Mathcad - LAPD condenser heat transfer area. rev ... - LArTPC DocDB

Calculation By: M. Adamowski
Checked By:
Project: LAPD
Date: 11/10/09
Revision: D
Tube Heat Transfer - Boiling Liquid N2 and Condensing Argon
The HX heat transfer area is estimated by calculating the heat transfer for
condensing Argon on horizontal tubes with boiling liquid Nitrogen inside the
tube.
Tube Data
Tube Wall Thickness Tube Outer Diameter
Tube outer_dia
wall th 0.028in
Tube outer_dia 0.25in
r Mo
2
Tube Length
Tube Inner Diameter
L 36in
Tube inner_dia Tube outer_dia 2wall th
metal thermal
conductivity (316 SS)
Tube inner_dia
0.194in
r Mi
Tube inner_dia
2
k M 8.11
W
mK
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Argon Data
Argon physical properties from NIST REPROP
argon liquid density argon vapor density argon liquid visc
ρ Ar_l 1396
kg
ρ Ar_v 0.4
lb
µ Ar_l .261cP
m 3
ft 3
argon liq thermal conductivity
argon ice thermal conductivity
k Ar.liq
128.5
mW
k ice 133
mW
mK
mK
argon condensing
argon heat of vaporization
temperature
T Ar 87.8K
h Ar_fg 161
kJ h Ar_fg 69.21754
BTU
kg
lbm
argon freezing temperature
T Ar_freeze
83.8K
T ice T Ar_freeze
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Nitrogen Data
Nitrogen physical properties from NIST REPROP
Nitrogen boiling temperature
Nitrogen liquid thermal cond.
T N2
77.3K
k N2_liq 144
mW
mK
Nitrogen liquid density
Nitrogen Heat of
Vaporization
ρ N2_liq 807
kg
Hvap N2 199
kJ
m 3
kg
Nitrogen Vapor
Density
ρ N2_gas 4.5
kg
m 3
Nitrogen Liquid
Viscosity
µ N2_l .162cP
Nitrogen Liquid specific
heat
Cp N2_l 0.77
kJ
kgK
Mass flow of N2 based on
70% outlet vapor quality
Massflow N2
240
lb hr
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Heat Load
The heat load on the HX is taken as twice the heat absorbed by the LAPD tank
from the environment. Using twice the tank heat provides a design margin.
Tank heat
2106W
Q req 2Tank heat
Q req 4212W
Boiling Nitrogen Heat Transfer Coefficient
Excess Nitrogen is used to keep the tube side wetted. Under these conditions
the Nitrogen boiling heat transfer coefficient will be uniform for the whole
tube length.
h N2_boil 1500
kW
m 2 K
this N2 boiling heat transfer coefficient is
at a a minimum N2 mass flux.
N2 massflux_for_h 70
kg
m 2 s
ref: "Flow boiling heat transfer characteristics of
nitrogen in plain and wire coil inserted tubes", International Journal of
Heat and Mass Transfer 50 (2007)
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Tube heat transfer
The tube heat transfer is calculated as concentric rings of heat transfer. The
rings are inner tube metal surface, tube metal wall, Argon ice layer and outer
ice surface. The calculations are arranged starting inside the tube at liquid N2
temperature and then proceeds through the concentric rings to the tube
outside at condensing Argon temperature.
To start the calculation, initial guesses are made for the tube inside metal
temperature and the heat flux, q.
Initial Guesses
h Mi
q 200W
h N2_boil
The heat transfer calculations are define with a Mathcad GIVEN block to allow
use of Mathcad's equation solving ability.
Given
q
T Mi T N2
2π
L
r Mi
h Mi
inner surface formula arranged to solve
for inside tube metal temperature
T Mo T Mi q
ln r Mo
2π
r Mi
k M
L
metal tube wall formula arranged to solve
for outside tube metal temperature
r ice r Mo exp T Mo T ice
2π
q
k ice
L
Argon ice layer formula arranged to
solve for the radius of the outside
ice surface.
wall ice r ice r Mo
Given block continues on next page >>>
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Given block continues from previous page
The ice outside heat transfer coefficent is for condensing Argon. This
coefficient is estimated as condenstion on a horizontal tube.
h Ar_condi
0.728 g ρ 3
Ar_l ρ Ar_l ρ Ar_v k Ar.liq
Tube outer_dia µ Ar_l T ice T Ar
h Ar_fg
1
4
h Ar_cond
Reh Ar_condi
use the real portion of the 4th root solution
ref: Heat, Mass and Momentum Transfer, by Rohsenow, 1961,
pg 248, Condensation on horizontal tube formula.
q
2π
r ice
Lh Ar_cond T ice T Ar
outer ice layer heat transfer formula
arranged to solve for heat
transferred.
