Annual Research Briefs: 1995

This report contains the 1995 annual progress reports of the Research Fellows and students of the Center for Turbulence Research (CTR). In 1995 CTR continued its concentration on the development and application of large-eddy simulation to complex flows, development of novel modeling concepts for engineering computations in the Reynolds averaged framework, and turbulent combustion. In large-eddy simulation, a number of numerical and experimental issues have surfaced which are being addressed. The first group of reports in this volume are on large-eddy simulation. A key finding in this area was the revelation of possibly significant numerical errors that may overwhelm the effects of the subgrid-scale model. We also commissioned a new experiment to support the LES validation studies. The remaining articles in this report are concerned with Reynolds averaged modeling, studies of turbulence physics and flow generated sound, combustion, and simulation techniques. Fundamental studies of turbulent combustion using direct numerical simulations which started at CTR will continue to be emphasized. These studies and their counterparts carried out during the summer programs have had a noticeable impact on combustion research world wide

Local dynamic subgrid-scale models in channel flow

The dynamic subgrid-scale (SGS) model has given good results in the large-eddy simulation (LES) of homogeneous isotropic or shear flow, and in the LES of channel flow, using averaging in two or three homogeneous directions (the DA model). In order to simulate flows in general, complex geometries (with few or no homogeneous directions), the dynamic SGS model needs to be applied at a local level in a numerically stable way. Channel flow, which is inhomogeneous and wall-bounded flow in only one direction, provides a good initial test for local SGS models. Tests of the dynamic localization model were performed previously in channel flow using a pseudospectral code and good results were obtained. Numerical instability due to persistently negative eddy viscosity was avoided by either constraining the eddy viscosity to be positive or by limiting the time that eddy viscosities could remain negative by co-evolving the SGS kinetic energy (the DLk model). The DLk model, however, was too expensive to run in the pseudospectral code due to a large near-wall term in the auxiliary SGS kinetic energy (k) equation. One objective was then to implement the DLk model in a second-order central finite difference channel code, in which the auxiliary k equation could be integrated implicitly in time at great reduction in cost, and to assess its performance in comparison with the plane-averaged dynamic model or with no model at all, and with direct numerical simulation (DNS) and/or experimental data. Other local dynamic SGS models have been proposed recently, e.g., constrained dynamic models with random backscatter, and with eddy viscosity terms that are averaged in time over material path lines rather than in space. Another objective was to incorporate and test these models in channel flow

Variational Multiscale Modeling and Memory Effects in Turbulent Flow Simulations

Effective computational models of multiscale problems have to account for the impact of unresolved physics on the resolved scales. This dissertation advances our fundamental understanding of multiscale models and develops a mathematically rigorous closure modeling framework by combining the Mori-Zwanzig (MZ) formalism of Statistical Mechanics with the variational multiscale (VMS) method. This approach leverages scale-separation projectors as well as phase-space projectors to provide a systematic modeling approach that is applicable to complex non-linear partial differential equations. %The MZ-VMS framework is investigated in the context of turbulent flows. Spectral as well as continuous and discontinuous finite element methods are considered. The MZ-VMS framework leads to a closure term that is non-local in time and appears as a convolution or memory integral. The resulting non-Markovian system is used as a starting point for model development. Several new insights are uncovered: It is shown that unresolved scales lead to memory effects that are driven by an orthogonal projection of the coarse-scale residual and, in the case of finite elements, inter-element jumps. Connections between MZ-based methods, artificial viscosity, and VMS models are explored. The MZ-VMS framework is investigated in the context of turbulent flows. Large eddy simulations of Burgers' equation, turbulent flows, and magnetohydrodynamic turbulence using spectral and discontinuous Galerkin methods are explored. In the spectral method case, we show that MZ-VMS models lead to substantial improvements in the prediction of coarse-grained quantities of interest. Applications to discontinuous Galerkin methods show that modern flux schemes can inherently capture memory effects, and that it is possible to guarantee non-linear stability and conservation via the MZ-VMS approach. We conclude by demonstrating how ideas from MZ-VMS can be adapted for shock-capturing and filtering methods.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145847/1/parish_1.pd

