Cfd Lecture 6f3o24

Introduction to Computational Fluid Dynamics Adapted from notes by: Tao Xing and Fred Stern The University of Iowa

Outline  What

is CFD?  Why use CFD?  Where is CFD used?  Physics  Modeling  Numerics  CFD process  Resources

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What is CFD? 

What is CFD and its objective? – –

– –

Computational Fluid Dynamics Historically Analytical Fluid Dynamics (AFD) and EFD (Experimental Fluid Dynamics) was used. CFD has become feasible due to the advent of high speed digital computers. Computer simulation for prediction of fluid-flow phenomena. The objective of CFD is to model the continuous fluids with Partial Differential Equations (PDEs) and discretize PDEs into an algebra problem (Taylor series), solve it, validate it and achieve simulation based design.

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Why use CFD?  Why

use CFD?

– Analysis and Design 

Simulation-based design instead of “build & test” – More cost effectively and more rapidly than with experiments – CFD solution provides high-fidelity database for interrogation of flow field



Simulation of physical fluid phenomena that are difficult to be measured by experiments – Scale simulations (e.g., full-scale ships, airplanes) – Hazards (e.g., explosions, radiation, pollution) – Physics (e.g., weather prediction, planetary boundary layer, stellar evolution)

– Knowledge and exploration of flow physics

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Where is CFD used? (Aerospace) •

Where is CFD used? – Aerospace – Appliances – Automotive – Biomedical

F18 Store Separation

– Chemical Processing – HVAC&R – Hydraulics – Marine – Oil & Gas – Power Generation – Sports

Wing-Body Interaction

Hypersonic Launch Vehicle

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Where is CFD used? (Appliances) •

Where is CFD used? – Aerospace

– Appliances – Automotive – Biomedical – Chemical Processing – HVAC&R – Hydraulics – Marine – Oil & Gas – Power Generation – Sports

Surface-heat-flux plots of the No-Frost refrigerator and freezer compartments helped BOSCH-SIEMENS engineers to optimize the location of air inlets. 6

Where is CFD used? (Automotive) •

Where is CFD used? – Aerospace – Appliances

– Automotive – Biomedical – Chemical Processing

External Aerodynamics

– HVAC&R

Undercarriage Aerodynamics

– Hydraulics – Marine – Oil & Gas – Power Generation – Sports Interior Ventilation

Engine Cooling 7

Where is CFD used? (Biomedical) •

Where is CFD used? – Aerospace – Appliances – Automotive

– Biomedical – Chemical Processing

Medtronic Blood Pump

– HVAC&R – Hydraulics – Marine – Oil & Gas – Power Generation

Temperature and natural convection currents in the eye following laser heating.

– Sports Spinal Catheter

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Where is CFD used? (Chemical Processing) •

Where is CFD used? – Aerospace – Appliances – Automotive – Biomedical

– Chemical Processing

Polymerization reactor vessel - prediction of flow separation and residence time effects.

– HVAC&R – Hydraulics – Marine – Oil & Gas – Power Generation

Twin-screw extruder modeling

– Sports Shear rate distribution in twinscrew extruder simulation 9

Where is CFD used? (HVAC&R) •

Where is CFD used? – Aerospace – Appliances – Automotive – Biomedical – Chemical Processing

Streamlines for workstation ventilation

– HVAC&R

Particle traces of copier VOC emissions colored by concentration level fall behind the copier and then circulate through the room before exiting the exhaust.

