Date: Friday Dec 11, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Riccardo Rossi, Laboratorio di Termofluidodinamica Computazionale, Universita' di Bologna, Italy

Title: Numerical simulation of scalar mixing from a point source over a wavy wall

Abstract: The release of a passive tracer from a point source over a wavy wall is analyzed using Direct Numerical Simulations (DNS) to obtain a detailed description of the scalar plume dynamics over a complex topography. Although the scalar source is located on top of one of the wave crests, thus representative of a ground release (GS), the comparison with available results for scalar mixing from elevated sources (ES) shows that the initial decay of mean concentration is affected by the flow separation occurring in the first-half of each wave. Nonetheless, in the far-field the concentration profiles are reasonably described by empirical correlations for flows over rough surfaces. The budget of scalar fluxes also shows that each component obeys a local balance between advection, production and the scalar-pressure-gradient correlation. Similar results have been previously reported for the vertical and lateral fluxes; however, it is interesting to note how the streamwise component is usually dominated by the production-dissipation balance under simple-shear conditions. Finally, algebraic flux models in the form of the Generalized Gradient-Diffusion Hypothesis (GGDH) and its High-Order extension (HOGGDH) are evaluated against the Standard-Gradient Diffusion Hypothesis (SGDH) to predict the decay of mean concentration downstream of the source. The results are found noticeably improved by the algebraic models, which also appear to be a reasonable approximation for the spanwise component of the scalar fluxes.

Date: Friday Dec 4, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Joseph W. Nichols, Center for Turbulence Research Postdoctoral Fellow, Stanford University

Title: Global mode decomposition of supersonic jet noise

Abstract: Instability wave mechanisms are considered for sound generation in supersonic jets from the perspective of global mode analysis. While instability waves traditionally are important to low Reynolds number transitional flows, laboratory experiments by Suzuki & Colonius (JFM, 2006) have confirmed their presence in turbulent jets at Reynolds numbers up to 10^6. Moreover, in a supersonic jet, the supersonic convection of instability waves couples directly to the acoustic field, causing Mach wave radiation (Tam, ARFM, 1995). In the present work, instability waves and their coupled acoustic radiation are treated as "global modes," which are three dimensional temporal perturbation eigenfunctions of the system. As fully 3D eigenfunctions, global modes capture directly effects of base flow non-parallelism. The least stable global modes are extracted from simulations governed by the fully compressible linearized Navier--Stokes equations using a shift-and-invert Arnoldi method and the massively parallel linear solver, SuperLU. To compare with results obtained from the Parabolized Stability Equations (PSE) technique (see Cheung et al., AIAA, 2007), a cold laminar supersonic jet at Mach number M=2.5 is first considered. Although globally stable, this jet still supports a maximum transient energy growth of 10^7 computed from an optimal superposition of the (convectively) non-normal global modes. While purely linear, this transient growth is composed of several frequencies, and as such may be key to predicting eventual nonlinear mode interactions responsible for low frequency sound production. Finally, to more fully demonstrate the power of global modes to resolve effects of base flow non-parallelism, preliminary results of global modes computed about mean flow fields measured from large eddy simulations of a turbulent jet at Mach number M=1.5 computed using the CDP-CF4 code (Khalighi & Ham, 2009).

Date: Friday Oct 30, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Gaurav Bansal, Center for Turbulence Research

Title: Computational Studies of Autoignition and Combustion Relevant to Modern Engines

Abstract: We present computational studies of autoignition and combustion behavior encountered in modern internal combustion engines in which combustion is achieved primarily via autoignition of the reactant mixture. Computational tools with varying levels of complexity are employed to systematically investigate the phenomena under consideration. Firstly, turbulence-autoignition interaction for nonpremixed n-heptane/air mixture is studied using a counterflow configuration in which a well defined unsteady scalar dissipation rate oscillation represents the effects of the turbulent flow field. A newly defined ignitability parameter is proposed which systematically accounts for all the unsteady effects. Next, we present the results of high-fidelity direct numerical simulations (DNS) of autoignition in thermally and compositionally stratified turbulent mixtures. Using non-reacting RANS engine simulations, different initial conditions to be studied using DNS are identified. Diagnostic techniques are developed to quantitatively identify the different heat release modes ranging from premixed deflagration to homogeneous autoignition which are present in stratified mixtures. Finally, to aid in subgrid scale modeling of these complex autoigniting systems, a novel methodology based on Principal Component Analysis (PCA) is used to identify the intrinsic low-dimensional manifolds in these systems.

