screw compressor basics

Screw Compressor Modelling, Design and Use

Screw Compressor Basics

Professor N. Stosic

Chair in Positive Displacement Compressor Technology

Centre forPositive Displacement Compressor Technology

City University London, U.K.

Screw Compressor Today

Highly competitive market, speciallyin air compression and refrigeration

Continuous improvement:more compact, efficient and cost effective compressors

New rotor generation, rotors optimizedfor certain compressor duty, specializeddesign

Scope for innovation, improvement and development

INTRODUCTION

INTRODUCTION

Basics

View from Front and Top

View from Bottom and Rear

Top and front: AdmissionBottom: Change of volumeBottom and Rear: Discharge

INTRODUCTION

Basics

INTRODUCTION

Swedish company SRM, pioneer and leader

Screw compressor profiles, Symmetric, Asymmetric, ‘D’ and ‘G’Screw compressor designScrew compressor technology

Licence system left many screw compressormanufacturers at margins of research anddevelopment

INTRODUCTION

Many companies started their own development

Gardner Denver, Atlas Copco, Compair, Kaeser, GHHTrane, Ingersol-Rand, Hitachi, Fu Sheng, Hanbel, Refcomp

Holroyd

Many more or less successful rotor profiles

Many more or less successful screw compressor designs

Need exists to concentrate efforts in R&D

Centre for Positive Displacement Compressor Technology

Improved methods of analysis

Experimental validation

Design of critical components

Complete machine design

Product development

Training in machine design

INTRODUCTION

Methods Applied

Advanced Computerized design toolsMachine process modelling 2-D and 3-D Computational Fluid Dynamics

Modern experimental techniqueComputerized data acquisition

Users

Renown and new companies, large and small manufacturers in the U.K and abroad

INTRODUCTION

SCREW COMPRRESSOR GEOMETRY

Before modelling the physical process, the rotor lobe profiles must be defined together with the remaining parameters with which the rotor and housing geometry can be fully specified.

Rotor profile: x and y coordinates, pressure angle

Helix/lead angle, rotor length

Interlobe, end and radial clearance

Suction/discharge ports

SCREW COMPRESSOR GEOMETRY

General case: non-parallel and non-intersecting

( ) [ ] [ ]1 1 1 1 1 01 01 01 01 1, , , cos sin , sin cos ,t x y z x y x y pθ θ θ θ θ θ= = = − +r r

∂∂+

∂∂

∂∂−

∂∂=

∂∂

∂∂=

∂∂ 0,cossin,sincos0,, 01010101111 θθθθ

ty

tx

ty

tx

ty

tx

tr

[ ]0,,0,, 0101111 xyyx −=

∂∂

∂∂=

∂∂

θθθr

Given profile

SCREW COMPRESSOR GEOMETRY

Meshing condition

Meshed profile

General case: non-parallel and non-intersecting

( ) [ ] [ ][ ]

2 2 2 2 2 1 1 1 1 1

02 02 02 02 2

, , , , , cos sin , sin cos

cos sin , sin cos ,

t x y z x C y z y z

x y x y p

θ τ

τ τ τ τ τ

= = = − Σ − Σ Σ + Σ =

− +

r r

[ ] [ ]( ) ( )

22 2 2 02 02 02 02 2

1 1 2 1 2 1

, , sin cos , cos sin ,

sin cos , sin cos , cos sin

y x p x y x y p

p y p x C p x C

τ τ τ ττ

θ

∂= − = + − =

∂Σ − Σ Σ + − Σ Σ − − Σ

r

1 1 1 1 1 2 0t tθ τ θ τ

∂ ∂ ∂ ∂ ∂ ∂ × ⋅ = − × ⋅ = ∂ ∂ ∂ ∂ ∂ ∂ r r r r r r

( ) ( )1 1 1 11 1 2 1 1 1 1 2cot cot 0

x y y xC x p p x y p p p Ct t t t

θ∂ ∂ ∂ ∂ − + − Σ + + + − Σ = ∂ ∂ ∂ ∂

SCREW COMPRESSOR GEOMETRY

General case: non-parallel and non-intersectingcorresponds to the rotor – hobbing tool relation