Find the solution to the given equations
Find( q)
q 214.57319W
wall ice 0.06621mm
q
heatflux Mi 2π
r Mo L
heatflux Mi 11.76293 kW
m 2
h Ar_cond 2880.66079
W
m 2 K
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Summary of results for require Q of: Q req 4212W
T N2
77.3 K
wall ice
0.06621mm
T Mi 77.30942K
T Mo 78.39797K
T ice
83.8 K
T Ar
87.8 K
Estimate the Total HX area based on outside tube diameter:
HX area_o
HX tube_count
Q req
2π
r Mo L
HX area_o 3.85428ft 2
q
HX area_o
HX tube_count 19.62967
2π
L
r Mo
N2 Mass flux
Massflux N2
Massflow N2
2
HX tube_count π
r Mi
The N2 massflux for the number of
tubes needed should be equal or
higher than the N2 massflux for the
N2 boiling heat transfer coefficient.
Ans if Massflux N2 N2 massflux_for_h
"solution is good"
"massflux low for N2 h data"
Ans
"solution is good"
Massflux N2 80.77943
kg
m 2 s
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Calc heat flux for tube inside surface
Heatflux i
2π
Q req
r Mi
L
Q req
q
Heatflux i 15158.41968
W m 2
Calc of overall U
U all
Q req
W
U all 1120.2794
T N2 T Ar HX area_o
m 2 U all 197.29261
K
BTU
hrft 2
R
Calc of tube inlet velocity
V tube_inlet
Massflux N2
V tube_inlet 0.32841
ft
s
ρ N2_liq
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N2 Horizontal Tube boiling heat transfer estimate
Shah Correlation with adjustment for horizontal plain tubes
ref: Engineering Databook III by Wolverine Tube, Inc.
Vapor quality to use in calc
x 0.1
Liquid Froude number
2
Massflux N2
Fr L Fr L 0.20728
2
ρ N2_liq g
Tubeinner_dia
IF Fr.L is greater than 0.04 then the following calc applies
calc Shah's C.o factor
1 x
C o
x
0.8
ρ N2_gas
ρ N2_liq
0.5
C o 0.43308
set Shah's N parameter equal to C.o for this method
N
C o
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calc liquid Reynolds number
Massflux N2 1 x Tube inner_dia
Re L Re L 2211.3819
µ N2_l
calc liquid Prandtl number
Cp N2_l µ N2_l
Pr L Pr L 0.86625
k N2_liq
calc liquid phase convective heat transfer coefficient
by Dittus-Boelter correlation
k N2_liq
0.8 0.4
α L 0.023Re L Pr L
α L 300.776
Tube inner_dia
W
m 2 K
calc convective boiling heat transfer coefficient from the
liquid phase convective heat transfer coefficient
α cb
1.8α L
α cb 277.18293
N 0.8
W
m 2 K
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calc the boiling number which characterizes nucleate boiling
B o
Heatflux i
Massflux N2 Hvap N2
B o 0.00094
set appropriate value for Shah's F.s constant
F s 15.43
F.s equals 14.7 when B.o is greater than 0.0011
F.s equals 15.43 when B.o is less than 0.0011
calc the nucleate boiling heat transfer coefficient
α nb
0.5
α L F s B o exp 2.74N
0.15
α nb 401.84662
W
m 2 K
the two phase flow boiling heat transfer coefficient is taken
as the larger valve of conventive boiling or nucleate boiling
α tp
max α cb α nb
α tp 401.84662
W
m 2 K
The Steiner and Taborek (1992) database has the nucleate boiling heat transfer
coefficient for Nitrogen as 4380 W/m2-K.
The literature value used, 1500 W/m2-K for Nitrogen boiling falls within between
the conservative estimate and the database value of Steiner and Taborek. The
values uses is not too conservative and not too aggressive.
ref: Engineering Data Book III, Wolverine Tube, Inc.
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