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Altitude CorrectionsAltitude Corrections
© 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary© 2010 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary
Overview
Introduction
• Air properties with elevation
• Fan laws
• System impedance, fan curves, operating points
• Thermal aspects
Case Study: Heat sink modeling at high altitudes with Icepak p
Summary
© 2010 ANSYS, Inc. All rights reserved. 2 ANSYS, Inc. Proprietary
Introduction
• Air properties vary with altitude:• Density of air decreases with increasing altitudey g
• Ambient air temperature decreases with increasing altitude
201.4
0
10
C
1
1.2
m3
−30
−20
−10
Temperature
0.6
0.8
Density kg/m
60
−50
−40
0
0.2
0.4
© 2010 ANSYS, Inc. All rights reserved. 3 ANSYS, Inc. Proprietary
0 0.5 1 1.5 2 2.5 3 3.5
x 104
−60
Height m0 0.5 1 1.5 2 2.5 3 3.5
x 104
0
Height m
The Effects of Altitude
Air density varies with altitude
Ai d it d ith ltit d• Air density decreases with altitude– Use of larger fans at higher altitudes may be required.
• Heat transfer rate is proportional to the air mass flow rate • Heat transfer rate is proportional to the air mass flow rate (decreasing with altitude).
Air temperature decreases with altitudeAir temperature decreases with altitude
• The density may actually increase within the first 10K ft. • The drop in temperature with altitude tends to increase the air
density; however, this effect is secondary.
The density of air at very high altitudes (e.g. >50K ft) is very low (much less air available for cooling)
© 2010 ANSYS, Inc. All rights reserved. 4 ANSYS, Inc. Proprietary
low (much less air available for cooling)
Fan Laws
Fan air speed proportional to rotational speed, ω
22 ωv
1
2
1
2
ωω
=vv
Pressure increase across fan is directly proportional to air density
vv
PPρvΔP ==
ΔΔ
≈ 211
222
211
222
1
22 ;ωρωρ
ρρ
AvQ =11111 ρρ
© 2010 ANSYS, Inc. All rights reserved. 5 ANSYS, Inc. Proprietary
Altitude Compensating Fans
Fan can be classified into two types:
(1) Typical (ω constant with elevation)
G Altit d ti f
(2) Altitude compensating (ω increases with elevation)
Generic fan Altitude compensating fan
Fan performance affected less for
© 2010 ANSYS, Inc. All rights reserved. 6 ANSYS, Inc. Proprietary
Fan performance affected less for altitude compensating fansΔP ~ reduction in density
Source: Belady, 1996
System Impedance: Flow Regime
Laminar flow( P i i t
Turbulent flow(∆P decreases with elevation)
(∆P invariant with elevation )
elevation)
• Not a function of density, ρ;
Laminar flowSource: Belady, 1996
CvΔP ≈y ρ
• Usually varies linearly with v
Turbulent flow
© 2010 ANSYS, Inc. All rights reserved. 7 ANSYS, Inc. Proprietary
2ρvΔP ≈• Linear variation with density, ρ;
• Usually quadratic variation with v
System Impedance
Turbulent Laminar
Source: Belady, 1996
Mixed flow
© 2010 ANSYS, Inc. All rights reserved. 8 ANSYS, Inc. Proprietary
Operating Point: Turbulent Flow
o Elevation affects
• Fan performanceFan performance.• System impedance.
o Fan Performance
• The volume flow rate stays almost yunchanged at higher elevations, but the resulting mass flow rate drops due to lower density. 2ρvΔP ≈
o System Impedance
• Lower density leads to lower Re at higher elevations due to lower density.
P tt ti t fl i t hi h l ti i ll t b l t fl t
© 2010 ANSYS, Inc. All rights reserved. 9 ANSYS, Inc. Proprietary
• Pay attention to flow regime at higher elevations as marginally turbulent flow at sea level may transition to laminar regime with elevation.
Operating Point: Laminar Flow
Laminar Mixed
Laminar Flows:
o Volume flow rate and mass flow rate decrease faster than turbulent flows (both velocity and density decrease).
Mixed Flows:
© 2010 ANSYS, Inc. All rights reserved. 10 ANSYS, Inc. Proprietary
o The flow behavior is intermediate between those of laminar and turbulent flows.
