Imperial College London

Dr Lu Tian

Faculty of EngineeringDepartment of Mechanical Engineering

Honorary Lecturer



l.tian14 CV




674City and Guilds BuildingSouth Kensington Campus





Publication Type

14 results found

Tian L, Lindstedt RP, 2023, On the impact of differential diffusion between soot and gas phase species in turbulent flames, Combustion and Flame, Vol: 251, ISSN: 0010-2180

The molecular diffusivities of larger PAHs and soot particles approach zero leading to differential diffusion with gas-phase species. The present work systematically quantifies the impact on soot moments, soot related statistical correlations and Particle Size Distributions (PSDs) using a fully coupled transported joint probability density function (JPDF) method featuring a 78-dimensional joint-scalar space, including enthalpy, gas phase species with the PSD discretised using 62 size classes via a mass and number density preserving sectional method. Differential diffusion of soot (DDS) is treated via a gradual decline of diffusivity among soot sections maintaining realisability and the expected exponential decay of variance. The solution of the flow field features a time-dependent second moment closure and an elliptic solver. The turbulent non-premixed Sandia C2H4 flame from the International Sooting Flame (ISF) data base was selected as a target along with the KAUST (C2H4/N2) variant of the same flame. Results show that reduced soot diffusion leads to a significant increase in the soot volume fraction RMS and that the correlation coefficient between soot volume fraction and temperature is further reduced in a particle-size-dependent manner. Similar observations are made for correlations between the soot volume fraction and the mass fractions of gas-phase species such as CO, OH, H and C2H2. The results suggest that computational methods that presume explicit (e.g. flame structure related) correlations between such scalars and with soot face leading order modeling challenges. It is also shown that the correlation between CO and soot increases due to oxidation of soot and that DDS leads to a modest downstream shift of PSDs towards larger particles.

Journal article

Greenblatt D, Tian L, Lindstedt RP, 2023, The impact of hydrogen substitution by ammonia on low- and high-temperature combustion, Combustion and Flame, ISSN: 0010-2180

The combustion behaviour of ammonia has attracted intermittent interest with the original patent by Lyon (US3900554A) relating to its use for nitric oxide reduction through selective non-catalytic reduction (SNCR) a focal point. The recent interest in ammonia stems from its use as a hydrogen rich energy carrier with practical use requiring a much wider parameter space. The corresponding challenges (e.g. Kobayashi et al., Proc. Combust. Inst. 37 (2019) 109–133) include different flame dynamics and high emissions of oxides of nitrogen. The current paper explores the complex nature of ammonia oxidation and provides a reduced size reaction mechanism that enables application, without approximation, to the computation of turbulent flames through a joint-scalar transported probability density function (JPDF) method. Comprehensive validation suggests similar accuracy to a reference mechanism (Glarborg et al., Prog. Energy Combust. Sci. 67 (2018) 31–68) and highlights some uncertainties. The selected turbulent flame configuration features auto-ignition stabilised flames supported by a coflow of hot combustion products. The base case features a H2/N2 fuel jet that permits flame stabilisation at 1045 K corresponding to the onset of the SNCR temperature window. The impact of a gradual substitution of hydrogen by ammonia on flame stabilisation, emissions of oxides of nitrogen and the flame structure is quantified. It is shown that ammonia substitution leads to more prevalent local extinction, a more distributed flame structure and requires substantially increased coflow temperatures to achieve a similar flame stabilisation point. A lowering of the coflow temperature to operate within the SNCR regime substantially reduces NOx and leads towards a homogeneous/distributed reaction mode. The reduced fuel reactivity highlights the importance of turbulence-chemistry interactions leading to complexities in the design of practical devices.

Journal article

Tian L, Lindstedt RP, 2023, The impact of ammonia addition on soot formation in ethylene flames, Combustion and Flame, ISSN: 0010-2180

