Single-phase ambient and cryogenic
temperature heat transfer coefficients
in microchannel
Seungwhan Baek and Peter E Bradley
NIST
Boulder, CO 80305 USA
Cryogenic Engineering Conference 2015
06-29-2015
11:45 AM
Material Measurement Laboratory
Contents
• Introduction
• Experiments
• Results
• Discussion
• Summary
Material Measurement Laboratory
2
Introduction
• Microscale J-T cryocooler development
– Requires microchannel heat exchanger
– Requires microchannel heat transfer characteristics
Revised MCC Design
Early prototype
Compressor
J-T valve
C
Evaporator
Microchannel Heat exchanger
Microchannel
Heat exchanger
Microchannel
Heat exchanger
Material Measurement Laboratory
3
Thermal design of MCC heat exchanger
• Operating condition of MCC
– Fluid flow in microchannel ( Dh < 100 μm )
– Extremely low flowrate ( Re < 100 )
– Low pressure ratio (Pr<4:1)
• Cooling Performance of MCC depends on
– Heat exchanger performance
– Need heat exchanger/heat transfer characteristics
for MCC operating condition
– No previous research at these condition)
Recuperative HX
• Two different heat exchanger in MCC
– Recuperative HX: Single phase (gas or liquid)
•
Isothermal HX
Phase I research
– Isothermal HX: two-phase (gas+liquid)
•
Phase 2 research
Dh: hydraulic diameter, Re: Reynolds number
Material Measurement Laboratory
4
Thermal design of heat exchanger
•
Heat transfer coefficient (h) required to determine geometry of heat exchanger
(Aht), heat transfer amount (𝑄)
– Geometry: Heat transfer area (Aht=L x W), thickness of the wall (th)
L
W
H
th
Aht: heat transfer area (m2)
𝑄: heat amount (W)
Tf: fluid temperature (K)
Tw: wall temperature (K)
𝑄
ℎ=
𝐴ℎ𝑡 (𝑇𝑓 − 𝑇𝑤 )
• Nusselt number
– Dimensionless number to define heat transfer performance
– Nusselt number (heat transfer characteristic) is dependent on fluid property (Pr) &
operating condition (Re)
ℎ𝐷ℎ
𝑁𝑢 =
𝑘𝑓
Material Measurement Laboratory
𝑁𝑢 = 𝑓(𝑅𝑒, 𝑃𝑟)
h: heat transfer coefficient (W/m2K)
kf: thermal conductivity of fluid (W/mK
Dh: hydraulic diameter (m)
Re: Reynolds number
Pr: Prandtl number
5
Nusselt number: Previous research
• Theoretical Nusselt number: Nu=4.36 const. (circular channel, Re < 2000)
• From previous research: single-phase Nu # correlation for Re < 2000
•
•
No experiment at low temperature (T < 200 K), low flow rate (Re = 10 - 50)
Experiments do not follow theory, Differ from each other, No recent research
• Need to verify heat transfer characteristic for better design of MCC
From previous research, Nu=f(Re, Pr) for Re < 2000
Kays
(1970)
Sieder & Tate
(1996)
Diameter
Dh > 1mm
Dh > 1mm
Shah and
London (1978)
Dh > 1mm
Shah and
London (1978)
Dh > 1mm
100
Correlation
𝑅𝑒𝑃𝑟𝐷
𝑁𝑢 = 1.86
𝐿
1/3
0.14
𝜇𝑓
𝜇𝑤
𝑅𝑒𝑃𝑟𝐷 0.8
0.19
𝐿
𝑁𝑢 = 3.66 +
𝑅𝑒𝑃𝑟𝐷 0.462
1 + 0.177
𝐿
𝑁𝑢 =
1
1.953𝑅𝑒𝑃𝑟𝐷/𝐿3
𝑁𝑢 = 4.861(1 − 3.656𝛼 + 12.821𝛼 2 −
27.441𝛼3 + 37.373𝛼 4 − 28.365𝛼 5 )
Wu & Little
(1983)
Dh = 150 μm
𝑁𝑢 = 0.00222Re1.09 𝑃𝑟 0.4
Choi et al.
