AU693106B2 - 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

FRGW08.000 1 A METHOD FOR SIZING A GALVANISING ENCLOSURE EQUIPPED WITH A DEVICE FOR THE MAGNETIC WIPING OF GALVANISED METALLURGICAL PRODUCTS This invention relates to a method for sizing a galvanising enclosure equipped with a device for the magnetic wiping of galvanised metallurgical products particularly applicable within the context of a continuous galvanising process.

It is known from classic hydrodynamic studies that the forces of inertia (mainly weight) and the forces of friction (viscosity, influence of the nature of the surface) totally govern development of the drainage of a liquid coating in proximity to the surface of a metallurgical product being coated.

Under given conditions of reactivity, that will be disregarded subsequently, with regard to the subject of the invention, the development of drainage in the zone close to said product largely governs the final thickness deposited on the latter.

In this respect, the establishment of laminar flow appears, a priori, to be desirable in the sense that it allows one, in the usual boundary layer approximation, to link, by simple and known laws, the feature physical quantities nanely, the velocity profile with respect to the surface of the metallurgical product, itself being transported at constant velocity, the dynamic viscosity of the coating liquid, its density and the surface tension between said metallurgical product and said liquid (parameters of wettability). The deposited thickness is then governed by the thickness of the liquid film which is drained by the metallurgical product when it is drawn out of the liquid bath, a usable approximation being, in this case, that established by Landau and Levitch in a report with the reference Acta Physicochimica USSR Vol 17, No.l-2, 1942 "Dragging of a liquid by a moving plate".

In the ideal laminar case, the thickness obtained is often too great for desirable galvanising applications r ti i-i i -i gi B:j I l ll wmc 2 this is why various forms of wiping have been envisaged, that is to say ways of reducing the deposited thickness and, proposals have mainly been made for pneumatic wiping techniques (the action of air knives creating a counter pressure on the free surf-ce of the metallurgical product emerging from the bath of liquid), mechanical wiping techniques (the action of rollers "licking" the metallurgical product by means of pads of asbestos) and, finally, magnetic wiping techniques, this invention relating to this last category.

Today there are in existence a very large number of prior magnetic wiping devices. This latter art advocates making use of the Lorenz force which can be developed in the coating liquid by a magnetic field, static or alternating, fixed or sliding, brought about by the presence of electric currents induced in said liquid (obviously a conductor when we are considering zinc, copper or aluminium) by the relative movement of said liquid and said field. In all cases that will subsequently be discussed, the Lorenz force is supposed to oppose the forces of inertia and of viscosity which have an effect on the flow, in so far, of course, that they are sufficiently intense to modify the velocity profile proximate to the surface of the metallurgical product. It is therefore understood that by means of a magnetic field, it is, a priori, possible to act on the thickness of the boundary layer, the effects being in the bath of coating liquid, before the metallurgical product leaves, the action of the field directly counter balances the forces of inertia, mainly reducing gravitational effects, outside the bath, the action of the field makes itself felt only on the entrained liquid film, or by the combination of these two effects.

In this regard, the techniques known under the respective names of the companies that have developed them, namely ASEA, ARBED, AUSTRAJIAN WIRE and LYSAGHT, represent examples of carrying out the process that cover

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7 3 almost all of the techniques in use today. For example, in Patent No. FR-2 41? 109, in the name of AUSTRALIAN WIRE IND PROPRIETARY, it is recommended that a fixed, single phase electromagnetic field is used, that is to say, a non-sliding field for which one may vary either the intensity or the frequency in order to adjust the deposited thickness. In the Patent FR-2 410 247, in the name of JOHN LYSAGHT AUSTRALIA LIMITED, an analogous device is shown but the geometry is different to that used in the preceding patent, with, apart from that, magnetic field pulse frequencies preferentially set at around kHz. In the prior ARBED art, described in Patent No. BE-882 069, amongst other things, it is envisaged that a sliding electromagnetic field is used which acts upon the excess of liquid metal carried along by a sheet of metal leaving a galvanising bath. Finally, in Patent No.DE-2 023 900 (in the name of ASEA) all the possibilities for wiping outside the galvanising bath are shown (longitudinal, transverse, alternating fixed field or sliding field).

The inventors are aware that the action of the magnetic field is only sensitive, and hence only effectively controllable, insofar as the purely hydrodynamic phenomena do not mask the effects of magnetic origin that are being sought. It is easy to see that this point is never tackled in any of the prior arts of magnetic wiping and that, as a consequence, it appears that the problem posed in the case in point is a completely new one.