The present work investigates computationally the impact of blending ammonia with ethylene on soot formation in four laminar diffusion flames and the corresponding turbulent partially premixed flames. The conditions conform to experimental investigations (Bennett et al., Combust. Flame, 2020, and Boyette et al., Combust. Flame, 2021) with both sets of flames featuring identical fuel blends. A mass and number density preserving sectional method was applied to all cases with the soot surface growth and oxidation models updated to include reactions with oxides of nitrogen. The gas phase chemistry was extended to include a comprehensively validated ammonia sub-mechanism. For the laminar flames, the inception of soot particles is based on detailed chemistry with pyrene treated as representative of the PAH pool. The accuracy of fitting a global acetylene-based inception step is evaluated for the different fuel blends and subsequently applied to the turbulent flames using a fully coupled transported joint probability density function method featuring an 84-dimensional joint-scalar space. Results obtained for laminar flames show that detailed chemistry coupled with the sectional soot model provides excellent agreement with the measured suppression of the soot volume fraction with increased use of ammonia. Computed particle size distributions (PSDs) show an increase in smaller soot particles under such conditions, consistent with experimental observations. The experimentally observed reduced impact in turbulent flames is also reproduced computationally. The suppression of soot is principally caused by changes in the radical pool leading to reduced soot surface growth and, to a lesser extent, soot inception. The contribution of oxides of nitrogen to soot oxidation is modest. Computed PSDs in laminar and turbulent flames highlight the importance of differences in flame structures and flowfield timescales.

Journal article

Tian L, Boyette WR, Lindstedt RP, Guiberti TF, Roberts WLet al., 2022, Transported JPDF modelling and measurements of soot at elevated pressures, Proceedings of the Combustion Institute, ISSN: 1540-7489

Accurate measurements and modelling of soot formation in turbulent flames at elevated pressures form a crucial step towards design methods that can support the development of practical combustion devices. A mass and number density preserving sectional model is here combined with a transported joint-scalar probability density function (JDPF) method that enables a fully coupled scalar space of soot, gas-phase species and enthalpy. The approach is extended to the KAUST turbulent non-premixed ethylene-nitrogen flames at pressures from 1 to 5 bar via an updated global bimolecular (second order) nucleation step from acetylene to pyrene. The latter accounts for pressure-induced density effects with the rate fitted using comparisons with full detailed chemistry up to 20 bar pressure and with experimental data from a WSR/PFR configuration and laminar premixed flames. Soot surface growth is treated via a PAH analogy and soot oxidation is considered via O, OH and O2 using a Hertz-Knudsen approach. The impact of differential diffusion between soot and gas-phase particles is included by a gradual decline of diffusivity among soot sections. Comparisons with normalised experimental OH-PLIF and PAH-PLIF signals suggest good predictions of the evolution of the flame structure. Good agreement was also found for predicted soot volume statistics at all pressures. The importance of differential diffusion between soot and gas-phase species intensifies with pressure with the impact on PSDs more evident for larger particles which tend to be transported towards the fuel rich centreline leading to reduced soot oxidation.

Journal article

Simatos P, Tian L, Lindstedt RP, 2021, The impact of molecular diffusion on auto-ignition in a turbulent flow, Combustion and Flame, ISSN: 0010-2180

The inclusion of molecular diffusion into the joint-probability density function (JPDF) method requires terms for molecular transport in physical space and mixing in composition space. The former is typically neglected for high Reynolds number flows but becomes important in flows close to surfaces and for flamelet related reaction-diffusion structures associated with high Damköhler numbers. McDermott and Pope (J. Comp. Phys., 2007) proposed an explicit addition of a molecular transport term to the equation for sub-grid molecular diffusion for the filtered density function method. A related approach was used by Fiolitakis et al. (Combust. Flame, 2014) for the JPDF method when combined with moment based closures. A variant of the method is here combined with comprehensive C1−C2 chemistry featuring 44 chemical species and 256 reactions to study the impact on auto-ignition and flame stabilisation in the well-characterised Cabra burner. It is shown that the contribution of the molecular transport term becomes significant at the flame stabilisation point with predictions of carbon monoxide and, in particular, molecular hydrogen showing a marked improvement. Conditional statistics and the PDF of temperature show that the improvement is due to increased molecular diffusion on the fuel rich side of the flame leading to increased chemical activity. The developed approach is viable for boundary layers while the spatial resolution requirements in terms of the mean scalar gradients may prove limiting for complex flows.

