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# Predicting Laminar vs. Turbulent Flow

Is it possible to determine from flow visualization alone whether the flow is laminar or turbulent?

In order to answer this question, one needs to reference back to the difference between
laminar and turbulent flow.  From "Introduction to Fluid Mechanics", 4th Edition, Fox & McDonald, pp. 35-36, we have:

"Viscous flow regimes are classified as laminar or turbulent on the basis of flow structure. In the laminar region, flow structure is characterized by smooth motion in laminae, or layers. Flow structure in turbulent regime is characterized by random, three dimensional motions of the fluid particles in addition to the mean motion. .... For steady laminar flow, the velocity at a point remains constant with time.  In turbulent flow, the velocity trace indicates random fluctuations of the instantaneous velocity (u), about the time mean velocity (u bar).

We can consider the instantaneous velocity (u), as the sum of the time mean velocity (u bar), and the fluctuating component (u prime).  Because the flow is steady (but still turbulent), then (u bar) does not vary with time (but (u prime) does).   Although many turbulence flows of interest are steady in the mean (u bar is not a function of time), the presence of the random, high frequency velocity fluctuations make the analysis of turbulent flows extremely difficult.  In one-dimensional laminar flow, the shear stress is related the velocity gradient by the relation (Tau = viscosity * gradient of velocity).  For a turbulent flow in which the mean velocity field is
one-dimensional, no such simple relation is valid.  Random, three dimensional velocity fluctuations (u prime or v prime or w prime) transport momentum across the mean flow streamlines, increasing the effective shear stress. Consequently, in turbulent flow, there is no universal relationship between the stress field and the mean velocity field."  (Note: Because of the random nature of (u prime), turbulent flows are often analyzed statistically.)

Also,  from "Fundamentals of Fluid Mechanics" , 2nd Ed., Gerhart, Gross, & Hochstein, pp. 126-131, we have:

"... If we generated instantaneous velocity profiles at another instant of time at the same location, the shape of the turbulent profile would be different, but the shape of the laminar profile would be the same. ..."

So, the determination of laminar versus turbulent is not necessarily "at the wall".  At the root of the definition, it really has to do if there are any "significant" fluctuations in the velocity field about its mean value.  If the user only has the  mean velocity (u bar), which is what is the standard output from most all CFD codes, then strictly speaking, you can not definitively tell if that flow is laminar or turbulent.  However, there are few things that you can more pragmatically do to figure this out:

a. If the solver provides a turbulent kinetic energy or dissipation term, then you can begin to quantify "how" turbulent the flow is. If the fluctuations about the mean are very small, you could then determine that the flow is 'laminar'.

EnSight Note:  If these variables exist, you can take a clip through the domain and color the clip by these variables to setup your visual analysis.]

b. Visual inspection of how well the flow conforms to this "laminae, or laminar" layers. This is where we engineers typically zoom into the region near the wall and try to determine if there
are any velocity vectors which are not aligned in layers (i.e. separation from an airfoil, recirculation zones... something that would indicate non-layer structure to the flow....). So, if you see a flat velocity profile to the wall, you could infer that that there is little velocity gradient; and thus, the flow would more likely remain within its 'laminae'. But it is important to note, this also depends (on the cell resolution.

EnSight Note:  See the following 5-10 minute screen-cast (short movie) under www.ensight.com > Tutorials > Graphing and Plotting, i.e. <http://www.ensight.com/Graphing-and-Plotting-Tutorials/>, and watch either:

http://www.ensight.com/screencasts/Velocity_Profile_Graph/Velocity_Profile_Graph.html

or

http://www.ensight.com/screencasts/LineNormalQuery/LineNormalQuery.html

for techniques on how to create velocity profiles.

c. Qualitatively speaking, flow in which the viscous forces are able to overcome the random inertial forces is called laminar. Again, qualitatively speaking, flow in which the inertial forces overcome the viscous forces is called turbulent.  Since the Reynolds number is a measure of the ratio of inertial forces to viscous forces, determining the Reynolds number of the flow can also help to indicate whether you would expect the flow to be laminar or turbulent, but this is an empirical guideline. Unfortunately, the Reynolds number is based off the user selecting a "length scale", which may or may not be easy to determine.

EnSight Note: Since the Reynolds (Re) number is usually specified by the solver in computing a solution, EnSight does not have a predefined calculator function to compute Re.  But you could compute this using the EnSight calculator by combining the appropriate dependent variables of your Reynolds number equation.   For example, by computing

Re = (u bar) * (length) * (density)  / (dynamic viscosity)
= (u bar) * (length) / (kinematic viscosity)

where:
u bar = the mean velocity
length = a characteristic linear dimension, or traveled length of the fluid.

In summary, our best recommendations is to revert back to item (a) above, and determine "how turbulent" the flow is and if very small, then you can classify the flow as laminar.
Then you can further your analysis by using item (b) above.  Item (c) above is usually given to the solver, or computed manually via your appropriate Re equation.