Question 1 Flashcards
(28 cards)
What are three key advantages that make CFD a valuable tool for engineers?
CFD allows in-situ measurement of all field variables anywhere and anytime.
It can replace complex and costly experiments, especially during early design stages.
CFD enables the analysis of dangerous or extreme conditions (e.g., very hot gases, reactive flows, radioactive substances) which are difficult to replicate experimentally
What factors are essential for ensuring the applicability of a CFD simulation to real-world scenarios? Why might this applicability not always be guaranteed?
Essential factors include:
Correct physical modeling (e.g., using valid assumptions like continuum hypothesis, correct material properties).
Accurate mathematical modeling (e.g., conservation equations).
Reliable numerical modeling (e.g., proper discretization, error minimization).
Applicability might fail due to model simplifications, multiscale interactions, or numerical limitations, leading to deviations from real behavior
What crucial aspect did Richardson overlook in his 1922 weather simulation, and how did this contribute to the failure?
He overlooked the effects of turbulence.
This omission caused his manually calculated simulation to diverge, making the prediction inaccurate
What does the acronym CFD stand for in English?
Computational Fluid Dynamics
Outline the three fundamental modeling steps that form the basis of every flow simulation.
Physical modeling – translating the real-world flow into a model using assumptions and approximations.
Mathematical modeling – formulating equations (e.g., Navier-Stokes) to describe the physical model.
Numerical modeling – discretizing and solving the equations computationally using algorithms
.
What is the greatest challenge in simulating the launch of a rocket? Provide an example.
The main challenge is handling multiscale, interacting physical phenomena, such as:
High-speed compressible flows, shock waves, combustion, and turbulence.
Example: Accurately predicting shock interactions in the nozzle and around the launch pad, which requires very fine resolution and coupled models
Describe the ‘Periodic Hill Flow’ benchmark experiment and its associated simulation challenges.
The experiment:
A benchmark test (ERCOFTAC 9.2) involving flow over periodic hills to evaluate simulation methods.
Features: flow separation on a curved surface, simple geometry, and incompressible flow at Re=10595.
b) Challenges:
Unsteady vortex structures (e.g., Kelvin-Helmholtz, Görtler instabilities).
Results are highly sensitive to numerical resolution and turbulence model used.
Significant discrepancies between models and simulation codes even in this “simple” setup
Name the three consecutive work steps for conducting a CFD simulation.
Preprocessing – Grid creation, model and boundary condition setup.
Solution – Numerical computation of the flow field.
Postprocessing – Visualization and evaluation of results
How do fluid and solid differ under shear stress?
Fluids: Shear stress ∝ rate of deformation (→ continues to deform).
Solids: Shear stress ∝ deformation itself (→ deforms to a point, then resists further)
The gas flow in the lung capillaries is to be calculated. By which dimensionless number can you determine whether a calculation with the finite volume method is justified? How is it defined? Which alternative method would you suggest if a finite volume method is not justified?
Knudsen number:
Kn=𝜆/𝐿 (mean free path / characteristic length)
If Kn ≪ 1, finite volume method is justified (continuum assumption holds).
If Kn > 10, use Molecular Dynamics Simulation instead
Which dimensionless number:
i. describes the ratio of inertial to frictional forces in a flow? Name and formula.
ii. describes the compressibility of a flow? Name and formula.
iii. represents the ratio of inertial to surface forces? Name.
iiii. plays an important role in unsteady flow separation around blunt bodies? Name.
iiiii. is relevant for describing a thermal boundary layer? Name.
iiiiii. represents the ratio of inertial to gravitational forces and is therefore relevant for calculating
gravity waves? Name.
Name: Reynolds number
Formula: Re=𝜌𝑈𝐿/𝜇
Name: Mach number
Formula: Ma=𝑈/𝑐
Name: Weber number
Name: Strouhal number
Name: Prandtl number
Name: Froude number
Given the total derivative of the quantity φ(x,t), what is the difference compared to
the material derivative? Why is the material derivative used more often in fluid
mechanics?
Mark local and convective terms in material derivative. Which becomes zero in steady flow?
Unknowns and equations in compressible 3D flow?
Unknowns (6): 𝜌,𝑢,𝑣,𝑤,𝑝,𝑇
Equations (3):
Mass conservation
Momentum conservation (x, y, z)
Energy equation
Equation of state (e.g., ideal gas law)
What describes the mass conservation of an incompressible fluid?
∇⋅ u =0 (divergence-free velocity field)
Which term in momentum conservation vanishes in creeping flow? Consequence?
Given the momentum conservation in integral form:
Mark with ① the dominant term in the case of a creeping flow and with ② the term
that can most likely be neglected. (2 pts)- Mark with ③ the dominant term in the case of a flow with Re → ∞. Mark with ④ the
term that can be neglected. (2 pts)
Which term of the Navier-Stokes equations is neglected in deriving the Euler
equations? What does this mean for the flow?
Neglected: Viscous (friction) term
Implication: Only inertia and pressure remain → valid for inviscid flows (e.g., high Re, compressible)
One application each for differential and integral momentum form:
Differential form: Used in CFD solvers for local field resolution.
Integral form: Used for force/momentum balance over control volumes (e.g., in engineering analysis)
The right-hand side of momentum conservation corresponds to the sum of acting
forces. Provide one example each for a point force, surface force, and volume force. (3
pts)
Point force: Holding a suspended object.
Surface force: Pressure on a wing surface.
Volume force: Gravitational force acting on a fluid volume
Name three flow mechanically relevant effects that a turbulent boundary layer has
compared to a laminar boundary layer.
Increased mixing
Higher wall friction and pressure loss
Delayed flow separation
Give three fundamental properties of turbulent flows.
Unsteady and chaotic
Three-dimensional and rotational
Wide range of length/time scales
Explain the term “turbulent energy cascade.”
Energy is transferred from large scales (input, geometry-driven) to small scales, where it’s dissipated by viscosity
Provide the basic properties of:
1. a) large scales and
2. b) small scales of a turbulent flow.
Large scales: Geometry-dependent, energy input.
Small scales: Universal, dominated by dissipation, less geometry-dependent
