and targeted procedure for their design will be described.

Functioning and parameters

Screw expanders are displacement machines without clearance volume, the working chambers of which are formed by the tooth gaps of two he-lically toothed gears, the rotors. The volume of a working chamber depen-ding on the rotation angle is exempla-rily demonstrated in Fig. 1. If a tooth of the female rotor on the high-pres-sure side (HP-side) unscrews from the tooth space of the male rotor, a wor-king chamber arises. With progressing rotation of the rotor, the volume of this working chamber increases up to a maximum before it is reduced again by a repeated tooth engagement or by the low-pressure side at the front edge, and the working chamber fi-nally disappears. The rotors are tight-ly enclosed by a casing which provides the working chambers with external sealing and sealing towards the front edge. The casing houses the inlet and outlet ports, the limitations of which

are called control edges. The outlet port in the front edge casing of the low-pressure side enables the working fluid to be discharged usually from the maximum chamber volume Vmax

up to the disappearance of the wor-king chamber. In the range in which the chamber is formed the inlet port represents a connection to the high-pressure side of the screw expander. This connection is maintained up to a selectable chamber volume VEx,th (Fig.1). The ratio

is called internal volume ratio vi and is one of the essential parameters of a screw machine.

The ideal comparison process for a screw expander consists of an isobaric chamber filling with the inlet pressure pE and the inlet density lE (high-pressure side) up to VEx,th, an isentro-pic expansion up to the discharge pressure pA (low-pressure side) and an isobaric discharge (Fig. 2) [2]. The isentropic work Ws this process deli-vers per working cycle together with the actually performed inner work per working cycle

forms the compression work ratio Wi/Ws.

The volumetric efficiency hL

with

describes the ratio of system mass flow mA to theoretical delivery mass flow mth, with the product of male ro-tor speed nMR and male rotor number of teeth zMR being the working cycle frequency. Another important para-meter of fluid energy machines is the inner isentropic efficiency dis with

In this case, the isentropic power Ps

corresponds to the product of specific isentropic work ws and system mass flow mA

and Pi of the indicated or internal power of the screw expander. In con-nection with the mechanical efficien-cy dm

the effective output power Pe and the effective isentropic efficiency des re-sults in

Fig. 1: Volume curve as well as inlet and discharge areas of a screw-type expander over the rotational angle of the male rotor (asymmetric SRM profile; vi = 8; zMR/zFR = 4/6; MR = 200°; L/D = 1.4)

Fig. 2: Indicator diagram of a screw expander optimized with regard to the output power and ideal comparison process (not represented from Vmax) (asymmetric SRM profile; vi= 8 ; zMR/zFR = 4/6; MR = 200°; L/D = 1.4)

..

.

Source: Brümmer, 2012

εv,cp ÷1−csteN.D

Source: BEP

8


Scroll expanders o  From mini-‐scroll to very large machines o  Currently, the trend in the compressor industry is to increase

the size (f.i. Emerson ZP725K with 158 kW cooling capacity) o  Large scroll compressors compete with small screw machines o  Mul) scroll ORCs have not been invesWgated yet (except

Enenech): modulaWon, PL performance o  Speed:

§  Mobile A/C: up to 10,000 rpm §  Permanent magnet generators: variable speed + higher

efficiency

Contact: Achim Frommann, Media Communication and Relations - [email protected] Emerson Climate Technologies GmbH, Pascalstr. 65, 52076 Aachen, Germany

T: +49 (0) 2408 929 0 F: +49 (0) 2408 929 570 www.emersonclimate.eu

2012_0327_PREL_ZP725_en Page 1 of 2

press release

R410A Copeland Scroll™ for systems up to 1 MW

MILAN, ITALY, March 27, 2012 – For large HVAC systems Emerson Climate Technologies designed the new Copeland Scroll™ ZP725K compressor for the refrigerant R410A. With a capacity of 158kW* the new Copeland Scroll™ ZP725K opens the door to a widespread use of this refrigerant for air-cooled multi-scroll chillers with a capacity up to 1 MW and up to 1.25 MW if water-cooled. This extra large scroll can easily be combined with other scroll compressors that are identical or lower in size or capacity to offer several possible combinations. This flexibility and reduced complexity is ideal for manufacturers who produce systems with different capacities and enables them to keep only a few compressors in stock. All the assembly designs are Copeland qualified and key in increasing the system seasonal efficiency due to the wide range of capacity modulation – up to the possibility of 12 steps with uneven trio assemblies. Publications from the Eurovent directory demonstrate that systems with scroll technologies and R410A have an overall better seasonal performance compared to similar systems using different refrigerants and compression technologies. Moreover, Emerson’s new CoreSense™ Communications provides the enhanced protection and diagnostic required and expected by this demanding range of applications in HVAC systems. Via RS485 Modbus the system controller is able to gather compressor’s status and working conditions and can adapt or avoid altogether system downtime.

New extra-large 60hp Copeland Scroll™ compressor beside the smallest commercial scroll (7.5hp)

*EN12900 rating conditions

Source: Emerson, 2012 60 HP 7.5 HP

9

Technical constraints Built-‐in volume ra3o



Over and under expansion losses

10


Scroll o  From 1.5 to 3.5 (HVAC&R), 4.0 (air compressors) o  Results from cost and performance consideraWons:

•  Performance: number of pairs of sealing points limited to 2 or 3, fricWon

•  Cost: prohibiWve scroll length, compactness Source: Manzagol et al., 2002

x [m]

y [m

]

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

involutetip

Source: Lemort, 2009

Piston expanders o  Could be large (f.i. internal combusWon engines) o  Limited by the specific work of the machine (compactness). o  In pracWce, between 6-‐14 Screw o  Up to 5.0 in pracWce. 8.0 is recorded (Brümmer, 2012) o  Moderate volume raWo expanders show be`er performance o  Stronger impact of leakage in expander mode.

