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Know Your True Colors

CFD Anlaysis Color Plot
June 27, 2014 By: Hsin-Hua Tsuei

Computational Fluid Dynamics (CFD) is often nicknamed “Colorful” Fluid Dynamics.  Rainbow color plots, from blue to red, are used for everything in CFD: to show pressure, velocity, temperature contours, as well as velocity vector and streamlines “colored” by a flow variable. I guess, in a way, the "colorful fluid dynamics" term is quite appropriate.  It is in a sharp contrast to pictures taken from traditional fluid dynamics experiments, such as wind tunnel tests or Schlieren photographs, which are all black-and-white - a world of little to no color.

Recent advancements in CFD algorithms and technology have made many CFD analysis software codes robust and easy to use, and applicable in many industries. Most often, these CFD codes have a set of default settings, from mesh element size, modeling constants, to numerical parameters.  They will generate a set of colorful results once a CFD analysis is complete. Now, the most important question arises.  How meaningful are those colors? When you see a CFD rainbow color plot with lots of blue and red, and every color in between, should you accept it without hesitation?  Or you should think about what you are trying to model, and do those colors make any sense when looking at the flow physics they are “trying” to represent?

Let’s go through a couple simple examples:

1) You’re asked to model an oscillatory flow, know that the flow field is unsteady, and are able to measure a frequency.  You develop a CFD model using a steady-state approach, then work very hard to adjust all sorts of numerical parameters to get the solution to converge.  After many fruitless pursuits, the residuals still remain at a high level, and will not reduce any further.  The CFD code will certainly provide a set of colorful results, with flow field variables still changing from iteration to iteration.  Care should be taken before you plot up the results.  An understanding of the value of the steady-state solution should always be assessed by comparing this data to a transient analysis.  In some cases, the steady state results can provide useful data, while in other cases there may be significant error in the results.  A thorough evaluation of  the colorful pressure and velocity contours should be performed before presenting these results.  

In some cases where the problem is unsteady with a known frequency, the steady-state assumption can be way off the mark. Secondly, using the steady-state approach in a true unsteady situation will lead to a non-converging solution, because the CFD solver can’t find a single answer – the solution is changing constantly. The results can be misleading, and the trained analyst should use this data carefully, realizing that the colors introduce error in the solution that should be quantified.  The beautiful color plots are only valuable when they are thoroughly understood.

2) Let’s look at the most fundamental pipe flow.  You’re trying to calculate pressure drop, and find out that the colorful pressure contour is not one-dimensional after the entrance region, which contradicts all known literature regarding pipe flows.  It could be a simple issue, like the default mesh element size is too large, with only two big elements in the pipe diameter. This situation is not close to resolving the flow gradient in the radial direction. Again, the user has to exercise engineering judgment to make sense of the color plots, not just believe in them blindly.

3) Another common application is Conjugate Heat Transfer (CHT) analysis.  The CHT CFD model will include both fluid and solid parts. In addition to the Navier-Stokes equations  for fluids, the CFD code solves the heat conduction equation in solids.  If you find a red dot in the middle of a blue sea in one solid part, before you take that as a “hot spot” and navigate your design to avoid that spot, you should think about what that red dot means. The heat conduction equation is elliptic, which is diffusive in nature, and will not generate any discontinuity in the solution.  Any high temperature will be dissipated gradually to nearby region, which produces a temperature gradient, or a color plot with red and blue at both ends and rainbow colors in between.  So if there is no span of colors next to the red dot and blue background, you’re probably looking at a numerical issue, not true physics. 

In my 25 years of experience as a CFD consultant, I’ve learned not to trust color plots unless I can prove they are meaningful and truly represent what I intend to solve. Using your engineering knowledge to verify your true colors is one of the most important things to understand when doing CFD analysis.