Download CFD ANALYSIS 5.7

Chapter 1
FLOTRAN Characteristics,
Capabilities and
Analysis Planning
Objectives
Describe the phenomena modeled with FLOTRAN elements
•
Discuss the FLOTRAN Element Characteristics
•
Explain CFD terminology
•
Present the governing equations
•
Discuss Solution Algorithm characteristics
•
Outline important user decisions
CFD ANALYSIS 5.7
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Training Manual
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The FLOTRAN Simulation
FLOTRAN simulates fluid flow and heat transfer
– The conservation equations (mass and momentum) are solved for a
fluid.
• The result is a flow distribution and pressure field.
– An energy equation may also be solved for the fluid domain.
• For the energy equation, the problem domain may contain both
fluid and non-fluid elements
– Turbulence, Multiple Species simulations are optional
•
CFD ANALYSIS 5.7
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Training Manual
Degrees of Freedom (DOF)
–
–
–
–
Velocities: VX,VY,VZ
Pressure: PRES
Turbulence (if necessary): ENKE,ENDS
Species Concentrations: SP01…SP06
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FLOTRAN Element Types and Shapes
Training Manual
• Pyramids are the required transition elements between Tet and Hex
shapes
– Elements are Linear (no mid-side nodes)
2D Basic
CFD ANALYSIS 5.7
2D Type: Fluid141 (triangles and quadrilaterals may be mixed)
3D Type: Fluid142 (hexahedrals, tetrahedrals, pyramids, wedges)
3D Basic
3D Transition
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FLOTAN Problem Domains
Two Dimensional
– Cartesian (x-y) or Polar (r-θ) Coordinates
P(r, )
y
r
x
Origin