Special cases:

p2=0, rotor - plate milling tool, grinding tool relation

Σ=0, screw compressor rotors

SCREW COMPRESSOR GEOMETRY

0101 01

01

sin cos 0dy C Cky kxdx i i

θ θ − + + =

02 01 01

02 01 01

cos sin cos

sin cos sin

x x k y k Ci

y x k y k Ci

θθ θ

θθ θ

= − −

= + +

Meshing condition

Rotor profile, Σ=0, i=p2/p1, k=1-1/i

Meshed profile

Rack profile

0 01 01

0 01 01 1

cos sinsin cos

r

r

x x yy x y r

θ θθ θ θ

= −= + −

Numerical solution of the meshing condition

Task: to find θ for a zero function

Simple iteration method:Fast and reliable, but valid only for certain function

Additional complicationIn certain areas two or more θ are the zero functionOnly one is valid, additional values found by half interval method

SCREW COMPRESSOR GEOMETRYDemonstrator profile

‘N’ ROTOR PROFILE- Rack generation procedure - Straight line on the rack - involute rotor contact- Small torque transmitted

- Short sealing line- Large displacement- Strong gate rotor,

SCREW COMPRESSOR GEOMETRY

SCREW COMPRRESSOR THERMODYNAMICS

Differential approach:

Set of differential equations solved simultaneouslyEquations of continuity, momentum and energy

Preintegrated equations inadequate and inaccurate if high leakage rate and heat transfer is involved

in in out outdU dVm h m h Q pd d

ω ωθ θ

= − + −! !

in outdm m md

ωθ

= −! !

2 22 1

2 2

1

2 lnl l l g g

p pm w A Apap

ρζ

−= =

+

!

Internal Energy

Continuity

Leakage Flow

, ,in in suc suc l g l g oil oilm h m h m h m h= + +! ! ! ! , ,out out dis dis l l l lm h m h m h= +! ! !

,in suc l g oilm m m m= + +! ! ! ! ,out dis l lm m m= +! ! ! m wAρ=!

SCREW COMPRESSOR THERMODYNAMICS

Momentum2

02l

l lg

wdp dxw dw fDρ

+ + =

SCREW COMPRESSOR THERMODYNAMICS

Ideal Gas( )1 u RTT p

R vγ= − =

Real gasp=f1(T,v) u=f2(T,v)

Wet vapour( ) ( )1 1f g f gu x u xu v x v xv= − + = − +

( ), ( ), ( ), ,VU m V vm

θ θ θ =

( )o o oiloil

oil oil

h A T TdTd m cθ ω

−= ,

1oil p

oil

T kTT

k−

=+

6oil oil S oil

o o o

m c d ckh A hω ω

θ θ= =

∆ ∆

( ) ( ) ,oil

U mu mu= +

Oil injection

Numerical solution, Runge-Kutta IV order solver ( )oil

U mcTu

m−

=

SCREW COMPRESSOR THERMODYNAMICS

Compressor integral parameters

in outm m m= −1 / 60m mz n=!

060 /V m ρ=!

( )1 2 1

60n n

t

F F Lnzm

ρ+=!

vt

mm

η =!!

indcycle

W Vdp= ∫

1

60ind

indW z nP =

sindcycle

VW dpm

= ∫

t at a

ind ind

W WW W

η η= =

( )21 2 1

1

ln1t a

pW RT W R T Tp

γγ

= = −−sin d

PPV

= !

