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Frame (SRF) Model
Frame (SRF) Model
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Outline
ntro uct on to o e ng
Navier-Stokes Equations for a Rotating Reference Frame Relative and Absolution Velocity Formulations
SRF Problem Setup
Solver
Physical Models
Material Properties
Boundary Conditions
Solver Settings Initialization
Troubleshooting SRF Problems
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Appendix
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Introduction to SRF Modeling
any pro ems w c nvo ve rotat ng components can e mo e e us ng a
single moving reference frame. Why use a rotating reference frame?
A flow field which is unsteady with respect to the stationary frame becomes
steady with respect to the rotating frame.
Steady-state problems are easier to solve...
mp er s
Lower computational cost
Easier to postprocess and analyze
e w scuss ssues re a e o mo e ng n s sec on, u many
concepts (e.g. solver settings, physical models, etc.) will also apply to MRF,
MPM, and SMM
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Characteristics of SRF Models
ov ng rame s assoc ate w t a s ng e u oma n.
In FLUENT, you may divide this domain up into several connected fluid zones,but each fluid zone must have the same moving reference frame speed and axis
Domain rotates with a constant, prescribed rotational speed about a specifiedax s o ro a on
No translation considered (though this may be included)
FLUENT only provides for a constant rotational speed in the user interface
cce era ng rames o re erence can e mp emen e roug user e ne
functions
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Characteristics of SRF Models
oma n typ ca y cons sts o
Inlets and outlets Walls
Rotationally periodic boundaries
Boundaries which move with the fluid domain may assume any shape.
Boundaries which are stationary (with respect to the laboratory or fixed
frame must be surfaces of revolution.
Rotationally periodic boundaries require spatial periodicity of all boundary
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Illustration of a Typical SRF ModelShroud/casing
Fluid domain
sur ace
Rotatingx
frameAxis of rotation
Hub surface
z
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Blade surface
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Stationary Walls in SRF Models
Stationary walla e
Rotor
Wron !
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Wall with baffles nota surface
of revolution!
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Rotating Reference Frames
e norma y escr e u mot ons w t respect to an a so ute or
inertial reference frame We can define a rotating reference frame as a reference frame which is
sp nn ng w t a prescr e or entat on an spee w t respect to an
inertial reference frame
The motion of the reference frame gives rise to additional accelerations
Non-inertial reference frame
The velocity of the fluid can defined with respect to either the absolute or
Absolute velocity - Fluid velocity with respect to the stationary (absolute)
reference frame
Relative velocity - Fluid velocity with respect to the rotating reference
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frame
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The Velocity Triangle
e re at ons p etween t e a so ute an re at ve ve oc t es s g ven y
UWVrrr
+= velocityabsolute=Vr
rUrrr
velocityrelative=Wr
In turbomachinery, this relationship can be illustrated using the laws of
vector addition. This is known as the Velocity Triangle
Wr
Ur
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Vr
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Navier-Stokes Equations (Rotating Reference Frame)
wo erent ormu at ons are use n
Relative Velocity Formulation (RVF) Obtained by transforming the stationary frame N-S equations to a rotating reference frame
Uses the relative velocit as the de endent variable in the momentum e uations
Uses the relative total internal energy as the dependent variable in the energy equation
Available for the Segregated Solver only!
Absolute Velocity Formulation (AVF)
Derived from the relative velocity formulation
Uses the absolute velocity as the dependent variable in the momentum equations
Uses the absolute total internal energy as the dependent variable in the energy equation
Available for all solvers Se re ated and Cou led NOTE: RVF and AVF are equivalent forms of the N-S equations!
