Exam Questions

Question 1

What are the different engineering approaches available to analuse a fluid problem and which approach is the most useful one?

Answer 1

Pure theory; pure experiment; CFD

Question 2

What is CFD

Answer 2

Combination of Applied Maths, ComSci, Fluid Mechanics (Physcis).

Question 3

5 steps of CFD analysis

UMN SP

Answer 3

Understand the physics

Mathematical model

Numerical model

Solution

Post-processing

Question 4

What are the physcial principles that can be used to analyse any fluid flow problem?

Answer 4

Conservation of mass

Conservation of energy

Conservation of momentum

Question 5

What is a closed (analytical) solution of a set of equations?

Answer 5

A solution that is expressed explicity using mathematical functions and formulae.

Question 6

What is the difference between a mathematical and numerical model?

Answer 6

Mathematical models are from physical principles to mathematical equations.

Numerical models are from mathematical equations to numerical/algebraic equations through use of a mesh.

Question 7

Why is CFD considered a “compromise” between having, or not having, a solution of the Navier-Stokes equations?

Answer 7

CFD provides an approximate, numerical solution to equations that are too complex to solve analytically.

Question 8

What is the difference between a Eulerian and Lagrangian approach when selecting a model of the flow?

Answer 8

Question 9

What is the physical meaning of the total derivative when quantifying a change in a fluid variable such as temperature? In this context, what is the physical meaning of the local and convective derivatives?

Answer 9

Substantial derivative: physically the time rate of change following a moving fluid element

Local derivative: physically the time rate of change at a fixed point

Convective derivative: physically the time rate of change due to the movement of the fluid

Question 10

What do the various terms in the continuity equation mean physically?

Answer 10

Question 11

Answer 11

(a), (c) are correct ((b) is wrong because it is 2D and unsteady, (d) is wrong because it is incompressible)

Question 12

Answer 12

(b) is correct ((a) is wrong because density is constant in the incompressible case, (c) is wrong because it is 2D, (d) is wrong because density is constant in the incompressible case)

Question 13

Answer 13

(a), (b), (c) are correct ((d) wrong because density is constant in the incompressible case)

Question 14

Answer 14

(b), (c), (d) are correct ((a) is wrong because it is steady)

Question 15

What types of forces can act on a fluid element?

Answer 15

Body/Volume forces: act on the volumetric mass of the fluid element “at a distance”. Eg. gravitational, electric, magnetic.

Surface forces: act on the surface of the fluiod element. Two types: pressure and viscous (shear/normal) stress.

Pressure imposed by outside fluid surrounding the fluid element (“thermodynmic pressure” associated with particle collision at microscopic level).

Viscous imposed by outside fluid “tugging” or “pushing” on surface by means of friction.

Question 16

Stokes’ hypothesis?

Answer 16

Relation between viscous stresses and velocity gradients.

Question 17

In a fully developed flow within a straight cylinder with its axis along the x direction, is du/dx significant or not? Is du/dy significant or not?

Answer 17

du/dx = 0

Question 18

Can you solve the Navier-Stokes equations analytically?

Answer 18

Only for a limited number of simple flow problems.

Question 19

What does “flow is fully developed” mean?

Answer 19

du/dx = 0

Shape of velocity profile is constant

Flow is steady in terms of velocity distribution

Question 20

Answer 20

Question 21

Role of viscous/inertial in laminar and turbulent flow

Answer 21

Laminar: viscous forces are sufficient to eliminate effect of any deviation.

Turbulent: viscous forces are inadequate and inertial forces are dominant.

Question 22

What other factors influence turbulence other than inertial and viscous forces?

Answer 22

Re

Question 23

What are the main features of turbulent flow?

DRLE

Answer 23

Diffusivity

Rotational

Large and small eddies

Energy dissipation

Question 24

What are the main differences between DNS, LES and RANS methods? What are the potential limitations when using empirical turbulence models as in RANS and LES?

Answer 24

DNS solves exact NS equations

LES solves filtered NS equations

RANS solves RANS equation

Question 25

What is the Law of the Wall?

Answer 25

Average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the wall or boundary of fluid region.

Question 26

What are u and y plus and equations?

