[en] Spectral element methods have previously been successfully applied to direct numerical simulation of turbulent flows with moderate geometrical complexity and low to moderate Reynolds numbers. A natural extension of application is to large eddy simulation of turbulent flows, although there has been little published work in this area. One of the obstacles to such application is the ability to deal successfully with turbulence modelling in the presence of solid walls in arbitrary locations. An appropriate tool with which to tackle the problem is dynamic estimation of turbulence model parameters, but while this has been successfully applied to simulation of turbulent wall-bounded flows, typically in the context of spectral and finite volume methods, there have been no published applications with spectral element methods. Here, we describe approaches based on element-level spectral filtering, couple these with the dynamic procedure, and apply the techniques to large eddy simulation of a prototype wall-bounded turbulent flow, the plane channel, using a mixing length-based eddy viscosity subgrid-scale model. The methods outlined here may be carried over without modification to more complex geometries

[en] A primitive-variable formulation for simulation of time-dependent incompressible flows in cylindrical coordinates is developed. Spectral elements are used to discretise the meridional semi-plane, coupled with Fourier expansions in azimuth. Unlike previous formulations where special distributions of nodal points have been used in the radial direction, the current work adopts standard Gauss-Lobatto-Legendre nodal-based expansions in both the radial and axial directions. Using a Galerkin projection of the symmetrised cylindrical Navier-Stokes equations, all geometric singularities are removed as a consequence of either the Fourier-mode dependence of axial boundary conditions or the shape of the weight function applied in the Galerkin projection. This observation implies that in a numerical implementation, geometrically singular terms can be naively treated by explicitly zeroing their contributions on the axis in integral expressions without recourse to special treatments such as l'Hopital's rule. Exponential convergence of the method both in the meridional semi-plane and in azimuth is demonstrated through application to a three-dimensional analytical solution of the Navier-Stokes equations in which flow crosses the axis

[en] Highlights: ► Study of effects of streamwise periodicity on turbulent heat transfer in pipe flow. ► Streamwise periodic length for convergence depends on the type of statistics and Pr. ► Explain the reasons for variation of thermal statistics in published literature. ► All statistics seem to converge with DNS carried out with a pipe length of 8πδ. - Abstract: We present results from direct numerical simulation of turbulent heat transfer in pipe flow at a bulk flow Reynolds number of 5000 and Prandtl numbers ranging from 0.025 to 2.0 in order to examine the effect of streamwise pipe length (πδ ≡ πD/2 ⩽ L ⩽ 12πδ) on the convergence of thermal turbulence statistics. Various lower and higher order thermal statistics such as mean temperature, rms of fluctuating temperature, turbulent heat fluxes, two-point auto and cross-correlations, skewness and flatness were computed and it is found that the value of L required for convergence of the statistics depends on the Prandtl number: larger Prandtl numbers requires comparatively shorter pipe length for convergence of most of the thermal statistics.

[en] Passive scalar transport involves complex interactions between advection and diffusion, where the global transport rate depends upon scalar diffusivity and the values of the (possibly large) set of parameters controlling the advective flow. Although computation of a single solution of the advection-diffusion equation (ADE) is simple, in general it is prohibitively expensive to compute the parametric variation of solutions over the full parameter space Q, even though this is crucial for, e.g. optimization, parameter estimation, and elucidating the global structure of transport. By decomposing the flows within Q so as to exploit symmetries, we derive a spectral method that solves the ADE over Q three orders of magnitude faster than other methods of similar accuracy. Solutions are expressed in terms of the exponentially decaying natural periodic patterns of the ADE, sometimes called 'strange eigenmodes'. We apply the method to the experimentally realisable rotated arc mixer chaotic flow, both to establish numerical properties and to calculate the fine-scale structure of the global solution space for transport in this chaotic flow. Over 10⁵ solutions within Q are resolved, and spatial pattern locking, a symmetry breaking transition to disordered spatial patterns, and fractally distributed optima in transport rate are observed. The method exhibits exponential convergence, and efficiency increases with resolution of Q