A numerical study of rotating annulus flows using a modified Galerkin method

Seasonally averaged 200-mb circulations for recent winters (1987/88 and 1988/89) that represent opposite phases of El Nino and a zonal-mean zonal flow index cycle are diagnosed using data assimilated by the Goddard Earth Observing System (GEOS) and operational analyses of the European Centre for Medium-Range Weather Forecasts (ECMWF). The comparison is undertaken to determine whether there are significant differences in the 200-mb vorticity dynamics implied by the mean meridional circulations in the two datasets and whether these differences can be related to the Incremental Analysis Update (IAU) method used in the GEOS assimilation. The two datasets show a high degree of similarity in their depictions of the large-scale rotational flow, but there are substantial differences in the associated divergent circulations. For the zonal-mean flow, the zonal winds are substantially the same, but the meridional wind in the Tropics and subtropics is considerably weaker in the GEOS assimilation than its counterparts in both the ECMWF data and the GEOS analyses used to produce the assimilation. The authors examine the assimilation of the Hadley circulation using a zonally symmetric f-plane model. For this model, the IAU method easily assimilates the rotational flow but fails to assimilate the divergent circulation. This deficiency of the IAU method may explain the weakness of the Hadley cell in the GEOS assimilation, at least in relation to the GEOS analysis. For this simple model, an alternative assimilation method, based on constraints imposed by the analyzed potential vorticity and mean meridional circulation fields, is proposed that simultaneously assimilates both rotational and divergent flow components. Barotropic modeling suggests that an accurate representation of mean meridional flow anomalies can be important for the diagnosis of both zonal-mean and eddy rotational flow perturbations, particularly during extreme phases of the zonal-mean zonal flow fluctuation.

The flow in an enclosed completely filled rapidly rotating cylinder that is driven by the differential corotation of the top lid is studied numerically. Although the flow is in a very simple geometry, the fast background rotation and large differential rotation of the lid lead to very thin boundary layers with a variety of instability modes with very fine spatial scales as well as inertial waves that are sustained in the fast rotating interior flow and that interact with the viscous modes in the sidewall boundary layer, leading to complex spatiotemporal dynamics. The numerical simulations are compared and contrasted to experimental visualizations of the sidewall boundary layer instabilities reported by Hart and Kittelman [“Instabilities of the sidewall boundary layer in a differentially driven rotating cylinder,” Phys. Fluids 8, 692 (1996)]. The experiments report observing axisymmetric rolls propagating down the sidewall layer for small differential corotation of the top lid. As the differential rotation was increased, backward tilted diagonal rolls that precess slightly retrograde with respect to the rotating sidewall and forward tilted rolls with prograde precession significantly faster than the sidewall rotation were observed. For still larger differential rotation, a wavy turbulent state that has backward tilted structures erupting from deep within the sidewall layer into the interior and is riding on the forward tilted diagonal rolls in the deep layer was observed. Our simulations capture all of these states and strongly suggest that the observed axisymmetric rolls are unstable and were only transiently observed due to the slow and continuous increase in the differential rotation employed in the experiments. The influence of inertial waves driven by the sidewall instabilities on the three-dimensional wavy turbulent state is discussed.

A horizontal turbulent boundary layer of air carrying heavy solid particles is investigated experimentally. Mean and r.m.s. velocities of air and particles are measured by LDA, and particle mass flux distributions are obtained by means of a sampling method. The influence of the saltation mechanism is revealed by the large particle r.m.s. velocity in the near-wall region, and by the velocity lag of the particles in the outer region of the boundary layer, which is shown to be closely related to their free fall velocity. The present original results are discussed and compared with available experimental data concerning other kinds of horizontal flows.

