Hi all,

I am looking for test data, pictures, frequency measurments etc for various cases of the onset of unsteadiness in low-speed flow regimes.

Certain cases like flow over a cylinder & blunt bodies - how was the onset of unsteadiness measured - visually, frequency etc. Are there decent ways to predict this phenomenon - other than the 'rough' Re,crit ~ 40...

I would really value good links on this issue. I have tried a number of avenues but solid information seems to be very sparse - most is at high-speed.

What kind of results & correlations have been emerging from the CFD community?

Thanks all for your kind assistance.

diaw...

Hi Diaw, As a first refernce I suggest you Schlichting, 2000 or recent edition, but I am not sure particularly your flow group is discussed there, another book "Stability of time dependent and spatially varying flows , by D.L. Dwoyer and M.Y. Hussaini, . Both discuss the basics esp. Tollmein-shilichting type waves, and at the early stage to transition they are responsible and models the phenomenon, onset of transition. but if you already referred them I also want to hear more on transition and its related area. thanks

Hi Taw,

Thanks for the references. They will be a great help.

I have on hand a book by Cebeci, & another by Drazin & Reid - but these are a little thin on physical examples.

I think that further deep investigation of the onset of the Tollmein-Schlichting phenomenon will be a good start on my end. I had a few concerns that in Cebeci these seemed to be observation of a local spark-driven event (external disturbance), rather than the observation of a natural progression of the onset of turbulence.

You've got me thinking... thanks...

diaw...

I think the one way to find out the onset is observing the lift coefficient (Cl). If the flow is steady, it will be zero and in case of unsteadyness it will be non-zero. You have to run the code for time enough to make sure about the steady/unsteadyness. The time to reach the decision abt steady/unsteadyness will vary from one problem (or condition) to other.

The best way is to give some possitive disturbance in the flow for say 5 or 10 time steps and then negative disturbence for same time steps, so that the flow is disturbed and then stop the distrubence and obtain the lift at each time step and observe the behavior. If the flow is steady at that Re then the Cl will go to zero after some time, otherwise it will be fluctuating....

Hope I m right...

Best regards, ramp

Thanks very much for your comments, Ramp...

What would be the theoretical reason for the lift coefficient being zero for steady flow & non-zero for unsteady? Due to temporally-induced velocity gradients? Very interesting...

Thanks, diaw...

I think ramp was referring to vortex shedding over a cylinder. The steady solution (below Re=47) gives zero lift, the unsteady solution shows lift oscillating about zero. You can monitor the lift over time to see the unsteadiness develop from the initial condition.

The onset of turbulence by Tollmien-Schlichting waves is a different animal. If you're interested in general onset of unsteadiness (in other words: stability of steady-state flows) I would rather study laminar vortex shedding first (e.g. over the cylinder). To me it seems less complex than transition to turbulence, although that may not necessarily be true.

Thanks Mani - excellent...

Mani wrote: The onset of turbulence by Tollmien-Schlichting waves is a different animal. If you're interested in general onset of unsteadiness (in other words: stability of steady-state flows) I would rather study laminar vortex shedding first (e.g. over the cylinder). To me it seems less complex than transition to turbulence, although that may not necessarily be true.

-------- Laminar vortex-shedding... These are my thoughts precisely. What I am trying to get to is a solid benchmark to set the N-S against.

What I 'feel' is that either Schlieren pictures of a gradual ramp-up in velocity for flow over a cylinder, or rear-facing step, will provide some valuable insights. I also feel that the onset of unsteadiness ?should? produce some disturbance which can be measured - say in the frequency range.

I would value any solid references in these areas - my literature-search attempts, so far, have all stumbled.

If N-S are indeed correct, in their current formulation, then, they should predict this phenomenon. The issues - in my mind at least - are 'bulk viscosity', mechanical vs thermodynamic pressure, & the 'Stokes approximations' for the stress terms.

diaw...