The 1999 Center for Simulation of Dynamic Response in Materials Annual Technical Report

Introduction: This annual report describes research accomplishments for FY 99 of the Center for Simulation of Dynamic Response of Materials. The Center is constructing a virtual shock physics facility in which the full three dimensional response of a variety of target materials can be computed for a wide range of compressive, ten- sional, and shear loadings, including those produced by detonation of energetic materials. The goals are to facilitate computation of a variety of experiments in which strong shock and detonation waves are made to impinge on targets consisting of various combinations of materials, compute the subsequent dy- namic response of the target materials, and validate these computations against experimental data

Numerical Analysis of Flux Reconstruction

High-order methods have become of increasing interest in recent years in computational physics. This is in part due to their perceived ability to, in some cases, reduce the computational overhead of complex problems through both an efficient use of computational resources and a reduction in the required degrees of freedom. One such high-order method in particular – Flux Reconstruction – is the focus of this thesis. This body of work relies and expands on the theoretical methods that are used to understand the behaviour of numerical methods – particularly related to their real-world application to industrial problems. The thesis begins by challenging some of the existing dogma surrounding computational fluid dynamics by evaluating the performance of high-order flux reconstruction. First, the use of the primitive variables as an intermediary step in the construction of flux terms is investigated. It is found that reducing the order of the flux function by using the conserved rather than primitive variables has a substantial impact on the resolution of the method. Critically, this is supported by a theoretical analysis, which shows that this mechanism of error generation becomes increasing important to consider as the order of accuracy increases. Next, the analysis of Flux Reconstruction was extended by analytically and numerically exploring the impact of higher dimensionality and grid deformation. It is found that both expanding and contracting grids – essential components of real-world domain decomposition – can cause dispersion overshoot in two dimensions, but that FR appears to suffer less that comparable Finite Difference approaches. Fully discrete analysis is then used to show that, depending on the correction function, small perturbations in incidence angle can cause large changes in group velocity. The same analysis is also used to theoretically demonstrate that Discontinuous Galerkin suffers less from dispersion error than Huynh’s FR scheme – a phenomenon that has previously been observed experimentally, but not explained theoretically. This thesis concludes with the presentation of a robust theoretical underpinning for determining stable correction functions for FR. Three new families of correction functions are presented, and their properties extensively explored. An important theoretical finding is introduced – that stable correction functions are not defined uniquely be a norm. As a result, a generalised approach is presented, which is able to recover all previously defined correction functions, but in some instances via a different norm to their original derivation. This new super-family of correction functions shows considerable promise in increasing temporal stability limits, reducing dispersion when fully discretised, and increasing the rate of convergence. Taken altogether, this thesis represents a considerable advance in the theoretical characterisation and understanding of a numerical method – one which, it has been shown, has enormous potential for forming the heart of future computational physics codes

