Implicit large eddy simulation of weakly-compressible turbulent channel flow

This paper concerns the accuracy of several high-resolution and high-order finite volume schemes in Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow. The main objective is to investigate the properties of numerical schemes, originally designed for compressible flows, in low Mach compressible, near-wall turbulent flows. Variants of the Monotone Upstream-centred Scheme for Conservation Laws and Weighted Essentially Non-Oscillatory schemes for orders of accuracy ranging from second to ninth order, as well as with and without low Mach corrections, have been investigated. The performance of the schemes has been assessed against incompressible Direct Numerical Simulations. Detailed comparisons of the velocity profiles, turbulent shear stresses and higher-order turbulent statistics reveal that the low Mach correction can significantly reduce the numerical dissipation of the methods in low Mach boundary layer flows. The effects of the low Mach correction have more profound impact on second and third-order schemes, but they also improve the accuracy of fifth order schemes. The ninth-order Weighted Essentially Non-Oscillatory scheme is the least dissipative scheme and it is shown that the implementation of the low Mach correction in conjunction with this scheme has a significant anti-dissipative effect that adversely affects the accuracy. Finally, the computational cost required for obtaining the improved accuracy using increasingly higher order schemes is also discussed

Near-wall behaviour of implicit large eddy simulations

This paper investigates the accuracy of implicit large eddy simulations (ILES) in compressible turbulent boundary layers (TBL). ILES are conducted in conjunction with Monotonic Upstream-Centred Scheme for Conservation Laws (MUSCL) and Weighted Essentially Non-Oscillatory (WENO), ranging from 2nd to 9th-order. The excess artificial dissipation occurring at low Mach numbers is counter-balanced by using low Mach corrections. The study concludes that high-order ILES provide accurate predictions of TBL even on relatively coarse grids

On the propagation and multiple reflections of a blast wave travelling through a dusty gas in a closed box

This paper concerns the propagation of shock waves in an enclosure filled with dusty gas. The main motivation for this problem is to probe the effect on such dynamics of solid particles dispersed in the fluid medium. This subject, which has attracted so much attention over recent years given its important implications in the study of the structural stability of systems exposed to high-energy internal detonations, is approached here in the framework of a hybrid numerical two-way coupled Eulerian-Lagrangian methodology. In particular, insights are sought by considering a relatively simple archetypal setting corresponding to a shock wave originating from a small spherical region initialized on the basis of available analytic solutions. The response of the system is explored numerically with respect to several parameters, including the blast intensity (via the related value of the initial shock Mach number), the solid mass fraction (mass load), and the particle size (Stokes number). Results are presented in terms of pressure-load diagrams. Beyond practical applications, it is shown that a kaleidoscope of fascinating patterns is produced by the “triadic” relationships among multiple shock reflections events and particle-fluid and particle-wall interaction dynamics. These would be of great interest to researchers and scientists interested in fundamental problems relating to the general theory of pattern formation in complex nonlinear multiphase systems

Analysis of transition for a flow in a channel via reduced basis methods

The study of the flow mechanisms leading to transition in a planar channel flow is investigated by means of a reduced basis method known as Dynamic Mode Decomposition (DMD). The problem of identification of the most relevant DMD modes is addressed in terms of the ability to (i) provide a fairly accurate reconstruction of the flow field, and (ii) match the most relevant flow structures at the beginning of the transition region. A comparative study between a natural method of selection based on the energetic content of the modes and a new one based on the temporal dynamics of the modes is here presented

An LES investigation of the 2D Tollmien-Schlichting wave instability in channel flow

Classical linear hydrodynamic stability analysis predicts the existence of an unstable 2D ‘Tollmien-Schlichting’ (T-S) wave, which may be excited in parallel boundary layer flows by mechanisms of receptivity. Of particular interest is the evolution of these disturbances beginning with the linear growth phase governed by the Orr-Sommerfeld equation, subsequent non-linearity with the development of 3D flow structures and the breakdown to turbulent flow. Understanding the mechanisms by which these unstable waves derive energy from the mean flow has significance with regard to the aim of maintaining laminar boundary layer flow and reducing the drag generated by aerodynamic surfaces. In this paper we solve the Orr-Sommerfeld eigenvalue problem numerically via a spectral method in MATLAB, approximating the solution via a truncated series of Lagrange polynomials. The stream function of the single unstable mode was found from the spectral solution from which the streamwise and wall-normal components of the perturbation’s velocity were derived

Physical insight into a Mach 7.2 compression corner flow

High-order implicit Large Eddy Simulations were conducted to study shock-boundary layer interaction around a 33° compression corner at Mach 7.2 and Reynolds number of Reθ = 3,500 based on the momentum thickness. A grid-convergence study was performed to reduce the computational uncertainty and the results were compared with experiments and theoretical predictions. Furthermore, the turbulent flow properties were analysed with respect to the Reynolds normal stress, skewness and flatness, and conclusions were drawn regarding the shock boundary layer interaction behavior

