Experimental Study of Turbulent Non-Turbulent Interface in ...
TURBULENCE MODELING IN PHOENICSphoenics/SITE_PHOENICS/AULAS/TURBULEN… · Turbulent flow features...
Transcript of TURBULENCE MODELING IN PHOENICSphoenics/SITE_PHOENICS/AULAS/TURBULEN… · Turbulent flow features...
TURBULENCE MODELING IN PHOENICS
• The purpose of this 2 hour class is to give basic directions to
undergraduate students to use Phoenics to simulate turbulent
flows.
• The lecture gives a brief introduction to turbulent flows
features, to scales and to the law of the wall.
• The lecture applies to RANS models (algebraic and two
equation models) and the focus is on the selection of a proper
grid size near the wall to have a successful turbulent flow
simulation.
Turbulent flow features
• Fluctuatiation or Irregularity: turbulent
flow is random ie not deterministic.
The velocity fluctuates in all three
directions, so does the pressure and
temperature.
• Turbulent flow is intrinsically transient.
• Increased exchange of momentum: Diffusivity - spreading rate of jets,
boundary layers etc.
• Large Reynolds numbers;
• Dissipation of kinetic energy to internal energy
• Wide range of time and length scales
• Almost all practical flows are turbulent.
Turbulent flow features: Eddies Side view of a turbulent boundary layer Water jet at symmetry plane, Re 2300
• Eddies are "packets" of fluid (identifiable flow structures) with different
sizes ranging from macroscopic dimensions to the microscopic scale also
known as Kolmogorov scale.
– The large eddies are responsible to the transport of mass, momentum and heat.
– The smallest eddies dissipate kinetic energy into heat through viscosity
• The largest eddies scale to the characteristic flow dimension.
– Boundary layer ~ boundary layer thickness;
– pipe flow ~ pipe diamenter;
– jet flow~ jet width and so forth.
Kolomogorov (1941) theory: the energy cascade
Large eddies,
contain kinetic energy
Small eddies dissipates energy
into heat (viscosity)
“Big-size whirls have little whirls that fed on their velocity
Little whirls have lesser whirls and so on to viscosity”
• The energy is transferred from the mean flow to produce the large eddies.
• The energy of the large eddies feed smaller eddies and these in turn transfer
energy to smaller eddies yet.
• This process results in a transfer of energy in the form of a cascade from
larger eddies to smaller ones.
• The smaller eddies dissipates the energy into heat due to the viscosity action.
• The energy cascade suggest the multiple scales (size and frequencies) present
in turbulent flow. This feature difficults the development of turbulence models.
Kolomogorov (1941) theory: length scales • Turbulence phenomenon has multiples scales: the largest contain energy and
the smallest are responsible to dissipate energy.
• The scales refers to the time, frequency spectrum or length sizes.
• The ratio between the largest ‘l ‘ to the smallest scales ‘lk ‘is:
3 4
w
k
uRe where Re and u
Re
(U.l/)
Rel
(u*l/)
No
Nodes
2.00E+04 116 1.58E+06
1.00E+06 1623 4.28E+09
• Consider the turbulent flow in a plane channel:
• For Re of 2.104 it is necessary a million nodes grid to a channel volume
equivalent to a one hydraulic diameter; for Re of 106 are necessary a billion
nodes grid!
• The length scale ratio impacts on the grid size definition necessary to
encompass the largest to the smallest length scales.
The eddies’ sizes and Re
• The images below displays a jet flow with Re of 400 and 20000.
Observe as Re increase the refinement of the length scale of the
eddies due to Kolmogorov scale law: 3 4
k Re
• The eddies’ smallest scale lk ratio for Re of 400 and 20000 is of 19:1
l h = l/ReL3/4
Direct numerical simulation (DNS)
Large eddy simulation (LES)
Reynolds averaged Navier-Stokes equations (RANS)
Prediction Methods
The focus of this presentation rests on RANS models only
Numerical Simulations : estimates of cost
of fixed wing calculation
Sample fixed wing of AR=10, Re=5E+06
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Boussinesq hypothesis
• Using the suffix notation where i, j, and k denote the x, y, and z
directions respectively, viscous stresses are given by:
• Many turbulence models are based upon the Boussinesq (1877)
hypothesis: Reynolds stresses are linked to the mean rate of
deformation.
