Analysis of Solar Hot Water Storage
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Transcript of Analysis of Solar Hot Water Storage
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ACESystems
Analysis of Solar Hot Water StorageBy
Kurt O. Lund
Applied Chemical and Engineering Systems135 Sixth Street, Del Mar, CA 92014
www.acesystems.com
Presented at the COMSOL Users Conference 2006 Las Vegas
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ACESystems
Description All Solar Hot Water Systems Use Storage Tanks. Hot Water From Solar Collector Enters at Top. Tank Water Exits at Bottom. Very Small Flow Rate.
Problem What is the Flow and Temperature Distribution? What is the Outlet Temperature Returning to the Collector? Can a Simple Solution be Derived for Overall Systems?
Approach Determine 2-D Multi-Physics Equations and Parameters. Scale and Solve Model with COMSOL. Simplify for 1-D Time-dependent Model Using PDE Mode. Derive Analytical Approximation for System Use.
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0.1 gpm @ 40 C
40 gal Solar Hot Water Storage Tank
~ 25 C ~
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Basic Axis-symmetric Equations Solved by FEM
0=++
zw
ru
ru
urp
zuw
ruu
tu 20 +
=
+
+
wzpg
zww
rwu
tw 2+
=
+
+
TkzTw
rTu
tTCp
2=
+
+
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ACESystems
**Re
1**
***
***
** 2 u
rp
zuw
ruu
tu
L
+=
+
+
**Re
1**
***
***
** 2 w
zp
zww
rwu
tw
L
+=
+
+
Scaled Isothermal Momentum Equations
(u* = u/U, p* = p/U2, ReL = UL/ 10)
ReL 10Moderately Thin Boundary Layers
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Isothermal Flow Distribution (No Buoyancy)
Central Jet Flow and Driven Circulation
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T [C]0 20 40 60 80 100
[
k
g
/
m
3
]
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0Water Density Correlation
[kg/m3] = 1000 - = 0.0088 T 1.84
Buoyancy Effect
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ACESystems
**Re*
****
***
** 2 u
rp
zuw
ruu
tu
L
+=
+
+
**Re*
*****
***
** 2 w
zp
zww
rwu
tw
L
+=
+
+
TzTw
rTu
tT
L
2*PrRe*
**
**
=
+
+
Scaled Equations with Buoyancy(Buoyancy is Largest Effect)
* = 100 /0 = O(1)p* = 100p/0gL, t* = tg/100U, = 100U2/gL 10-8, ReL = 0UL/ 10
ReL/ 109 VERY Thin Boundary Layers
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Buoyant Flow Distribution
Uniform, 10-5m/s, Downward Flow in Mid Section
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Top-Region Initial Temperatures & Buoyant Flows
Tin = 40 C, T0 = 25 C
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Top-region Temperatures & Buoyant Flows at 60 s
Tin = 40 C, T0 = 25 C
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Top-region Temperatures & Buoyant Flows at 110 s
Temperature Increases Only at Top Boundary
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One-D ModelInlet temperature spreads along top boundary... use one dimensional model with wA = winAin
(w 40 m/s = 14 cm/hr)
2
2
zT
zTw
tT
=
+
Let = (T T0)/(Tin T0), = z/L, = t/tc (tc = L/w 7 hr)
then (, 0) = 1, (0, ) = 0, and
2
2
=
+
where = /wL 0.0035
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Solution of One-D Model
0.050.2
0.4
= 0.6
0.8
1.0
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0+
Analytical Approximation(neglect small diffusion term)
)//()( cttLzFF ==
Translating Front Solution(F = any function)
Time to reach bottom is tb = tc = L/w
