Improvement of the Efficiency of Twin-Screw Refrigeration ......1428, Page 1 23 nd International Compressor Engineering Conference at Purdue, July 11 -14, 2016 Improvement of the Efficiency

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Improvement of the Efficiency of Twin-ScrewRefrigeration Compressors by means of Dual LeadRotorsMatthias UtriChair of Fluidics, TU Dortmund University, Germany, [email protected]

Andreas BrümmerChair of Fluidics, TU Dortmund University, Germany, [email protected]

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1428, Page 1

23nd International Compressor Engineering Conference at Purdue, July 11-14, 2016

Improvement of the Efficiency of Twin-Screw Refrigeration Compressors by means of Dual Lead Rotors

Matthias Utri1*, Andreas Brümmer2

1TU Dortmund University, Chair of Fluidics,

Dortmund, Germany Phone: +49 231 755 5724, Fax: +49 231 755 5722

E-mail: [email protected]

2TU Dortmund University, Chair of Fluidics, Dortmund, Germany

Phone: +49 231 755 5720, Fax: +49 231 755 5722 E-mail: [email protected]

* Corresponding Author

ABSTRACT The paper deals with a theoretical investigation of screw machines applied as refrigerant compressors, focusing on the compression process. The refrigerant used is R227ea with a pressure ratio of four. A wide range of geometric parameters such as rotor length, internal volume ratio and wrap angle are varied in order to show their influence on efficiency, with a view to finding out how energy conversion can be improved by using dual lead rotors. These rotors possess two segments with different rotor lead in order to optimize the progression of chamber volume, clearance size and outlet area. The rotor profile under investigation is an asymmetric SRM-profile whereas the diameter of the rotors as well as the clearance heights remain constant throughout the simulation. The impact of the machine geometry on efficiency is examined by performing a multi-chamber simulation. The improvement in energy conversion that can be achieved by using a dual lead is quantified in terms of isentropic efficiency and delivery rate. Especially for greater length-to-diameter ratios, benefits in efficiency and mass flow rate may be expected.

1. INTRODUCTION Screw machines are rotary positive displacement machines that are used in various applications for gas compression. The machine basically consists of two counter rotating rotors that are enclosed in a tight-fitting casing. Apart from its physical dimensions, the efficiency of a screw compressor depends to a great extent on its geometrical parameters, e.g. lobe count, length-to-diameter ratio, internal volume ratio, wrap angle and the rotor profile itself due to their influence on the main dissipative effects, throttling and volumetric clearance losses. In particular, the wrap angle needs to be adjusted individually for the intended application because it affects dissipation in two opposing ways: A major twisting of the rotors decreases the time-dependent change in chamber volume and enlarges the port areas of the machine, thus leading to reduced throttling effects, but increasing clearance mass flows due to greater clearance areas and a longer working cycle. The idea of combining the advantages of large and small wrap angles by using non-uniform rotor leads was patent-registered in the 1960’s (Gardner, 1969). Rane et al. (2014) performed a CFD simulation which presented advantages in energy conversion by varying the rotor lead continuously from the low to the high pressure intersection. Other studies (Utri and Brümmer, 2014; Fost, 2003) focus on the application of screw expanders and also possess potential, especially for high pressure applications, by using two different lead-segments on one rotor (“dual lead rotors”).

Screw compressors are widely chamber by absorbing itsstate 1→2)(2→3). Nextthrottled backThe change in state state 3, which is perthe indicator diagram in Fig. 1. The working cycle can be divided into three characteristic phases: During suctionthe working chamber increases in volume and is filled with the refrigerant through the low pressure port area. After reaching maximum chamber volume, the working chamber compression phase begins. phase, the working chamber is almost closedclearances. port and the decreases.

The thermodynamic simulation mainly based on mass and energy conservation. Multibehavior of displacement machinesalternative to the more complex CFD simulation that is contrast to singlemulti-chamber simulation is a zeromachine being examinedfunction of the rotation angle.

23nd International Compressor Engineering Conference at Purdue, July 11

2. REFRIGERATION AND

Screw compressors are widely chamber by absorbing its

2). To be re-liquefied the refrigerant needs to beNext the fluid is condensed by back to the low pressure conditions (4

The change in state whichstate 3, which is performed by the screw compressorthe indicator diagram in Fig. 1. The working cycle can be divided into three characteristic phases: During suctionthe working chamber increases in volume and is filled with the refrigerant through the low pressure port area. After reaching maximum chamber volume, the working chamber compression phase begins.

the working chamber is almost closedclearances. When it reaches

the discharge phase begins.

Figure 1: p-h

hermodynamic simulation mainly based on mass and energy conservation. Multi

r of displacement machinesalternative to the more complex CFD simulation that is contrast to single-chamber simulation

chamber simulation is a zerobeing examined

function of the rotation angle.

International Compressor Engineering Conference at Purdue, July 11

REFRIGERATION AND

Screw compressors are widely used in refrigeration. The purpose of refrigeration cycles is to refrigerate a cooling chamber by absorbing its heat by means of a refrigerant and

liquefied the refrigerant needs to bethe fluid is condensed by

the low pressure conditions (4which is investigated within the scope of this paper is the compression stroke

formed by the screw compressorthe indicator diagram in Fig. 1. The working cycle can be divided into three characteristic phases: During suctionthe working chamber increases in volume and is filled with the refrigerant through the low pressure port area. After reaching maximum chamber volume, the working chamber compression phase begins. The refrigerant is

the working chamber is almost closedit reaches the high pressure control edges

discharge phase begins. The

h-diagram of refrigeration cycle

hermodynamic simulation of the screw compressor mainly based on mass and energy conservation. Multi

r of displacement machines in different alternative to the more complex CFD simulation that is

chamber simulation, chamber simulation is a zero-dimensional chamber model which includes all relevant properties of the

being examined. The relevant function of the rotation angle. The connections of the working chamber are opening areas, which connect the


REFRIGERATION AND

in refrigeration. The purpose of refrigeration cycles is to refrigerate a cooling heat by means of a refrigerant and

liquefied the refrigerant needs to bethe fluid is condensed by transferring heat to the environment (3

the low pressure conditions (4→1). is investigated within the scope of this paper is the compression stroke

formed by the screw compressor. the indicator diagram in Fig. 1. The working cycle can be divided into three characteristic phases: During suctionthe working chamber increases in volume and is filled with the refrigerant through the low pressure port area. After reaching maximum chamber volume, the working chamber

igerant is now the working chamber is almost closed. It only interacts with other chambers and the machine ports through

the high pressure control edgesThe fluid is forced out through the

of refrigeration cycle

3. SIMULATION PRINCIPLE

of the screw compressor mainly based on mass and energy conservation. Multi

in different kindsalternative to the more complex CFD simulation that is

the fluid state inside all chambers is determined simultaneously. dimensional chamber model which includes all relevant properties of the

relevant parameters areonnections of the working chamber are opening areas, which connect the


