Short Answer Flashcards
What is the oldest turbulence model still in use, and when was it developed?
The mixing length model by Prandtl, in 1925
Who developed the first LES with an eddy viscocity model, and when?
Smagorinsky, in 1963
What did Smagorinsky develop in 1963?
The first LES with an eddy viscocity model
What did Jones and Launder develop in 1972?
The k-epsilon model, the first two-equation turbulence model for RANS
What was the first two-equation turbulence model for RANS called?
The k-epsilon model
Who developed the first two-equation turbulence model for RANS, and when?
Jones and Launder, in 1972
What did Rhie and Chow develop in 1983?
Methods for solving the pressure Poisson equation
Who developed the methods for solving the Poisson equation, and when?
Rhie and Chow, in 1983
Who developend the k-omega model, and when?
Wilcox, in 1988
What did Wilcox develop in 1988?
The k-omega model
Who developed the dynamic eddy viscocity LES model, and when?
Germano, in 1990
What did Germano develop in 1990?
A dynamic eddy viscocity LES model
Who developed the SST model, and when?
Menter in 1994
What did Menter develop in 1994?
The SST model
What does SST stand for?
Shear Stress Transport
Why do we use CFD (3)?
Cheap, hazard-free and field quantities simultaneously accessible without measurement errors
What are (in three words) the three steps of pre-processing?
Generation, conditions, modelling
What do we generate in the first step of pre-processing?
The computational grid and geometry
What do we model in the final step of pre-processing?
The fluid and turbulence
What are (in three words) the three steps of post-processing?
Visualization, quantification, interpretation
What do we quantify in the second step of post-processing?
The uncertainties and errors
What is the equation for the Knudsen number?
Kn = {\displaystyle \lambda}/L
What is the approximate value for Kn in continuum mechanics?
Kn «_space;1
What does the Knudsen number represent?
The ratio between the mean free path and representative physical length scale of a molecule
What is typical of the Lagrangian frame of reference?
It moves with the fluid element
What is typical of the Euler frame of reference?
It is a fixed frame, forming a stationary observer with relation to movement of the fluid element
When do we use Euler equations?
Analysis of steady, inviscid, compressible flows without jump discontinuities
When do we ignore viscous forces?
Re»_space; 1
What are potential flows?
Steady, incompressible, inviscid, irrotational flows
What dictates barotropic fluids?
The pressure is dependent only on density, removing the use of the energy equation
What are the three most common CFD methods?
Finite volume, finite difference, finite element
What characterizes the finite volume method?
Uses cell averages, is fast and robust
What characterizes the finite difference method?
Uses differences between point values, difficult for complex geometries
What characterizes the finite element method?
Uses coefficients of basis functions, arbitrary high order, but slow
What CFD-method is Ansys-CFX based on?
The finite volume method
What equation relates the inertial forces to the viscous forces?
The Reynolds equation
What number represents advection velocity to the speed of sound?
The Mach number
What number relates unsteady to the steady forces?
The Strouhal number
What is the equation for the Strouhal number?
St = fL/V
What equation relates the inertial forces to the gravity force?
The Froude number
What is the equation for the Froude number?
Fr = V/sqrt(Lg)
What equation relates the inertial forces to surfaces forces?
The Weber equation
What is the equation for the Weber number
(rhoLV^2)/sigma
What does it mean if the Weber number is large?
The inertial forces dominate the surface forces of a fluid
When do we use the Strouhal number?
The Strouhal number relates the unsteady to the steady forces, so oscillating flow mechanisms such as eddy vortices
Which number describes hydraulic jumps?
The Froude number
What is the Reynolds number for ‘creeping flow’?
Re «_space;1
What does a Reynolds number much smaller than 1 represent?
It represent a creeping flow, where the viscous forces in a flow dominate the inertial forces
What order does the Reynolds need to be for the flow to be laminar?
Of order 1
What Reynolds number depicts a turbulent flow?
Re»_space; 1
What are some characteristics of a turbulent flow?
Inertial forces dominate, randomness
What are advantages of having turbulent flow?
Enhanced mixing, reduces pressure drag (while skin friction drag increases)
Why would we want laminar flow?
It is stable, which means pertubations decay and flow remains determinate
What is the topology of a cell in a grid?
The relation to the neighbouring cells
What defines the geometry of a cell in a grid?
The shape and size of the cell itself
What are the three types of mesh grids we define?
Structured, unstructured and hybrid
What defines a hybrid grid?
A mix of structured and unstructured cells, usually structured around surface of interest
What are the (2) advantages of having a structured mesh grid?
