The Ultimate Fluid Model: Non-Equilibrium Modeling

In this blog series, I covered a lot of thermo-fluid options in engineering analysis, from the simplest perfect gas (When Perfect is Good Enough – Perfect Gas Models) and ideal liquid, (Fluid Modeling: Liquified ) to much more complex approaches (Going Through a Phase – Modeling Phase Change with Cubics) and (Getting Real – Advanced Real Gas Models). In this blog, I’ll cover the ultimate in thermo-fluid modeling: non-equilibrium modeling. It's rare and expensive, sort of like the Schorschbrau’s Schorschbock 57, a beer that sells for $275/bottle.

The term “non-equilibrium” means something does not respond instantly when external conditions change.  There are many everyday examples of non-equilibrium thermo-fluid behavior, such as bubbles in freshly poured glass of beer (Phase Change, Make Mine a Double), the chemical reactions in a combustor, or the formation of droplets in a steam turbine exhaust.  Each of these phenomena takes a certain amount of time to occur and therefore can lag behind changes in the ambient conditions. This can be a fairly slow process, like the half hour it takes for beer to go “flat” after the can is opened, or the tiny fractions of a second for a chemical reaction to occur once the fuel and air are mixed. Huh,  I just realized my blogs reference beer a lot - I wonder if it's because it comes out on Friday. Nah! 

Non-equilibrium thermo-fluid behavior example

Modeling non-equilibrium phenomena takes special models, carefully calibrated to capture the physical properties changing with time.  For example, phase change through condensation usually requires that a distribution of droplets be tracked along with a nucleation model to calculate the changing size and number of droplets with time.  For chemical reactions, the chemical species need to be tracked, along with the finite rate equations controlling the reactions. 

On the solver side, it goes without saying that capturing the time variation requires a time accurate solver.  This is usually a much more expensive and computationally intensive process than a steady-state solution.  Between the more advanced solver and the overhead of the underlying thermo-fluid model, one can expect some long calculation times and serious computer resources will be needed.   

For the most part, non-equilibrium modeling in turbomachinery is fairly rare.  Any finite rate effects that might be occurring are usually too small to justify the cost of modeling them.  On those rare occasions when it is required, many CFD providers offer specialized models to capture various non-equilibrium effects.  As mentioned before, these models can be complicated and can greatly affect the solution run time and stability, so make sure whatever improvement in accuracy you’re getting justifies the cost, like that Schorschbrau’s Schorschbock 57 previosuly mentioned. Cheers!

Blogs in this series:

Fluid Phenomena Primer: Energy Versus Temperature, Specific Heat

Phase Change - Make Mine a Double!

When Perfect is Good Enough - Perfect Gas Models

What's Better than Perfect? Semi-Perfect Gas Models

Going Through a Phase – Modeling Phase Change with Cubics

Getting Real – Advanced Real Gas Models

Fluid Modeling: Liquified

The Ultimate Fluid Model: Non-Equilibrium Modeling