14th European Conference on Turbomachinery Fluid dynamics & Thermodynamics

Paper ID:

ETC2021-659

Main Topic:

Basic phenomena

Authors

Nikul Vadgama - University of Oxford
J. Connolly - University of Oxford
M. McGilvray - University of Oxford
D. R. H. Gillespie - Department of Engineering Science, University of Oxford, Oxford, OX1 3UJ, United Kingdom

Abstract

Discrete phase particle tracking is a useful tool in many fluid simulations to determine the flow of particulates.  Typically, unsteadiness in the flow results in variation in particle trajectories and these are captured in computational simulations using turbulent transport models.  Even in a one-way coupled simulation, the computation scales with the number of particles tracked, so it is desirable to robustly determine the minimum number of particles which must be injected provide a statistically representative outcome. As the variance in outcome based on particle size, speed, shape, initial location etc. is unlikely to be à priori known, the criteria at which no further particle injections are required should be easily determinable in the course of the simulation. The number of particles required is dependent on the requirements of the investigation.  These could be as simple as to find the bulk percentage of particles injected which stick within a flow geometry or the full spatial distribution of particle impacts. Whereas bulk measurements may be sufficient to validate blockage in a specific geometry, full surface distributions allow the validation of sophisticated particle tracking codes, and are also critical for incremental design studies. When injecting particles their number can be altered through increasing the spatial density of particles in each injection modelled, or in stochastic simulations by creating multiple samples which are co‑located. While there have been efforts to calculate uncertainty for spatially variable properties, there is no standard method to ensure the distribution of the measured property is properly converged (statistically stationary). In this paper the Hellinger distance is shown to be a suitable metric to compare deposition distributions. A test case of a 90-degree bend where stochastic effects are appreciable is used. The Hellinger distance is used to compare distributions resulting both from increased injection spatial densities, and by repeated injection at the identical spatial densities. It is shown that a minimum spatial particle injection density can be determined to acquire converged solutions of particle deposition distributions.  Sensibly this shown to be greater than the injection density required for the convergence of integral deposition fraction. For the test case used it was found that as few as ten repeats of sample injection with spatial separation of approximately three centre-to-centre particle diameters sufficient to achieve convergence. Based on these results a methodology for ensuring the results are converged in the most computationally and time efficient manner is proposed.







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