Generally faster convergence and smaller numerical errors
What is the disadvantage of having a structured grid?
It is difficult for complex geometry
Why does having a structured mesh lead to smaller numerical errors?
Due to the numerical diffusion being reduced by aligned grid lines
What is the advantage of having an unstructured grid?
A more straightforward application to complex structures
Name a disadvantage of having an unstructured grid.
The computation time per element is larger, due to more complex relation to neighbouring cell
What are the three different types of structured grids we define?
H, O and C
What is the name of the method of triangulation defined by the fact that no point lies inside a defined triangle?
Delauney triangulation
What is the name of the method of triangulation defined by a layer being formed along the boundary of the domain in an iterative manner?
Advanced front triangulation
When does numerical diffusion occur?
When the truncation error of the discrete approximation of continuous operators affects the numerical solution
Why does an unstructured grid have an increased computational time compared to a structured grid?
An unstructured grid generally has more elements, but also numerical diffusion increases
How do we determine the grid resolution at the wall boundaries?
By computing the y-plus value
What do we use the y-plus value for?
Determining the grid resolution at wall boundaries
What can we use turbulence for (2)?
Enhanced mixing and postponing flow separation
When is the scale separation in the turbulence energy cascade most pronounced?
For high Reynolds numbers
Name 4 characteristics of turbulent flows
Unsteady, rotational, chaotic, breaking symmetry
DNS is not used very often, why?
Expensive
When do we use DNS, despite its expensive nature?
Low Reynolds flows, small devices
What is the core field for DNS?
Fundamental turbulence research
How do we define the Reynolds Stress Tensor?
Tensor in RANS to account for turbulence fluctuation
What does EVM stand for?
Eddy Viscocity Model
Name two EVM’s
k-epsilon, k-omega
What dows RSM stand for?
Reynolds Stress Model
Name two RSM’s
LLR RSM, SSG RSM
Which names does LLR stand for in the LRR RSM, and in what year was it developed?
Launder, Reece, Rody, in 1975)
Which names does SSG stand for in the SSG RSM, and in what year was it developed?
Speziale, Sarkar, Gatski, in 1991
What characterizes the LRR RSM?
Solves transport equations for each component of the Reynolds stress tensor, hence more accurate for complex turbulent flows.
What characterizes the SSG RSM?
Improved turbulence modeling by including pressure-strain correlations
Name a model which combines EVM and RSM?
EARSM of Wallin and Johansson in 2000
What is the pro of Prandtl one-equation model?
Modelling turbulence in external flows and attached boundary layers
What is the con of Prandtl one-equation model?
Bad at internal flows and flow separation, due to assumption constant mixing length
What is the pro of k-epsilon model?
External flows
What is the flaw of k-epsilon model?
Prediction of anisotropic influences, such as curvature and directional volume forces
What is the k-omega model good at?
Boundary layer flows and flows with gradients and separation
What is the flaw of the k-omega model?
It overestimates the production of turbulence at stagnation points
What is the pro of the Spalart-Allmaras model?
Good results for simple attached flows and slow-separation locations
What is the con for Spalart-Allmaras?
It is less suitable for prediction of flow reattachement and free shear layers
What do RSM directly solve for?
For all components of the unknown Reynolds Stress Tensor
What does the slow term of the pressure strain correlation stand for?
For the relaxation to the isotropic equilibrium state
What does the rapid term of the pressure strain correlation represent?
The immediate effects of the mean flow gradients and external forces
Which turbulence scales can be computed directly?
The resolved scales
Wich turbulence scales need to be modelled in order to be solved in LES?
The unresolved scales
Among which turbulence scales do we expect the most dissipation?
The unresolved scales
What is the Convolution theorem?
A convolution in real space corresponds to a (relatively simple) multiplication in the Fourrier space
What does too much dissipation mean for the turbulence energy cascade?
Cascade dies out early
What does too little dissipation mean for the turbulence energy cascade?
The cascade is disrupted
What is the approximate value for the Smagorinsky constant if a flow is isotropic and turbulent?
Around 0.20
What can we do to correct a Smagorinsky model near a wall?
Add van-Driest damping
What makes a dynamic Smagorinsky model dynamic?
The Smagorinsky constant is determined in a dynamic way (Cs = Cs(x,t))
Name two methods that combine LES and RANS
Zonal coupling, detached eddy simulation
In the finite volume method, what does the solution represent?
A cell average value
What do we cal a control volume for which the evolution of the mean values is computed?
A finite volume
What is quadrature?
The process of determining area
Which word do we use for the process of determining area?