Date: Friday Oct 16, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Ali Mani, Center for Turbulence Research

Title: Reflectivity analysis of sponges in compressible flow simulations

Abstract: In this talk, I will go through the common reflectivity mechanisms due to flow/sponge interactions. The work mostly involves derivation of back-of-envelop-type relations governing sponge reflectivity, and will be presented in a PDE course style. I will mostly use the white board for the analysis, but will present some numerical experiments to support the results. The following paragraph is an introduction to my talk: In finite-domain compressible flow simulations, one remedy to address lack of boundary information is to gradually relax the flow near the external boundary to a known consistent far-field solution of the Navier-Stokes equations. This treatment, called the sponge treatment, is adopted in many calculations owing to its simplicity, generality and robustness. In practical calculations however, interactions of the sponges with flow features can reflect unphysical signatures into the CFD domain. If the sponge is not carefully designed these reflections can overwhelm the physics of interest particularly when acoustics are concerned. In this work we examine the physics of sponge/flow interactions through analytical and semi-analytical approaches. The reflectivity due to non-linear terms, oblique waves intersecting, and sponge/vortex interactions are separately analyzed. The optimal sponge profiles and the reflection coefficients for asymptotically small or large sponges (compared to flow features) are investigated. These analyses provide estimates of the sponge requirements for CFD calculations in a relatively general framework.

Date: Friday Oct 2, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Guido Lodato, Center for Turbulence Research

Title: Three-dimensional Boundary Conditions for Direct and Large-Eddy Simulation of Turbulent Flows.

Abstract: Two main topics related to Direct and Large-Eddy Simulation of turbulence are discussed: (a) on one side, numerical aspects regarding the implementation of numerically transparent boundary conditions are addressed; (b) on the other side, a structural sub-grid scale (SGS) model for Large- Eddy Simulation of weakly compressible turbulent confined flows is presented. A three-dimensional procedure for characteristic boundary conditions is proposed. This very sensitive point of boundary conditions, which is seldom thoroughly discussed in literature, was found to be closely related to convection and pressure gradients developing in the directions parallel to boundary faces, also called transverse terms. A method involving the inclusion of these transverse effects in the computation of the incoming wave amplitude variations is developed and extended to chemically reacting flows. This method, which is based on the NSCBC approach, removes the original one-dimensional inviscid assumption-leading to the so called LODI system-that is, in general, too stringent to correctly deal with the very complex flow structure obtained from DNS and LES of turbulent flows. Additional problems of wave coupling at the edges and corners of three-dimensional structured computational domains are also discussed. Hence, based on the three-dimensional characteristic formulation for the Navier-Stokes equations, a systematic procedure to solve edges and corners is developed. With regards to LES of weakly compressible turbulent flows, a structural mixed model, based on the similarity assumption is developed and tested on the impinging round-jet at Reynolds numbers 23000 and 70000. The difficulties of purely dissipative functional models based on the eddy-viscosity hypothesis, when dealing with such a complex flow, are addressed and the necessity to improve the modeling strategy by better accounting for the peculiar interaction terms arising from the use of non Reynolds operators are analyzed. The eddy-viscosity term together with the modified Leonard tensor allows good representation of non-local interactions as well as local interactions near the cutoff length, these last being responsible for local events of reverse energy transfer. Furthermore, the unphysical alignment between the SGS stress tensor and the resolved strain tensor-a condition which is intrinsically enforced by any eddy-viscosity model-is automatically removed. The use of the WALE model, in particular, allows proper wall scaling of the wall shear stresses. The new model was developed with particular attention to the correct reproduction of the average theoretical scaling within the viscous sub-layer for each component of the SGS tensor.

Date: Friday Sep 18, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Jeroen Witteveen, Center for Turbulence Research

Title: Extremum diminishing uncertainty quantification with constant error in time for computational fluid dynamics and fluid-structure interaction

