Artur Tyliszczak

A high-order compact difference algorithm for half-staggered grids for laminar and turbulent incompressible flows

Abstract The paper presents a novel, efficient and accurate algorithm for laminar and turbulent flow simulations. The spatial discretisation is performed with help of the compact difference schemes (up to 10th order) for collocated and half-staggered grid arrangements. The time integration is performed by a predictor–corrector approach combined with the projection method for pressure–velocity coupling. At this stage a low order discretisation is introduced which considerably decreases the computational costs. It is demonstrated that such approach does not deteriorate the solution accuracy significantly. Following Boersma B.J. [13] the interpolation formulas developed for staggered uniform meshes are used also in the computations with a non-uniform strongly varying nodes distribution. In the proposed formulation of the projection method such interpolation is performed twice. It is shown that it acts implicitly as a high-order low pass filter and therefore the resulting algorithm is very robust. Its accuracy is first demonstrated based on simple 2D and 3D problems: an inviscid vortex advection, a decay of Taylor–Green vortices, a modified lid-driven cavity flow and a dipole–wall interaction. In periodic flow problems (the first two cases) the solution accuracy exhibits the 10th order behaviour, in the latter cases the 3rd and the 4th order is obtained. Robustness of the proposed method in the computations of turbulent flows is demonstrated for two classical cases: a periodic channel with Re τ = 395 and Re τ = 590 and a round jet with Re = 21 000 . The solutions are obtained without any turbulence model and also without any explicit techniques aiming to stabilise the solution. The results are in a very good agreement with literature DNS and LES data, both the mean and r.m.s. values are predicted correctly.

A new approach to sub-grid surface tension for LES of two-phase flows

In two-phase flow, the presence of inter-phasal surface - the interface - causes additional terms to appear in LES formulation. Those terms were ignored in contemporary works, for the lack of model and because the authors expected them to be of negligible influence. However, it has been recently shown by a priori DNS simulations that the negligibility assumption can be challenged. In the present work, a model for one of the sub-grid two-phase specific terms is proposed, using deconvolution of the velocity field and advection of the interface using that field. Using the model, the term can be included into LES. A brief presentation of the model is followed by numerical tests that assess the models performance by comparison with a priori DNS results.

LES modeling of converging-diverging turbulent channel flow

The paper presents the results of the application of large-eddy simulation (LES) to turbulent channel flow with a varying pressure gradient obtained by an appropriately specified shape of one of the walls. The main objective of the paper is to assess various subgrid scale (SGS) models implemented in two different codes as well as to assess the sensitivity of the predictive accuracy to grid resolution. Additionally, the role of SGS viscosity, controlled by a constant parameter of the SGS model, was investigated. The simulations were performed with inlet conditions corresponding to two Reynolds numbers: and . The consistency and the accuracy of simulations are evaluated using direct numerical simulation (DNS) results. It is demonstrated that all SGS models require a comparable minimum grid refinement in order to capture accurately the recirculation region. Such a test case with a reversal flow, where the turbulence transport is dictated by the dynamics of the large-scale eddies, is well suited to demonstrat...

Quality of LES Predictions of Isothermal and Hot Round Jet

The paper presents results of LES computations performed for isothermal and non-isothermal variable density jets using high order numerical code. According to the experimental data and linear stability theory the range of the density ratios between jet and the ambient fluids considered in this work encloses the regimes of absolute and convective type of instability. Much attention is paid to the quality of the solutions depending on the mesh resolution and turbulence intensity imposed at the inlet velocity profile. The differences between the solutions obtained using different (advective/conservative) form of the Navier–Stokes equations are also mentioned.

Self-sustained oscillations in a homogeneous-density round jet

The paper is devoted to a new phenomenon of self-sustained oscillations triggered in a round free homogeneous-density jet. It was shown by the experimental investigations supported by the numerical approach based on extensive-Large Eddy Simulations studies that such a self-sustained regime can be established in a homogeneous-density jet, provided that the boundary layer at the nozzle exit is sufficiently thin and the perturbation level sufficiently low. The growth rate of the naturally amplified unstable modes is high enough to induce backflow leading to self-excited oscillations.