REFRIGERATION AND THE SCREW COMPRESSOR CYCLE

in refrigeration. The purpose of refrigeration cycles is to refrigerate a cooling heat by means of a refrigerant and thereby changing its state from fluid to vapor

liquefied the refrigerant needs to be pressurized to the condenserheat to the environment (3

is investigated within the scope of this paper is the compression stroke The idealized

the indicator diagram in Fig. 1. The working cycle can be divided into three characteristic phases: During suctionthe working chamber increases in volume and is filled with the refrigerant through the low pressure port area. After reaching maximum chamber volume, the working chamber is disconnected from the low pressure port and

now compressed by the decreasing chamber volume.only interacts with other chambers and the machine ports through

the high pressure control edges, the workinforced out through the

of refrigeration cycle, idealized working cycle of a screw

SIMULATION PRINCIPLE

of the screw compressor is carried out by performing mainly based on mass and energy conservation. Multi-chamber simulation

kinds of applicationalternative to the more complex CFD simulation that is commonly used

fluid state inside all chambers is determined simultaneously. dimensional chamber model which includes all relevant properties of the

parameters are the volume of the woronnections of the working chamber are opening areas, which connect the


SCREW COMPRESSOR CYCLE

in refrigeration. The purpose of refrigeration cycles is to refrigerate a cooling thereby changing its state from fluid to vaporpressurized to the condenser

heat to the environment (3→4). Subsequ

is investigated within the scope of this paper is the compression strokelized working cycle

the indicator diagram in Fig. 1. The working cycle can be divided into three characteristic phases: During suctionthe working chamber increases in volume and is filled with the refrigerant through the low pressure port area. After

disconnected from the low pressure port and compressed by the decreasing chamber volume.

only interacts with other chambers and the machine ports through the working chamber

forced out through the high pressure port

, idealized working cycle of a screw

SIMULATION PRINCIPLE

is carried out by performing chamber simulations

of application (Janicki, 2007; Rohe, 2004commonly used for the simulation


the volume of the working chamber and its connections as a onnections of the working chamber are opening areas, which connect the

International Compressor Engineering Conference at Purdue, July 11-14, 2016


in refrigeration. The purpose of refrigeration cycles is to refrigerate a cooling thereby changing its state from fluid to vaporpressurized to the condenser-dependent temperature

4). Subsequently, the refrigerant is

is investigated within the scope of this paper is the compression strokeworking cycle of this compressor


disconnected from the low pressure port and compressed by the decreasing chamber volume.

only interacts with other chambers and the machine ports through g chamber connects with the high pressure high pressure port as

, idealized working cycle of a screw compressor

is carried out by performing a multi- are already used to simulate the

cki, 2007; Rohe, 2004for the simulation of turbo machines.


king chamber and its connections as a onnections of the working chamber are opening areas, which connect the

1428, Page

14, 2016


in refrigeration. The purpose of refrigeration cycles is to refrigerate a cooling thereby changing its state from fluid to vapor (Fig. 1

dependent temperatureently, the refrigerant is

is investigated within the scope of this paper is the compression stroke from state 2 to of this compressor is illustrated in


disconnected from the low pressure port and compressed by the decreasing chamber volume. During this

only interacts with other chambers and the machine ports through with the high pressure the chamber volume

compressor

-chamber simulationused to simulate the

cki, 2007; Rohe, 2004) and presentof turbo machines.

fluid state inside all chambers is determined simultaneously. The basis of dimensional chamber model which includes all relevant properties of the


, Page 2

in refrigeration. The purpose of refrigeration cycles is to refrigerate a cooling (Fig. 1,

dependent temperature ently, the refrigerant is

from state 2 to is illustrated in

the indicator diagram in Fig. 1. The working cycle can be divided into three characteristic phases: During suction, the working chamber increases in volume and is filled with the refrigerant through the low pressure port area. After

disconnected from the low pressure port and the During this

only interacts with other chambers and the machine ports through with the high pressure

the chamber volume

chamber simulation used to simulate the

present an of turbo machines. In

The basis of dimensional chamber model which includes all relevant properties of the


working chamber with thewith other The optimization we are aiming for requiresof chamber model generation has been been carried outrotor profile andlength. Thus the machine rotor lengthapproach eliminatestasks whichThe thermodynamic simulationChair of Fluidics at of the simulation areof the simulated between chambers and portsstate inside the working chamberstate inside thVenant and Wantzelpressure through a flow crossaccount, a Electrical and mechanical losses are not considered in the simulationhermetically sealed to the ambience

In order to optimize the screw compressor for the intended refrigeration cycle, boundary conditions forsimulation and the machineprofile as described in detail by Rinder (

Figure 2: The boundary conditions investigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of 0.25 MPa. The refrigerant temperature in the condenser is set to 328 K, resu


g chamber with the chambers as well as the ports.

optimization we are aiming for requiresof chamber model generation has been been carried out, supplying rotor profile and diameter, the progression of

Thus the machine rotor lengths and leads by “recombining” the

eliminates the major timewhich necessitate a high number of chamber models.hermodynamic simulation

Chair of Fluidics at the TU Dortmund Universityof the simulation are given asof the simulated rotary positive displacement machinebetween chambers and portsstate inside the working chamberstate inside the working chamberVenant and Wantzel (Sigloch, 2009)

through a flow cross flow coefficient α

Electrical and mechanical losses are not considered in the simulationally sealed to the ambience

4. BOUNDARY CONDITIONS

In order to optimize the screw compressor for the intended refrigeration cycle, boundary conditions forsimulation and the machine

described in detail by Rinder (

Figure 2: Asymmetric SRM

oundary conditions investigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of

MPa. The refrigerant temperature in the condenser is set to 328 K, resu


g chamber with the high and low pressure portchambers as well as the ports.

optimization we are aiming for requiresof chamber model generation has been

supplying all necessary information diameter, the progression of

Thus the machine under examination by “recombining” the

the major time penaltynecessitate a high number of chamber models.

hermodynamic simulation was carried out by using the simulation tool TU Dortmund University

given as integral values, e.g. for mass flow and rotary positive displacement machine

between chambers and ports, thereby influencingstate inside the working chambers influence

e working chambers is required(Sigloch, 2009) which

through a flow cross-section coefficient α is used to reduce the

Electrical and mechanical losses are not considered in the simulationally sealed to the ambience.

