In the discretised momentum equation, we have viscous terms (like stress terms) to redistribute momentum and smooth gradients etc.

But where is any momentum drained from the momentum equation, i.e. a loss of total momentum in the domain.

i.e. near a wall, the wall stresses will remove momentum from the flow, but all we add is a shear stress that will redistribute this momentum - where is the drain of momentum in the domain?

Newton's (Second) Law says that forces cause a net rate of change of momentum. The balance of momentum for a fluid body implies that a closed fluid volume conserves momentum when no external forces are acting on it. Internal forces (viscous, pressure) only act to redistribute it. However, pressure and shear forces exerted by the wall on the fluid are external forces and will change the momentum. Secondly, any flux of momentum in to / out of the domain will change the momentum accordingly.

Hi noHame,

So if there are walls in my simulation, and i accordingly increase the local visocity to account for the wall shear stress, where is the loss of momentum???

near walls and where visocity is high i would expect a temperature increase of the flow. i dont see how a CFD code deals with a loss of momentum due to walls etc.?

"and i accordingly increase the local visocity to account for the wall shear stress"

I have never seen any CFD codes that increase the viscosity to account for the presence of a wall. I really don't understand what you are trying to do.

"near walls and where visocity is high i would expect a temperature increase of the flow. i dont see how a CFD code deals with a loss of momentum due to walls etc.? "

CFD codes treat walls as no slip (most often), which exerts a surface shear force. Since this is an external force, it changes the momentum.

CFD codes can easily predict temperature changes due to viscosity, by solving the energy equation. Note that the energy equation and momentum equation are fundamentally different.

Hi again noName,

yes you are right, at the walls a force is exerted (in the momentum source term) so there is a change momentum.

one final question about viscosity and energy drain though...

In an LES, the viscosity is increased (a subgrid viscosity is applied) to account for the presence of the small scales - whose job is to dissipate energy into heat.

So here i dont see how we are dissipating energy? All we are doing is increasing viscoisty. So we are redistibuting momentum, but not detroying it?!?

So how does the subgrid viscosity drain energy?

Again, energy is not momentum. Viscous terms in the momentum equation do not "destroy" momentum. But viscous terms in the energy equation "dissipate = destroy" energy.

Hence SGS terms act as a sink for energy, not momemtum.

Through turbulence you have increased transport of momentum (among other things), i.e. increased shear stresses, which you might interpret (or model as) an increased viscosity. The main point is that the increased transport of momentum (e.g. as compared to laminar flow) will more efficiently get momentum from the free stream to the wall, leading to increased wall shear stress. This shear stress at the wall is one that's responsible for the momentum deficit in the domain (besides inflow and outflow boundaries) as noName explained to you. So don't you see how increased shear stress gives you increased loss of momentum? Depending on the type of wall (adiabatic or not?) you will also observe the temperature increase due to the increased friction.

The Navier Stokes equations do contain a source/sink term for the viscous dissipation and as such, there is destruction of momentum by viscosity. However, this term (it is argued in text books) is very small and it is therefore commonly neglected in the NS equations solved in the CFD codes.

On the other hand, there is a pressure gradient term as well in the momentum equations and that too has the form of a source/sink term. And when you look at e.g. flow in a pipe, there must be a pressure drop over the pipe to keep the flow rate (i.e. the momentum in the case of incompressible flow) constant.

hi Lars,

> The Navier Stokes equations do contain a source/sink
: term for the viscous dissipation and as such, there
: destruction of momentum by viscosity

which term is this???

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> And when you look at e.g. flow in a pipe, there must
: a pressure drop over the pipe to keep the flow rate
: constant.

i assume the pressure drop is required to 'power' the flow against the mometum lost by the shear stresses at the walls???

Sorry, I took that out of my memory and my memory failed me. There is indeed a commonly neglected term for viscous dissipation but it occurs in the energy equation, not the N-S equations. As mentioned, however, the pressure gradient acts as a source term in the N-S equations. I think your description of a pressure drop "powering" the flow to compensate for the loss of momentum is correct.