A fast, low cost, stable memory algorithm for implementing multicomponent transport in direct numerical simulations
I’ve developed a code that can accurately and efficiently evaluate how molecular diffusion, or the movement of chemical molecules from a high concentration to a low concentration, effects the type of combustion we use in jet and rocket propulsion. First let's talk about diffusion. Molecular diffusion, also know as mass diffusion, occurs all over the place; a common example is making tea. When soaked in hot water tea leaves release their flavors and color the water. If you watch you can actually see these flavors diffuse out from the tea bag to fill our cup. This process is called mass diffusion and it acts at scales smaller than one micrometer (1x10^-6 m); but, despite it’s small scale, diffusion can have large impacts on flames as a whole.
Our first question was how does this micro-scale phenomenon of diffusion impact an entire flame? The answer has to do with turbulence, the same phenomenon that causes your airplane to bump around when you fly through rough air. Turbulence is unique in that it can act over an extremely large range of length scales; it can be as big as the eye of Jupiter, about 40000 km, or smaller than the head of a pin, less than 1 micrometer. Even more interesting is that all of these scales of turbulence are linked such that the kinetic energy contained in the giant swirling eye of Jupiter will eventually cascade down to tiny microscopic little swirls and diffuse away.
Let’s go back to our tea example, if we just let our tea sit and brew it will slowly diffuse through the cup; but, with a simple stir from a spoon we can accelerate that process. When we stir the cup, turbulent swirls about as big as the width of the spoon form and quickly cascades down to the scale of diffusion, this enhances mass transport and speeds up our tea brewing.
Bringing this all back to combustion, flames are a bit special when it comes to the interaction between turbulence and diffusion. Where most turbulent flows transfer energy from large scales to small scales flames can transfer energy both ways. This is because flames release energy through chemical reactions and that energy needs to go somewhere. Much of that energy is released as heat but some of it moves back up our turbulent energy cascade adding energy back into the large scale turbulence. As engineers we utilize this energy to create thrust for aircraft and rockets, but in this study we were more interested in fundamentally how this process actually works.
Up until now, it’s been too expensive for scientists and engineers to study mass diffusion directly in flames; computers haven’t been fast enough and microscopes aren’t fireproof. As a result, engineers have had to use assumptions to simplify how we study diffusion and simulate combustion. Now, with modern computing speeds and a cleverly written algorithm our group has made it possible to properly simulate diffusion directly and affordably in virtual flames.
Using this tool and our understanding of how turbulence and diffusion are related, we’ve found that the previous assumptions engineers have used to approximate diffusion tend to consistently overestimate the amount of diffusion that is actually occuring. Zooming back out, we found that this poor-estimation of diffusion transport can lead to significant errors in overall flame simulations.
So why do we care? The types of simulations we run are called direct numerical simulation (DNS) and are supposed to be as close to a virtual experiment as possible. We need these simulations to be so hyper-accurate because they are the bases of much of the rest of combustion modeling. DNS simulations are used to make “models” or simplified mathematical assumptions we can use to more affordably approximate true physics in more complex simulations. These “models” are then used to run larger simulations of things like jet engines which directly influence the engine designs we ultimately build and fly through the air. Because DNS impacts so many other aspects of combustion engineering, it’s critical that it’s as close to true physics as possible and assumption free. Our presentation at the US national combustion meeting was a first step in convincing our fellow engineers to stop using assumptions in DNS by showing them how inaccurate they can be. Our hope is that our fellow engineers will begin to use our new tool for accurately simulating diffusion giving us new insight into combustion physics as a whole.