study on water-type stirling engine and its … · 2 today’s topics 1. introduce of myself and...

Division of Heat Transfer,Department of Energy Sciences,

Faculty of Engineering, Lund University

Group Seminar2009/12/02

Yoshiyuki Yamaguchi

1

STUDY ON WATER-TYPE STIRLING ENGINE AND ITS

REVERSE CYCLE

2

Today’s Topics

1. Introduce of myself and about University of Hyogo

2. Negative thermal expansion object

3. Water-type Stirling engine and its reverse cycle* What is “Water-type” Stirling engine?* Experiment & analysis model* Can it work as a “Water-type” Stirling refrigerator?* Duplex “Water-type” Stirling system* “Water-type” Vuilleumier heat pump

3

PROFESSIONAL EXPERIENCES

1992-04-01 - 2003-06-30Research Associate of Mechanical Engineering,Department of Mechanical Engineering,Graduate School of Engineering,Tokyo Metropolitan University.

2003-07-01 - PresentAssociate Professor of Mechanical Engineering,Department of Mechanical and System Engineering,Graduate School of Engineering,University of Hyogo.

2009-08-07 - (2010-08-05)Visiting Researcher of Heat Transfer,Department of Energy Sciences,Faculty of Engineering, Lund University

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Hyōgo PrefectureCapital KobeArea 8,393.34 km² Population 5,595,212 (2005)

Himeji CityLatitude: 34.5N, Longitude: 134.4EArea 533 km²Population 535,571 (2008)

5

School of Engineering, University of Hyogo

Academic Staff 130StudentsUndergraduates 1,597Postgraduates 303Doctoral students 20

Departments* Department of Electrical Engineering and Computer Scineces* Department of Mechanical and System Engineering* Department of Material Science and Chemistry

Estimation of Buoyancy Change of Estimation of Buoyancy Change of a NTE Capsule Using PCMa NTE Capsule Using PCM

Yoshiyuki Yamaguchi

Dept. Mech. & Sys. Eng., University of Hyogo

2167 Shosha, Himeji,Hyogo 671-2201, Japan

[email protected]

Koji Takanashi

Dept. Mech. Eng.,Tokyo Metropolitan University1-1 Minami-Osawa, Hchioji,

Tokyo 192-0397, Japan

6

Presented at IMECE2004, Anaheim, CA, USA

Objective

Negative Thermal Expansion

System heated from bottom and top

In general, natural convection is not generated in a fluid layer of top heat mode.If we can use a material of negative thermal expansion, we can cause a reverse natural convection in a fluid layer of top heat mode.

7

Fundamental Principle

Simplified dynamic model

260 280 300 320 3400

0.5

1

Temperature [K]

Sat

urat

ion

Pre

ssur

e [M

Pa]

Ps=8.36593×10-7×T3-6.32994×10-4×T2

　　+1.64438×10-1×T-1.46066×10

Data of Saturation Table Approximation

Boiling Pointat Normal Pressure

267.3

0.1013

Saturation pressure of RC318

8

RC318 = Freon C318Name: OctafluorocyclobutaneMolecular formula: C4F8

Operation Experiment

Experimental Apparatus

9

Result for L-type

0 10 20 30 40

0

0.2

0.4

0.6

0.8

1

Time after Releasing [min]

z [m

]

Bottom of Heater

10 20 30

0

0.2

0.4

0.6

0.8

1

Temperature [°C]

z [m

]

Beforereleasing

After120 minutes

0 20 40 60 80

0

0.2

0.4

0.6

0.8

1

Time after Releasing [min]

z [m

]

Bottom of Heater

10 20 30

0

0.2

0.4

0.6

0.8

1

Temperature [°C]z

[m] Before releasing

After 90 minutes

For L-type (Q=47W and Tc =5℃)

For L-type (Q=33W and Tc=13℃)

10

S-type

L-type

Two Types of NTE capsules 11

0 100 200 300

0

0.2

0.4

0.6

0.8

1

Time [sec]

z [m

]

Bottom of Heater

Result for S-type

15 20 25 30

0

0.2

0.4

0.6

0.8

1

Temperature [°C]

z [m

]

For S-type

12

Improvement Plan• Spring lock mechanism: It prevents its density from changing until

when its temperature reaches to sufficient value.