Abstract: Numerical errors in computer simulations have shown a tremendous decrease over the last decades due to the increased availability of computational resources and efficient algorithms. Intrinsic uncertainties in model parameter values, and initial and boundary conditions limit the current predictive capabilities of numerical simulations. The effect of these physical uncertainties cannot be quantified by a Monte Carlo simulation of performing a large number of random computations due to the already high computational costs involved in a single deterministic simulation. Stochastic Collocation has been developed as a more efficient uncertainty quantification method based on Gauss quadrature sampling and Lagrangian interpolation in probability space. Its recent utilization in computational fluid dynamics and fluid-structure interaction applications has, however, revealed a number of shortcomings of the approach. The accurate approximation of discontinuous responses and unsteady behavior are two of these central challenges addressed in this presentation. For treating discontinuous response surfaces an extremum diminishing uncertainty quantification method is presented based on Newton-Cotes quadrature sampling in an adaptive simplex elements discretization of probability space. The method also satisfies the total variation diminishing robustness concept, which assures that no non-zero probabilities for unphysical realizations are predicted due to overshoots at discontinuities. In addition a methodology for unsteady oscillatory problems is developed which maintains a constant accuracy in time with a constant number of samples. The method based on interpolation of scaled samples at constant phase results in a bounded error in time for periodic and non-periodic responses. Multi-frequency behavior of continuous structures is treated by employing a wavelet decomposition pre-processing step. Applications to transonic flow problems and aero-elastic simulations with randomness in the flow and the structure are considered. Results for transonic flows show that the local production of standard deviation in the shock region due to the sensitive shock wave location amplifies the input uncertainty also to output integral quantities of interest such as the lift force. In the fluid-structure interaction applications the randomness is found to trigger an earlier onset of unstable flutter behavior, which a deterministic simulation would have missed. This suggests that the presented uncertainty quantification approach forms a more reliable design practice than using safety margins in combination with deterministic simulation results.

Date: Friday Sep 4, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Aaron Brandis, Center for Turbulence Research

Title: Nonequilibrium Radiation Intensity Measurements and Modeling Relevant To Titan and Earth Entry

Abstract: The predictions of nonequilibrium radiation for a Titan aerocapture aeroshell vary significantly amongst Computational Fluid Dynamics (CFD) analyses and are limited by the physical models of the non- equilibrium flow. Of particular interest are the non-equilibrium processes associated with the cyanogen (CN) molecule which is known to be a strong radiator. It is therefore important to have experimental data for these radiating shock layers which will allow for validation of CFD models. Furthermore, a more detailed understanding of the chemical processes that lead to the formation of CN above equilibrium concentration is required. This thesis describes the modelling of the radiation behind a shock using a collisional-radiative (CR) model and presents measurements of radiation intensity behind a shock in simulated Titan and Martian atmospheres. The uncertainties in radiation is more significant at lower speeds (around 5-8 km/s) with these atmospheres when compared to Earth entry. This is due to the formation of CN and because of the highly non-equilibrium nature of the flow. The motivation for this work began with the successful landing of the Huygens probe on the surface of Titan which led to the renewed interest in inter-planetary missions. Thus radiative heating during atmospheric entry to Titan and Mars was the subject of several experimental campaigns and extensive computational analyses. In order to better understand the formation of CN, and the nonequilibrium radiation emitted under such atmospheric conditions, NASA Ames Research Center conducted a series of experiments on their Electric Arc Shock Tube facility, EAST. Furthermore, several research groups in Europe and the United States independently developed CR models to predict the measured levels of radiation. The results from these simulations showed some major discrepancies and highlighted a lack of knowledge and understanding about the fundamental physics behind the formation and decay of the CN molecule and its associated excited states. Based on a comparison of the various simulations with the CR models and the EAST experimental data, it was concluded that the absolute level of peak radiation was well predicted, however, there was a significant discrepancy related to the decay rate of the radiation. Therefore, to add to the relatively small amount of experimental data for these highly non- equilibrium radiating flow conditions, experiments were performed on the X2 shock tube at The University of Queensland with the aim of producing a comprehensive set of benchmark data for Titan entry. The data obtained from these experiments have been used to validate the results from the NASA Ames testing, and due to the large parametric variation, as a source for code validation. In addition to the experimental component of this thesis, an investigation into the simulation of CN nonequilibrium radiation was conducted. It has been previously concluded that there was a significant discrepancy between the experimentally measured radiation decay rate and the predicted value from CR models. Therefore, the primary aim of the simulation work presented in this thesis is to explain the reason behind this discrepancy. Through a parametric study of important reactions combined with an analysis of the reaction set, it was concluded that the coupling between the dissociation of N2 and the formation of CN (through the reaction N2 + C = CN + N) controlled the radiation decay rate. The reason for the super equilibrium concentrations was identified to be a result of the N2 + C = CN + N reaction continuing to over-produce CN after nominal equilibrium values are reached. This is due to the slow build up of N to drive the reverse reaction. Thus it has been shown in this thesis that the behaviour of the CN concentration is controlled by the rate of N2 dissociation. This led to the implementation of a more thorough method for simulating the dissociation process of molecular nitrogen. Therefore, a mono-quantum vibration state specific model that includes excitation and de-excitation reactions for all the vibrational states of nitrogen was incorporated into the CR model developed by Magin et al. The nitrogen vibration state specific model that was implemented was developed by Pierott and is based on SSH theory. The model developed in this thesis is known as the ViSpeN CR model (Vibrationally Specific Nitrogen). The ViSpeN results show significantly better agreement with experimental data in terms of the decay rate, initial rise of the radiation and the overall trends in the data. However, the work in this thesis has shown there are still discrepancies in predicting the absolute level of radiation measured in shock tunnel experiments. This led to the development of a modification to the ViSpeN model (known as ViSpeN-L) which includes a proposed new value for the radiative lifetime of the CN violet transition. The agreement between the experimental data and the ViSpeN-L model is excellent for conditions relevant to Titan entry.

