prediction of leakage flow of radial clearance in a

Clean energy & Micro spray application

07 13, 2016

2016 Purdue Conferences

1

July 11-14, 2016, Purdue, United States of America

Prediction of Leakage Flow of Radial Clearance

in A Rolling Piston Rotary Compressor

Graduate School of Mechanical Engineering, Pusan National University, Korea

Geon-woo Kim, Ki-youl Noh, Byung-chae Min, Sang jin Song, Sang-kyung Na, Tae-seung Yoon

Kenichiro teshima

Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Korea

Jang-sik Yang

Rolls-Royce University Technology Centre, Pusan National University, Korea

Gyung-min Choi, Duck-jool Kim

Department of Mechanical Engineering, Pusan National University, Korea

2Clean energy & Micro spray application

Thermodynamics

2

3

1 3 54 6CONTENTS

▣ Back ground


▷ Increasing global power consumption

Ref. World Energy Outlook 2014 New Policies scenario (IEA)

▷ Numerical compressor simulation

▷ Needs for improving the efficiency of compressors

Motor efficiency

Volumetric efficiency

Indicated efficiency

Mechanical efficiency

Compressor

Efficiency

Reduce the cost and time of development

DynamicsGeometric

characteristics

Need for accurate prediction

VariousCapacity

Various operating condition

Various geometric

2

4

1 3 54 6CONTENTS

▣ Back ground


▷ Compressor efficiency

�� = �� × �� × �� × �� η�� ∶ compressorefficiency

η" ∶ volumetricefficiency

η'()' ∶ indicatedefficiency

η��,�-:motorefficiency

η�/�0:mechanicalefficiency23 =

4566789

4566:;

▷ Type of leakage

70 %

① Radial clearance between wall of rolling piston and cylinder

② Clearances between the faces of the rolling piston and head walls of the cylinder

③ Faces of the sliding vane and head walls of the cylinder

④ Clearances between sides of the sliding vane and side cylinder

Oil Roller rotate FrictionOperating condition

▷ Influenced Factors

GeometricFrictionOperating condition

Geometric

2

5

1 3 54 6CONTENTS

▣ Previous research


(1985) (1990) (2012)

Insufficient investigation for consideration of geometric characteristics and operation condition of compressor

Flow pattern (single) & Friction

Flow pattern (two phase) & roller motion

Flow pattern (two phase)& bubble

Ref) Yanagisawa, T., Shimizu, T. Leakage losses in a rolling piston type rotary compressor, I. Radical clearance on the rolling piston,/int Refrig 8 (1985) 75-84

Ref) C.M.N.F et al. Considerations about the leakage through the minimal clearance in a rolling piston compressor, Int compressor engineering conference (1990) 780

Ref) Jose Luiz Gasche et al. A model to predict R134a refrigerant leakage through the radial clearance of rolling piston compressor, Int Ref 35(2012) 2223-2232

2

6

1 3 54 6CONTENTS

▣ Objective

- Flow chart -

Leakage Modeling

m< � =�P?A2k

k C 1 RT?

P)

P?

GH

CP)

P?

HIJH

• Operating condition of compressor

• Various geometric of radial clearance

• Applicability

Experiments CFD simulation

KL � MNO, QR , ST, SUV

Functionalization ofFlow coefficient

Investigation characteristics of flow coefficient under various condition


2

7

1 3 54 6CONTENTS

▣ Mass flow rate through the radial clearance

For W�� ≥ W�/WZ

For W�� < W�/WZ

m< = C"P?A2k

k − 1 RT?

P)

P?

GH

−P)

P?

HIJH

m< = C"P?Ak

RT?

2

k + 1

HIJG H^J

- Isentropic and one-dimensional compressible flow through the simple orifice

_ Area of the radial clearance (`G)

=� Flow coefficient of the radial clearancek Specific heat ratio4< Mass flow rate (kg/s)W�� Critical pressure ratio

W� Downstream pressure (Pa)W� Pressure ratioWZ Upstream pressure (Pa)R Gas constant ((N*m)/(kg*K))aZ Upstream temperature (K)

The flow coefficient b3 is affected by flow area of radial clearance, upstream pressure and pressure ratio

WZW�

Suction port Discharge port

(1)

(2)

(3)

