Spectral simulations of the reconnection process of two vortices

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2015-2016Ce mémoire investigue le phénomène de reconnexion visqueuse de deux tourbillons initialement placés de façon orthogonale ou antiparallèle. Les équations de Navier-Stokes pour un fluide incompressible sont résolues directement (DNS) à l’aide d’un algorithme pseudospectral utilisant des expansions périodiques dans les trois directions cartésiennes. La condition de circulation nulle inhérente à cette méthode numérique est contournée en résolvant les équations dans un repère tournant approprié. Une méthode simple utilisant des lignes de vorticité est proposée afin de calculer le pourcentage de reconnexion instantané η de deux tourbillons. Cette méthode est également employée pour séparer le champ de vorticité en ses composantes reconnectées et non-reconnectées, ce qui facilite l’identification visuelle des différentes étapes du processus de reconnexion. Finalement, l’échelle de temps de la reconnexion tourbillonnaire Trec est calculée pour différents nombres de Reynolds (500 ≤ Re ≤ 10000). Il est trouvé que l’ordre de grandeur de Trec varie de façon continue de [symbol] à mesure que Re augmente.This work focuses on the viscous reconnection phenomenon of two vortex tubes that are initially antiparallel or orthogonal to each other. The incompressible Navier-stokes equations are solved directly (DNS) using a Fourier pseudospectral algorithm with triply periodic boundary conditions. The associated zero-circulation constraint is circumvented by solving the governing equations in a proper rotating frame of reference. A simple method using vortex lines is proposed to compute the instantaneous reconnection level η of two vortices. The proposed method is also used to split the vorticity field into its reconnected and non-reconnected parts, which allows for a clear and intuitive visual identification of the different reconnection phases. Finally, the Reynolds number dependence of the reconnection timescale Trec is investigated for 500 ≤ Re ≤ 10000. The scaling is found to vary continuously as Re is increased from [symbol]

A cost-effective semi-implicit method for the time integration of fully compressible reacting flows with stiff chemistry

We present a simple method to remove the stiffness associated with the chemical source terms in the fully compressible Navier-Stokes equations when the classical fourth order Runge-Kutta scheme is used

A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations

Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast,efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. Then, as an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption leads to a 15% under-prediction of the normalized turbulent flame speed for a premixed hydrogen-air flame. This difference in the turbulent flame speed motivates further study into using the mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz number flames.Comment: 36 pages, 14 figure

Impact of pressure fluctuations on the dynamics of laminar premixed flames

Thermo-acoustic instabilities are problematic in the design of continuous-combustion propulsion systems such as gas turbine engines, rocket motors, jet engine afterburners, and ramjets. Conceptually, the coupling between acoustics and flame dynamics can be divided into two categories: flame area fluctuations and changes in the local flame speed. The latter can be caused by the thermodynamic fluctuations that accompany an acoustic wave. This coupling is the focus of the present work. In this paper, we are concerned with the dynamics of laminar premixed flames involving large hydrocarbon species. Through high-fidelity numerical simulations, we investigate the flame response for a wide range of fuels and acoustic frequencies. The combustion of hydrogen and methane is considered for verification purposes and as baseline cases for comparison with two large hydrocarbon fuels, n-heptane and n-dodecane. We extract the phase and gain of the unsteady heat release response, which are directly related to the Rayleigh criterion and thus the stability of the system. For all fuels, we observe a local peak in the heat release gain. At high frequencies, we find that the fluctuations of the different species mass fractions decrease with the inverse of the acoustic frequency, leading to chemistry being “frozen” in the high-frequency limit. This allows us to predict the flame behavior directly from the steady-state solution

Impact of pressure fluctuations on the dynamics of laminar premixed flames

Thermo-acoustic instabilities are problematic in the design of continuous-combustion propulsion systems such as gas turbine engines, rocket motors, jet engine afterburners, and ramjets. Conceptually, the coupling between acoustics and flame dynamics can be divided into two categories: flame area fluctuations and changes in the local flame speed. The latter can be caused by the thermodynamic fluctuations that accompany an acoustic wave. This coupling is the focus of the present work. In this paper, we are concerned with the dynamics of laminar premixed flames involving large hydrocarbon species. Through high-fidelity numerical simulations, we investigate the flame response for a wide range of fuels and acoustic frequencies. The combustion of hydrogen and methane is considered for verification purposes and as baseline cases for comparison with two large hydrocarbon fuels, n-heptane and n-dodecane. We extract the phase and gain of the unsteady heat release response, which are directly related to the Rayleigh criterion and thus the stability of the system. For all fuels, we observe a local peak in the heat release gain. At high frequencies, we find that the fluctuations of the different species mass fractions decrease with the inverse of the acoustic frequency, leading to chemistry being “frozen” in the high-frequency limit. This allows us to predict the flame behavior directly from the steady-state solution

The process of making an aerodynamically efficient car body for the SAE Supermileage competition

In the summer of 2010, a new body shell for the SAE Supermileage car of Laval University was designed. The complete shell design process included, amongst other steps, the generation of a shape through the parametric shape modeling software Unigraphics NX7 and the evaluation of aerodynamic forces acting on the chassis using the open source Computational Fluid Dynamics (CFD) software OpenFOAM. The CFD analyses were ran at steady-state using a k-omega-SST turbulence model and roughly 2.5 million cells. An efficient method for evaluating the effect of ambient wind conditions and vehicle trajectory on the track was developed. It considers the proportion of time that the car operates at each combination of velocity and wind yaw angle and computes the overall energy demand of the shell. An iterative process was conducted over a significant number of different shapes, which were generated by joining formula-based guide curves using intersection and tangency conditions. The new shell has a 25 % larger frontal area due to modified design constraints. When aerodynamically compared to the smaller and already highly efficient old vehicle, reductions of 50 % of the negative lift, 15 % of the energy demand when driving forward, and 5 % of the energy demand when turning are achieved by the new design. Also, the drag coefficient is reduced by 20 %. These improvements come from the quasi-NACA profiles on the side and top walls; a reduction of cavities to prevent redundant frontal areas; a short vehicle and smother wheel cover closures; and a thorough study of the nose and tail. This paper describes numerical flow simulations and the changes that were brought to the vehicle body to make it as aerodynamically efficient as possible

A fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations

Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast, efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan–Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. Then, as an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption leads to a 15% under-prediction of the normalized turbulent flame speed for a premixed hydrogen-air flame. This difference in the turbulent flame speed motivates further study into using the mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz number flames

Numerical Investigation of Compressibility Effects in Reacting Subsonic Flows

Direct numerical simulations (DNS) of reacting flows are routinely performed either by solving the fully compressible Navier-Stokes equations or using the low Mach number approximation. The latter is obtained by performing a Mach number expansion of the Navier-Stokes equations for small Mach numbers. These two frameworks differ by their ability to capture compressibility effects, which can be broadly defined as phenomena that are not captured by the low Mach number approximation. These phenomena include acoustics, compressible turbulence, and shocks. In this thesis, we systematically isolate compressibility effects in subsonic flows by performing two sets of DNS: one using the fully compressible framework, and one using the low Mach number approximation. We are specifically interested in the interactions between turbulence, acoustics, and flames. The addition of detailed chemistry in the compressible flow solver required the development of a novel time integration scheme. This scheme combines an iterative semi-implicit method for the integration of the species transport equations, and the classical Runge-Kutta method for the integration of the other flow quantities. It is found to perform well, yielding time steps limited by the acoustic CFL only. Furthermore, the computational cost per iteration of this hybrid scheme is low, being comparable to the one for the classical Runge-Kutta method. After extensive validation, the first application is the investigation of flame-acoustics interactions in laminar premixed flames. The thermodynamic fluctuations that accompany the acoustic wave are shown to significantly impact the flame response. Using the Rayleigh criterion, the flame-acoustics system is found to be thermo-acoustically unstable for various fuels, flow conditions, and acoustic frequencies. As expected, the low Mach number approximation and the fully compressible framework are in good agreement at low frequencies, since the flame is very thin compared to the acoustic wavelength. The two frameworks differ for very large acoustic frequencies only. In the high frequency limit, the gain reaches a plateau using the low Mach number approximation, while it goes to zero using the fully compressible framework. This is related to the spatial variations in the acoustic pressure field, which are not present in the low Mach number approximation. However, for practically relevant acoustic frequencies, the low Mach number framework is found to yield accurate results. Next, a numerical methodology to simulate compressible flows in geometries that lack a natural turbulence generation mechanism is presented. It is found that, unlike in incompressible flows, special care must be taken regarding the energy equation and the presence of standing acoustic modes. When using periodic boundary conditions, forcing the dilatational velocity field promotes the growth of unstable modes. This is explained by extracting the eigenvalues of the linearized forced Navier-Stokes equations. Based on these observations, it is found necessary to force the solenoidal velocity field only. This methodology is applied first to simulations of subsonic homogeneous non-reacting turbulence. We present simulations results for turbulent Mach numbers varying from 0.02 to 0.65. The Mach number dependence of various quantities, such as the dilatational to solenoidal kinetic energy ratio, is extracted. The Mach number scaling of all quantities of interest is found to be readily explained by the low Mach number expansion, specifically the zeroth and first order sets of equations, for turbulent Mach numbers up to 0.1. Finally, the interaction between subsonic compressible turbulence and premixed flames is investigated. Compressibility effects are isolated by comparing results obtained with the low Mach number approximation and the fully compressible framework, at the same flow conditions. Compressibility effects on chemistry are found to be limited for turbulent Mach numbers at least up to 0.4, especially when contrasted with the large impact of the Karlovitz number. Compressibility effects give rise to significant thermodynamic fluctuations away from the flame front, but these remain small compared to the large fluctuations due to the presence of the turbulent flame brush. The low Mach number approximation thus remains a valid framework for the Mach numbers considered, when the primary goal is to characterize the impact of turbulence on the chemical processes at play.</p

Fully compressible simulations of the impact of acoustic waves on the dynamics of laminar premixed flames for engine-relevant conditions

Thermo-acoustic instabilities remain problematic in the design of propulsion systems such as gas turbine engines, rocket motors, and ramjets. They arise from the constructive interaction of heat release rate and acoustic pressure oscillations, and can result in increased noise and mechanical fatigue. In the present work, we are concerned with the flame response to the thermodynamic fluctuations that accompany an incident acoustic wave. The objective is to investigate the flame dynamics under engine-relevant conditions using high-fidelity numerical simulations and detailed chemical kinetics. The focus is placed on the combustion of hydrogen and n-heptane, as they are both of practical interest and behave very differently when subjected to acoustic waves. We extract the phase and gain of the unsteady heat release response, which are directly related to the Rayleigh criterion and thus the stability of the system. We highlight the differences between results obtained using the fully compressible Navier-Stokes equations and the low Mach number approximation. The two simulation frameworks agree very well for acoustic wavelengths much larger than the flame thickness. However, they differ significantly at high frequencies. The gain erroneously reaches a plateau under the low Mach number approximation, while it decays to zero using the fully compressible framework. This difference is attributed to the spatial variations in the acoustic pressure, which are not captured by the low Mach number approximation