Fluid Dynamic Instabilities Research Articles

Multiscale coupling and multiphysics approaches in earth sciences: Applications

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtoseconds to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth’s core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth’s surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults. A particular interesting case is discussed in detail, where out of the fluid dynamic solution, ductile compaction bands appear which are akin and can be confused with their brittle siblings. The main difference is that they require the factor time and also a much lower driving forces to emerge. These low stress solutions cannot be obtained on short laboratory time scales and they are therefore much more likely to appear in nature than in the laboratory. We finish with a multiscale description of a seminal structure in the Swiss Alps, the Glarus thrust, which puzzled geologists for more than 100 years. Along the Glarus thrust, a km-scale package of rocks (nappe) has been pushed 40 km over its footwall as a solid rock body. The thrust itself is a m-wide ductile shear zone, while in turn the centre of the thrust shows a mm-cm wide central slip zone experiencing periodic extreme deformation akin to a stick-slip event. The m-wide creeping zone is consistent with the THM feedback length scale of solid mechanics, while the ultralocalised central slip zones is most likely a fluid dynamic instability.

The problem of clear air turbulence: Changing perspectives in the understanding of the phenomenon

Due to rapid improvements in on-board instrumentation and atmospheric observation systems, in most cases, aircraft are able to steer clear of regions of adverse weather. However, they still encounter unexpected bumpy flight conditions in regions away from storms and clouds. This is the phenomenon of clear air turbulence (CAT), which has been a challenge to our understanding as well as efforts at prediction. While most of such cases result in mild discomfort, a few cases can be violent leading to serious injuries to passengers and damage to the aircraft. The underlying physical mechanisms have been sought to be explained in terms of fluid dynamic instabilities and waves in the atmosphere. The main mechanisms which have been proposed are: (i) Kelvin–Helmholtz instability of shear layers, (ii) waves generated from flow over mountains, (iii) inertia-gravity waves from clouds and other sources, (iv) spontaneous imbalance theory and (v) horizontal vortex tubes. This has also undergone a change over the years. We present an overview of the mechanisms proposed and their implications for prediction.

Effect of Throttle Conditions on Fluid Dynamic Instabilities in Axial Compression Systems

An analysis of the effect of throttling on surge and rotating stall has been done to develop an insight on the possible behaviour of instabilities in a compression system subsequent to an initial disturbance. The ability to predict the nature of instabilities are highly important from the compressor design point of view since their consequences could result in widely varying difficulties with the fluid dynamic performance of the systems. The present paper discusses, in an approximate manner, the effect of throttle position in a compressor performance curve which is shown to create widely varying behaviour on fluid dynamic instabilities once the stall line is crossed. The physical reason for the behaviour is explained and the well-established Moore–Greitzer compression system model have been used for the present study. The results shown in this paper clearly elucidates the dominating effect of the operating parameter, the throttle, on the development of flow instabilities like rotating stall and surge. The trends of their behaviour reported in this paper are found to have a good agreement with the experimental results. As these results inform about the nature of instabilities that one could expect as the stall line is crossed, appropriate preventive measures could be adopted to avoid/control such instabilities.

Three-dimensional flow dynamics of an argon RF plasma with dc jet assistance: a numerical study

Time-dependent three-dimensional numerical simulation based on a large-eddy simulation approach is conducted to ascertain the complicated thermofluid dynamics of an argon radio-frequency (RF) inductively coupled plasma with a direct-current (dc) plasma jet assistance, considering non-uniform densities and properties in time and space as well as turbulence generation and suppression. Using a combination of numerical schemes suitable to capture vortices, the present simulation successfully shows unsteady behaviour of the plasma as well as wave-like interfaces between a high-temperature flow and a low-temperature flow as a result of the balance of fluid-dynamical instability and a viscous diffusion effect. Small cold vortices generated near a dc jet injector are entrained into and merged with vortices generated around the dc jet. Subsequently, they interact with large vortices in an RF induction coil region, which causes a much more complex vortex structure.

A Numerical Investigation of Rotating Instability in Steam Turbine Last Stage

The unsteady flow phenomenon (identified as rotating instability) in the last stage of a low-pressure model steam turbine operated at very low mass flow conditions is numerically studied. This kind of instability has been observed previously in compressors and can be linked to the high structural stress levels associated with flow-induced blade vibrations. The overall objective of the study is to enhance the understanding of the rotating instability in steam turbines at off design conditions. A numerical analysis using a validated unsteady nonlinear time-domain CFD solver is performed. The 3D solution captures the massively separated flow structure in the rotor-exhaust region and the pressure ratio characteristics around the rotor tip of the test model turbine stage in good comparison with the experiment. A computational study with a multi-passage whole annulus domain on two different 2D blade sections is subsequently carried out. The computational results clearly show that a rotating instability in a turbine blading configuration can be captured by the 2D model. The frequency and spatial modal characteristics are analyzed. The simulations seem to be able to predict a rotating fluid dynamic instability with the similar characteristic features to those of the experiment. In contrast to many previous observations, the results for the present configurations suggest that the onset and development of rotating instabilities can occur without 3D and tip-leakage flows, although a quantitative comparison with the experimental data can only be expected to be possible with fully 3D unsteady solutions.