SCREW COMPRESSOR THERMODYNAMICS

Calculation of pressure loads On compressor rotors

Radial forces

( )

( )

B

x B AAB

y B AA

R p dy p y y

R p dx p x x

= − = − −

= − = − −

∫

∫

Rotor torque

( )2 2 2 20.5B B

B A B AA A

T p xdx p ydy p x x y y= + − − + −∫ ∫

SCREW COMPRESSOR THERMODYNAMICS

Bearing reactions androtor deflections

2

2

d MEIdz

δ =

Optimization variables and target function

Single stage:Rotor variables:r0 Female rotor addendumr1 Male rotor lobe radiusr2 Male rotor tip radiusr3 Female rotor tip radiusCompressor variables:Built-in volume ratioOperation variables:Shaft speedOil flowInjection positionOil temperature9 Variables

Multistage:9 Variables x Number of stages+ Interstage pressures

Target function:Specific power combined with compressor price

F=w1L+w2C

SCREW COMPRESSOR OPTIMIZATION

Box constrained simplex method for efficient and reliable multivariable optimization

1 2( , ,..., )nf x x x

, 1,i i ig x h i n≤ ≤ = , 1,i i ig y h i n m≤ ≤ = + yn+1,…,ym

1 2F w L w C= +

1 2

1 2

( ) max ( ), ( ),..., ( )( ) min ( ), ( ),..., ( )

h k

g k

f x f x f x f xf x f x f x f x

==

1

1 ,1

ki i lj

ix x x x

k =

= ≠− ∑ ( )r lx x x xα= + −

( ) ( )0.5 (1 ) ( )(1 )(2 1)r new r old h hx x cx c x x x c R = + + − + − − − 1

1

r r

r

n kn

r

r r

ncn k

+ −

= + −

Dry Oil-Flooded Refrig.r0 [mm] 2.62 0.74 0.83r1 [mm] 19.9 17.8 19.3r2 [mm] 6.9 5.3 4.5r3 [mm] 11.2 5.5 5.2

Built-in volume ratio 1.83 4.1 3.7Rotor speed [rpm] 7560 3690 3570Oil flow [lit/min] - 12 8Injection position [o] - 65 61Oil temperature [o] - 33 32

Oil FreeOil FloodedRefrigeration

EXAMPLE OF CALCULATION

5-6-128 mm Oil-Flooded Air Compressor

7 m3/min, max 10 m3/min at 8 bar (abs)

5-14 bar (abs), max 15 bar (max)

EXAMPLES OF CALCULATION

5/6-128 mm, L/D 1.65Displacement 1.56 l/revInterlobe sealing line 0.13 mBlow-hole area 1.85 mm2

Rotors optimized foroil flooded operatedair compression

EXAMPLES OF CALCULATION

CAD Interface: Compressor ports

EXAMPLES OF CALCULATION

Experimental verification of the model

EXAMPLES OF CALCULATION

Compressor in the test bed

EXAMPLES OF CALCULATION

Comparison of thecalculated and test results Flow-Power

EXAMPLES OF CALCULATION

EXAMPLES OF 3-D CFD CALCULATION

Majority of design problems can be solved by the one-dimensional approach, some of them require thetwo dimensional calculation, however, there are situations where 3-D CFD must be applied

Such are

Oil flow distribution,Fluid-Solid Interaction

• Grid topology- polyhedral- O - grid- H - grid- C - grid

• Cell shape

Grid generation Grid generation -- 11

Grid generation - 2

- Male rotor - Female rotor

- Suction port - Discharge port- Suction and discharge receivers

- End clearancesRotor connections, clearances,

leakage paths

• Grid topology strongly affects accuracy, efficiency and ease of calculation • Full structured block generated hexahedral 3D-O mesh• Screw compressor sub-domains:

Automatic discretizationiscretization process:process:- The rack generating procedure-- Rack Rack -- a rotor with an infinite radiusa rotor with an infinite radius

-- Divides working domain in two parts Divides working domain in two parts male and female rotor,male and female rotor,

