Modern discontinuous Galerkin methods for the simulation of transitional and turbulent flows in biomedical engineering: A comprehensive LES study of the FDA benchmark nozzle model

Abstract

This work uses high-order discontinuous Galerkin discretization techniques as a generic, parameter-free, and reliable tool to accurately predict transitional and turbulent flows through medical devices. Flows through medical devices are characterized by moderate Reynolds numbers and typically involve different flow regimes such as laminar, transitional, and turbulent flows. Previous studies for the FDA benchmark nozzle model revealed limitations of Reynolds-averaged Navier-Stokes turbulence models when applied to more complex flow scenarios. Recent works based on large-eddy simulation approaches indicate that these limitations can be overcome but also highlight potential limitations due to a high sensitivity with respect to numerical parameters. The novel methodology presented in this work is based on two key ingredients. Firstly, we use high-order discontinuous Galerkin methods for discretization in space yielding a discretization approach that is robust, accurate, and generic. The inherent dissipation properties of high-order discontinuous Galerkin discretizations render this approach well-suited for transitional and turbulent flow simulations. Secondly, a precursor simulation approach is applied in order to correctly predict the inflow boundary condition for the whole range of laminar, transitional, and turbulent flow regimes. This approach eliminates the need to fit parameters of the numerical solution approach. We investigate the whole range of Reynolds numbers as suggested by the FDA benchmark nozzle problem in order to critically assess the predictive capabilities of the solver. The results presented in this study are compared to experimental data obtained by particle image velocimetry demonstrating that the approach is capable of correctly predicting the flow for different flow regimes.

The effect of turbulence on transitional flow in theFDA's benchmark nozzle model using large‐eddy simulation

“…The use of inlet disturbances in this work supports the findings from previous studies 22,23,27 ; that adding artificial disturbances helps to stabilise numerical simulation, making it robust to time-step selection, and that mean characteristics are insensitive to these disturbances throughout the model, even in laminar regions. This is the first study to assess the effects of numerical inlet disturbances on turbulence statistics.…”

“…19 In numerical simulation the addition of inlet disturbances reduces sensitivities and stabilises jet breakdown location; this has been observed in the current and previous studies. 22,23,27 Clearly, disturbances bring about very different effects in the experiment and LES simulation. It is likely that the LES overpredicts turbulence values in regions that would otherwise be laminar if inlet disturbances were not applied.…”

“…Subsequently, scale resolving simulations were conducted using large-eddy simulation (LES) and direct numerical simulation (DNS) methodologies. [21][22][23][24][25][26][27] Studies which considered the transitional regime 21,23,24 used variants of LES or DNS, and more accurately matched PIV data. Delorme et al 24 adopted a hybrid LES-immersed boundary method and found that velocity profiles agreed well with PIV data at the presented locations, with numerical viscous shear stresses overestimated.…”

“…Furthermore, they omitted results in the dominant jet breakdown location, which is arguably the most important location in the transitional regime and will later be discussed at length. Fehn et al 23 conducted simulations using a high-order discontinuous Galerkin method (LES based) and found that their jet did not breakdown at all. The authors investigated further by independently increasing Reynolds number and introducing inlet disturbances, which they found helped match simulation breakdown location to PIV.…”

Efficacy of the FDA nozzle benchmark and the lattice Boltzmann method for the analysis of biomedical flows in transitional regime

“…The study of Fehn et al [7] is the only exhaustive work to date in which authors applied a high-order DG method to study all the Re th , and even studied additional Re th to explore the Re crit , i.e., the critical Reynolds number at which the flow would transition in the nozzle. Several others demonstrated different jet breakdown locations compared with experiments [1,20], and some focused on outcomes like the ever changing location of jet breakdown with increasing spatial resolutions [1].…”