The ocean interacts with the atmosphere, ice, and the solid earth, and the properties transferred across these boundaries are moved and mixed in the ocean interior by a variety of processes.  Some of these processes have been known for just a few decades and act in curious and surprising ways which are difficult to understand. The lecture will outline the thermodynamic theory and the mixing processes which underpin our oceanographic practices, concentrating on some counter-intuitive examples.  For example, thermodynamic reasoning has recently led to clear but initially surprising interpretations of the temperature and salinity variables that are carried by our ocean and climate models. The observed bottom intensification of diapycnal mixing in the abyssal ocean implies that the diapycnal velocity in the ocean interior is downwards towards denser water, and it follows that the upwelling occurs in thin bottom boundary layers.  The use of simple buoyancy budgets shows that the upwards diapycnal transport in these thin boundary layers is twice or even three times the formation rate of Antarctic Bottom Water. 

Direct numerical simulation of turbulent free-surface high Prandtl number fluid flows in fusion reactors

Effects of mussel filtering activity on boundary layer structure

Four months of eddy correlation data collected over a grass field and a nearby sage brush community are analyzed to examine the adjustment of the boundary-layer structure as it flows from the heated brush to the snow-covered grass. The grass site includes a 34-m tower with seven levels of eddy correlation data. The midday heat flux over the snow-covered grass and bare ground surfaces is often downward particularly with melting conditions, while the corresponding heat flux over the brush is almost always upward. For most of these cases, a stable internal boundary layer over the snow is well defined in terms of vertical profiles of the buoyancy flux over the snow-covered grass. The stable internal boundary layer is generally embedded within a deeper layer of flux divergence corresponding to increasing upward heat flux with height above the internal boundary layer. With thin snow cover, the surface heat flux over the grass is weak upward due to heating of grass protruding above the snow so that the flow adjusts to a decrease of the upward surface heat flux in the downwind direction. This common case of an adjusting boundary layer contrasts with the formation of an internal boundary layer due to a change of sign of the surface heat in flux the downwind direction. The adjustment of the boundary layer to the decrease of the surface heat flux leads to vertical divergence of the upward heat flux in contrast to the usual heated boundary layer over homogeneous surfaces. The consequences of the cooling due to the vertical divergence of the heat flux are discussed in terms of the heat budget of the adjusting and internal boundary layers.

Best et al. (2004) propose a generic interface between land surface and atmospheric models, suitable for many existing GCMs and present modeling configurations, in order to facilitate modeling studies of the land–atmosphere exchange. As the authors state, a general interface would make model intercomparison (and therefore validation) easier and would allow differences between the simulated climates of different land– atmosphere coupled systems to be identified with specific modeling attributes or parameters. We propose a small modification to the generic interface that makes it more general in terms of the handling of the interaction between the atmosphere and a heterogeneous land surface. Best et al. (2004) state in their introduction that the tiles in a mosaic scheme can be coupled to a single, homogenized boundary layer because “[t]he idea is that the internal boundary layers from subsurfaces have merged at or below the bottom model level.” The authors themselves acknowledge that the assumption that the internal boundary layers have merged below the lowest model level may not be valid. The modification to the generic interface that we propose here would accommodate a model that does not make any specific assumption about the level of the blending height relative to the lowest model level. The importance of the suggested change in the generic interface is related to recent modeling and observational studies, summarized below, which suggest both that the blending height may be elevated in some regions (at 500 m or higher) and that model simulations are improved when the lowest model level is at 250 m (or less) above the ground. In addition, the choice of blending height in a model has been shown by Molod et al. (2004) to affect the simulated climate. Authors of modeling studies have considered the issue of an elevated blending height since the early discussion of mosaic techniques to model the interaction between a heterogeneous land surface and the atmosphere. Koster and Suarez (1992) first raised the issue that their assumption of a blended lowest layer may not be adequate, based on the scaling arguments that link the blending height and the horizontal scale of heterogeneity. Bringfelt (1999) also state that a mosaic assumes that the blending height is at the surface layer and that this might not be an adequate representation of the impact of surface heterogeneity. In addition, Arola (1999) introduced a technique designed to raise the level of the blending height in the model as an attempt to improve this drawback of the standard mosaic approach. The existence of organized mesoscale circulations, suggested by the modeling study of Avissar and Schmidt (1998), also raises the issue of whether the internal boundary layers have blended below some near-surface layer. The observational studies that suggest that the blending height may be elevated include Segal et al. (1989) in which patch-to-patch differences in temperature and moisture over an irrigated and a dry crop area were reported throughout much of the planetary boundary layer. An elevated blending height is also suggested by the lidar study reported in Angevine et al. (2003) and Banta and White (2003), where subCorresponding author address: Dr. Andrea Molod, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139. E-mail: amolod@mit.edu AUGUST 2006 N O T E S A N D C O R R E S P O N D E N C E 833