– Hydraulics – Marine – Oil & Gas – Power Generation – Sports Mean age of air contours indicate location of fresh supply air

Flow pathlines colored by pressure quantify head loss in ductwork 10

Where is CFD used? (Hydraulics) •

Where is CFD used? – Aerospace – Appliances – Automotive – Biomedical – Chemical Processing – HVAC&R

– Hydraulics – Marine – Oil & Gas – Power Generation – Sports 11

Where is CFD used? (Marine) •

Where is CFD used? – Aerospace – Appliances – Automotive – Biomedical – Chemical Processing – HVAC&R – Hydraulics

– Marine – Oil & Gas – Power Generation – Sports 12

Where is CFD used? (Oil & Gas) •

Where is CFD used? – Aerospace Volume fraction of gas

– Appliances – Automotive – Biomedical – Chemical Processing

Flow vectors and pressure distribution on an offshore oil rig

Volume fraction of oil

– HVAC&R – Hydraulics – Marine

Volume fraction of water

– Oil & Gas

Analysis of multiphase separator

– Power Generation – Sports Flow of lubricating mud over drill bit

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Where is CFD used? (Power Generation) •

Where is CFD used? – Aerospace – Appliances – Automotive – Biomedical

Flow in a burner

– Chemical Processing Flow around cooling towers – HVAC&R – Hydraulics – Marine – Oil & Gas

– Power Generation – Sports Flow pattern through a water turbine.

Pathlines from the inlet colored by temperature during standard operating 14 conditions

Where is CFD used? (Sports) •

Where is CFD used? – Aerospace – Appliances – Automotive – Biomedical – Chemical Processing – HVAC&R – Hydraulics – Marine – Oil & Gas – Power Generation

– Sports 15

Physics  CFD

codes typically designed for representation of specific flow phenomenon – – – – – – – –

Viscous vs. inviscid (no viscous forces) (Re) Turbulent vs. laminar (Re) Incompressible vs. compressible (Ma) Single- vs. multi-phase (Ca) Thermal/density effects and energy equation (Pr, , Gr, Ec) Free-surface flow and surface tension (Fr, We) Chemical reactions, mass transfer etc…

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Physics Fluid Mechanics Inviscid

Viscous Laminar

Compressible (air, acoustic)

Incompressible (water)

Internal (pipe,valve)

Turbulence External (airfoil, ship)

Components of Fluid Mechanics 17

      u   u   u  0 x y z tutxuxxyuxyxzuzxyxpzxyyxzzxgx Governing Equations

(Equations based on “average” velocity)

Continuity

Equation of motion

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Navier-Stokes Equations

Claude-Louis Navier

George Gabriel Stokes

C.L. M. H. Navier, Memoire sur les Lois du Mouvements des Fluides, Mem. de l’Acad. d. Sci.,6, 398 (1822) C.G. Stokes, On the Theories of the Internal Friction of Fluids in Motion, Trans. Cambridge Phys. Soc., 8, (1845)

D tvpvg

utuxtyzuxxuxuxxyzuyyuyuxyyzzuzuzxuzzyxpzyp2xu22xxuzy2yu22yxzy2zu22zxuzygxgzy 2 Navier-Stokes Equations (constant  and )

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uadtyyp yxu0dydauyx2txyu2xy20,duguyypyy0aztguzyLC11x2yp2xuy2yy2zuygy 0IBn.tCegr 12Ldypg C 2 Navier–Stokes Example

FinalExpresion uy21dypg(Lx-2)

Fluid L

y

x

Laminar Flow Static Parallel Plates

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Modeling 



Mathematical representation of the physical problem – Some problems are exact (e.g., laminar pipe flow) – Exact solutions only exist for some simple cases. In these cases nonlinear can be dropped from the N-S equations which allow analytical solution. – Most cases require models for flow behavior [e.g., K-, K-, Reynolds Averaged Navier Stokes equations (RANS) or Large Eddy Simulation (LES) for turbulent flow] Initial —Boundary Value Problem (IBVP), include: governing Partial Differential Equations (PDEs), Initial Conditions (ICs) and Boundary Conditions (BCs)

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Turbulent Flow Representation (K- as an example) u i  u  u' Where : u'  deviating velocity, u  constant net velocity in the direction of flow, and u i  instantaneous velocity

