EP0720663B1 - Method for dimensioning an electroplating enclosure with a magnetic wiping device for electroplated metallurgical products - Google Patents

Abstract

A method for dimensioning an electroplating enclosure with a device for magnetically wiping electroplated metallurgical products, particularly applicable to a continuous electroplating method. The method uses a wiping device which is preferably an inductive element arranged about an outlet channel of the enclosure in order to generate a transversal alternating sliding electromagnetic field at the surface of said products. Said method is characterised in that it comprises, mainly on the basis of the transversal dimensions and axial length of said enclosure, the cross section and velocity of the products, the dynamic viscosity and pressure of the coating fluid within the enclosure, the transversal dimensions of said outlet channel, the displacement speed and magnitude of the electromagnetic field in said liquid, and a parameter representative of the roughness, if any, of said metallurgical products, calculating or controlling the conditions in which the Couette lengths respectively associated with the flow of the coating fluid within the enclosure and in its outlet channel, are maintained below the critical values beyond which said flows become markedly turbulent.

Description

The present invention relates to a method for dimensioning a galvanizing enclosure provided with a device for magnetic wiping of galvanized metallurgical products, in particular usable within the framework of a continuous galvanizing process.

We know, by the classic results of hydrodynamics, that the inertial forces (gravity mainly) and the friction forces (viscosity, influence of the nature of the wall) totally govern the evolution of the flow of a coating liquid in the vicinity of the surface of a metallurgical product to be covered.

However, under given reactivity conditions which will be neglected later as regards the subject of the invention, the evolution of the flow in the region close to said product greatly conditions the thickness finally deposited on this material. latest.

In this respect, the establishment of a laminar flow appears a priori desirable in the sense that it allows, in the usual approximation of the boundary layer, to connect by simple and known laws the physical quantities characteristic of the flow , namely the profile of the speeds relative to the surface of the metallurgical product, itself driven at a constant speed, the dynamic viscosity of the covering liquid, its density and the surface tension between said metallurgical product and said liquid (wettability parameters ). The thickness deposited is then conditioned by that of the liquid film which is drained by the metallurgical product when it is pulled out of the liquid bath, a usable approximation being, in this case, that established by Landau and Levitch in an article referenced Acta Physicochimica USSR Vol 17, n ° 1-2, 1942: "Dragging of a liquid by a moving plate".

However, in this ideal laminar case, the thickness obtained is often too large for the desired galvanizing applications; this is why we have imagined various forms of wiping, that is to say of reducing the thickness deposited and, mainly, we have proposed pneumatic wiping techniques (action of air knives forming a counter pressure on the free surface of the metallurgical product emerging from the liquid bath), mechanical wiping techniques (action of rollers coming to "lick" the metallurgical product by means of asbestos pads) and, finally, magnetic wiping techniques, the present invention falling within the latter category.

• dans le bain liquide de recouvrement, avant la sortie du produit métallurgique, l'action du champ venant contrebalancer directement les forces d'inertie, en se soustrayant principalement à la pesanteur,
• hors du bain, l'action du champ se faisant sentir uniquement sur le film liquide entraîné,
• ou encore par combinaison de ces deux effets.

To date, there is a very large number of prior magnetic wiping devices. The latter technique recommends using the Lorenz force which can be developed in the covering liquid by a magnetic, static or alternating field, fixed or sliding, due to the presence of the electric currents induced in said liquid (obviously conductive when it is zinc, copper or aluminum) by the relative displacement of said liquid and said field. In all the cases which will be discussed later, the Lorenz force is supposed to oppose the inertia and viscosity forces acting on the flow, provided of course that it is intense enough to modify the profile of the velocities. near the surface of the metallurgical product. We therefore understand that it is a priori possible to act by a magnetic field on the thickness of the boundary layer, whether it be elsewhere:

• in the liquid covering bath, before the release of the metallurgical product, the action of the field directly counterbalancing the inertial forces, mainly by subtracting from gravity,
• outside the bath, the action of the field being felt only on the entrained liquid film,
• or by combining these two effects.

In this regard, the techniques known by the respective names of the companies that developed them, namely ASEA, ARBED, AUSTRALIAN WIRE and LYSAGHT, show examples of implementation covering almost all of the techniques implemented to date. For example, in patent FR-2 412 109 in the name of AUSTRALIAN WIRE IND PROPRIETARY, it is recommended to use a fixed single-phase electromagnetic field, that is to say non-sliding, the intensity of which is varied either the frequency to adjust the thickness deposited. In patent FR-2 410 247 in the name of JOHN LYSAGHT AUSTRALIA LIMITED, a similar device is shown but the geometries are different from those used in the previous patent with, in addition, pulsation frequencies of the magnetic field preferably established around 30 kHz. In the prior art ARBED, described in patent BE-882,069, it is envisaged, among other things, to use a sliding electromagnetic field acting on the excess of liquid metal entrained by a sheet leaving a galvanizing bath. Finally, in patent DE-2 023 900 (in the name of ASEA), the set of wiping possibilities outside the galvanizing bath is shown (fixed longitudinal, transverse alternating field or sliding field).