Date: Friday Aug 21, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Professor Javier Jimenez, U. Politecnica de Madrid and the Center for Turbulence Research

Title: Transitional structures in high-Reynolds number wall-bounded

Abstract: We will summarized recent work regarding what part, if any, of linearized theory is relevant to high-Reynolds number sheared turbulence. The best known example is the free-shear case, where energy production is dominated by the linearized instabilities of the mean profile, but the profiles of wall-bounded turbulence are known to be stable. The last decades have shown that stability is not equivalent to lack of growth, and that transient growth factors can be large enough to lead to nonlinear, self-sustained, dynamics. However, the linearized equations in the wall-bounded case depend on viscosity, and, except for the reasonably well-established structures of the buffer layer, even basic agreement with experiments requires an eddy viscosity model. In essence, the energy-containing eddies away from the wall can only be modelled in the sense of LES. Recent results, both linear and nonlinear, are reviewed, including the comparison between amplification factors and observed spectra, which is only fair. Possible reasons for the remaining disagreements are summarized, including recent solutions for some of them, and work in progress on others.

Date: Friday Aug 7, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Michael Frewer, Institute of Fluid Dynamics, Technische Universitat Darmstad

Title: A Consistent 4D Invariant Turbulence Modeling Approach

Abstract: A new turbulence modelling approach is presented. Geometrically reformulating the averaged Navier-Stokes equations on a 4-dimensional non-Riemannian manifold without changing the physical content of the theory, additional modelling restrictions naturally emerge which are absent in the usual Euclidean (3+1)-dimensional framework. The modelled equations show full form-invariance for all Newtonian reference frames in that all involved quantities transform as true 4-tensors. Frame accelerations or inertial forces of any kind are universally described by the underlying 4-dimensional geometry. By constructing a non-linear eddy viscosity model within the k-epsilon family for high turbulent Reynolds numbers the new invariant modelling approach demonstrates the essential advantages over current (3+1)-dimensional modelling techniques. In particular, new invariants are gained which allow for a universal and consistent treatment of non-stationary effects within a turbulent flow. Furthermore, by consistently introducing via a Lie-group symmetry analysis a new internal modelling variable, the mean form-invariant pressure Hessian, it will be shown that already a quadratic non-linearity is sufficient to capture secondary flow effects, for which in current non-linear eddy viscosity models a higher non-linearity is needed.

Date: Friday Jul 24, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Ivan Bermejo Moreno, Center for Turbulence Research

Title: On the non-local geometry of turbulence

Abstract: We present a methodology for the study of the non-local geometry of structures in turbulence. Starting from a three-dimensional field it consists of three main steps: extraction (through a multi-scale decomposition, based on the curvelet transform, followed by iso-contouring of each component field), characterization (based on differential-geometry properties and their area-based joint probability functions) and classification (using geometrical signatures and enhanced with clustering techniques) of individual structures. We apply this methodology to several fields - passive scalar fluctuation, enstrophy, dissipation obtained from turbulence numerical databases with different grid resolutions (256^3, 512^3 and 1024^3). A transition, with decreasing scale, from blob-like to tube-like to highly stretched sheet-like structures is found. The differences among fields are discussed, as well as the effect of the grid resolution on the educed geometries. Additionally, an assessment of the geometries educed by two existing local identification criteria in turbulence - Q, for tubes, and [A_ij]_+, for sheets - is performed. Finally we introduce a new methodology for the study of proximity issues among different sets of structures, based also on geometrical and non-local analyses. We apply it to four of the fields previously studied. Tube-like structures of Q are mainly surrounded by sheets of [A_ij]_+, which appear at close distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.