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Turbulent Boundary Layer y

Bulk Stream

x U0

Edge of boundary layer Outer layer



Fully turbulent layer Sublayer + buffer layer Wall 24

Wall Shear Stress  dU 

 w    

dy 

y u y y     



Friction Velocity

u  y 0

w 

Viscous Length Scale

 

 u

y+ is similar to a local Reynolds number. Small y+ - Viscous effects dominate Large y+ - Turbulence dominates

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y+ and Turbulence Models COMSOL has many turbulent models available Low-Re models require a y+ resolution of < 1 to guarantee accuracy Low-Re models are necessary to accurately estimate skin friction and flow separation High-Re models use wall functions to approximate averaged turbulent flow properties Less accurate, but more computationally efficient In COMSOL, a minimum y+ of 11.06 is enforced. To maintain accuracy, ensure cells meet this requirement 26

Numerics / Discretization  Computational

solution of the IBVP  Method dependent upon the model equations and physics  Several components to formulation – Discretization and linearization – Assembly of system of algebraic equations – Solve the system and get approximate solutions

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u  uxi,ji1,jxi,jx2ui,j2x3ui,j6x2 Finite Differences

Finite difference representation

Truncation error

Methods of Solution

Direct methods

Cramer’s Rule, Gauss elimination LU decomposition

Iterative methods

Jacobi method, Gauss-Seidel Method, SOR method 28

ui1,ji,jui,jx2ui,j2x23ui,j6x3 Numeric Solution (Finite Differences)

jmax j+1 j j-1

o

x

y

i-1 i i+1

imax

Discrete Grid Points

Taylor’s Series Expansion u i,j = velocity of fluid

x

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2 n 2 n afft((:x)x 2        f  f  x  f  x  xi,jn! x)s0in.?2ff((xx))f(x)f0.9xx512 xi,j2  fE (x0a.c2ts)olui0n.2for c(0.os[)2 (09.8)]302E )r .o98075percnt

Finite Difference Truncation Error

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CFD process  Geometry

description  Specification of flow conditions and properties  Selection of models  Specification of initial and boundary conditions  Grid generation and transformation  Specification of numerical parameters  Flow solution  Post processing: Analysis, and visualization  Uncertainty assessment 31

Geometry description  Typical

approaches

 – Make assumptions and

simplifications – CAD/CAE integration – Engineering drawings – Coordinates include Cartesian system (x,y,z), cylindrical system (r, θ, z), and spherical system(r, θ, Φ)

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Flow conditions and properties  Flow

conditions and properties required are unique for each flow code and application – FlowLab requires all variables in dimensional

form – Because of focused application, research codes often use non-dimensional variables.

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Selection of models for flow field 







Direct Numerical Simulations (DNS) is to solve the N-S equations directly without any modeling. Grid must be fine enough to resolve all flow scales. Applied for laminar flow and rare be used in turbulent flow. Reynolds Averaged Navier-Stokes (NS) equations (RANS) is to perform averaging of NS equations and establishing turbulent models for the eddy viscosity. Too many averaging might damping vortical structures in turbulent flows Large Eddy Simulation (LES), Smagorinsky’ constant model and dynamic model. Provide more instantaneous information than RANS did. Instability in complex geometries Detached Eddy Simulation (DES) is to use one single formulation to combine the advantages of RANS and LES.

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Initial and boundary conditions  For

steady/unsteady flow 



IC should not affect final solution, only convergence path, i.e. iteration numbers needed to get the converged solution. Robust codes should start most problems from very crude IC, . But more reasonable guess can speed up the convergence.

 Boundary

conditions

– No-slip or slip-free on the wall, periodic, inlet (velocity

inlet, mass flow rate, constant pressure, etc.), outlet (constant pressure, velocity convective, buffer zone, zero-gradient), and non-reflecting (compressible flows, such as acoustics), etc.

