Spatial reconstruction of steady scalar sources from remote measurements in turbulent flow

Identifying the source of passive scalar transported in a turbulent environment from remote measurements is an ill-posed problem due to the irreversibility of diffusive processes. A significant difficulty of the source reconstruction is due to different potential source locations generating very highly correlated signals at the sensor. A variational algorithm is formulated, which utilizes high-fidelity simulations to reconstruct the spatial distribution of the source. A cost functional is defined based on the difference between the true measurements and their prediction from the simulations with the estimated source. Using forward–adjoint looping, the gradient of the cost functional with respect to the source distribution is evaluated, and the estimate of the source is updated. The adjoint-variational approach naturally accommodates measurements from multiple sensors, with essentially the same computational cost. The algorithm is evaluated for scalar dispersion in turbulent channel flow. When a single sensor is placed directly downstream of the source, the reconstruction is accurate in the cross-stream directions and is elongated in the streamwise direction. The estimated source, however, can reproduce the measurements and the scalar plume downstream of the sensor location. In the channel centre and log layer, the scalar fields are dominated by dispersion, and therefore the reconstruction is better than in the near-wall regions, where the scalar fields are dominated by diffusion. When a sensor is placed near the wall, the accuracy of the source recovery deteriorates due to diffusive effects. By using more sensors that span the plume cross-section, improvement of performance can be demonstrated despite an enlarged domain of dependence.

Passive scalar dispersion in the near wake of a multi-scale array of rectangular cylinders

The near wakes of flows past single- and multi-scale arrays of bars are studied by means of planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV). The aim of this research is to better understand dispersion of passive scalar downstream of the multi-scale turbulence generator. In particular, the focus is on plausible manifestations of the space-scale unfolding (SSU) mechanism, which is often considered in the literature as the reason for the enhancement of the turbulent scalar flux in flows past fractal grids (i.e. specific multi-scale turbulence generators). The analysis of qualitative and quantitative PLIF results, as well as the simultaneously acquired PIV results, confirms the appearance of a physical scenario resembling the SSU mechanism. Unlike the anticipation of the literature, however, this scenario applies to some extent also to the flow past the single-scale obstacle. Application of a triple decomposition technique (which splits the acquired fields into their means, a number of coherent fluctuations and their stochastic parts) and a conditional-averaging technique reveals that the SSU mechanism is active in the vicinity of an intersection point between two adjacent wakes and is driven almost exclusively by coherent fluctuations associated with the larger of the intersecting wakes. This suggests that the SSU mechanism is related to the coherent fluctuations embedded in the flow rather than to the fine-scale turbulence and its underlying integral length scale, as proposed in previous works.

Mixing-scale dependent dispersion for transport in heterogeneous flows

Dispersion quantifies the impact of subscale velocity fluctuations on the effective movement of particles and the evolution of scalar distributions in heterogeneous flows. Which fluctuation scales are represented by dispersion, and the very meaning of dispersion, depends on the definition of the subscale, or the corresponding coarse-graining scale. We study here the dispersion effect due to velocity fluctuations that are sampled on the homogenization scale of the scalar distribution. This homogenization scale is identified with the mixing scale, the characteristic length below which the scalar is well mixed. It evolves in time as a result of local-scale dispersion and the deformation of material fluid elements in the heterogeneous flow. The fluctuation scales below the mixing scale are equally accessible to all scalar particles, and thus contribute to enhanced scalar dispersion and mixing. We focus here on transport in steady spatially heterogeneous flow fields such as porous media flows. The dispersion effect is measured by mixing-scale dependent dispersion coefficients, which are defined through a filtering operation based on the evolving mixing scale. This renders the coarse-grained velocity as a function of time, which evolves as velocity fluctuation scales are assimilated by the expanding scalar. We study the behaviour of the mixing-scale dependent dispersion coefficients for transport in a random shear flow and in heterogeneous porous media. Using a stochastic modelling framework, we derive explicit expressions for their time behaviour. The dispersion coefficients evolve as the mixing scale scans through the pertinent velocity fluctuation scales, which reflects the fundamental role of the interaction of scalar and velocity fluctuation scales in solute mixing and dispersion.