Dimitris Drikakis

BIFURCATION PHENOMENA IN INCOMPRESSIBLE SUDDEN EXPANSION FLOWS

A numerical study of laminar incompressible flows in symmetric plane sudden expansions was carried out. Computations were performed for various Reynolds number and expansion ratios. The results revealed that the flow remains symmetric up to a certain Reynolds number depending on the expansion ratio, while asymmetries appear at higher Reynolds numbers. The computations indicated that the critical Reynolds number of the symmetry‐breaking bifurcation reduces when increasing the expansion ratio while the flow regains symmetry downstream of an initial channel length. The flow asymmetries were verified by comparing several discretization schemes up to fourth order of accuracy as well as various iterative solvers.

Advances in turbulent flow computations using high-resolution methods

Abstract The paper reviews research activity in connection with the use of high-resolution methods in turbulent flow computations. High-resolution methods have proven to successfully compute a number of turbulent flows without need to resort to an explicit turbulence model. Here, we review the basic properties of these methods, present evidence from the successful implementation of these methods in turbulent flows, and discuss theoretical arguments and recent research aiming at justifying their use as an implicit turbulence model. Further, we discuss numerical issues that still need to be addressed. These include the relation of the dissipation and dispersion properties with turbulence properties such as turbulence anisotropy, as well as further validation of the methods in under-resolved simulations of near-wall turbulent attached and separated flows.

Simulation of transition and turbulence decay in the Taylor–Green vortex

Conventional large-eddy simulation (LES) and monotone integrated LES (MILES) are tested in emulating the dynamics of transition to turbulence in the Taylor–Green vortex (TGV). A variety of subgrid scale (SGS) models and high-resolution numerical methods are implemented in the framework of both incompressible and compressible fluid flow equations. Comparisons of the evolution of characteristic TGV integral measures are made with previously reported and new direct numerical simulation (DNS) data. The computations demonstrate that the convective numerical diffusion effects in the MILES methods can consistently capture the physics of flow transition and turbulence decay without resorting to an explicit SGS model, while providing accurate prediction of established theoretical findings for the kinetic energy dissipation, energy spectra, enstrophy and kinetic energy decay. All approaches tested provided fairly robust computational frameworks.

Large eddy simulation using high-resolution and high-order methods

Restrictions on computing power make direct numerical simulation too expensive for complex flows; thus, the development of accurate large eddy simulation (LES) methods, which are industrially applicable and efficient, is required. This paper reviews recent findings about the leading order dissipation rate associated with high-resolution methods and improvements to the standard schemes for use in highly turbulent flows. Results from implicit LES are presented for a broad range of flows and numerical schemes, ranging from the second-order monotone upstream-centered schemes for conservation laws to very high-order (up to ninth-order) weighted essentially non-oscillatory schemes.

Non-Newtonian flow instability in a channel with a sudden expansion

Abstract The paper presents a numerical investigation of instabilities occurring in non-Newtonian flows through a sudden expansion. Three non-Newtonian models, used in the literature for simulating the rheological behaviour of blood, are employed, namely the Casson, Power-Law, and Quemada models. The computations reveal that similar to Newtonian flow through a suddenly expanded channel, an instability also occurs in non-Newtonian flows. The instability is manifested by a symmetry breaking of the flow separation. The onset of the instability depends on the specific parameters involved in each model’s constitutive equation. The investigation encompasses a parametric study for each model, specifically the critical values at which transition from stable to unstable flow occurs. Due to the fact that for each of the Casson and Quemada models, two characteristic flow parameters exist, the relation between the critical values for each of these parameters is also examined.

On the implicit large eddy simulations of homogeneous decaying turbulence

Simulations of homogeneous decaying turbulence (HDT) in a periodic cube have been used to examine in a detailed and quantitative manner the behaviour of high-resolution and high-order methods in implicit large eddy simulation. Computations have been conducted at grid resolutions from 323 to 2563 for seven different high-resolution methods ranging from second-order to ninth-order spatial accuracy. The growth of the large scales, and dissipation of kinetic energy is captured well at resolutions greater than 323, or when using numerical methods of higher than third-order accuracy. Velocity increment probability distribution functions (PDFs) match experimental results very well for MUSCL methods, whereas WENO methods have lower intermittency. All pressure PDFs are essentially Gaussian, indicating a partial decoupling of pressure and vorticity fields. The kinetic energy spectra and effective numerical filter show that all schemes are too dissipative at high wave numbers. Evaluating the numerical viscosity as a spectral eddy viscosity shows good qualitative agreement with theory, however if the effective cut-off wave number is chosen above kmax/2 then dissipation is higher than the theoretical solution. The fifth and higher-order methods give results approximately equivalent to the lower order methods at double the grid resolution, making them computationally more efficient.

The influence of initial conditions on turbulent mixing due to Richtmyer-Meshkov instability

This paper investigates the influence of different three-dimensional multi-mode initial conditions on the rate of growth of a mixing layer initiated via a Richtmyer-Meshkov instability through a series of well-controlled numerical experiments. Results are presented for large-eddy simulation of narrowband and broadband perturbations at grid resolutions up to 3 x 10 9 points using two completely different numerical methods, and comparisons are made with theory and experiment. It is shown that the mixing-layer growth is strongly dependent on initial conditions, the narrowband case giving a power-law exponent θ ≈ 0.26 at low Atwood and θ ≈ 0.3 at high Atwood numbers. The broadband case uses a perturbation power spectrum of the form P(k) ∝ k -2 with a proposed theoretical growth rate of θ = 2/3 . The numerical results confirm this; however, they highlight the necessity of a very fine grid to capture an appropriately broad range of initial scales. In addition, an analysis of the kinetic energy decay rates, fluctuating kinetic energy spectra, plane-averaged volume fraction profiles and mixing parameters is presented for each case.

WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on various types of grids. Schemes of up to fifth order of spatial accuracy are considered.

Transverse jet injection into a supersonic turbulent cross-flow

Jet injection into a supersonic cross-flow is a challenging fluid dynamics problem in the field of aerospace engineering which has applications as part of a rocket thrust vector control system for noise control in cavities and fuel injection in scramjet combustion chambers. Several experimental and theoretical/numerical works have been conducted to explore this flow; however, there is a dearth of literature detailing the instantaneous flow which is vital to improve the efficiency of the mixing of fluids. In this paper, a sonic jet in a Mach 1.6 free-stream is studied using a finite volume Godunov type implicit large eddy simulations technique, which employs fifth-order accurate MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) scheme with modified variable extrapolation and a three-stage second-order strong-stability-preserving Runge–Kutta scheme for temporal advancement. A digital filter based turbulent inflow data generation method is implemented in order to capture the physics of the sup...

Hybrid upwind methods for the simulation of unsteady shock-wave diffraction over a cylinder

Abstract Assessment of three hybrid-upwind methods in unsteady shock-wave diffraction over a cylinder is presented. The study includes two hybrid Flux Vector Splitting (FVS) methods and a hybrid Riemann solver. The hybrid FVS schemes are constructed by a combination of flux vector splitting and second-order artificial dissipation. The hybrid FVS-Riemann solver is constructed by the combination of a characteristic flux averaging method and a FVS scheme. The above schemes are implemented in conjunction with an implicit unfactored method. Computations are performed for unsteady shock diffraction over a cylinder and comparisons are presented with other numerical and experimental results from literature, including recent unstructured adaptive-grid computations. Emphasis is given on the accurate prediction of the unsteady pressure loads on the cylinder surface since this is of interest in engineering applications related to explosions and fluid-structure interaction.