An incompressible fluid fills a container of fixed shape and size and of uniform cross-section in the (x, y)-plane, themrigid side walls and the two rigid end walls being in contact with the fluid. Here (x, y, z) are the Cartesian co-ordinates of a general point in the frame of reference in which the container is stationary. Fluid is withdrawn from the container atQcm3/sec via certain permeable parts of the side walls and replaced at the same steady rate via other permeable parts of the side walls. As, by hypothesis, the vorticity of the entering and leaving fluid relative to the container is zero, the concomitant fluid motion within the container, Eulerian velocityu= −∇ϕ − ∇ ×A, is irrotational when the container is stationary in an inertial frame. The present paper is concerned with the effects onuof uniform rotation of the whole system with angular velocity Ω about thez-axis when the normal component ofuon the side walls is independent ofz.In the simplest conceivable case,D≡zu−zlis infinite (butD/Qremains finite). End effects are then negligible anduis everywhere independent ofz.The solenoidal component ofu, − ∇ ×A, corresponds tojgyres, one for each of thejirreducible sets of circuits across which the net flow of fluid does not vanish that can be drawn within them-ply connected region bounded by the side walls. While ∇ϕ, which satisfies ∇2ϕ = 0, depends onQbut not on Ω,jandv(the coefficient of kinematic viscosity), ∇ ×Adepends on all these quantities but vanishes identically whenjΩ = 0. WhenjΩ ≠ 0 butv→ 0, ∇2A+ 2Ω, the absolute vorticity, tends to zero everywhere except in certain singular regions near the bounding surfaces, where boundary layers form.End effects cannot be ignored whenDis finite. WhenDis independent ofxandyand equal toD0(say) and Ω is sufficiently large for the boundary layers on the end walls to be of the Ekman type, 95% thickness δ = 3(v/Ω)½(δ [Lt ]D0), the end effects that then arise are only confined to these boundary layers whenj= 0. Whenj≠ 0 boundary-layer suction influences the flow everywhere; thus ∇2Aand ∇ϕ (but not ∇ ×A) are reduced to zero in the main body of the fluid, the regions of non-zero ∇ϕ and ∇2Abeing the Ekman boundary layers on the end walls and boundary layers of another type, 95% thickness δs(typically greater than δ), on the side walls. A theoretical analysis of the structure of these boundary layers shows that non-linear effects, though unimportant in the end-wall boundary layers, can be significant and even dominant in the side-wall boundary layers. The analysis of an axisymmetric system, whose side walls are two coaxial cylinders, suggests an approximate expression for Δs. WhenDis not everywhere independent ofxandy,non-viscous end effects arise which produce relative vorticity in the main body of the fluid even whenj= 0.Experiments using a variety of source-sink distribution generally confirm the results of the theory, show that instabilities of various kinds may occur under certain circumstances, and suggest several promising lines for future work.

We investigate the stability of an elastic plate in supersonic gas flow. This problem has been studied in many papers regarding panel flutter, where uniform flow is usually considered. In this paper, we take the boundary layer on the plate into account and investigate its influence on plate stability. Three problem formulations are studied. First, we investigate the stability of travelling waves in an infinite-length plate. Second, the nature of the instability (absolute or convective instability) is examined. Finally, by using solutions of the first two problems, instability of a long finite-length plate is studied by using Kulikovskii’s global instability criterion. The following results are obtained. All the eigenmodes of a finite-length plate are split into two types, which we call subsonic and supersonic. The influence of the boundary layer on these eigenmodes can be of two kinds. First, for a generalized convex boundary layer profile (typical for accelerating flow), supersonic eigenmodes are stabilized by the boundary layer, whereas subsonic disturbances are destabilized. Second, for a profile with a generalized inflection point (typical for constant and decelerating flows), supersonic eigenmodes are destabilized in a thin boundary layer and stabilized in a thick layer; subsonic eigenmodes are damped. The correspondence between the influence of the boundary layer on panel flutter and the stability of the boundary layer over a rigid wall is established. Examples of stable boundary layer profiles of both types are given.