Mas

s flow

rat

e

W�/WZ

W�� =c

d + e

dd^e


2

8

1 3 54 6CONTENTS

▣ Schematic diagram of experimental set-up

W(= WZ) W�Z�(= W�)

◈ Experimental conditions

Height of the cylinder 19.989 mm

Width of the radial clearance 20 μm

Inlet pressure (= f8) 3~8 bar

◈ measuring equipment

Pressure transducer KISTLER, 4260A

Thermocouple K-type

Mass flow rate Bubble meter

◈ Assumptions of the experiment

1 Working fluid (Only Nitrogen)

2 Incompressible flow

3 Steady state flow

Width of radial clearance: 20 μm

Height of radial clearance: 19.989 mm


2

9

1 3 54 6CONTENTS

(CFD : Computational Fluid Dynamics)

2-D analysis (Incompressible steady state flow)

Viscous model Realizable k-ε model

Inlet boundary condition Pressure inlet

Outlet boundary condition Pressure outlet

Pressure-Velocity coupling Coupled

In order to reduce time of computation, the geometry of experimental device was simplified

Simplify

▣ Setting for CFD simulation


▣ Calculation range for calculating the mass flow rate

Upstream pressure ~ 30 bar

Pressure ratio 0.1, 0.5, 0.9

Width of radial clearance 10 ~ 60 μm

Height of radial clearance 5 ~ 30 mm

2

10

1 3 54 6CONTENTS

5.1 Validation of CFD simulation

▣ Modeling the geometry of radial clearance based on data of SEM (Scanning Electron Microscope)and clearance gauge for CFD simulation

0.0 0.2 0.4 0.6 0.8 1.00.00000

0.00025

0.00050

Mas

s flo

w r

ate

(kg/

s)

Pressure ratio (Pd/Pu)

Exp. 4 bar Exp. 6 bar Exp. 8 bar CFD. 4 bar CFD. 6 bar CFD. 8 bar

Average error : 2.46 %

Maximum error: 3.53 %



Mass flow rate through the radial clearance obtained by CFD simulation showed tolerable errorsfor predicting the leakage flow rate


2

11

1 3 54 6CONTENTS

5.2 Functional formula of flow coefficient

• Radius of cylinder : 25 mm • Radius of roller : 20 mm • Height of radial clearance : 20 mm

▣ Results of CFD simulation with various width of radial clearance and upstream pressure

(a) : 10 μm (b) : 20 μm


(c) : 40 μm (d) : 60 μm

Flow coefficient at the radial clearance was affected by change of area of radial clearance, pressure ratio and upstream pressure

2

12

1 3 54 6CONTENTS


• Radius of cylinder : 25 mm • Radius of roller : 20 mm

▣ Results of CFD simulation with various height of radial clearance

(a) : 10 μm (b) : 20 μm


(c) : 40 μm (d) : 60 μm

2

13

1 3 54 6CONTENTS


• Radius of cylinder : 25 mm • Radius of roller : 20 mm

▣ Results of CFD simulation with various Height of radial clearance

gh =ijk

f

◈ Hydraulic diameter

lm ∶ nopqrsQtuptr`vwvq

Ox ∶ Kqyzzzvuwty{rQrqvr

S ∶ |vwwvp}vqt`vwvqyMw~vuqyzzzvuwty{

5.0E-3 1.0E-2 1.5E-2 2.0E-2 2.5E-2 3.0E-20.0

5.0E-5

1.0E-4

1.5E-4

Hyd

rau

lic d

iam

eter

(m

)

Height of radial clearance (m)

㎛ 10 ㎛ 20 ㎛ 40 ㎛ 60

Flow coefficient at the radial clearance was not affected by change of height of radial clearance

�< = =�WZ�hcd

d − e �aZ

W�

WZ

cd

−W�

WZ

dIed

KL = � + O ∗ log(�v)

Discharge flow coefficient through a venturi flow meter

Ref Colter L. Hollingshead., Discharge coefficient performance of venturi, standard concentric orifice plate, v-cone, and wedge flow meters at small reynolds numbers, All graduate theses and dissertations. (2011) pp869