13

Numerical Prediction

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60

Depth

(m

)

Time (min)

0N

16N

0

0.2

0.4

0.6

0.8

1

10 30 50

Temperature of

surrounding water [℃]

Force of spring lock

14

Result: Operation condition

0

10

20

30

40

50

60

70

0 5 10 15 20

Tem

pera

ture

diffe

rence (℃

)

Force of spring lock (N)

動作が継続

動作が停止

It operates favorably.

It stops.

15

Numerical Prediction of Performance of Water Type Stirling Engine Considering

Heat Exchange With Heat Sources

Yoshiyuki YAMAGUCHI and Tetsuya HIGUCHI

Dept. Mech. Sys. Eng., University of Hyogo

Y.Yamaguchi: University of Hyogo;

Presented at ISEC2007, Tokyo, Japan

16

Resonance tube

Displacer pistons

Power piston

Regenerator

Heating head

Cooling head

Water

Working gas (air)


Schematic of a water-type Stirling engine

Mathematical ModelKidachi et al. (1996)

Friction loss: proportional to the velocity

Working gas: constant temperature

Qualitative : ○

Quantitative : ×

Comparison to experiment

17

epe

dd

e

dd

pin

LHSS

H

SS

V~S

~1

20

Expansion / compression

Spring-mass systemVibration of power piston water column

122

ddn H

~

Isochor regeneration

Pendulum systemVibration of displacer water columns


Resonance model 18

Operating range

8 10 12 14 16 180.09

0.1

0.11

0.12

Length of Resonance Pipe Le=le/lc [-]

Char

acte

ristic

Fre

quen

cy [-

]

pin

dn

122

ddn H

~

epe

dd

e

dd

pin

LHSS

H

SS

V~S

~12

0


Resonance model (result)

: frequency of pendulum system is a function of Hd

(independent from Le).

: frequency of spring-mass system is a function of Le.

dn%

pin%

At an optimum value of Le, two frequencies become equal.

Heat transfer

Friction lossNegligible?

19

Spring-mass systemPendulum system

5 10 15 20 25

0.06

0.08

0.1

0.12

0.14

0.16


Cha

ract

eris

tic F

requ

ency

[-]

~pan

~pin

~dn

epe

dd

e

dd

pin

LHSS

H

SS

V~S

~12

0

122

ddn H

~

epe

dd

e

dd

pan

LHSS

H

SS

V~S

~12

0Adiabatic condition

Isothermal condition

Isothermal

Adiabatic


Resonance model – adiabatic condition 20

Motion equation of water columnWater

Air

Energy conservation equation of heating and cooling unit

Energy conservation equation of regenerator

State equation of gas

Mass conservation equation

Motion of a water-type Stirling engine


Heat transfer model 21

Non-dimensional motion equation

h1①

②

④

③

⑤

p

p1

h1.

1 111 1 1 1

1

2 222 2 2 2 2

2

3 333 3 3 3

3

1 11 2 1 1

222 2

2 1 3 3 2 31 1

2

2

2

12

1 12

f

c

e ee e

e e

H HHH H H P PD

H HHH H H P PD

H HHH H H P PD

H HH P P

D

S S LL L H H P PS S

& &&&

& &&&

& &&&

& &&&

&& &

①

②

③

④

⑤

22 1 2

3 4 3 32 1 1

12

e e e

e e e

L S H HD D S

& &


Motion equation of water column 22

Cooling unit

Heating unit The pressure of the working fluid is

uniform in the engine.The working fluid is ideal gas.Quantity of state of the gas is uniform in

the element.The energy transfer between elements is

caused only by the convection. The effect of the steam is not considered.

Assumptions

11111 prhmWQU &&&

Internal energy

Inflow heat

Work Inflow enthalpy

m1hpr1.