However, the inventors have realized that this action of the magnetic field is sensitive, and therefore effectively controllable, only to the extent that the purely hydrodynamic phenomena do not mask the desired effects of magnetic origin. It is easy to see that this point is never addressed in any of the prior magnetic wiping techniques and that it therefore appears that the problem in this case is entirely new.

In particular, in all the prior patents relating to magnetic wiping, the metallurgical products to be covered pass vertically through a galvanizing bath whose free surface is horizontal; there is therefore, in this case, no possibility for the covering liquid to leak out of the galvanizing enclosure. However, the new constraints of the surface treatment industry lead to the search for magnetic wiping solutions for a continuous galvanizing installation as described in patent FR-2 647 814 in the name of FRANCE GALVA LORRAINE, which is arranged horizontally; other embodiments of the same kind are also known, in particular from patents GB-A-777,213 and US-A-2,834,692. It is recalled that, in this type of installation, the galvanizing enclosure has orifices d 'inlet and outlet aligned with the movement of the products to be treated, the upper level of the covering liquid bath being situated above said orifices; therefore, it is necessary to provide sealing devices responsible for compensating for the hydrostatic pressure which tends, if not, to cause said liquid to flow outside the enclosure. In this respect, one can think that a continuous or alternative magnetic induction, of a type generally used for magnetic wiping, can, by an identical physical mechanism, help to retain at least partially the liquid in the enclosure.

However, insofar as a fixed alternating field does not develop, in principle, any force of a rotational nature in the covering liquid (unlike a sliding field), a Lorenz force sufficiently intense to compensate for the forces of inertias of the galvanizing bath can only be generated, with this type of field, for a very high frequency and / or an intense magnetic field; which leads, in the first case, to a skin thickness (depth of penetration of the field in the conductive liquid) too small to hope to retain said covering liquid in the vicinity of the metallurgical product and, in the second case, to costly oversizing of the installation. Consequently, the use of a fixed alternating field magnetic wiping device as a sealing means for a horizontal galvanizing enclosure is almost excluded.

On the other hand, we realized that the only metallurgical products which can be treated with previous magnetic wiping installations are systematically smooth. However, in practice, the inventors have highlighted the substantial role played by the roughness of the surface of the treated products, in particular in the case of the invalidity of the generally implicitly accepted approximation of the laminarity of the flow. covering liquid in the vicinity of said surface. In this regard, in the event that hydrodynamic turbulence phenomena appear, we know that the roughness of the treated products intervenes all the more since the covering liquid is located in a confined space - which is always the case in the middle of the air gap or winding of an electromagnetic system creating the induction necessary for the development of a notable Lorenz force in said liquid -.

It was finally observed, in connection with the preceding remark, that the transverse dimensions and the length of the confinement enclosure of the galvanizing bath were not unimportant from the hydrodynamic point of view. Similarly, the transition zone between the sheath and the sealing device and / or the magnetic wiping device, as well as the transverse dimensions and the length of the outlet channel around which a magnetic induction responsible for sealing is created. and / or magnetic wiping, in fact play a predominant role in the quality and thickness of the deposited layer; some of the conditions obtained are even contradictory with the trends previously implemented in the case of galvanizing smooth products.

• à mettre en évidence le problème nouveau de la réalisation d'un dispositif combiné d'étanchéité et d'essuyage magnétique horizontal, lié à des choix technologiques récents,
• à proposer diverses solutions pratiques sur le dimensionnement correct dudit dispositif d'essuyage magnétique, en fonction notamment de la géométrie des produits traités, ces solutions étant d'ailleurs également applicables aux installations de galvanisation verticales,
• à permettre la prévision de l'épaisseur déposée sur des produits substantiellement rugueux (par exemple des fers à béton), ce qui s'avérait impossible jusqu'à présent.

From these various observations, the present invention therefore aims:

• to highlight the new problem of producing a combined horizontal magnetic sealing and wiping device, linked to recent technological choices,
• to propose various practical solutions on the correct dimensioning of said magnetic wiping device, depending in particular on the geometry of the products treated, these solutions also being also applicable to vertical galvanizing installations,
• to allow the prediction of the thickness deposited on substantially rough products (for example concrete irons), which was previously impossible.

To this end, the present invention relates first of all to a method for dimensioning a galvanizing enclosure provided with at least one sealing and / or wiping device on the side from which the metallurgical products having passed through a liquid covering bath contained in said enclosure, said device preferably being an inducing element arranged for this purpose around an outlet channel of the enclosure to produce a transverse, alternating and sliding electromagnetic field, at the surface of said products, characterized in that it consists in calculating or verifying, mainly from: the transverse dimensions of said enclosure, its axial length, the cross section of said products, their speed, the dynamic viscosity of said covering liquid, its pressure in the enclosure, the transverse dimensions of the outlet channel of the enclosure, the speed of movement of the electrom agnetic sliding and its intensity in said liquid, and finally a parameter representative of the possible roughness of metallurgical products, the conditions for which the lengths of Duvet respectively associated with the flow of the covering liquid in the enclosure and in its outlet channel remain below the critical values beyond which said flows become clearly turbulent.

