CFD 3 Flashcards
(108 cards)
1
Q
What is the Eulerian point of view?
A
Stationary
2
Q
What is the Lagrangian point of view?
A
Moving
3
Q
Define: Total Derivative
A
Time rate of change following a moving fluid
4
Q
Define: Local Derivative
A
Time rate of change at a fixed point
5
Q
Define: Convective Derivative
A
Time rate of change due to movement of fluid
6
Q
Write down the continuity equation
A
drho/dt + div . (rho V) = 0
7
Q
Write down the continuity in total derivative form
A
Drho/Dt + rho div . V = 0
8
Q
What is conserved in the continuity euqation?
A
Mass
9
Q
What is conserved in the momentum equation?
A
Momentum
10
Q
Define the stokes hypothesis and what two quantities it relates
A
Relates viscous stresses and velocity gradients
11
Q
Give an example of a body force
A
Weight, EM
12
Q
Give an example of a surface force
A
pressure or viscous
13
Q
what are the two types of viscous forces
A
normal and shear
14
Q
Is there a pressure gradient in pressure driven flow
A
Yes
15
Q
Is there a pressure gradient in shear driven flow
A
no, zero pressure gradient
16
Q
What is the relationship of U and x for fully developed flow
A
du/dx = 0
17
Q
What can you say about laminar flow in terms of forces
A
Viscous effects dominate,
they eliminate any deviation
18
Q
What can you say about turbulent flow in terms of forces
A
Inertial effects dominate,
viscous forces are inadequate to overcome inertia forces
19
Q
What causes turbulence
A
surface roughness,
geometry,
pressure gradients,
outside disturbances
20
Q
What are the characteristics of turbulent flow?
A
Diffusivity, Transport, eddies
21
Q
What do large eddies cause
A
perpendicular motion
22
Q
What do small eddies cause
A
diffusion of particles
23
Q
what equations does the DNS solves
A
exact navier-stokes
24
Q
what turbulence scales are solved in DNS
A
all scales solved exactly
25
what are the downsides of DNS
computational expense
26
What equations do LES solves
filtered navier-stokes
27
what is the mesh requirement for DNS
mesh < smallest scale
28
what scales are solved exactly in LES
large scales
29
what scales are modelled in LES
small scales
30
what is the mesh requirement of LES
mesh < smallest exact large scales
31
what kind of filtering is applied to LES navier stokes
low pass,
removes small scale info
32
what equations does RANS solve
RANS
33
what is the mesh requirement of RANS
mesh < mean flow
34
what is the benefit of RANS
less computationally expensive
35
what is the reynolds decomposition
u = u bar + u'
36
what is u+
velocity parallel to the wall / frictional velocity
37
what is frictional velocity
sqrt(Tau_w / rho)
38
what Re flow is valid for DNS
low - Re, as Re increases eddy become smaller
39
which wall model is high - Re
wall function model
40
What is the reynolds stress equation?
rho u'u' bar
41
what are reynolds stresses
stresses due to velocity fluctuations
42
what is the order for RANS
1. reynolds decomposition
2. time averaging
3. linea/non-linear terms
43
What is the eddy viscosity concept? (Similar to the Stokes Hypothesis)
relates reynolds stresses to strain rates (velocity gradient) of mean flow
44
Who discovered eddy viscosity?
