Navier-Stokes Equations Flashcards
What do the Navier-Stokes Equations Describe?
How the Velocity, Pressure, Temperature, and the density of a moving fluid are related.
What is a number that is an indicator of continuum?
Knudsen number: Kn = lambda / l = mean free path length / characteristic length
For what Knood’s number is Navier-Stokes Applicable?
Kn < 0.01
What are the four independent variables in Navier-Stokes?
The spatial coordinates and time.
What are the six dependent variables for Navier-Stokes?
Pressure
Density
Temperature
Velocity components
What is the formula for Stokes hypothesis?
Lambda = -2/3 micro
What are the Euler Equations?
Set of partial Differential Equations governing adiabatic and inviscid flow. Momentum equation with simplifications of no viscosity and heat loss.
What do Navier-Stokes Equations Consist of?
Conservation of Mass, Momentum and Energy
What is Time Averaging?
Unsteady signal is decomposed in a mean and a fluctuating part.
What is the characteristic length of ambient pressurized air?
70nm
What dimensionless number is important in viscous / compressible flow?
Re / Ma
What is the focus of time averaging?
Stationary Turbulance
What is the closure problem in Reynolds Average Navier Stokes Equations (incompressible)?
Because of the introduction of the mean flow properties, we have ten unknowns but only four equations so the system is not closed and cannot be solved.
Which property do we need to calculate all the mean flow properties of turbulent flow?
Reynolds Stress Tensor
What else has to be considered in compressible flows (wrt averaging)?
We have significant density and temperature fluctuations. Needs to be decomposed into mean and fluctuating parts.
Why do we introduce mass averaged velocities in compressible turbulent flow?
Because of the double and triple correlations between the quantities (fluctuating density(not for RA), fluctuating velocity components)
What are possible forces for momentum equation?
- Volume Forces
- Body Forces
- Surface Forces
What are the four important components of the momentum equation?
- Variation
- Divergence
- Internal Source
- Diffusion
Where is Stokes hypothesis used?
To find the constant lambda in the Momentum equation for Newtonian fluids
What law is used to derive the energy equation in NS?
First law of thermodynamics
What is the formula for time averaging a function?
\bar f(x) = limt_{T->infty} (1/T) \int_(t)^(t+T) f(x, t) dt
What is the Reynolds stress tensor?
It is the additional term that appears in the RANS equation (incompressible), consists of the time averaged terms.
How many independent components does the Reynolds stress tensor have?
6
What is Favre averaging?
It is the averaging method for compressible flows where we also have to average the density distribution and because of this have to introduce mass averaged velocities.
