Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

Instability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.

Tranversal motion and flow structure of fully nonlinear streaks in a laminar boundary layer

Typical streak computations present in the literature correspond to linear streaks or to small amplitude nonlinear streaks computed using DNS or nonlinear PSE. We use the Reduced Navier-Stokes (RNS) equations to compute the streamwise evolution of fully non-linear streaks with high amplitude in a laminar flat plate boundary layer. The RNS formulation provides Reynolds number independent solutions that are asymptotically exact in the limit $Re \gg 1$, it requires much less computational effort than DNS, and it does not have the consistency and convergence problems of the PSE. We present various streak computations to show that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, that end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results.

Linear instability of orthogonal compressible leading-edge boundary layer flow

Instability analysis of compressible orthogonal swept leading-edge boundary layer flow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to efficiently analyze the effect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this flow as a function of the Mach number in the range 0 ≤ Ma ≤ 1. The present numerical results fully confirmed the asymptotic theory results of Theofilis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.

Fluid-physics-module experiments

Some floating-liquid-zone experiments performed under reduced-gravity conditions are reviewed. Several types of instabilities are discussed, together with the relevant parameters controlling them. It is shown that the bounding values of these parameters could be increased, by orders of magnitude in several instances, by selecting appropriate liquids. Two of the many problems that a Fluid-Physics Module, devised to perform experiments on floating zones in a space laboratory, would involve are discussed: namely (i) procedures for disturbing the zoneunder controlled conditions, and (ii) visualisation of the inner flow pattern. Several topics connected with the nonisothermal nature and the phase-changes of floating zones are presented. In particular, a mode of propagation through the liquid zone for disturbances which could appear in the melting solid/liquid interface is suggested. Although most research on floating liquid zones is aimed at improving the crystal-growth process, some additional applications are suggested.

Reduced order modeling of some fluid flows of industrial interest

Some basic ideas are presented for the construction of robust, computationally efficient reduced order models amenable to be used in industrial environments, combined with somewhat rough computational fluid dynamics solvers. These ideas result from a critical review of the basic principles of proper orthogonal decomposition-based reduced order modeling of both steady and unsteady fluid flows. In particular, the extent to which some artifacts of the computational fluid dynamics solvers can be ignored is addressed, which opens up the possibility of obtaining quite flexible reduced order models. The methods are illustrated with the steady aerodynamic flow around a horizontal tail plane of a commercial aircraft in transonic conditions, and the unsteady lid-driven cavity problem. In both cases, the approximations are fairly good, thus reducing the computational cost by a significant factor.

Low-dimensional modeling of streaks in a wedge flow boundary layer

This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

Choked flow in water/CO2 solutions on air-independent propulsion systems

We develop a simplified model of choked flow in pipes for CO2-water solutions as an important step in the modelling of a whole hydraulic system with the intention of eliminating the carbon dioxide generated in air-independent submarine propulsion. The model is based on an approximate fitting of the homogeneous isentropic solution upstream of a valve (or any other area restriction), for given fluid conditions at the entrance. The relative maximum choking back-pressure is computed as a function of area restriction ratio. Although the procedure is generic for gas solutions, numeric values for the non-dimensional parameters in the analysis are developed only for choking in the case of carbon dioxide solutions up to the pure-water limit.

Comparison of turbulence models for the computational fluid dynamics simulation of wind turbine wakes in the atmospheric boundary layer

An elliptic computational fluid dynamics wake model based on the actuator disk concept is used to simulate a wind turbine, approximated by a disk upon which a distribution of forces, defined as axial momentum sources, is applied on an incoming non-uniform shear flow. The rotor is supposed to be uniformly loaded with the exerted forces estimated as a function of the incident wind speed, thrust coefficient and rotor diameter. The model is assessed in terms of wind speed deficit and added turbulence intensity for different turbulence models and is validated from experimental measurements of the Sexbierum wind turbine experiment.