(1991)
Dh = 81 μm
𝑁𝑢 = 0.000972Re1.19 𝑃𝑟 3
Grigull and
Tratz (1965)
Dh > 1mm
𝑁𝑢 = 4.36 +
𝐷ℎ
𝑅𝑒𝑃𝑟
𝑥
𝐷ℎ
1 + 0.04
𝑅𝑒𝑃𝑟
𝑥
Material Measurement Laboratory
10
2
3
Previous Nu# for single phase flow (gas)
MCC
Operating
regime
Laminar
Turbulent
Nu=4.36
1
0.1
Yang et al (2012)
Choi et al. (1991)
Wu & Little (1983)
Morini et al. (2012)
0.01
1E-3
10
1
0.00668
Nusselt number (Nu)
Researcher
100
1000
Reynolds number (Re)
Review of heat transfer and pressure drop characteristics
6 of
single and two-phase microchannels, Asadi, 2014, (Review paper)
10000
Experiments
Material Measurement Laboratory
7
Experiments
• Measure the single phase heat transfer coefficients
• Nitrogen
• microchannels (180 μm, 110 μm, 65 μm)
• Operating condition
• cryogenic liquid flow (~70 K)
• ambient gas flow(~300 K)
180 μm
110 μm
Friction factor
300 K gas N2
Heat transfer
Coefficient
70 K Liquid N2
300 K Gas N2
Material Measurement Laboratory
65 μm
8
Experimental setup (schematic)
Vacuum Chamber
‘Not to scale’
Pressure sensor
Pressure sensor
Vacuum
chamber
Constant heat flux
2nd
stage
Microchannel
Tinlet
1st stage
GM
cryocooler
Twall_1 Twall_2
Twall_3
Toutlet
Feedthrough
collar +
Test section
Radiation shield
T=64 K
Flow conditioner
Recuperator
Mass flow meter
GM-cryocooler 2nd stage
Compressor
Microchannel assembly
GM-cryocooler
1st stage
Material Measurement Laboratory
Compressor
9
Microchannel test section
L/4
microchannel
L
L/2
Heating element
Thermal grease
Flow
‘Not to scale’
Solder
Epoxy
Tin
Setup for
Dh=180 μm
Tw1
Tw2
Tw3
Tout
thermocouple
Unit: mm
180 μm
36 AWG Do=130 μm
E-type thermocouples
Heating length=3cm
Material Measurement Laboratory
380 μm
Heating wire
Do=160 μm
380 μm
10
SEM pictures of microchannels
Identical magnification
Dr. Baek’s
hair cross section
Not typical human
100 μm
139 μm
139 μm
Dh=180 μm
Dh=110 μm
Dh=65 μm
Din (μm)
180
110
65
Dout (μm)
380
310
160
Din/Dout
0.47
0.35
0.4
Thinnest wall
Material Measurement Laboratory
Thickest wall
11
Scale comparison
Dr. Baek hair
110 μm
310 μm
Stainless steel tube
Dh= 110 μm
65 μm
160 μm
Stainless steel
tube
Dh= 65 μm
106 μm
300 μm
Thermocouple tip
Not able to measure fluid temperature
and wall temperature separately.
Material Measurement Laboratory
12
‘Classic’ Nu# estimation method
L
heater
Constant heat flux
Microchannel
x
Tinlet
Twall,x
Toutlet
1.
Find energy input to fluid
𝑄𝑓𝑙𝑜𝑤 = 𝑚𝑐𝑝 𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛 = 𝑚(𝑖𝑜𝑢𝑡 − 𝑖𝑖𝑛 )
2.
Estimate fluid temperature inside
microchannel (based on linear temperature
profile)
𝑄𝑓𝑙𝑜𝑤
3.
Measure the wall temperature
𝑇𝑤𝑎𝑙𝑙,𝑥
4.
Determine the heat transfer coefficient
ℎ=
5.
Calculate the Nusselt number
Material Measurement Laboratory
𝑥
= 𝑚𝑐𝑝 𝑇𝑓,𝑥 − 𝑇𝑖𝑛
𝐿
𝑇𝑓,𝑥 =
𝑄𝑓𝑙𝑜𝑤
𝑥 + 𝑇𝑖𝑛
𝑚𝑐𝑝 𝐿
𝑄𝑓𝑙𝑜𝑤
𝑚 𝑖𝑜𝑢𝑡 − 𝑖𝑖𝑛
=
𝐴𝐻𝑇 (𝑇𝑤 − 𝑇𝑓,𝑥 ) 𝐴𝐻𝑇 (𝑇𝑤 − 𝑇𝑓,𝑥 )
𝑁𝑢 =
ℎ𝐷ℎ
𝑘𝑓
13
Result & Discussion
Material Measurement Laboratory
14
Friction factor measurements (Gas, 300 K)
• Hydraulic characteristic of fluid in microchannels
– Friction factor follows conventional theory
10
Laminar theory
friction factor
Turbulent theory
friction factor
(Blasius equation)
𝑓𝑒𝑥𝑝 =
∆𝑃𝐷ℎ 𝜌
2𝐿𝐺 2
𝑓𝑅𝑒<2000 =
16
𝑅𝑒
1
f - friction factor
Experimental
friction factor
180 m Exp.
110 m Exp.
65 m Exp.
