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L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 1
Heat dissipation
Life span of the electrical machines
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Forced cooling• Cooling channel
– 236 mm long 1 mm wide– 1.5 mm parallel plates
• Convection – 140-160 W/m2K– Empiric vs FEM
• Flow rate– Previous
1-8 m3/min• Temperature
– 2D FEM conjugate heat transfer
– P/Q=constant for out=100oC
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PreviouslyEnergy loss in electriccircuitsqe=ρJ2
Energy loss in magnetic circuitsqΦ=ChB2f+Ce(Bf)2
Energy loss in mechanic circuitsqω=
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NextConductioncooling
Convectioncooling
Radiativecooling
Thermal
circu
it an
d th
ermal
desi
gn
Hea
t sou
rces,
hea
t sin
ks an
dhe
at fl
ow.
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 2
Avo R Design of Electrical Machines 5
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nContent
• Heat transfer (transport) vs heat and mass transfer– Conduction– Convection and advection – Radiation
• Temperature distribution and limitations– Insulation systems and realisations
• Thermal design– Coolant and cooling ducts– Conduction vs convection
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Equivalent circuit relations
P=Q·R
G=·A/l
Q=v·A
P=·l
Cooling circuit
=Q·RN·I=Φ·RU=I·ROhm’s Law
G=λ·A/lG=μ·A/lG=γ·A/lConductive element
Q=q·AΦ=B·AI=J·AFlow
=G·lN·I=H·lU=E·lPotential
Thermal circuit
Magnetic circuit
Electrical circuitRelation
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Thermal conductivity
• Conduction is heat transfer by diffusion in a stationary medium due to a temperature gradient. The medium can be a solid, a liquid or gas
• Diffusion through the substance
x
1
2
λ Q
A l
21
21
lAQ
lAQ
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Thermal conductivity
10SmCo
9NdFeB0.2Avg.ins.system
200-220Aluminum0.64Bonding epoxy
360Copper0.4-0.6Mica
20-40Laminated iron0.12Kapton
25-30Stainless-steel0.11Nomex
40-46Cast iron0.025-0.035Air
λ [W/mK]Materialλ [W/mK]Material
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 3
Avo R Design of Electrical Machines 9
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nConvection
ambn hknq
• Convection is heat transfer between either a hot surface and a cold moving fluid or a cold surface and a hot moving fluid. Convection occurs in liquids and gases
• Movement of the substance
x
1
2
α1
Q
A
amb
hot
α2
l
ambhot
amb
lAQ
AQ
21
22
11
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Transport of heatQ - the required flow rate, m3/s, Ph - required cooling power, W, ρ - the density of the heat carrier, kg/m3, c - the specific heat capacity, J/kg°C, Δ - the temperature difference between incoming and outgoing temperature °C
Natural convection
Forced cooled plane surface by air speed v
Empirical cooling capability
cP
Q h
2255mK
W
78.06.0208.7 v
25.21mkW
AP
cool
loss
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High Performance Cooling
• Electronics-cooling.com• Spray and jet cooling, continuous and fluctuating• Single-phase and two-phase flows, phase changing materials• Micro and minicahnnels, higher intensity cooling
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Conjugate heat transfer
dcool
dcond
L Lh
out in
win
cQPcool
cool
heat
hAP
• Heat transfer and pressure dropin the cooling channel is determined by flow
• Flow characterisation– Development: laminar, unstable
or transitional or turbulent– entrance length, – boundary layer
• Dimensionless quantities• Reynolds number characterizes
the flow and Mach number illustrates the compressibility of the flow.