Analysis of screw expander performance 129

I00

9O

70

6o

0 5 0 -

40 0

• rv ,2 (Smil) ] & r v -2.5 (Stair) / (Ref,14) • r~ -3.5 (Smi(] o r , -5 (Stall)

o r, -5.3 (lOmR) -- (Ref.15,16)

"%

I ) i I I I I 5 6 9 12 15 Ie 21 24

Pressure mtio %)

Fig. 9. Overal l isentropic efficiency of expanders.

t I 27 3O

expansion ratio. Equation (10) is found experimentally to be linear from the data of Mycom and Steidel, as shown in Fig. 10. The linear relationship reinforced the initial assumption made, i.e. the expansion follows a constant index path. In addition, it is observed that the gradient of the blowdown pressure ratio increases with decreasing volumetric ratio of the expanders. From Fig. 10, if a data point falls below 1.0, it means that the blowback process has occurred. Only two sets of the experimental data exhibit this phenomenon, i.e. rv = 2.5 of Mycom data and the Steidel data. Rearranging equation (10) gives

ln(r-E~ = - n ln(rJ. (11) \ rp /

Thus, the average value of the expansion index of the working fluid can be obtained, as shown in Fig. I I. The average expansion index, n, from all the experimental data is found to be about 1.074, a value which is quite close to the isentropic index of 1.13. Table 4 gives a detailed listing of the indices for different expanders. It is noted that there is a slight increase in the value of the expansion index as the volumetric ratio increases. Another point to note is that the difference between the expansion indices and the isentropic index, 7, indicates the presence of thermodynamic irreversibility.

=z

oo

A

I I l I I 3 6 9 12 15

D

& rv -2 (Mycom-Smit) • r v -2.5(Myo0m-Smit) • rv ,3.5 (Mycom- 5mit ) D r v , 5 (Myc=m-Smit) • ~, , 5 3 I M y ~ - l O m i l . )

18 21 24 27 Pressure rotio (r.)

Fig. I0. Var iat ion o f b l o w d o w n rp~ wi th operat ing rp.

I 3O

Source: Ng et al., 1990

11


o  Increase volume raWo? Ø  Two-‐stage expansion: o  Experience from Kane et al.(2009): rv,in: 4.2x3.0,

high speed permanent magnet generator (6000 rpm), 5 kWe (steam, 250°C, 25/1 bar)

o  OpWmal intermediate pressure (Quoilin, 2011)

Rapport HTScroll - 19 - Rapport final – 29 octobre 2009

5. Tests de design et de fonctionnement mécanique

5.1 Tests de pression et d’étanchéité

Un ensemble composé d’un étage HP et du générateur, comportant tous les points critiques d’assemblage, a été testé d’abord avec une charge de réfrigérant à 8 bars et ensuite complété avec une charge d’azote à 22 bars. Les joints et points d’assemblages externes ont été testés avec un détecteur de fuite. Aucune fuite importante n’a été trouvée et aucun dommage n’a été observé.

5.2 Tests de fonctionnement mécanique à l’air comprimé

Des tests à air comprimé ont été préparés pour vérifier le fonctionnement mécanique de la machine et en particulier le comportement au démarrage. Un système de filtre à air, de vanne de détente et de lubrificateur d’air sont montés sur le circuit de vapeur, en amont de la turbine. Comme le montre la photo du montage à la figure 16, une vanne d’isolation est mise en place sur la liaison externe de pression entre l’admission et la chambre de pression derrière le palier axial. La lubrification des paliers est effectuée sporadiquement par une injection d’huile au moyen d’une pipette ou d’une seringue. La pression maximale du circuit d’air est de 8 barg. Le démarrage de la turbine s’est effectué simplement en augmentant la pression à l’entrée de la turbine.

5.2.1 Tests fonctionnels à air comprimé pour le module HP

Pour la turbine mono-étagée HP comme illustrée sur la photo ci-dessous, une pression d’entrée de 4-5 barg est nécessaire pour la faire démarrer.

Figure 5-1 : Turbine HT Scroll montée avec un étage HP et connexion pour tests à air comprimé

Une mesure de la vitesse de rotation est effectuée mécaniquement en appliquant un appareil compte-tour sur l’arbre, de l’autre côté du module de détente par rapport au

Source: Kane et al., 2009

2 herme3c scrolls in series: Net power: 3 kWe, efficiency ORC: 10-‐12%, Tev=141C and Tcd=35C

12


Comparison of a variable (leX) and a constant (right) wall thickness geometries with the same volume ra3o (rv = 5)

Isentropic efficiency as a func3on of the compactness factor

Ø  Variable wall thickness scrolls: allows to generate more compact geometries. Hence, higher volume raWo can be achieved in pracWce (MIT/ULg)

Source: Dechesne, 2012

13

Technical constraints Supply pressure losses



14

Technical constraints Pressure losses

Piston expanders Inlet valves: o  Source of pressure losses o  different families of inlet valves: Sliding valves, Rota3ng valves,

Poppet valves

Source: Amovis, 2006

Outlet valves: o  F.i., use of exhaust ports (vs valves) allows for

•  thermal “coherence” (cross flow vs uniflow) •  Recover leakages through piston rings

o  Use of exhaust ports will lead to larger compression work (fluid is recompressed earlier) and lower fluid mass flow.

Source: Platell, 1993

15


Scroll expanders

Suc3on port blockage Subdivision of suc3on chamber (end of suc3on) (Yanagisawa et al., 2001)

0 1 2 3 4 5 6 73.5

4

4.5

5

5.5

6

6.5

7

7.5x 10

-5

θ [rad]

A su,s

uc [m

2 ]

0 0.5 1 1.5

x 10-4

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6x 10

5

V [m3]

P [P

a]

← beginning of expansionPsuPex

16


Screw expanders

Gdansk University of TeehnologyDortmund University of Teehnology

and between the working charnbers on the low and high prcssure sides of the machine respectively. The rotor geometrydetermines the length and form of the gaps [3].

Volume curve and in/er area

The volume curve represents the volurnetric progression of the working chamber depending on the rotation angle of the malerotor. In the zero position of the male rotor the volume of the working eh amber under examination is also zero (Fig.2). Thevolume curve characteristically shows a continuous slope up to the point where full profile intermeshing has taken pi ace,followed by a linear progression, anel a eliminishing rise up to the point where rnaxirnum charnber volume is reacheel.

The inlet area, which depends on the rotation angle. is theeross-section area which is available for the working fluid toflow through during the charging phase. This area is formed bythe apertures in the housing and thc rotor teeth, which circulatepast these gaps, covering and uncovering parts of them. Theinlet area can be represented as a function of the male rotorrotation angle. analogous to the volume curve. Depending onthe profile, the devclopment 01' the inlet area frequently beginsat a rotation angle differing from the zero position of the malerotor. The reason for this is a tooth gap area opening at the frontface, which runs ahead 01' the actual working chamber, and isconnected to the low pressure side [2]. The inlet areaprogression ends with arrival at the control edges, at therotational angle which inelicates the theoretical start ofexpansion.

