Nonlinear Stability and Control of Three-Dimensional Boundary Layers

The linear and nonlinear evolution of steady and traveling disturbances in three-dimensional incompressible boundary layer flows is studied using Parabolized Stability Equations (PSE). Extensive primary stability analyses for the model problems of Swept Hiemenz flow and the DLR Transition experiment on a swept flat plate are performed first. Second, and building upon these results, detailed secondary instability studies based on both the classical Floquet Theory and a novel approach that uses the nonlinear PSE are conducted. The investigations reveal a connection of unstable secondary eigenvalues to both the linear eigenvalue spectrum of the undisturbed mean flow and the continuous spectrum, as well as the existence of an absolute instability in the region of nonlinear amplitude saturation. Third, a passive technique for boundary layer transition control using leading edge roughness is examined utilizing a newly developed implicit solution method for the nonlinear PSE. The results confirm experimental observations and indicate possible means of delaying transition on swept wings. In the present work, both the solution of the boundary layer equations for the mean flow and the explicit PSE solver are based on a fourth-order-accurate compact scheme formulation in body-oriented coordinates. In the secondary instability analysis, the Implicitly Restarted Arnoldi Method is applied

Optimized energy calculation in lattice systems with long-range interactions

We discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long-range interactions. Although, since the introduction of the Luijten-Bl\"ote algorithm, Monte Carlo simulations of these systems no longer pose a fundamental problem, the energy calculation is still an O(N^2) problem for systems of size N. We show how this can be reduced to an O(N logN) problem, with a break-even point that is already reached for very small systems. This allows the study of a variety of, until now hardly accessible, physical aspects of these systems. In particular, we combine the optimized energy calculation with histogram interpolation methods to investigate the specific heat of the Ising model and the first-order regime of the three-state Potts model with long-range interactions.Comment: 10 pages, including 8 EPS figures. To appear in Phys. Rev. E. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

Criticality in one dimension with inverse square-law potentials

It is demonstrated that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse-square interactions exhibits a universal critical jump, in analogy with the superfluid density in helium films. Renormalization-group arguments are combined with numerical simulations of systems containing up to one million lattice sites to accurately determine the critical properties of these models. In strong contrast with earlier work, compelling quantitative evidence for the Kosterlitz--Thouless-like character of the phase transition is provided.Comment: To appear in Phys. Rev. Let

Abundance and scarcity: classical theories of money, bank balance sheets and business models, and the British restriction of 1797‐1818.

The thesis looks through the lens of bank balance sheet accounting to investigate the structural change in the British banking system between 1780 and 1832, and how classical quantity theorists of money attempted to respond to the ensuing financialisation of the wartime economy with its growing reliance on credit funded with paper-based instruments (the ‘Vansittart system’ of war finance). The thesis combines contributions to three separate fields to construct a holistic historical example of the challenges faced by monetary economists when ‘modelling’ financial innovation, credit growth, ‘fringe’ banking, and agent incentives – at a time of radical experimentation: the suspension of the 80-year-old gold standard (“the Restriction”). First, critical text analysis of the history of economics argues that the 1809-10 debate between Ricardo and Bosanquet at the peak of the credit boom, bifurcated classical theory into two timeless competing policy paradigms advocating the ‘Scarcity’ or ‘Abundance’ of money relative to exchange transactions. The competing hypotheses regarding the role of money and credit are identified and the rest of the thesis examines the archival evidence for each. Second, the core of the thesis contributes to the historical literature on banking in relation to money by reconstructing a taxonomy of bank business models, their relationships with the London inter-bank settlement system, and their responses to the Restriction - drawing on some 17,000 mostly new data points collected from the financial records of London and Country banks. The final section contributes to the economic history of money by constructing aggregated views of total bank liabilities from the firm-level data, scaled to recently available British GDP estimates. These are examined to establish (with hindsight) the relative merits and lacuna of the competing theoretical hypotheses postulated by political economists. It was the period of deleveraging after 1810 that revealed the lacuna of both paradigms

ON THE STABILITY OF THREE-DIMENSIONAL BOUNDARY LAYERS PART 1: LINEAR AND NONLINEAR STABILITY

The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment

National Aeronautics and

The secondary instability of three-dimensional incompressible boundary layers is studied using Floquet theory. Starting from the equilibrium solutions that we obtained from the PSE computations documented in Part 1, we investigate the region where a purely stationary crossflow disturbance saturates for its secondary instability characteristics utilizing developed global and local eigenvalue solvers that are based on the Implicitly Restarted Arnoldi Method, and a Newton-Raphson technique, respectively. The main focuses of this study are on the existence of multiple roots in the eigenvalue spectrum that could explain experimental observations of time-dependent occurrences of an explosive growth of traveling disturbances, on the routes by which high-frequency disturbances enter the boundary layer, as well as on gaining more information about threshold amplitudes for the growth of secondary disturbances

Experimental and numerical studies on highly loaded supersonic axial turbine cascades

For the small to medium thrust range of modern aero engines, highly loaded single stage HP turbines facilitate an attractive alternative to a more conventional 2-stage HPT architecture. Whereas the potential benefits of reductions in component length and part count, hence, in weight and cost do motivate their application, the related risks are in maintaining associated losses of supersonic flows at low values as well as managing the interaction losses between HPT and the downstream sub-component to arrive at competitive levels of component efficiencies. This paper focuses on fundamental aerodynamic concept studies and related cascade experiments in support of a future highly loaded high-pressure turbine architecture. Starting with some general remarks on low-loss supersonic aerodynamic concepts for high-pressure turbines, results from development efforts towards 2D airfoil concepts viable for high-pressure turbine airfoils are shown. In particular, CFD based design approaches are compared against experimental data taken at DLR Göttingen in un-cooled cascade tests and at engine representative levels of Mach and Reynolds numbers. For the airfoils investigated, it turns out that there is indeed a supersonic Mach number range were loss levels are comparable to high Mach number subsonic values, thereby enabling a competitive aerodynamic design concept for a 3D high-pressure turbine stag