Numerical Simulation of Inviscid Flows

Hirsch, Charles

doi:10.1016/b978-075066594-0/50055-2

Cited by 140 publications

(216 citation statements)

References 11 publications

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“…Eqs. (16) and (17). It is readily seen that a truncated series with a sufficiently large number of terms provides a very good approximation to the exact solution.…”

Section: D Results For Various Ecological Conditionsmentioning

confidence: 91%

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Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Bearup

Petrovskaya

Petrovskii

2015

Mathematical Biosciences

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Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. Firstly, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called "activity-density" problem). Secondly, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth.

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“…Eqs. (16) and (17). It is readily seen that a truncated series with a sufficiently large number of terms provides a very good approximation to the exact solution.…”

Section: D Results For Various Ecological Conditionsmentioning

confidence: 91%

“…A finite difference discretization scheme is a method widely used for numerical solution of parabolic differential equations (e.g. see Hirsch 1992, Holmes 2006, Morton 1994, Smith 1985. The scheme defines the approximate solution u(x, t n+1 ) at each grid node x i of a uniform grid G from solving a system of linear algebraic equations…”

Section: Methodsmentioning

confidence: 99%

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Bearup

Petrovskaya

Petrovskii

2015

Mathematical Biosciences

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“…The fluid viscosity follows the Sutherland law and the species diffusion coefficients are obtained using a constant species Schmidt number and diffusion velocity corrections for mass conservation. A second-order finite element scheme is used for both time and space advancement [47,48]. The Sub-grid stress tensor is modeled by the classical Smagorinsky model [49].…”

Section: Les Solvermentioning

confidence: 99%

Bistable swirled flames and influence on flame transfer functions

Hermeth

Staffelbach

Gicquel

et al. 2014

Combustion and Flame

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Large Eddy Simulations (LES) are used to study a lean swirl-stabilized gas turbine burner where the flow exhibits two stable states. In the first one, the flame is attached to the central bluff body upstream of the central recirculation zone which contains burnt gases. In the second one the flame is detached from the central bluff body downecirculation zone which is filled by cold unburnt gases and dominated by a strong Precessing Vortex Core (PVC). The existence of these two states has an important effect on the dynamic response of the flame (FTF): both gain and phase of the FTF change significantly in the detached case compared to the attached one, suggesting that the stability of the machine to thermoacoustic oscillations will differ, depending on the flame state. Bifurcation diagrams show that the detached flame cannot be brought back to an attached position with an increased fuel flow rate, but it can be re-attached by forcing it at high amplitudes. The attached flame however, behaves inversely: it can be brought back to the detached position by both decreasing or increasing the pilot mass flow rate, but it remains attached at all forcing amplitudes. IntroductionSwirling flows are commonly used to help flame stabilization in gas turbine combustion chambers. They feature several types of vortex breakdown and can exhibit bifurcation phenomena where different states can co-exist and the flow can jump spontaneously from one to another [1,2]. Bifurcations of flames in configurations which are close to real gas turbine chambers have not been investigated so far even though engineers report that they observe these mechanisms and that there is a link between flame states and thermoacoustic instabilities: when the flame changes from one state to another, its acoustic stability characteristics also change.Two dynamic phenomena are usually observed in swirled combustion chambers: (1) a helical flow instability, the so-called precessing vortex core (PVC) and (2) thermo-acoustic instabilites.The PVC is an hydrodynamic instability in swirling flows [3].I t is a large scale structure characterized by a regular rotation of a spiral structure around the geometrical axis of the combustion chamber. It can occur at high Reynolds and swirl number flows [4][5][6][7][8][9][10] and its precession frequency is controlled by the rotation rate of the swirled flow [3]. Several studies show that combustion can suppress the PVC [6,7,11], but other cases also show PVCs which are present in reacting flows [12][13][14][15]. The interaction of PVC with flames has been analyzed for example by Stöhr et al.[16]: they found the PVC to enhance mixing and to increase the flame surface. This was associated to structures in the inner shear layer, whereas Moeck et al. [15] observed the outer shear layer to create most of the flame perturbations. Both researchers as well as Staffelbach [13] using LES evidenced a ''finger-like'' rotating structure at the flame foot around which the PVC is turning. Furthermore, asymmetric fluctuations of the he...

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“…To determine the boundary conditions, characteristic-based Riemann invariants [72] are used. In this approach, based on the direction of the velocity vector and the sonic velocity, the corresponding Riemann invariants are extrapolated either from the interior or from the free-stream.…”

Section: Far-field Boundary Conditionmentioning

confidence: 99%

Computational Investigation of Microscale Coaxial-Rotor Aerodynamics in Hover

Lakshminarayan

Baeder

2010

Journal of Aircraft

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In this work, a compressible Reynolds-Averaged Navier Stokes (RANS) solver is extended to investigate the aerodynamics of a micro-scale coaxial rotor configuration in hover. This required the following modifications to the solver: implementation of a time-accurate low Mach preconditioner, implementation of a sliding mesh interface boundary condition, improvements in the grid connectivity and parallelization of the code.First, an extensive validation study on the prediction capability of the solver is performed on a hovering micro-scale single rotor, for which performance data and wake characteristics have been measured experimentally. The thrust and power are reasonably well predicted for different leading and trailing geometries.Blunt leading edge geometries show poorer performance compared to the sharp leading edge geometries; the simulations show that this is mainly because of the large pressure drag acting at the blunt front. The tip vortex trajectory and velocity profiles are also well captured. The predicted swirl velocities in the wake for the micro-rotor are found to be significantly larger as compared to those for a full-scale rotor, which could be one of the reasons for additional power loss in the smaller scale rotors. The use of twist and taper is studied computationally and is seen to improve the performance of micro-rotor blades.Next, the solver is applied to simulate the aerodynamics of a full-scale coaxial rotor configuration in hover, for which performance data is available from experiments. The global quantities such as thrust and power are predicted reasonably well. In the torque trimmed situation, the top rotor shares significant percentage of the total thrust at lower thrust levels, which decreases to about 55% of the total thrust at higher thrust values. The simulations reveal that the interaction between the rotor systems is seen to generate significant impulses in the instantaneous thrust and power. The characteristic signature of this impulse is explained in terms of the blade thickness effect and loading effect, as well as blade-vortex interactions for the bottom rotor (wake effect).Finally, the RANS solver is applied to investigate the aerodynamics of a micro-scale coaxial rotor configuration in hover. The overall performance is well predicted. The interaction between the rotor systems is again seen to generate 3-8% fluctuation in the instantaneous thrust and power. The wake effect in the simulation is seen to be very prominent and the phasing of the impingement of the tip vortex from the top rotor upon the bottom rotor plays a significant role in the amount of unsteadiness on the bottom rotor. Interaction of the top rotor vortex and inboard sheet with the bottom rotor results in significant shedding on the bottom rotor blade, and this is believed to be caused by the of sharp leading edge geometry. Significant blade-vortex and vortex-vortex interactions are observed for coaxial systems.

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Numerical Simulation of Inviscid Flows

Cited by 140 publications

References 11 publications

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration

Bistable swirled flames and influence on flame transfer functions

Computational Investigation of Microscale Coaxial-Rotor Aerodynamics in Hover

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