500(::I 80000...l 70000•• 60000E.g 50000>

.-------: vo: urne CUfVe./

· <, /··f\ · /· ·1--1 \ : Inlet area /.

.•.. :\V / LP, /' ··f :, / control edge :

/ :~HP' ··I · contral edge :L/ · :·

450 r400

350

'"300 EE

250 ~~200 (';J

10150 ~

Working cycle of a screw motor

In principle, a working cycle incIudes all processes in the working area, beginning at a particular therrnodynamic state andending at the next oecurrence of the same state. The working cycle of a screw motor consists of three characteristic phases:charging of the working chamber. expansion phase, anel discharge of the working fluid.

During thc charging phase, the POl1 on the high pressure side ischarged with the working fluid at high temperature and pressure,so that the medium flows into the tooth gap behind it through theinlet area. As the rotor continues to turn. the chamber volumegrows. The charging phase ends when the working charnber nolonger has any connection with the inlet aperture on the highpressure siele (Fig. 3). As the area of the in let port is small at thebeginning of the cycle, resulting in a high choking effect,maximum chamber pressure is not achieved immediately, but isreached as the rotor moves on. This difference eluring thecharging phase between the initial pressure and the maxirnumpressure in the chamber is characteristic for the charging phase.This difference is the result of pressure loss causeel by chokingas the fluid flows in, and gap losses from the working chamber.A further aspect of the real-Iife charging process is that Fig.3:expansion begins before the contro I edge on the high pressureside has been reached. The pressure gradient at the end of thecharging process is already comparable with that during the firstexpansion phase beginning at. when the control edges have been reached. The reason for the early start of expansion isessentially a combination of continuously rising chamber volurne combined with reducing area at the inlet pOI1. The point atwhich expansion actually starts is inherent in the system, and also occurs in an ideal scenario where choke effects and gaplosses are ignored.

:;; 40000.<JE 30000'".cu

Vth.e~

'0000

100

50

100000

oo

o50 '00 150 200 250 300 350 400 450 500

rotanon angle ['1 •

on

At the start 01' the expansion phase. the operaring behaviour of the screw motor is mainly influenced by gap flows, In oreler toassess the effect of gap flows on the energy conversion rating of the motor, a distinction has to be rnade between lass flows outof the working chamber under exami nation and flows into the chamber through other gap interconnections. Compared withisentropic expansion, the actual pressure progression during initial expansion rises more steeply in the theoreticalrepresentation. The reason for this is that the fluid losses from the chamber are proportionally higher than the gains. As rotationcontinues, real and isentropic charnber pressures converge, until, in the seconcl phase 01' expansion, pressures during the realprocess exceecl those for the isentropic expansion process. The more gradual pressure progression duri ng the real process is aconscquence of flows into the working chamber from those following it. This fluiel eloes not tlow directly into the low-pressureside 01' the motor, but helps to sorne extent to fill the expancling chamber uncler consideration, applying power to the rotor

Fig.2: Inlet area and volume curve as a function of the malerotor rotation angle on a typical steam-powered screwmotor

o~~~~~~~~-----+------+-----~o 20000 40000 60000

chamber volume [mm'l ----- ••.80000

Charnber pressure progressionchamber volume with• real and• isentropic expansion phases

depeneling

Source: Brümmer, 2011 and 2012

1478, Page 2

International Compressor Engineering Conference at Purdue, July 16-19, 2012

working chambers. When the rotors in a displacement machine rotate, typical cyclical changes in the volume of the working chambers occur. Several operating cycles take place sequentially, during which the working chambers on the high pressure side are continually enlarged during the charging phase, while those on the low pressure side reduce in size as they are emptied. Via areas in the housing, connections between the working chambers and the inlet and outlet ports are created, according to the rotation angle of the rotors. The chambers are normally enclosed except for the rotor clearances. The rims of these apertures, those which close off the charging phase and open for the discharge phase, are referred to as control edges. The rotation angle positions of the control edges determine the internal volume changes in the working chambers. In displacement machines, there is always an important functional separation of moving and stationary parts. The relative movement between the rotors and the internal surfaces of the housing inevitably results in gaps, which prevent mechanical friction between the rotors, and also between the rotors and the housing. There are various ways in which the gaps influence the operational efficiency and security of the machine. They are responsible for connections between the individual working areas, and between the working chambers on the low and high pressure sides of the machine respectively (Zellermann, 1996). The rotor geometry determines the length and form of the gaps. 2.1 Loss Mechanism The description of loss mechanisms during the working cycle of a screw motor is carried out on a typical machine, selected with reference to the indicator diagram in Fig.1.

0

1

2

3

4

5

6

7

8

0 20000 40000 60000 80000 100000Kammervolumen VK [mm3]

Druc

k p K

[bar

]

Figure 1: Chamber pressure progression dependent on chamber volume with real and isentropic charging /

expansion phase. (Hütker and Brümmer, 2010) As the inlet opening has a small area at the start of the working cycle, thus resulting in a high choking effect, maximum chamber pressure is not established instantaneously, but builds up gradually as the rotor turns. The pressure difference between the inlet pressure pi and the chamber pressure pc is characteristic for the charging phase. This pressure difference results from choking losses during inflow, on the one hand, and from gap mass flows, on the other hand. A further characteristic of the real charging procedure is the start of expansion before the high pressure side control edge is reached. The pressure gradient at chamber volume Vex already resembles that of the first expansion phase as the control edge is reached from Vex,th on. The reason for the early start of real expansion is mainly the combination of continually rising chamber volume and reduction in the area of the inlet opening towards the end of the charging phase. This early start is an inherent part of the system and it also occurs in an ideal simulation, ignoring choking and gap loss factors which result from flow obstruction in the inlet cross-section.

