CFD Lecture (5/8): Solvers- Compressible Flow

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Solvers: Compressible Flow
Introduction to Solver Terminologies

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©ZeusNumerixPvtLtd:ConfidentialDocument
Content
 FlowZ – Introduction
 Planning Execution – Mesh Quality & Options
 Boundary Attributes – Label & Tags
 File System – Structure of CGNS, Control, Monitor & Other Files
 Launching FlowZ
 Flow Model – Flow Type, Fluid Data, Scheme, Gradients
 Domain Motion – Moving / Rotating Zone, Grid Motion
 Boundary Conditions – Specifying Inflow, Outflow, Farfield & Wall
 Turbulence Model – SA, K Epsilon, SST models
 Execution – Initialization & Setup
 Monitoring Solution & Analysis
 Post Processing
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Compressible Flow Solver: Description of FlowZ™1-Mar-2020

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FlowZ – Introduction
Features
 Based on finite volume methodology
 Density based schemes for both compressible & incompressible flows
 Explicit Runge-Kutta time marching
 Accepts multi-block structured grids
 CGNS compatible
 Fully parallelized using MPI
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Case Study – Transonic Sajben Duct
Aim
 Replication of validation case
 Internal flow analysis
 Prediction of transonic flow features
 Creation of boundary layer & flow separation after shock
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Modeling & Planning the Simulation
Physics
 Turbulent Flow
 Important to Capture Boundary Layer
 Clustered Mesh – At least 10 grids points inside boundary layer
 Suitable convective scheme and turbulence model required
Mesh
 Quality is important
 Structured multi-block preferred over unstructured mesh
 Current mesh generated using GridZ
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CGNS & CGNSViewer
Why CGNS ?
 Grid coordinates in binary is a MUST
 CGNS, an ISO 9001 format from NASA & Boeing
 Provides interface to FlowZ™ for grids and solution data
CGNSViewer
 Free utility for viewing CGNS format structure (http://www.cgns.org)
 Stores zone-wise information for grid coordinates, solution fields, boundary
conditions & connectivity
 CGNSPlot, utility to plot grids in CGNS format
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Boundary Attributes
Tags & Labels
 Each boundary is given attributes
 Tag – CGNS defined boundary tags
 Label – User defined name to an entity
 Boundary condition parameters are unique for each label
 Use GridZ to visualize tags and labels in big complex meshes
 Labels for Block – Used for Domain Modeling
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Structure of Control File
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Import CGNS File
 Select ‘FlowZ’ from ‘Solver’ module of CFDExpert
 Graphics User Interface (GUI) for FlowZ appears
 Set up ‘Solver Control File’ (.scf)
Menu  File  Import CGNS File
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CGNS File Parameters
Scaling Factor
 To convert the unit grids into SI system
Conversion Options
 Planer
 Axisymmetric
 Equation of Axis: Ax + By = C for non-scaled coordinates values
 Axis to coincide with boundary tag ‘BCLineDegenerate’
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Basic Flow type
Menu  Flow Model  Basic Fluid Type
Basic Flow Type
 Compressible
 Density changes due to pressure
 Air flow at Mach No. > 0.3 & Liquid in cases like water hammer problem
 Incompressible
 Density is either constant or changes with temperature
 Low speed flow, M < 0.3 or most of the cases involving liquid
Viscous Effects
 Viscous – All practical cases requires viscous effect
 Inviscid – Good approximation as very high-speed analysis, where convective terms are significant
compared to viscous
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Fluid Data – Compressible Flow
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Default values fixed for
 Fluid – Air
 Thermal Properties – Calorically perfect gas
 Dynamic viscosity & Conductivity – Calculated
using Sutherland’s law
Menu  Flow Model  Fluid Data

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Fluid Data – Compressible Flow
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 Select Fluid – Water / Air
 Set density
 Use database value
 Provide constant value
 Input density as a function of temperature
 Provide density variation with temperature as Constant /
Expression in T
 Set Dynamic Viscosity & Conductivity through
Sutherland’s law / Constant value

