Underlying Velocity Field Research Articles

Prospects for Transport Modeling of Process Tanks

Mathematical modeling of process tanks has been dominated by one-dimensional and empirically derived “black box” techniques. This approach has until recently been justified by the intractability of the full equations of motion in these domains. Modern methods of computational fluid mechanics, however, offer the promise of obtaining underlying velocity fields with accuracy sufficient for the purposes of multidimensional transport models. This opens the prospect for calculation of spatial variations of particles, reactants, and products within a process tank. This would permit a realistic prediction of the influence of tank geometry on process performance. Basic approaches to transport modeling of process tanks are reviewed and applications to modeling of the activated sludge process are presented. It is proposed that multi-dimensional transport modeling, when coupled with full-scale and physical test work, can be used to conclusively determine geometric factors which determine tank performance.

An experimental study of the molecular mixing process in an axisymmetric laminar vortex ring

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.

Evolution of scalar spectra with the decay of turbulence in a stratified fluid

Temperature measurements taken in association with the velocity measurements described by Gargett, Osborn & Nasmyth (1984) are examined. With careful noise removal the temperature dissipation spectrum is fully resolved and χ, the dissipation rate of temperature-fluctuation variance, is determined directly. With directly measured values of χ and ε, the turbulent-kinetic-energy dissipation rate per unit mass, the observed temperature spectra are non-dimensionalized by Oboukov–Corrsin–Batchelor scaling. Shapes and levels of the resulting non-dimensional spectra are then examined as functions of the degree of isotropy (measured) in the underlying velocity field. Two limiting cases are identified: Class A, associated with isotropic velocity fields; and Class B, associated with velocity fields which are anisotropic (owing to buoyancy forces repressing vertical relative to horizontal dimensions of energy-containing ‘eddies’). The present observations suggest that the Corrsin–Oboukov–Batchelor theory does not provide a universal description of the spectrum of temperature fluctuations in water. Class A scalar spectra have neither subrange, an approach to a k−1 subrange, and a value of q ∼ 4 which is in rough agreement with most previous estimates. Previous oceanic and atmospheric measurements are re-examined in the light of the present results. It is suggested that these previous results are also affected by vertical scale limitation. Reasons underlying the discrepancies between theories and observations are discussed: these may be different in the two classes presented.