In particular, in all the prior patents relating to magnietic wiping, the metallurgical products to be coated pass vertically through a galvanising bath whose free surface is horizontal; hence, in this case there is no possibility for the covering liquid to escape out of the galvanising enclosure. However, the new constraints in thb surface treatment industry is leading to research into magnetic wiping solutions for a continuous galvanising Sinstallation, such as that described in the Patent iA Ilr 4- No.FR-2 647 814, in the name of FRANCE GALVA LORRAINE, which is arranged horizontally; other installations of the same sort are also known, notably from Patents Nos. GB-A-777 213 and US-A-2 834 692. It should be remembered that, in this type of installation, the galvanising enclosure has entrance and exit openings aligned with the path of the products to be treated, the upper level of the bath of coating liquid being situated above said openings because of this, it is necessary to provide sealing devices, with the task of compensating for the hydrostatic pressure which tends, otherwise, to cause said liquid to flow out of the enclosure. With regard to this, one can think that continuous or alternating magnetic induction, of the type generally used for magnetic wiping can, through an identical physical mechanism, contribute, at least partially, to retaining the liquid in the enclosure.

Insofar as an altexnating fixed field does not, in principle, develop any force of a rotational iature in the coating liquid, (the opposite of a sliding field), a Lorenz force sufficiently intense to compensate for the forces of inertia of the galvanising bath can only be generated, with this type of field, with a very high frequency and/or an intense magnetic field; which leads, in the first case, to a skin depth (depth of penetration of the field into the liquid conductor) too small to hope to retain said coating liquid in proximity to the metallurgical product and, in the second case, to an expensive oversizing of the installation. As a consequence, the use of a magnetic wiping device with an alternating fixed field as a sealing means for a horizontal galvanising enclosure is virtually ruled out.

From another aspect, one is aware that the only metallurgical products that can be treated with the prior magnetic wiping installations are entirely smooth. N w, in practice, the inventors have given prominence to the substantial part played by the roughness of the surface of the treated products, notably in the case of non-validity of the approximation, generally implicitly accepted, of the laminar nature of the coating liquid flow in proximity to said surface. In this regard, where phenomena of hydrodynamic turbulence appear, it is known that the roughness of the products treated is all the more involved because the coating liquid is situated in a confined space which is always the case in the centre of the gap or the coil of an electromagnetic system creating the induction necessary to develop a Lorenz force, notably in said liquid One has observed that, in connection with the preceding comment, that the transverse dimensions and the length of the confining galvanising bath enclosure were not without importance from the hydrodynamic point of view. Even so, the transition zone between the sleeve and the sealing device and/or the magnetic wiping device and the transverse dimensions and the length of the exit channel around which a magnetic induction responsible for the seal is being created, in fact play a dominant role in determining the quality and the thickness of the layer deposited; certain of the conditions obtained even contradict some of the trends previously made use of in the case of the galvanising of smooth products.

From these different assessments, this invention aims at giving prominence to the new problem of providing a combined sealing and horizontal magnetic wiping device, linked to recent technolDgical choices, providing various practical solutions to the problem of correctly sizing said magnetic wiping device, particularly in relation to the geometry of the products being treated, these solutions also being applicable moreover to vertical galvanising installations, allowing the thickness deposited on substantially rough products (for example concrete reinforcement bar) to be predicted, something that has proved impossible until now.

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6- To that end, this invention relates firstly to a process for sizing a galvanising enclosure provided with, at least one sealing device and/or wiping device on the side where the metal products emerge having passed through a bath of coating liquid contained in said enclosure, said device being preferably an induction device arranged for this purpose around an exit channel from the bath in order to produce a transverse electromagnetic field, alternating and sliding, at the surface of said products, characterised in that it consists of calculating or verifying, from principally the transverse dimensions of said enclosure, its axial length, the transverse section of said products, their speed, the dynamic viscosity of said coating liquid, its pressure in the enclosure, the transverse dimensions of the exit channel from the enclosure, the displacement speed of the sliding electromagnetic field and its intensity in said liquid and finally a parameter representative of the possible roughness of the metallurgical products, the conditions under which the Couette lengths, associated respectively with the flow of the coating liquid in the enclosure and in its exit channel remain lower than the critical values after which said flows become clearly turbulent.

One recalls that a Couette flow is one that characterises an incompressible and viscous fluid, that may or not be a conductor, situated between two supposedly infinite parallel plates, one of which is set in motion parallel to itself; the purpose of the Couette hydrodynamic calculation is to establish the parameters governing the profile of flow speeds between the two plates, and complications that may interfere in relation to the roughness of the surfaces in contact with the fluid one speaks of flow under shear.