Identical solutions should be obtained from either formulation with equivalent boundary
conditions
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Relative Velocity Formulation
(Continuity)0=+
Wt
r
(Momentum)
( ) rWWWt
W
r
rrrrrrrr
+++
)2(
brp ++=
&rrrr
etr b trtr
=r
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TermSourceGenerationHeat=Q&
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Relative Velocity Formulation
(Relative total internal energy)( )22
tr 2
1
UWee +=
Viscous stress += 2T
WWWvr rrr
(Rothalpy)2
22 UWpehtr
+
+=
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RVF Accelerations Due to Rotating Frame
or o s an centr uga acce erat ons are treate as source terms n t e
momentum equationsrrrrr
Coriolis
acceleration
Centrifugal
acceleration
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Absolute Velocity Formulation
(Continuity)0=+ Wt
r
V rrrrrr
omentumbp
t++=++
(Energy)( ) ( ) Qb &rrrrr+++=+
VFVUpTkhWt
et
t
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Absolute Velocity Formulation
(Relative total internal energy)2t21Vee +=
+= 2T
VVVrrr
3
(Total enthalpy)2
2Vpehtr ++=
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TermSourceGenerationHeatForcesBody
==
QFb&
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AVF Accelerations Due to Rotating Frame
rrrrrrr=
or o s an centr uga acce erat ons re uce to a s ng e term
Coriolis
acceleration
Centripetal
acceleration
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Scalar Equations
ener c sca ar transport equat on n a mov ng re erence rame
( ) ( )+=+
SWt
r
tcoefficiendiffusionscalar
iablescalar var
=
=
The use of the relative velocity in the convective term implies that, for
=
- ,
This form is employed for turbulence models, species and phase transport,
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e c.
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Summary of SRF Equations
wo orms o t e av er- to es equat ons can e app e to pro ems
(AVF and RVF) RVF only available for the pressure-based solver
Scalar transport equations can be transformed to moving frame by modified
convection term
Source terms may require modification depending on dependent variables
required (e.g. production term in turbulence model equation may need relative
velocity gradients)
Appropriate boundary conditions complete the problem specification
Inlet / outlet flow boundaries, walls, periodics, etc.
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SRF Problem Setup
e w ocus on aspects o mo e setup rect y re ate to pro ems
Topics SRF geometries (2D, 3D)
Solver Choices
Physical Models
Material Properties
Boundary Conditions
Solver Settings
Initialization
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SRF Geometries (2D)
p anar geometr es
Geometries rotate about axis normal to xy plane with specified origin (periodicboundaries are permitted)
ax symmetr c, ax symmetr c w t sw r
Geometries rotate about the x axis
y
x
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Planar Axisymmetric
x
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SRF Geometries (3D)
ee to e ne ot
rotational axis origin anddirection for the fluid
Rotationally periodic
boundaries permitted
Origin
Axis of
r
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ro a on
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Choice of Solver for SRF Models
ame cons erat ons or genera
flow field modeling apply to SRFsolver choice
egrega e o ver: ncompress e,
low speed compressible flows.
Fans
Pumps
Coupled Solvers: high speed
com ressible flows where Machnumber is above 0.3
High-pressure axial compressors
Turbines
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Turbochargers
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Velocity Formulation Recommendations
se w en n ow comes rom a
stationary domain
Absolute total pressure, total temperature,
Use RVF with closed domains (all surfaces
are moving) or if inflow comes from a
rotating domain
Relative total pressure, relative total
temperature or relative velocities are known
in this case
As noted previously, RVF and AVF are
equivalent, and therefore either can be used
successfully for many problems
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disappear with suitable mesh refinement.
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Disk Cavity Example
urpose ompare so u ons o a ne us ng ree eren pro emformulations
Case 1 - Stationary frame, moving walls
- ,
Case 3 - SRF, AVF
Disk cavity air flow study based on the experiments of Pincombe, 1981= = =
Solutions obtained for following conditions : Cw = Q/b = 1092,Re
= b2/ = 105
All cases use the same mesh 20576 uad cells 2D se re ated solver(axisymmetric with swirl), incompressible flow, RKE turbulence model,second order discretization.
Additional cases were computed using a fine mesh (82,304 cells) to examine the
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mes n epen ence o e so u ons
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Disk Cavity Mesh
Bot wa s rotate
Inlet tube
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InletAxis
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Disk Cavity Stream Function
Case 1 Case 2 Case 3
Separated flow
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Nearly identical flow patterns observed for all three cases.