BOUNDARY CONDITIONS

In order to optimize the screw compressor for the intended refrigeration cycle, boundary conditions forsimulation and the machine geometry need to be clarified. The investigated rotor profile is the asymmetric SRM

described in detail by Rinder (

Asymmetric SRM-profile with lobe count combinations of 3+5, 4+6 and 5+7 with D

oundary conditions which remaininvestigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of


Parameter [dimension]Cycle parameters:

- Fluid- Compressor inlet - Compressor inlet pressure [MPa]- Compressor outlet pressure [MPa]

Machine parameters:- Male rotor crown circle [mm]- Clearance heights [mm]

Operating parameters:- Circumferential speed [m/s]


high and low pressure portchambers as well as the ports. The fluid state inside

optimization we are aiming for requires a large number of machines to be simulated. of chamber model generation has been achieved. For a

all necessary information diameter, the progression of chamber

under examination can be used to generate chamber models of machines with different by “recombining” the chamber

penalty of chamber model generation and is highly suitable for optimization necessitate a high number of chamber models.

carried out by using the simulation tool TU Dortmund University (Kauder

integral values, e.g. for mass flow and rotary positive displacement machine

, thereby influencing pressurinfluences the mass flow.

required. Mass flow is calculated by meanswhich assumes

section to a volume with lower pressure. is used to reduce the theoretical mass flow.

Electrical and mechanical losses are not considered in the simulation

BOUNDARY CONDITIONS

In order to optimize the screw compressor for the intended refrigeration cycle, boundary conditions forgeometry need to be clarified. The investigated rotor profile is the asymmetric SRM

described in detail by Rinder (1979) and shown in Fig. 2.

profile with lobe count combinations of 3+5, 4+6 and 5+7 with D

which remain constant throughout all simulationinvestigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of


Table 1: Constant boundary conditions

Parameter [dimension]Cycle parameters:

Fluid [-] Compressor inlet Compressor inlet pressure [MPa]Compressor outlet pressure [MPa]

Machine parameters: Male rotor crown circle [mm]Clearance heights [mm]

Operating parameters: Circumferential speed [m/s]


high and low pressure ports, and clearancehe fluid state inside all working chamber

number of machines to be simulated. For a demonstration

all necessary information such as volume curve and clearance areas. Assuming constant chamber volume and clearances

can be used to generate chamber models of machines with different chamber model of the machine that

of chamber model generation and is highly suitable for optimization necessitate a high number of chamber models.

carried out by using the simulation tool (Kauder et al., 2002

integral values, e.g. for mass flow and rotary positive displacement machine. The connections maintain an exchange of mass and energy

pressure and temperathe mass flow. Due to this Mass flow is calculated by means

assumes an adiabatic and frictionless to a volume with lower pressure.

theoretical mass flow. Electrical and mechanical losses are not considered in the simulation

BOUNDARY CONDITIONS AND VARIATION PARAMETERS


and shown in Fig. 2.


constant throughout all simulationinvestigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of


Constant boundary conditions

Parameter [dimension]

Compressor inlet temperature [K]Compressor inlet pressure [MPa]Compressor outlet pressure [MPa]

Male rotor crown circle [mm] Clearance heights [mm]

Circumferential speed [m/s]


clearance areas, which connect the working chamber working chamber

number of machines to be simulated. ion machine a

volume curve and clearance areas. Assuming constant volume and clearances depends

can be used to generate chamber models of machines with different model of the machine that

of chamber model generation and is highly suitable for optimization

carried out by using the simulation tool “KaSim, 2002; Janicki, 2007; Temming, 2007

integral values, e.g. for mass flow and internal power, as well as the indicator diagram connections maintain an exchange of mass and energy

e and temperature inside Due to this interaction,

Mass flow is calculated by meansan adiabatic and frictionless

to a volume with lower pressure. Taking atheoretical mass flow.

Electrical and mechanical losses are not considered in the simulation and the compressor is assumed to be

AND VARIATION PARAMETERS


The diameters


constant throughout all simulations are summarized in investigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of

MPa. The refrigerant temperature in the condenser is set to 328 K, resulting in a high pressure of 1.02 MPa.

Constant boundary conditions

Value

emperature [K] Compressor inlet pressure [MPa] Compressor outlet pressure [MPa]

R227ea2910.251.02

1440.1

35


areas, which connect the working chamber working chambers is assumed to be homogeneous

number of machines to be simulated. A new and a complex geometrical analysis

volume curve and clearance areas. Assuming constant depends entirely

can be used to generate chamber models of machines with different model of the machine that has already


KaSim”, which was developed at the ; Janicki, 2007; Temming, 2007

power, as well as the indicator diagram connections maintain an exchange of mass and energy

ture inside all working chamberinteraction, an iterative calculation of the

Mass flow is calculated by means of the equation introduced by St. an adiabatic and frictionless flow from a volume with higher

Taking a flow involving friction

and the compressor is assumed to be



s of the rotors are


are summarized in investigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of

lting in a high pressure of 1.02 MPa.

Value

R227ea 291 0.25 1.02

144 0.1

35

1428, Page

14, 2016

areas, which connect the working chamber is assumed to be homogeneous

new and rapid approach complex geometrical analysis

volume curve and clearance areas. Assuming constant entirely on rotor lead and

can be used to generate chamber models of machines with different been analyzed


, which was developed at the ; Janicki, 2007; Temming, 2007). The r


working chambers. In turn, the an iterative calculation of the

the equation introduced by St. a volume with higher

flow involving friction




are equal.

profile with lobe count combinations of 3+5, 4+6 and 5+7 with DMR = DFR

are summarized in Table 1. investigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of


, Page 3

areas, which connect the working chamber is assumed to be homogeneous.

approach complex geometrical analysis has

volume curve and clearance areas. Assuming constant on rotor lead and

can be used to generate chamber models of machines with different analyzed. This


, which was developed at the results


In turn, the an iterative calculation of the

the equation introduced by St. a volume with higher

flow involving friction into


In order to optimize the screw compressor for the intended refrigeration cycle, boundary conditions for the geometry need to be clarified. The investigated rotor profile is the asymmetric SRM-

FR

able 1. The investigated refrigerant is R227ea with a vaporization temperature of 280 K, leading to a low pressure level of


1428, Page 4


The diameter of the male rotor is set to 144 mm with clearance heights of 0.1 mm for the housing, intermesh and front clearances, whereas the size of the blowhole and the width of the other clearances depend on the lead of the rotors and need to be calculated individually. Liquid-injected compressors are examined within the scope of this paper, so the circumferential male rotor tip speed is set to 35 m/s, leading to a rotational speed of 4642 min-1. The simulation is carried out assuming adiabatic chambers.