Comparing linear and non linear wind flow models

Assessing wind conditions on complex terrain has become a hard task as terrain complexity increases. That is why there is a need to extrapolate in a reliable manner some wind parameters that determine wind farms viability such as annual average wind speed at all hub heights as well as turbulence intensities. The development of these tasks began in the early 90´s with the widely used linear model WAsP and WAsP Engineering especially designed for simple terrain with remarkable results on them but not so good on complex orographies. Simultaneously non-linearized Navier Stokes solvers have been rapidly developed in the last decade through CFD (Computational Fluid Dynamics) codes allowing simulating atmospheric boundary layer flows over steep complex terrain more accurately reducing uncertainties. This paper describes the features of these models by validating them through meteorological masts installed in a highly complex terrain. The study compares the results of the mentioned models in terms of wind speed and turbulence intensity.

The B.I.E.M. applied to flow through porous media

This paper refers to the numerical solution of the classical Darcy's problem of plane fluid through isotropic media. Regarding the numerical procedure,the Laplace equation, is a classical one in mathematical physics and several procedures have been devised in order to solve it. So as to show the capability of the method, the paper presents some exemples.

Comparison of particle dispersion obtained with simple stochastic models and les in pipe flow

A hybrid Eulerian-Lagrangian approach is employed to simulate heavy particle dispersion in turbulent pipe flow. The mean flow is provided by the Eulerian simulations developed by mean of JetCode, whereas the fluid fluctuations seen by particles are prescribed by a stochastic differential equation based on normalized Langevin. The statistics of particle velocity are compared to LES data which contain detailed statistics of velocity for particles with diameter equal to 20.4 µm. The model is in good agreement with the LES data for axial mean velocity whereas rms of axial and radial velocities should be adjusted.

Multi-fluid Eulerian model of an electrospray in a host gas.

An Eulerian multifluid model is used to describe the evolution of an electrospray plume and the flow induced in the surrounding gas by the drag of the electrically charged spray droplets in the space between an injection electrode containing the electrospray source and a collector electrode. The spray is driven by the voltage applied between the two electrodes. Numerical computations and order-of-magnitude estimates for a quiescent gas show that the droplets begin to fly back toward the injection electrode at a certain critical value of the flux of droplets in the spray, which depends very much on the electrical conditions at the injection electrode. As the flux is increased toward its critical value, the electric field induced by the charge of the droplets partially balances the field due to the applied voltage in the vicinity of the injection electrode, leading to a spray that rapidly broadens at a distance from its origin of the order of the stopping distance at which the droplets lose their initial momentum and the effect of their inertia becomes negligible. The axial component of the electric field first changes sign in this region, causing the fly back. The flow induced in the gas significantly changes this picture in the conditions of typical experiments. A gas plume is induced by the drag of the droplets whose entrainment makes the radius of the spray away from the injection electrode smaller than in a quiescent gas, and convects the droplets across the region of negative axial electric field that appears around the origin of the spray when the flux of droplets is increased. This suppresses fly back and allows much higher fluxes to be reached than are possible in a quiescent gas. The limit of large droplet-to-gas mass ratio is discussed. Migration of satellite droplets to the shroud of the spray is reproduced by the Eulerian model, but this process is also affected by the motion of the gas. The gas flow preferentially pushes satellite droplets from the shroud to the core of the spray when the effect of the inertia of the droplets becomes negligible, and thus opposes the well-established electrostatic/inertial mechanism of segregation and may end up concentrating satellite droplets in an intermediate radial region of the spray.

Molecular Dynamics Simulations of Couette flow

The first steps towards developing a continuum-molecular coupled simulations techniques are presented, for the purpose of computing macroscopic systems of confined fluids. The idea is to compute the interface wall-fluid by Molecular Dynamics simulations, where Lennard-Jones potential (and others) have been employed for the molecular interactions, so the usual non slip boundary condition is not specified. Instead, a shear rate can be imposed at the wall, which allows to obtain the properties of the wall material by means of an iterative method. The remaining fluid region will be computed by a spectral hp method. We present MD simulations of a Couette flow, and the results of the developed boundary conditions from the wall fluid interaction.

Spatial linear global instability analysis of the HIFiRE-5 elliptic cone model flow

The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented