Dynamics of premixed flames in closed vessels

Krishnan, Gautham

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https://hdl.handle.net/2142/129816 Copy

Description

Title

Dynamics of premixed flames in closed vessels

Author(s)

Krishnan, Gautham

Issue Date

2025-05-19

Director of Research (if dissertation) or Advisor (if thesis)

Matalon, Moshe

Doctoral Committee Chair(s)

Matalon, Moshe

Committee Member(s)

• Fischer, Paul
• Panesi, Marco
• Ewoldt, Randy

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Darrieus-landau Instability
• Flames In Closed Vessels
• Hydrodynamic Theory
• Pressure Rise
• Voluminal Flame Stretch
• Markstein Length
• Rectangular Channels
• Cylindrical Vessels
• Planar Flame
• Cylindrical Flame
• Spherical Flame

Language

eng

Abstract

Premixed flame propagation within closed vessels is ubiquitous within diverse engineering applications such as IC engines, combustors and bomb calorimeters, as well as in fundamental experimental characterizations of combustible mixtures using constant-volume spherical bombs. Unlike freely propagating flames that propagate under nearly isobaric conditions, combustion in a closed vessel results in continuous increases in pressure, burning rate and flame temperature, and a progressive decrease in flame thickness. To model these flames crucial to the engineering design of combustion devices, their safety considerations, as well as fundamental physical understanding, a hydrodynamic theory of premixed flame propagation within closed vessels is developed assuming the flame is much thinner than all other fluid dynamic lengths. In this limit, the flame is confined to a surface separating the unburned mixture from burned combustion products, and propagates at a speed determined from the analysis of its internal structure. Through this asymptotic analysis, the flame speed is found to depend on the voluminal stretch rate, which measures the deformation of a volume element of the flame zone, and on the rate of pressure rise. Both effects are modulated by pressure-dependent Markstein numbers—parameters that lump the effects of heat release and mixture properties while capturing the effects of temperature-dependent transport and stoichiometry. The model, deduced from physical first principles, reduces the full combustion problem to a free-boundary hydrodynamic problem and applies to flames of arbitrary shape propagating in general flows, laminar or turbulent, within vessels of arbitrary configuration. It is employed to describe the canonical configurations of smooth planar, spherical and cylindrical flames in closed rectangular, spherical and cylindrical vessels respectively. The large gas expansion resulting from exothermic combustion reactions at the flame front is known to induce flame corrugation via the well-known Darrieus-Landau (DL) instability. Moreover, the propensity of premixed flames to become corrugated under the influence of intrinsic instabilities is strengthened under the pressure rise that manifests in closed vessel combustion. The hydrodynamic theory is particularly well-suited for investigating the flame wrinkling and acceleration driven by this hydrodynamic instability in mixtures of positive Markstein number. To study the dynamics of such multi-dimensional wrinkled flames, we resort to a numerical approach. For the numerical solution of the free-boundary hydrodynamic problem, a hybrid embedded-manifold/Navier-Stokes methodology has been developed and implemented within a variable-density zero-Mach number Navier-Stokes solver. An immersed boundary method is utilized to implement boundary conditions at the walls of vessels of arbitrary shape. The methodology is adept at developing a comprehensive understanding of the effects of instabilities and low-intensity turbulence on the propagation of premixed flames in closed vessels, being able to handle multiply-folded and disjoint surfaces, representing the highly corrugated flames that result under such conditions. This provides a tremendous opportunity to simulate and obtain fundamental understanding of the effects of turbulence and combustion instabilities on the burning rate, self-acceleration and fractal nature of the flame, which due to the sheer numerical costs is impractical to study by Direct Numerical Simulations (DNS) particularly when examining the large parametric space of interest and within large physically relevant domain sizes. The numerical approach is validated against exact analytical solutions of planar and cylindrical flames, and is shown to describe highly corrugated flame conformations resulting from intrinsic combustion instabilities, in rectangular and circular domains. As a first application of the model, the onset and subsequent nonlinear evolution of the DL instability is systematically investigated in the canonical configuration of a nominally planar flame within a rectangular channel closed at both ends. The onset of instability in the channel is shown to be delayed when compared to freely propagating flames under similar conditions due to the confinement of the burned gas flow between the flame and channel wall. The unstable flame is first observed to develop a cusp-like shape with an intrusion pointing toward the burned gas, which is a characteristic signature of the DL instability. However, unlike the steadily propagating cusp-like structure formed in open space, compression and pressure rise lead to a continually evolving morphology characterized by a repetitive cell splitting and merging behavior which affects the flame surface area and, consequently, the overall flame propagation rate. The tendency towards steady cusp-like propagation is observed only in extremely long channels. The dynamic change in Markstein number associated with the pressure rise in the vessel leads to corrugated flames even for conditions where freely propagating planar flames remain stable. To further analyze the effects of vessel geometry and pressure rise on instability development, outwardly expanding cylindrical flames within closed cylindrical vessels are investigated. This second configuration serves to highlight the distinct physical mechanisms relevant to experiments within spherical/cylindrical bombs used to measure some of the most important and fundamental properties that characterize a combustible mixture—the laminar flame speed and Markstein number. As uncovered in prior studies of freely expanding cylindrical flames, disturbances on the flame surface are found to initially be damped until the flame grows to a critical size where flame perturbations commence growth, marking the onset of the DL instability. This critical size is shown to be sensitive to the wavenumbers of flame surface perturbation modes, with numerical predictions of the most unstable mode consistent with theory. The subsequent nonlinear evolution of the instability exhibits cell-splitting and merging behavior with associated intermittent flame acceleration, highlighted first for a freely expanding flame and then contrasted with flame morphologies within vessels of various sizes. With a reduction in vessel size, these bouts of acceleration become dominated by an overall flame deceleration resulting from its propagation into an unburned mixture that becomes progressively denser with pressure rise. Consistent with experimental observations of the self-acceleration of such flames and the hypothesis of its dependence on a self-similar flame morphology, fractal dimensions are extracted from simulations highlighting greater flame corrugation and acceleration for smaller Markstein numbers.

Graduation Semester

2025-08

Type of Resource

Text

Handle URL

https://hdl.handle.net/2142/129816

Copyright and License Information

Copyright 2025 Gautham Krishnan

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