Answer 26

U+ represents the local velocity normalised by the wall shear. It tells you how fast the flow is moving at a given point relative to the shear-induced velocity scale near the wall.

Question 27

What are the differences between Navier-Stokes and Reynolds Averaged Navier-Stokes equations (RANS)?

Answer 27

RANS equations include additional unknowns (Reynolds stresses) which need modelling. Uses averaged velocity.

Question 28

What do we mean by linear and non-linear terms in the momentum equations?

Answer 28

Order of magnitude of a variable is greater than 1. Doesn't include ordered derivatives.

Question 29

Where do the Reynolds stresses come from?

Answer 29

Non-linear convection terms

Question 30

What is Boussinesq hypothesis?

Answer 30

Question 31

What is eddy viscosity based on?

Answer 31

Analogy between viscous and turbulent stresses.

Question 32

Can you describe how each term of the k-equation is treated in turbulence models (i.e., modelled or in exact form)? Also their meanings.

Answer 32

∂k/∂t - exact - time change Uj(∂k/∂xj) - exact - advection Pk - modelled - production by shear Epsilon - modelled - dissipation by viscosity ∂/∂xj[(v+(vt/σk))∂k/∂xj] - spread of turbulence

Question 33

Meaning of each term in epsilon equation

Answer 33

Question 34

In theory, one can develop a turbulence model based on any two turbulence variables. Can you write down the expression of eddy viscosity based on k and tau, and the latter is a turbulence time scale?

Answer 34

Question 35

Can you describe the general ideas about how model constants are determined using a couple of sentences?

Answer 35

They are tuned using various typical flows. Using simple flows, where equations will have fewer terms so only one or two constants appear in the equation, which can be tuned to experimental data.

Question 36

8. Calculate eddy viscosity for the pipe flow using the DNS dataset provided.

Answer 36

Question 37

Answer 37

Question 38

What are the differences between eddy viscosity turbulence models and Reynolds stress models?

Answer 38

Eddy viscosity models use 1-2 governing equations; Reynolds use 6 stress equations. EVMs are simpler, more efficient, and work well for many practical flows. RSMs are more complete and accurate, especially for complex turbulent behaviour. Higher complexity and computational power.

Question 39

Compare k-omega and k-epsilon

Answer 39

epsilon - dissipation rate of turbulent kinetic energy omega - specific dissipation rate (per unit of turbulent kinetic energy)

Question 40

What are the reasons that RSMs are not widely used?

Answer 40

Computationally expensive Tough to converge

Question 41

Wall function vs wall resolved y+

Answer 41

function y+>30 resolved y+ < 1

Question 42

Difference between enhanced wall treatment and standards, non-equilibrium wall functions

Answer 42

EWT: combines a two-layer model with an enhanced wall function EWT: first node placed anywhere in theory

Question 43

4. Why are low-Reynolds number turbulence models not necessarily for flows of low Reynolds number?

Answer 43

Low-Re models are for wall-resolved modelling, not necessarily low-Re models

Question 44

What is the requirement on the mesh when the Enhanced Wall Treatment of FLUENT is used?

Answer 44

1 < Y+ < 30

Question 45

What is a truncation error?

Answer 45

Arises because we truncate (cut off) a Taylor series expansion.

Question 46

What is the order of accuracy?

Answer 46

How fast numerical error decreases with mesh refinement. A method is said to be n-th order accurate. 2nd order: halving grid size reduces error by factor of 4, etc...

Question 47

Why is interpolation needed in the context of the FVM?

Answer 47

Question 48

What is the advantage of the first order upwind scheme?

Answer 48

It's always bounded.

Question 49

What does boundedness mean?

Answer 49

Values preducted by the scheme should be within realistic/physcial bounds

Question 50

Compare finite difference and finite volume methods?

Answer 50

FD most basic: Taylor series used to dicretise PDEs, allows schemes of higher orders of accuracy readily developed. Easy to apply for simple flow geometry, using structured mesh. Conservation not guarenteed. FV: flow domain divided into large number of small control volumes of any shape. PDEs then integrated over these CVs, before discretisation. Suitable for complex geometries using structured or unstructured mesh.