Screw Compressor FSI calculations Screw Compressor FSI calculations Comet Comet Mathematical model for screw compressor is based on conservationMathematical model for screw compressor is based on conservation laws laws of continuity, momentum, energy, concentration and space:of continuity, momentum, energy, concentration and space:

s( ) 0V S

d dV ddt

ρ ρ+ − ⋅ =∫ ∫ v v s

s( ) bV S S V

d dV d d dVdt

ρ ρ+ − ⋅ = ⋅ +∫ ∫ ∫ ∫v v v v s T s f

s

s

( ) +

( grad : grad ) p

hV S S

hV V S V

d hdV h d ddt

ds dV p dV d pdVdt

ρ ρ+ − ⋅ ⋅

+ ⋅ + − ⋅ +

∫ ∫ ∫

∫ ∫ ∫ ∫

v v s = q s

v S v v s

s( )o oo o c c

V S S V

d c dV c d d S dVdt

ρ ρ+ − ⋅ = ⋅ +∫ ∫ ∫ ∫v v s q s

22 div3

pµ µ= − −T D vI I!

oc grado oD cρ=q

h grad Tκ=q

( , ), ( , )p T e e p Tρ ρ= =

s 0V S

d dV ddt

− ⋅ =∫ ∫ v s

s

2

s 1 2 3

( ) ( ) ,

( ) ( )

kV S S V

V S S V

d kdV k d d P dVdtd dV d d C P C C dVdt k kε

ρ ρ ρε

ε ερε ρε ρ ρε

+ − ⋅ = ⋅ + −

+ − ⋅ = ⋅ + − + ∇ ⋅

∫ ∫ ∫ ∫

∫ ∫ ∫ ∫

v v s q s

v v s q s v

Closed by constitutive relations and equation of stateClosed by constitutive relations and equation of stateand accompanied by turbulence model.and accompanied by turbulence model.

( ) ( )2 div

3 2 rT Tη λ

λ η α= −

+ −T D + wI

I

Thermodynamic properties of real fluidsThermodynamic properties of real fluids-- pp--vv--TT equation equation

compressibility factor compressibility factor zz-- zz is assumed to change linearly is assumed to change linearly

with pressure err<2%with pressure err<2%

-- Antoine equation for saturationAntoine equation for saturationtemperaturetemperature

-- Clapeyron Clapeyron equation for latent heatequation for latent heat

-- Specific heat for constant pressureSpecific heat for constant pressure

-- Density of mixtureDensity of mixture

-- Coefficient in the pressure correctionCoefficient in the pressure correctionequation equation

( )p z RT z p RTρ

= ⋅ = ⋅

1 2z p B B= ⋅ +

11 v v

T

bdCdp zRT zρ

ρ ρρρ

⋅ = = − ⋅

2

1 logsatAT

A p=

−

2 30 1 2 3pvc C C T C T C T= + ⋅ + ⋅ + ⋅

1 1 satL

v l sat

dPh TdTρ ρ

= ⋅ − ⋅

2 2

11

v l

co coρ

ρ ρ

= − −

Multiphase flowMultiphase flow( )o o o o

o ol con massd m h dh dmm h Q Q

dt dt dt= + = +! !

-- OilOil is assumed to be a passive is assumed to be a passive ‘‘speciesspecies’’

-- Mass calculated from the concentration Mass calculated from the concentration Oil drag force influence concentrationOil drag force influence concentration

-- Energy source due to heat transfer Energy source due to heat transfer between working fluid and oil is:between working fluid and oil is:

sol olL

mass L L L Lm mdmQ h h h m

dt tδ−= ≈ =! !

1

o o

k k

con o p o pdT T TQ m C m Cdt tδ

−−= ≈!

( )pm sL

L

m C T Tm

h⋅ ⋅ −

=!