• Exceptions are DNS and partially LES.
i
j
j
i
ijijx
u
x
ue
jiij i j t
j i
UUu 'u '
x x
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Predicting the turbulent viscosity
• The turbulent viscosity can be estimated by algebraic models or by
solving a system of PDE.
• Algebraic models (mixing length and LVEL) employs expressions
similar to: T = C(dU/dy). They are computationally cheap but limited
to very simple flows (pipe and boundary layers)
• The 2nd category usually solves two equations to get T . So they are
called by two equation models: k-, k-, k-l, k- RNG, etc. For k-:
T = Ck2/ ; T derived by other 2 eq. models similarly follows k-.
• There is also the Reynolds stress model which instead of estimate T it
solves a system of six turbulent stress equations in order to get the
Reynolds turbulent stress tensor.
• The two equation models are largely applied to solve industrial
problems. Very often the constants are tuned to specific cases to
increase the accuracy.
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Comparison of RANS turbulence models
Model Strengths Weaknesses
Spalart-
Allmaras
Economical (1-eq.); good track
record for mildly complex B.L.
type of flows.
Not very widely tested yet; lack of submodels
(e.g. combustion, buoyancy).
STD k-
Robust, economical, reasonably
accurate; long accumulated
performance data.
Mediocre results for complex flows with severe
pressure gradients, strong streamline curvature,
swirl and rotation. Predicts that round jets spread
15% faster than planar jets whereas in actuality
they spread 15% slower.
RNG k-
Good for moderately complex
behavior like jet impingement,
separating flows, swirling flows,
and secondary flows.
Subjected to limitations due to isotropic eddy
viscosity assumption. Same problem with round
jets as standard k-.
Realizable
k-
Offers largely the same benefits
as RNG but also resolves the
round-jet anomaly.
Subjected to limitations due to isotropic eddy
viscosity assumption.
Reynolds
Stress Model
Physically most complete model
(history, transport, and anisotropy
of turbulent stresses are all
accounted for).
Requires more cpu effort (2-3x); tightly coupled
momentum and turbulence equations.
Wall bounded flows
• The presence of a wall damps the velocity and the turbulence near the
wall region.
• To capture the wall effect the turbulence models have to be modified
near the wall.
• The embodied wall models on the turbulence models are grid
dependent.
• The success of turbulent flow simulation starts on a careful choice of
the grid spacing near the wall.
• This presentation focus on near wall grid spacing selection to a
successful simulation. To beginners this a potential area to make
mistakes
Wall bounded flows and velocity damping near the wall
Experimental turbulent boundary layer
vel. Profiles for various pressure
gradients. Coles 1968
• The presence of a wall damps the
velocity and the turbulence near the
wall region.
• To capture the wall effect the
turbulence models have to be
modified near the wall.
• The success of turbulent flow
simulation starts on a careful choice
of the grid spacing near the wall.
The meaning of the layers
• Inner layer: is the layer closest to the wall and is ruled by the fluid
viscosity. The viscous length scale /v* is greater than the wall
distance, or yv*/ = y+ << 1. On this region, u+ = y+ or = u/y. For
modeling purposes the inner layer extends up to y+ = 5
• Overlap layer: is the region where the viscous action start loosing
influence and the inertial effects increases. For modeling purposes this
layer ranges from y+ = 5 up to 40.
• Log layer: it is sufficiently far from the wall such that it is completely
rulled by the inertial effects but close enough to the wall that the shear
stress is uniform and equal to the wall shear stress! Usually the log
layer ranges from y+ = 40 up to 200
• Outter layer: flow dominated by the eddies inertial effects, y+ > 200.
Inner + Buffer + Overlap Layers
The velocity profiles near the wall are universally expressed in a
dimensionless form:
*
*
*
W
y vy
uu
v
where
v
is the eddy
velocity scale.