The principles of similarity used in the mechanics of classic fluids, to resolve complex flow problems in an adimensional way, show that the Couette model is applicable to the problem of axially symmetric flow of a q ~liquid, set in motion in an annular space, the core of I I -7- I which is moving at a supposedly constant speed.

Consequently, this model is applicable on the one hand to the calculation of the profile of flow speeds of the coating liquid which is situated between the internal longitudinal walls of the cylindrical galvanising enclosure and the metallurgical product moving axially through the latter and, on the other hand, to the calculation of the profile of flow speeds of the coating liquid which is situated between the internal walls of the exit channel of the enclosure and said product.

According to the invention, it has been realised that these two flows (continuous of course) have a strong effect on the thickness of the boundary layer, laminar or turbulent and that it is advisable to take them into account in order to calculate the thickness of the liquid V film carried along by the metallurgical product when it emerges, vertically or horizontally, from the free surface of the liquid bath contained in the galvanising enclosure.

Generally, the thickness of the boundary layer, laminar or turbulent, of the flow at the entrance to the exit channel of the galvanising enclosure must be kept below a limiting value beyond which it is no longer possible to control its increase. This effect results directly from the fact that, in accordance with the results established by magnetohydrodynamic theory, the magnetic fields are dampened much more rapidly than the vorticity in liquid conductors 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 coating liquid zones within which the action of one or more Lorenz magnetic forces is wanted. Hence, in the favourable case, where the Couette lengths of the flow in the enclosure and in its exit channel are known and are brought under control, the sizing of the sealing device and/or the wiping device of the galvanising enclosure can be expressed by using the i A non-dimensional numbers normally used in .0 -8 magnetohydrodynamics, namely, the magnetic Reynolds number, the interaction parameter, the Hartmann number and two parameters linked to the geometry of the sliding alternating magnetic field which is selected to create one or more Lorenz magnetic forces in the interior of the flow.

In this regard, the solution presented by the invention is firstly going in the direction of a reduction in the length of the galvanising enclosure which, in relation to its transverse dimensions and the speed of the product must remain less than the Couette hydrodynamic length of the flow. This rule is not, moreover, in contradiction with the conditions set down notably in the patent FR-2 323 772 in the name of Jos6 DELOT in th.is patent, in effect, prominence is given to the fact that use of a short galvanising enclosure with low volume is sufficient to obtain a proper metallurgical reaction between the product to be treated and the coating liquid, insofar as the product to be galvanised has been cleaned, heated and kept under a controlled atmosphere at least upstream of the galvanising enclosure.

On the other hand, since proper sizing of the galvanising enclosure and its exit channel basically makes it possible to inhibit conditions under which turbulence appears, the flow in the exit region of the galvanising enclosure is close to the normal laminar flow that exists at the exit for products treated in vertical galvanising installations this simply means that the Lorenz force developed per unit volume in the liquid bath by the sliding alternating field, plays, in effect, an analogous role to gravity. This "gravitational hypothesis" for the Lorenz magnetic forces, developed in the galvanising bath by the induction unit fitted for this purpose around the exit channel of the galvanising enclosure, enables one to consider that the shape of the meniscus formed between the Sfree surface of the bath and the metallurgical product which is being extracted from it, almost totally controls i the thickness of the layer deposited on said product. As a I NT

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bT i 9 consequence, under the strict conditions laid down by the ivention, this thickness will be given by a formula which is completely analogous to that used in the Landau hydrodynamic model, which was referred to above.

It should also be noted that, if the meniscus is kept sufficiently close to the entrance to the exit channel of the enclosure which is desirable if one wishes to remain short of the Couette length corresponding to this part of the enclosure and that the induction unit zone where the sliding magnetic field is generated is relatively long, it is still possible to take effective action to reduce the thickness of the liquid film forming at said meniscus. In this regard, one recalls that, in principle, the forces of inertia due to the isostatic pressure of the liquid bath in the galvanising enclosure and to the entrainment effect of the metallurgical product will be balanced from the meniscus onwards consequently, behind said meniscus, the Lorenz forces per unit volume act only on the liquid film adhering to the metallurgical product and tend to make said film thinner, thus constituting "genuine" magnetic wiping (that is to say, all considerations relating to sealing are removed). The magnetic wiping in the exit channel of the enclosure at least downstream of the meniscus, is therefore similar to known studies carried out on the thinning out of a barotropic liquid flow with a "free surface" (barotropic since the gravitational hypothesis remains valid).