1 (2drag o drag o oA Cρ= − − −f v v v v)

-- Liquid phaseLiquid phase is assumed to be an active is assumed to be an active ‘‘speciesspecies’’

-- Mass source Mass source evaporated/condensed mass evaporated/condensed mass

-- Energy source Energy source energy of evaporation/condensationenergy of evaporation/condensation

o om m C= ⋅

EulerEuler--Lagrange approachLagrange approach

Boundary conditionsBoundary conditions

-- Wall boundaries with wall functions are Wall boundaries with wall functions are introduced on the housing and rotors. introduced on the housing and rotors.

constadd

p const const

p pdm Vmdt p t

ρδ=

− ⋅ = ≈ ⋅ !

addadd add add add

p const

dmQ h m hdt =

= = ⋅ !! !

-- Compressor positioned between suction Compressor positioned between suction and discharge receivers of small volumeand discharge receivers of small volume

-- Inlet & outlet receivers and oil port are Inlet & outlet receivers and oil port are treated as boundary domains:treated as boundary domains:

-- Mass equation corrected by mass Mass equation corrected by mass source to maintain constant pressuresource to maintain constant pressure

-- Energy equation corrected by energy Energy equation corrected by energy source to update energy balancesource to update energy balance

Screw Compressor performanceScrew Compressor performance

-- Volume flow (inlet and outlet)Volume flow (inlet and outlet)

-- Mass flow (inlet, outlet and oil) Mass flow (inlet, outlet and oil)

-- Boundary forcesBoundary forces

-- Restraint Forces and TorqueRestraint Forces and Torque

-- Compressor shaft powerCompressor shaft power

-- Specific powerSpecific power

-- EfficiencyEfficiencyVolumetric and adiabaticVolumetric and adiabatic

( ) ( )3

160 min ,

end

start

t It t

f f fi fit t i

V V m V v S= =

= ⋅ = ∑ ∑! ! !

[ ]( ) ( ) secend

start

tt t

ft t

m V kgρ=

= ⋅∑ !!

* ; * ; *x b xb y b yb z b zbF p A F p A F p A= = =

1 1

1 1

( ),[ ]; ( ), [ ]

( ),[ ]; ( ), [ ]

I I

rS rS rD rDi iI I

a ai i

F F i N F F i N

F F i N T T i Nm

= =

= =

= =

= =

∑ ∑

∑ ∑2 ( ) [ ]M FP n T T Wπ= ⋅ ⋅ ⋅ +

3 min1000speckWPP mV

= ⋅ !

; adv i

d

PVV Pη η= =!

Oil injected Oil injected -- Pressure in axial sectionPressure in axial section

Oil injected Oil injected -- Pressure and velocity Pressure and velocity

Oil injected Oil injected -- Pressure 3D viewPressure 3D view

Real fluid Real fluid -- Ammonia Ammonia –– pressurepressure

Experimental verification Experimental verification –– PP--αααααααα diagramdiagram

Oil injected Oil injected –– DeformationDeformationPressure1Pressure1 Pinl=1 b Pout=7 b n=5000 rpm

tinl=20 oC tout=40 oC

Pinl=1 b Pout=7 b n=5000 rpm tinl=20 oC tout=40 oC

Oil injected Oil injected –– DeformationDeformationPressurePressure--11

Pinl=1 b Pout=7 b n=5000 rpm tinl=20 oC tout=40 oC mag=20,000x

Oil injected Oil injected –– DeformationDeformationPressurePressure--22

Oil injected Oil injected –– DeformationDeformationTemperatureTemperature Pinl=1 b Pout=3 b n=5000 rpm

tinl=20 oC tout=150oC mag=1,000x

Oil injected Oil injected –– DeformationDeformationPressure+TemperaturePressure+Temperature Pinl=30 b Pout=90 b n=5000 rpm

tinl=0 oC tout=40 oC mag=2,000x

DESIGN EXAMPLES

Oil-free air compressorOil-flooded air compressorRetrofit rotors of an air compressorRefrigeration compressor

Compressors for Oil-Free Air Delivery

Design aims:

