Froude Similarity Research Articles

Hydrodynamic performance of steelmaking tundish systems: a comparative study of three different tundish designs

Extensive water modelling was carried out to ascertain the influence of various types of baffle designs on the hydrodynamic performance of three different designs of steelmaking tundish systems. These included, a two-strand slab casting tundish, a six-strand billet casting tundish and a five-strand, skewed, delta shaped tundish. Plant scale operating conditions were scaled down respecting both geometric and Froude similarity and on the basis of the latter, the inflow rate of water into the model tundish systems was estimated via: Qm = Λ5/2Qf.s. To quantify the hydrodynamic performance, residence time distribution (RTD) characteristics were measured using the conductivity measurement technique for a wide range of baffle designs. From such measurements as well as from flow visualisation studies, the following general observations have been made. The optimum design of baffles together with its number and position within the tundish appear to be a strong function of the basic tundish design (viz., the geometry, the number of operating strands etc.). Of the various types of baffles investigated in this work (dam, dam + weir, baffles with holes etc.), appropriately designed slotted baffles appear to modify the RTD characteristics most favourably towards superior metallurgical performances. Increase in the number of strands, asymmetricity in the tundish design and flawed operating conditions, (viz., large width to length ratio) were all found to influence the tundish performance adversely. A comparison of experimental results for the three tundish systems indicated that changing the characteristics of the baffle design can lead to significant performance improvement in the case of the two symmetric tundish systems (e.g., the two and the six strand tundishes), the five strand skewed, delta shaped tundish was, however, found to be somewhat insensitive to such changes. For such a tundish geometry, no design of the flow-modification devices tried, could bring the hydrodynamic performance any closer to the best results obtained for the two other tundish systems. Possible reasons for such observations are discussed in the text. Umfangreiche Wassermodellstudien sollten den Einfluß verschiedener Leitbleche auf die Hydrodynamik dreier verschiedener Tundishbauarten klären. Zur Diskussion standen je ein Gießverteiler einer 2-adrigen Brammen- und einer 6-adrigen Knüppelstrangießanlage als auch ein abgeschrägter, dreieckiger Tundish einer 5-adrigen Anlage. Die Betriebsbedingungen wurden unter Berücksichtigung der geometrischen Verhältnisse und der Froude-Zahl auf den Modellmaßstab übertragen. Auf dieser Basis ließ sich die Wassereintrittsgeschwindikeit in die Modelltundishsysteme mit der Gleichung Qm = Λ5/2Qf.S berechnen. Anhand von Leitfähigkeitsmessungen ließen sich die Merkmale der Verweilzeitverteilungen (RTD) bestimmen. Auf diese Art konnte die hydrodynamische Leistung quantifiziert werden. Bei diesen Messungen als auch bei Fließvisualisierungsstudien konnten eine Reihe von grundlegenden Zusammenhängen beobachtet werden. Die optimale Bauart, Anzahl und Position von Leitblechen im Tundish hängt offensichtlich stark vom grundlegenden Tundishdesign ab (Abmessungen, Anzahl der betriebenen Adern, etc.). Von allen hier untersuchten Leitblechen (Damm, Damm und Wehr, Lochplatten, etc.) scheinen geeignet entworfene, geschlitzte Bleche die RTD-Merkmale im Sinne einer besseren metallurgischen Leistung günstig zu verändern. Gegenteilig wirken eine Erhöhung der Stranganzahl, Asymmetrien in der Tundishauslegung und ungünstige Betriebsbedingungen. Ein Vergleich der Versuchsergebnisse für drei Tundishsysteme zeigt, daß Veränderungen der Charakteristika der Leitblechauslegung bei den beiden symmetrischen Gießverteilersystemen (z.B. beim 2- und 6-adrigen Tundish) zu einer bemerkenswerten Leistungsverbesserung führen können. Demgegenüber erwies sich der fünfadrige abgeschrägte, dreieckige Gießverteiler solchen Änderungen gegenüber ziemlich unempfindlich. Keine der untersuchten Einbauten zur Modifizierung des Flusses konnte die hydrodynamische Leistung dieser Tundishbauart auch nur ein wenig näher an die besten Ergebnisse heranbringen, die mit den beiden anderen Systemen erreicht wurden. Mögliche Gründe hierfür werden diskutiert.