Finally, according to a particularly advantageous feature of the sizing process conforming to the invention, it is recognised that the roughness of the treated metallurgical product has an effect on the nature of the flow and hence, on the thickness of the layer deposited on leaving the galvanising enclosure. Preferably the model used to do this is the Karman-Nikuradzd model. This model, which has been widely tested in the field of hydrodynamics enables one to know, notably from the bias of nomographs, the coefficient of friction to use according to the roughness of the product and the Reynolds hydraulic number 10 of the flow. More generally, it is essential to accurate knowledge of the flow to take into account what hydrodynamicists call "the law of surface effects" (proportionally dependent upon the loss of head pressure), even, moreover, in the case of smooth metallurgical products since as will be seen below, the law of the surface effects influences, to a considerable extent, the behaviour of the flow in immediate proximity to the metallurgical product to be coated.

Other features and advantages of the inventin will emerge from the description which will follow of an example of the sizing of a horizontal galvanising enclosure, provided with an exit channel around which is arranged an induction unit creating an alternating field, sliding in the axial direction, this enclosure being more particularly intended for the treatment of smooth wires or rough round section such as concrete reinforcement bars, this non-limiting example of the invention being illustrated on the appended drawing on which Figure 1 is a longitudinal section view of the ii Senclosure, its exit channel, the induction unit and the treated bar, Figure 2 is a graph giving, on the one hand the V thickness of zinc de-osited on a concrete reinforcement bar of given roughness and diameter as a function of its Sspeed of passage through the galvanising enclosure and, on the other hand, the length over which the molten zinc penetrates to the interior of the exit channel of said enclosure.

The galvanising enclosure 1 represented on the appended figure incorporates two orifices, an entrance 2 and an exit 3 aligned along the path taken )y a metallurgical product 4 to be galvanised this product 4 is, in the chosen example, a smooth steel wire or a concrete reinforcing bar which has notches distributed more or less regularly along its surface. Enclosure 1 is IN' arranged horizontally, downstream from a group of devices for cleaning and for heating, for example by induction and 11 (downstream) from a device for cooling, for example by water, these various classic post and pre-treatment units not being illustrated on the drawings so as not to obscure the portrayal of the galvanising and wiping means which are concerned here.

The galvanising enclosure 1 is intended to contain a liquid bath of a coating product, preferably a molten metal alloy such as zinc, copper, aluminium and their usual alloys (the bath may therefore also contain low amounts of lead, etc. Being arranged horizontally, the entrance 2 and exit 3 orifices of the enclosure 1 must be provided with sealing means which prevent the liquid escaping through said orifices 2, 3 in the case described, of metallurgical products 4 which are substantially cylindrical, the use of polyphase field coils 5, 6, is chosen, the coils being arranged respectively around the entrance 7 and exit 8 channels of the enclosure 1 in order to generate, in the manner of linear synchronous motors, a magnetic back pressure on the liquid conductor product which has a tendency to flow through said entrance 7 and exit 8 channels 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 being generated by circulation of an electric current in the coils of the induction units 5, 6, so that, in the longitudinal annular space separating product 4 and the internal walls of the channels 7, 8, the magnetic field lines are substantially transverse to the axial displacement of product 4. In the case of the treatment of cylindrical products of noncircular section, such as flat section, strip and other sections, one also endeavours to create a sliding magnetic field transverse to the annular space corresponding to the geometry in question, something which is always possible R with the help of magnetic sheeting or fans which shape the 11 IRAt.iz magnetic field in the manner desired. Furthermore, since 4

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12 normally one is content to produce a sliding magnetic field of low frequency, typically lower than a few hundred Herz, and preferably 50 Herz, the magnetic losses brought about, for example, in the magnetic sheeting will remain low.

Given that the galvanisinq process requires a I continuous supply of liquid coating product into the enclosure 1, compensating for that which is being deposited on the metallurgical products 4, passing through the product, a supply channel 9, in this case vertical, connects a liquid product reservoir to said enclosure 1 so that the hydrodynamic disturbances resulting from this feed should be as small as possible, according to an advantageous feature of the invention, one opts for a central position for the mouth of said supply channel 9 with respect to the two entrance 7 and exit 8 channels of the enclosure 1. A balancing channel 10 has also been fitted on the galvanising enclosure i, placed vertically in a central position, corresponding, for example, with the position of the supply channel 9, and into which the liquid coating product is introduced to a height which allows one to know accurately the isostatic pressure of the galvanising bath furthermore, the free surface of the column of liquid from the bath being in the balancing channel 10, is normally in contact with a protective gas i whose pressure can, if the case arises, be modified through conventional pressurising means. In this regard, the wholk galvanising assembly is preferably kept under a controlled atmosphere, either neutral or slightly reducing, for metallurgical reasons, which are well known to those skilled in the art.