Outter Wall
layers Inner
5
Overlap
40
Log
200
*
uu
v
*y vy
Overlap: sensitivity to adverse pressure gradient
Phoenics turbulence models
• Algebraic models: constant turbulent viscosity, mixing length, lvel.
Lvel is the most popular, it can be applied starting from the inner layer
or from the log layer. It is an algebraic expression which fits the near
wall flow. These models are computationally cheap and delivers good
results for channel or boundary layer flows.
• Two equation models (standard) : refers to the k-e and variants. The
distance from the wall of the first volume center has to lay within the
log layer, 40 < y+ < 200.
• Two equation models (low Re) : low Reynolds flows usually have the
first node distance for 40 < y+ < 200 corresponding to a significant
percentage of the domain (> 15%). To avoid numerical errors induced
by the coarse grid it is preferred to starting integrating the flow
starting from the wall. The first node must lay at y+ ~ 1 and at least 3
more volumes up to y+ < 5. This assures a smooth integration along
the inner, overlap and log layer.
How to get good results from turbulence models
• All models have limitations, one can not ask more than the model
can deliver.
• Algebraic models are the simplest and the most limited. Usually
work well for pipe flows and boundary layers.
• 2 equation models are more accurate than algebraic models but
their constants do not have universally, it is possible for certain types
of flow a better matching by tuning the constants.
• 2 equation models considers flow in equilibrium: all the
production of k is dissipated at the same point. Flow with sudden
changes in direction are prone to be out of equilibrium.
• In general, turbulent models demand a special care with the near
wall mesh. If you get this wrong your simulation will fail.
WKSP #1-Turbulent flow develop. 2D channel
• This WKSH deals with a turbulent flow development along a 2D
channel flow.
• The flow simulations will be done using Parabolic model (visit (1)
and (2) links to further information).
• Parabolic model apply only to one-way flows (no recirculation
zones present). It will used along the WKSH because it is far more
efficient than Elliptic model.
• Along the WKSH will be supplied specific hints to set up a problem
employing Parabolic model.
2D Channel dimensions & properties
(a) For parabolic model the main flow direction has to be aligned with the Z axis.
(b) Parabolic flow has w component always along z > 0 direction, if happens to have
w along z<0 it will fail. Due this feature it does not need specification of an outlet.
(c) Parabolic model visits only one slab at a time and stores only the last slab. To
provide full field storage go to VR-EDITOR box GRND and set IDSPA=1, IDSPB=1
and IDSPC=80 (always equal to NZ), IDSPD=1
L = 10m
Inlet
z (a)
y
H/2=0.05m
(b) no outlet
specification
Uniform GRID (c)
NX=1
NY=28
NZ=80
nwall (plate)
Center line
Properties
(~air)
= 1.0 kg/m3
= 10-5 m2/s
Objects
Inlet: Win = 10 m/s
Re = 2.105
Inlet: 5% turbulence
Plate: no slip, W=0
Numerics
Lsweep = 100
Relax (manual)
Output
Pause at end of run
Storg.: YPLUS & STRS
A C C E S S T H E V R - E D I T O R B O X E S A N D S E T:
Models
K-E
WSTRS
WYPLUS
Phoenics variables
2H URe
2D Channel Results –
W velocity at z/D of 2D, 10D and 40D
One may reproduce this figure using autoplot or get similar results
employing ‘Ploting variable’ in VRVIEWER.
2D Channel Results – W center-line velocity
overshoot
experimental
overshoot,
see link
16D 32D 48D 64D 80D
2D
Ch
an
nel
Res
ult
s –
Y
+ &
ST
RS
1st volume distance correct: 40 < Y+ < 100.
1st volume within Log Layer!
16D 32D 48D 64D
STRS = w/
STRS fully developed = 0.192
STRS Colebrook-White = 0.195 (1.5% off)
2D
Ch
an
nel
Res
ult
s –
T, k
an
d
Viscosity is a flow property: T = Ck2/
Near the wall the ‘turbulent viscosity’ is 16 times
greater than the molecular viscosity.
The largest changes on k and are near the wall.
At the centerline T is nearly 300 greater than .
