ALBERT

Notizen: This paper presents an experimental technique for obtaining fully resolved measurements of the vector velocity field u(x,t) throughout a four-dimensional spatiotemporal region in a turbulent flow. The method uses fully resolved four-dimensional scalar field imaging measurements in turbulent flows [Phys. Fluids A 3, 1115 (1991)] to extract the underlying velocity field from the exact conserved scalar transport equation. A procedure for accomplishing this is described, and results from a series of test cases are presented. These involve synthetically generated scalar fields as well as actual measured turbulent flow scalar fields advected numerically by various imposed flow fields. The imposed velocity fields are exactly known, allowing a careful validation of the technique and its potential accuracy. Results obtained from a zeroth iteration of the technique are found to be very close to the exact underlying vector velocity field. Further results show that successive iterations bring the velocity field from the zeroth iteration even closer to the exact result. It is also shown that the comparatively dense velocity field information that this technique provides is well suited for accurate extraction of the more dynamically insightful strain rate and vorticity fields ε(x,t) and ω(x,t).

Notizen: The concept of flow field velocimetry based on scalar imaging measurements [Phys. Fluids A 4, 2191 (1992)] is here formulated in terms of an integral minimization implementation, where the velocity field u(x,t) is found by minimizing weighted residuals of the conserved scalar transport equation, along with the continuity condition and a smoothness condition. We apply this technique to direct numerical simulation (DNS) data for the limiting case of turbulent mixing of a Sc=1 passive scalar field. The spatial velocity fields u(x,t) thus obtained demonstrate good correlation with the exact DNS fields, as do the statistics of the velocity and the velocity gradient fields. The results from this integral minimization implementation also show significant improvement over those from the direct inversion technique reported earlier. These results are shown to be largely insensitive to noise at levels characteristic of current fully resolved scalar field measurements. © 1996 American Institute of Physics.

Notizen: A local integral model for approximate simulations of the molecular mixing and chemical reaction processes in turbulent reacting flows is presented. The model is based on recent experimental results, which show that essentially all of the molecular mixing in turbulent flows occurs in thin strained laminar diffusion layers, and that the internal structure within these layers is essentially self-similar. This motivates a local integral treatment of the mixing and reaction processes in these layers that removes the resolution requirements imposed on full simulations by the steep gradients within the molecular diffusion and chemical reaction scales of the flow. The resulting integral model is applied to predict the mixing and reaction progress in a temporally developing shear layer over a range of Reynolds and Damköhler numbers, and to make comparisons with results obtained from full finite difference simulations. The resulting reactant and product concentration fields, as well as the temperature and reaction rate fields obtained from the model, are in good agreement with the full simulations. The results indicate that the model is able to accurately follow even highly sensitive nonlinear measures of the mixing and reaction progress such as the local extinction phenomenon characteristic of large Zel'dovich number Arrhenius kinetics.

Notizen: Results are presented from an experimental study of the molecular mixing of a dynamically passive conserved scalar quantity in an axisymmetric laminar vortex ring. The experiments are based on highly resolved laser-induced fluorescence imaging measurements of the scalar field ζ(x,t) in the diametral plane of the ring, from which the evolution of the molecular mixing rate field ∇ζ⋅∇ζ(x,t) can be directly examined. In particular, the structure and dynamics of the mixing process are addressed during the three characteristic stages in the ring evolution, namely, (i) the ring generation stage, (ii) the ring pinch-off stage, and (iii) the asymptotic stage of the ring. Results show a layering of the mixing process in which the diffusional cancellation term ∇(∇ζ):∇(∇ζ) plays a major role in setting the overall mixing rate achieved. The scalar field measurements are also used to extract detailed information about the underlying velocity field in the ring.

Notizen: Results from highly resolved, four-dimensional measurements of the fine structure of the fully space- and time-varying Sc(very-much-greater-than)1 conserved scalar field and the associated scalar energy dissipation rate field in a turbulent flow are presented. The resolution achieved in all three spatial dimensions and in time reaches down to the local strain-limited molecular diffusion scale in the flow, allowing all three components of the instantaneous scalar gradient vector field ∇ζ(x,t) and their time evolution at every point in the data space to be directly evaluated. Results are presented in the form of fine structure maps of the instantaneous dissipation field loge ∇ζ⋅∇ζ(x,t) in several spatially adjacent data planes within an individual three-dimensional spatial data volume, as well as in several temporally successive data planes from a sequence of such three-dimensional data volumes. The degree of anisotopy in the underlying scalar gradient field is characterized in terms of the joint distribution β(cursive-theta,cursive-phi) of spherical orientation angles. The probability density of true scalar energy dissipation rates is presented and compared with the distributions that would result from lower-dimensional measurements of the scalar gradient vector. From this the "spottiness'' of the scalar dissipation field is directly quantified by determining the true fraction of the total dissipation that occurs in any given volume fraction of the flow.