• Flow rate Q [L/min]• Flow speed v=Q/A [m/s]• Re=inertia force / viscous
force
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 4
Avo R Design of Electrical Machines 13
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nEstimation of heat transfer
• The character of flow is described by Reinoldsnumber,
• the heat transfer is expressed by Nusseltnumber
• and the coolant is described by Prandtl number
• The hydraulic diameter is related to the geometric layout of the cooling channel
hin
h DAQvD
1Re
bulkwall
hh k
qDDkhNu
kcpPr
perimeterareaDh
4
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Coolant
• Ideal coolant = high thermal capacity & low viscosity– Hydrogen is used in large turbo generators
• Ability to store and carry heat = mass density times specific heat capacity reduces with temperature
– Coolant steam
Tr OilH20C02H2
200100019141182318, uPas10211168659424162271783326λ,mW/mK8168799469991.361.830.060.080.891.20, kg/m3
2.111.714.254.190.940.8514.514.21.011.00c, kJ/kgK1202012020120201202012020, degC
Air
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Radiation
• Radiation is heat transfer between cooling surface A at temperature 2 and ambience at temperature ambvia electromagnetic waves
amb
ambrad
rad
ambrad
c
AcQ
2
442
2
442
100100
100100
x
1
2
α1
Q
A
amb
hot
α2
l
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Transient heat flow
• Steady state temperature• Heating time constant• Temperature rise during
the transient heating
x
1
α1
A
amb
hot
α2
l
QP QS QD
2
2AdtdcVP
RdtdCP
QQQ
thth
DSP
t
ambmamb
ththth
thm
th
e
AcVRC
APRP
1
2
2
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 5
Avo R Design of Electrical Machines 17
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nTransient heat flow
• Thermal model representing a physical model
• Mathematical formulation• Many simplifications and
approximations• Heat is not internally
generated in the body• Losses are applied to
specific node-point
1 Rth 2
Cth P
2
1
12
121
av
ththth CRCP
dtd
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Heat transfer problem formulation for electrical devices - machines
• Heat sources and sinks • Temperature distribution and limits
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Design target - Thermal limits
• The most critical component in the electrical machine is insulation and temperature dependent is magnet.
• Insulation lifetime is shortened radically if temperature exceeds the limit and that is due to accelerated oxidation process in the insulation material.
• Δ=100K -> ½ lifetimeAvo R Design of Electrical Machines 20
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Temperature dependence
• Materials’ temperature dependence is taken account with material thermal coefficients
coilcoilcoilcoilcoil 00 1
magnmagnBrmagnmagnRRmagn BB 00 1
magnmagnHcmagnmagnCCmagn HH 00 1
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 6
Avo R Design of Electrical Machines 21
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nEvaluation of thermal loading
• Heat transfer– Input: heat sources and
cooling conditions– Outcome: temperature
distribution• Computational tools
– Analytic, empiric, numeric– FEA, CFD, lumped circuits
for heat transfer and fluid flow
• Material characterization• Sub-model validation
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Machine slots
• Total conductor area 225.7 mm2 insulated slot area 508.4 mm2
• Specific conductor losses 4 W/mm3 reduced for winding 1.77 W/mm3
• Slot impregnation 0.21 W/mK selected equivalent thermal conductivity 0.4 W/mK
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Complexity
• Electrical machine is– A complex 3D electromagnetic structure– A complex spatial fluid dynamic structure with cooling
medium
• In order to determine the temperature distribution– A good estimate of losses has to be known– Properties of the cooling process has to be known– The thermal characteristics and properties has to be known
• An optimized thermal design can help increase machine rated power substantially
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Thermal design
• Good estimate of losses –the spatial and temporal distribution of heat sources– Waveform of a loss origin– Distribution of heat sources– Duty cycle – operational
cycle time often muchshorter than thermal time constant
– Short time operation– Intermittent
• Thermal characteristics of materials– Temperature dependence– Temperature limits
• Heat dissipation – thermal circuit and cooling system– Thermal efficiency– Cooling conditions (normal,
forced)• Maximum allowed loading
according to the thermal limits at cooling capability
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 7
Avo R Design of Electrical Machines 25
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nHeat transfer
• Steady state and transient• Heat transfer problem
according to temperature (potential) and heat balance between source, sink and storage
• heat transfer convection-diffusion equation