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Radial Velocity Profile (r/b = 0.633)
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Disk Cavity Results
x a orce an moment resu ts
Case Mesh Axial Force (103 N) Torque (103 Nm)
Coarse 6.431 7.231a onary
Fine 6.141 7.435
2 (RVF)Coarse
Fine
6.681
6.156
7.195
7.444
3 (AVF)Coarse
Fine
6.449
6.089
7.241
7.446
onc us ons
All three numerical approaches yield essentially the same results
Closer agreement is obtained through mesh refinement
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esu ts emonstrate t e equ va ence o stat onary, , ormu at ons
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S i C
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Heat Transfer
,
SRF zone
Note: BCs for stationary walls must be circumferentially uniform
,
distributions relative to the rotating frame
Conduction and radiation models can also be enabled with SRF models o e: or con uc ng so s w c are con a ne n a mov ng re erence
frame, you shouldNOTactivate the Moving Reference Frame option!
Reason MRF option activates convection terms in the solid, which arent
relevant to SRF modelin
( ) ( ) ( )+=+ s STkCTVCTr
Solid convection term
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velocitysolid=sVr
Fl t U S i C t
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DPM and Pathline Modeling
ou can use an
pathline models for SRFproblems
art c e pat s are compute
in the relative frame
If you want to see particlepat s n t e a so ute rame,
you can select this option in
the Pathlines panel.
o e a par c es mov ng n
absolute frame may hit wall
surfaces, since the rotation of
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Particle injection at fan blade tips
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Other Physical Models
VOF, ASMM, Eulerian (Fluent 6), Cavitation models are all
compatible with SRF (and MRF, Sliding Mesh) modeling in Fluent
Exam les: mixin tanks cavitatin um s flows
Real Gas Model
Can model specific fluids using non-ideal gas equation of state-
Two options are available (Fluent 6.1)
NIST Library (REFPROP) - available fluids include: carbon
, , , , , ,of refrigerants (e.g. R11, R134a)
User-Defined Function user can write custom real gas propertylibrary
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UDF source code available for Redlich-Kwong equation of state
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Boundary Conditions For SRF Models
u
Inlet BCs Pressure Inlet
Shroud
Velocity Inlet
Mass Flow Inlet
Outlet BCs Blade
Outle
Pressure Outlet
Non-reflecting BCs
Mass flow outlet
Inlet
Walls
Periodics
Conformal
Hub
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Non-conformal Axial Pump IGV
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Fluid Zone BCs
se u to se ect rotat ona ax s
origin and direction vector for rotatingreference frame
o e: a rec on vec ors s ou e
unit vectors, but FLUENT will
normalize them if they are not
Motion Type for SRF
Enter rotational speed
Can use negative value to reverse
sense of rotation
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Velocity Inlets
se or ncompress e, m ycompressible flows when inlet
velocity is known Can specify absolute or relative
velocities using Reference Frameoption
Can specify vector components orma nitude and direction in Cartesianor Cylindrical coordinates
For 2D, axisymmetric with swirl and3D problems you can specify
velocitntialuser tan e
inin,
=
+= V
VV
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locityangular veuserin
n,
=
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Flow Direction
ow rect on s e ne as
the velocity vector normalizedby its magnitude Polar)-al(Cylindric
)(Cartesian
aarr
zzyyxx
d
d
++=
++=
nput a ows artes an or
Cylindrical-Polar coordinate
forms
Frame)(AbsoluteV
Vdabs
r
r
r
=
ote t at t e ow rect ons
differ in absolute and relative
frames!