5. OPTIMIZATION OF CONSTANT ROTOR LEAD 5.1 Variation parameters for constant lead To reveal the potential of variable lead rotors the optimal machine for constant rotor lead is also determined using the same simulation tool “KaSim”. The varied properties of the machine are shown in Table 2. Three different lobe count combinations are investigated while the length-to-diameter ratio is varied from 0.97 up to 1.8. The internal volume ratio vi = Vmax / Vcompr,end defines the positions of the high pressure control edges, which influence the duration of compression and discharge. The variation up to vi = 5 is large enough to cover the optimal internal volume ratio for all simulated machines. The wrap angle is defined as the degree of twist between the front and the rear surface of the male rotor. The impact of the variations on the geometrical parameters of the machine, e.g. volume curve, opening and clearance areas, are described in detail by Fost (2003) and Utri and Brümmer (2014). These geometrical parameters influence the maximum chamber volume of the machine, affecting mass flow and internal power. With respect to the refrigeration cycle, each machine could realize another cooling capacity. The purpose of the variation is to optimize the screw compressor, not the refrigeration cycle itself. The auxiliary fluid, which partly seals the clearances and opening areas, is taken into account by varying the flow coefficient.

Table 2: Varied parameters for optimization of constant rotor lead

Parameter [dimension] Minimum / maximum value Step size Rotor length L [mm] 140 / 260 60 Internal volume ratio vi [-] 2 / 5 0.5 Male rotor wrap angle φMR [°] 200 / 600 50 Lobe count combination [-] 3+5, 4+6, 5+7 - Flow coefficient α [-] 0.6 / 0.8 0.2

5.2 Simulation results First results for a constant lobe count combination of 4+6 are shown in Fig. 3. For each point only the optimal internal volume ratio has been evaluated. Internal isentropic efficiency is defined as the ratio of the power which would be necessary in the case of isentropic compression, to the internal power of the compressor determined by multi-chamber simulation:

= = ∙ ∆ℎ

− ∮ ∙ ∙ (1)

The results show that an optimal value for the wrap angle exists between 300 and 400 degrees for each rotor length. For small wrap angles, port areas are also small, resulting in throttling effects during discharge, which increase internal power. For high wrap angles throttling effects are minor, but large clearance areas reduce efficiency. This is also indicated by the delivery rate (Fig. 3) which is defined as

=

=

∙ ∙ ∙

. (2)

The delivery rate relates mass flow in the machine to the theoretical mass flow which would be achieved in the case of an ideal machine operating without clearance losses and throttling during suction. Optimal internal isentropic efficiency is achieved for the most efficient compromise between clearance losses and throttling at the outlet port. Furthermore, the progression in isentropic efficiency indicates that longer rotors are advantageous for energy conversion, which can also be explained with reference to the delivery rate. Assuming a defined constant wrap angle, the length of the machine determines maximum chamber volume whereas the axial outlet area and the duration of the working cycle remain unaffected. Compared with shorter rotors the percentage of mass which is lost during compression due to clearance mass flow, and related to the total mass inside the working chamber, is much smaller and results in higher efficiency in terms of energy.

1428, Page 5


Figure 3: Internal isentropic efficiency and delivery rate as a function of wrap angle for different rotor lengths (lobe count combination 4+6, α = 0.8, vi optimized for each point)

Fig. 4 shows the impact of different lobe count combinations at a constant rotor length. Although the lobe count combination of 3+5 shows maximum values of delivery rate in the optimal range of wrap angle between 300 and 400 degrees, a lobe count combination of 4+6 achieves maximum values of internal isentropic efficiency up to ηis = 88 %. This can be explained in terms of the throttling effects which take place during discharge for the lobe count combination of 3+5, leading to an enlargement of the area in the indicator diagram (not shown), even after optimization of the internal volume ratio. The profile has small sealing lines, but the rapid decrease in chamber volume during discharge combined with a comparatively small outlet area mean that the poor efficiency of this kind of application cannot be improved. Results for other rotor lengths show similar progressions.

Figure 4: Internal isentropic efficiency and delivery rate as a function of wrap angle for different lobe count combinations (LRotor = 260 mm, α = 0.8, vi optimized for each point)

0.7

0.8

0.9

1

1.1

1.2

1.3

0.6

0.65

0.7

0.75

0.8

0.85

0.9

100 200 300 400 500 600 700

deliv

ery

rate

[-]

inte

rnal

isen

trop

ic e

ffic

ienc

y [-

]

constant wrap angle [°]

L = 140 mmL = 200 mmL = 260 mm

ηis

λL

0.7

0.8

0.9

1

1.1

1.2

1.3

0.6

0.65

0.7

0.75

0.8

0.85

0.9

100 200 300 400 500 600 700

deliv

ery

rate

[-]

inte

rnal

isen

trop

ic e

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ienc

y [-

]


3+54+65+7

ηis

λL

1428, Page 6


Figure 5: Internal isentropic efficiency and delivery rate as a function of wrap angle for different rotor lengths (lobe count combination 4+6, α = 0.6, vi optimized for each point)

Fig. 5 shows the variation of rotor length for a reduced flow coefficient of α = 0.6. Compared with the results for α = 0.8 (Fig. 3) the absolute values of delivery rate and internal isentropic efficiency are raised, and maximum efficiency is increased to a value of ηis = 88.6% for a rotor length of 260 mm. A lower flow coefficient reduces clearance mass flow but also increases the potential for outlet throttling. This results in higher optimal wrap angles, while, compared with Fig. 3, the influence of the wrap angle is reduced after maximum internal isentropic efficiency is achieved.