HP control edge

LP control edge

Vex,th

cham

ber

pres

sure

[105 P

a]

chamber volume [mm³]

isentropic expansion

real expansion

Supply port cross sec3onal area shrinks to zero and volume chamber is increasing

Supply port cross sec3onal area and volume start from zero (choked flow)

17

Technical constraints Leakages

DeformaWon of P-‐V diagram

18

Technical consideraWons Leakages and lubrica3on

Screw o  Oil used for lubricaWon and clearance gap sealing o  Synchronized machines can be oil-‐free

Ø  Unsynchronized ü  Approx. 90% of the sold screw

compressors (Brümmer, 2012) ü  Oil injected for rotors and bearing

lubricaWon (+sealing) ü  Be`er energy performance ü  Simpler, lighter, smaller size

Ø  Synchronized: ü  Higher )p speed: 60-‐120 m/s against

20-‐40 m/s for lubricated machines (Brümmer, 2012)

ü  No oil (gears are greased lubricated)

Pumps, Compressors and Process Components 2012 125

CompressorsScrew expander

Regarding the system parameters, it is evident that, for the reasons ini-tially mentioned, a superheating of the working fluid Ethanol is disad-vantageous. Furthermore, an increa-sed inlet pressure (here 40 bar) in con-nection with an increased internal

ever the maximum chamber pressure is considerably below the applied in-let pressure. The compression work ra-tio as well as the volumetric efficien-cy is correspondingly low. At the same time, the dimensions of the machine are increasing in relation to the inlet pressure so that the internal power reaches its maximum. With regard to other geometrical parameters it is to be noticed that a relatively small wrap angle of e. g. = 200° is advan-tageous and the combination of teeth numbers at male and female rotor as well as the L/D-ratio play a rather mi-nor role concerning the maximum possible internal power [4].

The effective output power of this screw expander calculated in design phase II is shown in Figure 4 over the system mass flow for different MR speeds. Here, a reduced system mass flow at fixed speed can only be rea-lized via reduced inlet pressure. Accor-dingly, the output power falls linearly with the mass flow. Due to the fixed internal volume ratios, overexpansion inside the screw expander occurs with decreasing inlet pressure. Apart from friction losses, the compres sion work required to compensate overexpan-sion offsets the effective area in the in-dicator diagram in case of diminishing

volume ratio (here vi = 8) turns out to be an advantage. Due to the large in-ternal volume ratio, the inlet area of the screw expander is small (Fig. 1). In order to never theless realize a suf-ficient chamber filling, a supercriti-cal influx is advantageous. Then how-

Fig. 3: Exemplary presentation of the design variant SK1D

Fig. 4: Effective output power over system mass flow for different MR speeds (inlet pressures)

Source: Brummer, 2012

19

Technical consideraWons Leakages and lubrica3on

Scroll o  Refrigerant compressors (hermeWc or open-‐

drive) are lubricated o  Few records on refrigerant oil-‐free machines.

𝜀 = ��(ℎ − ℎ , )

(2)

It should be noted that the traditional definition of the isentropic effectiveness cannot be used

in this case because this definition is valid for adiabatic processes only. In the case of

volumetric expanders, even insulated devices exchange a non-negligible amount of heat with

their environment (Lemort, 2011). The relation between both definitions can be obtained by

combining eq. (3) with the first law of thermodynamics:

𝜀 = .( , )

= .( ) .( , )

=,−

.( , ) (3)

Eq. (3) shows that both definitions only agree if the ambient heat losses Q are negligible.

As indicated in Figure 4Figure 4, the efficiency curve presents a maximum which is due to the

fixed built-in volumetric ratio of the expander.

Figure 3 : over/under expansion losses

Figure 6 : shaft power vs. pressure ratio

4.2 Empirical expression of the expander performance

To obtain a generic non-dimensional performance curve of the expander, a fitted expression

of the effectiveness can be defined using carefully selected input variables. If ambient heat

losses are neglected, scroll expanders can indeed be modeled by their isentropic effectiveness

and filling factor as defined in Eq. (2) and (4).

𝜑 = ��𝑣��

The three selected working conditions are the inlet pressure 𝑝 , the rotational speed 𝑁 and

the pressure ratio over the expander 𝑟 since they turned out to be the main representative

variables of the working conditions. The analytical form of the empirical expression was

0

0.5

1

1.5

2

2.5

2 3 4 5 6 7 8

Shaf

t pow

er [k

W]

Pressure ratio

2000 rpm (12 bar) 2500 rpm (12 bar) 3000 rpm (12 bar) 3500 rpm (12 bar) 2500 rpm (9 bar) 3000 rpm (9bar) 3500 rpm (9 bar)

(source: Lemort et al., 2012)

20

Technical consideraWons Leakages and ubrica3on

o  Air compressors (open drive, kinemaWcally rigid) can be oil-‐free. Use of a )p seal: limited operaWng life.

o  When retrofi`ed as expanders: (-‐) Wghtness, volumetric performance

o  SoluWon proposed by Air Squared: 10 kWe, 155 cc/rev, rvin: 5.25, magneWc coupling, dry/lubricated

50

55

60

65

70

75

80

2,5 3,5 4,5 5,5 6,5 7,5

Expa

nder isen

trop

ic efficency [%

]

Pressure ra)o [-‐]

2000 rpm (12 bar)

2500 rpm (12 bar)

3000 rpm (12 bar)

3500 rpm (12 bar)

Open-‐drive oil-‐free machine (R245fa)

Source: Declaye et al., 2012

Magne3c coupling

21

Technical consideraWons Leakages and design

1371, Page 4


Two further constraints are needed on the scroll geometry in order to fix the rest of the scroll geometry. Either ϕo0 or ϕi0 is a free variable, the other being fixed by the scroll wrap thickness for a given base circle radius. Increasing the value of ϕi0 just rotates the scroll wrap, so for simplicity, ϕi0 is set to zero. The value of ϕos is set to 0.3 radians. Therefore, with the additional constraints imposed here, there remains just one free variable, which can either be taken to be the scroll wrap height hs or the base circle radius rb, and here the base circle radius was taken as the free variable with the height adjusted to meet the displacement constraint. A method is presented in the next section to optimize the selection of the base circle radius. With these constraints, it is possible to obtain an analytic solution for the relevant scroll wrap parameters. The outer involute initial angle is then given by 0 /o s bt r (6) and after some algebra and simplification, the height of the scroll wrap is given by

20 02 ( )(2 3 )disp

sb ratio o os o

Vh

r V

(7)

and the ending angle of the scroll is given by

02

0

324 ( )

disp oie

s b o

Vh r

(8)

where both the fixed and orbiting scrolls have the same ending angle. If another set of constraints is desired, it is possible to use a non-linear solver to obtain the scroll wrap geometry. For the same volume ratio, scroll wrap thickness and displacement, the larger rb is, the smaller hs must be to maintain the same displacement, volume ratio and scroll wrap thickness. This yields a family of solutions from a very narrow cylinder to a “pancake” scroll design. Selected members of this family are shown in Figure 5. All scroll wraps are plotted at the same scale.