• incompressible Navier-Stokes equations for fluid dynamics
tcQ
zyx
Qzyx
pzyx
zyx
2
2
2
2
2
2
2
2
2
2
2
2
0
Qckt
c pp u
0
2
u
Fuuuu pt
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Thermal circuit at steady state
• Node points i, Qi [W], i [K]5. Coil loss and temperature4. Tooth loss and temperature6. Yoke loss and temperature7. 8. Ambience temperature
• Thermal conductivity elements Gij [W/K]– From coil to tooth G54
– From coil to yoke G56
– From tooth to yoke G46
– From yoke to ambience G67
cooling
heating
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Equivalent circuit
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Thermal modelling example I
• Determine heat sources – in regions• Specify cooling conditions – over cooling surfaces• Find heat balance i.e. temperature distribution
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 8
Avo R Design of Electrical Machines 29
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nThermal circuit – thermal contacts
• A bad electric conductor is usually also a bad thermal conductor
• No air-gaps in electrical circuit, many air-gaps in thermal circuit
• Thermal contact between stator core and housing– 0.1 mm +5K– 0.2 mm +10K
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Thermal circuit – heat carrier
• Experience from A3 A good electric conductor is usually also a good thermal conductor
• Interested in hotspots: 100% conductor in the middle of winding
• Heat is taken from end-windings: conduction, convection or both
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Thermal model
• Geometry of a PMSM• Material & thermal loading
– Winding– Permanent magnets
• Surface & cooling– Natural convection
• Temperature nodes– Nodes of interest
• Thermal circuits– Heat transfer rather than flow
network• Thermal resistances
– Focus on thermal ”air-gaps”
pm
win
surf
amb
pm
win
surf
amb
mwmwms
mwmwsws
mswswsasa
sasa
kkkkkkkkkk
kk
00
00
pm
win
00
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Model development
• Sorces and loads– Conductor losses– Convection cooling
• 2D heat transfer– Approximate rating– Extraction of elements
• 3D heat transfer– Extrucion from 2D– Focus on end turns
• Heat exchange through end-turns– Thermal conduction
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 9
Avo R Design of Electrical Machines 33
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nThermal modelling example II
• Calculating flux (and current) density waveform • Estimating losses densities in the symmetric part of machine• Calculating temperature distribution according to heat sources and sinks
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Multi-physics → FEM
• Different problems in physics ‘share’ the same geometry
• Calculate for a single element– The variation of loss origin– RMS power loss– MEAN temperature
• A field equation is solved for the finite size of volume
• boundaries suppose to specify a potential (essential), flow naturally given.
N 1 (x 1 ,y 1 )
N 2(x 2 ,y 2 )
N 3 (x 3 ,y 3 )
u 1
u 3
u 5
u 2
u 4
u 6
1
3
2
x
y
fe
cu
ptzyxBptzyxJ
,,,,,,
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Thermal modelling example III
• Directly cooled laminated windings
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Thermal design
0 100 200 300 400 500 600 700 800 900 10000
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flow rate, Q [L/min]
wal
l tem
pera
ture
, ou
t [ C
]
Cooling power, p=cpQ(out-in) [W]
• Peak heat sources– Jm=22.3…28.8 A/mm2
– p=10.0…16.6 W/cm3
– P=2.9 kW• Thermal management
– Limit winding, wall and outlet temperature
– 100 L/min = 1.25 m/s per div
• FEM heat transfer– Contribution from
conduction and natural convection
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 10
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• Ideal coil geometry and cooling conditions• non cooled spots overheated – terminal leads & small cross-section
layers close to the air-gap• cooling intensity -- flow rate -- control over hot-spot temperatures
Heat transfer analysis
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Mapping operation points
• Driving parameters for cooling P=f(out,Q) at in
• Flow (Re) and coolant (Pr) characterization
• Heat transfer – correlations (Nu) and – coefficient h
• Wall and winding temperature• Pressure across cooling channel
– Power for supply• Expected cooling power
P=f(w,Q) at in
0 100 200 300 400 500 600 700 800 900 100020
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outle
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, ou
t [ C
]
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flow rate, Q [L/min]
outle
t tem
pera
ture
, ou
t [ C
]
Reynolds number, Re=2dhQ/(A) [-]
0 100 200 300 400 500 600 700 800 900 100020
40
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200
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6.6
6 .6
6.6
6.8
6.8
6.8
7
7
77.
2
7.2
7.2
7.4
7.4
7.4
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7.6
7.6
7.8
7.8
7.8
8
8
8
8.2
8.28.
