Mathcad - 240W 1meter long stave4.9mm flat tubegilg/ATLASUpgradeRandD/240W_1meter long st… ·...
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W.MilleriTi
Pressure Drop in a 4.9mm OD Slightly Flatten Tube
LBNL-ATLAS
Reference: Boiling and Condensation and Gas-Liquid Flow, Whalley
Frictional Pressure Drop Analysis-Stave Barrel C3F8, Quality of 5% after injection using Friedelcorrelation
mbar 10 3 bar:= Pa 10 6 Pa:= kJ 1000J:=
Q 240W:= L1 2m:= tube length, round trip t .012in:=
ch 4.9mm 2 t:= cr4.92
mm t:= wc 2mm:= Ac wc ch cr2
+:=
Pc 2 wc 2 cr+:= Dh 4AcPc:= Dh 5.272mm= At Ac:=
C3F8 Fluid Properties at -25C
Ti 273.15 25( )K:= Ti 248.15 K= v 10.28Pa s:= liq 267.5Pa s:=
cliq 1019J
kg K:= liq 1565
kg
m3:= v 16.39
kg
m3:=
kv 0.009W
m K:= kliq 0.053
Wm K
:= .015Nm
:= perfluoropropane surfacetension at 253.15K
hliq 173.7kJkg
:= hv 275.6kJkg
:= h hv hliq:= h 101.9kJkg
= h:=
Tube Fluid Parameters, based on inlet and exit flow quality
x .05:= xo .85:= mdotQ
xo x( ) h:= mdot 2.944 10 3
kgs
= liqliqliq
:=
Gliq mdot 1 x( ):= Gliq 2.797 103
kgs
= Gv mdot Gliq:= Gv 1.472 104
kgs
=
Gtmdot 2
At:= Rliq
Gt Dh
liq:= Rliq 5.037 10
3=
RfgoGt Dh
v:= Rfgo 1.311 10
5= Cfgo 0.079 Rfgo
0.25:= Cfgo 4.152 10
3=
RfloGt Dh
liq:= Rflo 5.037 10
3= Cflo 0.079 Rflo
0.25:= Cflo 9.377 10
3=
22=E
3.24 F2 Hf
Fr( )0.045 We( )0.035+ basic equation for two phase flow correction to single
phase flow pressure drop
240W_1meter long stave4.9mm_flat_tube.xmcd
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W.MilleriTi
Pressure Drop in a 4.9mm OD Slightly Flatten Tube
LBNL-ATLAS
a1liq Cfgo
v Cflo:= a1 42.277= b1
Gt2 Dh
:= d1
Gt2
g Dh:=
Hfliqv
0.91vliq
0.19
1vliq
0.7
:= Hf 33.183=
We b1xv
1 xliq
+
:= Fr d1xv
1 xliq
+
2:= F2 x0.78 1 x( )0.224:= E 1 x( )2 x2 a1+:=
z 1 x( )2 x2 a1( )+3.24 x0.78 1 x( )0.224 Hf
d1xv
1 xliq
+
2
0.045
b1xv
1 xliq
+
0.035
+:= to be integrated over tubelength
dpdzlo2 Cflo Gt
2
Dh liq:= frictional pressure drop based on fluid being solely single phase
Pf dpdzloL1
0.85 0.05
0.05
0.85
x1 x( )2 x2 a1( )+3.24 x0.78 1 x( )0.224 Hf
d1xv
1 xliq
+
2
0.045
b1xv
1 xliq
+
0.035
+
d:=
Pf 1.13 104
Pa= Pf 113.045mbar=
0.05
0.85
x1 x( )2 x2 a1( )+3.24 x0.78 1 x( )0.224 Hf
d1xv
1 xliq
+
2
0.045
b1xv
1 xliq
+
0.035
+
d 30.455=
this is the correction for the two phase flow, as a multiplier
240W_1meter long stave4.9mm_flat_tube.xmcd
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W.MilleriTi
Pressure Drop in a 4.9mm OD Slightly Flatten Tube
LBNL-ATLAS
Reference: Evaporative Cooling-Conceptual Design for ATLAS SCT, T.O. Niinikoski
Pressure drop due to momentum transfer , inlet to outlet, Pm=mmdot2/(At2liq)
xin 0.05:= xout 0.85:=
hixinv
1 xin
liq+
1
:= homogeneous flow density hi 273.398kg
m3= at inlet
liqhi
5.724=vhi
0.06= volume fraction of constituents at the inlet
hoxoutv
1 xout
liq+
1
:= homogeneous flow density ho 19.247kg
m3= at outlet
Relative volume fraction of liquid and vapor phases at the inlet and exit
jinxin mdot
v At
1 xin( ) mdotliq At
+:= jin 0.467ms
= total volume flux at inlet
joxo mdot
v At
1 xo( ) mdotliq At
+:= jo 6.64ms
= total volume flux at exit
jvinxin
xin 1 xin( )vliq+
:= jvin 0.834= volume fraction of vapor at inlet
jliqin 1 jvin:= jliqin 0.166= volume fraction of liquid at inlet
jvoxo
xo 1 xo( )vliq+
:= jvo 0.998= volume fraction of vapor at inlet
jliqo 1 jvo:= jliqo 1.845 103
= volume fraction of liquid at inlet
240W_1meter long stave4.9mm_flat_tube.xmcd
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W.MilleriTi
Pressure Drop in a 4.9mm OD Slightly Flatten Tube
LBNL-ATLAS
m1 xo( )2
jliqo
1 xin( )2jliqin
xo
2
jvo
xin2
jvin
liqv
+:= m 75.588=
Pressure difference to momentum change Pm
Pm mmdot2
At2liq
:= Pm 7.888mbar=
Total Pressure Drop P Pf Pm+:= P 120.933mbar=
240W_1meter long stave4.9mm_flat_tube.xmcd
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