Figure 5: Family of scroll wraps for a volume ratio of 2.7, displacement of 104.8 cm3, and wrap thickness of 4.66 mm

3. DERIVATION OF OPTIMAL BASE CIRCLE RADIUS

As shown in the previous section, for a given volume ratio, displacement, and scroll wrap thickness, a family of different scroll wraps can be obtained. The range of scroll wraps, from a narrow cylinder to a pancake scroll, offer different performance due to the variation in the leakage rates. It is therefore useful to develop a simple model for the leakage terms in order get a first guess for the optimal scroll wrap geometry from a leakage standpoint. In the

!

1371, Page 6


and the results for the effective leakage areas as a function of base circle radius for a volume ratio of 2.7 and displacement of 104.8 cm3 are shown in Figure 6. The effective radial leakage increases quasi-linearly with the base circle radius, while the effective flank leakage decreases with the base circle radius. Under these constraints the sum of the two terms yields a minimum effective leakage area at a base circle radius of 3.91 mm. * * *

total radial flankA A A (16)

Figure 6: Effective flank and radial leakage areas for compressor with volume ratio of 2.7,

displacement of 104.8 cm3, scroll thickness of 4.66 mm

A numerical minimization routine can be employed to determine the optimal base circle radius that minimizes Atotal

*

over a range of displacement and volume ratios for a fixed scroll wrap width of 4.66 mm. Both flank and radial leakage gap widths are set to 12 µm. The results of this analysis are shown in Figure 7. The optimal base circle radii obtained from the detailed compressor modeling for the Liquid-Flooded Ericsson Cycle and the Liquid-Flooded CO2 analyses (Bell, 2011) are also overlaid in order to demonstrate the effectiveness of this method for calculating an approximate optimal base circle radius. While both of these sets of optimal geometry are based on a liquid-flooded compressor, it is interesting to note that their optimal base circle radii follow closely with the model presented here. The Python code required to carry out the optimization is listed as the appendix. It is straightforward to generate a similar plot for a different scroll wrap thickness. These results show that for a given displacement, as the volume ratio increases, the optimal base circle radius decreases. Furthermore, for a given volume ratio, as the displacement is increased, the optimal base circle radius increases. This chart can be generally employed in the design of scroll wraps, whether for flooded or dry compression applications. The inclusion of geometrically-dependent mechanical losses and scroll wrap manufacturing cost would result in different optimal scroll wrap geometry.

Source: Bell, et al. 2012

Source: Bel et al.l, 2012

22

Technical consideraWons Two phase gas-‐liquid

Screw o  Largest expansion machine handling 2-‐phase

flows: up to 85% in mass of liquid (Öhman, 2012).

o  Use of ammonia has been reported recently (Öhman, 2012): Waste heat recovery ORC in a pulp mill, 750 kWe

Source: Smith 2009

o  Wet steam cycle as an alternaWve to ORC for heat recovery in the range of 300-‐400°C (Smith et al., 2009)

4.1. Practical aspects

Several practical issues have been overcome during the testperiod, a significant such was the notoriously difficult task ofmeasuring the waste water flow correctly. (As the variation issignificant an accurate flow measurement is required in order toevaluate power plant efficiency. Unfortunately that task failedseveral times delaying the collection of proper data.)

The ORC power plant is installed according to the SwedishRefrigeration Industry Code rigorously addressing the validation ofsafety [5]. As the MUNKSJÖ plant at Aspa already had experiencefromhandling ammonia this did not cause any delays to the project.

Fouling and similar issues in heat exchangers were expected buthas not been experienced up to the time of writing this paper.

4.2. Functional aspects

The power plant is fully automatic except for restart after faultalarm. In this situation the plant is started remotely by the plantcentral operations.

Synchronisation between the generator and the grid net isautomatic. Starting time is 0.5e2 min to synchronisation, see Fig. 5,and further 1e2 min to full load.

NPO (Net Power Output) defined as measured at the walls of theORC unit, has exceeded predictions mainly due to the lack of heatexchanger fouling.

During the commercial operation availability has been goodalthough the measured period was short. An analysis of the avail-ability will be made after 12 months commercial operation.

4.3. WHR efficiencies

Electric output ratio, or first law thermal efficiency, is of limitedvalue in determining LTPC-efficiency with finite heat source andheat sink. The size of the ORC has a larger impact on thermal efficiencythan the quality of the process or its components, as indicated in [3].

Table 2Cooling water temperature at plant.

Jan Feb Mar Apr may Jun Jul Aug Sept Oct Nov Dec

3 2 6 8 13 16 21 21 14 8 5 4

Table 3Technical data for the ORC power plant in Aspa.

Power 950 kVA/50 Hz Length 11 m

Voltage 500 V Height 4 mGeneration Synchronous Width 3.5 mMedia NH3 Heat source Waste waterWeight 27.000 kg Heat sink Lake water

Fig. 1. Waste heat recovery at the MUNKSJÖ pulp mill at Aspa.

H. Öhman / Energy xxx (2012) 1e6 3

Please cite this article in press as: Öhman H, Implementation and evaluation of a low temperaturewaste heat recovery power cycle using NH3 inan Organic Rankine Cycle, Energy (2012), doi:10.1016/j.energy.2012.02.074

Source: Öhman, 2012

o  Dortmund Univ. (Prof. Brümmer) is invesWgaWng liquid injecWon as a way to increase volumetric performance

23


Scroll o  No valves, no clearance volume => Flooding expansion is

possible o  Flooding experienced on automoWve compressors fed

with a mixture of oil and nitrogen (Bell et al., 2012).

