WO1997041985A1 - Electromagnetic valve - Google Patents

Electromagnetic valve Download PDF

Info

Publication number
WO1997041985A1
WO1997041985A1 PCT/GB1997/001245 GB9701245W WO9741985A1 WO 1997041985 A1 WO1997041985 A1 WO 1997041985A1 GB 9701245 W GB9701245 W GB 9701245W WO 9741985 A1 WO9741985 A1 WO 9741985A1
Authority
WO
WIPO (PCT)
Prior art keywords
liquid
magnetic field
field
generator
valve apparatus
Prior art date
Application number
PCT/GB1997/001245
Other languages
French (fr)
Inventor
Keith Richard Whittington
Original Assignee
Keith Richard Whittington
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Keith Richard Whittington filed Critical Keith Richard Whittington
Priority to AU27072/97A priority Critical patent/AU2707297A/en
Priority to EP97920852A priority patent/EP0914223A1/en
Publication of WO1997041985A1 publication Critical patent/WO1997041985A1/en

Links

Classifications

    • BPERFORMING OPERATIONS; TRANSPORTING
    • B22CASTING; POWDER METALLURGY
    • B22DCASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
    • B22D41/00Casting melt-holding vessels, e.g. ladles, tundishes, cups or the like
    • B22D41/14Closures

