A short introduction to Fluid Dynamics , Heat Transfer and CFD
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description
A short introduction to Fluid Dynamics , Heat Transfer and CFD. Outline. Fluid Dynamics Heat Transfer CFD . Outline. Fluid Dynamics Heat Transfer CFD. Fluid Dynamics. - PowerPoint PPT Presentation
Transcript of A short introduction to Fluid Dynamics , Heat Transfer and CFD
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Fluid Dynamics
Study of fluids in motion, including aerodynamics, i.e. the study of gases (internal and external), and hydrodynamics, i.e. the study of liquids.
A fluid dynamical problem involves calculation of fluid properties, such as velocity, pressure, density and temperature A set of governing equations (conservation laws) are solved
using a numerical method (CFD)
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Fluid Dynamics -governing equations-
Based on conservation laws of mass, momentum and energy
Applied on a small fluid element; control volume (CV) Conservation of mass (continuity eqn):
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dSdVt SV
U CV
the rate of change of mass = net flow through the boundaries of the volume
(the control volume is fixed in space)
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Fluid Dynamics -governing equations-
Conservation of momentum (Navier-Stokes):
Substantial derivative: the rate of change of a property (F) for a CV moving with the fluid
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the rate of change of momentum = net force exerted on the volume
dAdvdvDtD
Aij
vv gU
CV
(the control volume moves with the fluid)
jj xFu
tFF
DtD )()()(
substantial or material derivative local or
Eulerian derivativeadvection
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Fluid Dynamics -governing equations-
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continuity equation
i
i
ii
i
j
ij
ii
xu
xxp
xuu
tu
DtDu
Re1
0
i
i
xu
t
Differential form (valid for arbitrary control volume)
momentum equations
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Fluid Dynamics -Reynolds number-
Most important dimensionless number in Fluid dynamics
For low Re-flows stabilizing viscous forces are dominant laminar flow
For high Re-flows inertia forces are dominant flow is unstable / turbulent
Re is used to determine scale similarity in experiments and simulations
forces viscousforces inertialRe
UL U: velocity scale
L: length scale
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Fluid Dynamics -boundary layer-
A thin layer of fluid, adjacent to the bounding surface, where viscosity is dominant
The treatment of the boundary layer is, due to the present physical processes, crucial Strong shear (wall friction) growth of instabilities, production of
turbulence Separation Heat/mass transfer Dissipation
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U=2m/s
U=10m/s
yU
y
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Fluid Dynamics -laminar flow-
Characterizes a flow in parallel layers In laminar flows
High momentum diffusion Low momentum convection U and P independent of time
The boundary layer in laminar flows is smooth
Smooth (weak) boundary layer low wall friction
Low energy level susceptible for adverse pressure gradients easy separation
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Fluid Dynamics -transitional flow-
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Transition from the laminar to the turbulent state
stable flow
unstableflow
turbulentflow
transit
ion
phase
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Fluid Dynamics -turbulent flow-
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Consists of a large number of vortices, i.e. eddies, of various size (scales) in space and time
Turbulent flows are of a random character
Extremely efficient in mixing processes
Nearly all practical flows are of a turbulent character
Turbulence is three-dimensional
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Fluid Dynamics -scales of motion-
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Turbulent flows are non-linear, i.e. there is transformation of information (energy) between different scales
Energy is supplied at the large scales, by the mean flow (production)
By, so-called, vortex stretching energy is transformed into smaller and smaller scales
Finally, at the viscous scales, energy is transformed into heat (dissipation)
Without production the turbulence decays
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Fluid Dynamics -statistical description-
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As turbulence is a non-repeatable random like process, statistical methods are needed to describe the flow
The flow is described by different statistical moments 1st-moment: mean
( ) 2nd-moment (about the mean): variance
( ) 3rd-moment (about the mean):
skewness ( ) 4th-moment (about the mean): kurtosis
( )
kk
k xx /
x2
3
4
n
i ixnx
1
12
std. deviation
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Fluid Dynamics -statistical description-
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0 500 1000 1500 2000 2500 30004
6
8
10
12
14
16
0 500 1000 1500 2000 2500 30004
6
8
10
12
14
16
75.1,10 x 75.1,10 x
63.2,03.0 43 5.1,0 43
Turbulent signal Sinus wave
Probe measurements would identify two identical flows w.r.t. mean and variance (and std. deviation)
Higher order statistics are needed
valu
e
sample sample
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Fluid Dynamics -statistical description-
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4 6 8 10 12 14 160
100
200
300
400
500
4 6 8 10 12 14 160
100
200
300
400
500
Histograms Turbulent signal Sinus wave
“heavy tails”
“high peakedness” symmetric
100
101
102
10310
-6
10-4
10-2
100
102
104
turbulent
sinus
Turbulent: energy concentrated to large scales Sinus: energy “solely” in the dominant frequency
power spectral density
value
sam
ples
value
frequency / wavenumber
psd
/ ene
rgy
Turbulent: distribution close to Gaussian Sinus: distribution heavy in the tails due to the intermittent
“flow character”
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Fluid Dynamics -terminology-
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Vorticity Potential flow Irrotational flow Stokes flow Wake flow Separation
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