Influence of periodically fluctuating material parameters on the stability of explicit high-order spectral element methods

This paper presents a mathematical analysis of the stability of high-order spectral elemetns with explicit time marching for the solution of acoustic wave propagation in heterogeneous media. Using a Von Neumann stability analysis, the origin for the instability that is often observed when the stability limit derived for homegenous media is adapted for heterogeneous media. In large scale projects such as the simulation of seismic wave propagation, this known issue results either in simulations that are too expensive due to a conservative choice of the time step or to simulations that lead to unstable results due to the inability to predict the suitability of the time step. The proposed work not only explain the mathematical origin of this problem but also derives exact stability bounds are given for cases when the heterogeneity is periodic

Stability of an explicit high-order spectral element method for acoustics in heterogeneous media based on local element stability criteria

This paper considers the stability of an explicit Leap‐Frog time marching scheme for the simulation of acoustic wave propagation in heterogeneous media with high‐order spectral elements. The global stability criterion is taken as a minimum over local element stability criteria, obtained through the solution of element‐borne eigenvalue problems. First, an explicit stability criterion is obtained for the particular case of a strongly‐heterogeneous and/or rapidly‐fluctuating medium using asymptotic analysis. This criterion is only dependent upon the maximum velocity at the vertices of the mesh elements, and not on the velocity at the interior nodes of the high‐order elements. Second, in a more general setting, bounds are derived using statistics of the coefficients of the elemental dispersion matrices. Different bounds are presented, discussed and compared. Several numerical experiments show the accuracy of the proposed criteria in one‐dimensional test cases as well as in more realistic large scale 3D problems

A review of the ONR/NAVAIR research option combustion instabilities in compact ramjets, 1983-1988

This paper consists of two parts summarizing two portions of the ONR/NAVAIR Research Option. The option began in 1983 and continued for five years, involving 11 organizations. Simultaneously, similar or related programs supported by other agencies or institutions were being carried out in several other places. Results of those programs have been briefly summarized in five papers collected in a document to be published by C.P.L.A. This paper contains two of the five papers in that document. Here we cover the subjects of approximate analyses and stability; and large-scale structures and passive control. The first is concerned chiefly with an analytical framework constructed on the basis of observations; it is intended to provide a means of correlating and interpreting data, and predicting the stability of motions in a combustion chamber. The second is a summary of recent experimental work directed to understanding the flows in dump combustors of the sort used in modern ramjet engines. Much relevant material is not included here, but may be found in the remaining papers of the document cited above. For completeness, we note briefly the substance of those reports. In their summary "Spray Combustion Processes in Ramjet Combustion Instability," Bowman (Stanford), Law (University of California, Davis) and Sirignano (University of California, Irvine) review several aspects of spray combustion relevant to combustion instabilities. The objectives of the works were: (1) to determine the effect of spray characteristics on the energy release pattern in a dump combustor and the subsequent effects on combustion instability; (2) to gain a fundamental understanding of the coupling of the spray vaporization process with an unsteady flow field; and (3) to investigate methods for controlling and enhancing spray vaporization rates in liquid-fueled ramjets. During the past five years considerable progress has been made in applying methods of computational fluid dynamics to the flow in a dump combustor including consequences of energy release due to combustion processes. Jou has summarized work done at Flow Research, Inc. and at the Naval Research Laboratory in his paper "A Summary Report on Large-Eddy Simulations of Pressure Oscillations in a Ramjet Combustor." The serious effects of combustion instabilities on the inlets of ramjet engines were discovered in the late 1970's in experimental work at the Aeropropulsion Laboratory, Wright Field, the Naval Weapons Center and the Marquardt Company. The most thorough laboratory work on the unsteady behavior of inlets has been accomplished at the McDonnell-Douglas Research Laboratory by Sajben who has reviewed the subject in his paper "The Role of Inlet in Ramjet Pressure Oscillations.

Swinging and tumbling of elastic capsules in shear flow

The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules both with spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximative theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we could reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.Comment: 20 pages, 7 figure

Swinging and tumbling of elastic capsules in shear flow

The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules both with spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximative theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we could reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.Comment: 20 pages, 7 figure

A spectral/hp element DNS study of flow past low-pressure turbine cascades and the effects of inflow conditions

The combined rapid progress of hardware capability and the development of cutting-edge numerical methods have recently provided an opportunity for Computational Fluid Dynamics to be inserted in the design loop, with the role of a virtual wind tunnel. This thesis tackles the development of a validated incompressible Direct Numerical Simulation capability to model complex configurations of interest for the turbomachinery Industry, adopting for the first time the spectral/hp element methods implemented in the Nektar++ software framework. First, an extensive analysis of the numerical convergence properties is carried out on an open geometry with clean inflow boundary conditions, to establish a set of best practices and relate accuracy and computational cost. Subsequently, the effect of stochastic and deterministic unsteadiness is analysed in detail, with particular focus on various methodologies to provide physical disturbances, their computational cost and accuracy with respect to reference experimental data. The findings are extended to a range of Reynolds numbers representative of realistic operating conditions, with focus on traditional performance indicators but also unsteady statistics to provide rich insight into the suction surface transition mechanism, which plays a crucial role in the generation of profile losses. As a result, a detailed characterisation of the flow physics is provided in a range of inflow conditions and Reynolds numbers. Excellent agreement with high fidelity experimental data is achieved especially at moderate and high Reynolds numbers, supporting the use of these methodologies in Industry as a preliminary standalone investigation tool.Open Acces

Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

Experiment definition phase shuttle laboratory, LDRL-10.6 experiment. Shuttle sortie to ground receiver terminal

System development and technology are described for a carbon dioxide laser data transmitter capable of transmitting 400 Mbps over a shuttle to ground station link

Oscillatory and unsteady processes in liquid rocket engines

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