Three-dimensional instabilities in tornado-like vortices with secondary circulations

AbstractTornadoes and other intense atmospheric vortices are known to occasionally transition to a flow structure with multiple vortices within their larger circulations. This phenomenon has long been ascribed to fluid dynamical instability of the inner-core circulation, and many previous studies have diagnosed low-wavenumber unstable modes in tornado-like vortices that resemble the observed structures. However, relatively few of these studies have incorporated the strong vertical motions of the inner-core circulation into the stability analysis, and no stability analyses have been performed using a complete, frictionally driven secondary circulation with strong radial inflow near the surface. Stability analyses are presented using the complete circulations generated from idealized simulations of tornado-like vortices. Fast-growing unstable modes are found that are consistent with the asymmetric structures present in these simulations. Attempts to correlate the structures and locations of these modes with instability conditions for vortices with axial jets derived by Howard & Gupta and by Leibovich & Stewartson produce only mixed results. Analyses of perturbation energy growth show that interactions between eddy fluxes and the radial shear of the azimuthal wind contribute very little to the growth of the dominant modes. Rather, the radial shear of the vertical wind and the vertical shear of the vertical wind (corresponding to deformation in the axial direction) are the primary energy sources for perturbation growth. Relatively weak axisymmetric instabilities are also identified that have some similarity to symmetric oscillations that have been observed in tornadoes.

Irradiated interfaces in the Ara OB1, Carina, Eagle Nebula, and Cyg OB2 massive star formation regions

Regions of massive star formation offer some of the best and most easily-observed examples of radiation hydrodynamics. Boundaries where fully-ionized H II regions transition to neutral/molecular photodissociation regions (PDRs) are of particular interest because marked temperature and density contrasts across the boundaries lead to evaporative flows and fluid dynamical instabilities that can evolve into spectacular pillar-like structures. When detached from their parent clouds, pillars become ionized globules that often harbor one or more young stars. H2 molecules at the interface between a PDR and an H II region absorb ultraviolet light from massive stars, and the resulting fluoresced infrared emission lines are an ideal way to trace this boundary independent of obscuring dust. This paper presents H2 images of four regions of massive star formation that illustrate different types of PDR boundaries. The Ara OB1 star formation region contains a striking long wall that has several wavy structures which are present in H2, but the emission is not particularly bright because the ambient UV fluxes are relatively low. In contrast, the Carina star formation region shows strong H2 fluorescence both along curved walls and at the edges of spectacular pillars that in some cases have become detached from their parent clouds. The less-spectacular but more well-known Eagle Nebula has two regions that have strong fluorescence in addition to its pillars. While somewhat older than the other regions, Cyg OB2 has the highest number of massive stars of the regions surveyed and contains many isolated, fluoresced globules that have head–tail morphologies which point towards the sources of ionizing radiation. These images provide a collection of potential astrophysical analogs that may relate to ablated interfaces observed in laser experiments of radiation hydrodynamics.

A Parametric Investigation of Geometric Variation on Fluid Dynamic Instabilities in Axial Compression Systems

The ability to predict the nature of instabilities is highly important from the compressor design point of view since their consequences could result in widely varying difficulties with the fluid dynamic performance of the systems. Even though the behavior of surge and rotating stall is reported in many literatures, it is noticed that an in-depth analysis is not undertaken. Hence in view of the importance for a deeper understanding, the present paper is aimed at tracking the chaos of these instabilities in a more detailed manner. Primarily the influence of geometric parameters on the nature of surge and rotating stall is investigated. The effect of each of the major geometric parameters such as compressor effective length, annulus area, and plenum volume is discussed. The physical reason for the onset of instabilities is also explained in each case, and the well-accepted Moore-Greitzer model has been used for the present study. The combined effect of physical parameters is determined through the Greitzer <svg style="vertical-align:-0.0pt;width:10.6125px;" id="M1" height="11.175" version="1.1" viewBox="0 0 10.6125 11.175" width="10.6125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x1D435" d="M594 511q0 -122 -171 -157l1 -2q158 -33 158 -159q0 -52 -34.5 -95t-90.5 -65q-76 -33 -217 -33h-223l8 28q63 5 79.5 19t26.5 72l83 426q9 48 -2.5 60t-77.5 17l6 28h259q195 0 195 -139zM499 509q0 59 -37 83t-91 24q-36 0 -51 -9q-17 -9 -22 -44l-35 -195h62&#xA;q82 0 128 37t46 104zM481 199q0 71 -48 102.5t-121 31.5h-56l-37 -201q-11 -58 7.5 -77t80.5 -19q76 0 125 44.5t49 118.5z" /></g> </svg> parameter. The results shown in this paper clearly elucidate the dominating effect of the geometric parameters on the development of flow instabilities like rotating stall and surge and hence can serve as a design guideline to avoid such instabilities.