On the other hand, as has already been stated in the description above, the transition zone 11 between the central zone of the enclosure 1 and its exit channel 7 is a converging tube which permits limitation of the risks of turbulence in the liquid product flowing through this part Sof said enclosure i.

iFRA4j 9-, ^i_ 13 According to the invention, the problem that first arises is to size the polyphase induction coil 6 at the exit so that a sealing effect can exist in the exit orifice 3 om enclosure 1, then to size all the other installation parameters which enable the desired wiping to be obtained. These two aspects of the invention will now be tackled one after the other.

1. The problem of the seal Dealing with the sealing problem, as has been specified above, requires knowledge of the total hydrodynamic pressure being exerted up to the balancing meniscus (or free surface) of the coating liquid in the exit channel 8 of the enclosure 1 the knowledge of the total pressure then allows calculation of the Lorenz force per unit volume which is necessary to keep the free surface of the coating liquid at a certain level from the exit channel 8 of said enclosure i, in accordance with the principles stated above.

Since the transverse dimensions of the enclosure 1 are normally of little significance in comparison with the transverse dimension of the metallurgical product 4 to be treated, it is necessary to treat the liquid flow in enclosure 1 as an axisymmetrica! Couette flow which is set up in the annular space between product 4 and the internal walls of said enclosure 1. The rules of similarity applicable to the subject show that this annular flow is simila:r to the flow of the same liquid between two flat plates which are spaced apart at a distance four times the value of the annular space (this will be shown subsequently), one of the two plates being displaced exactly at the speed of the metallurgical product which is passing through the galvanising enclosure i.

Of course, an analogous Couette calculation must also be carried out to know the physical flow conditions in the part of the exit channel 8 of enclosure 1 which the coating liquid enters.

1.1 Calculation of the total pre sure to be compensated for in order to seal the enclosure

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i~ -il~l~ L- ~UICC~D I 14 The total pressure is the sum of the following partial pressures the isostatic partial pressure Piso in the central part of enclosure 1, the value of which is given simply by the classic Archimedean calculation, namely the product of the density of the liquid (molten zinc), the acceleration due to gravity and the height of liquid between the walls of enclosure 1 and the product 4 for a column of molten zinc at 450 0 C, and a height of zinc of 2 centimetres, this 10 first partial pressure amounts to 1350 Pa (or 135 mbars in commca units). It should be noted that the supply pressure of enclosure 1 through the supply channel 9, balences totally the contribution due to the height of zinc in the balancing channel the partial pressure due to the upstream sealing device, that is to say to the polyphase induction coil fitted around the entrance channel 7 of the galvanising enclosure 1 it will be assumed that this pressure just balances the forces of inertia at the entrance orifice 2, which is true in all cases, since this downstream pressure contributes, in fact, to the height of the column of coating liquid in the balancing channel the partial pressure PC which results from the entrainment of the coating liquid by the metallurgical product 4 passing through the central zone of enclosure 1.

the partial pressure Pi which results from the entrainment of the coating liquid by the metallurgical product 4 passing through the exit channel of enclosure 1.

According to the invention, these two partial pressures arising from entrainment are calculated from similar Couette flows, taking into account the length of the central zone of the enclosure 1, the length of the exit channel 8 into which the zinc penetrates, as well as the losses of load oer unit of length in said central zone and respectively in said exit channel 8 of enclosure i.

a) lenath of the aalvanisina enclosure 1 to use The choice of the length of the enclosure has an effect on the behaviour of the liquid flow in proximity to 15 S7the metallurgical product 4 laminar, slightly turbulent or turbulent. The calculation consists of choosing, a priori, an enclosure length and verifying, a posteriori, that it is less than the critical Couette length in the enclosure i. In accordance with the geometry of the enclosure 1 shown on the drawing, which is symmetrical with respect to the central supply zone, the length to use in the calculation is, in fact, the half length Lc of the enclosure, taken here to be equal to 25 centimetres.