High Fidelity Simulation of Loss Mechanisms in Compressors

Further improvements in aero-engine efficiencies require better understanding of loss mechanisms. The rise of high performance computing is unlocking the potential of scale-resolving simulations for industrially relevant cases thus allowing new levels of simulation fidelity. As a result, previously unexplored effects of unsteadiness can be simulated and their impact on loss understood. The work undertaken in this thesis aims to establish a framework for accurate loss predictions using scale-resolving simulations and inform the field with regards to the effects of unsteadiness on loss mechanisms within the multi-stage compressors. The lack of computational requirements for accurate industrial simulations lead to inconsistent loss predictions even for scale-resolving simulations depending on the chosen convergence criteria. This work studies aspects of loss generation by employing two test-cases: Taylor-Green vortex and compressor cascade subjected to freestream turbulence. The results show that both resolving local entropy generation rate and capturing the inception and growth of instabilities are critical to accuracy of loss prediction. In particular, the interaction of free-stream turbulence at the leading-edge and development of instabilities in the laminar region of the boundary layer are found to be important. These two outcomes allow for a formulation of resolution criteria that ensure accurate loss predictions for compressor flows. One of the major sources of uncertainty in the current simulation methods for compressor flows is the level of unsteadiness and its impact on loss This work makes a series of steps towards understanding the nature and the origin of unsteadiness within multi-stage machines and investiages the impact of gapping on mid-span compressor loss. It is found that freestream turbulence levels rise significantly as the size of the rotor-stator axial gap is reduced. This is because of the effect of axial gap on turbulence production mechanisms, which amplify at smaller axial gaps and drive increases in dissipation and loss. This effect is found to raise loss by between 5.5 - 9.5\% over the range of conditions tested here. This effect was found to significantly outweigh the beneficial effects of wake recovery on loss.Financial support for this work was provided by the Whittle Laboratory and the University of Cambridge through the Denton Scholarship fund and the CDT in Gas Turbine Aerodynamics, funded by the EPSRC $EP/L015943/1$

Numerical Simulations of Incompressible Flows in Complex Geometries.

A mainly spectral code along with domain-decomposition, a combination that is not widely in use in complex problems, has been developed for the solution of the 3-D unsteady incompressible Navier-Stokes equations. The code uses fully spectral or a combination of spectral-collocation and finite difference approximations and a 3-step splitting time-marching scheme. The developed Poisson solver utilizes matrix diagonalization and incorporates a direct sub-structuring method based on the influence matrix technique. As a first step, laminar and turbulent confined flows were simulated, initially with DNS, then with LES, using a modified Smagorinksi model. The domain-decomposition technique and parallel implementation were tested on the Poisson solver. The study focused on fluid flow phenomena and did not involve chemical reactions. We compared our calculations with numerical experiments performed on turbulent developed channel and pipe flow at Retau = 180. Annular flow, interesting but less popular, was also simulated. Finally we attempted to approach the problem of pipe flow with sudden expansion (confined jet) at low and moderate Reynolds numbers to investigate the ability of the code to handle complex geometries

Large-eddy simulations of a jet in crossflow using Julia

The jet in crossflow (JICF) is a complex flow that has applications in many fields, from pollutant dispersion into air or water to the injection and mixing of fuel in engines. In this thesis, large-eddy simulations, using a stretched-vortex sub-grid model, of a JICF with a non-reactive scalar are performed using a discrete numerical method that is implemented using code written in the computational language Julia. Velocity profiles, trajectories, entrainment, power spectra, turbulent kinetic energy and dissipation of energy are analysed for simulations run at velocity ratios varying between 0.405 and 3.3, crossflow boundary layer thicknesses between 0.28 and 2.06 and Reynolds numbers between 243 and 20500. Simulations are compared to published experimental and simulation-based results, and a full comparison was performed with a simulation provided by Mattner, run on the same computational grid. It was found that the mathematical model used in this thesis performs better at higher velocities and Reynolds numbers. An investigation into the effect of the ratio of average jet inlet velocity to maximum crossflow velocity was performed. It was found that a jet with a higher velocity ratio showed increased penetration into the crossflow. The amount of turbulent kinetic and scalar energy in the system, as well as the amount of dissipation of energy from the system, also increased with velocity ratio. Finally, a comparison of large-eddy simulation (LES) and direct numerical simulation (DNS) of a JICF was performed on the same computational grid for low and moderate Reynolds numbers. At low Reynolds numbers the di↵erences in results between the LES and DNS are minor, although it is not possible to resolve the flow on the computational grid that is used. At moderate Reynolds numbers, above Re = 1 x 10⁴, the differences between the LES and DNS are more pronounced. Deeper jet penetration is seen in the LES than in the DNS, and the distribution of energy in the system is different, with the sub-grid model used in the LES dissipating more energy from the high wavenumber scales.Thesis (M.Phil) -- University of Adelaide, School of Mathematical Sciences, 201