Proveden

1
Computer Fluid Dynamics E181107
2181106
CFD6
Turbulent flows,
Remark foils with black background could be
skipped, they are aimed to the more advanced
courses
Rudolf Žitný, Ústav procesní a zpracovatelské
techniky CVUT FS 2010
Some figures and equations are copied from
Wikipedia
2
Turbulence
CFD6
Source of nonlinearities of NS equations are
inertial and viscous terms
for incompressible fluids the equivalent
conservative form
The convection term is a quadratic function of
velocities source of nonlinearities and
turbulent phenomena
3
Instabilities Rayleigh Benard convection
CFD6
Horizontal liquid layer heated from below is in
still (viscous forces attenuate small
disturbances) until the buoyancy exceeds a
critical level RaL. Then the more or less regular
cells with circulating fluid are formed.
Even if the stability limit was exceeded the flow
pattern is steady and remains laminar. At this
stage the nonlinear convective term is not so
important. Only if RaLgt109 (approximately) eddies
start to be chaotic, velocity fluctuates and the
flow is turbulent.
4
Instabilities Karman vortex street
CFD6
Repeating pattern of swirling vortices caused by
the unsteady separation of flow of a fluid over
bluff bodies. A vortex street will only be
observed above a limiting Re value of about 90.
L
Even if the stability limit was exceeded the flow
pattern is steady and remains laminar.
5
Turbulence
CFD6
Relative magnitude of inertial and viscous terms
is Reynolds number
Increasing Re increases nonlinearity of NS
equations. This nonlinearity leads to sensitivity
of NS solution to flow disturbances.
Laminar flow ReltRecrit Turbulent flow
RegtRecrit
6
Turbulence - fluctuations
CFD6
Turbulence can be defined as a deterministic
chaos. Velocity and pressure fields are
NON-STATIONARY (du/dt is nonzero) even if
flowrate and boundary conditions are constant.
Trajectory of individual particles are extremely
sensitive to initial conditions (even the
particles that are very close at some moment
diverge apart during time evolution). .
Velocities, pressures, temperatures are still
solutions of NS and energy equations, however
they are nonstationary and form chaotically
oscillating vortices (eddies). Time and spatial
profiles of transported properties are
characterized by fluctuations
Actual value at given time and space
Mean value
fluctuation
7
Turbulence - fluctuations
CFD6

• Statistics of turbulent fluctuations
• Mean values (remark
  mean values of fluctuations are zero)
• rms (root mean square)
• Kinetic energy of turbulence
• Intensity of turbulence
• Reynolds stresses

8
Turbulent eddies - scales
CFD6
Kinetic energy of turbulent fluctuations is the
sum of energies of turbulent eddies of different
sizes
Large energetic eddies (size L) break to smaller
eddies. This transformation is not affected by
viscosity
Inertial subrange (inertial effects dominate and
spectral energy depends only upon wavenumber and
?)
Smallest eddies (size is called Kolmogorov scale)
disappear, because kinetic energy is converted to
heat by friction
wavenumber (1/size of eddy)
Typical values of frequency f10 kHz, Kolmogorov
scale ?0.01 up to 0.1 mm Kolmogorov scale ?
decreases with the increasing Re
9
Viscous subrange - scales
CFD6
Kolmogorov scales (the smallest turbulent eddies)
follow from dimensional analysis, assuming that
averything depends only upon the kinematic
viscosity ? and upon the rate of energy supply ?
in the energetic cascade (only for small
isotropic eddies, of course)
velocity scale
Time scale
Length scale
These expressions follow from dimension of
viscosity ? m2/s and the rate of energy
dissipation ? m2/s3
10
Viscous scale - tutorial
CFD6
Derive time scale of the smallest turbulent eddies
Time scale
11
Inertial subrange - scales
CFD6
Spectral energy E decreases in the turbulent
cascade when turbulent eddies are decomposed to
smaller and smaller eddies. Energy transformation
is not affected by viscosity in the inertial
subrange
Dimension analysis in the inertial subrange
And this is the famous Kolmogorovs law of 5/3
12
Turbulent eddies - scales
CFD6
Wikipedia (abbreviated) Turbulent flow is
composed by "eddies" of different sizes. The
sizes define a characteristic length scale for
the eddies, which are also characterized by
velocity scales and time scales (turnover time)
dependent on the length scale. The large eddies
are unstable and break up originating smaller
eddies, and the kinetic energy of the initial
large eddy is divided into the smaller eddies
that stemmed from it. The energy is passed down
from the large scales of the motion to smaller
scales until reaching a sufficiently small length
scale such that the viscosity of the fluid can
effectively dissipate the kinetic energy into
internal energy. In his original theory of 1941,
Kolmogorov postulated that for very high Reynolds
number, the small scale turbulent motions are
statistically isotropic. In general, the large
scales of a flow are not isotropic, since they
are determined by the particular geometrical
features of the boundaries (the size
characterizing the large scales will be denoted
as L). Kolmogorov introduced a hypothesis for
very high Reynolds numbers the statistics of
small scales are universally and uniquely
determined by the kinematic viscosity (?) and the
rate of energy dissipation (?). With only these
two parameters, the unique length that can be
formed by dimensional analysis is
13
Turbulent eddies - scales
CFD6

