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Learning sources John D. Anderson, Jr., Fundamentals of Aerodynamics Pijush K. Kundu, Ira M. Cohen, Fluid Mechanics. 4th edition, 2008, Academic Press; Books on Fluid dynamics / Fluid mechanics / Hydrodynamics / Aerodynamics; Research papers, especially on methods of computation;

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es174 car aerodynamics

Learning sources

John D. Anderson, Jr., Fundamentals of Aerodynamics

Pijush K. Kundu, Ira M. Cohen, Fluid Mechanics. 4th edition, 2008, Academic Press;

Books on Fluid dynamics / Fluid mechanics / Hydrodynamics / Aerodynamics;

Research papers, especially on methods of computation;

http://mathworld.wolfram.com/

http://scienceworld.wolfram.com/

http://wikipedia.com/

Warning! Be careful when using any info from Wikipedia as it can be inaccurate

Flow visualisation: For example http://serve.me.nus.edu.sg/limtt/#Flow_Gallery

http://alexl.wordpress.com/fascinating-flows/

ES174, car Aerodynamics

computational fluid dynamics cfd
Computational Fluid Dynamics (CFD)

CFD software solves equations

Input: Equations + Boundary Conditions + Grid parameters

Output: Flow structure, Velocity Profiles, Pressure distribution

Flow visualization:

Streamline: A line that is always the same direction as the local flow velocity;

Streak line (Filament line): The line taken up by successive particles of fluid passing through some given point;

Pass line: The path traced by any one particle of the fluid in motion.

notations
Notations

Fluid Velocity, m/s

t Time, s

x, y, z Coordinates, m

Continuity equation

When fluid is treated as incompressible (Mach number << 1, subsonic flow),

so that

equations of motion 2nd newton s law
Equations of motion: 2nd Newton’s law

compare with

Euler Equations

(components separately)

Navier-Stokes Equations: Euler Equations + viscosity

cfd approaches
CFD approaches

Full Navier-Stokes equations: computationally intensive, often unnecessarily

Reynolds-Averaged Navier-Stokes (RANS): Mean Flow + Turbulent pulsations

Large Eddied Simulation (LSE): a relatively new method for turbulent flows

Boundary Conditions: fluid velocity, pressure

Can be more complicated: waves, droplets, compliant walls etc

Grid: must be of an appropriate spacing

Non-uniform grids are very common

warning cfd is not a magic9
Warning! CFD is not a magic

From

the Album of Fluid Motion

by Milton Van Dyke

pressure bernoulli law
Pressure: Bernoulli Law

Higher velocity  Lower pressure

Air Density approximately  1.2 kg/m3

Back-of-the envelope estimate for the Pressure Drag force:

slide16

L

h

Then..

Laminar flow, turbulent flow;

Reynolds number similarity: when Re is high enough, the flow structure does not change

Big whorls have little whorls

That feed on their velocity,

And little whorls have lesser whorls

And so on to viscosity.

Lewis F. Richardson

Lift, form drag, skin friction

..heat conduction etc

Cavity flows + unsteady

Boundary layers: laminar, turbulent + thickness estimates

slide17
Then..

Laminar flow, turbulent flow;

Reynolds number similarity: when Re is high enough, the flow structure does not change

Lift, form drag, skin friction

Cavity flows + unsteady

Boundary layers: laminar, turbulent + thickness estimates

Turbulent boundary layer + CFD movies

http://flow.kaist.ac.kr/bbs/board.php?bo_table=databaseinturbulen&wr_id=5

efluids image gallery: turbulence

http://www.efluids.com/efluids/gallery/gallery_pages/1turbulence_page.jsp

VOLVO car (next page)

http://knol.google.com/k/-/-/yvfu3xg7d7wt/8nue4f/volvocar.jpg

slide18
Cars

Does the flow separation occur

in the simulation as it does in reality?

http://www.fenics.org/w/upload/1/14/Volvo.jpg

meshes
Meshes

Meshes

http://www.scorec.rpi.edu/~garimell/blmesh.html

slide20

Viscous scale  -1

S,

m3/s2

Dynamic range

S = 2/3K-5/3

Energy scale L-1

k, m -1

Then..

Full Navier-Stokes equations: computationally intensive, often unnecessarily

intermediate

Large Eddied Simulation (LSE): a relatively new method for turbulent flows

Reynolds-Averaged Navier-Stokes (RANS): Mean Flow + Turbulent pulsations

Issues: mesh, numerical precision, time dependence (unsteady cavity flow)

Unsteady cavity flow

http://www.hector.ac.uk/casestudies/circular_cavity_flows.php

numerics discretisation

j-2 j-1 j j+1

i+1

i

i-1

x

t (time)

Numerics: discretisation

Vj Vj+1

Euler method: 1st order, i.e. error proportional to  2

Runge-Kutta 45 method: better than 4th order, i.e. error proportional less 4

numerics boundary conditions

inlet:

normal velocity

outlet:

pressure

walls: smooth, zero normal velocity (impermeable)

Numerics: boundary conditions

Turbulence intensity is assumed 2% everywhere (may be varied).

This defines the Turbulent Viscosity (Eddy Viscosity).

Step-by-step instructions (will be posted to the course website):

http://go.warwick.ac.uk/fluidseminar/es174_cfd_2008.pdf

numerics time dependence

f(t)

t (time)

f(t)

t (time)

Numerics: time dependence

Flow simulation toolbox: N-S equations are solved as time-dependent

until the flow stabilises.

When a chosen parameter reaches a constant value, computation terminates.

In reality, this may never happen by either physical or numerical reasons.

When numerical instability occurs, the artificial viscosity is introduced

in the form of higher order derivatives:  4V/ x 4 etc.

more pictures unsteady flow
More pictures: unsteady flow

Helmholtz instability

http://www.iag.uni-stuttgart.de/people/

andreas.babucke/work.html

Instability of a smoke jet

Instability of a jet:

http://alexl.wordpress.com/fascinating-flows/

numerics general

inlet:

normal velocity

outlet:

pressure

walls: smooth, zero normal velocity (impermeable)

Numerics: general

Step-by-step instructions (will be posted to the course website):

http://go.warwick.ac.uk/fluidseminar/es174_cfd_2008.pdf

A general advise:

Do not pay too much attention to detailed sketching of the car.

Instead, try to understand results of the simulation for a relatively simple shape:

● plot streamlines, try to understand if the flow separation occurs;

● plot velocity and pressure profiles along and across the tunnel;

● calculate the pressure force acting on upstream-facing panels

… etc.

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