b) loss of load per unit of length in the central zone of the enclosure The loss of load per unit of length is classically linked to the frictional force per unit of surface. In the case of the axially symmetrical galvanising enclosure being considered, this relationship is expressed simply as a function of the hydraulic diameter of the annular space between the metallurgical product 4 and the internal walls of said enclosure 1, the density of the coating liquid, the square of the flow speed and a coefficient of loss of load, itself proportional to an overall coefficient of friction dependent on the roughness of the surfaces and the Reynolds number characterising the flow, that is to say ultimately, the law of surface effects, proximate to the metallurgical produ.ct 4.

bl) hydraulic diameter to use in the calculation A purely hydrodynamic analysis of the speed profile Sof a turbulent Couette flow between two flat plates enables one to calculate quite easily that the hydraulic diameter to use in the calculation for an annular channel is equal to four times the annular space. It should be noted that one is adopting the position of assuming that the flow is turbulent since an approximate calculation of the hydraulic Reynolds number in proximity to the metallurgical product 4 moving at rather high speed (namely Vb 1 m/s) shows that the flow regime is surely turbulent.

Typically, the galvanising enclosure 1 is isizcylindrical almost throughout and has a diameter Tc which LNrO i* 16 is more or less constant and which in the numerical examples subsequently developed will be taken as equal to millimetres.

The diameter of the metallurgical product 4 treated in it is taken to be equal to 10 millimetres, which gives an annular space ec equal to 15 millimetres and an hydraulic diameter Dhe of 60 millimetres in the central zone of the enclosure 1.

b2 law of surface effects In the case of an annular channel of given roughness, where a flow is established, the Reynolds number of which is known, the coefficient of loss of load is known to be proportional to an overall coefficient of friction CF which can be obtained with the aid of formulae or the Karman-Nikuradze nomograpis these formulae are equally valid for entirely smooth surfaces.

the hydraulic Reynolds number Rec is calculated as a function of the hydraulic diameter Dhc, the speed Vb (which is a maximum for the mean flow speed) and the kinematic viscosity of the zinc at the -nperature being considered (of the order of 4500). A value of Rec 120,000 is found which signifies that the flow is certainly slightly turbulent.

the equivalent uniform roughness of the surface of the metallurgical product 4 is taken to be equal to 0.35 millimetres, for concrete reinforcement bars of millimetre diameter.

the Karman-Nikuradzd nomographs then give an overall coefficient of friction Cfc 0.0083, which allows the calculation of the coefficient of loss of load in the central zone of the enclosure 1.

c) partial oressure due to entrainment in the central zone of the enclosure This partial pressure Pc is equal to the half length Lc of the enclosure multiplied by the coefficient of loss of load calculated previously. The value found is Pc 190 Pa (or 19 millibars).

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Si i 17 d) partial pressure due to entrainment in the Dart of the exit channel 8 of the enclosure into which the zinc penetrates This partial pressure Pi is equal to the length L i of zinc in the channel 8 multiplied by the coefficient of loss of load of the flow into said channel 8.

The principle of the calculation of this latter coefficient is identical to that detailed previously for the calculation of the coefficient of loss of load in the central zone of enclosure 1, the only difference being the numerical values put into the calculation.

In this regard, the hydraulic Reynolds number Rei is calculated as a function of the hydraulic diameter DHi of She annular channel between the metallurgical product 4 and the internal walls of the exit channel 8, whose diameter Tf is equal to 16 millimetres, which gives an annular space e i equal to 3 millimetres and, hence, DHi equal to 12 millimetres. In these conditions, Rei has a value of about 24,000.

Since the equivalent uniform roughness of the surface of the metallurgical product 4 is still of course the same, the Karman-Nikuradz6 nomographs give an overall coefficient of friction CFC 0.0146.

Since, a priori, the length Li is not known, one firstly calculates the gradient of the entrainment I pressure in the exit channel 8, which is equal to 12,900 Pa/m, then the pressure equilibrium at the meniscus at the exit from the galvanising bath is written down.

r1.2. Calculation of the Lorenz force required to 30 keep the slug of zinc within the galvanising enclosure 1 The sum of the pressures previously calculated, namely (Piso Pc Pi) must be balanced by the magnetic pressure per unit volume Pm generated in the zinc by the sliding transverse field created by the polyphase induction coil 6 at the exit of the enclosure 1.