Recall that a Couette flow is that which characterizes an incompressible and viscous fluid, conductive or not, located between two parallel plates assumed to be infinite, one of which is set in motion parallel to itself; the purpose of Couette's hydrodynamic calculation is to establish the parameters governing the profile of the velocities of the flow between the two plates, complications which can occur depending on the roughness of the surfaces in contact with the fluid; one speaks of a flow in shear.

• d'une part, au calcul du profil des vitesses de l'écoulement du liquide de recouvrement qui est situé entre les parois longitudinales de l'enceinte de galvanisation cylindrique et le produit métallurgique circulant axialement au travers de cette dernière et,
• d'autre part, au calcul du profil des vitesses de l'écoulement du liquide de recouvrement qui est situé entre les parois du canal de sortie de l'enceinte et ledit produit.

The similarity principles used in classical fluid mechanics, to solve dimensionally complex flow problems, show that the Couette model is applicable to the problem of the axisymmetric flow of a liquid set in motion in an annular space whose the nucleus moves at an assumed constant speed. Therefore, this model is applicable:

• on the one hand, when calculating the profile of the velocities of the flow of the covering liquid which is located between the longitudinal walls of the cylindrical galvanizing enclosure and the metallurgical product circulating axially through the latter and,
• on the other hand, to the calculation of the profile of the velocities of the flow of the covering liquid which is located between the walls of the outlet channel of the enclosure and said product.

According to the invention, it has been observed that these two flows (of course continuous) strongly condition the thickness of the boundary layer, laminar or turbulent, which should be taken into account when calculating the thickness of the entrained liquid film. by the metallurgical product when it emerges, vertically or horizontally, outside the free surface of the liquid bath contained in the galvanizing enclosure.

In general, the thickness of the laminar or turbulent boundary layer of the flow at the entrance to the outlet channel of the galvanizing enclosure must be kept below a limit value beyond which it n is no longer possible to control increase. This effect results directly from the fact that, in accordance with the results established by the theory of magnetohydrodynamics, magnetic fields absorb much faster than vorticity in conductive liquids; as the vorticity, also called the vortex vector, is directly representative of the turbulence of the flow, it is understood that its influence must be limited to the level of the areas of the covering liquid where it is desired to act on the magnetic force or forces of Lorenz. Thus, in the favorable case where the quilt lengths of the flow in the enclosure and its outlet channel are known and controlled, the dimensioning of the sealing and / or wiping device of the galvanizing enclosure can be '' express via dimensionless numbers usual in magnetohydrodynamics, namely the magnetic Reynolds number, the interaction parameter, the Hartmann number as well as two parameters related to the geometry of the sliding alternating magnetic field which is chosen to create the Lorenz magnetic force (s) inside the flow.

In this regard, the solution posed by the invention goes first of all in the direction of a reduction in the length of the galvanizing enclosure which, depending on its transverse dimensions and the speed of the product, must remain less at the hydrodynamic quilt length of the flow. This rule is moreover not contradictory with the conditions notably laid down in patent FR-2 323 772 in the name of José DELOT; in this last patent, it is indeed demonstrated that the use of a short galvanizing enclosure and of small volume is sufficient to obtain a correct metallurgical reaction between the product to be treated and the covering liquid, provided that the product to be galvanized has been pickled, heated and maintained in a controlled atmosphere at least upstream of the galvanizing enclosure.

On the other hand, since the correct sizing of the galvanizing enclosure and its outlet channel essentially makes it possible to inhibit the conditions of appearance of turbulence, the flow in the outlet zone of the galvanizing bath is close to the normally laminar flow which exists at the level the exit of processed products in vertical galvanizing installations; which simply means that the volume Lorenz force, developed in the liquid bath by the sliding alternating field, plays, in fact, a role analogous to gravity. This "gravity hypothesis" of the magnetic Lorenz forces, developed in the galvanizing bath by the inducing element arranged for this purpose around the outlet channel of the galvanizing enclosure, makes it possible to consider that the shape of the meniscus formed between the surface free from the bath and the metallurgical product which is extracted therefrom almost completely conditions the thickness of the coating deposited on said product. Consequently, under the strict conditions laid down by the invention, this thickness will be given by a formula completely analogous to that used in the hydrodynamic model of Landau and Levitch, of which the references have been cited above.

It will also be observed that, if the meniscus is kept close enough to the inlet of the outlet channel of the enclosure - which is desirable if one wishes to remain below the length of duvet corresponding to this part of the enclosure - and that the area of the inducing element where the sliding magnetic field is generated is relatively long, it is still possible to act effectively on reducing the thickness of the liquid film forming at said meniscus. In this regard, it is recalled that, in principle, the inertial forces due to the isostatic pressure of the liquid bath in the galvanizing enclosure and to the entrainment effect of the metallurgical product are compensated for as soon as they leave the meniscus; consequently, behind said meniscus, the Lorenz volume forces act alone on the liquid film adhering to the metallurgical product and tend to thinning said film, thus constituting a "real" magnetic wiping (that is to say free of all considerations relating to sealing). The magnetic wiping in the outlet channel of the enclosure, at least downstream of the meniscus, is therefore similar to the known study of the thinning of a barotropic liquid flow called "with free surface" (barotrope because the gravity hypothesis remains valid).