Quadrature
What do we call the type of estimation which construct new data points within the range of a discrete set of known data points?
Interpolation
What do we call the method where an integral is approximated by the product of the integrand with the area of cell phase Ae?
Midpoint rule
What determines the rate of grid convergence of a sufficiently smooth solution?
The order of the method
What order is the trapezoidal rule?
Second order
What is the trapezoidal rule?
A quadrature rule based on approximating the area under a graph as a trapezoid
What order is Simpsons rule?
Fourth order
What does UDS stand for?
Upwind Difference Scheme
What does CDS stand for?
Central difference Scheme
What is the numerical effect of a truncation error?
Higher order methods converge faster
What is the CFL number?
The ratio of the physical distance a wave (or particle) travels in one time step to the size of the spatial grid cell
What does CFL stand for?
Courant Friedrichs Lewy
How do we calculate the CFL number?
(dt*V)/dx
What is the advantage of using a higher order method?
Faster convergence after suffciently refined grid
When should one not use a higher order method?
If grid not sufficiently refined
What are three types of interpolation schems in Ansys-CFX?
1st order upwind, 2nd order central, 2nd order upwind
What does the solution of an unsteady problem rely on?
Initial and boundary conditions
What is the most simple solution for an unsteady problem?
The explicit Forward Euler method
What are the two types of time-marching methods?
Explicit and implicit
Name three implicit time-marching methods
Backwards Euler, the mid-point rule, the trapezoidal rule
How do we determine a sufficiently small timestep?
Dividing the influenced domain by the signal speed in order to find the maximum timestep
What are three benefits to explicit time-marching?
No iteration needed, straight-forward implementation, low memory requirements
What are two detriments to explicit time-marching?
Unstable for large timesteps, time step needs to be adjusted for velocity and grid size
What are two benefits of implicit time-marching methods?
Stable for larger timesteps, costs per timestep can be countered by fewer, larger steps
What are two detriments of implicit time-marching methods?
High memory requirements, more complex implementation required
When should you not use an implicit time-marching method?
If timestep is sufficiently small for explicit
Why would one choose a local timestep?
Accelerate convergence to steady state solution
What is the physical timestep in a domain limited by?
The smallest cell
Name the four types of boundary conditions?
Dirichlet, Neumann, Robbin, periodic
What is a Dirichlet boundary condition?
Apply a value on a boundary
What is a Neumann boundary condition?
Apply a gradient on a boundary
What is a Robbin boundary condition?
A combination of a Dirichlet and a Neumann boundary condition
What is an example of a periodic boundary condition?
Symmetry
How many boundary conditions do we exactly need to specify a supersonic inflow?
Five Dirichlet
How many boundary conditions do we exactly need to specify a subsonic/incompressible inflow?
Four Dirichlet
In a direct solution with N grid points, how many entries are there?
The system matrix will have (NxN) is order N^2 entries
Why do programs generally not use direct solution methods?
Large amounts of memory, high operation count, unnecessary
Name two methods for direct solution?
Gauss-elimination, LU-factorisation
How many operations does a Gauss elimination of dense matrices require?
Of order N^3
Why does it generally not matter to solve matrices exactly?
Modelling and discretisation errors are larger than computer round-off errors
What is the definition of an error?
A deviation from the exact solution, where the solution is generally unknown
What is the definition of residuum
A deviation from the equation that is solved by the iterative solution to the exact solution
Between the error and the residuum, which one converges faster?
The residuum
What is the condition for convergence?
That the spectral radius is smaller than 1
Why should the spectral radius G for convergence be smaller than one?
Otherwise the solution will grow and diverge
What does ILU-factorisation stand for?
Incomplete Lower Upper
What type of factorisation does Ansys-CFX use?
Coupled ILU for u,v,w and p
Name two multigrid methods
Geometric and algebraic
What defines the geometric multigrid method?
The coarsening is based on an user-defined or automatically generated grid
What defines the algebraic multigrid method?
The coarsening is based on a coefficient matrix, no actual grid is required
What is the definition of verification?
Assesses if the model is build correctly
What is the definition of validation?
Assesses if the model is fit to model the reality of interest
What is a bias error?
A systematic offset, which can be calibrated
What is a precision error?
A random error that can be cancelled when statistic averages are performed
How does one check for a discretisation error?
A mesh convergence study
What does a mesh convergence study look like?
Run simulations for different mesh resolutions and compare
How small should the order of the residual be to be acceptable?
In the order of 10^-3
How to check for turbulence modelling errors in RANS?
Perform simulations with different models and compare
