CFD

What are the physical principles that govern any fluid flow?

Conservation of mass, momentum and energy

What is the conservation form of the continuity equation?

Mass is conserved - net mass flow out element = time rate of decrease of mass inside

How are stresses related in the momentum equation?

Viscous, shear and normal stresses related to time rate of change of deformation of fluid element

What is the no-slip condition?

Viscous flow so zero relative velocity at the wall u=v=w=0

What is Inviscid flow?

Finite non-zero relative velocity value at wall - must be tangent to wall v.n=0

How is turbulent flow characterised?

Small fluctuations in magnitude and direction of fluid particle velocities

How do forces in fluid affect turbulence?

Inertia - carry particle in new direction when disturbed

Viscous forces - tend to make particles conform to motion of main stream

What are characteristics of turbulent flow?

Irregularity

Diffusivity

Rotational

Large and small eddie

Energy dissipation

What is the Direct Numerical Simulation (DNS) method for solving turbulent flow?

Solves exact Navier-Stokes equations

All turbulence scales calculated exactly

No turbulence models used

Mesh needs to be small enough for smallest dissipative scales

Very computationally expensive

What is the Largest Eddy Simulation (LES) method for solving turbulent flow?

Solves filtered Navier-Stokes equations - involves 'turbulence models' for small scale tu

What is the Reynolds Averaged Navier Stokes equations (RANSE) method for solving turbulent flow?

Models all turbulence scale using empirical models

Instantaneously velocity decomposed into time-averaged and fluctuating components

What is the closure problem?

Transport equations derived from Reynolds stresses add more unknowns

What is a solution to the closure problem?

Develop turbulent models to approximate turbulence stresses

What is the concept of eddy viscosity?

Relating Reynolds stresses to mean flow strain rates

What is the Prandtl hypothesis?

Eddy viscosity is proportional to the product of a characteristic turbulence velocity (u) and turbulence length scale (l)

What are advantages of zero-equation turbulence models?

Easy to implement

Fast

Good for simple flows

What are disadvantages of zero-equation turbulence models?

Unable of describing flows where turbulence length scale changes

Only calculates mean flow properties and turbulent shear stress

Can't switch from one region type to another

What are advantages of one-equation turbulence models?

Good for attached, wall bounded flows, mild separation

What are disadvantages of one-equation turbulence models?

Bad for:

Massively separated flows

Free shear flow

Complex internal flows

What are advantages of k-E turbulence models?

Simple to implement

Converge easily

Reasonable predictions for many flows

What are disadvantages of k-E turbulence models?

Poor for strong separation and rotation

Bad for axisymmetric flow

Needs wall function implementation

What are advantages of k-w turbulence models?

Better than k-E for transitional flow

Numerically stable

Low-Re version more economical

What are disadvantages of k-w turbulence models?

Not consistent

Sensitive to free stream boundary conditions

What happens to velocity and wall distance in the law of the wall?

Normalised using inner scale (U+ vs ln(y+))

What is the law of the wall?

Mean velocity is proportional to log of distance from a solid wall for turbulent flow

What do wall function based on law of the wall assume?

Universality of turbulent flows - fails at flows influenced by pressure gradients deviate from universal profile

What is the wall-function turbulence model?

Used to bridge wall & outer region of flow

Only applicable to outer region

First node must be away from wall (y+ >30)

What is the wall-resolved turbulence model?

Directly solves near-wall flow

Considers viscous, high strain rate and wall effects

First node close to wall (y+<1)

Near-wall boundary layer needs to be well-resolved

What is the enhanced wall treatment?

Combines two-layer zonal model with advanced wall function

What are advantages of standard wall functions (wall-function)?

Economical

Robust

Reasonably accurate

What are disadvantages of standard wall functions (wall-function)?

Bad for:

Adverse pressure gradients - separation

Strong body force

Strong 3D effects

What are benefits of structured meshes?

Less memory

More accurate

What are disadvantages of unstructured meshes?