Finally, according to a particularly advantageous characteristic of the dimensioning method according to the invention, it is known to take into account the roughness of the metallurgical product treated on the nature of the flow and, therefore, on the thickness of coating deposited at the outlet of the galvanizing enclosure. Preferably, the model chosen to do this is that of Karman-Nikuradzé. This model, widely tested in the field of hydrodynamics, makes it possible to know, in particular by means of abacuses, the coefficient of friction to be taken into account according to the roughness of the product and the hydraulic Reynolds number of the flow. More generally, taking into account what hydrodynamicists call the "wall law" (which depends in proportion to the pressure drop) is essential for a detailed knowledge of the flow itself, moreover, in the case of products smooth metallurgical since, as will be seen later, the wall law has a considerable influence on the behavior of the flow in the immediate vicinity of the metallurgical product to be coated.

• la figure 1 est une vue en coupe longitudinale de l'enceinte, de son canal de sortie, de l'élément inducteur, du fil traité,
• la figure 2 est un graphe donnant, d'une part, l'épaisseur de zinc déposée sur un fer à béton de rugosité et de diamètre donnés en fonction de sa vitesse de défilement au travers de l'enceinte de galvanisation et, d'autre part, la longueur sur laquelle pénètre le zinc fondu à l'intérieur du canal de sortie de ladite enceinte.

Other characteristics and advantages of the present invention will emerge from the description which follows of an example of dimensioning of a horizontal galvanizing enclosure, provided with an outlet channel around which is arranged an inducing element creating an alternating field. sliding in axial direction, this enclosure being more particularly intended for the treatment of smooth or rough wires such as concrete irons, this nonlimiting example of the invention being illustrated in the attached drawing in which:

• FIG. 1 is a view in longitudinal section of the enclosure, of its outlet channel, of the inductor element, of the treated wire,
• FIG. 2 is a graph giving, on the one hand, the thickness of zinc deposited on a concrete iron of roughness and diameter given as a function of its speed of travel through the galvanizing enclosure and, on the other hand part, the length over which the molten zinc penetrates inside the outlet channel of said enclosure.

The galvanizing enclosure 1 shown in the appended figure comprises two inlet 2 and outlet 3 orifices aligned with the passage of a metallurgical product 4 to be galvanized; this product 4 is, in the example chosen, a smooth steel wire or a concrete iron, therefore having notches distributed more or less regularly along its surface. The enclosure 1 is arranged horizontally, downstream from a set of pickling and heating devices, for example by induction, and downstream from a cooling device, for example with water, these different units conventional post- and pre-treatment are not illustrated in the drawings so as not to obscure the representation of the means of galvanization and wiping which is discussed here.

The galvanizing enclosure 1 is intended to contain a liquid bath of a coating product, preferably a molten metal alloy such as zinc, copper, aluminum and their usual alloys (the bath can therefore also contain small proportions of lead, etc. ...). Being arranged horizontally, the inlet 2 and outlet 3 orifices of the enclosure 1 must be provided with sealing means preventing the liquid bath from leaking through said orifices 2, 3; in the case described here of substantially cylindrical metallurgical products 4, it is chosen to use polyphase inductor windings 5, 6, which are respectively arranged around inlet 7 and outlet 8 channels of the enclosure 1 to generate, in the manner of synchronous linear motors, a magnetic back pressure on the conductive liquid product tending to flow by inertia through said channels inlet 7 and outlet 8; the transverse dimensions of these latter channels 7, 8 are calculated as a function of the diameter of the metallurgical product 4, of its relative magnetic permeability (of the order of 20 for steel) and of the intensity of the sliding magnetic field generated by the circulation of an electric current in the coils of the inductors 5, 6 so that, in the longitudinal annular space separating the product 4 and the internal walls of the channels 7, 8, the lines of the magnetic field are substantially transverse to the axial displacement of said product 4. In the case of the treatment of cylindrical products with non-circular section, such as plates, strips and other profiles, we will also endeavor to create a transverse magnetic field sliding at the level of the annular space corresponding to the geometry in question, which is always possible using laminates or magnetic combs shaping the magnetic field as desired. In addition, as it will normally be sufficient to produce a sliding magnetic field of low frequency, typically less than a few hundred herz and preferably equal to 50 herz, the magnetic losses caused, for example in magnetic laminates, will remain low.