Date: Friday Jul 10, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. Jan Nordstrom, Visiting Professor from Uppsala University

Title: Accurate and Stable Calculations Involving Shocks Using a New Hybrid Scheme

Abstract: We develop a hybrid scheme consisting of a combination of a second order MUSCL scheme and a high order scheme. The full hybrid scheme is constructed in such a way that we can prove that it is conservative and stable for linear problems. We show by numerical experiments that it is high order accurate in smooth domains and oscillatory free close to shocks.

Date: Friday Jul 10, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Ms. Sofia Eriksson, Visiting Graduate Student from Uppsala University

Title: Analysis of mesh and boundary effects on the accuracy of node-centered finite volume schemes

Abstract: The accuracy of the node-centered finite volume method in one-dimension is analyzed. Numerical simulations and analysis are performed for both a hyperbolic and a elliptic case, for various types of grids. The results from the simulations agree with the analysis. The boundary conditions are implemented weakly using penaly technique. For the hyperbolic case we see that the type of grid has large impact on the order of accuracy, whereas the choice of penaly parameter only affect the error constant. For the elliptic case the grid has less impact on the order of accuracy. For both the hyperbolic and elliptic problem we show that the error contribution from the primal and dual grid can be treated separately.

Date: Friday Jun 19, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Mr. Daniel Mitchell, Visiting Researcher at Stanford University

Title: Spatially resolved thermometry in shock tube environments by way of toluene planar laser induced fluorescence

Abstract: Planar laser induced fluorescence has long been recognized as a valuable research tool in the study of both fluid mechanical and combustion phenomena. The present research project details the development and application of a toluene based PLIF technique to the study of shock tube flows. Toluene offers unprecedented sensitivity to temperature variation, and very high fluorescent quantum yield, allowing for much more precise measurements of spatial temperature variation than were previously possible. Shock tubes present a difficult challenge for the experimentalist, with the phenomena under investigation being high temperature and pressure, as well as extremely transient. Toluene PLIF has provided the opportunity to obtain quantitative maps of temperature in a variety of gas dynamic flows. Many of these flows have, in the past, only been accessible to qualitative techniques such as schlieren. This ability to obtain quantitative measurements yields opportunities for a better understanding of the underlying physics of the flow structure, as well as a greatly improved ability to validate numerical codes.

Date: Friday Jun 12, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Pierre Wolfe, CERFACS, Toulouse, France

Title: Massively parallel LES of azimuthal thermo-acoustic instabilities in annular gas turbines

Abstract: Increasingly stringent regulations and the need to tackle rising fuel prices have placed great emphasis on new designs for aeronautical gas turbines. These are often prone to combustion instabilities. In the particular field of annular combustion chambers, these instabilities usually take the form of azimuthal modes. To predict these modes, one must compute the full combustion chamber, which remained out of reach until very recently and the development of massively parallel computers. Since one of the most limiting factors in performing Large Eddy Simulation (LES) of real combustors is the mesh size, the effects of mesh resolution are investigated by computing full annular LES of a realistic helicopter combustion chamber on two grids, respectively made of 38 and 93 million elements. Results are compared in terms of mean and fluctuating fields. Two versions of this helicopter combustor, which differ only on the swirlers' design, are also computed. In both computations, LES captures self-established rotating azimuthal modes. However, the two cases exhibit different thermo-acoustic responses and the resulting limit-cycles are different. With the first design, a self-excited strong instability develops, leading to pulsating flames and strong heat release fluctuations. In the second case, the flames are much less affected by the azimuthal acoustic mode and remain stable, allowing an acceptable operation. This study therefore highlights the potential of LES for discriminating injection system designs.

Date: Friday Jun 5, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Simon Mendez, CTR Postdoctoral Fellow, Stanford University

Title: Large-Eddy Simulations for Supersonic Jet Noise Predictions

Abstract: Supersonic jet noise has been the topic of numerous investigations from the first studies on aeroacoustics. Jet noise is one of the most important components of aircraft noise, at take-off for example. Currently, motivations for supersonic jet noise research are multifold. For example, reducing the noise generated by military aircrafts is of course an important motivation, but it becomes crucial on aircraft carriers, where sailors are very close to the aircrafts at take-off. The present research project is funded by NASA in the framework of the NASA Research Opportunities in Aeronautics. The aim is to determine if sufficient noise reduction can be achieved in order to use supersonic aircrafts for civil transport in the future. One way of achieving noise reduction for jets at the engine exhaust is to modify the nozzle geometry: the most famous example is chevrons. In the last ten years, numerical predictions of jet noise have developed. In particular, Large-Eddy Simulation seems a promising method. However, structured solvers are often used, so that LES are limited to relatively simple geometries. To be able to support the development of innovative noise reduction techniques, handling complex geometries is crucial. In this presentation, we will present results for supersonic jet noise computed using an unstructured solver developed at CTR. For the moment, an axisymmetric nozzle is considered to validate the approach. In the presentation, the difficulties of performing LES for supersonic jet noise predictions will be stressed and preliminary results will be shown and analyzed.

