Hi,

In my simulation, I want to add a perturbation to the inlet velocity profile to see its influence on the flow.

I am using a K-E model, I wonder if this perturbation is allowed to be added to the K-E model?

Because K-E model takes the time-average value, I was suggested that the perturbation would be eased off by the model and it is not proper to add a perturbation to a K-E model. Is this true?

Please Guide. Thank you.

In my opinion, a perturbation is supposed to die down further downstream. This shows the stability of a scheme.

Thank you.

I guess you are detecting if the flow can develop unstable flow structure by adding artifical perterbation. Since K-e model is for fully developed turbulent flow, it is assumed that the flow has already passed the transition stage. The addation of perturbation is allowed in any stage as long as it is small in quantity (the same size as numerical discreate error), but what do you expect from it ?

The purpose I introduce the perturbation to the flow is to check the wave theory: the wave develops due to the flow instability triggered by perturbation.

I already simulated a wave, and I want to see what this wave will further develop if a perturbation is introduced.

By the way, I would like to ask one question: if this perturbation can be the following form?

1/10*V*sin(wt)

Thanks for your response and time, Versi.

To check the wave theory you should use perturbation methods rather than the computational ones.

Hi, Leo. What do you mean "use the perturbation methods"? Would you please specify? Thank you.

Perturbation methods are the most powerful tool (mathematical) for theoretical analysis of the fluid equations, especially when understanding of physical process governing fluid motion is the primary goal of the study.

Check out the book "Perturbation Methods in Fluid Mechanics" by Milton Van Dyke.

Perturbation methods are especially useful when examining transition from laminar to turbulent flow.

If you want to simulate a wave, why not use the wave form perturbation that contains spatially sturcture like SIN (w*z) term ? Theses structures maybe eigenfunctions of a certain linearized flow.

Hi, Leo and Versi,

Thanks for your time and kind help. I understand what you mean. Here I want to ask one more question:

As an inlet boundary condition, assume the inlet velocity is V. If the velocity is changed to the form of V+ asin (wt) (t is the time and a is constant). If we could say a perturbation (asin(wt))is added to the inlet velocity V?

Hi,

Thanks for your time and kind help. I understand what you mean. Here I want to ask one more question:

As an inlet boundary condition, assume the inlet velocity is V. If the velocity is changed to the form of V+ asin (wt) (t is the time and a is constant). If we could say a perturbation (asin(wt))is added to the inlet velocity V?

Yes. both V + a*sin(wt),and V+ a* (rand() - 0.5), are added perturbation. Here rand() is usually a computer-internal function that produces random number betwenn 0 and 1 with averaging of 0.5 (as I remeber). But for any numerical simulation, the period of imposition of artificial perturbation should be limited. The duration of imposition is on the order for instability to occur. The rule of thumb is the time for a disturbance to travel across the whole flow domain in open flow, or the time for the viscous diffusion to arrive at the chracteristic length for closed flow domain.

Versi, thank you very much for your further gudiance!