Since the galvanizing process requires a permanent supply of liquid coating product in the enclosure 1, gradually compensating for that which is deposited on the metallurgical products 4 passing through it, a supply channel 9, here vertical, connects a reserve of liquid product to said enclosure 1; so that the hydrodynamic disturbances resulting from this contribution are as low as possible, we opt, according to an advantageous characteristic of the invention, for a central position of the mouth of said supply channel 9 with respect to the two inlet 7 and outlet 8 channels of the enclosure 1. On the galavanization enclosure 1, an equilibrium channel 10 has also been arranged, placed vertically at a central position corresponding for example to that of the feed channel 9, and into which the covering liquid product is introduced over a height, the measurement of which enables the isostatic pressure of the galvanizing bath to be known with precision; in addition, the free surface of the liquid column of the bath located in the equilibrium channel 10 is normally in contact with a protective gas, the pressure of which can, if necessary, be modified by conventional compression means. In this regard, the entire galvanizing installation is preferably maintained under a controlled, neutral or slightly reducing atmosphere, for metallurgical reasons which are moreover perfectly known to those skilled in the art.

On the other hand, as already mentioned above in the description, the transition zone 11 between the central zone of the enclosure 1 and its outlet channel 7 is a converging nozzle, which makes it possible to limit the risks of turbulence of the liquid product flowing at this level from said enclosure 1.

According to the present invention, the problem arises first of all in dimensioning the polyphase inductor winding 6 for the outlet so that a seal can exist at the outlet orifice 3 of the enclosure 1, then in dimensioning the all the other parameters of the installation to obtain the desired wiping. These two aspects of the invention will now be discussed successively.

1. Sealing problem

The sealing problem requires knowing, as defined above, the total hydrodynamic pressure exerted up to the equilibrium meniscus (or free surface) of the covering liquid in the outlet channel 8 of the enclosure 1; knowledge of the total pressure then makes it possible to calculate the Lorenz volume force which is necessary to maintain the free surface of the covering liquid at a certain level of the outlet channel 8 of said enclosure 1, according to the principles set out above.

As the transverse dimensions of the enclosure 1 are normally small compared to the transverse dimension of the metallurgical product 4 to be treated, it is necessary to treat the liquid flow in the enclosure 1 as an axisymmetric quilt flow, establishing itself in the annular space between the product 4 and the internal walls of said enclosure 1. The similarity rules applicable in the matter thus show that this annular flow is similar to the flow of the same liquid between two flat plates four times apart the value of the annular space (which will be shown later), one of the two plates moving exactly at the speed of the metallurgical product 4 which passes through the galvanizing enclosure 1.

Of course, a similar Duvet calculation must also be carried out to know the physical conditions of the flow in the part of the outlet channel 8 of the enclosure 1 where the covering liquid is introduced.

1.1 Calculation of the total pressure to compensate for sealing the enclosure

• la pression partielle isostatique P_iso dans la partie centrale de l'enceinte 1, dont la valeur est simplement donnée par le calcul classique d'Archimède, à savoir par le produit de la densité volumique du liquide (zinc fondu), de l'accélération de la pesanteur et de la hauteur de liquide comprise entre les parois de l'enceinte 1 et le produit 4 ; pour une colonne de zinc fondu à 450 °C, et une hauteur de zinc de 2 centimètres, cette première pression partielle vaut 1350 Pa (ou 135 mbars dans les unités usuelles). On notera que la pression d'alimentation de l'enceinte 1, au travers du canal d'alimentation 9, équilibre par contre totalement la contribution due à la hauteur de zinc dans le canal d'équilibre 10.
• la pression partielle due au dispositif d'étanchéité amont, c'est-à-dire à l'enroulement inducteur polyphasé 5 aménagé autour du canal d'entrée 7 de l'enceinte de galvanisation 1 ; cette pression sera supposée venir juste équilibrer les forces d'inertie à l'orifice d'entrée 2, ce qui est vrai dans tous les cas puisque cette pression aval contribue, de fait, à la hauteur de la colonne du liquide de recouvrement dans le canal d'équilibre 10.
• la pression partielle P_c qui résulte de l'entraînement du liquide de recouvrement par le produit métallurgique 4 défilant dans la zone centrale de l'enceinte 1.
• la pression partielle P_i qui résulte de l'entraînement du liquide de recouvrement par le produit métallurgique 4 défilant au travers du canal de sortie de l'enceinte 1.

The latter is the sum of the following partial pressures:

• the isostatic partial pressure P _iso in the central part of the enclosure 1, whose value is simply given by the classical calculation of Archimedes, namely by the product of the volume density of the liquid (molten zinc), of the acceleration gravity and height of liquid between the walls of the enclosure 1 and the product 4; for a column of zinc melted at 450 ° C, and a height of zinc of 2 centimeters, this first partial pressure is worth 1350 Pa (or 135 mbar in the usual units). It will be noted that the supply pressure of the enclosure 1, through the supply channel 9, on the other hand completely balances the contribution due to the height of zinc in the equilibrium channel 10.
• the partial pressure due to the upstream sealing device, that is to say to the polyphase inductor winding 5 arranged around the inlet channel 7 of the galvanizing enclosure 1; this pressure will be assumed to just balance the inertial forces at the inlet 2, which is true in all cases since this downstream pressure contributes, in fact, to the height of the column of the covering liquid in the balance channel 10.
• the partial pressure P _c which results from the entrainment of the covering liquid by the metallurgical product 4 passing through the central zone of the enclosure 1.
• the partial pressure P _i which results from the entrainment of the covering liquid by the metallurgical product 4 passing through the outlet channel of the enclosure 1.