16D 32D 48D 64D 80D
experimental
overshoot, ENUT
KE
EP
Phoenics adjustable constants for KE model
• The choice of one constant value by other depends on previous
knowledge about a specific flow and also knowledge about the
meaning of the constants within the model, for KE visit turbulence.
Exp
lori
ng t
he
gri
d s
ensi
tiv
ity
to
Y+
an
d S
TR
S • Evaluating Cf thru Colebrook-White is possible to estimate, at the fully
developed region: (i) 1st node distance from the wall (), (ii) number of volumes
NY (uniformly distributed), (iii) STRS = w/. The last will be used to check the
numerical solution. Keep in mind that H/2 = 50mm.
KE – Low Re
KE – Low Re
KE - Standard
KE - Standard
2
W fU CSTRS
2
Workshop#1 – adjusting grids
• Based on the table below select between ‘standard’ or ‘low Re’ KE
models to cases where W = 1 and 50 m/s, also define a new NY. Do
these changes on the previous Q1.
• For reference, the previous case velocity is W = 10m/s or Re 2E+05,
• STRS Cole is the w/ value estimated by Colebrook-White for a fully
developed flow.
• Y+ = 1 thru 100 are the estimated first node distance to the wall.
W Re2H Cf Cole STRS Cole Y+=1 Y
+=40 Y
+=100
(m/s) (---) (---) (m/s)2 mm mm mm
1 2.00E+04 0.0065 0.0032 0.18 7.03 17.58
10 2.00E+05 0.0039 0.1954 0.02 0.90 2.26
50 1.00E+06 0.0029 3.6389 0.005 0.21 0.52
Workshop – adjusting grids
• Case W = 1m/s – ‘Low Re’ because the 1st volume for y+ = 40 would
be at 7mm from the wall which is nearly 14% of the Y length. One can
use a uniform grid or a more economical 2 region grid, the near wall
grid extends up to y+ = 40 (~7mm)
• Case W = 50m/s – Standard,
W Re2H KE NY Q1
(m/s) (---)
1 2.00E+04 LowRe 142 unif 2 reg
10 2.00E+05 Standard 28 unif
50 1.00E+06 Standard 48 unif ellip
Workshop#2 – Flow in backward face step
• A simple backward step flow challenges the 2 equation turbulence
models because it has a shear layer, a recirculation zone, null wall
shear stress point and a redeveloping boundary layer!
• Compare the reattachment point position employing: k-e model, the
Chen-Kim k-e model, the RNG k-e model, the k-omega model and the
LVEL model.
Workshop#2 – Flow in backward face step
• Load case T103 from library. Step height, H = 0.038m and ReH =
45000.
H
Y
3H
X
L = 0.762 m or 20H
s = 0.1524 m or 4H
Uin = 13 m/s
• Change X grid regions to 10 and 60 cells (no power)
• Change Y grid regions to 8 and 10 cells (the last with pwr 1.5 sym)
• Start with the KE standard model
Workshop#2 – Flow in backward face step
• Key flow features to
explore are the wall shear
stress and if possible the
pressure distribution at the
channel bottom wall.
• The reattachment point
is determined by the x
distance where the wall
shear is null. stress is null.
Workshop#2 – Flow in backward face step
• Fill in the table
x (m) x/H
k-e
Chen-Kim k-e
RNG k-e
k-omega
LVEL
Workshop#2 – Flow in backward face step
• As the reattachment point is approached w 0 and Y+ 0
• Would you consider Low Re type models to capture the
reattachment point?
• If so use k-e low re, same grid as before but modify Y 1st region to
60 cells, use pwr of + 1.6 and in Numerics set to 10000 sweeps
• Discuss the validity
of the results in view
(k-e model) of the y+
values
Lower bound to two eq. Standard models
Workshop#2 – Flow in
backward face step
• The k-e low re apparently
estimates nearly the same
reattachment point position as
predicted by k-e standard!
• But the magnitude of the
STRS has changed
significantly!
• In fact the k-e standard made
wrong STRS estimations
because it employed an
inappropriate grid which
resulted in y+ values lower than
40 at the neighborhood of
reattachment point!
END