• Why and when it is important to know the
  turbulent scales
• Rate of chemical reactions depends upon the rate
  of micromixing determined by the frequency and
  the size of turbulent eddies
• Breakup of droplets depends upon the energy and
  size of turbulent eddies (too large eddies only
  move but do not break a droplet)
• Coalescence of bubbles depends upon collision
  frequency, collision speed, and these parameters
  are correlated with the energy dissipation rate ?
  and the length microscale l corresponding to
  radius of bubbles

Ronnie Andersson and Bengt Andersson. Modeling
the Breakup of Fluid Particles in Turbulent
Flows. AIChE Journal June 2006 Vol. 52, No. 6
H. Venneker, Jos J. Derksen and Harrie E. A. Van
den Akker. Population balance modeling of aerated
stirred vessels based on CFD . AIChE J. Volume
48, Issue 4, April 2002, 673685
14
DNS Direct Numerical Simulation
CFD6
In order to resolve all details of turbulent
structures it is necessary to use mesh with grid
size less than the size of the smallest
(Kolmogorov) eddies. N-grid points in one
direction should be
(based upon dimensional ground)
Velocity scale u in previous expression is
related to magnitude of turbulent fluctuations
(rms of u, or ?k). The Re? related to the
velocity fluctuation is called turbulent Reynolds
number.
No.of grid points in DNS No.of time steps
12300 380 6.7 M 32 k
30800 800 40 M 47 k
61600 1450 150 M 63 k
230000 4650 2100 M 114 k
Table concerns DNS modelling of channel flow
experiments (rewritten from Wilcox Turbulence
modelling, chapter 8).
Remark Re106 or 107 at flow around a car or
flow around wings
15
DNS Direct Numerical Simulation
CFD6
Direct numerical simulation of transition and
turbulence in compressible mixing layer FU Dexun
, MA Yanwen ZHANG Linbo Vol 43 No.4, SCIENCE IN
CHINA (Series A), April 2000
Abstract The three-dimensional compressible
Navier-Stokes equations are approximated by a
fifth order upwind compact and a sixth order
symmetrical compact difference relations combined
with threestage Runge-Kutta method. The computed
results are presented for convective Mach number
Mc 0.8 and Re 200 with initial data which
have equal and opposite oblique waves. From the
computed results we can see the variation of
coherent structures with time integration and
full process of instability, formation of A
-vortices, double horseshoe vortices and mushroom
structures. The large structures break into small
and smaller vortex structures. Finally, the
movement of small structure becomes dominant, and
flow field turns into turbulence. It is noted
that production of small vortex structures is
combined with turning of symmetrical structures
to unsymmetrical ones. It is shown in the present
computation that the flow field turns into
turbulence directly from initial instability and
there is not vortex pairing in process of
transition. It means that for large convective
Mach number the transition mechanism
for compressible mixing layer differs from that
in incompressible mixing layer.
16
DNS Direct Numerical Simulation
CFD6
DNS AND LES OF TURBULENT BACKWARD-FACING
STEP FLOW USING 2ND- AND 4TH-ORDER
DISCRETIZATION ADNAN MERI AND HANS
WENGLE Abstract. Results are presented from a
Direct Numerical Simulation (DNS) and Large-Eddy
Simulations (LES) of turbulent flow over a
backward-facing step with a fully developed
channel flow utilized as a time-dependent inflow
condition. Numerical solutions using
a fourth-order compact (Hermitian) scheme, which
was formulated directly for a non-equidistant and
staggered grid in 1 are compared with
numerical solutions using the classical
second-order central scheme. The results from LES
(using the dynamic subgrid scale model) are
evaluated against a corresponding DNS reference
data set (fourth-order solution).
17
Transition Laminar-Turbulent
CFD6
Bacon
18
Transition Laminar-Turbulent
CFD6