Frame)(RelativeW
drel r=
e oc y r ang e ru e
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Pressure Inlets
ressure n ets can e use w t e t er ncompress e or compress e ows
Definitions of total pressure and total temperature depend on velocityformulation and compressibility:
Incompressible, AVF+=+=
2
22
2
2
1
p
ttC
VTTVpp
Neglected for
incompressible flow
Incompressible, RVF+=+= 2 2
2 p
trtrC
TTWpp
Incompressible, AVF
+=
+=
1
22
11
21
21 tt MTTMpp
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Incompress e, RVF
+= += 2121 rtrrtr TTpp
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Pressure Inlets
pec y appropr ate tota pressure
and total temperature
If inlet flow is supersonic, you
such that desired the Mach number
corresponds toptotal/pstatic
Specify flow direction vector
Frame of flow direction depends
on velocity formulation!
If using AVF: absd
Specify other scalar BCs as
appropriate (energy, turbulence,
species, etc.)
re
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Mass Flow Inlets
ass ow n ets can e use w t
incompressible or compressible
flows
flux
Same flow direction options as
Velocity Inlet
Specify other scalar BCs as
appropriate (energy, turbulence,
species, etc.)
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Flow Direction and Mass Flow Inlets
ow o you eterm ne t e ve oc ty magn tu e now ng t e mass ow rate
and flow direction?
dVV=r&
r
)( ndVnVA
Vn ===
V
tV
d)( ndA
mV
=
&
n
areafaceboundary
rateflowmass
=
=
A
m& NOTE: For relative frame, substitute
relative velocity and direction (W) for
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velocitytangentialvelocitynormal
==tn
VV absolute velocity (V)
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Pressure Outlets
pec y stat c pressure constant or pro e at t e out et.
Can employ a simple radial equilibrium assumption which computes a radialpressure variation from
The specified pressure is then
R
V
R
p =
assumed to be the hub static
pressure.
Appropriate for axial compressors
an ur nes, w ere e ow sparallel to rotational axis.
You must also specify appropriate
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Backflow
ac ow reverse ow at a oun ary typ ca y occurs w en t e stat c
pressure in a cell adjacent to a pressure boundary (Pc) forces the flow in adirection opposite to what is intended
or a ressure n e b < c : oun ary o a pressure s assume o e a
static pressure for the purposes of determining the flow velocity
Backflow scalars (temperature, species, etc.) are obtained from the solution b c
total pressure for the purposes of determining the flow velocity
Backflow scalars (temperature, species, etc.) are prescribed in the GUI panel
P < P P > P c
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cb
Pressure Inlet
c b
Pressure Outlet
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Backflow
or a pressure n e , e ow rec on comes rom e ve oc y componen scalculated in the cell
For a pressure outlet, there are three methods for determining the direction of reversedflow:
Normal to boundary
From adjacent cell
Prescribed direction vector,
relative to the boundary in the absolute frame if AVF is used
relative to the boundary in the relative frame if RVF is used
Recommendations
As some backflow may occur during the solution process, prescribe reasonable values forall backflow quantities
Try to minimize (or eliminate) backflow by extending your boundaries further upstream ordownstream
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Target Mass Flow BC
or some pro ems t e n et mass ow rate an n et tota pressure an
temperature are known, and the exit pressure is unknown Example: fans and compressors for which the pressure rise is unknown
Fluent can address this situation with the target mass flow outlet BC
How it works
User sets the exit BC to a pressure outlet
Desired mass flow rate is prescribed
As calculation proceeds, exit pressure is adjusted automatically to achieve desired
mass flow rate
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Target Mass Flow Methods
wo met o s are ava a e or comput ng t e pressure or a prescr e mass
flow Method 1 (best suited for turbomachinery applications)
ass ow rate at t e out et oun ary s compute an compare to t e es re
mass flow rate
A pressure increment is determined based on the required change in mass flowrate the basic behavior is to:
Increase the exit pressure if computed mass flow > desired mass flow
Decrease the exit pressure if computed mass flow < desired mass flow
Method 2 (best suited for incompressible flows)
Same basic algorithm except the pressure increment is determined from a
linearized form of Bernoullis equation
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Target Mass Flow Outlet Setup
o act vate target mass ow
outlet , simply enable the Targetmass-flow rate option in pressure
desired mass flow rate
ou can spec y t e mass ow
outlet method in the text interface:
- -mass-flow-rate-settings>
enable? set method verbosity?
