massflow.png pressure.png

URANS channel simulation

The simulation performed is a URANS one - K-omega turbulence model - where the inlet condition is defined as a constant massflow for the initial 3000 time steps, and then a sinusoidal fluctuation starts. This leads to a fluctuating massflow rate.shear.urans.png

The pressure shows a very strange behaviour: when the sinusoidal massflow begins there is a pressure jump! There seems to be a connection between the pressure instantaneous value and the massflow derivative (although theoretical considerations do not confirm it!!!) which gives us some negative inlet pressure for some time steps: behaviour non-physical, while the pressure average value seems to be influenced by the velocity (as Bernoulli states!!)

A GIF animated picture lets understand more easily the pressure problem.

pressure.urans.png

I though the cause of the positive pressure gradient may be traced back to a non predictable behaviour of the shear stresses (the pressure in fact has to equilibrate the losses generated by these stresses). The following graphs shows the shear stresses integral!!

shear

pressure_gif.gif

Something has to be sure: the pressure gradient must balance all the losses subjected to the fluid! Among these losses there are, of course, the wall shear stresses, which basically subtracts momentum to the fluid!! But there are internal losses as well: the turbulence model in fact introduces the term which expresses an energy transfer mechanism from the mean flow to the single particles through a series of vortexes (...). In my mind it was not perfectly clear the influence an instantaneous modification of the flow field (since we are varying the inlet and the flow is incompressible we are basically applying a new massflow along the whole channel) to this term: basically I was wondering if such variation might affect the . To find out an easy answer I run a simulation without any turbulence model (laminar simulation) and ...

pressure.istant.png in here a further simulation result: the inlet is here define to be constant for 3000 iterations and then it is instantaneously increased. The pressure showed as earlier a behaviour influenced by the derivative of the mass flow!

A possible explanation ?!?!

In these days I went through the equations solved and in particular the meaning of each of their terms!!

Something has to be sure: the pressure gradient must balance all the losses subjected to the fluid! Among these losses there are, of course, the wall shear stresses, which basically subtracts momentum to the fluid!! But there are internal losses as well: the turbulence model in fact introduces the $ \varepsilon $ term which expresses an energy transfer mechanism from the mean flow to the single particles through a series of vortexes (...). In my mind it was not perfectly clear the influence an instantaneous modification of the flow field (since we are varying the inlet and the flow is incompressible we are basically applying a new massflow along the whole channel) to this term: basically I was wondering if such variation might affect the $ \varepsilon $. To find out an easy answer I run a simulation without any turbulence model (laminar simulation) and ...

pression.laminar.png

The first conclusion is that this behaviour is not affected by the turbulence model!!

Where can it come from then?

Another idea I had: the code solves basically a Poisson equation for the pressure, which comes from the navier-stokes and the continuity ones! The equation is here written:

$ \nabla^2 p = -\rho \cfrac{\partial U_i}{\partial x_j} \cfrac{\partial U_j}{\partial x_i} $

The term on the right side of this equation is zero in a steady channel flow (since $ \cfrac{\partial U_i}{\partial x_j} = 0 $ , except i=1 and j=2 - the initial part of the channel must not be considered!). When a variable mass flow is introduced, the right term is no more zero (and this lead to a different pressure distribution compared to the steady case) and we have a dependency with the velocity derivatives (highlighted earlier in some graphs).

My question is now: are all these considerations correct? If so: I am not able to find an explanation to the "energy gain" the flow seems to deal with (...)!


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Topic revision: r6 - 2011-01-17 - 16:57:13 - RuggeroPoletto
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21 Jul 2018

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