• Hydrodynamic instability due to prevailing
  inertial forces (convection term in NS equations)
  is the cause of turbulence.
• Inviscid instabilities
• characterised by
  existence of inflection point of velocity profile
• - jets
• - wakes
• - boundary layers wit adverse pressure gradient
  ?pgt0
• Viscous instabilities
• Linear eigenvalues analysis (Orr-Sommerfeld
  equations)
• - channels, simple shear flows (pipes)
• - boundary layers with ?pgt0

Poiseuille flow 5700 Couette flow stable?
There is no inflection of velocity profile in a
pipe, however turbulent regime exists if Regt2100
19
Transition Laminar-Turbulent
CFD6

• How to indentify whether the flow is laminar or
  turbulent ?
• Experimentally
• Visualization, hot wire anemometers, LDA
  (Laser Doppler Anemometry).
• Numerical experiments
• Start numerical simulation selected to unsteady
  laminar flow. As soon as the solution converges
  to steady solution for sufficiently fine grid the
  flow regime is probably laminar
• Recrit
• According to value of Reynolds number
  using literature data of
  
  critical Reynolds number

20
Transition Laminar-Turbulent
CFD6
Stability analysis
Linear stability analysis
Momentum equation for disturbance
Velocity disturbance
Production (extracting energy from the mean flow
to fluctuations)
Mean (undisturbed) flow
linear stability theory can predict when many
flows become unstable, it can say very little
about transition to turbulence since this
progress is highly non-linear
21
Transition Laminar-Turbulent
CFD6
Geometry Recrit
Jets 5-10
Baffled channels 100
Couette flow 300
Cross flow 400
Planar channel 1000
Geometry Recrit
Circ.pipe 2000
Coiled pipe 5000
Suspension in pipe 7000
Cavity 8000
Plate 500000
22
Turbulent structures evolution
CFD6
Journal of Fluids and Structures 18 (2003)
305324 Force coefficients and Strouhal numbers
of four cylinders in cross flow K. Lama, J.Y.
Lib, R.M.C. Soa
Re200
Relt4
Relt40
Re800
Relt200 2D von Karman vortex street
23
Fully developed turbulent flows
CFD6
Free flows (self preserving flows) Jets
Mixing layers Wakes
umax
Jet thickness x, mixing length x see
Goertler, Abramovic Teorieja turbulentnych struj,
Moskva 1984
x
Circular jet Planar jet
x
24
Example - tutorial
CFD6
Entrainment in jets (increase of volumetric
flowrate)
umax
Planar jet
x
1/?x
Circular jet
1/x
25
Fully developed turbulent flows
CFD6
Flow at walls (boundary layers)
y
Friction velocity
Log law
Buffer layer
Laminar sublayer
u
INNER layer (independent of bulk velocities)
laminar ylt5 uy
buffer 5ltylt30 u-35lny
Log law 30ltylt500 ulnEy/?
OUTER layer (law of wake)
26
Fully developed turbulent flows
CFD6
Flow at walls (turbulent stresses)
?t
Prandtls model
vanDriest model of mixing length lm
5 30
27
Example tutorial
CFD6
Calculate thickness of laminar sublayer at flow
of water in pipe (D2 cm) at flowrate 1 l/s.
Turbulent region, well within validity of Blasius
correlation
Wall shear stress from Blasius
Friction velocity
Dimensionless thickness of laminar sublayer
28
TIME AVERAGING of turbulent fluctuations
CFD6
Benton
29
TIME AVERAGING of turbulent fluctuations
CFD6
RANS (Reynolds Averaging of Navier Stokes eqs.)
Time average
Favres average
Proof
Remark Favres average differs only for
compressible substances and at high Mach number
flows. Magt1
30
TIME AVERAGING of turbulent fluctuations
CFD6

• Trivial facts
• Averaged value of fluctuation is zero
• Average value of gradient of fluctuations is zero
• Average value of product is not the product of
  averaged values