Torch Design Modification Using Micro-jets to Suppress Fluid Dynamic Instabilities in Plasma Arc Cutting

Highly constricted plasma arcs are widely used for metal cutting. One important characteristic of the cutting process is the consistency of the cut edge around the perimeter of the workpiece. Cut edge properties, including surface roughness, edge shape and dross formation, are presumed to depend on the local temperature and chemical composition of the cutting arc adjacent to the cut edge. Fluid dynamic instabilities in the arc boundary leading to entrainment of the low temperature ambient gas can have a strong effect on cutting performance. This paper describes the use of micro-jets to suppress fluid dynamic instabilities in the boundary layer of a plasma cutting arc. Previously developed optical diagnostics and analysis methods are used to characterize the arc boundary layer. Multiple nozzle designs have been investigated to quantify the effects of utilizing micro-jet flow around the arc column, and some relationships between nozzle design and cut quality are presented.

Baroclinic Turbulence with Varying Density and Temperature

The explosive or volcanic scenes in motion pictures involve complex turbulent flow as its temperature and density vary in space. To simulate this turbulent flow of an inhomogeneous fluid, we propose a simple and efficient framework. Instead of explicitly computing the complex motion of this fluid dynamical instability, we first approximate the average motion of the fluid. Then, the high-resolution dynamics is computed using our new extended version of the vortex particle method with baroclinity. This baroclinity term makes turbulent effects by generating new vortex particles according to temperature/density distributions. Using our method, we efficiently simulated a complex scene with varying density and temperature.

Improvement of IFMIF/EVEDA bayonet concept back-plate design

In the frame of the Engineering Validation and Engineering Design Activities (EVEDA) phase of the International Fusion Materials Irradiation Facility (IFMIF) project, a supporting lithium loop has been designed and is currently under construction at Oarai (Japan) with the main objective to test several technological solutions to be adopted in the future IFMIF plant. Among these, the lithium target system represents one of the most critical components as it will be exposed to high-energy intense neutron flux and consequently to severe irradiation damage rates (up to 60 dpa/fpy). For this reason, it must be designed for periodic replacement. The solution proposed by ENEA is based on the so-called back-plate bayonet concept which consists of a replaceable element that can be inserted to and removed from the permanent structure of the target assembly by means of a sliding-skate mechanism. Recently, the design of the bayonet back-plate has been revised and some important modifications have been introduced in order to improve its functionality and optimize its features in terms of compactness, robustness and remote maintainability. Several design solutions have been conceived to achieve better performance including smaller overall dimensions, sealing load reduction, gasket retention system improvement, positioning and centering effectiveness and optimized detachment mechanism. Moreover, a new variable-curvature geometry for the lithium channel profile has been calculated using an analytic approach based on the simplified Navier–Stokes equations in order to avoid the fluid dynamic instabilities evidenced in the old profile. In this paper, the new design features of the back-plate are presented, along with the main outcomes obtained from the engineering assessment performed so far.

Porosity‐driven convection and asymmetry beneath mid‐ocean ridges

Seismic tomography of the asthenosphere beneath mid‐ocean ridges has produced images of wave speed and anisotropy that are asymmetric across the ridge axis. These features have been interpreted as resulting from an asymmetric distribution of upwelling and melting. Using computational models of coupled magma/mantle dynamics beneath mid‐ocean ridges, I show that such asymmetry should be expected if buoyancy forces contribute to mantle upwelling beneath ridges. The sole source of buoyancy considered here is the dynamic retention of less dense magma within the pores of the mantle matrix. Through a scaling analysis and comparison with a suite of simulations, I derive a quantitative prediction of the contribution of such buoyancy to upwelling; this prediction of convective vigor is based on parameters that, for the Earth, can be constrained through natural observations and experiments. I show how the width of the melting region and the crustal thickness, as well as the susceptibility to asymmetric upwelling, are related to convective vigor. I consider three causes of symmetry breaking: gradients in mantle potential temperature and composition and ridge migration. I also report that in numerical experiments performed for this study, the fluid dynamical instability associated with porosity/shear band formation is not observed to occur.