Notizen: It is shown that measurements of lower-dimensional projections of the scalar gradient in an isotropic conserved scalar field ζ(x,t) are sufficient to construct the probability density function (pdf) for the true scalar dissipation χ. With this general method, the true scalar dissipation pdf is obtained from the result reported recently for the approximate pdf based on ||∇ζ||2(approximate)3⋅(∂ζ/∂x)2. Results show that (i) the pdf of the true scalar dissipation is virtually lognormal and (ii) the most probable value of χ increases and the rms fluctuations of χ decrease in comparison with their one-dimensional estimates.

Notizen: Results are presented from an assessment of the applicability of Taylor's hypothesis for approximating streamwise derivatives and obtaining dissipation estimates in turbulent flows. These are based on fully resolved measurements of a conserved scalar field ζ(x,t) throughout a four-dimensional spatio-temporal volume in a turbulent flow. The data allow simultaneous evaluation of all three components of the true gradient vector field (bold del)ζ(x,t) and the time derivative field (∂/∂t)ζ(x,t) at the small scales of a turbulent shear flow. Streamwise derivatives obtained from Taylor's frozen flow hypothesis yield a correlation of 0.74 with the true streamwise derivative field at the present measurement location in the self-similar far field of an axisymmetric turbulent jet. Direct assessments are also presented of approximations invoking Taylor's hypothesis to estimate energy dissipation rates in turbulent flows. The classical single-point time series approximation yields a correlation of 0.56 with the true scalar energy dissipation rate, while a mixed estimate that combines one spatial derivative and the time derivative gives a correlation of 0.72. A general analytical formulation is presented for assessing various dissipation estimates, and for determining the optimal dissipation estimate that maximizes the correlation with the true dissipation rate. The resulting optimal mixed dissipation estimate yields a correlation of 0.82 at the point of maximum turbulence intensity in a jet, and a value of 0.92 on the jet centerline. © 1997 American Institute of Physics.

Notizen: Scalar imaging velocimetry is here applied to experimental turbulent flow scalar field data to yield the first fully resolved, non-intrusive laboratory measurements of the spatio-temporal structure and dynamics of the full nine-component velocity gradient tensor field ∇u(x,t), as well as the pressure gradient field ∇p(x,t), in a turbulent flow. Results are from turbulent flows at outer scale Reynolds numbers in the range 3,000≤Reδ≤4,200, with Taylor scale Reynolds numbers Reλ≈45. These give a previously inaccessible level of detailed experimental access to the spatial structure in the velocity gradient tensor field at the small scales of turbulent flows, and through the much longer temporal dimension of these four-dimensional data spaces allow access to the inertial range of scales as well. Sample spatio-temporal data planes and probability distributions spanning more than 75 advection time scales (λν/U) are presented for various dynamical fields of interest, including the three components of the velocity field u(x,t), the nine components of the velocity gradient tensor field ∇u(x,t) through the full vector vorticity field ωi(x,t) and tensor strain rate field cursive-epsilonij(x,t), the kinetic energy dissipation rate field Φ(x,t)≡2νcursive-epsilon:cursive-epsilon(x,t), the enstrophy field 1/2ω⋅ω(x,t), the enstrophy production rate field ω⋅cursive-epsilon⋅ω(x,t), and the pressure gradient field ∇p(x,t). Continuity tests show agreement with the zero divergence requirement that exceeds the highest values reported from single-point, invasive, multi-probe measurements. Distributions of strain rate eigenvalues as well as alignments of the strain rate eigenvectors with both the vorticity and scalar gradient vectors are in agreement with DNS results, as are distributions of the measured helicity density fields u⋅ω(x,t). Results obtained for the true kinetic energy dissipation rate field show good agreement, up to 14th-order, with previous inertial range structure function exponents measured by Anselmet et al. [J. Fluid Mech. 140, 63 (1984)] at much higher Reynolds numbers. In addition, probability distributions scaled on inner variables show good agreement among buoyant and non-buoyant turbulent flow cases, further suggesting that these results are largely indicative of the high Reynolds number state of the inner scales of fully developed turbulent flows. © 1996 American Institute of Physics.