Boussinesq
45
What is the Boussinesq hypothesis
Tau_xy = - rho u'v' bar = mu_t (dU/dy)
46
What are some eddy viscosity models
k-epsilon,
k-omega,
mixing length
47
what is the prandtl hypothesis
V_t proportional to u . l
48
what is the turbulent velocity scale in both k-epsilon and k-omega
k^1/2
49
what is the turbulent length scale in k-epsilon
k^3/2 / epsilon
50
what is the turbulent length scale in k-omega
k^1/2 / omega
51
what is the relation between omega, k and epsilon
omega = epsilon / k
52
what is the eddy viscosity equation for k - epsilon
v_t = C_mu k^2 / epsilon
53
what is the eddy viscosity equation for k - omega
v_t = k / omega
54
what is the relation between omega and tau
omega = 1 / tau
55
what is tau in eddy viscosity models
turbulent time scale
56
what is the relation for the mixing model for velocity
u proportional to lm |dU/dy|
57
what is the relation for the mixing model for eddy viscosity
v_t = (ky)^2 |dU/dy|
58
what are the two categories of models that fall under RANS
Eddy viscosity and reynolds stress model (RSM)
59
what types of flow would you choose to use a RSM
swirling or strong curvature
60
how many equations are in the prandtl mixing length model
zero
61
what are the benefits of zero equation models
fast, easy
62
what are the disadvantages of zero equation models
simple flows only,
not good when length scale varies
63
what are the benefits of the one equation model
economical,
good for mild separation and attached flow
64
what are the downsides of the one equation model
bad for large separation or complex geometry
65
what are the benefits of the k - epsilon two equation model
simple,
easy convergence,
reasonable accuracy
66
what are the downsides of the k - epsilon two equation model
not good for separation,
insensitive to pressure gradients or rotating flows
67
what are the benefits of the k - omega two equation model
good for transitional flows,
good BL accuracy
68
what are the downsides of the k - omega model
inconsistent for freestream/simple flows,
computational cost
69
what are non - linear models best suited to
streamwise curvature
70
what does the wall-resolved model consider
strain rates and viscous effects
71
what are the benefits of the equilibrium wall function
economical,
robust,
reasonable accuracy
72
what are the downsides of the equilibrium wall function
no good for adverse pressure gradients or 3D effects
73
what is the benefit of using the non - equilibrium wall function
it sensitises pressure gradients
74
What are the benefits of the Finite Difference method?
Higher order (more accurate)
Easier to implement
structured mesh
75
What are the downsides of the Finite Difference method?
Simple geometry only,
conservation not guaranteed,
unstable
76
What are the benefits of the Finite Volume method?
Good for complex geometry,
conservation is inherent,
stability
77
What are the downsides of the Finite Volume method?
unstructured mesh,
harder to implement,
less accurate (lower order)
78
what are the benefits of 1st order upwind
stable (bounded)
79
what are the downsides of 1st order upwind
less accurate
80
what is the benefits of 2nd order upwind
more accurate
81
what are the downsides of 2nd order upwind
unsteady (unbounded)
82
What is meant by excplicit?
Next depends on current and previous
83
What are the benefits of explicit?
Cheap (not iterations)
84
What are the downsides of explicit?
Unstable
85
What is the CFL number and what is its range?
CFL = U delta t / delta x < 1 (keeps a small timestep)
86
What are the benefits of implicit?
Stable
87
What are the downsides of implicit?
Expensive
88
What does implicit mean?
Current depends on current and previous
89
Central Difference equation
(phi_i - phi_j) / dx_ji
90
What are density based solvers for
compressible flow, explicit and implicit
91
What are pressure based solvers for
incompressible flow, implicit only
92
What is pressure correction used to conserve?
Mass
93
What are the benefits of direct methods?
Accurate (such as LU decomposition)
94
What are the downsides of direct methods?
Expensive
95
What are the benefits of iterative methods?
efficient (Gauss-Siedel)
96
What are the downsides of iterative methods?
approximate
97
What are the benefits of multigrid methods?
Global errors reduce faster
98
What does the under relaxation factor do?
Stabilises convergence
99
What are the downsides of an unstructured mesh?
Numerical diffusion,
less accurate,
computationally expensive
100
What are some mesh quality measurements?
Skewness,
aspect ratio,
smoothness,
flow alignment
101
What causes divergence?
poor mesh,
BC's
bad initial flow
102
What is verification?
Am I solving the equations right?
103
What is validation?
Am I solving the right equations?
104
Which direction is best for convection?
Upwind
105
In the FVM method where are the unknowns applied in discretisation?
In the middle of all control volumes
106
In the FDM method where are the unknowns applied in discretisation?
At the CV faces (vertical lines) but not the edges which are Boundary Conditions
107
What are the ways to reduce oscillations in residuals?
reduce the under relaxation factors,
check mesh quality,
improve initial flow
108
What is the number of discretised equations equal to
internal cells, oner variable per CV
