1

Absorber Heat Transfer and Other Issues A Comparison between MICE and the

Forced Flow Absorber System

Michael A. GreenLawrence Berkeley National Laboratory

Berkeley CA 94720, USA

MUCOOL Workshop MeetingFermilab, Batavia IL, USA

22 February 2003

2

A Summary of MICE Absorber Issues

• The Heat transfer on the helium side is forced convection in the absorber case tube. The flow of the helium is set by the flow from the refrigerator.

• Heat transfer on the hydrogen side is by free convection. Buoyancy determines the mass flow of the sub-cooled hydrogen. The hydrogen mass flow goes up as the heat load (QB + QH) to the 0.5 power. The change in the bulk hydrogen temperature goes as the heat load to the 0.5 power.

• Freezing the liquid hydrogen in the absorber is not allowed when there is no heat load into the absorber, so the helium enters the absorber body at 14 K.

3

A Summary of Forced Flow Absorber Issues

• The Heat transfer in the forced flow absorber heat exchanger between the helium gas and the sub-cooled hydrogen in the absorber flow circuit is marginally OK.

• The position of the heat exchanger with respect to the absorber and the hydrogen pump is of concern.

• The condensation of liquid hydrogen into the absorber circuit can be a key operational issue.

• One can circulate the liquid hydrogen through the absorber by natural convection. One should be able to remove up to 1000 W of heat from the absorber using natural convection.

4

A Simplified Schematic of the MICE Absorber Heat Loads

QR2

QR2

QB

Heater = QHQC2

QC2

Beam Heat =

Vacuum

304 St St Tube5456 Al Tube

Vacuum Window Cryogen Window

T T1 2

He Mass Flow = mHe

LH or LHe2

QC = 20 WQR = 10 WQB+QH = 70 WQT = 100 W

Window T > 55 K

5

Thermal Modeling the MICE Absorber using an Electrical Network Analogy

THe

TR TI

Twin

TW

Tf

QT

QHQB

QR

QC

Rwin

Rt1 Rt2

Rc2

Rc1

Rr1 Rr2

TR

QC = 20 W

QR < 10 W

QT = 100 W

QB + QH > 70 W

TI > 55 K when QR = 0

Tf < 20 K

TR = 300 K

6

LH2 Pump

Absorber

14 K He

He Out

Heat Exchanger

QW

QC

QB

QP QO

QWQCQBQPQO

= Radiation heating of windows = Conduction to Absorber Body = Beam Heating = Pump Work Heating = Other Heat Loads Total

Case #1

10 W

20 W

150 W

up to 30 W

~15 W

~225 W

Case #2

10 W

20 W

300 W

up to 30 W

~15 W

~375 W

Simplified Forced Flow Absorber Schematic

Desired

7

A Comparison of the MUCOOL Forced Flow Absorber with the MICE Free Convection Absorber

Parameter Type of Helium Flow Helium Mass Flow (g/s) Type of Hydrogen Flow Hydrogen Mass Flow (g/s) Helium inlet T (K) Heat Exchanger Area (m ) Heat into the Absorber (W)

MUCOOL Case #1

Forced

up to 27 g/s Forced

up to 450 g/s 14

0.267 180

MUCOOL Case #2

Forced

up to 27 g/s Forced

up to 450 g/s 14

0.267 330

MICE

Forced 5 to 10 g/s

Free Convection variable w load

14 0.410 100

2

8

Possible MICE Absorber Heat Exchangers

Parallel Flow Counter Flow

Mixed Flow

9

Counter Flow Heat Exchangers versus Parallel Flow and Mixed Heat Exchangers

• In a parallel flow heat exchanger, the coldest temperature of the warm stream is always higher than the warmest temperature of the cold stream. This restriction does not apply for a counter flow heat exchanger.

• For a given heat exchanger U factor and heat exchanger area, a counter flow heat exchanger will nearly always have the lowest log mean temperature difference.

• A mixed flow heat exchanger has all of the disadvantages of a parallel flow heat exchanger plus the heat exchange and hydrogen flow in the absorber is unbalanced. Heat from the outlet stream is shorted to the colder inlet stream.

• In situations where a change of phase occurs on one side of the heat exchanger, any type of heat exchanger works.

10

Parallel Flow and Counter Flow Heat Exchangers

Q = UA THE LM

1

ln( 1 2

2

LMHeat Exchanger U Factor

Heat Exchanger Area

Log Mean T

U1

h1

kt

h1= + +

c1 c2

w

w

T1

T2T

x

Parallel Flow

T1

T

x

T2

Counter Flow

11

An Estimate of the Pumped Hydrogen Forced Flow Heat Exchanger U Factor

h = 0.023 Re Prc0.8 0.33 k

DfH

Turbulent Forced Flow in a Pipe

for Helium 15 g/s to 25 g/sc1h = 1161 to 1747 W m K-2 -1

c2h = 179 to 2720 W m K-2 -1 for Hydrogen 15 g/s to 450 g/s

ktw

w = 208000 W m K-2 -1 for Copper pipe t = 0.7 mm @ 17 Kw

15 g/s 100 g/s 450 g/s H2 flow

15 g/s 20 g/s 25 g/s

He FlowU factor (W m K )-2 -1

based on fluid properties @ 17K

155 159 162

478 523 555

812 948 1058

The U factor for the MICE absorber Heat Exchanger is much lower.