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Approximate Riemann Solvers
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Roe Scheme (‘Flux Difference Roe’)
 Based on characteristic wave disturbances
 Less dissipative in nature and can capture stationary discontinuity. Recommended for
viscous calculations
Entropy Fix
 To avoid unrealistic solutions like expansion shocks near sonic expansions, it is
necessary to introduce entropy fix formulations to Roe scheme
 FlowZ uses Harten-Hyman entropy fix
 Choose ‘Entropy Fixed Roe’ for supersonic flows over blunt objects. ‘Averaged Roe’ &
‘Entropy Fix Roe’ are computationally expensive

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Flux Vector Splitting Schemes
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 Eigenvalues and fluxes (f) are split into f+
and f
-
 f+
is discretized with a backward difference and f
-
with a forward difference
Stegar Warming
 Fluxes are split based on the sign of eigen values
Vanleer
 Split fluxes have discontinuous slope at sonic velocities, hence ‘glitch’ at sonic
transition
 Flux components are function of M
 Above scheme are found to be very stable
 They are diffusive in nature and hence should not be used for resolving boundary
layers

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Other Compressible Schemes
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HLLC
 Another Approximate Riemann solver type scheme
 Unlike Roe, HLLC performs better at high mach flows
 Recommended for viscous supersonic calculation
AUSM
 Blending of flux vector splitting & flux difference splitting
 Efficient to solve (Vanleer) & has advantage of increased accuracy (Roe)
AUSMPW
 Removes numerical oscillations near wall and overshoot phenomena behind shock
waves
 Uses pressure weighted function at cell interfaces

