3. adv altitude corrections

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


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)


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


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


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


2ρvΔP ≈• Linear variation with density, ρ;

• Usually quadratic variation with v

System Impedance

Turbulent Laminar

Source: Belady, 1996

Mixed flow


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


• 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:


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.


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


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:


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


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)


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


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


altitudeft 50K at the m/s 400altitudeft 20K at them/s220

−==

in

in

uuAverage inlet velocity


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


15 160.4537 25.8 8797.183 42701.09

18 192.5444 30.96 10556.62 51241.3


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


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


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


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.)



Operating points

Sea level


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


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






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


• 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


invariant with altitude)

3. adv altitude corrections

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