Computational Fluid Dynamics Multiple Choice Questions on “Turbulence Modelling – Reynolds Averaged Navier-Stokes Model”.
1. Which of these properties of turbulence is ruled out in Reynolds averaged equations?
a) Fluctuations
b) Turbulence
c) Non-linearity
d) Randomness
Answer: a
Clarification: The flow properties of turbulent flow can be decomposed into mean and fluctuating components. These fluctuating components result in an unsteadiness in the flow. This unsteadiness is ruled out by means of Reynolds averaging.
2. The averaging interval in RANS equation is based on ____________
a) the grid size
b) the eddy size
c) the fluctuations
d) the time interval of the problem
Answer: c
Clarification: Time averaging is used only when the flow is steady and time-independent. The time interval taken to average the fluctuations depend upon the time scale of the fluctuations itself. If this interval is large enough, the lower limit of the integral does not even matter.
3. For unsteady turbulent flows, which of these averaging method is used?
a) Time averaging
b) Ensemble averaging
c) Spatial averaging
d) Volume averaging
Answer: b
Clarification: Time averaging is generally used to remove the fluctuations in RANS model. But it cannot be used when the problem is unsteady. In these cases, ensemble averaging is used to eliminate the fluctuations.
4. Which of these terms arise in the conservation equations when using the RANS model?
a) Reynolds stresses and turbulent scalar flux
b) Cross stresses and turbulent scalar flux
c) Leonard stresses and turbulent scalar flux
d) Leonard stresses and cross stresses
Answer: a
Clarification: While the conservation equations are Reynolds averaged, they get additional terms due to the decomposition of the flow variables. These additional terms include Reynolds stresses and turbulent scalar fluxes. This occurs because of the mean of the product of the fluctuating components.
5. Reynolds averaging makes the conservation equations ____________
a) non-conservative
b) non-linear
c) unstable
d) inconsistent
Answer: b
Clarification: Reynolds averaging add extra terms to the conservation equations. So, the number of unknowns becomes more than the number of equations. This leads to a linearity problem and makes the conservative equations non-linear.
6. How many additional terms are present in the x-momentum equation Reynolds-Averaged Navier-Stokes equations?
a) No additional terms
b) Six additional terms
c) Three additional terms
d) Two additional terms
Answer: c
Clarification: The non-reduced x-momentum equation is
(frac{partial(rho u)}{partial t}+div(rho u vec{V})=-frac{partial p}{partial x}+div(mu,grad(u))+S)
The Reynolds-Averaged x-momentum equation is
(frac{partial(overline{rho}tilde{u})}{partial t} + div(overline{rho}tilde{u}widetilde{(vec{V})}) =
-frac{partialtilde{p}}{partial x} + div(mu gradwidetilde{(vec{V})}) + (-frac{partialoverline{(overline{rho} u{‘}^2)}}{partial x} – frac{partialoverline{(overline{rho}u{‘}v{‘})}}{partial y} – frac{partialoverline{(overline{rho}u{‘}w{‘})}}{partial z})+S)
Here, the terms (ρu’2), (ρu’v’) and (ρu’v’) are the three extra terms.
7. From which of these terms does the turbulent viscosity arise from?
a) (frac{partial(overline{rho}tilde{u})}{partial t})
b) (-frac{partialtilde{p}}{partial x} )
c) (div(mu gradwidetilde{(vec{V})}))
d) (frac{partialoverline{(overline{rho}u{‘}v{‘})}}{partial y})
Answer: d
Clarification: The term (overline{(overline{ρ}u’v’)}) represents the turbulent shear stress (Reynolds stress) in the momentum equation. This leads to the turbulent or eddy viscosity in the turbulent models.
8. The Reynolds stress term arises in the turbulent equation only when ____________
a) two quantities are correlated
b) two quantities are uncorrelated
c) the flow is steady
d) the flow is unsteady