Subcritical Junction Flow

The main flow features of subcritical junction flows are explored, based on an extended hydraulic model study. The flow conditions chosen resulted in flows that are governed by the Froude similarity law. So-called simple junctions with junction angles of 30°, 60°, and 90° were tested. The main emphasis was made in determining the characteristics of the lateral flow and the flow contraction in the tailwater branch. Further, expressions for the momentum correction coefficients, the lateral wall pressure force, and the ratio of flow depths in the lateral and upstream branches were provided. A rational approach for the momentum contribution of the lateral branch is presented and applied for the prediction of the backwater effect across a simple junction. The complex flow pattern is further documented with selected photographs such that a rather complete description of junction flow is now available.

Unconfined Expansion of Supercritical Water Flow

The spread of supercritical free-surface flow on a smooth horizontal plane is considered. Experiments with selected approach Froude numbers are presented indicating that the effect of the Froude number may be dropped for hypercritical flow, that is, for values larger than 3. Also, a simple relation between local streamline direction and local flow depth is established. For sufficiently large approach flow depth, the Froude similarity law governs the phenomenon. Assuming that the streamwise velocity component is constant yields a system of equations identical to the one-dimensional simple wave problem. The solutions are compared with observations, and reasonable agreement is noted. Further particularities of hypercritical channel flow are established that are important for the numerical simulation of such currents. The features of expansion flow are documented with selected photographs. Supercritical unconfined expansion flow on a horizontal plane is studied. The governing equations can be shown to simplify considerably for hypercritical flow. A complete description is given based on both computations and experiments.

An empirical velocity scale relation for modelling a design of large mesh pelagic trawl

Physical models of fishing nets are used in fishing technology research at scales of 1:40 or smaller. As with all modelling involving fluid flow, a set of rules is required to determine the geometry of the model and its velocity relative to the water. Appropriate rules ensure that the model is subject to similar forces and behaves in a similar way to the full-scale net. It is not possible however, to choose a completely compatible set of modelling rules and a compromise is necessary. The common practice is to assume that similarity is achieved when a constant Froude Number is maintained. This is often found to be inadequate in that drag is increasingly overestimated as the scale is reduced. A new empirical relation between net drag coefficient and Reynolds Number at constant net geometry for one design of large mesh pelagic trawl is derived which applies over a wide range of Reynolds Numbers (based on mean twine thickness) from 63 to 1.67 × 10 4. Six sizes of the same net design from full-scale to 1:40 were investigated. From this relation a new velocity scale relation has been proposed which relates velocity scale to linear scale for this particular trawl design. It is argued that not only the net mouth but also all the individual netting panels will maintain the correct geometry over this range of model sizes. The traditional Froude similarity law states that the velocity scale is equal to the linear scale to the power of 0.5. The new relation suggests a power of approximately 0.6. Lower velocities may be necessary to compensate for the increase in drag coefficient as Reynolds Number decreases at constant Froude Number. Until more experiments are done on radically different net designs it will not be possible to assess how widely this new relation may apply.

Criteria for Water Modeling of Melt Flow and Inclusion Removal in Continuous Casting Tundishes.

Water modeling of tundish melt flows offers useful insight into the underlying flow phenomena occurring in the tundish. Most of the water modeling studies have been carried out under isothermal conditions with water at room temperature, and have employed full as well as reduced scale models. In water modeling, a reduced scale model can not simultaneously satisfy the Reynolds as well as Froude similarity criteria. Many industrial modeling studies have employed full scale models while many university researchers have used small scale models based on the Froude similarity criterion. This paper discusses the importance and validity of these criteria. For simulation of inclusion flotation in water models, gravitational force becomes important. The choice of model inclusion to water density and the model inclusion size needed for proper simulation of a given inclusion size in molten steel are discussed. A criterion for quantitative determination of inclusion agglomeration in the water model is also suggested. Thus, a procedure and appropriate criteria for water modeling of flow and inclusion flotation and removal are outlined.

Non-breaking undular hydraulic jump

The differences between the undular jump and the undular surge are described. Further, the limit approach flow depth and the channel width are defined for undular jumps governed by the Froude similarity law. Based on previous and present observations, the main flow characteristics of undular jumps are established. These include surface characteristics along the axis and the walls of the rectangular channel. Also, generalized surface profiles are presented. Finally, the formation of shocks is physically explained as a breakdown of the supercritical approach flow.