0 0.2 0.4 0.6 0.8 1

1

1.5

2

2.5

3

xl [-]

Vol

um

etric

E!

cien

cy[-]

Increasing"p

Expander (N=875)Expander (N=1167)Expander (N=1750)Compressor

Figure 7: Experimental volumetric e!ciency of scroll machines

0 0.2 0.4 0.6 0.8 10.3

0.4

0.5

0.6

0.7

0.8

0.9

1

xl [-]

Ove

rall

Isen

trop

icE

!ci

ency

[-]

CompressorExpander (N=1750)Expander (N=1167)Expander (N=875)

Figure 8: Experimental overall isentropic e!ciency of scroll machines

The fundamental goal of liquid flooding is to approachisothermal compression and expansion processes. Asshown in Figure 10, the ratio of the high to low tempera-ture for the compressor and the expander both approach1.0 as the oil mass fraction increases, that is the processbecomes more and more isothermal. In the compressor,the high temperature is the outlet temperature, and in theexpander, the high temperature is the inlet temperature.

0 0.2 0.4 0.6 0.8 10.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

xl [-]

Inte

rnal

Isen

trop

icE

!ci

ency

[-]

CompressorExpander (N=1750)Expander (N=1167)Expander (N=875)

Figure 9: Experimental internal isentropic e!ciency of scroll ma-chines

The di!erence in slope for the scatter plots for both com-pressor and expander is due to the di!erence in pressureratios experienced by the two machines. Since the test rigis quite large with significant piping and a large numberof fittings, the pressure drop between the compressor andexpander is quite large. As a result, the imposed pres-sure ratio on the compressor will always be higher thanthat imposed on the expander. In the limit of no pressuredrops in the system, the two curves should come signifi-cantly nearer. There will still be some di!erence in slopedue to di!erences in scroll machine e"ciency, manifestingitself as a di!erence in the outlet temperature.

4. Model Validation

After developing a detailed component model for boththe compressor and the expander with flooding, it is nec-essary to validate the model against experimental dataas well as tune several parameters di"cult to estimatedirectly. The scroll machine models operate as in theschematic shown in Figure 11, where all the parame-ters listed as model input parameters must be estimated,tuned, or correlated based on physical input parameters.

4.1. Compressor Model Validation and Model Tuning

Tuning of the compressor model is carried out in a two-step process. First the mass flow rate is tuned based onleakage and pressure drop parameters, and then the shaftpower is tuned based on mechanical loss and external heattransfer parameters.

6

Expander fed with a mixture of nitrogen and oil (up to 80% in mass of oil)

Ericsson cycle cooler (quasi-‐isothermal compression and expansion)

24


Flooded ORC cycles: Research at Purdue UniversiWes on scroll expanders (Brandon Woodland from Groll’s and Braun’s team)

ü  Increase in expander power ü  Increase in refrigerant temperature at

expander outlet ü  Ability to adjust the built-‐in volume raWo

of the expander « seen » by the refrigerant

ü  Existence of an opWmal mass raWo of oil

0 1 2 3 4 5 6 7 80

2.5

5

7.5

10

12.5

15

Mass ratio of oil to refrigerant [kgoil / kgrefrigerant ]

Rel

ativ

e ne

t wor

k im

prov

emen

t [%

]

IsopentaneIsopentaneR245faR245faR134aR134a

AmmoniaAmmoniaWaterWater

Evaporating temperature : 90°C

Figure V.2 shows a schematic of the ORC cycle with regenerator and flooded expansion. The

flooded expansion is carried out with oil. An oil loop is therefore added to the basic ORC. It is

composed of a pump, a heater and an oil separator. The oil is pumped to the same pressure

as the high pressure line on the refrigerant side. It is then heated to the same temperature

as the superheated refrigerant after the evaporator. Oil and refrigerant are then mixed

before entering the expander. After the expansion process, they are separated in the oil

separator. The oil is pumped back to the oil heater, whereas the refrigerant, st

temperature, goes through the regenerator to preheat the refrigerant exiting the pump and

reduce the heat transfer rate at the evaporator.

Figure V.2: Schematic of the ORC cycle with regenerator

V.2 First approach -

This initial exploration of flooded expansion

Solver, S.A. Klein). The compressor lubricating oil zerol

medium and different working fluids are considered.

V.2.1 Oil properties

The zerol-60 is an alkyl-benzene lubricant oil for compressors. Unfortunately, its properties

are not currently available in EESa function of temperature as follows

shows a schematic of the ORC cycle with regenerator and flooded expansion. The

ed out with oil. An oil loop is therefore added to the basic ORC. It is



s the superheated refrigerant after the evaporator. Oil and refrigerant are then mixed


separator. The oil is pumped back to the oil heater, whereas the refrigerant, st


reduce the heat transfer rate at the evaporator.

: Schematic of the ORC cycle with regenerator and flooded expansion

- Fixed expander isentropic efficiency

exploration of flooded expansion was carried out in EES (Engineering Equation

The compressor lubricating oil zerol-60 is investigated as the

medium and different working fluids are considered.

Oil properties

benzene lubricant oil for compressors. Unfortunately, its properties

EES. However, its specific heat and density can be expr

a function of temperature as follows [11]:

= +

78

shows a schematic of the ORC cycle with regenerator and flooded expansion. The

ed out with oil. An oil loop is therefore added to the basic ORC. It is



s the superheated refrigerant after the evaporator. Oil and refrigerant are then mixed


separator. The oil is pumped back to the oil heater, whereas the refrigerant, still at high


and flooded expansion

Fixed expander isentropic efficiency

(Engineering Equation

60 is investigated as the flooding

benzene lubricant oil for compressors. Unfortunately, its properties

. However, its specific heat and density can be expressed as

(V-2)

Source: Georges, 2012

25

Technical constraints Inlet temperature

Piston o  High temperature allowed o  Could be used with high pressure/t° steam Scroll o  HermeWc compressors: discharge temperature limited to

145°C-‐160°C o  Temperature limited by thermal expansion and oil degradaWon

Ø  PotenWal advantage of Wp seal vs compliant (clearance allows for dilataWon)

o  Currently a lot of development for high temperature heat pumps Ø  f.i. Altereco project

o  Records in literature: Ø  Air expander: 165°C (Kane et al., 2009) Ø  Steam expander: 215°C (Lemort et al., 2006)

!(Source: Inaba et al., 1986)

(Source: Eckard and Brooks, 1973)