Delivery: 350-700 and 700-1000 m3/hWorking pressure: 1-2.5 (2.7) bar

Volumetric efficiency 90 % +Low specific powerSimple, reliable and compact machine

DESIGN EXAMPLES

3/5 lobe rotorsLarge displacementConvenient gear ratio 5/3=1.67

DESIGN EXAMPLES

Features of 3/5 ‘N’ Rotors

- Highest possible displacement- Higher delivery- Better volumetric efficiency- Better adiabatic efficiency- Stronger gate rotor- Long durability- High reliability- Easy manufacturing- Easy compressor assembly- Reasonable noise

DESIGN EXAMPLES

General ArrangementXK18 Screw CompressorDESIGN EXAMPLES

New design, fully customized by the manufacturer

New rotors,

New, improved compressor

New concept, better screw compressor compared with competition

DESIGN EXAMPLES

Comparison of Test Results

R1- GHH C80R2- Drum D9000R3- Mouvex TyphoonR4- GHH CS-1000

DESIGN EXAMPLES

Screw Compressor Family for Oil-Flooded Operation

Design aims:

Delivery: 0.6-60 m3/minWorking pressure: 5-13 bar

Volumetric efficiency 90 % +Low specific powerSimple, reliable and compact machine

DESIGN EXAMPLES

Improved capacity and efficiencyLower power consumptionReduced manufacturing cost

Reasonable efficiency formoderate pressure ratios, at least thesame as for 4/6 rotors

4/5 Rotors

DESIGN EXAMPLES

Five compressors, rotor diameters:

74, 102, 159, 225 and 285 mm, L/D 1.55

Performance of the Compressor Family

DESIGN EXAMPLES

Proven design, fully customized to the the manufacturer’s needs

New rotors,

New, improved compressor

DESIGN EXAMPLES

Test Results, Compressors 73 and 159 mm

DESIGN EXAMPLES

Retrofit ‘N’ Rotors

5.4 % more displacement6.5 % higher delivery4 % better volumetric efficiency2.5 % better adiabatic efficiency75 % less torque on the gate rotor

DESIGN EXAMPLES

‘N’ Rotor retrofit for more efficient screw compressors

Asymmetric Rotors,the most common screw compressor rotors

DESIGN EXAMPLES

Design of a semihermetic compressor for air-conditioning and refrigeration

based on ‘N’ rotors

• Semihermetic, convertible to open• All existing refrigerants• Modern, better than competition • 5/6-102 mm L/D=1.55• Efficient rotors for air condition and

refrigeration

DESIGN EXAMPLES

5/6-102 mm L/D=1.55 compressor

• Theoretical displacement 0.72 l/rev• Gear-box 1500-10000 rpm• Delivery 0.920-5.80 m3/min • R-22• Air condition 5/40 oC 60-380 kW• COP 4.20 at 3000 rpm• Refrigeration -5/30 oC 33-210 kW• COP 3.95 at 3000 rpm

DESIGN EXAMPLES

Refrigeration Application

DESIGN EXAMPLES

Application of Design Optimization: A Family of Two-Stage Compressors

1st

2nd

Range: 22-250 kW8-16 bar (abs)

Two-stages: 19 Variables Target Function:Minimum specific power And only specific power

Number of framesVFD vs gearboxStage sizeStage speedStage rotor profile

CONCLUSIONSThe screw compressor is a mature product at the milleniummeeting point. Orchestrated efforts of a large number of companies driven by market forces resulted in the compact and efficient compressor machine. Every detail counts today. A small difference will give a small, but distinctive improvement which may be used as an individual advantage.

Optimization opens hidden spots still left for better compressors. They result in stronger but lighter rotors with higher displacement, more compact and more efficient compressor machines at all areas of their application.

EPILOGUE

The Centre for Positive Displacement Compressor Technology carries out research and provide a service to manufacturing companies in all aspects of compressor design and development. Through the everyday activity the Centre is gaining experience in the compressor research, development and design. Some of the recent experience is given in this presentation.