Joint-velocity-scalar probability density function method for modelling high-speed turbulent combustion
File(s)
Author(s)
Un, Tin-Hang
Type
Thesis
Abstract
This thesis presents a joint-velocity-scalar probability density function (VSPDF) model aimed at improving dual-mode ramjet engine simulations. This model stands out as a unified closure for sub-grid turbulence interactions in large eddy simulations (LES), requiring minimal coefficients and making no assumptions about specific flame structure or combustion regime. The VSPDF is transported using a conservative and thermodynamically consistent stochastic fields (SF) formulation, ensuring stability in shocked turbulent flows. The Eulerian nature of SF allows direct implementation of a high-order numerical scheme and adaptive mesh refinement (AMR). Various cases showcase the model’s unique capabilities, such as the ability to distinguish between laminar shear and turbulence, and to capture extreme events such as autoignition.
Two improvements to the model are proposed. The first uses a tensor-based neural network to replace existing sub-grid mixing model. By respecting physical symmetries and dimensional consistency, this approach outperforms both the original simplified Langevin model and a conventional neural network.
The second improvement targets the computational cost for resolving boundary layers by integrating an ODE-based wall model with the SF, producing accurate wall fluxes with 10 to 50 times coarser grids. A coupling procedure is proposed to maintain stability and ensure correct sub-grid fluctuation profiles. Simulations of a supersonic channel agree well with direct numerical simulations, showing significant improvement over LES without a wall model.
Finally, the wall-modelled SF is applied to simulate a dual-mode ramjet engine. The method shows good agreement with experimental results in terms of shock train length, pressure profile, and flame position, in two fundamentally different conditions. This demonstrates the model's wide applicability, allowing for confident use in the design and optimisation of ramjet and scramjet engines.
This study represents the first application of VSPDF in simulating ramjet engines, as well as the first solver to integrate SF, AMR, and wall modelling.
Two improvements to the model are proposed. The first uses a tensor-based neural network to replace existing sub-grid mixing model. By respecting physical symmetries and dimensional consistency, this approach outperforms both the original simplified Langevin model and a conventional neural network.
The second improvement targets the computational cost for resolving boundary layers by integrating an ODE-based wall model with the SF, producing accurate wall fluxes with 10 to 50 times coarser grids. A coupling procedure is proposed to maintain stability and ensure correct sub-grid fluctuation profiles. Simulations of a supersonic channel agree well with direct numerical simulations, showing significant improvement over LES without a wall model.
Finally, the wall-modelled SF is applied to simulate a dual-mode ramjet engine. The method shows good agreement with experimental results in terms of shock train length, pressure profile, and flame position, in two fundamentally different conditions. This demonstrates the model's wide applicability, allowing for confident use in the design and optimisation of ramjet and scramjet engines.
This study represents the first application of VSPDF in simulating ramjet engines, as well as the first solver to integrate SF, AMR, and wall modelling.
Version
Open Access
Date Issued
2025-08-05
Date Awarded
01/12/2025
License URL
Advisor
Navarro-Martinez, Salvador
Publisher Department
Department of Mechanical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)