WorksheetsTurbulence and Flow Dynamics Quiz
Total questions: 81
Worksheet time: 41mins
Which of the following is NOT a characteristic of turbulent flow?
Unsteady motion
Regular and predictable patterns
Three-dimensionality
Enhanced mixing of transported quantities
What is the name of the process where energy is transferred from larger eddies to smaller eddies in turbulent flow?
Reynolds Averaging
Energy Dissipation
Energy Cascade
Vortex Breakdown
Reynolds number is used to determine:
Flow compressibility
Laminar or turbulent nature of flow
Temperature gradient in a fluid
Density variation
What is the typical critical Reynolds number for internal flow to become turbulent?
Re > 500
Re > 2,300
Re > 1,000
Re > 50,000
Which of the following defines Reynolds number?
(μ / ρUL)
(ρUL / μ)
(U² / gL)
(F / A)
What is the main goal of turbulence modeling in CFD?
Increase computational time
Solve molecular diffusion directly
Approximate the effects of turbulence without resolving all scales
Eliminate the need for boundary conditions
What does RANS stand for?
Reynolds Analyzed Navier-Stokes
Rapid Anisotropic Numerical Solver
Reynolds-Averaged Navier-Stokes
Rotational Averaged Navier Scale
In RANS modeling, the velocity U is decomposed into:
Time and space
Instantaneous and fluctuating components
Turbulent and non-turbulent components
Viscous and inertial components
What is the mathematical expression for turbulent kinetic energy k?
½(u'² + v'² + w'²)
u + v + w
μ∇²u
ρU²
The closure problem in turbulence modeling arises because:
The Navier-Stokes equations are complete
Turbulence introduces additional knowns
Reynolds stresses introduce new unknowns
The continuity equation becomes invalid
Which hypothesis is used in eddy viscosity models to relate Reynolds stresses to mean flow?
Navier Hypothesis
Kolmogorov Hypothesis
Boussinesq Hypothesis
Prandtl Mixing Length Hypothesis
Reynolds stress models (RSM) are more suitable for:
Simple 2D laminar flows
Isotropic turbulence
Complex 3D flows with strong curvature and swirl
Inviscid flows
In turbulent flow simulations, specifying what kind of conditions at inlets is essential?
Laminar slip conditions
Inviscid boundary conditions
Turbulence boundary conditions
Pressure boundary conditions only
Which type of modeling approach is required near walls in turbulent flows?
Inviscid model
Free-slip condition
Near-wall modeling
Laminar wall assumption
What does the turbulent kinetic energy (k) represent?
Potential energy in eddies
Average fluid velocity
Energy in turbulent velocity fluctuations
Viscous dissipation rate
In two-equation models, which quantities are solved?
Pressure and density
Temperature and velocity
Turbulent kinetic energy (k) and dissipation ( or )
Eddy viscosity and flow rate
The Standard k-ε model is recommended for:
Highly accurate separation flows
Crude estimates of turbulence
Swirling dominated flows
Supersonic shock interactions
Which two models are recommended for standard cases?
RNG k-ε and Spalart-Allmaras
Realizable k-ε and SST k-ω
Standard k-ε and LES
DES and DNS
For precise wall resolution, especially flow separation or heat transfer, which model is preferred?
RNG k-ε
Standard k-ε
SST k-ω
Spalart-Allmaras
Which approach has the highest computational cost per iteration?
RANS
LES
DNS
Standard k-ε
Which model assumes isotropic turbulence for calculations?
Reynolds Stress Model (RSM)
Large Eddy Simulation (LES)
Standard k-ε
Direct Numerical Simulation (DNS)
In which region does the velocity profile transition from linear to logarithmic behavior?
Free stream
Wake region
Near-wall region
Separation zone
What is the typical range of y+ for the first cell when using wall functions?
0 < y+ < 10
10 < y+ < 30
30 < y+ < 300
300 < y+ < 500
When the viscous sublayer needs to be resolved, what should the first cell's y+ value be?
100
1
10
50
Which turbulence model is recommended when resolving the viscous sublayer?
RNG k-ε
Standard k-ε
SST k-ω
Realizable k-ε
Which situation would make wall functions unsuitable?