It is known that the magnetic pressure Pm is equal to the product of the electrical conductivity of zinc at the temperature being considered, the square of the r o" 18 effective induction Beff, the length L i over which the field is acting and a coefficient Vm which takes into account the geometry of induction coil 6. If one selects a polar half pitch equal to 7 centimetres and an excitation frequency of 50 Hz these two values supplying the axial displacement speed of the sliding magnetic field, sometimes called the drift speed the effective induction Beff having been chosen to be equal to 0.07 Teslas, the magnetic pressure gradient necessary to keep the slug of zinc inside the galvanising enclosure is found to be 87,000 N/m 3 o The value of the length Li can then be calculated and it can be verified that it remains lower than the Couette length. In this case a value L i 2.1 centimetres is found which indicates that the zinc only penetrates to a small extent into the exit channel 8, since the length of the induction coil 6, given by the polar half-pitch, is equal to 28 centimetres.

Generally, it is always arranged that the coating liquid does not penetrate further than half the length of the induction coil 6, a condition that can simply be satisfied either by adjusting the excitation frequency of the -Llt,rating current creating the effective induction Bef or by adjusting the intensity of said alternating current.

2. The wipina problem SThe thickness deposited on the metallurgical product 4 is normally calculated in two stages, namely i -within the zone of the exit channel 8 into which the zinc penetrates (or over the length Li), the force per unit volume of magnetic origin Vm is comparable to a gravitational force it can therefore be accepted that results from the Landau and Levitch model, which was developed in order to know the thickness transported by a flat plate being extracted vertically from a horizontal ~i'R 4 19 bath of liquid, are applicable in this zone of the exit channel 8.

in the part of the exit channel 8 situated behind the balancing meniscus of the liquid bath, the sliding transverse magnetic field acts on the liquid film and thins it out, the thickness of the film at said meniscus being equal to that predicted by the previous Landau and Levitch calculation.

2.1. Thickness of the liguid film given by the Landau Levitch model This model, through the use of a complex formula which can be found under the reference mentioned above, takes account of the surface tension of the liquid (in this case, the molten zinc at 450 0 its turbulent dynamic viscosity (itself proportional to the overall coefficient of friction CFi), the speed Vb of the product 4 and the intensity of the forces per unit volume developed in the zinc, that have just been calculated in connection with the sealing problem.

While calculating the thickness given by this model, one observes that it varies inversely with the square root of the intensity of the forces of magnetic origin per unit volume; this expected result indicates that it is possible to modify the thickness concerned quite finely, by increasing or decreasing the intensity of the forces per unit volume, by, in the main, making use of the intensity of the effective magnetic induction Beff This adjustment, which modifies the position of the meniscus in the exit channel 8, is possible within the range of values for Beff for which, according to the criterion mentioned above, the coating liquid does not penetrate into the exit channel 8 beyond half-way along the induction coil 6. This criterion roughly overlaps with that, according to which

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i does not exceed the Couette length of the flow in the exit channel 8 of the galvanising enclosure 1, that is to say, said flow remains slightly turbulent if one of these criteria is not observed, the turbulence makes the Landau and Levitch model totally inadequate.

rO/. 20 2.2. Effective magcrnetic wiping length This effective magnetic wiping length is defined as the residual length of the exit channel 8, situated behind the balancing meniscus of the galvanising bath and on which the transverse sliding magnetic field is in a position to act.

The possibilities of making adjustments to the thickness by these means are however reduced since all the features of the enclosure 1 and the induction coil 6 are already fixed. The calculation of the thinning out of the liquid film occurring up to the downstream end of exit 8, I. can be carried out by calculating the flow at a "free surface" of the liquid film on the surface of the rough metallurgical product 4. In fact this thinning out remains U 15 negligible in most cases.

When calculating the wiping, a practical approximation which is generally correct consists of only taking into account the thickness of the liquid film given by the Landau and Levitch model.

3. General points The sizing of a galvanising enclosure 1 and of its induction coil at the exit depends firstly on the dimensions and on the possible roughness of the metallurgical products to be coated with the chosen molten metal. The geometry of the induction co. 6 is then established so that, close to the s: f ace of the products 4, the magnetic field created s transverse and sliding. One then looks for, for a wide .ange of speeds Vb for the passage of the products 4 through the enclosure 1, the frequency, the polar pitch and ,he intensity of the effective induction Beff which it is advisable to take to balance the pressures beneath the first half of the induction coil 6. So that magnetic leakage does not become too great, an additional rule for sizing consists of taking a gap such that the ratio of the polar half pitch to said gap is not greater than 3 this defines a coefficient called "the casing coefficient" between the effective induction Beff and the induction B 0 created by 41 I a 21 the induction coil 6, which is given by a law of Byot and Savard, and corresponds to the geometry of the windings of the induction coil 6. The model of Landau and Levitch is then used to calculate the thickness deposited on the metallurgical products 4 corresponding to each of the chosen speeds Vb. It is equally possible, to show, on the same graph, the length L i along which the coating liquid penetrates into the exit channel 8 of the enclosure 1.