6. OPTIMIZATION OF VARIABLE ROTOR LEAD 6.1 Machine parameters for dual lead rotors The purpose of dual lead rotors is to combine large and small wrap angles on a single rotor as shown in Fig. 6. This makes it possible to reduce the duration of the compression phase - thus decreasing clearance mass flow - and to influence both the duration of the discharge phase and the available port area in order to avoid throttling losses. Compared with constant lead rotors, this kind of geometry provides new parameters which need to be adjusted: the total wrap angle φtotal, which is still defined as the degree of twist between the front and rear surface, and the lengths LHP and LLP with their wrap angles φHP and φLP on the high and low pressure side (all wrap angles refer to the male rotor). As with the total wrap angle φtotal the wrap angle sections φHP and φLP are related to the overall length LRotor, which results in the following equations:

LRotor · φtotal = LHP · φHP + LLP · φLP

LRotor = LHP + LLP

(3)

(4)

Thus, for a defined set of total length LRotor, wrap angles φtotal, φHP and φLP, the lengths of the sections LHP and LLP are clearly defined. As for a setup with a constant rotor lead, the total wrap angle together with the total rotor length define maximum chamber volume and the duration of the working cycle. The parameters which are varied to optimize the geometry of dual lead rotors are shown in Table 3. Rotor length, internal volume ratio and flow coefficient are varied according to the optimization of a constant rotor lead. In contrast, only a lobe count combination of 4+6 is examined. With respect to the optimal wrap angle range for a constant rotor lead, the total wrap angle is investigated between 200 and 400 degrees. High and low pressure side wrap angles are adjusted systematically between the lowest wrap angle of 50 and the highest wrap angle of 700 degrees. This guarantees that the optimal balance between clearance and discharge losses for each total wrap angle will be achieved. Considering all parameters, 2160 different machines were simulated for seven internal volume ratios and two flow coefficients, resulting in a total of 30240 multi-chamber model generations and machine simulations.

0.7

0.8

0.9

1

1.1

1.2

1.3

0.6

0.65

0.7

0.75

0.8

0.85

0.9

100 200 300 400 500 600 700

deliv

ery

rate

[-]

inte

rnal

isen

trop

ic e

ffic

ienc

y [-

]


L = 140 mmL = 200 mmL = 260 mm

ηis

λL

6.1 Simulation resultsThe internalmaximum values outlet area be improved because clearance areas increase whereas maximum chamber volume decreases, resulting in a lower mass flow.comparison diameter ratios. Maximum (α = 0.6) by using variable lead rotors. total wrap anglesport areas, which prevents The performance map in Fig. 8 shows the influence of isentropic efficiencyefficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and length of housing, differences related to the area, which depend boundary conditions should possess a wrap angle oflow pressure sideoccurs, which reduces


Parameter [dimension]Length LRotorInternal volume ratio vTotal male rotor wrap angle High pressure wrap angle Low pressure wrap angle Lobe count combination [Flow coefficient

Simulation resultsThe internal isentropic efficiency that can be maximum values for all investigated machines

for small wrap anglesbe improved because clearance areas increase whereas maximum chamber volume decreases, resulting in a lower mass flow. The curves show significant improvement in efficicomparison with a constant lead (Fig. 3 and Fig. 5) diameter ratios. Maximum

0.6) by using variable lead rotors. wrap angles between 250 and 275 degrees.

areas, which prevents The performance map in Fig. 8 shows the influence of isentropic efficiency, withefficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and length of housing, along with differences related to the area, which depend to a large extend boundary conditions should possess a wrap angle oflow pressure side, as shown in Fig. 8

which reduces efficiency.


Figure

Table 3: Varied parameters for

Parameter [dimension]Rotor [mm]

volume ratio vi [-Total male rotor wrap angle High pressure wrap angle Low pressure wrap angle Lobe count combination [

coefficient α [-]

Simulation results isentropic efficiency that can be

all investigated machinesfor small wrap angles causes outlet throttling. For wrap angles greater than

be improved because clearance areas increase whereas maximum chamber volume decreases, resulting in a lower The curves show significant improvement in effici

constant lead (Fig. 3 and Fig. 5) diameter ratios. Maximum efficiency η

0.6) by using variable lead rotors. between 250 and 275 degrees.

areas, which prevents outlet throttling.The performance map in Fig. 8 shows the influence of

with the total wrap angle remainefficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and

along with front and differences related to the time-dependent emergence of the clearances as well as the sizes of the outlet and blowhole

to a large extend on the boundary conditions should possess a wrap angle of

as shown in Fig. 8. For high pressure wrap angles below 400 degrees efficiency.


Figure 6: Screw machine with dual lead rotors

Varied parameters for


-] Total male rotor wrap angle φtotal [°] High pressure wrap angle φHP [°] Low pressure wrap angle φLP [°] Lobe count combination [-]

isentropic efficiency that can be achievedall investigated machines are shown in the diagram.

causes outlet throttling. For wrap angles greater than be improved because clearance areas increase whereas maximum chamber volume decreases, resulting in a lower

The curves show significant improvement in efficiconstant lead (Fig. 3 and Fig. 5)

efficiency ηis can be raised0.6) by using variable lead rotors. Compared to

between 250 and 275 degrees. Dual lead rotoroutlet throttling.

The performance map in Fig. 8 shows the influence of the total wrap angle remain

efficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and front and intermesh

dependent emergence of the clearances as well as the sizes of the outlet and blowhole on the lead progression. The map shows that the optim

boundary conditions should possess a wrap angle of . For high pressure wrap angles below 400 degrees


Screw machine with dual lead rotors

Varied parameters for the optimization of variable rotor

Minimum / maximum value140 / 260

200 / 400φtotal50 /

0

achieved by means of dual lead rotors is shown in Fig. 7. are shown in the diagram.