Impedance Coefficient
mPP c
vPc −∝
Δ=
2Re , 1 ρ
mmv
PP
v−−
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=
ΔΔ
2
2
1
22
2
ρ
ρ
m
PP
vP−
⎥⎦
⎤⎢⎣
⎡≈
ΔΔ
⎥⎦
⎢⎣
⎥⎦
⎢⎣Δ
1
22
111
:flowsTurbulent ρ
ρ
Pressure drop is a function of density and velocity.
P ⎥⎦
⎢⎣Δ 11 ρ
p y y
For turbulent flows, pressure drop is a function of density only.
© 2010 ANSYS, Inc. All rights reserved. 11 ANSYS, Inc. Proprietary
m may be a function of altitude or constant but it is system dependent.
Procedure to Determine m
1 Determine the impedance coefficient at the sea level for 1. Determine the impedance coefficient at the sea level for u=0..umax
2. Determine m
3. Repeat step1 for a different altitude, alt14. Determine m for alt15. Check if m’s determined at step2 and step4 are equal
6. If different, determine m as a function of altitude
© 2010 ANSYS, Inc. All rights reserved. 12 ANSYS, Inc. Proprietary
Thermal Aspects
( )QTTQT /ΔΔΔ&
• Conservation of energy:
( )ppp QcqTTQcTcmq ρρ /; =ΔΔ=Δ=
• Elevation ↑, volume flow rate • remains the same for turbulent flow • remains the same for turbulent flow • decreases for laminar flow
• For a given q, • ∆T increases for turbulent flow as ρ decreases • ∆T increases for turbulent flow, as ρ decreases. • ∆T increases even more for laminar flow as both ρ and Q
decrease.
( );airs TThAq −=
• Heat transfer coefficient:
© 2010 ANSYS, Inc. All rights reserved. 13 ANSYS, Inc. Proprietary
khLNu /=h prescribed using
Heat Transfer: Flat Plate
nn vhCNu ⎥
⎤⎢⎡
=≈ 222;Re ρxx vh
CNu ⎥⎦
⎢⎣ 111
;Reρ
• Laminar flow over a flat plate
( ) 2/1
3/12/1 PrRe332.0/
vh
kxhNu
x
xxx
ρ∝
==
• Turbulent flow over a flat plate
5/45/4
3/15/4
)(
PrRe0296.0
ρρ ∝∝
=
vh
Nu
x
xx
© 2010 ANSYS, Inc. All rights reserved. 14 ANSYS, Inc. Proprietary
System Modeling at High Altitudes with Icepako Use the appropriate air densityo Flow regime:
Icepak
• Flow regime might change with elevation• Make the necessary changes in the flow field, e.g. use fluid blocks in
potentially laminar flow areas
o Fan curve modification:• multiply pressure drop by the density ratio (high altitude density / sea level
density) for standard fandensity), for standard fan.• Account for changes in the rotational speed of the fan (if any)
o Use proper temperature for the ambient air (if required)o Use proper temperature for the ambient air (if required)o Use proper operating pressure (for simulations with ideal gas
assumptions)
© 2010 ANSYS, Inc. All rights reserved. 15 ANSYS, Inc. Proprietary
Resistance at High Altitudes
11
Most generally, the relationship between the pressure drop and the velocity is given as:
43421321termquadratic
q
termlinear
l vkvkP 2
21
21 ρρ +=Δ
• Linear term dominant for low speed flows
kl: linear loss coefficientkq: quadratic loss coefficient
• Quadratic term dominant for high speed flows,
• In general, both terms play a role in the pressure drop across systems.
• If a quadratic relationship exists for a resistance element at sea level for (very) low speed flows, it may not be applicable at very high altitudes.
• Try defining the ΔP vs. speed relationship as a combination of linear and d ti t
© 2010 ANSYS, Inc. All rights reserved. 16 ANSYS, Inc. Proprietary
quadratic terms.
Case Study: Heat sink modeling at high altitudes
•Extruded Aluminum HS
•53 fins, 0.025 in thick1000 W
altitudes
•0.3 in base thick.