Smooth, steady external flow
Flows with boundary layer separation
High Reynolds number free stream flow
Subsonic flow over a flat plate
When using Enhanced Wall Treatment (EWT) with a k-ε model, the method is:
y+ dependent and requires y+ = 1
y+ insensitive and adapts to grid placement
only valid for laminar flows
only used with Reynolds Stress Models
What are typical default values for turbulence at an inlet?
Intensity = 1%, Viscosity Ratio = 1
Intensity = 5%, Viscosity Ratio = 10
Intensity = 10%, Viscosity Ratio = 50
Intensity = 20%, Viscosity Ratio = 100
Why perform a hand calculation of first cell height during pre-processing?
To avoid computing the Reynolds number
To ensure the first cell lies within the desired y+ range
To save computational time
To avoid using turbulence models
What is the typical range of turbulence intensity for normal turbulent flows?
0.1% to 1%
1% to 5%
5% to 10%
10% to 20%
For external flows, what is the recommended turbulent viscosity ratio?
0.1-1
1-10
10-100
100-200
Which turbulence model is preferred for cases where the viscous sublayer needs to be resolved?
Standard k-ε
RNG k-ε
SST k-ω
Realizable k-ε
Which turbulence model severely underpredicts the size of the separation bubble in flow over a blunt flat plate?
Realizable k-ε
RNG k-ε
Reynolds Stress Model
Standard k-ε
Which turbulence model is best suited for applications with swirling flows?
SST k-ω
Realizable k-ε
Standard k-ε
Reynolds Stress Model (RSM)
In the diffuser example, which model predicts flow separation more accurately?
RNG k-ε
SST k-ω
Realizable k-ε
Reynolds Stress Model
What is the first step in solving the example problem using the Finite Volume Method (FVM)?
Define boundary conditions
Convert to algebraic form
Start from the governing equation
Choose the type of discretization
In the Finite Volume Method, what does the general energy balance for each control volume include?
Convection and conduction only
Heat in from left and right, and a source term
Only the source term
Time-dependent terms
What form must the energy balance equation be converted into to solve it numerically?
Trigonometric form
Exponential form
Algebraic form
Integral form
In the context of the example, what is defined at each node?
Temperature gradients
Coefficients
Boundary fluxes
Volume integrals
Which nodes have special treatment in this example?
Node 2 and Node 4
Node 1 and Node 5
Node 3 and Node 4
Node 1 and Node 3
What type of boundary condition is applied at Node 1 in the example problem?
Neumann boundary condition
Dirichlet boundary condition
Robin boundary condition
Periodic boundary condition
At Node 5, which of the following best describes the boundary condition?
Fixed temperature
Adiabatic (zero heat flux)
Convective heat loss
Uniform source term
What is the role of the source term (S) in the general energy balance?
To model conduction effects
To represent heat addition or generation inside the control volume
To enforce boundary conditions
To ensure mass conservation
In the finite volume formulation, what does the term typically represent?
Flux across control surfaces
Net energy storage
Coefficient of the central node in the discretized equation
Volume of the control element
What is the purpose of defining coefficients , , and at each node?
To simplify the geometry
To improve accuracy of boundary conditions
To structure the system of algebraic equations
To enforce temperature constraints
Why do we apply special treatment to boundary nodes in FVM?
To avoid numerical instability
Because they require integration over half control volumes
They have no heat transfer
To apply periodic constraints
In the finite volume method (FVM), what is the key step that distinguishes it from other CFD techniques?
Using staggered grids
Integration over control volumes
Assuming constant properties
Applying boundary conditions manually
What is the primary governing equation considered for one-dimensional steady-state diffusion in FVM?
Navier-Stokes equation
Bernoulli’s equation
Diffusion equation
Energy conservation equation
In the notation used for grid points, what do P, W, and E represent?
Pressure, Weight, Energy
Present, Western, Eastern nodes
Past, Western, Eastern control volumes
Peak, Width, Elevation
In central differencing, which approximation is used for gradients and interface values?
Linear interpolation
Quadratic approximation
Taylor series expansion
Finite difference method
What does the coefficient aP represent in the discretized equations?
Average pressure at node P
Total flux at node P
Sum of contributions from neighboring nodes and source terms
Temperature difference at P
What technique is commonly used to solve the resulting linear system of equations in FVM?
Newton-Raphson method
Gauss Elimination
Runge-Kutta method
Euler integration
In a 2D diffusion problem, which of the following is not a neighboring node of P?