Journal article

Tian L, Schiener MA, Lindstedt RP, 2021, Fully coupled sectional modelling of soot particle dynamics in a turbulent diffusion flame, Proceedings of the Combustion Institute, Vol: 38, Pages: 1365-1373, ISSN: 0082-0784

Soot particle dynamics, including particle size distributions (PSDs) and related statistics, are of increasing practical significance due to evolving regulatory demands. The combination of a mass and number density preserving sectional model with a transported joint probability density function (JPDF) method ensures a full coupling of the joint scalar space, e.g. soot and gas phase reactions and radiative heat losses, within a method that can represent ignition/extinction phenomena as well as the slow (low Damköhler number) soot inception and oxidation chemistry in turbulent flames. This approach is here applied to the sooting non-premixed Sandia ethylene jet flame via a 78-dimensional joint-scalar space, including enthalpy, gas phase species and 62 soot sections. Soot nucleation is treated as a global step from acetylene to pyrene with the rate fitted using comparisons with full detailed chemistry. Soot surface growth is treated via a PAH analogy and soot oxidation is considered via O, OH and O2 using a Hertz–Knudsen approach. Comparisons with measured temperature, gas phase species and the mean soot volume fraction show good agreement while the introduction of zero soot diffusivity leads to substantially improved predictions of the RMS of the soot volume fraction. The calculated PSDs at the burner centreline show a transition from one to two-peaks along the axial direction with the mode of the second peak increasing from 14 to 32 nm. Scatter plots, joint statistics of soot parameters and temperature, and the chemical source terms across soot sections suggest that surface growth is dominant when PSDs are unimodal and that the competition of oxidation, coagulation/aggregation and surface growth leads to a PSD shape transition. It is also shown that local extinction events lead to the presence of soot in cool fuel lean mixtures.

Journal article

Tian L, Lindstedt RP, 2019, Impact of molecular mixing and scalar dissipation rate closures on turbulent bluff-body flames with increasing local extinction, Combustion and Flame, Vol: 206, Pages: 51-67, ISSN: 0010-2180

The Combustion Institute Bluff-body turbulent CH 4 : H 2 (1:1) flames at 50% (HM1), 75% (HM2) and 91% (HM3) of the blow-off velocity (235 m s−1) were studied experimentally by Masri and co-workers and found to exhibit gradually increasing periodic and shear layer instabilities. The latter are coupled with increasing levels of local extinction with subsequent re-ignition further downstream. This study provides a systematic evaluation of the sensitivity of predictions to molecular mixing and scalar dissipation rate closures. The latter include extended forms of the Euclidean Minimum Spanning Tree (EMST) and modified Curl's (MC) models, applicable to premixed turbulent flames via a closure that accounts for local Damköhler number effects (EEMST and EMC), and a conceptually related blended scalar time-scale approach (BEMST and BMC). Computations are performed using a hybrid finite volume (FV) – transported Joint Probability Density Function (JPDF) algorithm featuring stochastic Lagrangian particles, a comprehensive 48-scalar systematically reduced C/H/N/O mechanism, and a second moment method based on the Generalised Langevin Model that provides a partial resolution of the unsteady fluid motion. The sensitivity to solution parameters affecting the temporal resolution is quantified using Fourier transforms of the time histories of velocity and scalar traces. Radial profiles, conditional means and scatter plots are compared to the experimental data along with burning indices based on the conditional mean temperature. Vortex related instabilities ∼ 1 kHz in the outer shear layer appear for all closures with EMC showing periodic local extinction and re-ignition in the neck region for HM3 and flame turbules (i.e., discrete pockets of hot gas) separating periodically at frequencies ∼ 85 Hz. Results are similar to well–resolved JPDF/LES simulations for HM1. It is shown that the EMC and (E)EMST models essentially enclose the experimental data for

Journal article

Tian L, Lindstedt RP, 2019, Evaluation of reaction progress variable - Mixture fraction statistics in partially premixed flames, Proceedings of the Combustion Institute, Vol: 37, Pages: 2241-2248, ISSN: 1540-7489

The mixture fraction and reaction progress variables are key for presumed probability density function (PDF) based flamelet models for partially premixed flames. The importance of the joint statistics of these two variables are evaluated using a joint composition-enthalpy transported PDF/Finite Volume method applied to established databases for inhomogeneous jet flames. The accuracy of the approach is first examined for three flames with different mixture fraction inlet profiles and departures from blow-off. The (joint-) statistics of mixture fraction and reaction progress variable are subsequently analysed with the covariance of the two variables used to evaluate the assumption of statistical independence. Results show that the current approach is able to reproduce the near-field features of both homogeneous and inhomogeneous jet flames. The latter leads to a stratified premixed flame that evolves to diffusion-dominated combustion as the influence of the pilot fades. In agreement with measured data, the mixture fraction variance is strongly affected by the near-field combustion mode and the misalignment with the reaction progress variable variance is obvious in the stratified premixed flame. It is shown that the covariance of the mixture fraction and reaction progress variable is influenced by turbulence-chemistry interactions and that, generally, the two parameters remain strongly correlated with the consequence that the assumption of statistical independence is implausible.