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Grid generation 

Grids can either be structured (hexahedral) or unstructured (tetrahedral). Depends upon type of discretization scheme and application – Scheme  Finite differences: structured  Finite volume or finite element: structured or unstructured – Application  Thin boundary layers best resolved with highly-stretched structured grids  Unstructured grids useful for complex geometries  Unstructured grids permit automatic adaptive refinement based on the pressure gradient, or regions of interest (FLUENT)

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Grid Resolution

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Grid generation and transformation 

 



Grids designed to resolve important flow features which are dependent upon flow parameters (e.g., Re) Commercial codes such as Gridgen, Gambit For research code, grid generated by one of several methods (algebraic vs. PDE based, conformal mapping) For complex geometries, body-fitted coordinate system will have to be applied (next slide). Grid transformation from the physical domain to the computational domain will be necessary

Sample grid established by Gambit of FLUENT

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Grid transformation y



o Physical domain Transformation

x

between physical (x,y,z) and computational () domains, important for body-fitted grids. The partial derivatives at these two domains have the relationship (2D as an example)

o



Computational domain f f  f  f f    x  x x  x  x   f f  f  f f    y y y  y  y  

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Numerical parameters & flow solution Numerical parameters are used to control flow solution. – Under relaxation factor, tridiagonal or pentadiagonal solvers – CFD Labs using FlowLab  Monitor residuals (change of results between iterations)  Number of iterations for steady flow or number of time steps for unsteady flow  Flow solution – Solve the momentum, pressure Poisson equations and get flow field quantities, such as velocity, turbulence intensity, pressure and integral quantities (drag forces) 

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Numerical parameters & flow solution  Typical

time history of residuals  The closer the flow field to the converged solution, the smaller the speed of the residuals decreasing.

Solution converged, residuals do not change after more iterations 41

Post-processing 

Analysis, and visualization – Calculation of derived variables

Vorticity  Wall shear stress – Calculation of integral parameters: forces, moments – Visualization (usually with commercial software)  Simple X-Y plots  Simple 2D contours  3D contour carpet plots  Vector plots and streamlines (streamlines are the lines whose tangent direction is the same as the velocity vectors)  Animations (dozens of sample pictures in a series of time were shown continuously) 

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Post-processing (Parallel Plates)

43

Post-Processing (example)

 Pressure

contour and velocity vectors .  Note the locations of the highest and lowest pressure regions.

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Uncertainty assessment 

Rigorous methodology for uncertainty assessment using statistical and engineering concepts – Verification: process for assessing simulation numerical uncertainty  Iterative convergence: monitoring point & integral quantities should change within the convergence criterions  Grid independent studies: 3-grids and Richardson Extrapolation – Validation: process for assessing simulation modeling uncertainty by

using benchmark experimental data



Certification: full Verification and Validation done for a certain range of geometries & parameters which are well known and then extrapolated, qualitatively as well as quantitative – Simulating flows for which experiments are difficult (e.g., full-scale

Reynolds numbers, hypersonic flows, off-design conditions) – Objective: Simulation-based design

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CFD Example

Sulzer Chemtech 250 Y Plastic Structured Packing

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Geometry • CT > STL > CFD • CT = 0.322 mm Min Resolution • Copy/Pasted 2x • Surface Wrapping • Adaptive Meshing • Tetrahedral Mesh • Polyhedral Mesh 47

Mess Dimensions

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Experiment vs. Simulation

49

Velocity Map

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Software and resources  



CFD software was built upon physics, modeling, numerics . Two types of available software – Commercial (e.g., FLUENT, CFX, Star-CCM, COMSOL) – Research (e.g., CFDSHIP-IOWA, U2RANS) More information on CFD can be got on the following website: – CFD Online: http://www.cfd-online.com/ – CFD software  FLUENT: http://www.fluent.com/  COMSOL http://www.comsol.com/  CD-adapco: http://www.cd-adapco.com/ – Grid generation software  Gridgen: http://www.pointwise.com  GridPro: http://www.gridpro.com/ – Visualization software  Telot: http://www.amtec.com/  Fieldview: http://www.ilight.com/

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