North (N)
Top (T)
East (E)
West (W)
For a 3D control volume, how many neighboring nodes are associated with an internal node?
4
5
6
8
How are boundary conditions typically incorporated in FVM?
Ignored if source terms exist
By introducing artificial nodes
By modifying source terms and cutting links
By increasing the mesh size
What does the linearized source term allow in the discretized equations?
Variable grid size
Implicit treatment of source effects
Neglect of boundary fluxes
Direct calculation of node positions
In the finite volume method, where are the control volume boundaries placed in a 1D grid?
At the nodal points
At the domain edges only
Midway between adjacent nodes
Randomly within the domain
What is the physical interpretation of the discretized diffusion equation?
Conservation of momentum
Flux difference equals generation within control volume
Constant temperature across the domain
Heat loss equals temperature rise
What is typically the first step in solving a diffusion problem using FVM?
Apply boundary conditions
Generate the grid
Solve the algebraic system
Define material properties
In 2D FVM, what is the face area associated with the north and south faces of a control volume?
Δy
Δx
Δx * Δy
A constant value
What is the key feature of the example involving a circular fin?
Uniform internal heating
Convective heat loss as a sink term
No boundary condition at the base
Nonlinear conductivity
What is the governing equation in the circular fin example?
d²T/dx² = 0
d²T/dx² − hP(T − T∞)/kA = 0
∇²T = 0
∂T/∂t = α∇²T
In the 1D conduction example (Example 4.1), the relation implies:
Constant property values
Conservation of energy
Symmetric boundary conditions
Fixed temperature
What numerical method is suggested for solving the linear algebraic system?
Jacobi method
Gauss-Seidel method
Gauss Elimination
Multigrid method
In Example 4.2, which physical phenomenon is modeled?
Convective cooling
Uniform heat generation in a plate
Heat sink with variable conductivity
Advection-diffusion
In 3D FVM problems, how many control volume faces does an internal node have?
3
4
6
8
The discretized equation for a node P in 3D involves which neighboring directions?
Only East, West, North
East, West, South, North
All six directions: W, E, S, N, B, T
Diagonal neighbors only
What happens to the source terms at boundary nodes in FVM?
They are eliminated
They become zero
They are modified to include boundary effects
They are ignored
The finite volume discretized equation has the general form:
aPφP = aWφW + aEφE + Su
∇φ = 0
φP = φW + φE
aP = Su + SpφP
What grid refinement technique improves the accuracy of the numerical solution?
Using higher-order time schemes
Employing finer control volumes
Ignoring boundary conditions
Increasing the temperature difference
Which software is suggested for plotting the final numerical results?
MATLAB
ANSYS Fluent
Tecplot
Excel
What is the first step in solving the example diffusion problem using the finite volume method?
Apply boundary conditions
Solve the matrix equation
Start from the governing equation
Define nodal temperatures
In the energy balance for a control volume, what terms are considered?
Kinetic energy and potential energy
Heat conduction only
Heat in from west, heat in from east, and source term
Convection, radiation, and mass flow
What is the result of discretizing the governing equation using the finite volume method?
A differential equation
A matrix of second derivatives
An algebraic equation
A Fourier series
What is the key feature of the discretized form at each node?
It includes velocity terms
It excludes the source term
It is based on energy conservation
It varies for each time step
Which nodes require special treatment in the discretized system?
Interior nodes only
Nodes at the top and bottom
Node 1 and Node 5 (boundary nodes)
Even-numbered nodes only
In the example problem, what type of boundary condition is typically applied at Node 1?
Adiabatic
Fixed temperature (Dirichlet)
Convective
Insulated
What modification is made to the coefficients at boundary nodes?
They are averaged
They are doubled
They are adjusted to include boundary contributions
They are zeroed
What method is used to calculate temperature at each node after forming the equations?
Numerical integration
Finite element iteration
Solving a system of linear equations
Curve fitting
In the general energy balance for FVM, if there is no source term, what is the balance?
Heat in = Heat out
Heat in from west = Heat in from east
Heat in from both sides = 0
Sum of heat in = 0
Which part of the FVM process converts physical principles into solvable algebraic equations?
Boundary condition application
Integration over the domain
Discretization step
Initial condition setting