Physical Model of Niagara River Discharge

Development of a physical model study for the Niagara River discharge into Lake Ontario is described. The model is designed on the basis of (distorted) Froude and Rossby similarity and the results demonstrate clearly the effects of rotation on the flow. Important features of the plume are shown to be reproduced by the model, including its anticyclonic (right-turning) flow and the subsequent formation of a near-shore current along the southern coastline. A scaling analysis of the integrated longitudinal momentum equation is suggested as a framework for analyzing this type of flow. This analysis considers three regions of the flow: (1) a near-field, where inertial forces are balanced by pressure and bottom drag; (2) an intermediate-field where the balance is between inertia and buoyancy; and (3) afar-field characterized by nearly geostrophic flow (balance between buoyancy and rotation). This scheme is then tested against conditions characteristic of the Niagara River discharge during spring flows and also with observations from the physical model tests, showing reasonable agreement. One particular result of interest is that the distance at which rotation starts to turn the flow scales approximately with the internal Rossby radius. Results of the study help to distinguish between the relative effects of buoyancy and rotation.

Modified, Trapezoidal Venturi Channel

The flow pattern resulting from a circular cone immersed in a rectangular channel is investigated under critical flow conditions. The apparatus may be used for both permanent and mobile discharge evaluation in open channels. Owing to the low weight, the high precision of finishing, and its reasonable price when compared to the conventional structures, the modified Venturi Channel may be regarded as a useful instrument. The circular cone is particularly well suited to watercourses in which discharge spectrum is considerable, thereby resulting in moderate approaching flow depth variation. Its rating curve is investigated by accounting for streamline curvature effects. Experiments corroborate the theoretical predictions and indicate that the flow characteristics are governed by the Froude similarity law.

Quelques travaux de correction sur le cours de l'Isère

The river Isere winds its way down the Gresivaudan valley to Grenoble and intersects a cross-valley at Voreppe just after leaving the city. A number of river training schemes have been implemented since the mid-nineteenth century (e.g. canalisation and bank protection works), which were governed by liberal policies along the river above the city and a more directorial outlook downstream, in accordance with prevailing tendencies at the various times they were put into effect. Major bend-cutting and dyke reinforcement work has been carried out since the middle of the twentieth century, including correction of the river's longitudinal profile, some sections of which were tending to build up by sediment deposition, whilst gravel extraction from others was unduly increasing their depth. Work has just started on irnplementation of a new river flood protection programme for Grenoble. Because of considerable past and predicted river bed level variations, this programme has required more detailed research and testing than earlier schemes, which has involved fresh determination of water levels associated with the predicted rates of river flow, up to and including for the hundred-year peak flood discharge. For the necessary tests, a 1:100 scale model of an 8 km stretch of the river Isere through Grenoble was designed and run in accordance with Froude similarity laws. In addition, a mathematical model of the part of the Isere from its confluence with the river Arc to the sill at Saint Gervais, i.e. about 80 km in length, was subsequently designed and operated. In designing this model, several very complicated computer calculations had to be carried out. In addition to dyke protection and provision of a channel down the middle of the river bed, a number of sub-river sills are to be installed as a means of stabilising the river and its aquifers. Preservation of present flood areas to attenuate major flood peaks above Grenoble is also being envisaged. In view of the highly complex problems involved on both horizontal and longitudinal scales, the physical and mathematical models in use for the study are invaluable assets as regards accurate prediction of data for present and future river engineering projects.

Dispersion Models in Coastline Waters with Predominant Transverse Shear

SYNOPSISMixing problems in a shallow coastline water with horizontal velocity distribution are cosidered. The maximum scale within which mixing phenomena are classified into diffusion in coastline waters is first inferred from existing data. Law of similitude in a reasonably straight channel is reconsidered for a distorted Froude similarity model focusing our attention on the three-dimensional velocity distribution. An analysis of the dispersion in the flow field which has the deviation of flow velocity in transverse direction due to meso-scale turbulence of topographical origin has been performed through a circulation model.The circulation model permits the estimation of the longitudinal dispersion coefficient from the geometry and the flow velocity of the system, making use of the experimental relationship between the transverse diffusion coefficient and the intensity of the circulation in wake regions obtained in a simple hydraulic model. Agreement of the predicted value of the longitudinal dispersion ...