CFD ANALYSIS 5.7
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Training Manual
Origin
– Axisymmetric Coordinates (about x or y axis)
•
Three Dimensional
– Cartesian
– Cylindrical: VR,V field must be parallel to ANSYS XY plane
• VX(VR) ; VY(V ) ;VZ(VZ)
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Problem Domain - Geometry
Equations are formulated in the coordinate system chosen
– Required for use of periodic boundaries
•
Stationary or Rotating coordinate systems
•
Structured or Unstructured meshes
•
ALE formulation enables pre-determined change in problem
domain.
CFD ANALYSIS 5.7
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Training Manual
– ALE formulation activates UX,UY,UZ DOF.
– Use functions to program both displacements and velocities for
boundary movement.
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Problem Domain - Coordinate System
FLOTRAN Coordinate System Assignment - Command line
– 2D:
•
et,1,141,,,1 Axisymmetric about Y axis
•
et,1,141,,,2 Axisymmetric about X axis
• et,1,141,,,3 Polar Coordinates
– 3D:
• et,1,142,,,3 : Cylindrical Coordinates
•
CFD ANALYSIS 5.7
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Training Manual
GUI Access to the Coordinate System Assignment
– Accessed through PREP7
– Element Type > Add/Edit/Delete > Options
– FLOTRAN Setup Menu >Flow Environment > Coordinate System
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CFD Terminology
We provide definitions of the these terms….
– CFD
– Turbulent flow
– Mach Number
– Incompressible fluid
– Compressible fluids
– Conjugate heat transfer
– Distributed resistance
– Periodic boundaries
– Multiple species transport
– Newtonian and non-Newtonian fluids
– Free Surface
CFD ANALYSIS 5.7
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Training Manual
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CFD Terminology
Define CFD
Computational Fluid Dynamics (CFD)
– The science (and art) of obtaining a numerical solution to the set of
equations which describe the motion of a fluid.
•
Partial differential equations are discretized, resulting in a series
of algebraic equations of the form:
Ax  b
CFD ANALYSIS 5.7
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Training Manual
– In a completely coupled system, the vector X contains all the DOF
– In a segregated Scheme, the variables are solved for sequentially.
– In some instances approximate solutions to the matrix systems are
suffcient for intermediate steps.
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CFD Terminology
Define Turbulent Flow
According to Webster’s New Collegiate Dictionary, turbulent flow is
defined as “a fluid flow in which the velocity (pressure, temperature,
species concentration, etc.) at a given point varies erratically in
magnitude and direction”.
– Turbulence is a flow regime characterized by velocities, pressures,
temperatures, and species mass fractions that fluctuate in response to
shearing forces.
•
These shear forces can cause an orderly flow to break into eddies
with discernible disorder.
•
The flow is in reality constantly changing. In principle, turbulent flow
is a transient phenomena.
•
Steady state solutions are obtained through time-averaging.
CFD ANALYSIS 5.7
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Training Manual
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Turbulence
Training Manual
Velocity (mm/s)
4
Actual velocity (mm/s)
3
Average velocity (mm/s)
CFD ANALYSIS 5.7
Velocity Fluctuations in Time
2
0
1
2
3
4
5
6
Time (seconds)
•
When averaged over time, the velocity fluctuations are zero.
Calculating the fluctuations is generally not computationally
practical.
•
Turbulence models are designed to determine the effect of the
fluctuations on the mean flow.
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Turbulence (continued)
Training Manual
•
The optional k-ε turbulence model should be activated when the
Reynold’s number for the flow indicates the presence of a turbulent
regime.
•
The Reynold’s number is a dimensionless parameter which
represents the ratio of the inertial to viscous forces. It is defined as:
CFD ANALYSIS 5.7
FLOTRAN’s default treatment is a two-differential equation model,
the k-ε model
ρVD
h
Re 
μ
•
ρ is the density, V is the characteristic velocity, μ is the dynamic
viscosity, and DH is a characteristic length or diameter, typically the
hydraulic diameter for internal flows.
HydraulicDiameter 
4*Area
WettedPerimeter
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Turbulence (continued)
Reynold’s number ranges for laminar and turbulent flow can be
found in fluid dynamics texts, literature, handbooks, etc. Some
examples:
Example
Characteristic
Length
Turbulent
Reynolds No.
Internal pipe flow
Internal pipe
diameter
External flow
along a plate
Distance along
Re ~ 500,000
plate from leading
edge
External flow over Chord length
an airfoil
CFD ANALYSIS 5.7
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Training Manual
Re ~ 2300
Re ~ 500,000
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CFD Terminology
Mach Number
Mach number
– speed of fluid divided by the speed of sound.
•
In general,
M
V
γRT
CFD ANALYSIS 5.7
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Training Manual
Note that supersonic flow is characterized by M>1 while
subsonic flow exists when M<1.
We estimate the Mach number before analysis to decide
whether or not to activate the Solution option for
Compressible flow.
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CFD Terminology
Define Incompressible Fluids
In FLOTRAN, the terms “compressible” and “incompressible”
denote the algorithm chosen by the user to solve the coupled
momentum and pressure equations.
– This concerns which terms are considered in the momentum equation.
Terms which are zero if the density is perfectly constant are dropped
from the equations. This applies to fluids where large pressure
changes result in only slight variations in density.
– Density variations are primarily a function of temperature gradients
rather than pressure gradients. The flow of liquids is generally
incompressible, even when natural convection is present.
CFD ANALYSIS 5.7
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Training Manual
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CFD Terminology
Define Compressible Fluids
Compressible flow
–
It refers to (generally high velocity) flow problems where density
varies appreciably as a result of pressure and temperature. The
static temperature becomes a function of velocity and stagnation
temperature.
•
The use of the compressible option should be considered for
Mach numbers above 0.3. The compressible option is not
appropriate for low mach number flows. Note that for many
applications, the incompressible option may be used up to Mach
numbers of 0.7.)
•
The equation of state for density must be woven into the
pressure equation. The Ideal Gas Law is used:
CFD ANALYSIS 5.7
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Training Manual
P  RT
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Compressible Flow Option
CFD ANALYSIS 5.7
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Training Manual
In a compressible/thermal problem, the total energy equation is
solved for total temperature. Static temperature is then
determined from:
1  V 2 
Ttotal  To  Tstatic 
2  C p 
•
Shock waves (where discontinuous changes in velocity and
properties take place) occur frequently in supersonic flows.
•
The solution benefits from mesh refinement in regions near shock
waves.
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CFD Terminology
Define Conjugate Heat Transfer
Conjugate heat transfer
– the solution of the energy equation in a problem domain with both
fluids and solids (i.e., we are solving for the temperature distributions
in both fluids and solids simultaneously).
•
These problems are generally considered as “ill-conditioned”,
meaning that the solution of the matrix equation derived from the
energy (a.k.a. temperature) equation can be difficult….
CFD ANALYSIS 5.7
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Training Manual
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CFD Terminology
Define Distributed Resistances
Distributed resistances
– Simulation of the hydrodynamic effects of a feature without modeling
its detailed geometry. The distributed resistance is the CFD analogy
of a beam element. Examples include flow through screens, porous
media, or small obstructions.
– Values can be obtained from Handbooks or calculated by simulation
with FLOTRAN for use in larger simulations.
• One case with the feature
CFD ANALYSIS 5.7
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Training Manual
• One case without the feature
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CFD Terminology
Define Periodic Boundaries
Periodic Boundaries
– two boundaries where the conditions are unknown but identical. All
the degrees of freedom are coupled.
CFD ANALYSIS 5.7
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Training Manual
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CFD Terminology
Define Multiple Species Transport
Multiple Species Transport
– This capability enables the user to track species concentration levels
for several fluids as they mix, subject to the limitations that a single
momentum equation is solved for the flow field and no chemical
reactions are simulated.
– Thus, it is not possible to simulate the separation of two fluids that
occurs due to density changes.
CFD ANALYSIS 5.7
•
Training Manual
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CFD Terminology
Define Newtonian and
Non-Newtonian Fluids
Newtonian fluids
– have a linear relationship between the stress and rate-of-strain.
Newtonian fluids have no memory of past configurations or
deformations.
•
Non-Newtonian fluids
– have a viscosity which may be a function of not only the fluid velocity,
but also the velocity gradient.
•
CFD ANALYSIS 5.7
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Training Manual
Common Newtonian fluids
– include air and water
•
Common non-Newtonian fluids
– include blood, polymers and clay slurries
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The FLOTRAN Elements (continued)
Training Manual
The fluid is single phase but can be a mixture of up to six different
fluids or species.
•
You can use Elements 141 & 142 to model heat transfer in solids
as well as fluids, but FLOTRAN elements cannot be combined with
other ANSYS elements.
•
Conservation laws provide the basis for the formulation:
CFD ANALYSIS 5.7
•
– Conservation of Mass
– Conservation of Momentum
– Conservation of Energy
•
Transport equation solved for multiple species.
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Conservation of Mass
The Conservation of Mass equation to a FLOTRAN analysis:
  ( ui )