-Q1Inflow

11111 hmWQU &&&Outflow

Outflow enthalpy

For cooling unit


Energy conservation in heating and cooling unit 23

Cooling unit

Heating unit

1 1 1 11

1 1 1 1

1 1 1 11

1 1 1

0

0

v L L

p r v

v L L

p v

M C S AMPV M C C

M C S AMPV M C C

&&

&% &

&&

&% &

Inflow

Outflow

Cooling unit


Energy equation of working gas

2 2 2 22

2 2 2

2 2 2 22

2 2 2

0

0

v H H

p rn v

v H H

p v

M C S AMPV M C C

M C S AMPV M C C

&&

&% &

&&

&% &

Inflow

Outflow

Heating unit

24

Local equilibrium between gas and heat storage material.

Constant gas density．

i i-1i+1

m1hpri+1. m1hpri

.

priprirsiri hmhmUU 111 &&&&

Inflow enthalpy

Outflow enthalpy

Internal energy of gas

Internal energy of heat storage material

Toward the cooling unit


Energy conservation in regeneratorAssumptions

1 1 10 ri v rsi rs ri p ri riM M C M C M C& & &

From the heating unit to the cooling unit

From the cooling unit to the heating unit

1 1 10 ri v rsi rs ri p ri riM M C M C M C& & &

Energy equations

i-th element of regenerator

25

Power piston

Resonance tube

Displacer

CoolerHeater Case 1 Case 2Initial height of liquid columns 400mm 370mm

Temperature of the heater 100℃

Temperature of the cooler 20℃

Experimental conditions

400mm 370mmCase 1 Case 2


Experimental setup 26

Power piston Heating part Cooling part

Case 1Le=18.6

Case 1 ： Le=16.1~21.6

Case 2 ： Le=13.6~19.1

Range of the resonance tube length

While the resonance tube length was changed to every 0.5, the vibrations of water columns were observed.


Snap shot of the experiment 27

12 14 16 18 20 22 240

0.1

0.2

0.3

Am

plitu

de o

f Liq

uid

Col

umns

[-]

H1 Exp.H2 Exp.H3 Exp.H1 Cal.H2 Cal.H3 Cal.

Length of Resonance Pipe Le=le/lc [-]12 14 16 18 20 22 240

0.1

0.2

0.3


Am

plitu

de o

f Liq

uid

Col

umns

[-]

Case 1 Case 2

18.6 16.1

The estimated optimum value of Le by the resonance model


Result of optimum resonance tube length

For Case 1 ; Le = 12.9 For Case 2 ; Le = 11.0

28

Case 1 (Le = 18.6) Case 2 (Le = 16.1)

0 2 4 6 8 101.5

2

2.5

3

Time = t/(lc/g)1/2 [-]

Hei

ght o

f Liq

uid

Col

umns

H=h

/l c [-

]

0 2 4 6 8 101.2

1.6

2

2.4

2.8

3.2

3.6

Time = t/(lc/g)1/2 [-]

Hei

ght o

f Liq

uid

Col

umns

H =

h/l c

[-]

Heat transfer model and experimental result agreed well at the optimum resonance tube length.


Result of vibrations of water columns

ISEC07[A16] sheet 17

For each optimum resonance tube length

29

Enlarged parameterThe optimum

length of resonance pipe

Work

Cross-sectional area of resonance pipe Se

Longer Increase

Loss coefficient 1 Constant Decrease drastically

Loss coefficient 3 Constant Decrease gentlyHeat transfer area

SH, SLSlight longer Increase

Pressure in displacer P Longer Increase


Influence of each parameters 30

Development of Water-type Vuilleumier Heat Pump

Yoshiyuki Yamaguchi&

Hibiki Kamei University of Hyogo, Japan

31

Presented at ISEC2009, Groningen, Netherlands

University of HyogoLund University


Mechanical Stirling cooler

Stirling Refrigerator

Air

Water

Hose

Heating Head

Cooling Head

Engine part

Refrigerator part

1. Verifying the reverse cycle.

2. Construction of the numerical model.

3. Elucidation of operating characteristics.

Objectives

Duplex Water-Type Stirling EngineTemperature DifferencePower

動力温度差 PowerTemperature Difference

＋

32



Duplex Water-type Stirling Engine/Heat-pump

Qin

Qout

Qout

Engine part Refrigerator partL

1. Cooling Head2. Heating Head3. Expansion Head4. Compression Head5. Regenerator6. Displacer U-tube7. Resonance Pipe

1 2

3 4

5

6 7

Heat removal Qc

33

Structure



Experiment

Cooling machine

Heater

Refrigerator part

Resonance Pipe

Engine part

Table. Experimental setup

Initial temperature [K] 303Heating temperature [K] 383Cooling temperature [K] 283Charged pressure [kPa] 101.32