Definitions

  • This invention relates to valves, and concerns in particular valves for controlling the flow of electrically-conductive fluids, for example molten metals, from a reservoir thereof.
  • the liquid, molten, metal is poured under gravity from a reservoir container known as a tundish into an open-bottomed, water-cooled mould from which a solidifying strand of steel is withdrawn continuously; the tundish may have either an open nozzle or an elongate pouring tube the free end of which is actually submerged in the mould contents.
  • pouring tubes which have internal diameters ranging from 12mm to 25mm. Similar processes are in use in the casting of other metals and alloys.
  • the trend in the primary metals industries is towards higher product quality and faster casting speeds. Both requirements necessitate accurate control of pouring, determined by factors such as the cooling rate, the reciprocation rate of the mould, and the withdrawal speed of the solidifying metal strand. Most preferably the pouring rate should be decoupled from, and independent of, the head of liquid metal in the tundish, and ideally the pouring should be amenable to continuous, rapid, automatic modulation under computer control.
  • the traditional control of the pouring rate is by hydraulic manipulation of a slide gate fitting across the nozzle or pouring tube, or of a conical ceramic stopper which is inside the tundish and in operation is raised from or lowered into the tundish outlet.
  • these devices are subject to blockage and erosion, to freezing-up of the apertures through which the melt passes, to leakage, and to wear, all of which make accurate control difficult and necessitate frequent replacement of the moving parts.
  • a slide gate may also suck in air through the clearances between the sliding surfaces, and the air thus sucked in causes oxidation of the molten steel and so increases the impurity content of the casting.
  • a control valve for use in an application such as a continuous casting process should have no moving parts, should be capable of rapid and continuously-variable flow rate adjustment (preferably from full flow to zero flow) under computer control, should be usable with standard pouring tubes, and should be small and light enough that it is capable of being fitted into position with minimum difficulty by one or two men.
  • a desideratum might be met by an electromagnetic valve rather than a mechanical one, and the present invention proposes a novel form of electromagnetic valve which substantially or wholly meets the desired criteria.
  • a variation on this technique employs a relatively complex structure of baffles in the pouring tube, which baffles distort the magnetic field, resulting in a net upward force on the liquid metal.
  • these pumps require an electrical contact to be made with the liquid metal, and in all cases the channel through which the liquid metal flows is configured to optimize the performance of the pump; it may, for example be a wide, narrow slot, or it may have side branches to allow return current flows through the liquid metal.
  • the invention proposes a simple but significant and surprising variation of the various techniques suggested hitherto. More specifically, the invention suggests that there be created across or around the outlet/pouring tube of the molten metal reservoir (the tundish, for example) an alternating electromagnetic field, that there be induced electrical currents - eddy currents - in the molten metal as it passes through this field, which eddy currents interact with the applied magnetic field, and that the directions and magnitudes of the field and of the induced eddy currents are arranged such that forces are generated in the molten metal which oppose the downward flow of the liquid and so provide the desired controllability of the passage of the metal through the outlet.
  • the molten metal reservoir the tundish, for example
  • the directions and magnitudes of the field and of the induced eddy currents are arranged such that forces are generated in the molten metal which oppose the downward flow of the liquid and so provide the desired controllability of the passage of the metal through the outlet.
  • the invention proposes that, for use with a uniform-section output tube/channel, there be employed two adjacent out- of-phase magnetic fields which each cause eddy currents in the field space of the other that are in phase with that field and so create Lorenz forces the effects of which in that field are directed to impede/control liquid flow.
  • the invention provides valve apparatus for controlling the flow of an electrically-conductive liquid along a channel, which valve apparatus comprises: a first magnetic field generator, for creating across the flowing liquid a first alternating magnetic field, this first generator being shaped and disposed adjacent the channel to create that first field in a direction substantially orthogonal to the liquid flow direction; and a second magnetic field generator, also for creating across the flowing liquid an alternating magnetic field, this second field being of the same frequency as the first magnetic field but having a substantial component 90° out of phase with it, this second generator being shaped and disposed adjacent the channel to create that second field in a direction substantially orthogonal to the liquid flow direction and substantially parallel to the first field; the two generators being so disposed that the path of the eddy currents induced in the flowing liquid by each generator lies at least partially in the field of the other generator; whereby in operation the eddy currents induced in the liquid by each magnetic field in the field space of the other magnetic field interact with that other magnetic field to create within the liquid Lorenz forces acting to impede
  • the invention provides valve apparatus for controlling the flow of an electrically-conductive liquid along a channel.
  • the liquid could be any electrically-conductive liquid - an ionic aqueous liquid, for example, or mercury - and the channel be any channel, tube, passageway or duct along which the liquid is required to flow in a controlled manner
  • the primary purpose of the invention is to control the flow of liquids which are molten metals, and in particular steel which, as noted above, is being poured out of a tundish into an open-bottomed mould from which it will then be drawn in a continuous-casting process.
  • the apparatus of the invention includes means for creating across or around the channel through which the conductive liquid is to flow an alternating magnetic field. Most conveniently this field is formed using an electromagnet suitably fed with an AC electrical supply. If, as is very much preferred, the apparatus is to be handleable - lifted into position - by one or two men, then it should be as light as possible, and this can be brought about if the electromagnet's windings are of aluminium rather than the more conventional copper. And because of the relatively high-frequency field required it is advantageous to use multi-strand, Litz-wound wire for these windings.