48.6
flow rate, Q [L/min]
outle
t tem
pera
ture
, ou
t [ C
]
Nusselts number, Nu=f(Re,Pr) [-]
0 100 200 300 400 500 600 700 800 900 100020
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flow rate, Q [L/min]
outle
t tem
pera
ture
, ou
t [ C
]
Heat transfer coefficient, h=Nu k/Dh [W/(m2K)]
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flow rate, Q [L/min]
outle
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, ou
t [ C
]
Temperature across boundary, Pcool/(hAcool) [C]
0 100 200 300 400 500 600 700 800 900 100020
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20002 0 00
40 00400 0
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flow rate, Q [L/min]
outle
t tem
pera
ture
, ou
t [ C
]
Pressure drop, dP [Pa]
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flow rate, Q [L/min]
outle
t tem
pera
ture
, ou
t [ C
]
Ideal cooling supply power, dPQ [-]
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flow rate, Q [L/min]
wal
l tem
pera
ture
, ou
t [ C
]
Cooling power, p=cpQ(out-in) [W]
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7kW@120oC&4m3/min
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t tem
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, ou
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]
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flow rate, Q [L/min]
cooling power, p=cpQ(out-in) [W]
0 1000 2000 3000 4000 5000 6000 7000 80000.2
0.4
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1
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2
chan
nel h
eigh
t, d
[mm
]
500500
500
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1000
100 0
1 50 0
15001500
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25002500
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flow rate, Q [L/min]
Reynolds number, Re=2dhQ/(A) [-]
0 1000 2000 3000 4000 5000 6000 7000 80000.2
0.4
0.6
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1
1.2
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2
chan
nel h
eigh
t, d
[mm
]
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8
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flow rate, Q [L/min]
Nusselts number, Nu=f(Re,Pr) [-]
0 1000 2000 3000 4000 5000 6000 7000 80000.2
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nel h
eigh
t, d
[mm
]
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flow rate, Q [L/min]
heat transfer coefficient, h=Nu k/Dh [W/(m2K)]
0 1000 2000 3000 4000 5000 6000 7000 80000.2
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]
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flow rate, Q [L/min]
temperature drop across boundary layer, Pcool/(hAcool) [K)]
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flow rate, Q [L/min]
pressure drop, dP [Pa]
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0.6
0.8
1
1.2
1.4
1.6
1.8
2
chan
nel h
eigh
t, d
[mm
]
40
40
40
40
100
100
100
100
200
200
200
200
400
400
400
400
10001000
1000
2000
20002000
40004000 4000
1000010000
flow rate, Q [L/min]
ideal cooling supply power, dPQ [-]
Defining designing cooling channels
• Driving parameters for cooling P=f(out,Q) at in
• Flow (Re) and coolant (Pr) characterization
• Heat transfer – correlations (Nu) and – coefficient h
• Wall and winding temperature• Pressure across cooling channel
– Power for supply• Expected cooling power
P=f(w,Q) at in
0 1000 2000 3000 4000 5000 6000 7000 80000.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
chan
nel h
eigh
t, d
[mm
]
130
130
130
130
140
140
140
140
150
150
150
150
160
160
160
170
170
180
190
flow rate, Q [L/min]
winding temperature, Tw =Tout+Pcool/(hAcool) [C]
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Parallel plates, laminar flow, …• Narrow cooling channels allow higher surface speed, thus higher
cooling capability for the same flow rate • Narrow channels results higher pressure drop and is difficult to secure
in production • Lack of cooling (flow leakage) results high risk for overheating
– Slide sow: L from 25 mm to 200 mm @ 12 m/sL=25 mmc=0.2 mm
L=50 mmc=0.4 mm
L=100 mmc=0.6 mm
L=200 mmc=0.8 mm
L10 – Thermal Design
EIEN20 Design of Electrical Machines, IEA, 2016 11
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nThermal circuit – cooling circuits
• Natural and Forced• Integrated cooling as a
result of machine integrated construction
• Slotted stator operates as a cooling circuit
• Directly cooled heat sources– Cooling ducts, cooling
jackets, cooling channels
• Cooling capability– Maximize the cooling
surface area– Improve cooling medium
parameters and velocity
• Smallest temperature rise is the goal when designing a thermal circuit
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Cooling Concepts• Structure
– Where the energy conversion, heat transfer and temperature drop (Δ)takes place
• Heat sources– Energy converted to heat
• Cooling sources– Heat dissipation
• Cooling concepts – arrangement of heating and
cooling sources– Indirect Cooling (high Δ)– Direct cooling (low Δ)
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Summary
• Thermal constrains and dependences
• Thermal circuits, heat sources and cooling options
• Heat transfer model and modelling
• Learning skills from the assignments