According to the invention, these two partial drive pressures are calculated from similar quilt flows taking into account the length of the central zone of the enclosure 1, the length of the outlet channel 8 on which the zinc penetrates. , as well as pressure losses per unit of length in said central zone and, respectively, in said outlet channel 8 of enclosure 1.

a) length of the galvanizing enclosure 1 to be taken into account

The choice of the length of the enclosure conditions the behavior of the liquid flow in the vicinity of the metallurgical product 4: laminar, slightly turbulent or turbulent. The calculation consists in choosing a length of enclosure 1 a priori, which is checked a posteriori that it is less than the length of the critical quilt in the enclosure 1. According to the geometry of the enclosure 1 shown in the drawing, which is symmetrical with respect to the central supply zone, the length to be taken into account is , in fact, the half length L _c of the enclosure, taken here equal to 25 centimeters.

b) pressure drop per unit length in the central area of the enclosure

The pressure drop per unit length is conventionally related to the friction force per unit area. In the axisymmetric case of the galvanizing enclosure 1 considered, this relationship is expressed simply as a function of the hydraulic diameter of the annular space comprised between the metallurgical product 4 and the internal walls of said enclosure 1, of the volume density of the liquid of overlap, of the square of the flow velocity and of a pressure drop coefficient, itself proportional to an overall friction coefficient depending on the roughness of the surfaces and the Reynolds number characterizing the flow, c ' that is to say, finally, of the wall law in the vicinity of the metallurgical product 4.

b1) hydraulic diameter to be taken into account

A purely hydrodynamic analysis of the velocity profile of a turbulent Couette flow between two flat plates makes it fairly easy to realize that the hydraulic diameter to be taken into account for an annular channel is equal to four times the annular space. It will be noted that one places oneself automatically in the case of a supposed turbulent flow because an approximate calculation of the hydraulic Reynolds number in the vicinity of the metallurgical product 4, which moves at fairly high speed (namely V _b = 1 m / s), shows that the flow regime is surely turbulent.

Typically, the galvanizing enclosure 1 is almost everywhere cylindrical and has a substantially constant diameter T _c which, in the numerical examples developed below, will be taken to be 40 millimeters.

The diameter of the metallurgical product 4 is, for its part, taken equal to 10 millimeters, which gives an annular space e _c equal to 15 millimeters, and a hydraulic diameter D _He of 60 millimeters in the central zone of the enclosure 1.

b2) wall law

• le nombre de Reynolds hydraulique R_ec est calculé en fonction du diamètre hydraulique D_Hc, de la vitesse V_b (qui est un maximum pour la vitesse moyenne de l'écoulement) et de la viscosité cinématique du zinc à la température considérée (de l'ordre de 450°). On trouve R_ec = 120 000, ce qui signifie que l'écoulement est bien légèrement turbulent.
• la rugosité uniforme équivalente de la paroi du produit métallurgique 4 est prise égale à 0,35 millimètres, pour un fer à béton de diamètre égal à 10 millimètres.
• les abaques de Karman-Nikuradzé fournissent alors un coefficient de frottement global C_Fc = 0,0083, ce qui permet de calculer le coefficient de perte de charge dans la zone centrale de l'enceinte 1.

In the case of an annular duct of given roughness, where a flow is established of which one knows the Reynolds number, it is known that the coefficient of pressure loss is proportional to an overall coefficient of friction C _F which one can obtain using the formulas or Karman-Nikuradze charts; these formulas are also valid for fully smooth walls.

• the hydraulic Reynolds number R _ec is calculated as a function of the hydraulic diameter D _Hc , the speed V _b (which is a maximum for the average speed of flow) and the kinematic viscosity of zinc at the temperature considered (from l 'order of 450 °). We find R _ec = 120,000, which means that the flow is slightly turbulent.
• the equivalent uniform roughness of the wall of the metallurgical product 4 is taken to be 0.35 millimeters, for a concrete reinforcement with a diameter equal to 10 millimeters.
• the Karman-Nikuradze abacs then provide an overall coefficient of friction C _Fc = 0.0083, which makes it possible to calculate the pressure drop coefficient in the central zone of enclosure 1.

c) partial drive pressure in the central zone of the enclosure

This partial pressure P _c is equal to the half length L _c of the enclosure multiplied by the pressure drop coefficient calculated previously. We find P _c = 190 Pa (or 19 millibars).

d) partial drive pressure in the part of the outlet channel 8 of the enclosure 1 where the zinc penetrates

This partial pressure P _i is equal to the length L _i of zinc in channel 8 multiplied by the coefficient of pressure drop in the flow in said channel 8.

The principle of calculation of this last coefficient is identical to what has been detailed previously for the calculation of the pressure drop coefficient in the central zone of enclosure 1, only differing the numerical values to be taken into account.