Memory & CPU overhead

More diffusive - less accurate

What is discretisation?

Approximation of RANS using algebraic equations for nodal values of velocity, pressure, etc

What is the Finite Difference (FD) method of discretisation?

Uses Taylor series to discretise PDEs

What are advantages of the Finite Difference (FD) method of discretisation?

Show truncation errors explicitly

Allows schemes higher orders of accuracy to be readily developed

Easy to apply for simple geometry

What are disadvantages of the Finite Difference (FD) method of discretisation?

Hard for complex geometry

Conservation not guaranteed

What is the Finite Volume (FV) method of discretisation?

Flow domain split into small control volumes (CVs)

PDEs integrated over CVs then discretised

What are advantages of the Finite Difference (FD) method of discretisation?

Suitable for complex geometry

Conservation ensured

What is the First-Order Upwind Scheme?

Simple scheme for approximating cell face values for convective terms

Accounts for direction of flow

What are advantages of First-Order Upwind Scheme?

Stable

Bounded

What are disadvantages of First-Order Upwind Scheme?

Very diffusive - only 1st order accurate

What is the Second-Order Upwind Scheme?

Determines value of phi(e) by firing line through 2 nodes upstream of face 'e'

What are advantages of Second-Order Upwind Scheme?

Second order accurate

What are disadvantages of First-Order Upwind Scheme?

Not bounded - can produce over/undershoots in regions of steep gradients

What is the QUICK convection scheme?

Fits parabola between 3 points to approximate phi(e)

What are advantages of the QUICK Scheme?

Third order accuarte

What are disadvantages of the QUICK Scheme?

Not bounded - over/undershoots

What are segregated algorithms for incompressible flows?

Solves transport equations iteratively until convergence

Used for pressure-based solvers

What are coupled algorithms for incompressible flows?

Conservation equations for U, V, W and continuity solved simultaneously at every iteration for pressure and velocity

Used for pressure-based solvers

What are density-based solvers?

Continuity, momentum and energy equations solved simultaneously at each cell during iteration

Used for compressible flows

What do residuals do?

Measure error in solving conservation equations

What is verification?

'Solving the equations right'

Determines accuracy of CFD model

What is validation?

'Solving the right equations'

What is the explicit scheme for unsteady flows?

No iterations - cheap to run

May be unstable

Requires small time step

First order accuracy

What is the implicit scheme for unsteady flows?

Stable in theory - may be unstable if time step too big

Solves large set of equations - expensive

First order accuracy

What is a Eulerian approach?

Observes fluid properties at fixed locations in space

What is the Lagrangian approach?

Track individual fluid particles

What is the total/subtsantial derivative?

Represents total rate of change experienced by a moving fluid particle

Local change + convective change

What is the Boussinesq hypothesis?

Assumes Reynolds stresses are proportional to mean strain rate through and eddy viscosity

What are under-relaxation factors?

Damps solution updates to improve stability and convergence

What Mach number does flow usually become compressible?

0.3

What is U+?

Ratio of velocity parallel to the wall and friction velocity

What is friction velocity?

Velocity scale used to represent boundary shear stress (u = sqrt(tau/rho))

What do the terms in the momentum equations accounting for turbulent effects contain?

Reynolds stresses

What is the kinematic turbulent viscosity proportional to?

Product of turbulent length and time scales

What bias should the numerical convection schemes have?

Upwind - more stable

What do explicit methods requires?

CFL (Courant-Friedrichs-Lewy) number < 1

What does the pressure correction scheme ensure?

Mass conservation

What is the Stokes relationship?

Relationship between viscous stresses and velocity gradients

What are Reynolds stresses?

Stress due to velocity fluctuations

What is the turbulence velocity scale?

Square root of turbulent kinetic energy

What is dynamic eddy viscosity proportional to?

Turbulence kinetic energy (k) and turbulence time scale (tau)

When are Reynolds stress turbulence models useful?

When flow is dominated by swirl

What is the number of discretised equations equal to?

Number of discretised internal cells