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Preconditioned Incompressible Scheme
Compressible Flow Solver: Description of FlowZ™
Convergence Stiffness
 Compressible schemes show convergence stiffness at low speed
 Reason – Difference in magnitude of eigen values
 Modification in primitive variables and flux calculation
 Preconditioning was proposed by Weiss & Smith (1995)
Variable Density
 Low speed compressible flow, 0.1 > M > 0.3
Constant Density
 Density can also vary with temperature
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Gradient Calculation
Green’s Theorem
 Utilizes the values at face center to evaluate gradient in the cell
Least Square
 Variable is approximated as a polynomial,
 Weighted errors to be minimized over neighbouring cells
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∇𝜑 =
𝜑 𝑓 𝐴
𝑉𝑜𝑙𝑢𝑚𝑒
𝜑 𝑥, 𝑦, 𝑧 = 𝑎0 + 𝑎1 𝑥 + 𝑎2 𝑦 + 𝑎3 𝑧
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Domain Motion
 Solver can model the domain motion using following two methods:
ALE (Arbitrary Lagrangian Eulerian)
MFR (Multiple Frame of Reference)
 Various motion mode can be modeled like
Rigid translation
Linear deformation
Rigid body rotation
 Solver also has the capability to model the physical motion of grid for transient flow
modeling with following motion
Rigid translation
Linear deformation
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Inflow Boundary Condition
Inflow Boundary Types
 Total Pressure
 Total pressure and total temperature are held fixed
 If supersonic static pressure is also held fixed
 Mass Flux
 Mass flux and total temperature of incoming fluid is fixed
 Velocity
 Velocity magnitude and temperature is held fixed. Total pressure is allowed to vary at inflow
 Velocity boundary type is not applicable for compressible flow
 Total Pressure type BCs are recommended for External flows
 Internal flows are modeled by Velocity or Mass Flux type BCs
 Inflow Direction
 Direction cosines can be specified or user can choose the flow to enter normal to the boundary
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Outflow Boundary Conditions
 Static pressure value is required at outflow
 If outflow is at supersonic conditions, static pressure is extrapolated from domain
Backflow
 Certain physical conditions or intermediate transients gives backflow as solution
 Total temperature value is utilized
 Static pressure is assumed as total pressure
 For subsonic external aerodynamics, outflow should be placed at distance of 6 times
the body length
 Complete supersonic outflow can be placed close to the body
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Wall Boundary Condition
 A wall can be tagged BCWall, BCWallInviscid, BCWallViscous or
BCWallViscousIsothermal
 A wall without label is assumed stationary and adiabatic
 Moving wall effect can be simulated by providing either constant wall velocity or
velocity as a function of coordinate position
 Wall tagged with BCWallViscousIsothermal requires specifying wall temperature
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Farfield Boundary Condition
 For external aerodynamic flow, the boundary of the domain is modeled through
farfield conditions or boundary where inflow/outflow is not known. Applicable for
compressible flows only
 Free stream values for Direction & Mach No. of flow & associated Pressure and
Temperature are required
 At the farfield, the normal velocity & speed of sound are obtained from the Riemann
invariants:
 R- is evaluated from conditions inside the domain & R+ from conditions outside the
domain
 The entropy, is determined using values of free stream conditions for inflow &
from inside the domain for outflow
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𝑅± = 𝑢 ±
2𝑎
𝛾 − 1
𝑝/𝜌 𝛾
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Spalart Allmaras Turbulence Model
 It is one equation turbulence model with transport equation for turbulent viscosity
assembled using empiricism and dimensional analysis
 It has good numerical stability & insensitivity to free-stream
 SA model is integrated to the wall
 It requires at least 15 grid points inside boundary layer and 1st grid point at y+ ~ 1
 It is very well accepted by aerospace community for external aerodynamics
 If grids are coarse, wall functions are used to model near wall turbulence
 Distance of each grid points from nearest wall is required in the model. This
calculation is computationally expensive step and distance is stored in solution CGNS
File
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K Epsilon Turbulence Model
Standard K Epsilon Model
 It is a two equation turbulence model derived from RANS modeling: Ensemble
Averaging
 k is turbulent kinetic energy
 ε is turbulence dissipation rate
 Turbulence viscosity is derived from k & ε and its effect is modeled in momentum
equation
 Most widely used industrial model
 Applicable for fully turbulent flow (free shear flow)
 It fails in boundary layer and requires wall function for near wall modeling
 It is not recommended for separated flow
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K Epsilon Turbulence Model
Low Reynolds No. Chien K Epsilon Model
 Wall function are very limited approximations and do not perform well in flow fields
where law of wall does not hold good like flow with high strain rate and adverse
pressure gradients
 Turbulence closure equations and closure coefficients are modified to take into
account the viscous and preferential damping effects offered by wall
 When it comes to applicability over a variety of flows, such Low Re corrections
perform better than wall function approach
 It requires atleast 10 grid points inside boundary layer and 1st grid point at y+ ~ 1-3
 Distance of each grid points from nearest wall is required in the model. This
calculation is computationally expensive step and distance is stored in solution CGNS
File
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SST Turbulence Model
 It is a blend of two most successful model in two-equation model regime
 K-omega and k-epsilon model are blended in such a fashion that it behaves like k-
omega model near wall and like k-epsilon model in free shear layer zone