Range of resonance pipe length [m] 3.07~7.07

34

Equipment



Motion of Water Columns ① ②

①②

RefrigeratorPart

Engine Part

Oscillations of water columns of the refrigerator partFrequency：0.75Hz Amplitude：0.02m

35



4.95 5 5.05 5.1 5.15 5.20

0.01

0.02

0.03

Length of resonance pipe [m]

Am

plitu

de o

f liq

uid

colu

mns

[m]

AAAA

1 2 3 4

ExperimentResult

Oscillation was observed in each water column

Engine part

Refrigerator part

A1A2A3A4

20mm

36



Numerical AnalysisModeling

Euler equation of motion

lzg

lp

lhh

th 1&&

&

＋ 2

2hdlploss

&

Pressure drop

211

1

11111

HHDHPPHHH E

&&

Dimensionless form

・・・①

・Momentum equations of water・Energy equations of working gas・Equation of state of working gas・Equation of mass conservation

37



Result of calculation Oscillation in each water column

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0 20 40 60 80 100Time　[-]

Hei

ght

of

liqui

d co

lum

ns　

[-]

　H1 　H2

　H3 　H4

Engine part

Refrigerator part

Heat input causes oscillation of water columns.

For; Initial temperature:T0=293K, Heating temperature:Th=373K,Cooling temperature:Tc=293K, Length of Resonance pipe: Le=4300mm

38



Water-type Stirling engine can operate as refrigerator

44

44.5

45

45.5

46

46.5

47

1.72 1.74 1.76 1.78 1.8 1.82

Volume [-]

Pre

ssure

[-]

L

Q

Volume [-]

Pres

sure

[-]

39

Result of calculationP-V diagram of refrigerator part



0

0.05

0.1

0.15

0.2

0.25

0.3

5 10 15 20 25 30 35Length of resonance pipe　[-]

Am

plit

ude

of liq

uid

colu

mns　

[-]

A1

A2

A3

A4

The resonance tube length is an important parameter.

Engine part

Refrigerator part

40

Result of calculation Effect of the resonance tube length on water column amplitudes



Engine part

Refrigerator part

Summaries of duplex water-type Stirling engine 1. From the experiment, oscillation in each water column was observed.2. By inputted heat, steady oscillation is generated in each water column. 3. On the P-V diagram, heat pump cycle was confirmed. 4. Coincidence of natural frequencies is necessary for the performance

improvement.

The coincidence of natural frequencies is broken Poor performance

Proposal of water-type Vuilleumier heat pump

Qin

Setup

Setup

Heated

Heated

41



Vuilleumier Heat Pump

1. Cold displacer2. Hot displacer3. Cold cylinder space

7. Mechanical spring C8. Regenerator

Stirling Refrigerator part

Stirling Engine part

4. Warm cylinder space5. Hot cylinder space6. Gas spring

Heat removalQc

Qin

The coincidence of natural frequencies is kept after heating.

1

24

3

5

Qout

L

7

8

6

Qin

Qout

Qc

Qout

L

PE=PR

42



ConclusionsExperiment and numerical analysis were carried out for elucidation of the operating characteristic of combined water-type Stirling heat pump. 1. From the experiment, oscillation in each water column was

observed.2. By inputted heat, steady oscillation is generated in each water

column.3. On the P-V diagram, heat pump cycle was confirmed.4. The resonance tube length is an important parameter.

5. Proposal of water-type Vuilleumier heat pump.

Future works:1. Evaluation of the operation experiment and comparison to the

numerical result.2. Elucidation of operation characteristic of water-type Vuilleumier

heat pump

An optimum resonance tube length exists.

43

study on water-type stirling engine and its … · 2 today’s topics 1. introduce of myself and...

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