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Target Mass Flow Outlet Example
Convergence HistoryMass flow outlet BCapplied at compressor
outlet
Target mass flow:
. g s
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Eckardt centrifugal compressor
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Non-Reflecting Boundary Conditions
tan ar pressure s or compress e ow x spec c ow var a es at
the boundary (e.g. static pressure at an outflow boundary)
Result: pressure waves incident on the boundary will reflect in an unphysical
Can lead to local errors and convergence degradation
Effects are more pronounced if the boundary is close to the blade (e.g. truncated,
Non-reflecting boundary conditions (NRBCs) permit waves to pass through
the boundaries without spurious reflections
Turbo-specific NRBCs
General NRBCs
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Turbo-Specific NRBCs
ur o-spec c s are ase on t e axer- es stea y-state ormu at on
NRBCs are available for pressure inlets and pressure outlets only All pressure boundaries will be affected (cannot selectively activate NRBCs for
specific boundaries)
can coexist with other BCs (e.g. mass flow inlet)
NRBCs require the use of the steady-state, coupled solver Mesh requirements
The mesh at the pressure inlet/outlet boundaries must be a structured quad (2D)
or hex (3D) mesh
Note that away from the boundaries, any mesh type is permissible (e.g. hybrid tri-
quad mesh is permitted in 2D)
You can use NRBCs with mixing planes!
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Using the Turbo-Specific NRBCs
ur o- pec c s areactivated using the TUI
select enable? and answeres
/define/boundary-conditions/non-reflecting-
bc/turbo-specific-nrbc>enable? show-status
NRBC Controls (under the set/menu in the TUI)
discretization option to
/define/boundary-conditions/non-reflecting-
bc/turbo-specific-nrbc> enable
enable non-reflecting b.c.'s [no] yes
permit first or second orderreconstruction at boundary faces
under-relaxation sets
the under-relaxation factor for
- - -
bc/turbo-specific-nrbc>
enable? set/
initialize show-status
NRBCs (0 < URF < 1)
verbosity option to enableprinting of debugging messages
/define/boundary-conditions/non-reflecting-
bc/turbo-specific-nrbc>
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Turbo-Specific NRBC Example: 2D Turbine Vane
mp e vane c or = . m
Compressible flow, ideal gas (air)
Boundary conditions
n e o a pressure = . a m
Inlet total temperature = 300 K
Inlet turbulence intensity = 1%= .
Hybrid quad-tri mesh used (quad block at inlet)
Solutions on two meshes compared
- - Short mesh - mesh truncated near trailing edge - NRBCs required
Compare solutions on long mesh with solutions on the short mesh with andwithout NRBCs
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2D Vane Long Mesh
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2D Vane Short Mesh
Truncated downstream
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2D Vane Long Mesh
Shock wave at
vane trailing edge
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2D Vane Short Mesh NBRCs Off
onstant pressure
results in incorrect shock
location
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2D Vane Short Mesh NRBCs Activated
Non-reflecting boundary
conditions permit shockwave to pass t roug t e
boundary - shock location
is correctly predicted!