High-brightness water-window electron-impact liquid-jet microfocus source

We demonstrate stable high-brightness operation of an electron-impact water-jet-anode soft x-ray source. A 30 kV, 7.8 W electron beam is focused onto a 20 μm diameter jet resulting in water-window oxygen line emission at 525 eV/2.36 nm with a brightness of 3.0×109 ph/(s×μm2×sr×line). Monte Carlo-based modeling shows good quantitative agreement with the experiments. The source has potential to increase the x-ray power and brightness by another 1–2 orders of magnitude and fluid-dynamical jet instabilities is determined to be the most important limiting factor. The source properties make it an attractive alternative for table-top x-ray microscopy.

Cellular burning in lean premixed turbulent hydrogen-air flames: Coupling experimental and computational analysis at the laboratory scale

One strategy for reducing US dependence on petroleum is to develop new combustion technologies for burning the fuel-lean mixtures of hydrogen or hydrogen-rich syngas fuels obtained from the gasification of coal and biomass. Fuel-flexible combustion systems based on lean premixed combustion have the potential for dramatically reducing pollutant emissions in transportation systems, heat and stationary power generation. However, lean premixed flames are highly susceptible to fluid-dynamical combustion instabilities making robust and reliable systems difficult to design. Low swirl burners are emerging as an important technology for meeting design requirements in terms of both reliability and emissions for next generation combustion devices. In this paper, we present simulations of a lean, premixed hydrogen flame stabilized on a laboratory-scale low swirl burner. The simulations use detailed chemistry and transport without incorporating explicit models for turbulence or turbulence/chemistry interaction. Here we discuss the overall structure of the flame and compare with experimental data. We also use the simulation data to elucidate the characteristics of the turbulent flame interaction and how this impacts the analysis of experimental measurements.

Interaction of turblence and chemistry in a low-swirl burner

New combustion systems based on ultra-lean premixed combustion have the potential for dramatically reducing pollutant emissions in transportation systems, heat, and stationary power generation. However, lean premixed flames are highly susceptible to fluid-dynamical combustion instabilities, making robust and reliable systems difficult to design. Low-swirl burners are emerging as an important technology for meeting design requirements in terms of both reliability and emissions for next-generation combustion devices. In this paper, we present simlations of a laboratory-scale low-swirl burner using detailed chemistry and transport without incorporating explicit models for turbulence or turbulence/chemistry interaction. We consider two fuels, methane and hydrogen, each at two turbulent intensities. Here we examine some of the basic properties of the flow field and the flame structure. We focus on the differences in flame behavior for the two fuels, particularly on the hydrogen flame, which burns with a cellular structures.

The Acoustic Resonance of Rectangular and Cylindrical Cavities

An investigation is conducted on the acoustic resonance that develops in rectangular and cylindrical cavities with rigid walls. An analytical model for the small amplitude acoustic perturbations inside an enclosure with rigid walls is developed from classical linerized acoustics. The method is first applied to a rectangular geometry and the normalized mode shapes and frequencies of the first six standing wave modes are given. The results are used to diagnose whether coupling is likely to occur between the first two Rossiter modes and the acoustic standing waves, which may lead to a reinforcement of the flow instability. At the selected test conditions, the method indicates that the second Rossiter mode can couple with the first longitudinal acoustic mode. The acoustic resonant mode predictions for a cylindrical cavity of length to depth ratios 0.71 and 2.5, tested at near-incompressible speeds, suggest that the acoustic resonant modes and the main fluid dynamic instability in the enclosure are sufficiently apart in frequency not to strongly interact with one another. The parametrized analytical solutions developed in this study enable the aero-acoustic engineer to diagnose whether coupling between a given fluid dynamic instability and acoustic resonance is likely to affect a rectangular or cylindrical cavity component.

Setup of a High-Speed Optical System for the Characterization of Flow Instabilities Generated by Cavitation

The present paper illustrates the setup and the preliminary results of an experimental investigation of cavitation flow instabilities carried out by means of a high-speed camera on a three-bladed inducer in the cavitating pump rotordynamic test facility (CPRTF) at Alta S.p.A. The brightness thresholding technique adopted for cavitation recognition is described and implemented in a semi-automatic algorithm. In order to test the capabilities of the algorithm, the mean frontal cavitating area has been computed under different operating conditions. The tip cavity length has also been evaluated as a function of time. Inlet pressure signal and video acquisitions have been synchronized in order to analyze possible cavitation fluid-dynamic instabilities both optically and by means of pressure fluctuation analysis. Fourier analysis showed the occurrence of a cavity length oscillation at a frequency of 14.7Hz, which corresponds to the frequency of the rotating stall instability detected by means of pressure oscillation analysis.

