Zonal Embedded Grids for Numerical Simulations of Wall-Bounded Turbulent Flows

Wall-modeling is required to make large-eddy simulations of high-Reynolds number wall-bounded turbulent flows feasible in terms of computational cost. Here, an extension of the integral wall-model for large-eddy simulations (iWMLESs) for incompressible flows developed by Yang et al. [“Integral wall model for large eddy simulations of wall-bounded turbulent flows,” Phys. Fluids 27(2), 025112 (2015)] to compressible and isothermal flows is proposed and assessed. The iWMLES approach is analogous to the von Kármán-Pohlhausen integral method for laminar flows: the velocity profile is parameterized, and unknown coefficients are determined by matching boundary conditions obeying the integral boundary layer momentum equation. It allows non-equilibrium effects such as pressure gradient and convection to be included at a computing cost similar to analytical wall-models. To take into account density variations and temperature gradients, the temperature profile is also parameterized and the integral compressible boundary layer energy equation is considered. Parameterized profiles are based on the usual logarithmic wall functions with corrective terms to extend their range of validity. Instead of solving a set of differential equations as wall-models based on the thin boundary layer equation approach, a simple linear system is solved. The proposed wall-model is implemented in a finite-volume cell-centered structured grid solver and assessed on adiabatic and isothermal plane channel flows at several friction Reynolds and Mach numbers. For low Mach number cases, mean profiles, wall fluxes, and turbulent fluctuations are in agreement with those of Direct Numerical Simulation (DNS). For supersonic flows, the results are in good agreement with the DNS data, especially the mean velocity quantities and the wall friction, while standard analytical wall-models show their limits.

Data-driven wall modeling for turbulent separated flows

Generating inflow fields for scale-resolving simulations of turbulent flow is crucial for a wide range of applications and is an active area of research. In this thesis, a method for inflow generation employing a precursor turbulent channel flow simulation is proposed. A procedure for determining the parameters of the precursor simulation based on the properties of the inflow is given. To evaluate the performance of the method, results from a simulation of a flat-plate zero-pressure-gradient turbulent boundary layer are analysed. The adaption length is quantified in terms of the development of integral quantities and the statistical moments of the velocity field. The performance is also compared with that of a state-of-the-art rescaling method for the generation of inflow data. It is shown that both approaches result in adaption lengths of comparable sizes, which makes the proposed method an attractive alternative due to its conceptual simplicity and robustness.As part of the work on inflow generation, a Python package, eddylicious, was developed. The purpose of the package is to be a framework within which various generation methods can be implemented. The package is available online under an open-source license. An overview of the architecture and currently implemented functionality of the package is given in this thesis.Furthermore, the results of a preparatory study on large-eddy simulation of wall-bounded turbulent flows are discussed. Fully-developed turbulent channel flow is used as a model problem, and the general-purpose computational fluid dynamics solver OpenFOAM is employed. The accuracy of the results with respect to the resolution of the computational mesh is analysed. Several modelling approaches for the subgrid scale stresses are considered.

The numerical simulation of a flow through a duct requires an externally specified forcing that makes the fluid flow against viscous friction. To this end, it is customary to enforce a constant value for either the flow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct flow before and after a geometrical modification that induces a change of the viscous drag, both approaches lead to a change of the power input across the comparison. Similarly, when carrying out direct numerical simulation or large-eddy simulation of unsteady turbulent flows, the power input is not constant over time. Carrying out a simulation at constant power input (CPI) is thus a further physically sound option, that becomes particularly appealing in the context of flow control, where a comparison between control-on and control-off conditions has to be made. We describe how to carry out a CPI simulation, and start with defining a new power-related Reynolds number, whose velocity scale is the bulk flow that can be attained with a given pumping power in the laminar regime. Under the CPI condition, we derive a relation that is equivalent to the Fukagata–Iwamoto–Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of naturally including the required control power. The implementation of the CPI approach is then exemplified in the standard case of a plane turbulent channel flow, and then further applied to a flow control case, where a spanwise-oscillating wall is used for skin-friction drag reduction. For this low-Reynolds-number flow, using 90 % of the available power for the pumping system and the remaining 10 % for the control system is found to be the optimum share that yields the largest increase of the flow rate above the reference case where 100 % of the power goes to the pump.