Journal article

Tian L, Lindstedt, 2017, The impact of dilatation, scrambling and pressure transport in turbulent premixed flames, Combustion Theory and Modelling, Vol: 21, Pages: 1114-1147, ISSN: 1741-3559

Premixed turbulent flames feature strong interactions between chemical reactions and turbulence that affect scalar and turbulence statistics. The focus of the present work is on clarifying the impact of pressure dilatation/flamelet scrambling effects with a comprehensive second-moment closure used for evaluation purposes. Model extensions that take into account flamelet orientation and molecular diffusion are derived. Isothermal pressure transport is included with an additional variable density contribution derived for the flamelet regime of combustion. Full closure is assessed by comparisons with Direct Numerical Simulations (DNSs) of statistically ‘steady’ fully developed premixed turbulent planar flames at different expansion ratios. Subsequently, the prediction of lean premixed turbulent methane–air flames featuring fractal grid generated turbulence in an opposed jet geometry is considered. The overall agreement shows that ‘dilatation’ effects contribute to counter-gradient transport and can also increase the turbulent kinetic energy significantly. Levels of anisotropy are broadly consistent with the DNS data and key aspects of opposed jet flames are well predicted. However, it is also shown that complications arise due to interactions between the imposed pressure gradient and combustion and that redistribution is affected along with the scalar flux at the leading edge. The latter is strongly affected by the reaction rate closure and, potentially, by pressure transport. Overall, the derived models offer significant improvements and can readily be applied to the modelling of premixed turbulent flames at practical rates of heat release.

Journal article

Tian L, Lindstedt RP, 2017, Transported PDF modelling and analysis of partially premixed flames, 8th European Combustion Meeting, Publisher: The Combustion Institute

A hybrid finite volume – transported joint probability density function (FV/JPDF) method is used to model piloted flames with inhomogeneous inlets. The flames were experimentally investigated using a retractable central tube within the main burner to control the degree of mixing at the exit. A five-gas (C2H2, H2, CO2, N2, air) co–flow pilot located outside the burner was used to match the composition and adiabatic temperature of a stoichiometric methane/air flame. The applied hybrid method features a flow field calculation using a time-dependent finite-volume based method closed at the second-moment level with the scalar field obtained at the joint-scalar (JPDF) level. The current methodology is applicable to both premixed combustion and diffusion-dominated regions without assumption regarding the inclusion of the chemistry. Results show that the current method can accurately capture the stratified premixed flame mode near the burner exit as well as the diffusion-dominated flame far downstream. The transition between the combustion modes occurs around ten tube diameters downstream of the burner exit and it is observed that the flame structure is very sensitive to the prediction of the flow field in this region.

Conference paper

Tian L, Chen LH, Chen Q, Zhong FQ, Chang XYet al., 2015, Engine performance analysis and optimization of dual-mode scramjetwith varied inlet conditions, Acta Mechanica Sinica, ISSN: 1614-3116

Journal article

Tian L, Lindstedt, 2015, Redistribution and Dilatation Effects in Turbulent Premixed Opposed Jet Flames, the 7th European Combustion Meeting

Conference paper

Tian L, Chen L, Chen Q, Li F, Chang Xet al., 2014, Quasi-One-Dimensional Multimodes Analysis for Dual-Mode Scramjet, JOURNAL OF PROPULSION AND POWER, Vol: 30, Pages: 1559-1567, ISSN: 0748-4658

Journal article

Tian L, Chen L, Chen Q, Li F, Chang Xet al., 2012, Modeling and measurements of heat release distributions in dual-mode scramjet combustor

To better evaluate the performance of dual-mode scramjet combustor, the axis distribution of heat release must be predicted accurately. Current work is based on a modified 1-D model assisted by measurements acquired in a dual-mode combustor on direct- connected scramjet facility. CH* images have been employed to study the combustion stabilization modes and further determine the start position of heat release for 1-D model. The heat release distributions of multi-ports and sing-port injections have been numerically investigated by 1-D model and validated by TDLAS measurements. The results show that heat release distributions depend on the arrangements of injections and flameholders. Close multi-ports injections bring higher combustion efficiency but further propagation of pre-combustion shock. On the contrary, sing-port injection with pure three-dimensional flowfield can obtain both high efficiency and more stable pre-combustion shock. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Conference paper

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