L
length of the rotor of the centrifuge, m
n
revolutions per minute, rpm
p
pressure, Pa (N m-2)
pc permeability,
m2
rbowl
bowl radius, m
rweir
weir radius, m
rboundary layer
radius of boundary layer, m
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Si
sink term, N m-3
t
time, s
u
velocity in x direction, m s-1
v
velocity in y direction, m s-1
vax
axial velocity, m s-1
v velocity,
m
s-1
w
velocity in z direction, m s-1
x
particle diameter, m
xcell
cell length, m
y+
characteristic width of viscous sublayer, dimensionless
Greek letters
α
volume fraction, dimensionless
δ
thickness of the axial boundary layer, mm
δn
normal overlap, m
δt
tangential overlap, m
ε
turbulent kinetic energy dissipation rate, m2 s-3
εs sediment
porosity,
dimensionless
µ
dynamic viscosity, kg m-1 s-1
µt
turbulent viscosity, kg m-1 s-1
density, kg m-3
s
solids density, kg m-3
density difference between liquid and solid, kg m-3
τt
turbulent stress tensor, Pa (N m-2)
τw
wall shear stress, Pa (N m-2)
i Poissons
ratio,
dimensionless
specific turbulent kinetic energy dissipation rate, s-1
Indices
‘
fluctuating component of a variable
q
phase
Abbreviations
LES
large-eddy simulation
RBR
rigid body rotation
RSM
Reynolds Stress Model
VOF
Volume of Fluid
St
Stokes number
10. Acknowledgments
We acknowledge support by Deutsche Forschungsgemeinschaft and Open Access
Publishing Fund of Karlsruhe Institute of Technology.
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7
CFD and Thermography Techniques
Applied in Cooling Systems Designs
Samuel Santos Borges and Cassiano Antunes Cezario
Research and Technological Innovation Department, WEG
Brazil
1. Introduction
The focus of this work consists in optimizing the water flow inside a water cooled electric
motor frame, aiming at the maximization of the power/frame size ratio, the minimization of
pressure drop and the avoidance of hot spots. For the development of this work
computational fluid dynamics (CFD) and thermography techniques were used.
For many years water cooled electric motors have been used by industry, especially in
specific applications that require features that can not be provided by conventional fan
cooled motors. Among theses features are a better power/frame size relation, low noise
levels, enclose applications, among others.
Cooling by means of water circulation is frequently used in large motors, typically frame
sizes above IEC 315. A justification for this practice not to be widely used in smaller motors is its higher cost compared to air cooling systems. However, provided that it presents some
technical and/or economical viability, water cooling can also be used in smaller frame sizes.
The technological progress have resulted in the development of new tools that facilitate the study of this motor type, such as the computational fluid dynamics and the thermography
techniques, which consist, respectively, in the use of numeric models applied to fluid
mechanics and the obtaining of the motor surface temperature distribution.
2. Benefits and drawbacks
The following advantages and disadvantages of this kind of motor can be mentioned, in
comparison with air cooled motors.
2.1 Advantages
Greater power/frame size ratio;
Lower noise level;
Higher efficiency;
The outside waste deposit on the frame does not damage the motor cooling;
No problems with waste deposit on the external fan blade;
It can be used in totally enclosure environment;
The heat removed from the motor is not directly dissipated into the environment;
Possibility of using the same cooling fluid of the load and/or machine where it is
installed;
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Applied Computational Fluid Dynamics
Better resistance to local impact.
2.2 Disadvantages
Higher manufacturing cost;
Auxiliary system to provide water;
Need to control the water chemical composition;
Risk of corrosion inside of the water circuit;
Risk of fouling in the water circuit;
Risk of leaks;
More precautions on maintenance.
3. Fundamental concepts
3.1 Cooling system
The cooling systems are apparatus usually comprised of several components that interact to
keep the temperature of machines and systems in general controlled in order not to exceed
the limits imposed by quality, safety, performance and/or efficiency. For instance, systems
such as internal combustion engines, turbines, compressors, bearings, electric machines,
electronic structures, electrical conductors, chemical and welding processes, among many
others, can be mentioned as some examples of systems comprising thermal restrictions.
Consequently, the cooling systems are very important to industries and should therefore be
designed to keep a good performance and reliability.
The more commonly used coolants are gases and liquids. Among them, due to their wide
occurrence, low cost and practicality, air and water are customarily employed. They can be
used in many different ways: in direct or indirect contact with the systems, by means of one or more fluid combinations, separated or mixed. And they can be forcedly or naturally moved,
by physical mechanisms respectively known as forced convection and natural convection.
3.2 Heat transfer
Heat transfer concerns the exchange of thermal energy from one region of higher
temperature to another of lower temperature in one or more means. This exchange occurs
by mechanisms as conduction, convection, radiation and phase-change.
3.2.1 Conduction
The conduction occurs due to interactions between the particles of fluids. Thermal
insulation, tanks, plates and ducts walls, fins, and others are examples of devices that
exchange heat by conduction. It is described by Fourier’s Law and the following equation:
T
q
k
kA
(1)
n
Where,
qk: Heat flux of conduction;
K: Thermal conductivity;
A: Heat transfer area;
T
: Temperature gradient;
n: Direction.
CFD and Thermography Techniques Applied in Cooling Systems Designs
137
3.2.2 Convection
The convection is the heat transfer between a solid surface and a moving fluid. This
phenomenon can be natural, induced by density difference (low fluid velocity), or forced,
customarily supplied by fans or pumps (high fluid velocity).
q h (
A T T)
h
s
(2)
Where,
qh: Heat flux of convection;
h: Convection coefficient;
A: Heat transfer area;
Ts: Surface temperature;
T∞: Fluid temperature.
3.2.3 Radiation
The thermal radiation is provided by electromagnetic waves emission. The classic example
of this phenomenon is the heat transfer between sun and earth. It is given by Stefan-
Boltzmann Law.
4
4
q (
1
T
2
T )
r
(3)
Where,
qr: Heat flux of radiation;
ε: Emissivity;
σ: Stefan-Boltzmann constant;
T1, T2: Surface temperatures.
3.2.4 Phase – Change
It is boiling, condensation, freezing and melting. These processes are given by following
equations.
Q .
m H
(4)
Where,
Q: Amount of heat;
m: Mass;
ΔH: Specific latent heat.
3.2.5 Heat transfer in conduits
In the heat transfer in the fluid flowing in a conduit, the temperature is neither uniform in the fluid flow direction nor in the heat flux direction. Therefore, the bulk temperature is
assumed as reference temperature. The use of a temperature reference allows to execute the
heat balance in steady state. In this case, the transferred heat per time unit is a direct
measure of the bulk temperature difference between two conduit sections. That is,
q .
m c .
p
b
T (5)
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Applied Computational Fluid Dynamics
Where,
q: Amount of heat per time unit;
m : Mass flow rate;
cp: Specific heat of fluid;
ΔTb: Bulk temperature difference of fluid among two conduit sections.
3.3 Fluid dynamics
3.3.1 Mass flow rate
The mass flow rate is given by the mass of fluid which passes through a surface per time
unit and can be calculated from the following equation:
m . .
v A (6)
Where,
m : Mass flow rate;
ρ: Fluid density;
v: Mean velocity in the section;
A: Area of conduit section.
3.3.2 Pressure drop
The pressure drop in pipes may be occasioned by means of:
Localized drops (valves, curves, and others);
Friction;
Difference of piping height.
The pressure drop is obtained as a function of Reynolds number, which depends on the
flu