MEC320 FLUIDS

What defines a Newtonian fluid

The flow curve is a straight line through the origin with gradient mu.

What defines a Non-Newtonian fluid

The flow curve is non-linear or does not pass through the origin.

CFD Advantages

relatively cheap
detailed results
consistent results
complex applications

CFD Disadvantages

Assumptions
needs validation
approximate solution

Governing Principles of a fluid flow

Conservation of Mass
Conservation of Momentum
Conservation of Energy

Steps of CFD process

Understand the physics
Mathematical model
Numerical Model
Solution
Post-processing

What are the two forms of flow model

Eulerian - Conservation form
Lagrangian - Non-Conservation form

What is the Eulerian flow model

Finite control volume fixed in space with the fluid moving through it.

What is the Lagrangian flow model

Finite control volume moving with the fluid such that the same fluid particles are always in the same control volume

Net Mass flow out of element equation?

[d(pu)/dx + d(pv)/dy + d(pw)/dz]dxdydz

Continuity equation 3D - steady state compressible flow

d(pu)/dx + d(pv)/dy + d(pw)/dz = 0

Continuity equation 3D - incompressible, steady or transient

du/dx + dv/dy + dw/dz = 0

Continuity equation - 3D

dp/dt + [d(pu)/dx + d(pv)/dy + d(pw)/dz] = 0

Substantial Derivative Equation

D/Dt = d/dt + u d/dx + v d/dy + w d/dz

what is the local derivative

d/dt = physically the time rate of change at a fixed point

what is the connective derivative

u d/dx + v d/dy + w d/dz = physically the time rate of change due to the momentum of the fluid

meaning of substantial derivative

physically the time rate of change following a moving fluid element

Definition of fully developed flow

no changes in velocity with respect to x distance, du/dx =0

What are numerical solution methods for turbulent flows

Direct numerical simulations (DNS)
Large Eddy simulations (LES)
Reynolds-Averaged Navier Stokes Method (RANSE)

what is u+

the ratio of velocity parallel to the wall to the friction velocity

Who introduced turbulent viscosity

Boussinesq

what is the prandtl eddy viscosity hypothesis

vt ~ u . l = eddy viscosity is proportional to the product of a characteristic turbulent velocity and a turbulence length

What does k and e stand for in the k-e model

k = turbulence kinetic energy
e = its dissipation

What is the turbulence velocity in k - e model

(k^1/2)

what is the turbulence length in the k - e model

k^3/2 / e

what is the turbulence velocity in the k - w model

(k^1/2)

what is the turbulence length in the k - w model

k^1/2 / w

what models are eddy viscosity models

k-e model
k-w model
k-equation model
prandtl mixing length model

what do the terms in the momentum equations accounting for turbulent effects contain

reynolds stresses

what is the stokes relationship

the relationship between viscous stresses and velocity gradients

what is reynolds stress

stress due to velocity fluctuation

y+ equation and variables ?

Uty/v
y = distance from wall
v = kinematic viscosity
Ut = friction velocity

Near wall modelling strategies including y+ values

Wall function model y+ > 30
Wall resolved model y+ < 1
Enhanced wall treatment 1 < y+ < 30

what are low-Re models used for

wall-resolved modelling not low-Re flows

Strengths and weaknesses of wall function model

strengths: robust, economical
weaknesses: poor for low-Re effects, strong body forces, highly 3D flows

Strengths and weaknesses of wall resolved model

strengths: does not rely on empirical relations, good for complex flows

weaknesses: requires very fine mesh, hence expensive

what are the main discretisation methods

Finite difference
Finite volume
Finite element

What are the different pressure based solution schemes

SIMPLE
SIMPLER
SIMPLEC
PISO
Coupled

Difference between segregated and coupled solvers

segregated solvers solve equations sequentially, long solution time. coupled solvers conservation equations are solved simultaneously, converges faster.

What does the mesh affect

rate of convergence
solution accuracy
CPU time required

Important mesh considerations

Mesh topology: shape
mesh density
mesh quality
boundary layer mesh

mesh quality variables

skewness
aspect ratio
smoothness
flow alignment

what do you look at to monitor convergence

residuals
changes in a chosen flow parameter

what is pressure correction used to restore

mass continuity

why use a higher order convection scheme

higher accuracy

What is the requirement for achieving a stable solution, in terms of CFL number

CFL < 1

what does the CFL number represent

the ratio of the time step to the time required for the flow information to be convected across the cell