The curves show significant improvement in efficiency for constant lead (Fig. 3 and Fig. 5) efficiency can be

raised from 88.0 to 89.1 % to a constant lead

Dual lead rotors allow the machine to

The performance map in Fig. 8 shows the influence of the high and low pressure the total wrap angle remaining constant. Each shell covers a range of in

efficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and clearance, due to the constant overall wrap angle.

dependent emergence of the clearances as well as the sizes of the outlet and blowhole progression. The map shows that the optim

425 degrees on the high . For high pressure wrap angles below 400 degrees



optimization of variable rotor

Minimum / maximum value140 / 260

2 / 5 200 / 400

total + 25 / 700 50 / φtotal - 25

4+6 0.6 / 0.8

by means of dual lead rotors is shown in Fig. 7. are shown in the diagram. As for constant lead


ency for φtotal betweencan be increased

from 88.0 to 89.1 % (α = 0.8) and constant lead setup, maximum values are

allow the machine to

high and low pressure constant. Each shell covers a range of in

efficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and due to the constant overall wrap angle.

dependent emergence of the clearances as well as the sizes of the outlet and blowhole progression. The map shows that the optim

425 degrees on the high pressure side . For high pressure wrap angles below 400 degrees



optimization of variable rotor lead

Minimum / maximum value Step60 0.5255025

0

by means of dual lead rotors is shown in Fig. 7. As for constant lead, the small size of the

causes outlet throttling. For wrap angles greater than φtotal = 275be improved because clearance areas increase whereas maximum chamber volume decreases, resulting in a lower

between 225 and 250 degreesincreased, especially for

α = 0.8) and from 8maximum values are

allow the machine to function with

high and low pressure side wrap angle on inconstant. Each shell covers a range of in

efficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and due to the constant overall wrap angle.

dependent emergence of the clearances as well as the sizes of the outlet and blowhole progression. The map shows that the optimal machine for the given

pressure side and 160 degrees on the . For high pressure wrap angles below 400 degrees detrimental

1428, Page

14, 2016

Step size 60 0.5 25 50 25 -

0.2

by means of dual lead rotors is shown in Fig. 7. , the small size of the 75° efficiency cannot

be improved because clearance areas increase whereas maximum chamber volume decreases, resulting in a lower 25 and 250 degrees

, especially for greater lengthfrom 88.6 to 90.6

maximum values are achieved for lower function with larger outlet

wrap angle on inconstant. Each shell covers a range of internal isentropic

efficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and due to the constant overall wrap angle. There are

dependent emergence of the clearances as well as the sizes of the outlet and blowhole machine for the given

and 160 degrees on the detrimental outlet throttling

, Page 7

by means of dual lead rotors is shown in Fig. 7. Only , the small size of the

efficiency cannot be improved because clearance areas increase whereas maximum chamber volume decreases, resulting in a lower

25 and 250 degrees. In greater length-to-

8.6 to 90.6 % for lower

larger outlet

wrap angle on internal sentropic

efficiency of 0.5 percent. All machines examined in the diagram possess the same maximum chamber volume and There are

dependent emergence of the clearances as well as the sizes of the outlet and blowhole machine for the given

and 160 degrees on the outlet throttling

Figure 7:

Figure 8:

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explainedprogression length of the low pressure segment Lpressure side (50 to 125 degrees)which dependsamount of leakage(125 to 225 degrees) throttling.


Figure 7: Internal isentropic efficiency as a function coefficients

Figure 8: Internal isentropic efficiency as a function

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explainedprogression in the delivery ratelength of the low pressure segment Lpressure side (50 to 125 degrees)

depends entirely on the rotor leadamount of leakage, internal(125 to 225 degrees) the

0.8

0.82

0.84

0.86

0.88

0.9

0.92

150

inte

rnal

isen

trop

ic e

ffic

ienc

y [-

]


isentropic efficiency as a function coefficients (lobe count combination 4+6

isentropic efficiency as a function φtotal =

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explaineddelivery rate, which is

length of the low pressure segment LLPpressure side (50 to 125 degrees) the delivery rate

on the rotor leadternal isentropic efficiency diminishes as well. the delivery rate

150 200

α = 0.6


isentropic efficiency as a function (lobe count combination 4+6

isentropic efficiency as a function = 250°, α = 0.8, lobe count combination 4+6)

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explained, which is shown in Fig. 9.

LP increases according to eq. delivery rate decreases,

on the rotor lead, which is active for isentropic efficiency diminishes as well.

delivery rate is fine, but the high pressure segment is short

250total wrap angle

L = 140mmL = 200mmL = 260mm


isentropic efficiency as a function of total wrap angle for different rotor lengths(lobe count combination 4+6, machine geometry optimized for each point

isentropic efficiency as a function of low and high pressure250°, α = 0.8, lobe count combination 4+6)

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explainedshown in Fig. 9. For higher wrap angles on the high pressure side the

according to eq. decreases, an effect

is active for the major isentropic efficiency diminishes as well.

, but the high pressure segment is short

300total wrap angle φtotal

L = 140mmL = 200mmL = 260mm


wrap angle for different rotor lengths, machine geometry optimized for each point

high pressure side250°, α = 0.8, lobe count combination 4+6)

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explainedFor higher wrap angles on the high pressure side the

according to eq. (3) and (4). For small wrap angles on the low an effect caused mainly by the blowhole

major part of the working cycle. Due to the high isentropic efficiency diminishes as well. For higher wrap angles on the low pressure side

, but the high pressure segment is short

350 400total [°]


wrap angle for different rotor lengths, machine geometry optimized for each point

side wrap angle 250°, α = 0.8, lobe count combination 4+6)

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explainedFor higher wrap angles on the high pressure side the

. For small wrap angles on the low mainly by the blowhole

of the working cycle. Due to the high For higher wrap angles on the low pressure side

, but the high pressure segment is short and causes

400 450

α = 0.8

1428, Page

14, 2016

wrap angle for different rotor lengths and flow, machine geometry optimized for each point)

angle (LRotor = 260 mm,

The decrease in efficiency for high pressure wrap angles above 450 degrees can be explained by referring to the For higher wrap angles on the high pressure side the

. For small wrap angles on the low mainly by the blowhole, the size


causes increased

, Page 8

flow

mm,

referring to the For higher wrap angles on the high pressure side the

. For small wrap angles on the low size of


outlet

Figure 9:

Table


Rotor geometry

Flow coefficientTotal male rotor wrap angle High pressure wrap angle Low pressure wrap angle Internal volume ratio vInternal PowerInternal isentropic efficiencyRelative increaseefficiency [%]Delivery rate Mass flow Relative increase

Optimal machine properties for possess an internal volume ratio of 3.5. 1.25 %. Due to the lower total wrap angle maximum chamber volumehigher mass flow rate. throttling, increased.


