11 Replies Latest reply on Jun 26, 2014 9:41 AM by Bill McEachern

# Can flow simulation handle combustation (asymmetric stress tensor)?

Hello,

There are important situations where swirl of particle/parcel is encountered, such as in combustion. For these cases there is an important question: is stress tensor assumed to be symmetric?

We know that in NS equation only linear momentum is considered, and the general form of NS equation does not assume that stress tensor is symmetric. Physically, if the tensor is asymmetric then there is torque on the microscopic volume m, and within its streamline in general it is subjected to the influence of:

1. gravity
2. normal stress
3. shear force torque angular acceleration mra (r assumed to be mean radius of m) I think this understand is basically correct regarding torque: visualize a crowed square in which thousands of people, shoulder-to-shoulder, are moving toward a same direction (for example pilgrims in Mecca), then each body is subjected to torque from the neighbor, and in general he will not always orient toward the same direction during his course along the streamline. The orientation change is therefore due to the angular a above, and his movement can always be decomposed into

1. linear translation normal stress
2. rotation about his own axis torque

therefore the assumption seems perfectly valid, especially when liquid swirl is encountered.

And although in general is a present, the accumulated mrv(rotational) is small because temporarily (time) microscopically, and individual “rotation” not in-phase/aligned with its neighbors increases stress which soon acts to decelerate that.

However, if many places I read that the symmetry of stress is assumed, such as with Rutherford Aris’s Vectors, Tensors, and the Basic Equations of Fluid Mechanics, in section 6.41 and he also used a somewhat questionable term “polar fluid” to refer to fluid with torque/asymmetric stress.

I would like to know that in popular CFD packages Solidworks Flow Simulation, Fluent, CFX or FloEFD, is stress tensor assumed to be symmetric or not? I wonder if they do assume symmetric, then for viscous fluid symmetric shear stress implies a symmetric velocity field which is unrealistic for example for swirls, so the software will fail.

I just started learning this subject for a few days so the question might seem very basic to experienced users. Sincerely hope someone could resolve my puzzle!

Andy

• ###### Re: Is stress tensor assumed to be symmetric?

I believe you're referring to the Reynolds stress tensor, which is symmetric (the diagonal elements are the normal stresses, the off-diagonal elements are the shear stresses; the shear stresses are symmetric so R_ij = R_ji)

• ###### Re: Is stress tensor assumed to be symmetric?

Travis,

I am referring to the general stress tensor in Derivation of the Navier–Stokes equations, not the averaged Reynolds Stress in Reynolds-averaged Navier–Stokes equations.

Particulary the question is about the actual treatment in CFD packages: Is symmetric stress tensor assumed or not?  If yes, the advantage is the great simplification of the algorithm, but how does the software handle swirls/vortex (for a propeller) ?

Andy

• ###### Re: Is stress tensor assumed to be symmetric?

My only experience is with RANS solutions. If you're referring to time-accurate solutions I can't help you, sorry!

But, if you're talking about steady-state solutions, then the equations FlowSim is solving are the RANS equations, and the stress tensor is symmetric.

• ###### Re: Is stress tensor assumed to be symmetric?

Travis,

Good point! I am check RANS. Thanks!

• ###### Re: Is stress tensor assumed to be symmetric?

But even for steady-state flow, particles (or larger "parcel"s) still flow and most likely change orientation (the pilgrim queue can reach steady state, but people sitll chang orientation along the streamline). So what makes the symmetric stress tensor assumption valid?

• ###### Re: Is stress tensor assumed to be symmetric?

first, the answer to your question probably lies in the technical reference.

second this is a relatively deep question that you're asking, if your answer isn't in the technical reference, then i'd suggest speaking with your var to get the answer. personally i don't have a background in the coding behind CFD but rather my experience lies in the application of the software and the results relative to physical results expectations.

with that, I think similar to previous posts that you've made, what is the context of the question. how does it apply to the solutions you are trying to obtain? as far as i can see, if the software supports one method vs another, you add another approximation/assumption to your list. otherwise not. but in the long run, how much effect will it have on your solution and how many solutions would be affected?

• ###### Re: Is stress tensor assumed to be symmetric?

Jared,

Yes this is more a question on the theory side.

But there are cases like combustatin in which swirl needs to be considered. Without knowing flow simulation's modeling assumption I cannot have confidence on the results obtained.

Andy

• ###### Re: Is stress tensor assumed to be symmetric?

there is no combustion in flow, so you're probably safe there

rather than digging into the equations, i'd recommend looking through the validation examples and setting up some real tests if you need to add confidence to your use of the software. in the long run this is a design tool to help evaluate design alternatives and cut down the number of prototypes.

if you spend your time trying to eliminate every assumption and approximation (which you can do if you want), you will spend more time setting up and running simulations than actually doing design and engineering

• ###### Re: Is stress tensor assumed to be symmetric?

Really there is no steady flow in CFD, hence the D in CFD. A more accurate term would be quasi steady. Not trying to nit pick but just making sure we all understand what's really going one. B'layers are not "steady".

• ###### Re: Can flow simulation handle combustation (asymmetric stress tensor)?

Hi Andrew, what I understand that you are essentially asking is whether a fluid molecule can rotate, and thus leads to swirling.  The answer is yes.  It appears that you like equations, so you can also read more about the formulation here

Flow Sim can show this by plotting the Vorticity visualization parameter and Band type of flow trajectories.  I submit the following examples:

Flow impingement in a Pipe Tee And thanks to Bill McEachern for the following image of an external flow over a disc (at 60° AoA) • ###### Re: Can flow simulation handle combustation (asymmetric stress tensor)?

The other thing to realize is the NS equations do not predict vortex cores accurately. I believe this is well known. If you want a reference (maybe Irfan can chip in here) or a more elaborate explanation of this I can probably get you one.