4,822 research outputs found

    Linear Amplification in Nonequilibrium Turbulent Boundary Layers

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    Resolvent analysis is applied to nonequilibrium incompressible adverse pressure gradient (APG) turbulent boundary layers (TBL) and hypersonic boundary layers with high temperature real gas effects, including chemical nonequilibrium. Resolvent analysis is an equation-based, scale-dependent decomposition of the Navier Stokes equations, linearized about a known mean flow field. The decomposition identifies the optimal response and forcing modes, ranked by their linear amplification. To treat the nonequilibrium APG TBL, a biglobal resolvent analysis approach is used to account for the streamwise and wall-normal inhomogeneities in the streamwise developing flow. For the hypersonic boundary layer in chemical nonequilibrium, the resolvent analysis is constructed using a parallel flow assumption, incorporating N₂, O₂, NO, N, and O as a mixture of chemically reacting gases. Biglobal resolvent analysis is first applied to the zero pressure gradient (ZPG) TBL. Scaling relationships are determined for the spanwise wavenumber and temporal frequency that admit self-similar resolvent modes in the inner layer, mesolayer, and outer layer regions of the ZPG TBL. The APG effects on the inner scaling of the biglobal modes are shown to diminish as their self-similarity improves with increased Reynolds number. An increase in APG strength is shown to increase the linear amplification of the large-scale biglobal modes in the outer region, similar to the energization of large scale modes observed in simulation. The linear amplification of these modes grows linearly with the APG history, measured as the streamwise averaged APG strength, and relates to a novel pressure-based velocity scale. Resolvent analysis is then used to identify the length scales most affected by the high-temperature gas effects in hypersonic TBLs. It is shown that the high-temperature gas effects primarily affect modes localized near the peak mean temperature. Due to the chemical nonequilibrium effects, the modes can be linearly amplified through changes in chemical concentration, which have non-negligible effects on the higher order modes. Correlations in the components of the small-scale resolvent modes agree qualitatively with similar correlations in simulation data. Finally, efficient strategies for resolvent analysis are presented. These include an algorithm to autonomously sample the large amplification regions using a Bayesian Optimization-like approach and a projection-based method to approximate resolvent analysis through a reduced eigenvalue problem, derived from calculus of variations.</p

    Design of effective heat transfer structures for performance maximization of a closed thermochemical energy storage reactor through topology optimization

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    This study addresses the need for heat transfer intensification in closed thermochemical energy storage reactors using topology optimization as a design approach. We introduce a novel topology optimization framework to simultaneously optimize fins geometry and amount of enhancer material while meeting specific discharge time, bed size, and bed porosity requirements. The proposed topology optimization framework is thoroughly tested by optimally designing innovative fin structures in a reference thermochemical storage reactor aimed at heat storage in industrial applications and operated with Strontium Bromide in the range 150-250 °C. The generated designs show performance improvement up to +286% compared to state-of-the-art designs. Our findings also indicate that the optimal amount of enhancer material varies significantly; large bed sizes with high packing factors maximize reactor energy density while highly packed reactive beds provide a larger amount of energy in fixed discharge times compared to less packed reactive beds. Finally, the benefits and limitations of the proposed topological optimization approach, as well as the extent to which the optimal designs found are generally applicable are thoroughly discussed to provide guidelines for configuring high-performing closed system thermochemical energy storage reactors

    Reconstruction of the time-dependent source in thermal grooving by surface diffusion

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    In hot polycrystalline materials, when a vertical flat grain boundary meets a horizontal surface the grain boundary forms a groove in the surface. Mathematically modelling features of such thermal grooving mechanism is therefore very important in characterizing polycrystalline materials composed of tiny grains intersecting an external free surface. With this aim in mind, we formulate and investigate a novel inverse problem of reconstructing the unknown time-dependent source term entering the fourth-order parabolic equation of thermal grooving by surface diffusion from a given integral observation. We formulate and prove in Theorems 2.3–2.7 that this linear inverse problem is well-posed. However, in practice, the ideal regularity of data under which the inverse source problem is stable is never satisfied due to the inherent non-smoothness of the measurement. Consequently, this leads to the inverse problem with raw data becoming ill-posed. In order to obtain accurate and stable solutions, we develop and compare two numerical methods, namely, a time-discrete method and an optimization method. We obtain error estimates and convergence rates for the time-discrete method. For the optimization method, an objective functional, which is proved to be FrĂ©chet differentiable, is introduced and the conjugate gradient method (CGM), regularized by the discrepancy principle, is developed to compute the minimizer yielding the source term. The results of two numerical tests illustrate the performance of the two methods for both exact and noisy measured data

    Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

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    Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators

    Analysis of a thermoelastic problem with the Moore–Gibson–Thompson microtemperatures

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    In this paper, we study, from both an analytical and a numerical point of view, a poro-thermoelastic problem with microtemperatures. The so-called Moore–Gibson–Thompson equation is used to model the contribution for the temperature and microtemperatures. An existence and uniqueness result is proved by using the theory of linear semigroups of contractions and, for the one-dimensional case, the exponential energy decay is found under some conditions on the constitutive coefficients. Then, a fully discrete approximation is introduced by using the finite element method and the implicit Euler scheme. We show that the discrete energy decays and we obtain some a priori error estimates from which, under some adequate additional regularity conditions on the continuous solution, we derive the linear convergence of the approximations. Finally, we perform some numerical simulations to demonstrate the accuracy of the approximations and the behavior of the discrete energy and the solutionPeer ReviewedPostprint (published version