A three-dimensional computation was conducted to understand effects of the inlet boundary layer thickness on the internal flow and the loss characteristics in a low-speed axial compressor operating at the design condition (φ = 85%) and near stall condition (φ = 65%). At the design condition, independent of the inlet boundary layer thickness, flows in the axial compressor show similar characteristics such as the pressure distribution, size of hub corner-stall, tip leakage flow trajectory, limiting streamlines on the blade suction surface, etc. But, as the load is increased, for the thick inlet boundary layer at hub and casing, the hub corner stall grows to make a large separation region between the hub and suction surface, and the tip leakage flow is more vortical than that observed in the case with thin inlet boundary layer and has the critical point where the trajectory of the tip leakage flow is suddenly turned to the downstream. For the thin inlet boundary layer, the hub corner stall decays to form the thick boundary layer from hub to midspan on the suction surface owing to the blockage of the tip leakage flow and the tip leakage flow leans to the circumferential direction more than at the design condition. In addition to these, the severe reverse flow, induced by both boundary layers on the blade surface and the tip leakage flow, can be found to act as the blockage of flows near the casing, resulting in a heavy loss. As a result of these differences of the internal flow made by the different inlet boundary layer thickness, the spanwise distribution of the total loss is changed dramatically. At the design condition, total pressure losses for two different boundary layers are almost alike in the core flow region but the larger losses are generated at both hub and tip when the inlet boundary layer is thin. At the near stall condition, however, total loss for thick inlet boundary layer is found to be greater than that for thin inlet boundary layer on most of the span except the region near the hub and casing. In order to analyze effects of inlet boundary layer thickness on total loss in detail, total loss is scrutinized through three major loss categories available in a subsonic axial compressor such as profile loss, tip leakage loss and endwall loss.

A synthetic-turbulence and temperature-fluctuation-generation method is developed and embedded in large-eddy simulations to investigate the effects of weak stable stratification (i.e. Richardson number Rile 1) on turbulence and dispersion following a simulated rural-to-urban transition. The modelling approach is validated by comparing predictions of mean velocity, turbulent stresses, and point-source dispersion against data from a wind-tunnel experiment that simulates a stable atmospheric boundary layer (Ri=0.21) approaching a regular array of uniform rectangular blocks. The depth of the internal boundary layer (IBL) that develops from the leading edge of the block array is determined using the wall-normal turbulent stress method proposed by Sessa et al. (J Wind Eng Ind Aerodyn 182:189–291, 2018). This shows that the depth and growth rate of the IBL are sensitive to the thermal stability and the turbulence kinetic energy (TKE) prescribed at the inlet, such that the IBL depth reduces as the TKE of the inflow is reduced while maintaining the same Ri, or as the Ri is increased while maintaining the same inflow TKE. When a ground level line source is introduced it is found that increasing Ri evidently reduces the vertical scalar fluxes at the canopy height, while increasing the mean concentrations within the streets. Furthermore, as with IBL development it is found that for a given value of Ri the effect of stratification becomes more pronounced as the inflow level of TKE is reduced, affecting scalar fluxes within and above the canopy, and volume-averaged mean concentrations within the streets.

