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Small Scale Turbulence in High Karlovitz Number Premixed Flames


Bobbitt, Brock Douglas (2016) Small Scale Turbulence in High Karlovitz Number Premixed Flames. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9Z03649.


The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.

Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.

Subsequently, enstrophy, ω2 = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τη, just as in homogeneous isotropic turbulence. As τη is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.

Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.

Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO2 and soot production to increasing engine efficiency.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:premixed flames, turbulent flames, vorticity, small scale turbulence, enstrophy, direct numerical simulations, high Karlovitz
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Blanquart, Guillaume
Thesis Committee:
  • Hunt, Melany L. (chair)
  • Blanquart, Guillaume
  • Colonius, Tim
  • Shepherd, Joseph E.
Defense Date:1 March 2016
Non-Caltech Author Email:bobbitt.brock (AT)
Funding AgencyGrant Number
U.S. Air Force Office of Scientific ResearchFA9550-12-1-0144
ARCS Foundation Los Angeles ChapterUNSPECIFIED
John and Ursula Kanel Foundation Charitable ScholarshipUNSPECIFIED
Record Number:CaltechTHESIS:03102016-211538603
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 2 adapted for ch. 4-5
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9611
Deposited By: Brock Bobbitt
Deposited On:18 Mar 2016 20:54
Last Modified:25 Oct 2023 21:05

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