Chapter Two - Direct numerical and large–eddy simulation of complex turbulent flows

Large-eddy simulation of turbulent channel flows with conservative IDO scheme

The purpose of the present paper is to study theoretically the stability and accuracy of dualtime-stepping methods for the advection-diffusionequation, in conjuction with high-order upwindbiased space-discretizations, and high-order backward-differences time-discretizations. These results are in particular analyzed for typical nondimensional time-steps encountered in the simulation of wall-bounded turbulent flows. We attempt to define optimal subiterative strategies (and dual-time-step choice), with respect to stability and accuracy requirements. Typical computational examples are presented.

This work focuses on the development of efficient computational tools for the simulation of turbulent multiphase polydispersed flows. In terms of methodologies we focus here on the use of Large Eddy Simulation (LES) and Quadrature-Based Methods of Moments (QBMM). In terms of applications the work is finalised, in order to be applied in the future, to particle production processes (precipitation and crystallisation in particular). An important part of the work concerns the study of the flow field in a Confined Impinging Jets Reactor (CIJR), frequently used in particle production processes. The first part is limited to the comparison and analysis of micro Particle Image Velocimetry (μPIV) experiments, carried out in a previous work, and Direct Numerical Simulation (DNS), carried out in this thesis. In particular the effects of boundary and operating conditions are studied and the numerical simulations are used to understand the experimental predictions and demonstrate the importance of unavoidable fluctuations in the experimental inlets. This represents a preparatory work for the LES modelling of the CIJR. Before investigating the accuracy of LES predictions for this particular application, the model and the implementation are studied in a more general context, represented by a well-known test case such as the periodic turbulent channel flow: the LES model implementation in TransAT, the code used in this work, is compared with DNS data and with predictions of other codes. LES simulations for the CIJR, provided with the proper boundary conditions obtained by the previous DNS/μPIV study, are then performed and compared with experiments, validating the model in a more realistic test case. Since particle precipitation and crystallization often result in complex interactions between particles and the continuous phase, in the second part of the work particular attention has been paid in the modelling of the momentum transfer and the resulting velocity of the particles (relative to the fluid). In particular the possibility of describing poly-disperse fluid-solid systems with QBMM together with LES and Equilibrium Eulerian Model (EEM) is assessed. The study is performed by comparing our predictions with DNS Lagrangian data in the turbulent channel flow previously described, seeded with particles corresponding to a realistic Particle Size Distribution (PSD). The last part of the work deals with particle collisions, extending QBMM to the investigation of non-equilibrium flows governed by the Boltzmann Equation with a hard-sphere collision kernel. The evolution of the particle velocity distribution is predicted and compared with other methods for kinetic equations such as Lattice Boltzmann Method (LBM), Discrete Velocity Method (DVM) and Grad's Moment Method (GM). The overall results of this thesis can be extended to a broad range of other applications of single-phase, dispersed multiphase and non-equilibrium flows

The near-wall, subgrid-scale (SGS) model [Chung and Pullin, Large-eddy simulation and wall-modeling of turbulent channel flow, J. Fluid Mech. 631, 281--309 (2009)] is used to perform large-eddy simulations (LES) of the incompressible developing, smooth-wall, flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. This is then used to study several aspects of zero- and adverse-pressure gradient turbulent boundary layers. First, LES of the zero-pressure gradient turbulent boundary layer are performed at Reynolds numbers Reθ based on the free-stream velocity and the momentum thickness in the range Reθ = 103 - 1012. Results include the inverse skin friction coefficient, √2/Cf, velocity profiles, the shape factor H, the Karman constant, and the Coles wake factor as functions of Reθ. Comparisons with some direct numerical simulation (DNS) and experiment are made, including turbulent intensity data from atmospheric-layer measurements at Reθ = O(106. At extremely large Reθ, the empirical Coles-Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot of itself probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that the LES is suggestive of the asymptotic, infinite Reynolds-number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum Reθ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger Reθ could be achieved with quad- or higher-precision arithmetic. Second, the time series velocity signals obtained from LES within the logarithmic region of the zero-pressure gradient turbulent boundary layer are used in combination with an empirical, predictive inner--outer wall model [Marusic et al., Predictive model for wall-bounded turbulent flow, Science 329, 193 (2010)] to calculate the statistics of the fluctuating streamwise velocity in the inner region of the zero-pressure gradient turbulent boundary layer. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers Reτ based on the friction velocity and the boundary layer thickness, Reτ =7,300, 13,600 and 19,000. LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers Reτ =62,000, 100,000 and 200,000 that lie within a gap in log(Reτ) space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a log-like increase in the near-wall peak of the streamwise turbulence intensities with Reτ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows. Finally, we apply the wall model to LES of a turbulent boundary layer subject to an adverse pressure gradient. Computed statistics are found to be consistent with recent experiments and some Reynolds number similarity is observed over a range of two orders of magnitude.