Date: Friday May 29, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Didier Lucor, Institut Jean Le Rond d'Alembert, Université Pierre et Marie Curie

Title: Spectral Stochastic Approaches for Uncertain Nonlinear Hyperbolic Systems

Abstract: Uncertainty quantification through stochastic spectral methods has been recently applied to several kinds of non-linear stochastic PDEs. However, strong physical non-linearities such as steep fronts and shocks are tricky as they easily translate to the parametric stochastic space. Several numerical approaches can be pursued depending on the solution discontinuity with respect to the parametric uncertainty and/or the growth of the stochastic dimensionality of the problem. We will present two different approaches through several applications. The first part of the talk will focus on numerical investigation of airfoil performance at stochastic transonic flow regimes. Studies will be presented where a deterministic RANS compressible solver is coupled to a non-intrusive stochastic collocation solver to propagate several aerodynamic uncertainties through a steady flow around a NACA0012 and a OAT15A airfoils. The stochastic model is based on the generalized Polynomial Chaos theory combining the advantage not to modify the existing deterministic code while remaining accurate in the computations of the statistical moments of the stochastic flow. The robustness and efficiency of the present methodology are evaluated for the propagation of random disturbances associated to the angle of attack and the free-stream Mach number. Different stochastic flow regimes are analyzed in details by means of various post-processing procedures, including error bars, probabilistic density function of the aerodynamic field Sobol's coefficients... Two kinds of non linearities seem to be critical with respect to the skin-friction uncertainties: on one hand, the leeward shock movement and on the other hand, the boundary-layer separation on the aft part of the airfoil downstream the shock. In this case, the sensitivity analysis shows that a strong coupling exists between the uncertain parameters. In the second part of the talk, we introduce an intrusive formalism to tackle uncertain hyperbolic systems of conservation laws with Polynomial Chaos (PC) methods. The idea is to introduce a new variable, the entropic variable, in bijection with our vector of unknowns, which we develop on the polynomial basis: by performing a Galerkin projection, we obtain a deterministic system of conservation laws. We state several properties of this deterministic system in the case of a general uncertain system of conservation laws. We then apply the method to the case of the inviscid Burgers’equation with random initial conditions and we present some preliminary results for the Euler system. We systematically compare results from our new approach to results from the stochastic Galerkin method. In the vicinity of discontinuities, the new method bounds the oscillations due to Gibbs phenomenon to a certain range through the entropy of the system without the use of any adaptative random space discretizations.

Date: Friday May 22, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Florian Kummer, TU Darmstadt, Department of Mechanical Engineering, Germany

Title: BoSSS: Bounded Support Spectral Solver - A generic discontinuous Galerkin framework

Abstract: In the past 1 1/2 years, the authors have been working on an object-oriented framework for the discontinuous Galerkin (spectral element, DG) method, with a strong aim on CFD applications. This library was programmed in C# for Microsoft .NET and Mono framework. Up to our knowledge, it's the first ambitious CFD code which was implemented using the .NET framework. The talk is split into two parts, the first one giving an introduction into the Discontinuous Galerkin method, especially into the problems that arise when one tries to solve the Poisson equation. We present our actual work on the p-multigrid - method, which enables us to overcome the slow convergence of the Poisson Solver, caused by the bad condition number of the matrix resulting from the DG discretization. The second part of the talk cares about the software engineering aspects. In our opinion, managed languages offer a new perspective to supercomputing software development. We demonstrate that the key issues for supercomputing, portability (to supercomputers/clusters) and performance are ensured and demonstrate the benefits that we gain from using such languages. These benefits are binary platform independence, rich debugging features, and a runtime that classical languages can't compete with.