Controlled mixing enhancement in turbulent rectangular jets responding to periodically forced inflow conditions

We present numerical studies of active flow control applied to jet flow. We focus on rectangular jets, which are more unstable than their circular counterparts. The higher level of instability is expressed mainly by an increased intensity of mixing of the main flow with its surroundings. We analyse jets with aspect ratio Ar = 1, Ar = 2 and Ar = 3 at Re = 10,000. It is shown that the application of control with a suitable excitation (forcing) at the jet nozzle can amplify the mixing and qualitatively alter the character of the flow. This can result in an increased spreading rate of the jet or even splitting into nearly separate streams. The excitations studied are obtained from a superposition of axial and flapping forcing terms. We consider the effect of varying parameters such as the frequency of the excitations and phase shift between forcing components. The amplitude of the forcing is 10% of the inlet centreline jet velocity and the forcing frequencies correspond to Strouhal numbers in a range St = 0.3–0.7. It is shown that qualitatively different flow regimes and a rich variety of possible flow behaviours can be achieved simply by changing aspect ratio and forcing parameters. The numerical results are obtained applying large eddy simulation in combination with a high-order compact difference code for incompressible flows. The solutions are validated based on experimental data from literature for non-excited jets for Ar = 1 at Re = 1.84 × 105 and Ar = 2 at Re = 1.28 × 105. Both the mean velocities as well as their fluctuations are predicted with good accuracy.

Multi-armed jets: A subset of the blooming jets

This study focuses on excited circular jets obtained through axial and helical excitations superimposed on an inlet velocity profile. Various forcing frequency ratios (axial to helical) were analysed in the range of 1.6 ≤ fa/fh ≤ 3.2, with occurrence of bifurcating, trifurcating, and blooming jets reported in the literature. Analytical investigations of a spatio-temporal behaviour of forcing show that, apart from the above mentioned jets observed for particular frequency ratios, different types of multi-armed jets are likely to occur. This was reflected by direct numerical simulation performed in the paper. The simulations showed the existence of very strong and noticeable splitting of the jet into a fivefold jet and weaker splitting into 12- and 13-armed jets.

Projection method for high-order compact schemes for low Mach number flows in enclosures

Purpose – Variable density flows play an important role in many technological devices and natural phenomena. The purpose of this paper is to develop a robust and accurate method for low Mach number flows with large density and temperature variations. Design/methodology/approach – Low Mach number approximation approach is used in the paper combined with a predictor-corrector method and accurate compact scheme of fourth and sixth order. A novel algorithm is formulated for the projection method in which the boundary conditions for the pressure are implemented in such a way that the continuity equation is fulfilled everywhere in the computational domain, including the boundary nodes. Findings – It is shown that proposed implementation of the boundary conditions considerably improves a solution accuracy. Assessment of the accuracy was performed based on the constant density Burggraf flow and for two benchmark cases for the natural convection problems: steady flow in a square cavity and unsteady flow in a tall ...

LES/CMC predictions of spark ignition probability in a liquid fuelled swirl combustor

The Large Eddy Simulation / Conditional Moment Closure approach with closures for the spray terms appearing in the CMC equation and for the mixture fraction sub-grid variance has been used to predict ignition probability, Pign, for a swirling spray ame for which relevant experimental data are available. The localised spark was modelled as a small region where the conditionally averaged reactive scalars were kept constant for a short time. For each of 20 locations across the ow, Pign was estimated by launching 16 separate simulations from di erent coldow realisations and monitoring the ame evolution. The predicted large variability in ignition behaviour, the overall time for ame expansion, and the spatial distributions of Pign agree qualitatively well with the experiment. The failure of a ame kernel to grow is traced to high scalar dissipations in the spark neighbourhood, which in turn depends on the mixture fraction sub-grid variance model, showing that the spray a ects both quantities and that the corresponding models need further validation.

Immersed boundary method combined with a high order compact scheme on half-staggered meshes

This paper presents the results of computations of incompressible flows performed with a high-order compact scheme and the immersed boundary method. The solution algorithm is based on the projection method implemented using the half-staggered grid arrangement in which the velocity components are stored in the same locations while the pressure nodes are shifted half a cell size. The time discretization is performed using the predictor-corrector method in which the forcing terms used in the immersed boundary method acts in both steps. The solution algorithm is verified based on 2D flow problems (flow in a lid-driven skewed cavity, flow over a backward facing step) and turns out to be very accurate on computational meshes comparable with ones used in the classical approaches, i.e. not based on the immersed boundary method.