In this regard, the hydraulic Reynolds number R _ei is calculated as a function of the hydraulic diameter D _Hi of the annular conduit between the metallurgical product 4 and the walls of the outlet channel 8, the diameter T _{f of which} is equal to 16 millimeters, this which gives an annular space e _i equal to 3 millimeters and, therefore, D _Hi equal to 12 millimeters. Under these conditions, R _{ei is} worth approximately 24,000.

The equivalent uniform roughness of the wall of the metallurgical product 4 being of course always identical, the Karman-Nikuradze abacs provide an overall coefficient of friction C _Fc = 0.0146.

As we do not know a priori the length L _i , we first calculate the gradient of the drive pressure in the outlet channel 8, which is equal to 12,900 Pa / m, then we write the balance of pressures at the outlet meniscus of the galvanizing bath.

1.2. Calculation of the Lorenz force necessary to maintain the zinc bubble in the galvanizing enclosure 1

The sum of the pressures calculated previously, namely (P _iso + P _c + P _i ), must be balanced by the volume magnetic pressure P _m generated in the zinc by the transverse sliding field created at the level of the polyphase inductive winding 6 of exit from enclosure 1.

We know that the magnetic pressure P _m is equal to the product of the electrical conductivity of zinc at the temperature considered, the square of the effective induction B _eff , the length L _i on which the field acts and a coefficient V _m taking into account the geometry of inductor 6. If we choose a polar half-step equal to 7 centimeters and an excitation frequency of 50 Hz - these two values providing the speed of axial displacement of the sliding magnetic field, also called drift speed -, l 'effective induction B _eff being chosen to be equal to 0.07 Teslas, there is the magnetic pressure gradient necessary to maintain the zinc bubble in the galvanizing enclosure 1, ie 87,000 N / m ³ .

We are then able to calculate the value of the length L _i and to verify that it remains less than the length of Couette. Here we find L _i = 2.1 centimeters, which means that the zinc penetrates very little into the outlet channel 8, since the length of the inductor winding 6, given by the polar half-step, is equal to 28 centimeters .

• soit en réglant la fréquence d'excitation du courant alternatif créant l'induction efficace B_eff,
• soit en réglant l'intensité dudit courant alternatif.

Generally, we will always "arrange" so that the covering liquid does not penetrate, in the outlet channel 8, beyond half the length of the inductor winding 6, this condition can be simply fulfilled :

• either by adjusting the excitation frequency of the alternating current creating the effective induction B _eff ,
• either by adjusting the intensity of said alternating current.

2. Problem of wiping

• dans la zone du canal de sortie 8 où pénètre le zinc (soit sur la longueur L_i), la force volumique d'origine magnétique V_m est comparable à une force d'origine gravitaire ; on peut ainsi admettre que les résultats du modèle de Landau et Levitch, développé pour connaître l'épaisseur entraînée par une plaque plane extraite à la verticale d'un bain liquide horizontale, sont applicables dans cette zone du canal de sortie 8.
• dans la partie du canal de sortie 8 située derrière le ménisque d'équilibre du bain liquide, le champ magnétique transverse glissant agit sur le film liquide pour l'amincir, l'épaisseur du film au niveau dudit ménisque étant égale à celle prévue par le calcul précédent de Landau et Levitch.

The thickness deposited on the metallurgical product 4 is normally calculated in two stages, namely:

• in the zone of the outlet channel 8 where the zinc penetrates (ie over the length L _i ), the volume force of magnetic origin V _m is comparable to a force of gravity origin; one can thus admit that the results of the model of Landau and Levitch, developed to know the thickness entrained by a plane plate extracted vertically from a horizontal liquid bath, are applicable in this zone of the outlet channel 8.
• in the part of the outlet channel 8 located behind the meniscus of equilibrium of the liquid bath, the transverse sliding magnetic field acts on the liquid film to thin it, the thickness of the film at the level of said meniscus being equal to that provided by the previous calculation by Landau and Levitch.

2.1. Thickness of the liquid film given by the Landau Levitch model

This model takes into account, by a complex formula that can be found on the reference mentioned above: the surface tension of the liquid (here zinc molten at 450 ° C), its turbulent dynamic viscosity (itself proportional to the coefficient of friction global C _Fi ), the speed V _b of the product 4 and the intensity of the volume forces developed in the zinc, which we have just calculated for the sealing problem.

By calculating the thickness given by this model, we note that it varies inversely with the square root of the intensity of the volumic forces of magnetic origin; this result, of course expected, means that it is possible to modify the thickness in question quite appreciably, by increasing or decreasing the intensity of the volume forces, this mainly by playing on the intensity of the effective magnetic induction B _eff . This adjustment, which modifies the position of the meniscus in the outlet channel 8, is possible within a range of values of B _eff where, according to the criterion indicated above, the covering liquid does not penetrate, in the outlet channel 8, beyond half the length of the inductor winding 6. This criterion roughly covers that according to which L _i does not exceed the length of the quilt of the flow located in the outlet channel 8 of the enclosure galvanizing 1, that is to say that said flow remains slightly turbulent; if one of these criteria is no longer observed, the turbulence makes the Landau and Levitch model totally inadequate.