Such a graph, corresponding to the example dealt with above, is given in Figure 2.

Most of the preceding results remain valid in the case of a vertical galvanising installation.

J

Claims (9)

1. A method for sizing a galvanising enclosure provided with at least one sealing device and/or wiping device on the side where metallurgical products exit, having passed through a bath of coating liquid contained in said enclosure, said device being preferably an induction unit arranged to this end around an exit channel from the enclosure in order to produce a transverse, alternating and sliding electromagnetic field, at the surface of said products, the method including calculating and verifying, mainly from the transverse dimensions of said enclosure, its axial length, the transverse section of said products, their speed, the dynamic viscosity of said coating liquid, its pressure in the enclosure, the transverse dimensions of the exit channel from the enclosure, the speed of displacement of the sliding electromagnetic field and its intensity in said liquid and finally a parameter representative of the possible roughness of the metallurgical products, the conditions under which the Couette lengths associated respectively with the flow of the coating liquid in the enclosure and in its exit channel remain less than the critical values beyond which said flows become clearly turbulent.

2. A method for sizing a galvanising enclosure according to the preceding claim, wherein the thickness of the laminar or turbulent boundary layer of the flow at the entrance to the exit 6 4 channel frnm the galvanising enclosure is kept below a limit value beyond which it is no 4 4 longer possible to control its increase.

3. A method for sizing a galvanising enclosure according to the preceding claim, wherein the thickness deposited on the treated metallurgical products is given, as a function of their speed of passage through the galvanising enclosure by a formula analogous to that used in the hydrodynamic model of Landau and Levitch. -23

4. A method for sizing a galvanising enclosure according to any one of the preceding claims, wherein the possible roughness of the treated metallurgical products is taken into account in the calculation of the thickness deposited through application of the law of surface effects on the flow in immediate proximity to the metallurgical product to be coated.

A method for sizing a galvanising enclosure according to the preceding claim, wherein the law of surface effects to be taken into account is that known under the name of Karmann-Nikuradze.

6. A method for sizing a galvanising enclosure according to any one of the preceding claims, such that in the case where an induction unit in the form of a polyphase coil is used, the intensity of the alternating current creating the effective induction B. is adjusted so that the coating liquid does not penetrate beyond half-way along the length of the induction coil S which is arranged around the exit channel from the galvanising enclosure.

7. A method for sizing a galvanising enclosure according to any one of claims I to 15 such that in the case where an induction unit in the form of a polyphase coil is used, the excitation frequency of the alternating current creating the effective induction Beff is adjusted so that the coating liquid does not penetrate beyond half-way along the length of the induction coil which is arranged around the exit 3 channel from the galvanising enclosure.

8. A method for sizing a galvanising enclosure according to the preceding claim characterised in that the gap of the polyphase induction coil is ciosen so that the ratio of the polar half-pitch to said gap is not greater than 3. l RA 4 V 24

9. A method for sizing a galvanising enclosure substantially as hereinbefore described with reference to the drawings. Dated this 30th clay of April 1998 PATENT ATTORNEY SERVICES Attorneys for DELOT PROCESS 0 4 0 0 .000 CS 0 a S 0 S t. C.. *0 S t *S CS.. 0 S *S 0 SCS S SC., OSC. Sv(Y*'L-C. ~v. 1 ABSTRACT OF THE DISCLOSURE This invention relates to a method for sizing a galvanising enclosure provided with a device for the magnetic wiping of galvanised metallurgical products, and which is used particularly within the context of a continuous galvanising process. This method, according to which the wiping device is preferably an induction unit arranged to this end around an exit channel of the enclosure in order to produce a transverse, alternating and sliding electromagnetic field at the surface of said products, is characterised in that it consists of calculating or verifying, from principally the transverse dimensions of said enclosure, its axial length, the transverse section of said products, their speed, the dynamic viscosity of said coating liquid, its pressure in the enclosure, the transverse dimensions of the exit channel of the enclosure, the displacement speed of the sliding electromagnetic field and its intensity in said liquid, and finally a parameter representative of the possible roughness of the metallurgical products, the conditions under which the Couette lengths associated respectively with the flow of the coating liquid, in the enclosure and in its exit channel, remain below critical values beyond which said flows become clearly turbulent. Ak Figure 1 k-o