A normalised residence time transport equation for the numerical simulation of combustion with high-temperature air

Abstract

This study concerns the numerical simulation of turbulent non-premixed combustion in highly preheated air streams. One of the objectives is to settle an efficient computational procedure to proceed with the numerical simulation of large-scale industrial devices. It is also expected that the availability of such a computational framework may facilitate comprehensive sensitivity analyses as well as the development of mathematical models able to represent turbulence-chemistry interactions (TCI) in such conditions. Based on the salient physical ingredients that characterise scalar mixing, propagation, and self-ignition processes, a turbulent combustion modelling framework is thus introduced and applied to the numerical simulation of well-documented laboratory flames. In the corresponding geometries, the bulk flow velocities of the reactants streams can reach rather large values, which lead the flame to lift from the burner rim. Partially premixed flame edges thus stabilise the whole flame structure and the temperature of the oxidising stream can be increased by vitiation with burned gases so as to promote the corresponding flame-stabilisation processes. For sufficiently large values of the vitiated airstream temperature, self-ignition mechanisms may be triggered thus leading to a competition between mixing, propagation, and ignition processes. In this context, the ratio of the residence time to the self-ignition delay is thought to be a relevant variable to delineate the possible influence of ignition phenomena. Therefore, a modelled transport equation for this normalised residence time is considered. The performance of the corresponding modelling proposal is analysed with special emphasis placed on its ability to reproduce ‘memory’ or ‘lagrangian’ effects related to thermal aging processes. In this respect, it is noteworthy that the present set of computations makes use of tabulated quantities associated to (i) steady laminar one-dimensional diffusion flamelets, so as to describe the composition of combustion products, (ii) steady laminar one-dimensional premixed flamelets, to describe the flame brush propagation, and (iii) temporal evolution of zero-dimensional homogeneous mixtures to account for the possible occurrence of self-ignition phenomena. In particular, the tabulated self-ignition time value is used to evaluate the increase in the normalised residence time. Finally, two modelling parameters are put into evidence and studied through a detailed sensitivity analysis.

Keywords:

• turbulence-chemistry interaction
• non-premixed combustion
• self-ignition
• residence time
• highly preheated air stream

Acknowledgements

The authors also acknowledge Dr. K.Q.N. Kha and A. Er-raiy for their technical assistance and input at the beginning of this study.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Arnaud Mura http://orcid.org/0000-0001-9625-9962

Notes

1. We are referring to species concentrations and temperature.

2. Its instantaneous counterpart is $\mathcal{L}\left(\rho \varphi \right)=\mathrm{\partial }\left(\rho \varphi \right)/\mathrm{\partial }t+\mathrm{\partial }\left(\rho u_k\varphi \right)/\mathrm{\partial }{x}_k-\mathrm{\partial }/\mathrm{\partial }{x}_k\left(\rho D\mathrm{\partial }\varphi /\mathrm{\partial }{x}_k\right)$.

3. It is noteworthy that this terminology differs from the one introduced initially in reference [27].

4. Several forms of this equation have been considered in the literature, see for instance references [12–15,29,30].

5. It is noteworthy that, for security reasons, the condition ${\tau }_i\gg \tau$ is indeed met in experimental devices.

6. It should be emphasised that $x_1=0.0$ corresponds to the nozzle exit plane.

7. The burned products composition is determined from the mixture field using Equation (9(9) ${\tilde{Y}}_{j,b}={\int }_0^1{Y}_{j,b}\left({\xi }^{\ast }\right)\tilde{P}({\xi }^{\ast };\tilde{\xi },{\tilde{V}}_{\xi })\mathrm{d}{\xi }^{\ast },$(9) ).

Additional information

Funding

This work is financially supported by Région Nouvelle-Aquitaine. Ms. Xiaodong Wang also gratefully acknowledges the complementary funding of the Civil Aviation University of China (CAUC, Tianjin).