2.2. Effective magnetic wiping length

This effective magnetic wiping length is defined as the residual length of the outlet channel 8, located behind the equilibrium meniscus of the galvanizing bath, and on which the magnetic field transverse sliding is always likely to act.

The possibilities of adjusting the thickness at this level are however reduced since all the characteristics of the enclosure 1 and of the inductor 6 are already fixed. The calculation of the thinning of the liquid film up to the downstream end of the outlet channel 8 can be carried out by calculating the "free surface" flow of the liquid film on the surface of the rough metallurgical product 4. In fact , we see that this thinning remains negligible in most cases.

A generally correct practical approximation therefore consists, in the calculation of wiping, of only taking into account the thickness of the liquid film given by the Landau and Levitch model.

3. Generalization

The dimensioning of a galavanization enclosure 1 and of its output inductor 6 depends first of all on the dimensions and the possible roughness of the metallurgical products 4 to be coated with the chosen molten metallic material. The geometry of the inductor 6 is then established so that, near the surface of the products 4, the magnetic field created is transverse and sliding. We then seek, for a wide range of running speed V _b of the products 4 through the enclosure 1, the frequency, the pole pitch and the intensity of the effective induction B _eff which should be taken to balance the pressures under the first half of the inductor 6. So that the magnetic leaks are not too great, an additional dimensioning rule consists in taking an air gap such that the ratio of the polar half-step to said air gap is not greater than 3; this defines a so-called "housing" coefficient between the effective induction B _eff and the induction B ₀ created by the inductor winding 6, which is then given by a Byot and Savard law corresponding to the geometry of the coils of the inductor 6. Finally, we apply the Landau and Levitch model to calculate the thickness deposited on metallurgical products 4 corresponding to each of the speeds V _b chosen. It is also possible to refer, on the same graph, the length L _i over which the coating liquid penetrates into the outlet channel 8 of the enclosure 1. Such a graph, corresponding to the example treated above, is given on Figure 2.

Most of the above results remain valid in the case of a vertical galvanizing installation.

Claims (8)

1. A method of dimensioning an electroplating enclosure provided with at least one sealing device and/or wiping device at the point where the metallurgical products exit, having passed through a liquid coating bath contained in the said enclosure, the said device being preferably an inductive element arranged to this effect around an exit port of the enclosure in order to produce a transverse electromagnetic field alternating and sliding at the surface level of the said products, characterised in that it consists of calculating or verifying principally the transverse dimensions of the said enclosure, its axial length, the transverse section of the said products, their speed, the dynamic viscosity of the said coating liquid, its pressure in the enclosure, the transverse dimensions of the exit port of the enclosure, the displacement speed of the sliding electromagnetic field and its intensity in the said liquid, and finally a parameter representative of the possible roughness of the metallurgical products, the conditions for which the 'Couette' lengths associated respectively with the coating liquid flow in the enclosure and in its exit port remain below the critical values above which the said flow becomes substantially turbulent.
2. A method of dimensioning an electroplating enclosure according to the preceding Claim, characterised in that the thickness of the laminar or turbulent coating limit, of the flow at the inlet of the exit port of the electroplating enclosure is maintained below a limit value above which it is no longer possible to control its increase.
3. A method of dimensioning an electroplating enclosure according to the preceding Claim, characterised in that the thickness deposited on the treated metallurgical products is given as a function of their flow speed in the electroplating enclosure by a formula similar to that used in the hydrodynamic model of Landau and Levitch.
4. A method of dimensioning an electroplating enclosure according to any one of the preceding Claims, characterised in that the possible roughness of the treated metallurgical products is taken into account for calculating the thickness deposited, by means of the law of flow partition in the immediate vicinity of the metallurgical product to be coated.
5. A method of dimensioning an electroplating enclosure according to the preceding Claim, characterised in that the law of flow partition to be taken into account is the one known by the name of Karmann-Nikuradzé.
6. A method of dimensioning an electroplating enclosure according to any one of the preceding Claims, characterised in that in the event that an inductive element of the polyphase winding (6) type is used the intensity of the alternating current is regulated creating the effective B_eff induction in order that the coating liquid does not penetrate beyond half the length of the inductive winding (6) which is arranged around the exit duct (8) of electroplating enclosure (1).
7. A method of dimensioning an electroplating enclosure according to any one of Claims 1 to 5, characterised in that in the event of using an inductive element of the polyphase winding (6) type the excitation frequency of the alternating current is regulated creating an effective induction B_eff in order that the coating liquid does not penetrate beyond half the length of the inductive winding (6) which is arranged around the exit duct (8) of the electroplating enclosure (1).
8. A method of dimensioning an electroplating enclosure according to the preceding Claim, characterised in that the air gap of the polyphase inductive winding (6) is selected such that the ratio of the polar half-thread on the said air gap is no greater than 3.

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