Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems

The new two-time-level dispersion improved CABARET scheme is developed as an upgrade of the original CABARET for improved wave propagation modelling in multiple dimensions and for nonlinear conservation laws including gas dynamics. The new upgrade retains many attractive features of the original CABARET scheme such as shock-capturing and low dissipation. It is simple for implementation in the existing CABARET codes and leads to a greater accuracy for solving linear wave propagation problems. A non-linear version of the dispersion-improved CABARET scheme is introduced to efficiently deal with contact discontinuities and shocks. The properties of the new linear and nonlinear CABARET schemes are analysed for numerical dissipation and dispersion error based on Von Neumann analysis and Pirrozolli's method. Numerical examples for one-dimensional and two-dimensional linear advection, the one-dimensional inviscid Burger's equation, and the isothermal gas dynamics problems in one and two dimensions are presented

Zonal jets in the Southern Ocean: a semi-analytical model based on scale separation

A reduced-order semi-analytic model of multiple zonal jets in the Southern Ocean is proposed based on the statistical approach and scale decomposition. By introducing two dominant scales in the vorticity equation, the model describes the large-scale and mesoscale dynamics using the explicit momentum dissipation in the horizontal and vertical directions. For validation and physical insights, the results of the reduced-order model are compared with solutions of two eddy-resolving ocean models: i) a realistic primitive-equation HYCOM (HYbrid Coordinate Ocean Model) simulation of the Southern Ocean and ii) an idealized quasi-geostrophic model of a shear-driven channel flow

Broad Band Shock Associated Noise Modelling for High-Area-Ratio Under-Expanded Jets

Broadband Shock Associated Noise (BBSAN) is an important component of supersonic jet noise for jets at off-design conditions when the pressure at the nozzle exit is different from the ambient. Two high area ratio under-expanded supersonic jets at Nozzle Pressure Ratios (NPRs) 3.4 and 4.2 are considered. The jets correspond to conditions of the experiment in the Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC) in the Supersonic Jet Facility of Monash University. Flow solutions are obtained by the Large Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) methods. The solutions are validated against the Particle Image Velocimetry (PIV) data. For noise spectra predictions, the LES solution is combined with the time-domain Ffowcs Wiliams -Hawkings method. To probe accuracy of the reduced-order method based on acoustic analogy, the RANS solutions are substituted in the Morris and Miller BBSAN method, where different options for modelling of the acoustic correlation scales are investigated. The noise spectra predictions are compared with the experimental data from the non-anechoic LTRAC facility and the NASA empirical sJet model. Apart from the low-frequencies influenced by the jet mixing noise, the RANS-based acoustic predictions align with those from LES for most frequencies in the range of Strouhal numbers (St) 0.4<St<2 within 1-2 dB

Fast spectral solutions of the double-gyre problem in a turbulent flow regime

Several semi-analytical models are considered for a double-gyre problem in a turbulent flow regime for which a reference fully numerical eddy-resolving solution is obtained. The semi-analytical models correspond to solving the depth-averaged Navier–Stokes equations using the spectral Galerkin approach. The robustness of the linear and Smagorinsky eddy-viscosity models for turbulent diffusion approximation is investigated. To capture essential properties of the double-gyre configuration, such as the integral kinetic energy, the integral angular momentum, and the jet mean-flow distribution, an improved semi-analytical model is suggested that is inspired by the idea of scale decomposition between the jet and the surrounding flow

Excitation of the Earth's Chandler wobble by a turbulent oceanic double-gyre

We develop a layer-averaged, multiple-scale spectral ocean model and show how an oceanic double-gyre can communicate with the Earth's Chandler wobble. The overall transfers of energy and angular momentum from the double-gyre to the Chandler wobble are used to calibrate the turbulence parameters of the layer-averaged model. Our model is tested against a multilayer quasi-geostrophic ocean model in turbulent regime, and base states used in parameter identification are obtained from mesoscale eddy resolving numerical simulations. The Chandler wobble excitation function obtained from the model predicts a small role of North Atlantic ocean region on the wobble dynamics as compared to all oceans, in agreement with the existing observations

Effect of large-scale mixing on the axisymmetric structure of turbulence correlations in complex dual stream jets