31
TIME AVERAGING of NS equations
CFD6
Continuity equation
Navier Stokes equations
Reynolds stresses
32
TIME AVERAGING of transport equations
CFD6
Turbulent fluxes
33
Boussinesq hypothesis
CFD6
Turbulent fluxes and turbulent stresses are
defined by the same constitutive equations as in
laminar flows, just only replacing diffusion
coefficients and viscosity by turbulent transport
coefficients.
34
Boussinesq hypothesis
CFD6
Analogy to Fourier law
Analogy to Newtons law
Rate of deformation based upon gradient of
averaged velocities
35
TRANSPORT coefficients-analogy
CFD6
It is assumed that the rate of turbulent
transport based upon migration of turbulent
eddies is the same for momentum, mass and energy,
therefore all transport coefficients should be
almost the same
Prandtl number for turbulent heat
transfer Schmidt number for turbulent mass
transfer
?t0.9 at walls ?t0.5 for jets according to
Rodi
36
Turbulent viscosity models
CFD6
Botero
37
Turbulent viscosity models
CFD6

• Turbulent viscosity is not a material parameter.
  It depends upon the actual velocity field and
  fluctuations at current point x,y,z. There exist
  different RANS models for turbulent viscosity
  prediction
• Algebraic models (not reflecting transport of
  eddies)
• 1 equation models (transport equation for
  turbulent viscosity)
• 2 equations models (viscosity derived from
  transport equations of other characteristics of
  turbulent eddies)
• Nonlinear eddy viscosity models (v2-f)
• RSM Reynolds Stress Modelling (transport
  equations for components of reynolds stresses)

38
Algebraic models
CFD6
Prandtls model of mixing length. Turbulent
viscosity is derived from analogy with gases,
based upon transport of momentum by molecules
(kinetic theory of gases). Turbulent eddy (driven
by main flow) represents a molecule, and mean
path between collisions of molecules is
substituted by mixing length. Excellent model for
jets, wakes, boundary layer flows. Disadvantage
fails in recirculating flows (or in flows where
transport of eddies is very important).
u(y)
Circular jet
Planar jet
Mixing length
Mixing layers
Currently used algebraic models are Baldwin
Lomax, and Cebecci Smith
39
2 equations models
CFD6

• Two equation models calculate turbulent viscosity
  from the pairs of turbulent characteristics k-?,
  or k-?, or k-l (Rotta 1986)
• k (kinetic energy of turbulent fluctuations)
  m2/s2
• (dissipation of kinetic energy) m2/s3
• ? (specific dissipation energy)
  1/s

Wilcox (1998) k-omega model, Kolmogorov (1942)
Jones,Launder (1972), Launder Spalding (1974)
k-epsilon model
C? 0.09 (Fluent-default)
40
Tutorial 2 equations models
CFD6
Derive relationship for turbulent viscosity
Launder Spalding k-epsilon model
41
k transport equation
CFD6
All two equation models (and also Prandtls one
equation model) are based upon transport equation
for the kinetic energy of turbulence
Transport equation for k is derived in a similar
way like the transport equation of mechanical
energy by multiplying NS equation by vector of
velocities (unlike mechanical energy only by the
vector of velocity fluctuations)
Transport of pressure viscous stress
reynolds stress rate of dissipation
turbul.production (p)
(2?e) (?uu)
42
k transport equation
CFD6
Dispersion terms (viscous and reynolds stresses)
and production term can be expressed using
turbulent viscosity (Boussinesq)
Example approximation of Reynolds stress
transport term
?k 1 Fluent
-??
Rate of dissipation of kinetic energy of velocity
fluctuation
Laminar and not turbulent viscosity!
43
? transport equation
CFD6
Transport equation for dissipation ? looks like
the k-transport. Just substitute ? for k.
Production and dissipation terms are modified by
universal constants C1? and C2?
Production term (generator of turbulence)
Dissipation term
This term follows from dimensional analysis
C1? 1.44 C2? 1.92 ?? 1.3 Fluent (default)
44
k-? modifications (RNG, realizable)
CFD6
Corrections of dispersion, production and
dissipation terms with the aim to extent
applicability of k-? for low Reynolds number flows
Functions of turbulent Reynolds
45
Effective viscosity (RNG)
CFD6
Blending formula for effective viscosity
46
? - estimate
CFD6
Dissipated energy in a mixing tank
n
Power number
d
47
k-? boundary conditions
CFD6
k and ? must be specified at inlets. Estimate of
kinetic energy k is based either upon measurement
(anemometers) or experience (from estimated
intensity of turbulence I). Dissipation is
estimated from correlations for power consumption
estimates. Values of k and ? at wall (must be
also defined as boundary conditions) can be
approximated by wall functions
This is implemented in majority of CFD programs
Friction velocity
Distance of the nearest boundary node from wall
48
Reynolds stresses (k-?)
CFD6
Constitutive equation for Reynolds stresses must
be modified with respect to isotropic pressure
This term is zero for incompressible liquids
Remark Turbulent stresses determine kinetic
energy of turbulent fluctuations
49
Assesment of k-? models
CFD6