Figure 9: Delivery rate as a function

Table 4: Properties of optimized machine geometries for L = 260


geometry

coefficient α [-] Total male rotor wrap angle High pressure wrap angle Low pressure wrap angle

volume ratio vi Power Pi [kW] isentropic efficiencyincrease in internal

efficiency [%] Delivery rate λL [%] Mass flow m [kg/s]

increase in mass flow [%]

machine properties for possess an internal volume ratio of 3.5. 1.25 %. Due to the lower total wrap angle maximum chamber volumehigher mass flow rate. This effect is even greater for a

the wrap angleincreased. Efficiency can be enhanced


Delivery rate as a function

Properties of optimized machine geometries for L = 260


Total male rotor wrap angle φtotal [°] High pressure wrap angle φHP [°] Low pressure wrap angle φLP [°]

[-]

isentropic efficiency ηis [%] ternal isentropic

in mass flow [%]

machine properties for the assumedpossess an internal volume ratio of 3.5. 1.25 %. Due to the lower total wrap angle maximum chamber volume

This effect is even greater for a the wrap angle in a constant lead fficiency can be enhanced relatively


Delivery rate as a function of low and high pressure α = 0.8, lobe count combination 4+6)


Constant lead

350- -

3.5 70.288.0

isentropic

91.83.45

the assumed flow coefficients are summarized in Tpossess an internal volume ratio of 3.5. For a flow coefficient of 0.8 energ1.25 %. Due to the lower total wrap angle maximum chamber volume

This effect is even greater for a constant lead setup,

relatively by 2.3


low and high pressure side 0.8, lobe count combination 4+6)


Constant lead Dual

0.8

350

70.2 88.0

1.25

91.8 3.45

10.7

coefficients are summarized in Tcoefficient of 0.8 energ

1.25 %. Due to the lower total wrap angle maximum chamber volumeThis effect is even greater for a flow coefficient of 0.6.

setup, and on the high pressure siby 2.3 % whereas the


side wrap angle 0.8, lobe count combination 4+6)

Properties of optimized machine geometries for L = 260 mm and lobe count combination of 4+6

Dual lead Constant lead

250 400 175 3.5

76.6 89.1

93.4 3.82

coefficients are summarized in Tcoefficient of 0.8 energy-related

1.25 %. Due to the lower total wrap angle maximum chamber volume for dual lead rotorscoefficient of 0.6.

on the high pressure sithe mass flow rate is


angle (LRotor = 260 mm, φ

mm and lobe count combination of 4+6

Constant lead

400 - -

3.5 64.2 88.6

90.2 3.18

coefficients are summarized in Table 4. All optimized machines related efficiency

for dual lead rotors is greater and leads to a coefficient of 0.6. As a result of

on the high pressure side of a dual leadmass flow rate is more than

1428, Page

14, 2016

mm, φtotal = 250°,


Constant lead Dual lead

0.6

250 500 150 3.5

76.5 90.6

2.3

94.8 3.87

21.7

All optimized machines can be improved by

is greater and leads to a As a result of increased outlet

dual lead setup, ismore than 20 % higher.

, Page 9

250°,


lead

All optimized machines can be improved by

is greater and leads to a increased outlet

is also 20 % higher.

For the refrigerant dual lead rotors. low pressure sideincreases clearance mass flow.Compared withshould be reducedtotal wrap angles increaserates on a machine

D Diameterh Specific enthalpyL Lengthm Mass flown Rotational speedP Powerp Pressures Specific V Volumevi Internal volume ratioz Number of lobesα Flow coefficient

ηis Internal isentropic efficiency

Fost, C., 2003,

Dortmund, 168 p.Gardner, J. W., 1969, Janicki, M., 2007,

Dortmund, 170Kauder, K.,

Displacement Machines, Rane, S., Kovacevic, A., Stosic, N., Kethidi,

geometry screw compressors, Rinder, L., 1979, Rohe, A., 2005, Sigloch, H., 2009, Temming, J., 2007,

Universität Dortmund, 140 p.Utri, M., Brümmer, A., 2014, A comparative examinat

pitch,

The work leading to these results has received funding from the European Community’s Horizon 2020 Programme (2014under grant agreement no 678727.the document are of the authors only and no way reflect the European Commission’s opinions. The European Union is not liable for any use that may be made of the information.


For the refrigerant process dual lead rotors. Wrap angle segments for dual lead rotors should be

pressure side wrap angle segment is too clearance mass flow.

Compared with constant lead rotorsbe reduced, resulting in decreased clear

wrap angles increasemachine of a given size

Diameter Specific enthalpy Length Mass flow Rotational speed Power Pressure Specific entropy Volume Internal volume ratioNumber of lobes Flow coefficient Internal isentropic efficiency

Fost, C., 2003, Ein Beitrag zur Verbesserung der Kammerfüllung von SchraubenmotorenDortmund, 168 p.

Gardner, J. W., 1969, Variable lead compressorJanicki, M., 2007, Modellierung und Simulation von Rotationsverdrängermaschinen

Dortmund, 170 p. ., Janicki, M., Rohe, A., Kliem, B., Temming, J., 2002, Thermodynamic Simulation of Rotary

Displacement Machines, Rane, S., Kovacevic, A., Stosic, N., Kethidi,

geometry screw compressors, Rinder, L., 1979, Schraubenverdichter

2005, Wärmehaushalt von SchraubenspindelSigloch, H., 2009, Technische Fluidmechanik

, J., 2007, Stationärer und instationärer Betrieb eines unsynchronisierten SchraubenladersUniversität Dortmund, 140 p.

Utri, M., Brümmer, A., 2014, A comparative examinatpitch, International Conference on Screw Machines 2014

The work leading to these results has received funding from the European Community’s Horizon 2020 Programme (2014under grant agreement no 678727.the document are of the authors only and no way reflect the European Commission’s opinions. The European Union is not liable for any use that may be made of the information.


process under examinationWrap angle segments for dual lead rotors should be

wrap angle segment is too clearance mass flow.

constant lead rotors, the, resulting in decreased clear

wrap angles increase maximum chamber volume.of a given size.

(m)

(J/kg)(m) (kg/s)

(1/s) (W) (Pa)

(J/kg/K)(m³)

Internal volume ratio (-) (-) (-)

Internal isentropic (-)

Ein Beitrag zur Verbesserung der Kammerfüllung von Schraubenmotoren

Variable lead compressorModellierung und Simulation von Rotationsverdrängermaschinen

Janicki, M., Rohe, A., Kliem, B., Temming, J., 2002, Thermodynamic Simulation of Rotary Displacement Machines, VDI-Berichte 1715

Rane, S., Kovacevic, A., Stosic, N., Kethidi,geometry screw compressors, Computers & Fluids

Schraubenverdichter, SpringerWärmehaushalt von Schraubenspindel

Technische FluidmechanikStationärer und instationärer Betrieb eines unsynchronisierten Schraubenladers

Universität Dortmund, 140 p. Utri, M., Brümmer, A., 2014, A comparative examinat

ernational Conference on Screw Machines 2014

The work leading to these results has received funding from the European Community’s Horizon 2020 Programme (2014under grant agreement no 678727. The opinions ethe document are of the authors only and no way reflect the European Commission’s opinions. The European Union is not liable for any use that may be made of the information.