A mechanism for the local production of faculae

We offer a new viewpoint that can explain some of the recently obtained high-resolution observations of granules and faculae. Examining the data of Scharmer, Gudiksen, Kiselman et al. (2002) we observe many granules undergo an evolution that results in faculae emerging from within their boundaries, and moving towards and into intergranular lanes. These faculae have a characteristic hairpin substructure. The evolving morphology can be closely described by a fluid dynamic instability we call the “vortex/shear layer” (VSL) interaction. It occurs in all granules whose underlying structure has vorticity when they emerge into the photosphere through the sub-photospheric turbulent boundary layer (SPTBL). The VSL results in the creation of vortices from the distributed vorticity of the SPTBL. The subsequent stretching of these vortices results in high amplification of vorticity, and the concurrent high amplification of the background magnetic field. Magnetic field lines spiral around the vortices, as well as being stretched along their axis. Thus, the VSL is also the origin of a coherent local dynamo. The spiral sheathing of high magnetic flux results in a simple explanation for the “hot wall” effect. The VSL also creates the “dark lanes” observed by Lites, Scharmer, Berger et al. (2004) and groupings of bright hairpins/vortex sheet ensembles, which look like the ribbon faculae (Berger, Rouppe van der Voort, Lofdahl et al., 2004). The SPTBL results in emerging tilted granules, which when combined with the VSL create the three-dimensionality which Lites, Scharmer, Berger et al. (2004), also observed. Both the VSL and the SPTBL result, on average, in a west side bias of hairpin faculae and granular three-dimensionality.

Experimental investigation of fluid dynamic instability in a transonic cavity flow

The acoustic and fluid dynamic resonance in a two-dimensional cavity flow was investigated experimentally. In order to visualize a periodic oscillation of the shear layer and the behavior of vortices, the schlieren method was used with an ordinary CCD camera and a high-speed video camera. Particle image velocimetry (PIV) measurements were also carried out to obtain the vorticity distribution during the oscillation in the cavity flow. Shedding and interaction of vortices in the shear layer were observed near the trailing edge of the cavity, which causes the generation of pressure waves. The feedback process of the oscillation was determined using high-speed camera images. From these results, the x − t diagram for the oscillation cycle was obtained. Based on the flow visualization, for Rossiter’s constants, it was confirmed that the dominant acoustic mode was m = 2 and that K c = 0.5 in the present experiment. Also, the pressure level for mode m = 2 was the most intense for a wide range of flow Mach numbers. The results obtained by PIV measurement show that there is outgoing and incoming flow near the trailing edge of the cavity. It was found that a very strong change of vorticity associated with the detachment and attachment of boundary layer was induced on the trailing edge due to the fluid dynamical instability.

A Mechanism for the Local Production of Faculae

We offer a new viewpoint that can explain some of the recently obtained high-resolution observations of granules and faculae. Examining the data of Scharmer, Gudiksen, Kiselman et al. (2002) we observe many granules undergo an evolution that results in faculae emerging from within their boundaries, and moving towards and into intergranular lanes. These faculae have a characteristic hairpin substructure. The evolving morphology can be closely described by a fluid dynamic instability we call the “vortex/shear layer” (VSL) interaction. It occurs in all granules whose underlying structure has vorticity when they emerge into the photosphere through the sub-photospheric turbulent boundary layer (SPTBL). The VSL results in the creation of vortices from the distributed vorticity of the SPTBL. The subsequent stretching of these vortices results in high amplification of vorticity, and the concurrent high amplification of the background magnetic field. Magnetic field lines spiral around the vortices, as well as being stretched along their axis. Thus, the VSL is also the origin of a coherent local dynamo. The spiral sheathing of high magnetic flux results in a simple explanation for the “hot wall” effect. The VSL also creates the “dark lanes” observed by Lites, Scharmer, Berger et al. (2004) and groupings of bright hairpins/vortex sheet ensembles, which look like the ribbon faculae (Berger, Rouppe van der Voort, Lofdahl et al., 2004). The SPTBL results in emerging tilted granules, which when combined with the VSL create the three-dimensionality which Lites, Scharmer, Berger et al. (2004), also observed. Both the VSL and the SPTBL result, on average, in a west side bias of hairpin faculae and granular three-dimensionality.