• Problems and erroneous results can be expected
• Unconfined flows (wakes, jets). k-? model
  overestimates dissipation, therefore jets are
  overdumped.
• Pressure transport term (up) is neglected
  (errors in flows characterised by high pressure
  gradients)
• Curved boundaries or swirling flows
• Fully developed flows in noncircular ducts should
  be characterized by secondary flows due to
  anisotropy of normal Reynolds stresses (these
  features cannot be predicted by linear viscosity
  models)
• Problems in buoyancy driven flows

50
Discrepancies?
CFD6
Special case Steady unidirectional flow,
constant density, homogeneous turbulence
These terms are identically zero in homogeneous
turbulence
Further reading
C1? 1.44 C2? 1.92 ?k 1 ?? 1.3
51
Reynolds Stress Models (RSM)
CFD6
Centrifugal forces
6 transport equations
Dissipation
production
Pressure transport
diffusion
1 dissipation
52
Large Eddy Simulation (LES)
CFD6
Demuth
53
Large Eddy Simulation (LES)
CFD6
Instead of time averaging of NS equations,
spatial fluctuation filtering of NS equations
(only small eddies are removed, motion of large
eddies is calculated). Filter is realized by
convolution integral
Convolution, Greens function G
54
LES G-function example
CFD6
u
x
?
55
LES filtering - properties
CFD6
Basic difference in comparison with time averaging
56
LES NS equations
CFD6
Continuity equation without changes
Lij Leonard stresses
Rij SGS (sub grid stresses)
Cij cross stresses
57
LES NS equations
CFD6
Leonard stresses are usually neglected because
they are of the second order almost the same as
discretisation error. Cross and subgrid stresses
are usually modeled together using turbulent
viscosity approach.
It looks like Reynolds stresses
58
LES Smagorinski SGS
CFD6
Smagorinski model of subgrid stresses is almost
the same as the Prandtls model of mixing length,
only instead of the mixing length is substituted
a filter size.
Smagorinskis constant Cs0.1 in Fluent
Remark in the vicinity of wall the Cs? mixing
length is limited by ?y (karman constant times
the distance from wall)
59
LES RNG SGS
CFD6
Crng0.157 in Fluent
Crng100 in Fluent
For small ?s the effective viscosity equals the
laminar viscosity ?, while ?eff?s holds for a
high level of turbulence.
60
LES boundary conditions
CFD6
Inlet Simulated noise of velocities (normal
distribution superposed to specified intensity of
turbulence I)
Wall For a fine mesh resolving laminar sublayer
a linear (laminar) velocity profile is assumed,
otherwise velocity is calculated from the buffer
layer model
Von Karman constant 0.41
Friction velocity
61
Fluent turbulent models
CFD6

• Spalart Almaras (viscosity transport 1 PDE)
• k-? dissipation of k (standardRNGrealizable)
• k-? specific dissipation (standardSST shear
  stress transport)
• k-kl-? transition model laminar?turbulent
• v2-f boundary layer detachment (low Re)
• RSM
• DES (Detached Eddy Simulation, Spalart
  AlmarasrealizableSST), like LES at wall
• LES (Large Eddy Simulation)