2

14

1 3 54 6CONTENTS


• Width of radial clearance : 40 μm

▣ Results of CFD simulation with various diameter ratio

• Height of radial clearance : 20 mm

• Diameter of cylinder : 25 mm • Upstream pressure : 4 bar

QR =2��x

v 1 − �G J G⁄� = 1 − �/v

Ref) Yanagisawa, T., Shimizu, T. Leakage losses in a rolling piston type rotary compressor, I. Radical clearance on the rolling piston,/ntJ Refrig 8 (1985) 75-84

◈ Friction length

25/18 25/19 25/20 25/210.008

0.009

0.010

0.011

0.012

Fri

ctio

n le

ng

th (

m)

Ratio of Diameter

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Flo

w c

oeffi

cien

t

Pressure ratio (Pd/Pu)

25/18 25/19 25/20 25/21

Friction length increase 0.00091 m Flow coefficient decrease 0.03


2

15

1 3 54 6CONTENTS

5.3 Numerical compressor simulation


▣ Compressor calorimeter experiment ▣ Compressor calorimeter experiment

Width of radial clearance

Upstream pressure

Pressureratio Friction length

�< = =�WZ_cd

d− e �aZ

W�

WZ

cd

−W�

WZ

dIed

▷ Functional formula

▷ 0.3 (suggested by previous work)

50

60

70

80

90

100

Eff

icie

ncy

(%

)

EXP 0.3 FUNC

50

60

70

80

90

100

Eff

icie

ncy

(%

)

EXP 0.3 FUNC

2

16

1 3 54 6CONTENTS


▣ Results of the compressor performance simulation


Case 1 Case 2Suction pressure(bar, absolute) 9.95 9.95

Discharge pressure(bar, absolute) 33.8 33.8

Capacity of Comp. (cc) 14.1 12.5Comp. type Twin rotary Twin rotary

Frequency (Hz)

(a) Case 1

Frequency (Hz)

(b) Case 2

-2.03 %

Volumetric Mechanical & Indicated Compressor

40 60 80 40 60 80 40 60 80


40 60 80 40 60 80 40 60 80

-3.16 %-1.57 % +0.10 %

+2.29 %-2.17 %

-1.93 % -0.94 %-3.70 %

-7.84 %-7.21 %

-5.63 %

+5.64 %+5.88 %+2.51 %

-1.89 %-1.76 %

-3.26 %-4.74 %

-5.38 %-2.38 %

+0.91 %+2.76 %

-2.21 %

-3.88% -2.77 %-4.53%

-10.76 %-10.46 %

-6.97 %

+5.60 %+6.19 % +2.81 %

-4.15 % -4.34 %-4.36 %

2

17

1 3 54 6CONTENTS


▣ Results of the compressor performance simulation


Case 3Suction pressure(bar, absolute) 10.15

Discharge pressure(bar, absolute) 23.37

Capacity of Comp. (cc) 14.1Comp. type Twin rotary

Frequency (Hz)

(c) Case 3

50

60

70

80

90

100

Eff

icie

ncy

(%

)

EXP 0.3 FUNC


40 60 80 40 60 80 40 60 80

-5.42 %-5.89 % -4.17 %

-9.52 %-7.11 %

-12.01 %

-15.23 %-12.61 %

-15.70 %

-7.51 %-7.64 %

-4.75 %

-8.89 %

-6.82 %

-12.51 %

-16.54 %-13.94 %

-16.32 %

�< = =�WZ_cd

d− e �aZ

W�

WZ

cd

−W�

WZ

dIed

Need for consideration of other factors

Friction

Operating conditionGeometric

Prediction of leakage through the radial clearance

Friction

Geometric Operatingcondition

Roller rotate Oil

Will investigate the sensitivity of influence factors of leakage through the radial clearance

Prediction of leakage through the radial clearance

2

18

1 3 54 6CONTENTS


The developed functional formula is helpful for predict the performance of compressor in the design process of novel compressor.

In this paper, the flow coefficient through the radial clearance in the rolling piston type rotary compressor was functionalized. The results are summarized as follows.

1. The functional formula of flow coefficient through the radial clearance was developed with consideration about operating of compressorand geometric characteristics.

2. The range of flow coefficient is from 0.08 to 0.85 under the various widthof radial clearance (10 μm - 60μm) and upstream pressure (4 bar – 30 bar)and different from 0.3 under the various operating condition.

3. The results of compressor performance with functional formula showedmore accuracy than results with 0.3

19

Thank you for your attention!


prediction of leakage flow of radial clearance in a

Documents