The problem with Turbulent Reacting Flow Modelling

The problem with Turbulent Reacting Flow Modelling

On 13 June 2019, Dr Edward Richardson from the Aerodynamics and Flight Mechanics group gave a talk on modelling turbulent reacting flow within the context of combustion. Dr Richardson’s research involves reactive and multi-phase turbulent flows, with application focused towards gas turbines and internal combustion engines. He is also involved in research projects in advanced modelling for two-phase reacting flow and split-injection diesel engine modelling.

Even in the midst of the today’s transition towards renewable energy, combustion remains a vital process as the world’s primary method of generating energy. Consequently, efforts to accurately simulate these chemical reactions to approximate the energy and the biproducts released to the atmosphere remains an important area of research. This is especially true given tighter regulations on emissions, as shown by the motif behind the Volkswagen scandal, and ever-increasing instances of unwanted combustion (i.e. Grenfell tower fire and Li-ion battery fires). This research also plays an important role from an environmental perspective, as there are conflicting priorities presented to policymakers, where the trade-off between NOx and CO2 is becoming an increasingly problematic dilemma.

Despite the humanity’s use of combustion and the role it has played since the industrial revolution, turbulent combustion is a relatively recent field of research with a diverse range of applications from explosions of supernovae to internal combustion engines. Dr Richardson’s research looks into simulating these combustion reactions, by reconciling the chaotic behaviour of the Navier-Stokes equation whilst attempting to account for chemical reactions which occur within the process. Given the size of the simulation, it is difficult enough to accurately simulate the turbulence without the added complexity of chemical interactions. When the chemical reactions are added to the equation, it becomes even more challenging to come up with a sufficiently accurate result. This is partly due to the practice of filtering the well-known governing equations of the field in order to simplify the simulation. In addition, due to the non-homogenous nature of fuel and the existence of intermediary steps, as well as the varying reaction rate as a function temperature, pressure, and concentration, these simulations become exponentially expensive, and poses a problem when extended to larger problems. This is bad news amid today’s demand for higher precision reports, despite the lack of appropriate equipment or model certainty offered by the scientific community.

Dr Richardson proposes a few different approaches to this research. Firstly, in order to encompass the full range of timescales attributed to various turbulence phenomena, taking an average across some of the input variables significantly reduces the required resolution for the simulation. Secondly, when chemical reactions are added to the combustion models, an average reaction rate is used to estimate the averaged turbulence equations, further cutting down the computational costs. However, on top of the expected fall in accuracy attributed to these cost-saving assumptions, this methodology now presents a new issue in the form the underlying equations exhibiting non-linear properties. This can lead to misleading, or worse inaccurate, model outputs for variables such as the temperature. To prevent this, Dr Richardson augments his approach slightly, by using an exact reaction rate of chemicals via a probability density function (hereafter PDF) using transport modelling. This transported PDF is then solved using Monte Carlo simulation in the high dimensional problem space. These methods convert the initial model from a high resolution, computationally intense form, to a medium resolution, transported PDF form. Despite this transformation, the methodology maintains the accuracy of the system in large, as the reaction rate is calculated at every point in the flow.

On top of this, Dr Richardson further discussed the possibilities of reducing the model’s computational costs. This included incorporating adaptive methods on the three individual components of simulation fidelity: the model fidelity, the resolution of turbulence, and the chemical fidelity. Adaptive methods add or remove calculation elements as required, in order to decrease the overall cost of the simulation. This type of grid-based approach is widely used and well documented in literature. However, Dr Richardson described another method to model chemical reactions. which is able to determine regions of high commutation error using the aforementioned PDF. This in turn allows the model to run additional Monte Carlo calculations on these regions to enhance their accuracy. This allows the model to recast the particle-based approach for typical chemical reaction model to a grid-based approach, in conjunction with other components within the overall method. After these adjustments are made, overall optimisation of the model utilises adaptive methods for all components which add to the simulation fidelity. This allows adaptive mesh refinement to be used in turbulent flow modelling, in sync with Dr Richardson’s method for the chemical modelling, resulting in optimised modelling methodology with minimal cost.

With the progress made by Dr Richardson and his team, researchers hope to convince the industry to utilise these different methods of simulating turbulent combustion. Although this may seem like a difficult task, given the regulatory and sentimental changes towards combustion, the academic community remains hopeful that these enhanced modelling methodologies may soon be adopted by industrial partners. This, in turn, will enhance our understanding of the combustion process, in order to minimise the negative impacts of combustion during our transition towards renewable energy. 

Posted by Chris Cho and Liam Tope