Laminar Theory: 16/Re
Turbulent: Blasius
0.1
0.01
𝑓𝑅𝑒>2000 = 0.079𝑅𝑒 −1/4
Laminar
1E-3
10
100
Turbulent
1000
Reynolds number
Material Measurement Laboratory
15
10000
Nu # measurement
Gas N2 (300 K)
•
•
•
100
Liquid N2 (70 K )
•
•
•
Nu # degrades from Re < 1000
Nu #: 180 μm > 65 μm > 110 μm
Similar trend with previous research
(Morini, Choi, Little)
Nu # degrades from Re > 200
Nu # : 180 μm ~= 65 μm ~= 110 μm
No other research to compare
100
65 m Gas N2 Exp.
110 m Gas N2 Exp.
180 m Gas N2 Exp.
10
Nu=4.36
1
Laminar
Turbulent
0.1
Nusselt number
Nusselt number
10
1
Laminar
Turbulent
0.1
0.01
0.01
Nu=4.36
65 m Liquid N2 Exp.
110 m Liquid N2 Exp.
180 m Liquid N2 Exp.
1E-3
10
100
1000
Reynolds number
Material Measurement Laboratory
10000
1E-3
10
100
1000
Reynolds number
16
10000
Scaling effect
• Scaling effect can influence the thermal behavior of fluid flow in microchannels*
Non-D number
Effect
Ignored when
Kn
Knudsen
Ma
Mach
Br
Brinkman
λ
Lambda
axial conduction of wall
λ < 0.01
Pe
Peclet
axial conduction of fluid
Pe > 50
Microchannel
Phase
Re
Kn
(<0.001)
gas rarefaction
Kn < 0.001
flow compressibility
Ma < 0.3
viscous heating
Br < 0.005
Ma
(<0.3)
Re=1
Re=3000
gas
0.00007
0.0006
0.10
liquid
0.00001
0.0003
0.04
gas
0.00012
0.0018
0.27
liquid
0.00002
0.0007
0.11
gas
0.00021
0.0031
0.46
liquid
0.00005
0.0010
0.20
Dh=180 μm
Dh=110 μm
Dh=65 μm
Br
(<0.005)
1.5×
10−6
2.9
× 10−6
8.7 ×
10−6
λ
(<0.01)
Pe
(>50)
Re=1
Re=3000
Re=1
Re=3000
2.18
0.005
10
2340
0.10
0.0002
3
200
1.63
0.006
10
2400
0.80
0.0002
5
200
1.10
0.002
8
2430
0.20
0.0004
5
2700
*Guo Z-Y and Li Z-X, 2003 International Journal of Heat and Mass Transfer 46 (1) 149-159
Material Measurement Laboratory
17
Nu # degradation
•
•
•
•
Nu # degradation is related to axial conduction effect through the wall.
Axial conduction changes temperature profile to ‘non-linear’. (Baek et al, 2014)
Non-linear temperature profile violates the assumption in classic Nu # measurement.
Classic Nu # measurement including axial conduction effect leads to estimate ‘apparent
Nu #’.
•
Apparent Nu # is neither actual nor theoretical Nu #.
•
Apparent Nu # (Lin & Kandlikar, 2012)
– Nu # degrades due to axial conduction effect with classic Nu# measurement method
Nuapp
Nutheory

happ
hx

1 4
1
kw Aw Nutheory
(1)
k f Af (Re Pr) 2
Baek et al., 2014, Cryogenics 60 49-61
Lin T-Y and Kandlikar S G, 2012 Journal of Heat Transfer 134 (2) 020902
Material Measurement Laboratory
18
Comparison of Experiment & Nuapp
• Comparison shows identical trend with experiment & equation (1).
• Comparison implies actual Nu=4.36 holds in low Re # flow.
100
65 m
Apparent Nusselt number
180 m
10
Simulations for Liquid N2, eqn. (6)
Simulations for Gas N2, eqn. (6)
110 m
1
0.1
65 m Liquid N2 Exp.
180 m
110 m Liquid N2 Exp.
180 m Liquid N2 Exp.
65 m Gas N2 Exp.
0.01
110 m Gas N2 Exp.
65 m
1E-3
10
180 m Gas N2 Exp.
110 m
100
1000
10000
Reynolds number
Material Measurement Laboratory
19
Summary
Material Measurement Laboratory
20
Summary
•
Design of heat exchangers influence development of MCC
– High uncertainty in operation  Due to very small Dh, Low Re# , Low temperature
•
The hydraulic and thermal characteristics of fluid in the microchannel are
investigated by the experiments.
–
–
Friction factors : comparable to macro-scale tubes
Nu # : decreased value @ low Re# , which are affected by axial conduction
•
Axial conduction effect influence the fluid & wall temperature profile to become
non-linear.
•
Comparison of experimental result and theoretically derived Nuapp imply validation
of Nu = 4.36 In laminar flow for single-phase fluid.
Material Measurement Laboratory
21
Experiment vs Previous work
Material Measurement Laboratory
22
Thank you!
Test Specimen is available!
Ask Peter & Seungwhan for
observation!
Material Measurement Laboratory
23