0
t
xi
•
The Conservation of Mass equation (or Continuity equation) when
combined with the Conservation of Momentum equation leads to an
equation for pressure. The above form of the Continuity equation is
stated in indicial notation (a repeated index implies a summation of
terms). It can be rewritten in 2D, Cartesian coordinates as:
CFD ANALYSIS 5.7
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Training Manual
  ( u )  ( v)


0
t
x
y
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Conservation of Momentum
Training Manual
Discuss the application of the Conservation of Momentum
equation to a FLOTRAN analysis.
•
FLOTRAN solves the complete Navier-Stokes Equations:
Time-dependent
terms
Advection
terms
Source terms
CFD ANALYSIS 5.7
•
 (ρu ju i )
 (ρu i )
p


 ρg i  β i
t
x j
x i
  u i 
  u j 
 μ


μ

x j  x j 
x j  x i 
Diffusion terms
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Conservation of Momentum
(continued)
Training Manual
Additional source terms (ßi) such as Lorentz forces may exist.
•
The Navier-Stokes equations can be rewritten for 2D, Steady State,
Constant properties in Cartesian coordinates as:
  2u
u
u
p
 2u 

u
 v

 g x   x   

2
2 
x
y
x
y 
 x
CFD ANALYSIS 5.7
•
  2v
v
v
p
 2v 

u
 v

 g y   y   

2
2 
x
y
y
y 
 x
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Conservation of Energy
Training Manual
Discuss the application of the Conservation of Energy equation to
a FLOTRAN analysis.
•
For incompressible flow, the energy equation is simplified into a
transport equation:
 ( C pT )  ( C puiT )


S
t
xi
xi
 T 
 k

 xi 
•
The specific heat may vary.
•
The density for non-fluid regions must be constant.
•
The conductivity for non-fluids may be orthotropic and also vary
with temperature.
CFD ANALYSIS 5.7
•
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Compressible Flow Total
Energy Equation
Training Manual
Discuss the application of the Conservation of Energy equation
for compressible flow to a FLOTRAN analysis.
•
For compressible flow, the energy equation is solved in terms of
total temperature.
Viscous dissipation
 ( C pTo )  ( C p uiTo )