12

A MICE Absorber Heat Exchanger

14 K Helium Gas In G = 7 g / s

16.7 K He Out16.7 K He OutNeck Dia. ~ 50 mm

Al Heat Exchanger

G-10 Duct Wall

LH2

Q = 100 W T = 18.8 K P = 1 bar

~320 mm

~460 mm

Aluminum Absorber Case

Al Neck to Buffer Volume

150 mm

215 mm 160 mm

Liquid Hydrogen

Heat path from Vacuum Window

14 to 18 K Helium Gas

T < 20.3 K

180 mm

350 mm

13

MICE Peak Bulk LH2 Temperature Vs 14 K Helium Mass Flow and Heat Load into the Absorber

2015105014

15

16

17

18

19

20

21

Q = 50 WQ = 100 WQ = 150 WQ = 200 W

Mass Flow of Helium at 14 K (g/s)

Peak

Hyd

roge

n Te

mpe

ratu

re (

K)

Inlet He T = 14 K

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MICE Peak Bulk Helium Temperature Versus the Heat Load into the Absorber

40353025201510504.2

4.4

4.6

4.8

5.0

5.2

Heat Load Entering the Absorber (W)

Hig

hest

Hel

ium

Tem

pera

ture

(K)

Helium Critical T

Two-phase Helium T Helium Inlet T = 4.3 K

Note: The two-phase helium flow is at least 3.5 g/s.

15

The pumped Hydrogen Forced Flow Absorber Configuration Studied

Hydrogen Pump

Heat Exchanger A = 0.267 m^2

He OutHe In

H2 Gas

Absorber

The configurationshown was given atlast week’s telephonemeeting. This week’sconfiguration is not the same. The new configuration will have improved performance.

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Forced Flow Peak Bulk Hydrogen Temperature VsHelium and Hydrogen Mass Flow for Q =225 W

25.022.520.017.515.014

15

16

17

18

19

20

21

22

15 g/s50 g/s100 g/s200 g/s450 g/s

14 K Helium Circuit Mass Flow (g/s)

Hig

hest

Bul

k H

ydro

gen

Tem

pera

ture

(K)

Hydrogen Flow

Q = 225 WA = 0.267 m^2

17

Forced Flow Peak Bulk Hydrogen Temperature VsHelium and Hydrogen Mass Flow for Q = 375 W

25.022.520.017.515.014

15

16

17

18

19

20

21

22

15 g/s50 g/s100 g/s200 g/s450 g/s

14 K Helium Mass Flow (g/s)

Hig

hest

Bul

k H

ydro

gen

Tem

pera

ture

(K)

Hydrogen Flow

Q = 375 WA = 0.267 m^2

18

Problems with the Pump Loop• The heat exchanger area

is too small. Increasing heat exchanger area will reduce the log mean temperature difference and improve efficiency.

• The pump flows against buoyancy forces.

• The heat exchanger will flood as hydrogen is condensed into the pump loop. As result, hydrogen condensation will slow to a snails pace.

Hydrogen Pump

Heat Exchanger A = 0.267 m^2

He OutHe In

H2 Gas

Absorber

19

A Better Pump Loop Solution• The heat exchanger area

is increased a factor of three. As a result, the system is more efficient.

• The pump and the heat exchanger are oriented to use buoyancy forces to help hydrogen flow.

• The top of the heat exchanger is above the liquid level. The heat exchanger is an efficient hydrogen condenser.

Heat Exchanger A = 0.80 m^2

H2 Gas He Out

He In

Absorber

Hydrogen Pump

20

Can a Free Convection Loop be used?

• Circulation of the hydrogen using free convection should be seriously considered. Preliminary calculations suggest that up to 1000 kW can be removed from the absorber using a free convection loop.

• The hydrogen flow through the absorber is proportional to the square root of the heat removed. The bulk hydrogen temperature rise is proportional to the square root of the heat removed.

• The heat exchanger must be vertical with the hydrogen flowing in the downward direction. The helium will flow in the upward direction. The top of the heat exchanger should be above the hydrogen liquid level.

• It is not clear if a free convection hydrogen flow loop will fit in the lab G solenoid.

21

16.7 K He Out

14 K He In 70 g/s

Average Head H ~ 1.0 m

~0.4 L = 1.8 m

Minimum Volume LH2 Absorber, ID = 320 mm

ID = 75 mm

LH2 Buffer Volume

Q ~ 1000 W

Thin Window Dia = 300 mm

Hydrogen Circulation using Free Convection

Absorber

H2 Mass Flow ~ 190 g/s at Q = 1000 W

T = 18.9 K

T = 19.5 K

Heat Exchanger

A = ~5 m 200 tubes ~12.7 mm OD

D = 250 mm L = 850 mm

U = 54 W m K T = 3.75 K

-2 -1

2

LM

22

Some Concluding Comments• The MICE absorber appears to be OK for heat loads to the

hydrogen of up to 100 W. (30 W is transferred to the helium gas directly.) The MICE absorber appears to work with liquid helium in the absorber with total heat loads up to about 45 W. (30 W goes to the two-phase helium directly.)

• The new MUCOOL forced flow experiment will work as designed. The flow experiment works because the mass flow in the both streams of the loop is larger than the optimum.

• Increasing the MUCOOL pump loop heat exchanger area will improve the pump loop heat transfer efficiency at lower hydrogen mass flows. Correct orientation of the pump and heat exchanger should improve the loop performance.

• A free convection hydrogen loop appears to be feasible. A free convection loop may not fit into the lab G solenoid.