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# ES174, car Aerodynamics - PowerPoint PPT Presentation

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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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

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.

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

compare with

Euler Equations

(components separately)

Navier-Stokes Equations: Euler Equations + viscosity

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

From

the Album of Fluid Motion

by Milton Van Dyke

Higher velocity  Lower pressure

Air Density approximately  1.2 kg/m3

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

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

Boundary layers: laminar, turbulent + thickness estimates

Laminar flow, turbulent flow;

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

Lift, form drag, skin friction

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)

Does the flow separation occur

in the simulation as it does in reality?

Meshes

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

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)

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

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

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

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.

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/

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