26

Content of the presentaWon

1.  IntroducWon 2.  Technical constraints 3.   Modeling and Simula)on

4.  SelecWon 5.  Conclusions

27

Modeling and simulaWon

3 levels of models: Ø  Empirical or “black-‐box” models:

§  Very low computaWonal Wme §  Very robust §  No extrapolaWon beyond calibraWon range

Ø  Semi-‐empirical or “grey-‐box” models §  Low computaWonal Wme §  Robust §  Physical meaning of parameters §  ParWal extrapolaWon

Ø  Determinis)c or “white-‐box” models §  Large computaWonal Wme §  Exact physical meaning of parameters

Dynamic simula3on of ORCs

Steady-‐state simula3on of ORCs (design of ORC)

Design of expanders

28

Modeling and simulaWon Semi-‐empirical

shW•

S=ct V=ct

S=ct

ΔPsu ΔPex

suhm•

exhm•leakm

•

inm•

su su,1 2

3

ex,3 exex,2

ambQ•

6 System layout 5

4

suQ•

su,2

lossW•

0

•

m

V=ct1

exQ•

ex,1

shW•

S=ct V=ct

S=ct

ΔPsu ΔPex

suhm•

exhm•leakm

•

inm•

su su,1 2

3

ex,3 exex,2

ambQ•

6 System layout 5

4

suQ•

su,2

lossW•

0

•

m

V=ct1

exQ•

ex,1

Scroll/screw expander

Limited number of parameters (9) with physical meaning to be idenWfied based on performance points

29


Open-‐drive oil-‐free scroll expander

0.016

0.018 0.0

20.0

220.0

240.0

260.0

28 0.03

0.032

0.034

0.036

0.038 0.0

40.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

vr,su,exp [m3/kg]

Mr [

kg/s

]

2296 rpm

1771 rpm1771 rpm

2660 rpm2660 rpm2% error bars

measuredmeasuredcalculatedcalculated

nMAUamb [W/K] AUsu

[W/K] AUex [W/K]

[kg/s] Aleak [mm2] rv,in

[-] Vs [cm3] dsu

[mm] Tloss [N-m]

6.4 21.2 34.2 0.12 4.6 4.05 36.54 5.91 0.47

also, it can be observed that the agreement is good. The maximumdeviation between the model predictions and the measurements is5%.

Fig. 10 compares the evolutions of the exhaust temperature(measured and predicted by the model) with the mean measuredtemperature of the fluid between the expander supply andexhaust.

The model predicts the exhaust temperature within 3 K. How-ever, the model seems to slightly overestimate the exhaust tem-perature for high expander mean temperatures and to slightlyunderestimate it for the lower mean temperatures.

This figure also shows the evolution of the predicted exhausttemperature if the model did not account for ambient losses. Thedeviation between the predicted exhaust temperature and themeasured one increases with the mean temperature. This confirmsthat the model should account for the ambient losses to better pre-dict the exhaust temperature.

5. Model analysis

The validated model of the expander is used to quantify the dif-ferent losses and to indicate how the design of the expander mightbe altered to achieve better performances.

Fig. 11 shows the evolution of the overall isentropic effective-ness with the pressure ratio imposed to the expander. Operatingconditions, related to one of the measured performance points,correspond to a supply pressure of 10.03 bar, an exhaust pressureof 2.01 bar, a supply temperature of 142 !C and a rotational speedof 2296 rpm. The measured overall isentropic effectiveness for thisoperating point is also indicated in Fig. 11 (with error bars associ-ated with measurement uncertainties).

The evolution at the top of the figure is predicted by a modelthat only accounts for under- and over-expansion losses. The effec-tiveness goes through 1.0 at a pressure ratio equal to the internalpressure ratio (Pad = Pex). For smaller and larger pressure ratios,the fluid is over-expanded and under-expanded respectively.Experimental results showed that the maximum achieved pressureratio was around 5.5. If much larger pressure ratios were imposed,a machine with a larger built-in volume ratio than 4.05 would yieldbetter performances.

The overall isentropic effectiveness decreases when accountingfor the heat transfers in the modeling because of the supply coolingdown of the fluid. This decrease could slightly be tempered by bet-ter insulating the expander (in the limiting case, AUamb = 0 W/K).

Introducing the mechanical losses and the supply pressure dropin the modeling largely reduces the isentropic effectiveness. Fur-ther work should investigate the possibility of reducing mechani-cal losses by using better adapted tip seals. As already mentionedby Yanagisawa et al. [5], the supply pressure drop is an inherentcharacteristic of the scroll machine. A detailed modeling of the ex-pander should answer the question of how to reduce this pressuredrop by modifying the expander geometry.

The internal leakage is responsible for the major part of the per-formance loss. Under the assumption that the tip seals work cor-rectly (they seal the radial gap between the tip of each scroll andthe plate of the opposite scroll), the identified leakage area (Table3) may be explained by a large flank clearance between the twoscrolls. This large clearance is characteristic of scroll machinesoperating with a kinematically rigid configuration, where a flankgap is maintained.

6. Conclusions

An experimental study was carried out on a prototype of a scrollexpander integrated into an Organic Rankine Cycle. The evolutionof the expander performance, expressed in terms of global isentro-pic effectiveness and filling factor, with the operating conditions

70 80 90 100 110 120 130 140 15050

60

70

80

90

100

110

120

130

140

150

(Tsu + Tex,meas )/2 [C]

Tex

[C

]

Tex,measTex,meas

Tex,calcTex,calc

3K error bars

Tex,calc with Qamb=0Tex,calc with Qamb=0

Fig. 10. Evolution of the exhaust temperature (measured and predicted by themodel) with the mean fluid temperature between the expander supply and exhaust.

3 4 5 6 7 8 9 100.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Psu / Pex [-]

! s [-

]

+ built-in volume ratio

+ heat transfers (AUamb=0 W/K)+ heat transfers (AUamb=0 W/K)

+ mechanical losses+ mechanical losses

+ pressure drop+ pressure drop

+ leakage+ leakage

+ heat transfers (AUamb=6.4 W/K)+ heat transfers (AUamb=6.4 W/K)

measured performance

Fig. 11. Evolution of the calculated overall isentropic effectiveness with the imposed pressure ratio.

