TY - JOUR

T1 - Dense velocity reconstruction from tomographic PTV with material derivatives

AU - Schneiders, Jan

AU - Scarano, Fulvio

PY - 2016

Y1 - 2016

N2 - A method is proposed to reconstruct the instantaneous velocity field from time-resolved volumetric particle tracking velocimetry (PTV, e.g., 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. The constraint to the measured temporal derivative of the PTV particle tracks improves the consistency of the reconstructed velocity field. The method is christened as pouring time into space, as it leverages temporal information to increase the spatial resolution of volumetric PTV measurements. This approach becomes relevant in cases where the spatial resolution is limited by the seeding concentration. The method solves an optimization problem to find the vorticity and velocity fields that minimize a cost function, which includes next to instantaneous velocity, also the velocity material derivative. The velocity and its material derivative are related through the vorticity transport equation, and the cost function is minimized using the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. The procedure is assessed numerically with a simulated PTV experiment in a turbulent boundary layer from a direct numerical simulation (DNS). The experimental validation considers a tomographic particle image velocimetry (PIV) experiment in a similar turbulent boundary layer and the additional case of a jet flow. The proposed technique (‘vortex-in-cell plus’, VIC+) is compared to tomographic PIV analysis (3D iterative cross-correlation), PTV interpolation methods (linear and adaptive Gaussian windowing) and to vortex-in-cell (VIC) interpolation without the material derivative. A visible increase in resolved details in the turbulent structures is obtained with the VIC+ approach, both in numerical simulations and experiments. This results in a more accurate determination of the turbulent stresses distribution in turbulent boundary layer investigations. Data from a jet experiment, where the vortex topology is retrieved with a small number of tracers indicate the potential utilization of VIC+ in low-concentration experiments as for instance occurring in large-scale volumetric PTV measurements.

AB - A method is proposed to reconstruct the instantaneous velocity field from time-resolved volumetric particle tracking velocimetry (PTV, e.g., 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. The constraint to the measured temporal derivative of the PTV particle tracks improves the consistency of the reconstructed velocity field. The method is christened as pouring time into space, as it leverages temporal information to increase the spatial resolution of volumetric PTV measurements. This approach becomes relevant in cases where the spatial resolution is limited by the seeding concentration. The method solves an optimization problem to find the vorticity and velocity fields that minimize a cost function, which includes next to instantaneous velocity, also the velocity material derivative. The velocity and its material derivative are related through the vorticity transport equation, and the cost function is minimized using the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. The procedure is assessed numerically with a simulated PTV experiment in a turbulent boundary layer from a direct numerical simulation (DNS). The experimental validation considers a tomographic particle image velocimetry (PIV) experiment in a similar turbulent boundary layer and the additional case of a jet flow. The proposed technique (‘vortex-in-cell plus’, VIC+) is compared to tomographic PIV analysis (3D iterative cross-correlation), PTV interpolation methods (linear and adaptive Gaussian windowing) and to vortex-in-cell (VIC) interpolation without the material derivative. A visible increase in resolved details in the turbulent structures is obtained with the VIC+ approach, both in numerical simulations and experiments. This results in a more accurate determination of the turbulent stresses distribution in turbulent boundary layer investigations. Data from a jet experiment, where the vortex topology is retrieved with a small number of tracers indicate the potential utilization of VIC+ in low-concentration experiments as for instance occurring in large-scale volumetric PTV measurements.

UR - http://resolver.tudelft.nl/uuid:f6c1d567-201b-46f9-bacf-275b1abf1055

U2 - 10.1007/s00348-016-2225-6

DO - 10.1007/s00348-016-2225-6

M3 - Article

SN - 0723-4864

VL - 57

JO - Experiments in Fluids: experimental methods and their applications to fluid flow

JF - Experiments in Fluids: experimental methods and their applications to fluid flow

M1 - 139

ER -