Effect of Local Turbulent Structures on the Hot Jet in Transitional Flow

Turbulent parts localized in flow direction may arise in a pipe with transitional regime of the stable laminar Poiseuille flow. A key condition for occurrence of such structures is a pipe with rather long length relative to its diameter. Our paper presents numerical modelling of the hot air jet flowing from the long pipe into the cold open volume at Re=2426. The modelling was performed in OpenFOAM software on the basis of the large eddy simulation (LES) method. The WALE (Wall-adapting local eddy-viscosity) model was used for closure of Navier-Stokes equations on subgrid scales. We demonstrated that local turbulent structures have a weak effect on the hot jet at flowing into the cold open volume.

Resolvent-based estimation of turbulent channel flow using wall measurements

We employ a resolvent-based methodology to estimate velocity and pressure fluctuations within turbulent channel flows at friction Reynolds numbers of approximately 180, 550 and 1000 using measurements of shear stress and pressure at the walls, taken from direct numerical simulation (DNS) databases. Martini et al. (J. Fluid Mech., vol. 900, 2021, p. A2) showed that the resolvent-based estimator is optimal when the true space–time forcing statistics are utilised, thus providing an upper bound for the accuracy of any linear estimator. We use this framework to determine the flow structures that can be linearly estimated from wall measurements, and we characterise these structures and the estimation errors in both physical and wavenumber space. We also compare these results to those obtained using approximate forcing models – an eddy-viscosity model and white-noise forcing – and demonstrate the significant benefit of using true forcing statistics. All models lead to accurate results up to the buffer layer, but only using the true forcing statistics allows accurate estimation of large-scale logarithmic-layer structures, with significant correlation between the estimates and DNS results throughout the channel. The eddy-viscosity model displays an intermediate behaviour, which may be related to its ability to partially capture the forcing colour. Our results show that structures that leave a footprint on the channel walls can be accurately estimated using the linear resolvent-based methodology, and the presence of large-scale wall-attached structures enables accurate estimations through the logarithmic layer.

Unsteady Simulation of a Transonic Turbine Stage with Focus on Turbulence Prediction

The flow in a transonic turbine stage still poses a high challenge for the correct prediction of turbulence using an eddy viscosity model. Therefore, an unsteady RANS simulation with the k-ω SST model, based on a preceding study of turbulence inlet conditions, was performed to see if this can improve the quality of the flow and turbulence prediction of an experimentally investigated turbine flow. Unsteady Q3D results showed that none of the different turbulence boundary conditions could predict the free-stream turbulence level and the maximum values correctly. Luckily, the influence of the boundary conditions on the velocity field proved to be small. The qualitative prediction of the complex secondary flows is good, but there is lacking agreement in the prediction of turbulence generation and destruction.

An Accurate Model for Prediction of Turbulent Frictional Pressure Loss of Power-Law Fluids in Eccentric Geometries

Summary The effect of axial flow of power-law drilling fluids on frictional pressure loss under turbulent conditions in eccentric annuli is investigated. A numerical model is developed to simulate the flow of Newtonian and power-law fluids for eccentric annular geometries. A turbulent eddy-viscosity model based on the mixing-length approach is proposed, where a damping constant as a function of flow parameters is presented to account for the near-wall effects. Numerical results including the velocity profile, eddy viscosity, and friction factors are compared with various sets of experimental data for Newtonian and power-law fluids in concentric and eccentric annular configurations with diameter ratios of 0.2 to 0.8. The simulation results are also compared with a numerical study and two approximate models in the literature. The results of extensive simulation scenarios are used to obtain a novel correlation for estimation of the frictional pressure loss in eccentric annuli under turbulent conditions. Two new correlations are also presented to estimate the maximum axial velocity in the wide and narrow sections of eccentric geometries.

Errors Characterization of a RANS Simulation

This research uses data from direct numerical simulation (DNS) to characterize the different errors associated with a Reynolds-averaged Navier-Stokes (RANS) simulation. The statistics from DNS (Reynolds stresses, kinetic energy of turbulence, $\kappa$, and dissipation of turbulence, $\epsilon$), are fed into a RANS simulation with the same Reynolds number, geometry, and numerical code used for DNS. Three integral metrics error based on the mean velocity, the moduli of the mean rate-of-strain tensor, and the wall shear stress are used to characterize the errors associated with the RANS technique, with the RANS model, and with the linear eddy viscosity model (LEVM). For developed and perturbed flow, it is found that the mean velocity of the RANS simulations with the DNS statistics is almost the same as the mean velocity from DNS data. This procedure enables the study of the relative importance of the different Reynolds stresses in a particular flow. It is shown that for the bounded perturbed turbulent flows studied here, almost all the necessary effects of turbulence are contained in the Reynolds shear stress.