62
Fluent example flow in a pipe
CFD6
Material water-liquid (fluid) Property
Units Method
Value(s) -------------------------------
-------------------------------- Density
kg/m3 constant
998.20001 Cp (Specific Heat)
j/kg-k constant 4182 Thermal
Conductivit w/m-k constant 0.6
Viscosity kg/m-s
constant 0.001003 Molecular Weight
kg/kgmol constant 18.0152
WALL
VELOCITY INLET
AXIS
Tube geometry L0.5m, D0.04m. Velocity at
inlet (uniform) u1m/s Mesh 50 x 20, compression
2 (last/first)
PRESSURE OUTLET
63
Fluent example flow in a pipe
CFD6
Voda
Def.?Model?Visc. Def.?Solv.?Axisym.
Def.?Boundary?u1
Display?Vectors
64
Fluent example flow in a pipe
CFD6
Air Laminar Mass-Weighted Average
Static Pressure (pascal) -----------
--------------------- --------------------
velocity_inlet.3 0.61464286
Spalart Almaras Mass-Weighted Average
Static Pressure
(pascal) --------------------------------
--------------------
velocity_inlet.3 0.62425083 k-epsilon
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 1.2050774 RNG
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 1.2050774 Realizable
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 1.1221648 k-omega
Mass-Weighted Average
Static Pressure (pascal) -------------
------------------- --------------------
velocity_inlet.3 0.78146631
Results?Surface average (pressure at inlet)
Water Spalart Almaraz Mass-Weighted Average
Static Pressure
(pascal) --------------------------------
--------------------
velocity_inlet.3 141.57076 RNG
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 245.41853 k-epsilon
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 274.16226 k-omega
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 258.04153
65
Fluent example flow in a pipe
CFD6
this value was calculated for finer mesh with 40
cells in radial direction
Buffer layer 5ltylt30 Wall functions must be used
as boundary conditions at wall
66
Fluent example flow in a pipe
CFD6
/ Journal File for GAMBIT 2.4.6, Database 2.4.4,
ntx86 SP2007051421 / Identifier "pipe2dn" / File
opened for write Mon Nov 28 082827
2011. identifier name "pipe2dn" new
nosaveprevious face create width 1 height 0.02
xyplane rectangle window matrix 1 entries 1 0 0 0
0 1 0 0 0 0 1 0 -0.2624999880791 \
0.2624999880791 -0.1590357869864 0.1590357869864
-1 1 face move "face.1" offset 0.5 0.01 0 undo
begingroup edge delete "edge.1" keepsettings
onlymesh edge mesh "edge.1" firstlast ratio1
1.981 intervals 100 undo endgroup undo
begingroup edge delete "edge.3" keepsettings
onlymesh edge modify "edge.3" backward edge mesh
"edge.3" firstlast ratio1 2 intervals 100 undo
endgroup undo begingroup edge delete "edge.4"
keepsettings onlymesh edge modify "edge.4"
backward edge picklink "edge.4" edge mesh
"edge.4" lastfirst ratio1 2 intervals 40 undo
endgroup undo begingroup edge delete "edge.2"
keepsettings onlymesh edge mesh "edge.2"
firstlast ratio1 0.5 intervals 40 undo
endgroup face mesh "face.1" map physics create
btype "WALL" edge "edge.3" physics create btype
"AXIS" edge "edge.1" physics create btype
"VELOCITY_INLET" edge "edge.4" physics create
btype "PRESSURE_OUTLET" edge "edge.2" solver
select "FLUENT/UNS" export fluent5 "pipe2dn.msh"
nozval save / File closed at Sat Nov 26 135619
2011, 1.39 cpu second(s), 3331408 maximum
memory. save name "pipe2dn.dbs" export fluent5
"pipe2dn.msh" nozval / File closed at Mon Nov 28
083130 2011, 0.50 cpu second(s), 4639176
maximum memory.
the simplest way how to modify geometry is the
journal file modification (L1m, mesh 100x40)
By comparing results for tubes of different
lengths (L1,L2) it is possible to eliminate the
entrance effect
67
Fluent example flow in a pipe
CFD6
Water L1m Spalart Almaraz Mass-Weighted Average
Static Pressure
(pascal) --------------------------------
--------------------
velocity_inlet.3 282. RNG
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 410. k-epsilon
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 445 k-omega
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 481
Water L0.5m Spalart Almaraz Mass-Weighted
Average Static Pressure
(pascal) --------------------------------
--------------------
velocity_inlet.3 141.57076 RNG
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 245.41853 k-epsilon
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 274.16226 k-omega
Mass-Weighted Average Static
Pressure (pascal) --------------------
------------ --------------------
velocity_inlet.3 258.04153
141Pa error 1 165Pa error 18 171Pa
error 22 223Pa error 59
RSM failed, negative pressure drop predicted
-230.0078 Pa !