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General NRBC Formulation
new genera ormu at on as een eve ope or
Uses general characteristics-based algorithms from the literature Applies to pressure outlets only
Benefits
Can be used for both steady-state and unsteady flows
No geometry or mesh restrictions
Limitations
Can only be used with the coupled-explicit or coupled-implicit solvers (no
segregated solver implementation at this time)
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General NRBC User Interface
pt on se ecte n pressure out et pane
Permits selected enabling of the NRBCs (unlike Turbo-Specific NRBCs). Two options available
Pressure at Infinity
Assumes specified pressure
is defined downstream of-
Example: rocket nozzle
Average Boundary Pressure
is an average pressure at the
outlet boundary
Example: turbine blade row
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ex t oun ary
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General NRBCs: 2D Stator Vane
Constant Pressure BC Non-Reflecting Pressure BC
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Contours of Static Pressure (atm)
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Wall Boundary Conditions
a s en orce zero normavelocity at all wall surfaces
no slip (zero velocity) forviscous flows
For moving reference frames,you can specify the wallmotion in either the absolute
or relative frames
Recommended specificationof wall BCs for all movingreference frame problems
lab frame) use zeroRotational speed, Absolute
For moving surfaces, usezero Rotational s eed,
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Relative to Adjacent CellZone
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Conformal Periodic Boundary Conditions
on orma per o c s requ re t at t e oun ary ace mes
element match one-for-one on the periodic boundary.
Rotationally periodic BCs rely on the rotational axis
.
Rotationally periodic boundaries can be used in SRF
problems to reduce mesh size, provided that both the
geometry and flow are periodic.
If you are using themake-periodic TUI command,
make sure you set the rotational axis
in the Fluid BC anel first beforecreating the periodic boundaries.
Once the periodic BCs have
been set, perform a grid check to see
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Non-conformal Periodic Boundary Conditions
perm ts t e use o non-con orma rotat ona y per o c s.
Non-conformal periodics do not require a matching mesh on the boundaries. Coupling of the periodic zones is accomplished using the same algorithms
employed in non-conformal interfaces.
Setting up a non-conformal periodic BC is performed in the TUI:
define/grid-interfaces/make-periodic.
Shadow zone [()] interface.5
Rotational periodic? (if no, translational) [yes] yes
Rotation angle (deg) [0] 90
Periodic zones
Create periodic zone? [yes] yes
grid-interface name [] int1
er o c ang e
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Conformal vs. Non-Conformal Periodic Boundaries
Conformal
-
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Pressure-Based Solver Settings
ressure- e oc y oup ng e o
Coupled
Recommended (provides robust, fast convergence) Requires twice the memory relative to other schemes
SIMPLE, SIMPLEC, PISO
Use when computer memory is an issue (large mesh)
Pressure Interpolation
For highly swirling flows, use PRESTO! scheme
Other equations - use second order discretization
Can start with first order for stability, especially for problems with high rotational
spee s Compressible flows with Pressure-based solvers
May need to under-relax Density (0.1 is recommended)
Can also run with energy equation initially turned OFF enable the energy equation
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after establishing a reasonable, isothermal flow field.
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Density-Based Solver Settings
mp c t sc eme s recommen e un ess computer memory s an ssue
Flux type options Roe-FDS baseline methods
AUSM can provide enhanced accuracy for strong shocks
Use first order discretization to begin your calculation, then switch to second
order when the solution is close to convergence
Use default Courant numbers as a start (1 for explicit solver, 5 for implicit
solver)
For coupled-explicit solver
Use 4 levels of FAS MultiGrid for most problems
helps propagate solution more rapidly through the domain
Use more levels of you have a very large mesh
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Initialization
oo n a za on o e so u on s o en e ey o o a n ng rap anrobust convergence of turbomachinery problems
Less of an issue for
Fixed flow rate provides stability to the calculation
Problems with favorable pressure gradients (e.g. turbines)
Less propensity for reverse flow at boundaries Often critical for
Compressible flows with adverse pressure gradients (e.g. compressors, diffusers)
Adverse pressure gradient leads to reverse flows, solution instability
Use grid interpolation to patch a coarse mesh solution onto a fine mesh.
Use Full Multigrid (FMG) initialization technique.
