Engineering topics
Publications and source records attributed to Buell, J. C..
It has been shown that small scale turbulence is produced by the interactions of the merging spanwise structures (rollers) and the streamwise vortices (ribs). In this study, we examine the dissipation rate of the three dimensional kinetic energy and length scales associated with the dissipation rate in a temporally evolving mixing layer.
A study has been initiated on the effects of compressibility (Mach number) on turbulent boundary layers. An understanding of both qualitative (turbulence structures, physical processes) and quantitative (turbulence statistics) effects are desired. This understanding should lead to better turbulence models for applications involving supersonic wall-bounded flows. Direct numerical simulations of an idealized problem will be used to accomplish these objectives. Among several possibilities we chose plane Couette flow with constant-temperature walls as the first problem to be studied. The lack of mean streamwise pressure gradient plus isothermal walls implies that both horizontal directions can be assumed to be homogeneous and that the flow can reach a statistically steady state. Together, these features greatly simplify the calculations and analyses of the results. To date, an algorithm has been developed and implemented (but not yet fully tested) for the accurate solution of the Navier-Stokes equations with the assumptions noted above.
The first goal of this research is to understand the dynamics of three dimensional vortical structures, especially the interaction of the ribs and two dimensional rollers. Because of vortex stretching effects, this requires accurate and well resolved simulations. Another goal is to distinguish temporally- and spatially-growing shear layers in terms of the dynamics and observed vortical structures. This is important since the former is much easier to compute, but the error incurred in using temporal results for certain applications is unknown. The third goal is to investigate the effects of asymmetry on passive scalar mixing and fast-chemistry product formation. In this report a brief summary of a new numerical method is presented, followed by results for mixing layers and wake flows.
A spatially-developing plane mixing layer was analyzed for chaotic behavior. A direct numerical simulation of the Navier-Stokes equations in a 2-D domain infinite in y and having inflow-outflow boundary conditions in x was used for data. Spectra, correlation dimension and the largest Lyapunov exponent were computed as functions of downstream distance x. When forced at a single (fundamental) frequency with maximum amplitude, the flow is periodic at the inflow but becomes aperiodic with increasing x. The aperiodic behavior is caused by the presence of a noisy subharmonic caused by the feedback between the necessarily nonphysical inflow and outflow boundary conditions. In order to overshadow this noise the flow was also studied with the same fundamental forcing and added random forcing of amplitude upsilon prime sub R/delta U = 0.01 at the inlet. Results were qualitatively the same in both cases: for small x, spectral peaks were sharp and dimension was nearly 1, but as x increased a narrowband spectral peak grew, spectra decayed exponentially at high frequencies and dimension increased to greater than 3. Based on these results, the flow appears to exhibit deterministic chaos. However, at no location was the largest Lyapunov exponent found to be significantly greater than zero.
The numerical simulation of incompressible spatially-developing shear flows poses a special challenge to computational fluid dynamicists. The Navier-Stokes equations are elliptic and boundary equations need to be specified at the inflow and outflow boundaries in order to compute the fluid properties within the region of interest. It is, however, difficult to choose inflow and outflow conditions corresponding to a given experimental situation. Furthermore the effects that changes in the boundary conditions or in the size of the computational domain may induce on the global dynamics of the flow are presently unknown. These issues are examined in light of recent developments in hydrodynamic stability theory. The particular flow considered is the spatial mixing layer but it was expected that similar phenomena were bound to occur in other cases such as channel flow, the boundary layer, etc. A short summary of local/global and absolute/convective instability concepts is given. The results of numerical simulations are presented which strongly suggest that global resonances may be triggered in domains of finite streamwise extent although the evolution of the perturbation vorticity field is everywhere locally convective. A relationship between finite domains and pressure sources which might help in devising a scheme to eliminate these difficulties is discussed.
Several direct numerical simulations were performed and analyzed to study various aspects of the early development of mixing layers. Included are the phase jitter of the large-scale eddies, which was studied using a 2-D spatially-evolving mixing layer simulation; the response of a time developing mixing layer to various spanwise disturbances; and the sound radiation from a 2-D compressible time developing mixing layer.
The subharmonic resonance phenomenon in a spatially evolving mixing layer is studied using direct simulations of the 2-D Navier-Stokes equations. The computational domain extends to + or - infinity in the cross-stream direction with U(1) = 1.25 and U(2) = 0.25 imposed at + infinity and - infinity respectively. The domain is finite in the streamwise direction with inflow and outflow boundary conditions imposed at x/delta sub omega = 0 and 100, respectively. A hyperbolic-tangent mean velocity profile is assumed at the inlet and the Reynolds number based on the inlet vorticity thickness and velocity difference is Re = 600. It is observed that the phase angle between the fundamental and its subharmonic plays a key role in the spatial development of these modes. Contour plots of vorticity show that varying the phase will have a dramatic effect on the dynamics of the vortices. Pairing or shredding is observed depending on the phase. Fourier decomposition of the time traces show that the fundamental grows, saturates and decays with the downstream distance. The subharmonic has a similar behavior. However, the level at which the modes will saturate is affected by the phase. At 0 deg phase, it was found that as the fundamental saturates, the growth rate of the subharmonic is enhanced. At 90 deg phase, it was found that as the fundamental saturates, the growth rate of the subharmonic is inhibited. In the later case, the growth rate of the subharmonic recovers after saturation of the fundamental. These results are in qualitative agreement with experimental data.
The aim of the research was to explore the space-time structure of homogeneous turbulence by computing and then interpreting the two-point spectra and correlations of the velocity and pressure fields. Many of these statistics are of considerable practical importance. In particular, it is of interest to compare the different time and length integral scales and microscales for Eulerian and Lagrangian qualities, and to compare the space and time spectra.