    Analysis of an implicitly extended Crank-Nicolson scheme for the heat equation on a time-dependent domain

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    We consider a time-stepping scheme of Crank-Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step is required. Following Lehrenfeld \& Olskanskii [ESAIM: M2AN, 53(2):\,585-614, 2019], we apply an implicit extension based on so-called ghost-penalty terms. For spatial discretisation, a cut finite element method is used. We derive a complete a priori error analysis in space and time, which shows in particular second-order convergence in time under a parabolic CFL condition. Finally, we present numerical results in two and three space dimensions that confirm the analytical estimates, even for much larger time steps

    Proceedings of SIRM 2023 - The 15th European Conference on Rotordynamics

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    It was our great honor and pleasure to host the SIRM Conference after 2003 and 2011 for the third time in Darmstadt. Rotordynamics covers a huge variety of different applications and challenges which are all in the scope of this conference. The conference was opened with a keynote lecture given by Rainer Nordmann, one of the three founders of SIRM “Schwingungen in rotierenden Maschinen”. In total 53 papers passed our strict review process and were presented. This impressively shows that rotordynamics is relevant as ever. These contributions cover a very wide spectrum of session topics: fluid bearings and seals; air foil bearings; magnetic bearings; rotor blade interaction; rotor fluid interactions; unbalance and balancing; vibrations in turbomachines; vibration control; instability; electrical machines; monitoring, identification and diagnosis; advanced numerical tools and nonlinearities as well as general rotordynamics. The international character of the conference has been significantly enhanced by the Scientific Board since the 14th SIRM resulting on one hand in an expanded Scientific Committee which meanwhile consists of 31 members from 13 different European countries and on the other hand in the new name “European Conference on Rotordynamics”. This new international profile has also been emphasized by participants of the 15th SIRM coming from 17 different countries out of three continents. We experienced a vital discussion and dialogue between industry and academia at the conference where roughly one third of the papers were presented by industry and two thirds by academia being an excellent basis to follow a bidirectional transfer what we call xchange at Technical University of Darmstadt. At this point we also want to give our special thanks to the eleven industry sponsors for their great support of the conference. On behalf of the Darmstadt Local Committee I welcome you to read the papers of the 15th SIRM giving you further insight into the topics and presentations

    Development, Implementation, and Optimization of a Modern, Subsonic/Supersonic Panel Method

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    In the early stages of aircraft design, engineers consider many different design concepts, examining the trade-offs between different component arrangements and sizes, thrust and power requirements, etc. Because so many different designs are considered, it is best in the early stages of design to use simulation tools that are fast; accuracy is secondary. A common simulation tool for early design and analysis is the panel method. Panel methods were first developed in the 1950s and 1960s with the advent of modern computers. Despite being reasonably accurate and very fast, their development was abandoned in the late 1980s in favor of more complex and accurate simulation methods. The panel methods developed in the 1980s are still in use by aircraft designers today because of their accuracy and speed. However, they are cumbersome to use and limited in applicability. The purpose of this work is to reexamine panel methods in a modern context. In particular, this work focuses on the application of panel methods to supersonic aircraft (a supersonic aircraft is one that flies faster than the speed of sound). Various aspects of the panel method, including the distributions of the unknown flow variables on the surface of the aircraft and efficiently solving for these unknowns, are discussed. Trade-offs between alternative formulations are examined and recommendations given. This work also serves to bring together, clarify, and condense much of the literature previously published regarding panel methods so as to assist future developers of panel methods

    On slope limiting and deep learning techniques for the numerical solution to convection-dominated convection-diffusion problems

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    As the first main topic, several slope-limiting techniques from the literature are presented, and various novel methods are proposed. These post-processing techniques aim to automatically detect regions where the discrete solution has unphysical values and approximate the solution locally by a lower degree polynomial. This thesis's first major contribution is that two novel methods can reduce the spurious oscillations significantly and better than the previously known methods while preserving the mass locally, as seen in two benchmark problems with two different diffusion coefficients. The second focus is showing how to incorporate techniques from machine learning into the framework of classical finite element methods. Hence, another significant contribution of this thesis is the construction of a machine learning-based slope limiter. It is trained with data from a lower-order DG method from a particular problem and applied to a higher-order DG method for the same and a different problem. It reduces the oscillations significantly compared to the standard DG method but is slightly worse than the classical limiters. The third main contribution is related to physics-informed neural networks (PINNs) to approximate the solution to the model problem. Various ways to incorporate the Dirichlet boundary data, several loss functionals that are novel in the context of PINNs, and variational PINNs are presented for convection-diffusion-reaction problems. They are tested and compared numerically. The novel loss functionals improve the error compared to the vanilla PINN approach. It is observed that the approximations are free of oscillations and can cope with interior layers but have problems capturing boundary layers
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