•No side/top by-pass
1000 W source underneath the HS
Across = 7.825 in * 1.0 in
altitudeft20Kat them/s220SL at the m/s 180
−=−=in
uu
Average inlet velocity
© 2010 ANSYS, Inc. All rights reserved. 17 ANSYS, Inc. Proprietary
altitudeft 50K at the m/s 400altitudeft 20K at them/s220
−==
in
in
uuAverage inlet velocity
Case Study: Heat sink modeling at high altitudes
Re’s based on hydraulic diameterSea Level
u (m/s) CFM ufin(m/s) Re(fin) Re(ch)
altitudes
Cabinet : LaminarHeat sink : Laminar
0 0 0 0 0
0.1 1.069691 0.172 58.64789 284.6739
0.2 2.139382 0.344 117.2958 569.3478
0.3 3.209073 0.516 175.9437 854.0217
Cabinet : TurbulentH t i k L i
0.5 5.348455 0.86 293.2394 1423.37
0.75 8.022683 1.29 439.8592 2135.054
1 10.69691 1.72 586.4789 2846.739
1.25 13.37114 2.15 733.0986 3558.424
Heat sink : Laminar1.5 16.04537 2.58 879.7183 4270.109
2 21.39382 3.44 1172.958 5693.478
3 32.09073 5.16 1759.437 8540.217
4.5 48.1361 7.74 2639.155 12810.33
Cabinet : TurbulentHeat sink : Turbulent
6 64.18146 10.32 3518.873 17080.43
7.5 80.22683 12.9 4398.592 21350.54
9 96.27219 15.48 5278.31 25620.65
12 128.3629 20.64 7037.746 34160.87
© 2010 ANSYS, Inc. All rights reserved. 18 ANSYS, Inc. Proprietary
15 160.4537 25.8 8797.183 42701.09
18 192.5444 30.96 10556.62 51241.3
Case Study: Heat sink modeling at high altitudes
20000 feetu (m/s) CFM ufin(m/s) Re(fin) Re(ch)
0 0 0 0 0
Re’s based on hydraulic diameter
(viscosity decreases with altitude)
altitudes
Cabinet : LaminarH t i k L i
0.1 1.069691 0.172 32.4478 157.5
0.2 2.139382 0.344 64.8956 315
0.3 3.209073 0.516 97.3434 472.5
0.5 5.348455 0.86 162.239 787.5
Heat sink : Laminar0.75 8.022683 1.29 243.3585 1181.25
1 10.69691 1.72 324.478 1575
1.25 13.37114 2.15 405.5975 1968.75
1.5 16.04537 2.58 486.717 2362.5
Cabinet : TurbulentHeat sink : Laminar
2 21.39382 3.44 648.956 3150
2.5 26.74228 4.3 811.195 3937.5
3 32.09073 5.16 973.434 4725
4.5 48.1361 7.74 1460.151 7087.5
Cabinet : Turbulent
6 64.18146 10.32 1946.868 9450
7.5 80.22683 12.9 2433.585 11812.5
9 96.27219 15.48 2920.302 14175
12 128.3629 20.64 3893.736 18900
© 2010 ANSYS, Inc. All rights reserved. 19 ANSYS, Inc. Proprietary
Heat sink : Turbulent15 160.4537 25.8 4867.17 23625
18 192.5444 30.96 5840.604 28350
22 235.332 37.84 7138.516 34650
Case Study: Heat sink modeling at high altitudes
Re’s based on hydraulic diameter
(viscosity decreases with altitude)50000 feet
u (m/s) CFM ufin(m/s) Re(fin) Re(ch)
0 0 0 0 0
altitudes
Cabinet : Laminar
0 0 0 0 0
0.5 5.348455 0.86 46.68044 226.5845
1 10.69691 1.72 93.36087 453.169
1.5 16.04537 2.58 140.0413 679.7535
2 21.39382 3.44 186.7217 906.338
Heat sink : Laminar3938 3 86 906 338
2.5 26.74228 4.3 233.4022 1132.923
3 32.09073 5.16 280.0826 1359.507
4 42.78764 6.88 373.4435 1812.676
5 53.48455 8.6 466.8044 2265.845
Cabinet : TurbulentHeat sink : Laminar
6 64.18146 10.32 560.1652 2719.014
8 85.57528 13.76 746.887 3625.352
10 106.9691 17.2 933.6087 4531.69
12 128.3629 20.64 1120.33 5438.028
14 149.7567 24.08 1307.052 6344.366
17 181.8475 29.24 1587.135 7703.873
20 213.9382 34.4 1867.217 9063.38
24 256.7258 41.28 2240.661 10876.06
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Cabinet : TurbulentHeat sink : Turbulent
28 299.5135 48.16 2614.104 12688.73
34 363.6949 58.48 3174.27 15407.75
40 427.8764 68.8 3734.435 18126.76
Case Study: Operating Point
6
7
•Fan curves modified Increasing altitude
Operating points
4
5
.w.g
.)