Significant equipment like electric arc furnaces (EAFs) and ladle refining furnaces (LRFs) are among the highly dynamic and nonlinear electrical loads found in steel production facilities like Surana Industry. Reactive power imbalance, harmonic distortion, and voltage instability are just a few of the significant power quality issues caused by these complex loads. Because of this, accurate modeling and thorough analysis of these complex power systems are essential to ensuring operational dependability and maintaining power quality. The current literature tends to emphasize mostly steady-state conditions that are frequently not verified empirically with respect to actual operating data, despite the fact that the Electrical Transient Analyzer Program (ETAP) is a common tool used for load flow analysis in industry applications. With an emphasis on accurately simulating the real system behavior under various operating regimes, this paper provides a thorough power flow analysis of the Surana Steel Industry using ETAP. Two 100 MVA, 220/110 kV transformers step down the 110 kV supply that powers the plant, which is drawn from the Chikkasagur substation. The primary loads—a 35-ton rolling mill, a 4 MW EAF, and an LRF are supplemented with a captive power generation system and a harmonic filter to improve power quality and reliability. Under five different operating conditions with different load levels and generator configurations, key performance metrics such as voltage regulation, reactive power flow, harmonic suppression, and generator dynamic response are thoroughly assessed. The power system of the Surana Steel Industry is accurately simulated by the analytical method employed here. Even though a real-time comparison with SCADA data was not attempted, the ETAP model was painstakingly built with detailed equipment specs, typical operating conditions, and performance patterns actually observed at the facility. Accurate simulation of industrial environments, including the complex, unbalanced, and nonlinear loads present in steel mills, was made possible by this all-encompassing approach. Thus, this study shows that when appropriately configured and backed by extensive empirical data, ETAP has a considerable ability to accurately model these difficult environments. These results offer practical information that can be used right away for large-scale industrial power system planning, assessment, and enhancement.

Abstract

Experiments examining the effect of surface roughness on vortex-induced vibration (VIV) and drag of flexible cylinders at critical and supercritical Reynolds numbers have been conducted. Four levels of surface roughness were tested for their effect on VIV and drag of a circular cylinder that was 20 diameters upstream of a downstream cylinder (i.e. effectively an isolated cylinder). The rougher cylinders experienced vibrations of up to 3rd mode (in transverse bending). A surprising discovery was that the smooth cylinder experienced low drag and virtually no VIV as the boundary layers became turbulent in the critical Reynolds number range. Introduction and Background The study of flow separation and vortex shedding past a circular (or approximately circular) cylinder has a long history. Simple observation of flow past a vertical stick or reed in a stream indicates that man has probably observed this phenomenon well before recorded history. Similarly, vortexinduced vibration (VIV), which results when something free to move experiences vortex shedding, has an equally long history. The vibration felt when attempting to move one's arm through the water as fast as possible is evidence that VIV was also observed in antiquity. A parameter that strongly influences flow past a circular cylinder is the Reynolds number (Re), which represents the ratio of the convective forces to the diffusive forces, defined as Re=V*D/?. Another important parameter, for the purposes of this paper, is the surface roughness k/D, where k is the average "peak to trough" height of the surface protrusions. Figure 1 illustrates the basics of flow past a circular cylinder. As the fluid approaches the cylinder, a thin boundary layer (exaggerated in the figure for illustration purposes) forms on each side of the cylinder (shown on only one side). The fluid closest to the cylinder wall is impeded by friction on the cylinder's surface, hence the region between the wall and where the velocity is close to that of the free stream is known as the boundary layer. As the boundary layer fluid proceeds around the cylinder surface, the retardation of the fluid near the surface eventually causes it to come to a halt, thereby resulting in separation of the boundary layer into a "shear layer". Because the outer fluid in the shear layer is moving faster than the inner fluid of the shear layer, the layer rolls up into a vortex. For Reynolds numbers larger than about 40, the vortex pattern is unstable, and thus there is an alternating vortex street that is shed from the cylinder. Numerous studies have been made of flow past a stationary circular cylinder, most of these with air as the flowing fluid1–6. These studies have covered Reynolds numbers well exceeding 1×107. Figure 2 illustrates the general relationship that these studies have found between drag coefficient (defined as Cd = Fd/(0.5*?*V2*D*L) and Reynolds number for flow past a stationary cylinder. This figure shows that, at a Reynolds number of about 1×105 (the "critical" Reynolds number range), the drag coefficient diminishes dramatically, a phenomenon known as the "drag crisis". This corresponds to a change in the boundary layers from laminar to turbulent.