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Solution Interpolation
roce ure
Run coarse grid version of your
model
r e a a o n erpo a on e
Set up fine mesh model
Read interpolation file to initialize
Advantages
Can be applied to nearly any
, Easy to use
Disadvantage
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equ res eve opmen o coarse mes
model
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Full Multigrid (FMG) Initialization
n t a zat on opt on n uses t e u u t gr a gor t m n
FLUENTs Coupled Explicit solver to generate a system of coarse meshes
Solves the inviscid equations on coarsest mesh, interpolates to next finest, and so
Inviscid solution used as initial condition for subsequent full Navier-Stokes
calculation
Benefits
Convenient for user (no separate meshes or solutions required)
ny so ver can e use segrega e , coup e -exp c or mp c
Permits very large Courant numbers for coupledimplicit solver
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FMG Interface (TUI) FMG controls can be set in TUI usin
solve/initialize/set-fmg-
initialization
Permits setting of convergence
,
on each coarse grid level, Courant
number, verbosity
Once FMG arameters set the
initialization can be started using the
text command
solve/initialize/fmg-
n t a zat on
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FMG Initialization Eckardt Rotor
With FMG
Initialization
Without FMG
Initialization
~
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,
Number of iterations reduced by a factorof 5 using FMG initialization!
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Troubleshooting SRF Problems
pro ems may e cu t to so ve ecause o arge ow gra ents
resulting from the rotation of the fluid domain
May need to use lower under-relaxations than default
Some things to consider for troublesome cases
Make sure the mesh quality is good (max cell skewness < 0.9 0.95)
Use FMG initialization for hard-to-start problems
Reduce under-relaxation factors and/or Courant numbers
Consider running the problem as a transient calculation
Can provide more robust convergence versus the standard steady-state approach
Use first order discretization in time and about 2-3 time steps per iteration
Run until steady-state is achieved
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Summary
mo e ng s t e s mp est mo e ng approac or rotat ng mac nery
Applications typically involve a single passage of a rotating machine (e.g.
single compressor blade row)
Some example applications are provided in Appendix A
FLUENT provides two formulations of the Navier-Stokes equations for
rotating reference frames
Absolute Velocity Formulation
Relative Velocity Formulation
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which are compatible with SRF modeling.
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SRF Examples
SRF Examples
3D propeller fan
3D cavitating centrifugal pump
3D propeller fan
3D cavitating centrifugal pump
2D axisymmetric flow in a labyrinth seal
3D flow in a transonic axial compressor blade row
2D axisymmetric flow in a labyrinth seal
3D flow in a transonic axial compressor blade row
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Propeller Fan
mo e o a our a e prope er an
Results compared with data from open literature:
, . . an ang, . ., umer ca nves ga on o e ua er ormanceCharacteristics of a Small Propeller Fan Using Viscous Flow Calculations,Computers and Fluids, 28 (1999), pp. 815-823.
Solutions obtained for a range of flow rates at 2000 rpm.
Numerical model Mesh size = 269265 cells (tets + wedges)
Segregated solver with moving reference frame
Incompressible flow (air)
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Realizable k model with non-equilibrium wall functions
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Propeller Fan - Mesh
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Comparison to Data: Head Coefficient
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Comparison to Data: Power Coefficient
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Fan Flow Field: Flow Coefficient = 0.1Significant flow reversalu stream of fan face
Static pressure contoursdisplayed on fan surfaces
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Fan Flow Field: Flow Coefficient = 0.35
Strong radial outflow
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Fan Flow Field: Flow Coefficient = 0.5Strong axial outflow
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Cavitating Centrifugal Pump
was use to s mu ate ow n a centr uga pump w t cav tat on
effects
Geometry based on pump design reported in paper by Hoffman et al. (2001):o man, ., o e , ., r e r c s, ., osyna ., m ar es an eome r ca
Effects on Rotating Cavitation in Two Scaled Centrifugal Pumps, Proc. 4th
International Symposium on Cavitation, Pasedena, CA, June 2001.