 It is free from free stream turbulence sensitivity also provides good results in near
wall region
 Modeling of Eddy Viscosity is modified to take into account the higher production to
destruction ratio in adverse pressure gradient flows, hence good performance in APG
flows
 It requires about 10 grid points inside boundary layer and 1st grid point at y+ of 1-3
 It is a popular model in flows with APG for its robustness
 Distance of each grid points from nearest wall is required in the model. Calculation is
computationally expensive step and distance is stored in solution CGNS File
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Boundary Turbulence Parameters
Spalart Allamaras Model
 For external aerodynamic application, free-stream / inflow eddy viscosity ratio is set
as 0.1 assuming that surface turbulence dominates the physics
K-Epsilon / SST Model
 It is difficult to provide direct values for k, ε, ω. Following derived quantities are
used:
 Turbulence Intensity – Usually 1 - 5 % for most of the cases. ~ 0.16 Re-1/8.
 Eddy Viscosity Ratio – For external flows, 1 < μT
/μ < 10
 Turbulence Length Scale – For internal flow, L = 0.07D, where D is hydraulic diameter
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𝑘 = 1.5 𝐼 𝑈 2
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Global Initial Conditions
Menu Execution Initial Condition
 Explicit methods start from an initial state and proceed towards steady state through
time steps
 User should provide the initial condition as close as expected steady state solution
 For external aerodynamic studies, initial conditions same as free-stream / inflow
conditions are recommended
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Zone Specific Initialization
 Some cases may require different initialization for different zones e.g., transient
simulations, multiple frames, multi-physics. Accordingly one can choose to initialize
any specific zone or group of zones.
 Go to Execution  Initial Condition  Zone Specific Initialization
 Select zones to be initialized and move them to selected zone column
 Enter initial values of variables in corresponding boxes
 Click OK to confirm
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Execution Setup
Time Accuracy
 Steady
 Residues are driven to zero
 Most aerodynamic application are steady state calculation
 Unsteady
 Residues oscillates with iteration
 Bluff bodies shed vortices behind them
 Time Marching
 Global
 Properties at each cell are updated by equal time step, which is minimum in the domain
 Compressible unsteady calculation requires global marching
 Local
 Each cell is updated with its own maximum stable time step. Time accuracy is destroyed.
 Convergence is faster. Suitable for viscous calculations
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Execution Setup
Runge-Kutta Order
 Runge-Kutta scheme integrates the discretized equation over a time step
 Higher Runge-Kutta order produces time accurate solutions for compressible
unsteady cases
 4th order Runge-Kutta is most efficient in terms of accuracy and convergence
Advanced Parameters
 CFL (Courant, Friedrich, Lewy Number)
 CFL limits the time marching steps for explicit methods
 Lower CFL values increases accuracy and stability but at the expense of convergence time
 CFL ~ 0.2 is recommended for most of the steady state cases in FlowZ
 Larger values of CFL are applied for higher Runge-Kutta order
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Execution Setup
 Incompressible unsteady flows simulations employ dual time stepping, multistage
time integration method
 It is three-point backward difference in time and require two additional inputs
 Physical time-step – Every outer iteration covers the time step value as defined here
 No. of sub-iterations – Outer iterations consist of several sub-iterations required to converge
the solution at each physical timestep
 Residue Norm
 Three options are available to normalize the cell residues
 L Infinity – Maximum cell residue is picked
 L1 – Sum of absolute values is evaluated
 L2 – Mean RMS values of cell residues
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Run Solver
Menu  Execution  Run
 Name Output CGNS File
 User can view the setup in solver control file through ‘View Execution Setup’
 It is recommended that user Save Control File for its future use
 Solver monitor file (.smf) would store the residues during execution
 ‘Run Solver’ would launch the solver
 User should monitor the residue fall for initial 10 iterations before firing it for large
number of iterations
 Use Gnuplot to visualize
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Execution Analysis
 Use Gnuplot / MSExcel to plot ‘solver monitor file’ (.smf) over iterations for:
Residue fall
 Should go down as much as possible (preferably 4 order fall)
Pressure and frictional forces & moments
 Should stabilize
Global Mass Convergence
 Should be achieved
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Initialization from Existing Solution
 Menu  File  Read Control File
 Read existing solver control file (.scf)
 Menu  Turbulence  Spalart Allmaras
 Pick ‘distance from wall’ from CGNS file
 Menu  Execution  Initial Condition
 Select “All Values from CGNS File”
 Import solution CGNS file
 To Continue Execution
 Change the number of iteration
 Set output CGNS file, control file & Run Solver
 To Post Process
 Set No. of Iteration to Zero
 Set Post Process options & Run Solver 36
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Monitor Data
 The progress of the simulation can be monitored at each iteration through derived
physical quantities.
 For external aerodynamics, pressure & skin forces in the three directions on selected
surfaces can be stored in monitor file.
 For internal flows, global conservation of mass can be monitored by evaluating &
storing amount of mass coming in & going out of the domain.
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www.zeusnumerix.com
+91 72760 31511
Abhishek Jain
abhishek@zeusnumerix.com
Thank You !

CFD Lecture (5/8): Solvers- Compressible Flow

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CFD Lecture (5/8): Solvers- Compressible Flow