How a jet flow interacting with a streamwise/spanwise corrugated surface causes an increase in turbulence kinetic energy

Rapid-distortion theory (RDT) uses linear analysis to study the interaction of turbulence with solid surfaces. It applies whenever the turbulence intensity is small and the length (or time) scale over which the interaction takes place is short compared to the length (or time) scale over which the turbulent eddies evolve. The basic theory can be used to model the sound radiated by a turbulent flow interacting with a leading or trailing edge embedded in the flow (Goldstein et al. JFM, vol. 824,pp.477-512, 2017). One way of reducing of possibly reducing the sound is to change the spatial morphology of the surface of the flat plate. While there are several ways one can achieve this, in this study we use CFD simulations to show what happens when to the local turbulence kinetic energy when the surface is morphed with streamwise or spanwise oscillations. In Figure 1 we show that a typical example of the surface meshed using Pointwise and solved in STAR CCM+. The acoustic Mach number of the jet flow is Ma=UJ/c∞= 0.9and the temperature ratio, TR=TJ/T∞= 1.0. The streamwise surface corrugations effectively reduce the vertical stand-off distance between the jet and the discontinuity. This has the effect of increasing the turbulence kinetic energy by almost a factor of 2. Assuming that the low-frequency structure of the propagation of sound (determined by the Wiener-Hopf technique) after interacting with a wavy surface is similar to the flat plate solution, the sound will be proportional to the turbulence kinetic energy

Direct numerical simulation of supersonic flow and acoustics over a compression ramp

We present direct numerical simulations of the shock wave boundary layer interaction (SBLI) at Mach number 2.9 over a 24° ramp. We study both the numerical accuracy and flow physics. Two classes of spatial reconstruction schemes are employed: the monotonic upstream-centered scheme for conservation laws and the Weighted Essentially Non-Oscillatory (WENO) scheme, of accuracy ranging from 2nd- to 11th-order. Using the canonical Taylor–Green vortex test-case, a simple and computationally inexpensive rescaling of the candidate stencil values—within the context of the high-order WENO scheme—is proposed for reducing the numerical dissipation, particularly in under-resolved simulations. For the compression ramp case, higher-order schemes are shown to capture the size of the SBLI separation zone more accurately, a consequence of resolving much finer turbulence structures. For second- and fifth-order schemes, the energy of the unresolved small scale turbulence shifts the cascade of the turbulence kinetic energy (TKE) spectrum, thus resulting in more energetic large scale turbulent structures. Consequently, the λ-shock foot shifts further downstream, leading to a smaller separation bubble size. Nonetheless, other statistical quantities, such as the turbulence anisotropy invariant map and the turbulence kinetic energy budget terms, show little dependence on the type and order of the spatial reconstruction scheme. Finally, using the more accurate ninth-order WENO results, it is reasoned that the interaction of the λ-shock with the post-shock relaxation region drives the low-frequency oscillation of the λ-shock

Two-equation and multi-fluid turbulence models for Richtmyer-Meshkov mixing

This paper concerns an investigation of two different approaches in modeling the turbulent mixing induced by the Richtmyer–Meshkov instability (RMI): A two-equation K-L multi-component Reynolds-averaged Navier–Stokes model and a two-fluid model. We have improved the accuracy of the K-L model by implementing new modifications, including a realizability condition for the Reynolds stress tensor and a threshold in the production of the turbulence kinetic energy. We examine the models in the one-dimensional (1D) form in the (re)-shocked mixing of a double-planar air and sulfur-hexafluoride (SF6) interface of the Atwood number |At| ≃ 0.6853. Furthermore, we investigated the models’ accuracy to RMI-induced mixing of a (re)-shocked planar-inverse chevron air–SF6 interface. Relevant integral quantities in time, as well as instantaneous profiles and contour plots, are used to assess the models’ accuracy against high-resolution implicit large eddy simulations. The proposed modifications improve the efficiency of the K-L model. The model is designed as a simple model capable of capturing the self-similar growth of Rayleigh–Taylor and Richtmyer–Meshkov flows. The two-fluid model remains more accurate but is also computationally more expensive

The Coanda Effect anomaly present in 2D CFD simulations of installed rectangular jets

The Coanda Effect describes the attachment of a jet flow to a nearby surface. In this paper, we show that a Computational Fluid Dynamics (CFD) solution of an installed rectangular jet introduces an anomalous Coanda Effect (i.e. bending of the jet towards the trailing edge of the flat plate positioned adjacent to the nozzle lower lip line) when the simulation is performed in 2D. The latter is often used for fast estimation of a full3DRANS calculation (that can take up to 6 days for the residuals to converge to 1x10−4 on a grid of 7 million cells using 16 cores). Our results show that for a3D simulation, the jet flow passed smoothly over the surface without producing significant bending