TFA pump design used in the present study
Impeller diameter = 278 mm
Number of blades = 5
Speed = 2160 rpm
Single blade passage modeled with rotationally-periodic boundaries
Mesh Type: Hex mesh, 284,955 cells
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Pump Geometry
diffuser
impeller
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inlet tube
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Pump Model Mesh
Single blade
passage
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Physical / Numerical Models
tea y-state so ut ons, segregate so ver
Incompressible flow, SRF, AVF
Multiphase cavitation model enabled
Mixture model used
Primary phase = water (density = 1000 kg/m3)
Pvap = 2620 Pa; surface tension = 0.0717 N/m,
Non-condensible gas = 1.510-5
Secondary phase = water vapor (density = 0.01927 kg/m3,
viscosity = 8.810-6Ns/m2)
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Realizible k turbulence model with standard wall functions
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Case Studies
on-cav tat ng cases
Model run over a range of flowrates (100 275 m3/hr) to obtain non-cavitating
pump curve
ump ea r se pressure r se pre c e an compare o non-cav a ng a a
Cavitating Cases Flow rate fixed at design flow (210 m3/hr)
Exit pressure initial set to 600 kPa to ensure non-cavitating flow
Exit pressure decreased in 50 kPa increments to gradually develop cavitating
con t ons
Predicted head rise vs NPSH compared with data
NPSH =PinletPvapor
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Non-Cavitating Flow Comparison with Data
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Midspan Pressure Non-Cavitating Flow
Design Flow rate
03.0=
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Midspan Relative Velocity Non-Cavitating Flow
Design Flow rate
03.0=
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Cavitating Flow Comparison to Data
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Cavitating Midspan Pressure
Exit Pressure: 500 kPa
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Cavitating Midspan Pressure
Exit Pressure: 400 kPa
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Cavitating Midspan Pressure
Exit Pressure: 300 kPa
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Cavitating Vapor Volume Fraction
Exit Pressure: 500 kPa
Cavitation
inception
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Cavitating Vapor Volume Fraction
Exit Pressure: 400 kPa
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Cavitating Vapor Volume Fraction
Exit Pressure: 300 kPa
Significant
cavitation on
pressure side
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Illustration of Cavitation Induced Separation
Separation bubble
downstream of
vapor cavity
Exit Pressure
300 kPa
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Labyrinth Seal
ax symmetr c mo e o ve-toot a yr nt sea
Results compared with experimental data of Millward and Edwards (ASME
94-GT-56)
Numerical model Steady state, incompressible flow
2D axisymmetric with swirl and viscous dissipation
Se re ated solver
Realizable k turbulence model
Solutions calculated over a range of rotational speeds (3000 13000 rpm)
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Labyrinth Seal - Mesh
InletOutlet
-
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straight seal
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Labyrinth Seal - Stream FunctionPR = 1.5 , N = 13000 rpm
Seal leakage flow
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Labyrinth Seal - Total Temperature
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Total Temperature
Windage heating due
to viscous dissipation
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Comparison with Data
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Transonic Axial Compressor
ranson c compressor rotor otor
36 blades
Design conditions
17188 rpm, PR = 2.1, mass flow = 20.2 kg/s
Numerical model
steady-state, compressible flow
coupled implicit solver
mesh: ~90,000 hex cells
standard KE turbulence model inlet TU=3.5%
inlet profiles from test data
back pressure varied to obtain speed line
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Rotor 37 - Mesh
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Comparison with Data - Pressure Ratio
Choked mass flow
predicted: 20.80 kg/s
data: 20.93 kg/s
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Pressure Ratio (Choked Flow)
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Relative Mach Number (Choked Flow)
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Pressure Ratio (94.3% Relative Mass Flow)
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Relative Mach Number (94.3% Relative Mass Flow)
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Centrifugal Compressor
c ar t otor otor- geometry
20 blades
Design conditions
14000 r m PR = 2.0 mass flow = 5.31 k /s
Numerical model
- , Coupled implicit solver
Mesh: 199,480 hex cells
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Inlet profile from 2D axisymmetric solution
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Centrifugal Compressor Mesh
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Centrifugal Compressor Surface Pressure
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Centrifugal Compressor esu ts es gn on t on
Mass flow Pressure Efficiency
Fluent 5.31 2.08 88.8
Test Data 5.284 2.066 89.2
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