1. Developing a CFD model suitable for
combustion analysis – The TPDF Code
Author: Bradley Alderton
Supervisor: A/Prof. Evatt Hawkes, Joshua Tang, Austin Kong
Background and Motivation
Combustion engines play an integral role in todays modern society with our ever increasing
reliance on manufacturing, power generation, and automobile transport, and unfortunately greenhouse gas
emissions are increasing in conjunction with this. Modelling combustion with computer simulations enables
researchers and designers to discover methods to make combustion engines more fuel and power efficient.
Direct Numerical Simulation (DNS) provides extreme accuracy for modelling purposes, but
come at the cost of being computationally costly. Conventional Computational Fluid Dynamics (CFD) methods
struggle to predict the complex nature of combustion, but are quite computationally cheap, and Transported
Probability Density Function (TPDF) methods are able to predict the chemistry of combustion exactly and are
just as computationally cheap. The TPDF method involves a number of different mixing models which control
how the mixing occurs within the TPDF, and one of these must be chosen for each simulation. Hawkes et. al.
have developed a TPDF code which uses a Composition Transported Probability Density Function (c-TPDF),
that creates a TPDF predicting the composition of the test case. This c-TPDF code is currently limited to
solving simple 1D temporally evolving cases which are not highly practical, and hence the need for a c-TPDF
code with 3 spatial inputs and 1 temporal input arises, which would be able to evaluate highly complex
modelling scenarios and hence assist in developing highly efficient engines. The DNS data will be used as a
validation source to verify the accuracy of the TPDF code, mixing models, and spatial consistency.
Aims and Objectives
To extend the c-TPDF code to simulate in two and three spatial dimensions, for the Euclidean Minimum
Spanning Tree (EMST), Interaction by Exchange with the Mean (IEM), and Modified Curl (MC) mixing models.
Conclusion
Testing the three mixing models in the three axes has shown that our TPDF code is
dimensionally analogous. Although 3D DNS data could not be used, the code has shown
promising results and once 3D DNS data can be accessed, the TPDF code should be able
to predict the results accurately.
Method and Results
TPDF Approach
The workflow for using the TPDF code is as follows
1. Pre-process DNS data in Matlab for input to TPDF
2. Run TPDF code with DNS input to produce output
3. Post-process TPDF results in Matlab to produce visual colour maps, and temperature plots
Project Approach
The approach taken to implement the 3D TPDF code is as follows
1. Copy 1D DNS data onto another dimension
2. Test and debug until producing correct results
3. Extrude 1D DNS data onto second dimension to create 2D data
4. Test and debug until producing correct results
References
[1] E.R. Hawkes, R. Sankaran, J.C. Sutherland, J.H. Chen, Proc. Combust. Inst. 31
(2007) 1633–1640.
Figure 1: Configuration of the DNS domain for case M Syngas fuel [1]
Figure 3: Temperature plot for Syngas case M at 30tj for IEM mixing model
Figure 2: Temperature plot for Syngas case M at 30tj for EMST mixing model
Figure 4: Temperature plot for Syngas case M at 30tj for MC mixing model