7. CONCLUSION

under examination, energyWrap angle segments for dual lead rotors should be

wrap angle segment is too long, efficiency decreases due to the

, the simulation results show that the, resulting in decreased clearance mass flow

maximum chamber volume.

NOMENCLATURE

(J/kg)

(kg/s)

(J/kg/K)

REFERENCES


Variable lead compressor, US patent US3424373 AModellierung und Simulation von Rotationsverdrängermaschinen

Janicki, M., Rohe, A., Kliem, B., Temming, J., 2002, Thermodynamic Simulation of Rotary Berichte 1715, VDI Verla

Rane, S., Kovacevic, A., Stosic, N., Kethidi, 2014, Deforming grid generation and CFD analysis of variable Computers & Fluids

, Springer-Verlag, WWärmehaushalt von Schraubenspindel

Technische Fluidmechanik, 7th edition, Stationärer und instationärer Betrieb eines unsynchronisierten Schraubenladers

Utri, M., Brümmer, A., 2014, A comparative examinaternational Conference on Screw Machines 2014

ACKNOWLEDGEMENT

The work leading to these results has received funding from the European Community’s Horizon 2020 Programme (2014

The opinions expressed in the document are of the authors only and no way reflect the European Commission’s opinions. The European Union is not liable for any use that may be made of the information.


CONCLUSION

energy-related and volumetricWrap angle segments for dual lead rotors should be

long, efficiency decreases due to the

imulation results show that theance mass flow, which raises

maximum chamber volume. Consequently,

NOMENCLATURE Δ Difference φ Wrap λL Delivery rate ρ Density Subscript compr,end FR HP MR max LP s

i

REFERENCES


, US patent US3424373 AModellierung und Simulation von Rotationsverdrängermaschinen

Janicki, M., Rohe, A., Kliem, B., Temming, J., 2002, Thermodynamic Simulation of Rotary , VDI Verlag, Düsseldorf, p.

Deforming grid generation and CFD analysis of variable Computers & Fluids, vol. 99, p. 124

Verlag, Wien New YorkWärmehaushalt von Schraubenspindel-Vakuumpumpen

7th edition, Springer-Stationärer und instationärer Betrieb eines unsynchronisierten Schraubenladers

Utri, M., Brümmer, A., 2014, A comparative examination of the potential of screw expanders with variable rotor ernational Conference on Screw Machines 2014, VDI

ACKNOWLEDGEMENT

The work leading to these results has received funding from the European Community’s Horizon 2020 Programme (2014-2020)

xpressed in the document are of the authors only and no way reflect the European Commission’s opinions. The European Union is not liable for any use that may be made of the information.


CONCLUSION

and volumetric efficiency Wrap angle segments for dual lead rotors should be finely adjusted to

long, efficiency decreases due to the

imulation results show that the optimalwhich raises the delivery rate. Furthermore, smaller

Consequently, dual lead rotors allow

NOMENCLATURE Difference Wrap angle Delivery rate Density

Subscript compr,end End of compression

Female rotorHigh pressureMale rotorMaximumLow pressureConstant entropyInternal

REFERENCES


, US patent US3424373 A. Modellierung und Simulation von Rotationsverdrängermaschinen

Janicki, M., Rohe, A., Kliem, B., Temming, J., 2002, Thermodynamic Simulation of Rotary g, Düsseldorf, p. 1-16.

Deforming grid generation and CFD analysis of variable , vol. 99, p. 124-141

ien New York, 252 p. Vakuumpumpen, Dissertation, Universität Dortmund, 160 p.

-Verlag, Heidelberg London New York, 581 p.Stationärer und instationärer Betrieb eines unsynchronisierten Schraubenladers

ion of the potential of screw expanders with variable rotor , VDI Verlag, p. 249

ACKNOWLEDGEMENT


efficiency can be enhanced by using adjusted to improve the efficiency. If

long, efficiency decreases due to the large blowhole area

al total wrap angle of the machine the delivery rate. Furthermore, smaller

dual lead rotors allow much higher mass flow

(-) (°) (-) (kg/m³)

End of compression Female rotor High pressure Male rotor Maximum Low pressure Constant entropy Internal

Ein Beitrag zur Verbesserung der Kammerfüllung von Schraubenmotoren, Dissertation, Universität

Modellierung und Simulation von Rotationsverdrängermaschinen, Dissertation, Universität

Janicki, M., Rohe, A., Kliem, B., Temming, J., 2002, Thermodynamic Simulation of Rotary 16.

Deforming grid generation and CFD analysis of variable

, Dissertation, Universität Dortmund, 160 p.

Verlag, Heidelberg London New York, 581 p.Stationärer und instationärer Betrieb eines unsynchronisierten Schraubenladers

ion of the potential of screw expanders with variable rotor , p. 249-266.

1428, Page

14, 2016

be enhanced by using improve the efficiency. If

blowhole area,

wrap angle of the machine the delivery rate. Furthermore, smaller

much higher mass flow

(kg/m³)

, Dissertation, Universität


Janicki, M., Rohe, A., Kliem, B., Temming, J., 2002, Thermodynamic Simulation of Rotary

Deforming grid generation and CFD analysis of variable

, Dissertation, Universität Dortmund, 160 p.Verlag, Heidelberg London New York, 581 p.

Stationärer und instationärer Betrieb eines unsynchronisierten Schraubenladers, Dissertation,

ion of the potential of screw expanders with variable rotor

, Page 10

be enhanced by using improve the efficiency. If the

which

wrap angle of the machine the delivery rate. Furthermore, smaller

much higher mass flow



, Dissertation, Universität Dortmund, 160 p. Verlag, Heidelberg London New York, 581 p.

, Dissertation,

ion of the potential of screw expanders with variable rotor

Improvement of the Efficiency of Twin-Screw Refrigeration ......1428, Page 1 23 nd International Compressor Engineering Conference at Purdue, July 11 -14, 2016 Improvement of the Efficiency

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