If you decide to use laminar 2D-planar flow over a circular cylinder with Re < 180 (based on cylinder diameter), you should be able to run a Navier-Stokes code from very small Re (Re < 4) showing no vortices forming behind (in the wake of) the cylinder, attached vortices forming behind cylinder for Re < 49 (this number may vary slightly for various researchers/experiments), and shedding vortices for Re > 49.

I put the restriction Re < 180, since above this Re, the three-dimensional nature of the flow can begin to become important (see reference below).

The following references may be helpful:

"Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders", R. Mittal and S. Balachandar, Phys. Fluids, Vol 7, No. 8, p.1841, 1995.

"Perspectives on Bluff Body Wakes", A. Roshko, J. Wind Eng. Indus. Aerodyn, Vol 49, p.79, 1993.

Hi Jeff,

Thanks so much for your wonderful contribution. It will be very, very useful.

Could you provide additional information on the 'exact model geometry' used in your simulation? Bounding dimensions, position of test sample, types of boundaries used in the simulation (all) - pressure, velocity imposition (sudden, or gradual)... This information is vital to placing the results in the correct context.

I am currently deeply inside the mathematics of this phenomenon - from a pure-physics approach - a 'birds-eye view' approach. It appears that we are dealing with a non-linear event for the onset of instability, with definite cross-linking into the other spatial directions. It is fascinating.

Thanks so much for your input.

Regards, diaw...

---------------------------- Jeff Moder wrote: If you decide to use laminar 2D-planar flow over a circular cylinder with Re < 180 (based on cylinder diameter), you should be able to run a Navier-Stokes code from very small Re (Re < 4) showing no vortices forming behind (in the wake of) the cylinder, attached vortices forming behind cylinder for Re < 49 (this number may vary slightly for various researchers/experiments), and shedding vortices for Re > 49.

I put the restriction Re < 180, since above this Re, the three-dimensional nature of the flow can begin to become important (see reference below).

The following references may be helpful:

"Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders", R. Mittal and S. Balachandar, Phys. Fluids, Vol 7, No. 8, p.1841, 1995.

"Perspectives on Bluff Body Wakes", A. Roshko, J. Wind Eng. Indus. Aerodyn, Vol 49, p.79, 1993.

I have only run the 2d-planar flow over cylinder at Re=100 as one validation case to check that an unsteady code was working correctly for laminar viscous flow.

For my Re=100 case, a cell-centered compressible finite-volume code with low-Mach number preconditioning and dual-time stepping was used. A structured quad grid with 12600 vertices and 12474 cells was used. The grid used radial lines starting at the cylinder surface and extending out 20x the cylinder diameter. The other grid lines were circles concentric to the cylinder. The grid near the cylinder is fine (first cell radial length about 0.008xD, D=cylinder diameter). The number of cells in the circumferential direction is about 130 with 45 cells used in the "upstream" half-circle of the grid and 85 cells used the wake ("downstream") half-circle of the grid. There are only 3 boundary conditions: (1) cylinder surface is a no-slip wall; (2) "upstream" half-circle is treated as inflow with uniform velocity; (3) "downstream" half-circle is treated as outflow with uniform static pressure condition. The flow was intialized by running the case as steady for enough iterations to get down to about 1% difference in the ratio (mass out - mass in)/(mass in). Since the experimental results for lift Strouhal number were known (0.16 to 0.17) in this case, the value of St=0.165 was used to compute a constant physical time step such that a complete lift period was represented computationally by at least 600 time steps per lift period. (In my case, freq = u/D * St = 0.1/0.1 * 0.165 = 0.165 1/sec, period of lift = 1/0.165 = 6.06 sec, dt = 1.0e-02 sec, 6.06/1.0e-02 = 606 time steps per lift period IF THE CODE actually compute a St of 0.165 (or close to this). )

The code predicts St = 0.165 to 0.166 depending on the pseudo-time iteration convergence criterion and the number of complete lift cycles used to compute the above average.

Thanks very much Jeff for providing your experimental details, in detail. They will be of much use to my research. I'll feed back to the forum as things progress on my end.

diaw...