V. Lemort et al. / Applied Thermal Engineering 29 (2009) 3094–3102 3101

Predic3on of the mass flow rate Impact of pressure losses, fric3on, leakages

30


shW•

S=ct V=ct

S=ct

ΔPsu ΔPex

suhm•

exhm•leakm

•

inm•

su su,1 2

3

ex,3 exex,2

ambQ•

6 System layout 5

4

suQ•

su,2

lossW•

0

•

m

V=ct1

exQ•

ex,1

shW•

S=ct V=ct

S=ct

ΔPsu ΔPex

suhm•

exhm•leakm

•

inm•

su su,1 2

3

ex,3 exex,2

ambQ•

6 System layout 5

4

suQ•

su,2

lossW•

0

•

m

V=ct1

exQ•

ex,1

Pressur,bar

Volume,m3

2

4

3

Vs

Psu,2

Pex,2

P3

5

6

V0

P6

ΔPsu

Pex

Psu

ΔPex

1

VSfa VSfp

Pressur,bar

Volume,m3

2

4

3

Vs

Psu,2

Pex,2

P3

5

6

V0

P6

ΔPsu

Pex

Psu

ΔPex

1

VSfa VSfp

Piston expander

Re-‐compression of gas at the end of discharge phase (source: Glavatskaya et al., 2012)

31


Axial piston expander

Predic3on of the shaX power Isentropic effec3veness vs pressure ra3o

32

Modeling and simulaWon Determinis3c Scroll

DefiniWon of the working chambers

Crank angle evoluWon of the volumes of the chambers

33


•  Differen3al equa3ons of Mass & Energy conserva3on

Numerically solved for each chamber

•  Internal leakages between chambers

•  Heat transfers between the fluid and the scroll wraps

•  Simple mechanical loss model

⎟⎟⎠

⎞⎜⎜⎝

⎛+==

c

hc

DB RD77.10.1K

NuNu

( )∑∑ −⋅π⋅

=θ exsu MM

NddM

21

∑∑ ⋅π⋅−

⋅π⋅+

θ−

⋅π⋅=

θ exsusu MN

hh.MNd

dVPN

QddU

221

2

34


2.5 3 3.5 4 4.5 5 5.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

rp [-]

ε s [-]

1771 rpm2296 rpm2660 rpmmeasuredcalculated

PredicWon of the isentropic effecWveness

5 parameters

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

x 10-4

1

2

3

4

5

6

7

x 105

V [m3]

P [P

a]

← beginning of expansion

original suction diameterlarger suction diameter

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

x [m]

y [m

]

fixed scrollorbiting scroll

!

35

Content of the presentaWon

1.  IntroducWon 2.  Technical constraints 3.  Modeling and SimulaWon

4.   Selec)on 5.  Conclusions

36

SelecWon Limita3ons of posi3ve displacement machines

•  Built-‐in internal volume raWos

⇒ Under and over-‐expansion ⇒ Recompression work (piston) ⇒ rv,in,max: 4 (scroll), 5 (screw),

10 (piston) •  Volume coefficient (m3/MJ) •  Range of volume flow rates

See Quoilin et al. (2012)

Energies 2012, 5

1755

Figure 2. PV diagram representing the internal expansion process.

Pres

suer

,bar

Volume,m3

2

4

3

Vs

Psu,2

Pex,2

P3

5

6

V0

P6

㰱Psu

Pex

Psu

㰱Pex

1

VSfa VSfp

Pres

suer

,bar

Volume,m3

2

4

3

Vs

Psu,2

Pex,2

P3

5

6

V0

P6

㰱Psu

Pex

Psu

㰱Pex

1

VSfa VSfp

In order to describe the expansion process, the following geometrical parameters of the expander were defined.

The duration of the supply fa and exhaust fp processes influence the mass flow rate swept by the expander. The duration of the supply process, or cut-off ratio (fa), can vary between 0.1 and 0.25 [28]. The volume of the admitted and residual fluids is determined in the model by Equation (1). According to the expander data provided by the manufacturer, the duration of the supply and exhaust processes can be 0.25 for a supply valve and 0.4 for an exhaust valve:

3

2

VVfa ;

4

5

VVf p (1)

The values of the expander displacement VS and clearance volume V0 were taken from the expander manufacturer’s data. The ratio C between the clearance and the expander displacement is 0.072.

sVCV � 0 (2)

2.1. Supply and Exhaust Pressure Drops

The pressure drops within the supply and exhaust valves are computed by reference to the flow through a simple nozzle. For a compressible fluid, the stream velocity (subsonic or sonic flow) determines the pressure at the nozzle throat and depends on the critical pressure given by Equation (3):

εs = εin.ηmec

37

SelecWon Opera3ng maps

(screw+n-‐pentane)

Condensing temperature

EvaporaW

ng te

mpe

rature

38


screw piston

39

SelecWon Limita3ons of turbines

•  Min/max specific speed •  Maximum Wp speed •  Maximum mach number in the

nozzle •  Maximum mach number in the

rotor •  Maximum rotaWng speed

(depending on the bearings)

40


n-‐pentane:

41

SelecWon Power ranges

rpm < 50000

Piston 1.25 l/s 75 l/s

42

Conclusions

o  PosiWve displacement machines show some advantages over turbines, among them their ability to handle a liquid phase: lot of opportuniWes of research in 2-‐phase flows

o  Larger industrial maturity of screw expanders vs scroll expanders, niche-‐market applicaWons for piston expanders

o  Developments on posiWve displacement expanders beneficiate from developments of compressors: increase of performance, reliability & extension of operaWng ranges (f.i. compressors for high temperature heat pumps)

o  Different types of modeling/simula)on models for different purposes

o  The selec)on of the expansion machine depends on the working condiWons and on the selected fluid ü  OperaWng maps of opWmal working condiWons for each combinaWon of

expander/fluid were presented ü  Useful tool for the preliminary selecWon of expanders and fluids for a given cycle.

43

Thank you for your a`enWon!

44

Acknowledgments

o  Rémi Daccord from Exoes (France) o  Stéphane Wa`s from Danfoss (France) o  Prof. Ian Smith and Prof. Nikola Stosic from City University (U.K.) o  Prof. Andreas Brümmer from Dortmund University (Germany)

45

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Part I: experimental invesWgaWon, Int. J. RefrigeraWon 28: 141-‐151 •  Bel, I., E. A. Groll, J.E. Braun, and W. T. Horton. 2012. DerivaWon of opWmal scroll compressor wrap for minimizaWon of leakage

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