Wall-resolved Large Eddy Simulation in grid-free 5 × 5 rod bundle of MATiS-H experiment

We describe the possibilities of a numerical method based on quasi-gas dynamic (QGD) equations for the numerical simulation of a turbulent boundary layer. A subsonic Couette flow in nitrogen is used as an example, with dynamic Reynolds numbers of 153 and 198. The QGD system differs from the system of Navier---Stokes equations by additional nonlinear dissipative terms with a small parameter as a coefficient. In turbulent flow simulation, these terms describe small-scale effects that are not resolved on the grid. Comparison of our results (velocity profiles and mean-square velocity pulsations) with direct numerical simulation (DNS) results and benchmark experiments show that the QGD algorithm adequately describes the viscous and the logarithmic layers near the wall. Compared with high-accuracy DNS methods, the QGD algorithm permits using a relatively large spatial grid increment in the interior part of the viscous sublayer. Thus, the total number of grid points in the turbulent boundary layer may be relatively small. Unlike various versions of the large-eddy simulation (LES) method, the QGD algorithm does not require introduction of near-wall functions, because the additional terms vanish near the wall. For small Reynolds numbers, the QGD algorithm describes laminar Couette flow.

We compare the space-time correlations calculated from direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent channel flows. It is found from the comparisons that the LES with an eddy-viscosity sub-grid scale (SGS) model over-predicts the space-time correlations than the DNS. The overpredictions are further quantified by the integral scales of directional correlations and convection velocities. A physical argument for the overprediction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions. This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows. It suggests that enstrophy is crucial to the LES prediction of space-time correlations. The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.

The direct numerical simulation (DNS) offers useful information about the understanding and modeling of turbulent flow. Few direct numerical simulations of wall-bounded compressible turbulent flows have been performed however. The objective of our study is to construct the DNS algorithm which can simulate the compressible turbulent flow between adiabatic and isothermal walls. The flow is selected since it is the simplest turbulent flow with an adiabatic wall, and therefore it is ideal for the modeling of compressible turbulent flow near the adiabatic wall. From the applicability and efficiency, we construct the new DNS algorithm based on the B-spline collocation method in the wall-normal direction. The validity and efficiency of the DNS algorithm are confirmed by comparing our results with those of an existing DNS in the compressible turbulent flow between isothermal walls. Then the DNS of compressible turbulent flow between the adiabatic and isothermal walls exhibits the applicability and usefulness of the algorithm.

Data-parallel DNS of tubrulent flow

Direct numerical simulations of turbulent free shear flows have been shown to be in generally good agreement with self.-similarity theory and laboratory data. The temporal development of a number of important statistical quantities has been shown to have the proper behavior, and the spatial evolution of the flow field is consistent with predictions. The main potential difficulties with the application of these methods are the inadequate initialization procedure and statistical scatter in the data. However, we do not see these problems as being insurmountable. The evolution of turbulence in a free shear flow is governed by a complex balance among the following mechanisms: generation of energy from the mean flow, turbulent diffusion by the turbulence, intercomponent transfer of energy, and dissipation. Our statistical results indicate that the direct numerical simulations are indeed faithfully representing these physical processes. We are quite optimistic about the future usefulness of direct numerical simulations as a scientific research tool.