Vorticity isotropy in high Karlovitz number premixed flames

The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence

Vorticity transformation in high Karlovitz number premixed flames

To better understand the two-way coupling between turbulence and chemistry, the changes in turbulence characteristics through a premixed flame are investigated. Specifically, this study focuses on vorticity, ω, which is characteristic of the smallest length and time scales of turbulence, analyzing its behavior within and across high Karlovitz number (Ka) premixed flames. This is accomplished through a series of direct numerical simulations (DNS) of premixed n-heptane/air flames, modeled with a 35-species finite-rate chemical mechanism, whose conditions span a wide range of unburnt Karlovitz numbers and flame density ratios. The behavior of the terms in the enstrophy, ω^2 = ω ⋅ ω, transport equation is analyzed, and a scaling is proposed for each term. The resulting normalized enstrophy transport equation involves only a small set of parameters. Specifically, the theoretical analysis and DNS results support that, at high Karlovitz number, enstrophy transport obtains a balance of the viscous dissipation and production/vortex stretching terms. It is shown that, as a result, vorticity scales in the same manner as in homogeneous, isotropic turbulence within and across the flame, namely, scaling with the inverse of the Kolmogorov time scale, τ_η. As τ_η is a function only of the viscosity and dissipation rate, this work supports the validity of Kolmogorov’s first similarity hypothesis in premixed turbulentflames for sufficiently high Ka numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and finally the physical configuration

Turbulence-Flame Interaction

A fluid dynamics video was created using data from a Direct Numerical Simulation of a premixed n-heptane flame at high Karlovitz number. The magnitude of vorticity and progress variable(a monotonically increasing variable through the flame) illustrate the turbulence-flame interaction.Comment: Two videos are included for the 2013 Gallery of Fluid Motio

Vorticity isotropy in high Karlovitz number premixed flames

The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence

Design and Demonstration of a New Small-Scale Jet Noise Experiment

A facility capable of acoustic and velocity field measurements of high-speed jets has recently been built and tested. The anechoic chamber that houses the jet has a 2.1 m × 2.3 m × 2.5 m wedge tip to wedge tip working volume. We aim to demonstrate that useful experiments can be performed in such a relatively small facility for a substantially lower cost than in larger facility. Rapid prototyping allows for quick manufacturing of both simple and complex geometry nozzles. Sideline and 30° downstream acoustic measurements between 400 Hz and 100 kHz agree well with accepted results. Likewise, nozzle exit-plane data obtained using particle image velocimetry are in good agreement with other studies

Small Scale Turbulence in High Karlovitz Number Premixed Flames

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.</p

On the Determination of General Resolution Requirements of Direct Numerical Simulations using Detailed Chemistry

Numerical simulations of reacting flows often rely on direct integration of the continuity and momentum equations while transporting each chemical species and integrating their source term. However, requirements on the grid size and time step to resolve all the relevant physics is not generally well defined. In practice, information regarding convergence is gathered from the corresponding non-reacting flow, one-dimensional laminar flame, and full convergence studies. The establishment of general criteria or benchmarks relating convergence of these three aspects would decrease research and computational effort performing detailed convergence studies and increase consistency in the literature. To support this goal, studies were performed relating the convergence of the global flow field of a laminar reacting flow to the convergence, in space and time, of the corresponding one-dimensional flame and non-reacting flow. It was found that grid convergence of the global flow field was related to, but had more stringent requirements than either of the two separate cases while the required time step was the same. These results contribute to the development of satisfactory general criteria and benchmarks for determining convergence across specific flow cases, chemical mechanisms, and numerical implementations

Investigation of Vortex-Premixed Flame Interaction with Detailed Chemistry

The interaction of a vortex with an initially planar premixed stoichiometric hydrogen-air flame is investigated to characterize the evolution of the vortex across the flame and identify the different regimes of behavior. These characteristics include vortex circulation, peak vorticity, peak velocity, and size. There are two key non-dimensional parameters. The first is the ratio of length scales, l_v/l_F, being the ratio of the vortex diameter to the laminar flame width and the second is the ratio of velocity scales, u_v/S_L, being the ratio of the characteristic velocity of the vortex to the laminar flame speed. The parameter space is explored with values of l_v/l_F ranging from 0.3 to 10 and values of u_v/S_L ranging from 0.1 to 50 corresponding to over 20 separate conditions. By performing simulations which vary these parameters over two and three orders of magnitude, the intermediary and limiting cases of each parameter are investigated. The simulations are performed using a low-Mach number Navier- Stokes solver, detailed hydrogen-air chemistry with 9 species, and unity Lewis number transport. Under stoichiometric hydrogen-air, the assumption of unity Lewis number is justified. Viscous and simulations with a reduced viscosity are preformed highlighting aspects of the coupling of the chemistry and the fluid mechanics. The results demonstrate the existence of four different regimes of the vortex-premixed flame interaction. In the limit u_v/S_L ≫ 1 and l_v/L_F ≫ 1, the vortex wraps the flame within itself and the vortex survives after passing through the flame. In the limit u_v/S_L ≫ 1 and l_v/l_F ≪ 1 the vortex mixes individual layers of the flame within itself and the vortex survives after passing through the flame. In the limit u_v/S_L ≪ 1 and l_v/l_F ≫ 1, the vortex creates sufficient flame curvature to produce baroclinic torque which destroys the incoming vortex. In the limit u_v/S_L ≪ 1 and l_v/l_F ≪ 1, the vortex has negligible effect on the flame and simply stretches in the flame normal direction. All four regimes correspond to qualitatively different vortex flame interactions and therefore the changes in vortices follow different behavior. The use of detailed chemistry for these simulations provides for additional insight into the coupling of chemistry and fluid mechanics in describing the behavior of vortex-premixed flame interactions