Dual-stream flows are a ubiquitous feature of turbofan engines used in civil aviation. In this paper we analyze the spatial structure of turbulence correlations in a high speed round coaxial jet operating at heated conditions. In particular we consider the effect of axisymmetry of a second rank correlation tensor and the usual fourth order Reynolds stress auto-covariance tensor that enters the Goldstein’s generalized acoustic analogy formulation. The invariants of these tensors can be reduced to a simpler form depending on whether isotropy or axisymmetry was assumed. We show that an axisymmetric turbulence approximation remains accurate in the core region but tends to break down in the bypass stream and especially in the interfacial region between both streams where high level of mixing of turbulence takes place. In the paper we present some of our latest results and provide a road map for the future calculations that we have planned

Analysis of the non-parallel flow-based Green's function in the acoustic analogy for complex axisymmetric jets

This paper considers how a complex axisymmetric jet modifies the structure of the propa- gator tensor in Goldstein’s generalized acoustic analogy. The jet flow we consider is in general a dual stream flow that operates either as a single jet or a complex co-axial jet flow. The latter of which is of interest to turbofan engine manufacturers. The form of the acoustic analogy that we use here is based on our recent work on jet noise modeling (Afsar et al. 2019, PhilTrans. A., vol. 377) that highlighted the importance of non-parallel flow effects in the correct calcu- lation of the propagator. The propagator calculation takes advantage of the fact that mean flow non-parallelism enters the lowest order asymptotic expansion of the former at sufficiently low frequencies of the same order as the jet spread rate. Whilst this might seem restrictive, our previously reported calculations at high subsonic and mildly supersonic jets indicate that the subsequent jet noise predictions remain accurate up to the peak frequency (typically at a Strouhal number based on jet velocity and diameter of ≈ 0.5 − 0.6) for the small angle acoustic radiation. One of critical assumptions of this approach is that the mean flow speed of sound squared is given by either the Crocco relation (in unheated jets) or the Crocco-Busemann relation for heated flows. Our analysis for the dual stream complex axisymmetric jet however shows that the latter assumption (in the form of Crocco-Busemann formula) is no longer an accurate representation of the speed of sound variation. We therefore present a more general form of the asymptotic analysis than that used in Afsar et al. (2019a & b). For the complex jet mean flow field, the mean flow speed of sound is otherwise arbitrary but must remain a single-valued function of the streamwise mean flow. The predictions based on this approach are shown to remain accurate up to the peak frequency. We discuss how to extend the range of validity by utilizing a suitable composite asymptotic solution for the Green’s function problem

Statistical analysis of high-speed jet flows

The spatiotemporal dynamics of pressure fluctuations of a turbulent jet flow is examined from the viewpoints of symbolic permutations theory and Kolmogorov-Smirnov statistics. The methods are applied to unveil hidden structures in the near-field of the two jets corresponding to the NASA SHJAR SP3 and SP7 experiments. Large Eddy Simulations (LES) are performed using the high-resolution Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) accelerated on Graphics Processing Units (GPUs). It is demonstrated that the decomposition of the LES pressure solutions into symbolic patterns of simpler temporal structure reveals the existence of some orderly structures in the jet flows. To separate the non-linear dynamics of the revealed structures from the linear part, the results based on the pressure signals obtained from LES are compared with the surrogate dataset constructed from the original data

Application of Genetic Programming and Artificial Neural Network Approaches for Reconstruction of Turbulent Jet Flow Fields

Two Machine Learning (ML) methods are considered for reconstruction of turbulet signals corresponding to the Large Eddy Simulation database obtained by application of the high-resolution CABARET method accelerated on GPU cards for flow solutions of NASA Small Hot Jet Acoustic Rig (SHJAR) jets. The first method is the Feedforward Neural Networks technique, which was successfully implemented for a turbulent flow over a plunging aerofoil in (Lui and Wolf, 2019). The second method is based on the application of Genetic Programming, which is well-known in optimisation research, but has not been applied for turbulent flow reconstruction before. The reconstruction of local flow velocity and pressure signals as well as timedependent principle coefficients of the Spectral Proper Orthogonal Decomposition of turbulent pressure fluctuations are considered. Stability and dependency of the ML algorithms on the smoothness property and the sampling rate of the underlying turbulent flow signals are discussed