Flow physics of strained turbulent axial vortices

Brijesh Eshpuniyani, Purdue University

Abstract

The flow physics of strained turbulent axial vortices has been studied using direct numerical simulations (DNS) as an investigative tool. These simulations use a b-spline/Fourier spectral method. Two specific cases have been considered. A vortex that has no axial flow in its initial laminar state is first studied (this simulation is called STRN4). This allows us to focus exclusively on the effect of the strain field. The strain field causes the streamlines to be elliptical, thereby introducing a short wavelength instability called the elliptic instability. This is followed by studying a vortex that has a wake-like axial flow profile in its initial laminar state (this simulation is called STRN2). We now have the instability due to shear in the axial flow in addition to that due to the strain field. In both these cases the initially laminar vortex is perturbed randomly. Evolution of the overall level of turbulence is studied by computing the global turbulent kinetic energy (GTKE). In STRN4 the GTKE evolves in an “oscillatory” fashion, with periods of exponential growth followed by saturation and decay. The growth rate decreases for successive exponential GTKE rises. In STRN2 the first exponential GTKE rise occurs with a much larger growth rate than the first exponential GTKE rise for STRN4. This is due to the instability associated with the axial flow. We then observe an “oscillatory” pattern, followed by a period during which the GTKE maintains an almost uniform level, and then a final period of growth. In both the cases, the simulation had to be stopped towards the end of the final GTKE rise because the turbulence outgrows the computational domain. Flow visualization is used to study the evolution of the vortex in terms of its structure. In STRN4 we observe the presence of left and right running helical waves along with a sinusoidal bending of the vortex along its axis. As the simulation progresses, the wavelength of this sinusoidal bending is seen to increase. This is reflected in the dominant modes found by computing the two dimensional energy spectra. The dominant modes are found to shift from (k&thetas;, kz) = (±1, 4) to (±1, 1) as the simulation progresses. In STRN2, we initially observe helical waves with positive azimuthal wavenumbers. The initially dominant modes are computed to be (k&thetas;, kz) = (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5). As the simulation progresses, the vortex structure shows the presence of features that correspond to a varied set of dominant modes. Towards the end of the simulation (±1, 1) are found to be the dominant modes. Two dimensional energy spectra also give us information about how the turbulent kinetic energy is spread over different wavenumbers (length scales). In general, increases in GTKE are accompanied by the presence of more small scale structure and vice versa. In addition to the broad understanding obtained in this manner, the evolution of some mean and statistical quantities of interest is discussed. Formulation for large eddy simulation (LES) in the context of the numerical method used in this study has been completed. The DNS code has been modified to perform large eddy simulations. Validating this code and using it to perform LES to study the vortex at higher Reynolds numbers is one of the major suggestions for future work.

Degree

Ph.D.

Advisors

Blaisdell, Purdue University.

Subject Area

Aerospace materials|Atmosphere|Fluid dynamics|Gases

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