S
t
xi
xi
  2u

i
 ui 

 x j x j xi
 u j

 x
j

Viscous work terms
•
 To 
P
 k
   
t
 xi 
CFD ANALYSIS 5.7
•
2 


    k   1 V 
   x C x  2

i 
P
i

Kinetic energy terms
The viscous work, kinetic energy and viscous dissipation terms
can be significant at high velocities.
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Species Transport Equation
Training Manual
Discuss the application of the transport equation for multiple
species to a FLOTRAN analysis.
•
The transport equations are solved for the mass fraction of each
specie and based on advection and diffusion processes only.
(Yi ) (ui Yi )  
Yi 
 Di
 0


t
xi
xi 
xi 
•
CFD ANALYSIS 5.7
•
In these equations, Yi is the mass fraction for the ith species and
Di is the mass diffusion coefficient for the ith specie in relation to
the bulk mixture.
Note:
To ensure the sum of N specie mass fractions at any
location is 1, only N-1 equations are actually solved.
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FLOTRAN Analysis Capabilities
– Ramped, Step time dependent boundary conditions
• Laminar or Turbulent flow
– User choice
• Incompressible or Compressible flow
CFD ANALYSIS 5.7
• Transient or Steady-state flow
Training Manual
• Newtonian or non-Newtonian flow
– Power Law, Carreau, Bingham models available
– User Programmable models possible
• Subsonic, Transonic, or Supersonic flow
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FLOTRAN Analysis Capabilities
(continued)
Internal or External flow
•
Forced flow or buoyancy driven flow
– Incompressible algorithm with variable density
•
Forced, free or mixed convection heat transfer
•
Conjugate heat transfer
•
Distributed resistance/Fan model
•
Free Surface (2D) with Surface Tension
•
ALE formulation for changing problem domain
•
Interpolation of solution onto revised mesh
CFD ANALYSIS 5.7
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Training Manual
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FLOTRAN Solution Algorithm
Characteristics
Training Manual
CFD ANALYSIS 5.7
•
Sequential solution of the governing equations.
•
Iterative matrix solvers - the symmetric and non-symmetric
iterative solvers are separate from those used in the rest of
ANSYS.
•
In-memory solution - Memory requirements are minimized by
storing only the non-zero matrix terms.
•
Equal Order Method (velocity-pressure) - Equal order interpolation
functions simplify boundary condition specification and
interpretation of results.
•
Streamline upwind method - the default for treating the non-linear
advection terms. Inexpensive, bounded and stable method. (The
Streamline Upwind Petrov Galerkin method is a more accurate but
slightly less stable alternative.)
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FLOTRAN Analysis Decision Making
You must make decisions about the expected flow characteristics
and subsequently verify these decisions.
–
–
–
–
–
–
•
Are fluid property variations with temperature important?
Is the flow steady state or transient in nature?
Is the flow laminar or turbulent?
Are “compressible” effects important?
How much of the problem domain should be modeled?
Where should the mesh densities be greatest?
CFD ANALYSIS 5.7
•
Training Manual
Continued advances in CFD will help automate these decisions,
but this will not relieve the engineer of the need to understand
what phenomena are important.
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The Sequence of Events
Geometry:
– Create within ANSYS (PREP7) or..
– Import from a CAD program (Use Connection Products!)
• Ensure that the flow domain volume is imported
•
Meshing
– Use mapped meshing as much as possible.
– Slice volumes as necessary for Mesh sweeping.
– ICEM CFD mesh is easily imported into ANSYS.
•
Boundary Conditions
– Use solid model boundary conditions if possible
•
FLOTRAN execution
– Stability parameters and restarts as necessary
•
Post-Processing
CFD ANALYSIS 5.7
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Training Manual
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Exercise
Training Manual
1. Is the flow laminar or turbulent?
2. Is the flow compressible or incompressible?
3. Are property variations with temperature important?
4. Where should the mesh be fine?
CFD ANALYSIS 5.7
Answer the following questions for cases A through D shown below.
CASES A and B: Consider water flowing through a channel.
Twall = 20°C
Vinlet
H=1
Tinlet
Insulated
wall, q" = 0
P=0
Density =  = 998 kg/m3
Viscosity =  = 1.0(10-3) kg/m-s
Speed of sound = a = 1480 m/s
CASE A: Vinlet = 0.1 m/s, Tinlet = 95°C
CASE B: Vinlet = 1 m/s, Tinlet = 25°C
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Exercise (continued)
Training Manual
Tambient = 20°C
P=0
Vinlet
H = 0.5 m
Tinlet
C
L
CASE C: Vinlet = 50 m/s, Tinlet = 20°C
CASE D: Vinlet = 500 m/s, Tinlet = 20°C
Answers:
CFD ANALYSIS 5.7
CASES C and D: Consider air flowing through an expanding duct.
Density =  = 1.20 kg/m3
Viscosity =  = 1.81(10-5) kg/m-s
Speed of sound = a = 340 m/s
CASE A
CASE B
CASE C
CASE D
Laminar (L) or Turbulent (T)?
Compressible (C) or Incompressible (I)?
Are property variations with temperature
important (Yes or No)?
Location of fine mesh?
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