Date: Friday May 8, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. Abdellah HADJADJ, Visiting Scholar, National Institute of Applied Sciences, INSA & CORIA - Rouen - France

Title: High-fidelity numerical simulation of high-speed flows including shock/shock and shock/boundary-layer interactions

Abstract: The first part of the presentation deals with numerical simulation of supersonic turbulence when shock/turbulent boundary layer interaction occurs. Such flows reveal the existence of complex mechanisms, which have to be well understood for an efficient design of propulsion systems. In this study, both DNS and LES are used to investigate unsteady mechanisms. Since a shock-capturing scheme is used, a hybrid numerical scheme has been developed to reduce its dissipative properties. The obtained results are analysed and discussed in terms of mean and turbulent quantities. Excellent agreement between LES, DNS and experimental data is obtained. Some features relative to the organization of the large eddies are given and the importance of the low frequencies shock unsteadiness is discussed in relation to the SBLI. Also, the validity of the assumptions of the strong Reynolds analogy (SRA) in SBLI is addressed. The second part of the presentation relates to numerical flow visualizations in high-speed aerodynamics. Numerical schlieren pictures as well as computed interferogram techniques are used to visualize the major features of physical phenomena that can be mostly encountered in supersonic flows, such as supersonic turbulence including shock/shock and shock/boundary layer interactions, shear-layer instability and transient flows. Some of the numerical visualization results constructed from computed Navier-Stokes flow-fields are directly compared to experimental images. Most of the features observed in the experiment are accurately reproduced by the simulations. The results of this study provide in general better understanding of the main characteristics of complex supersonic flows that are not easily accessible experimentally, and may be useful for flow controlling and practical high-speed aerodynamics design and improvement.

Date: Friday Apr 24, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Sergei Chumakov, Stanford University

Title: Development of one- and two-equation models in Large-Eddy Simulation

Abstract: One-equation subgrid models for Large Eddy Simulation use auxiliary quantities to close the equation of motions, and these quantities are calculated by adding an extra transport equation to the problem. One- equation models tend to be more accurate and have wide application area than zero-equation models such as classical Smagorinsky model. I will discuss several different approaches and present a new model for the dissipation rate of subgrid-scale kinetic energy - a work in progress that leads to a two-equation model that combines characteristic features of two very different one-equation approaches developed recently.

Date: Friday Mar 20, 2009

Time: 4:00pm

Location: Building 300, Room 300

Speaker: Prof. Julian C. R. Hunt, University College of London

Title: Thin shear layers –the key to turbulence structure (with collaborators, I.Eames, P. Davidson, J.Westerweel, J.Fernando,S.Voropayev, M.Braza)

Abstract: Sharply sheared interfaces determine the structure of turbulent motions both on large and small scales, as recent experiments and simulations have demonstrated. They form wherever there are very large gradients in turbulence intensity and gradients in the large scale velocity field ; they move through the flow as a result of local scale ‘nibbling’ by Kelvin-Helmholtz instabilities and mixing at the interface , and by larger scale ‘engulfing’ motions of the interface of low turbulence fluid ; shear layers become stronger through the combined action of the large scale shear and the blocking of the inhomogeneous turbulence by the interface ; with low curvature of the large scale shear profile (such as in free shear layers), and high levels of external or internal perturbations , the engulfing motions of the interface are more effective than ‘nibbling’. Where turbulence exists outside shear layers, idealised models and experiments show how smaller eddies are distorted, and then disappear which transfers their energy to larger scales .Because they are inhomogeneous these eddies stretch and distort the larger scale vorticity so as to counter the diffusive tendency of the interface to thicken. These concepts are applied to the structure of high Reynolds number turbulence by focusing on the shear layers observed between or on the boundaries of large eddies. The numerical simulations of Ishihara, Gotoh and Kaneda (2009) show that on the edges of the layers and in their interiors thin viscous layers form, on the Taylor microscale. Intermittent small-scale vortices within these viscous layers are amplified up to the limit set by viscous diffusion –their reduced thickness reduces to the Kolmogorov micro length scale. But estimates of rms vorticity and velocity have to take into account the two length scales of this process, and the degree to which the thin layers are sufficiently convoluted to be ‘space-filling’ By blocking the external scale eddies impinging onto the interfaces ,a wide range of inertial range upscale and down scale inertial range motions scales are generated outside the layers with a characteristic power law spectrum, and where the skewness of the velocity derivatives is negative . The upscale motions may be significant for amplifying the shear layers. One of the most significant implications of this ‘interface dynamics ’ mechanism, is that small scale turbulence is produced significantly faster –as is observed- than by the more gradual ‘cascade’ mechanism proposed by L.F. Richardson., or by equivalent models based on statistical physics .There are possibilities for improved turbulence modeling based on this inhomogeneous-zonal analysis where processes on different ranges of scales occur in different parts of the flow field.