with density ratio•Flow tends to be more laminar with altitude
2
3P (in
SL DP
20K DP
(turbulent flow at SL may become laminar at a certain altitude)
0
1
0 50 100 150 200 250 300
50K DP
SL Fan
20K Fan
50K Fan
O ti i tQ (CFM)
TurbulentTurbulent100.852.46
Heat SinkCabinetQ(CFM)P (in.w.g.)
TurbulentTurbulent100.852.46
Heat SinkCabinetQ(CFM)P (in.w.g.)
Operating points
Sea level
© 2010 ANSYS, Inc. All rights reserved. 21 ANSYS, Inc. Proprietary
LaminarTurbulent *78.260.373
Turbulent *Turbulent84.181.44
LaminarTurbulent *78.260.373
Turbulent *Turbulent84.181.4420K ft
50K ft
Case Study: Determining m
0.35
0.40
SL-120K-1
0.25
0.3050KSL-220K-250K-2Power (50K)
y = 12.145x-0.9067
R2 = 0.9982
y = 3.5421x-0.6261
R2 = 0.9950.10
0.15
0.20cp
Power (50K)Power (SL-2)
0.00
0.05
0.10
0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 10 0 11 00.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0
Re_fin/1000
2000Re if 91.0 <= finm • Laminar flow ~ v, Turbulent flow ~ρ, v
© 2010 ANSYS, Inc. All rights reserved. 22 ANSYS, Inc. Proprietary
2000Re if 63.0 >= fin
fin
m • m is
• a function of Refin
• invariant with altitude
Case Study: Heat Transfer
Density(kg/m3) Density ratio mo *1000 (kg/s) mo ratio Ts,max (C) ΔT (C)
Sea level 1.164 1 55.4 1 48.5 28.5
20K ft 0.56 0.481 22.25 0.402 75.6 55.6
50K ft 0.143 0.123 5.28 0.095 217.1 197.1
Turbulent *Turbulent84.181.44
TurbulentTurbulent100.852.46
Heat SinkCabinetQ(CFM)P (in.w.g.)
Turbulent *Turbulent84.181.44
TurbulentTurbulent100.852.46
Heat SinkCabinetQ(CFM)P (in.w.g.)n
nx v
vhhCNu ⎥
⎦
⎤⎢⎣
⎡=≈
11
22
1
2;Reρρ
LaminarTurbulent *78.260.373 LaminarTurbulent *78.260.373⎦⎣ 111 ρ
• Following steps similar to those to determine m, n can be determinedg p
• At 20K ft altitude:
• Air density decreases by 52%, mdot decreases by 60%
• Flat plate HTC degraded by 45 3% (case study heat sink HTC
© 2010 ANSYS, Inc. All rights reserved. 23 ANSYS, Inc. Proprietary
• Flat plate HTC degraded by 45.3% (case study heat sink HTC degraded by 51%)
Summary
• Flow regime in a system may change due to the drop in density (air flow tends to be more laminar at higher altitudes)
• P d i f ti f• Pressure drop is a function of• density only for turbulent flows• velocity and density for laminar flows
• P l ffi i t d • Power law coefficients, m and n• system dependent• can be estimated
• O ll h t t f ffi i t d d t hi h ltit d t b bl • Overall heat transfer coefficient decreases due to high altitude, most probably less than the density ratio• in typical electronics cooling applications, the decrease in heat transfer coefficient
due to high altitude of 10,000 ft above sea level is about 20-25% whereas this decrease is 45-50% at 20000 ft.
• The percent degradation in junction temperatures is likely to be less, as the overall thermal resistance also includes conduction resistance inside the solid (which is
© 2010 ANSYS, Inc. All rights reserved. 24 ANSYS, Inc. Proprietary
invariant with altitude)