Preface to special issue on Direct numerical simulations of turbulent flows—Part II

Abstract

This issue and its preceding twin issue are devoted to the simulation of turbulent fluid flows. The focus is on numerical solutions of the governing Navier–Stokes equations, in which all temporal and spatial scales are resolved and which are known as direct numerical simulations (DNS) [8]. For a brief introduction to DNS, the reader is referred to the preface of the preceding issue [1], and references therein. The two issues contain a broad spectrum of topics which includes the study of sound generation mechanisms in combustion [4], the extraction of dominant spatiotemporal patterns and coherent structures in several canonical flows [12,14], the active control of turbulence in compressible fluid flows [9], the modeling of jets impinging on rough surfaces [10], the high-order, low-dissipation modeling of compressible multi-phase flows [2] and the accurate simulation of particleand bubble-laden fluid flows [3]. In what follows, we briefly summarize the three contributions to the second issue. Flows driven by pressure gradients and by temperature-induced buoyancy forces are referred to as mixed convection flows and are common in nature and in engineering, for example, in heat exchangers, cooling systems, and air-conditioned rooms and spaces, such as an airplane cabin. Wagner and Wetzel [12] discuss results of recent DNS of a pressure-driven flow in a differentially heated, vertical channel [13]. They demonstrate that differential heating induces a strong asymmetry in the turbulent flow, when compared to an isothermal fluid. Specifically near the cooled wall, turbulence is enhanced, whereas it is damped in the heated wall. This effect, which is quantified with a thorough analysis of the coherent structures in the flow, becomes more pronounced as the thermal driving is increased. Compressible, multiphase flows exhibit very complex dynamics acting in a wide range of scales, ranging from molecular (shock waves, fluid–fluid interfaces) up to the largest coherent structures in the flow, dictated by the geometry and the driving. On the one hand, the experimental measurement of such flows is very difficult and limited to gross features. On the other hand, their simulation is particularly challenging, as numerical diffusion (dissipation) must be introduced to stabilize the numerical solutions against unphysical oscillations. As a consequence, compressible multiphase flows remain poorly understood. Fleischmann et al. [2] present an overview of recent improvements in high-order, low-dissipation schemes for compressible multi-phase flows. Level sets are employed to model discontinuous phase-interface interactions. The very good accuracy of the implementation in the code ALPACA [5,6] is demonstrated for several paradigmatic examples of considerable difficulty. Overall, the paper provides an introduction to several advanced techniques, such as multiresolution data compression, and includes detailed elaborations of the treatment of floating-point induced disturbances and shock-stable flux functions. Finally, Froehlich et al. [3] present an overview of the immersed boundary method (IBM) applied to the computation of particleand bubble-laden flows. The IBM is an Euler–Lagrange approach which allows to directly impose interphase coupling conditions (such as no-slip/no-penetration) at the interface between two phases in an efficient, accurate and relatively simple way. Froehlich et al. [3] focus their description of the numerical procedure, which builds upon on the seminal work of Uhlmann [11], on the treatment of the nonslip interface condition, the computation of the hydrodynamic forces driving the particle motion, and the important topic of the treatment of light particles [7]. The authors show the capabilities of their approach by simulating flows of notable complexity, including particles in microfluidic systems, bubble dynamics in liquid metals with superimposed electro-magnetic fields and pattern formation in polymorph and poly-disperse sedimentary flows. Overall, the contributions in these two issues beautifully and compellingly show how DNS has become an extremely powerful tool for the detailed characterization of canonical turbulent flows, enabling enhanced reduced-order modeling, and also for accurate predictions of multiphase, reactive, and compressible fluid flows.