Date: Friday Feb 27, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Qiqi Wang, Stanford University

Title: A high order multivariate approximation scheme on arbitrary grids with potential applications in uncertainty quantification and numerical methods

Abstract: We construct a high order multi-variate interpolation scheme for arbitrary scattered data sets. The estimated approximation error is minimized by solving a equality constrained least squares. The approximation function is an interpolation when the data points are exact or a regression function when there are measurement errors. Using this formulation, the gradient information on each datapoint can be used to significantly reduce the interpolation error. The approximation converges exponentially on smooth functions for a variety of grids, including randomly scattered nodes. The output of the approximation scheme includes the estimated approximation error. Therefore, it is a natural method of estimating the uncertainties generated by the interpolation, as well as propagating uncertainties from the data points to the interpolated value. We also present methods of solving differential equations with collocation and tau methods using this interpolation scheme.

Date: Friday Feb 20, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. Jan Nordstrom, Uppsala University

Title: Well Posed and Weakly Coupled Fluid Structure Interaction Problems

Abstract: We investigate model problems of fluid structure interaction type and aim for a formulation that leads to a well-posed problem and a stable numerical procedure. Our first objective is to investigate if the generally accepted formulations of the FSI problems are well posed and the only possible ones. Our second objective is to prove that the numerical coupling is truly stable. To accomplish that we will use a weak coupling summation-by-parts operators and penalty terms. In multiple dimensions this is a formidable task and we start by investigating the simplest possible model problem available. As a flow model we use the linearized Euler equations in one dimension and as the structure model we consider a spring.

Date: Friday Jan 16, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. Chi-Wang Shu, Brown University

Title: High Order Well Balanced Schemes and Applications to Non- Equilibrium Flow with Stiff Source Terms

Abstract: The modeling of unsteady flow problems containing finite-rate chemistry or combustion poses additional numerical difficulties over and above the different scales associated with turbulence flows. One of the main difficulties stems from the appearance of the source terms, which are sometimes stiff. A well-balanced scheme, which can preserve certain non-trivial steady state solutions exactly, may help to resolve some of these difficulties. In this talk, we will first describe the general strategy to design high order well balanced finite difference schemes. We will then move to the discussion of a few schemes, including the high order WENO finite difference scheme based on the Roe building block, the high order WENO finite difference scheme based on the Lax-Friedrichs building block, and three well known second order TVD schemes, in terms of their well-balanced properties for a simple 1D model with one temperature and three species. We show through numerical experiments that, for the stationary steady state solutions of the reactive flow, the well balanced schemes will give machine round-off errors regardless of the mesh sizes, while the non-well balanced schemes give truncation errors consistent with the formal order of accuracy for the schemes. For a small perturbation of such steady state solutions, the well balanced schemes can resolve them well with very coarse meshes, while the non-well balanced schemes would give spurious structures in the numerical solutions, which will decrease and eventually disappear with a mesh refinement. Our work indicates the advantage of well balanced schemes: they can be used to resolve small perturbations of the steady state solutions using much coarser meshes than that for the non-well balanced schemes, thereby saving a lot of CPU time. This is a joint work with Wang, Yee and Sjogreen.

Date: Thursday Jan 15, 2009

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Joseph W. Nichols, Laboratoire d’Hydrodynamique (LadHyX), Ecole Polytechnique

Title: Simulation and global stability analysis of round fuel jets

Abstract: Direct numerical simulation (DNS) suggests that a light round fuel jet transitions to turbulence through a sequence of primary and secondary global instabilities. First, an axisymmetric primary global instability originates from a pocket of absolute instability near to the nozzle. The pocket of absolute instability acts as a “wavemaker” supporting self-sustaining oscillations which impart their frequency to the rest of the flow. This mechanism for global instability is verified by considering the effect of a lifted flame which forms on the fuel jet when ignited. For sufficiently low liftoff heights, the flame enters the pocket of absolute instability, destroys the wavemaker, and stabilizes the entire flow. For larger liftoff heights, a Krylov-subspace method is used to extract the least stable linear global perturbation modes, revealing their quenched spatial structure. Further downstream, axially elongated structures known as side jets form at regular intervals around the perimeter of the jet core. The same Krylov-subspace method, applied to the monodromy operator rather than the Jacobian, results in secondary global modes, one of which is found to be unstable. Furthermore, the superposition of these modes suggests that side-jet formation owes to a competition between a slow but exponentially growing global mode and a highly non-normal transient response. Finally, we propose to apply the same global stability methodology to study the phenomenon of combustion instability, a problem often arising in lean-burning gas turbine systems. We hypothesize that purely hydrodynamic modes owing to absolute instability may interrupt the coupling between heat-release and acoustic modes necessary to sustain combustion instability.