  • Such a device is a solid state inverter fed from a single or three-phase mains supply.
  • the degree of flow control achieved naturally depends upon the value of the magnetic field and the eddy currents interacting with it. Fields in the region of half a tesla - say, from 0.3 up to about I T - should provide sufficient control.
  • One method of applying such fields is to utilise an electromagnet with a C-shaped laminated iron core, with an air gap of a size sufficient for the pouring tube to be comfortably passed therethrough (typically, around 25mm is acceptable for a 20mm pouring tube).
  • the laminations should be not more than about 0.05mm thick. Strip-wound cores are preferred over cores built from stampings because the former result is less stray field.
  • the required field can be generated in this way using from 10,000 to 20,000 ampere-turns; the actual number of turns, and hence the actual current therethrough, will naturally depend on the operating frequency and voltage (for a given number of turns the coil impedance - which depends upon the pole area - varies directly as the frequency, and so for a given supply voltage the current varies inversely).
  • a suitable electromagnet is one with two coils per core each of 55 turns connected in parallel with 200 amps through each (the core cross- section is 45 20mm tapering to 25x20mm at the poles); those experienced in this Art will be able to construct electromagnets suitable for their particular requirements.
  • the invention's apparatus includes means for inducing two sets of electrical eddy currents in the liquid as it passes through the two applied alternating magnetic fields. Each set of eddy currents arises from the other of the two magnetic fields, which is the means, and it is the out-of-phase nature of the two that causes a resulting Lorenz force component.
  • the valve apparatus of the invention includes a first magnetic field generator, for creating across the flowing liquid a first alternating magnetic field, and a second magnetic field generator, also for creating across the flowing liquid an alternating magnetic field, this second field being of the same frequency as the first magnetic field but having a substantial component 90° out of phase with it; the idea is that each field's associated eddy currents are formed at least partly within the other field's space, and because of the substantial component 90° out of phase the generated Lorenz forces in each case act together to oppose liquid flow.
  • energising current sources By selection of suitable energising current sources, it is possible to provide two alternating fields that are exactly 90° out of phase; however, in practice it may be more convenient to employ the conventional three-phase mains electricity supply, and simply to utilise two of the available phases to control the means - the inverters, say - energising the two electromagnets. Of course, if this is done then the two alternating fields, like the two energising alternating currents, will be not 90° out of phase but rather 120° out of phase; that, however, is quite satisfactory, for each resulting field has a component, of around 86% of the whole, which is the desired 90° out of phase.
  • the invention's valve apparatus includes two magnetic field generators so disposed adjacent one another that the path of the eddy currents induced in the flowing liquid by each generator lies at least partially in the field of the other generator.
  • the vertical separation between the pole faces is preferably kept small.
  • an electromagnetic shield be fitted between the two electromagnet yokes in the region where they are close to each other.
  • the thickness of the electromagnetic shield which may be a plate of copper or other high conductivity metal, should be as small as possible, but should be greater than the skin depth of magnetic fields in the shield material at the frequency of operation. For an operating frequency of 2.5kHz, a copper plate of 2-3mm thickness is preferred.
  • the invention's embodiments include means for arranging the directions and magnitudes of the field and of the induced eddy currents such that the generated forces have a component against the liquid flow direction which has a value sufficient to provide the desired controllability of the passage of the liquid along the channel.
  • the desired control may be attained simply by appropriately varying the driving current to the magnetic field generator, but other factors, such as the phase of the two alternating magnetic fields, may be used for this purpose. Normally, though, any adjustment of the forces is attained by current variation.
  • the magnetic-coil-driving currents necessary to achieve the necessary magnetic fields are high, and there is inevitably a concomitant, and usually undesirable, heating effect.
  • a stream of molten metal at several hundred degrees Celsius, may be passing through the centre of the apparatus, and much of that heat will be transferred to the apparatus, that heating will be considerably increased. Accordingly, it is desirable to provide such apparatus with means for cooling, both to deal with its proximity to the molten stream and to enable the windings to be run at a higher current density (so allowing the size and weight of the apparatus to be reduced).
  • cooling channels or a cooling jacket should be incorporated through which a cooling agent such as transformer oil, Freon, cold air, or a low melting point alloy such as Wood's metal can be circulated (water is not a preferred cooling agent because of safety hazards arising if the water comes into contact with the liquid metal).
  • a cooling agent such as transformer oil, Freon, cold air, or a low melting point alloy such as Wood's metal
  • the valve apparatus of the invention is, as noted above, primarily for use for controlling liquid - specifically molten - metal flows. It has particular relevance to controlling the flow of molten metal from the tundish to the mould during the continuous casting of steel; in this application it provides a controllable force to counteract the static head of liquid metal, and so to reduce and control the flow rate.
  • a particular advantageous is that it can be retrofitted to an existing caster without modification to the ceramic pouring tube, and without making contact with the liquid metal.
  • the whole assembly may be designed as two fitting halves, into which it may be split for ease of assembly around the pouring tube.
  • It is a fully-proportional flow control valve in which either a retarding or an accelerating force is applied resulting from the interaction of an alternating magnetic field with either an alternating electrical current induced in the liquid metal or the magnetic field produced by such a current.
  • the operating frequency is chosen to maximise the required forces, in accordance with the electrical conductivity of the liquid metal and the diameter of the liquid metal stream.
  • two pairs of alternating magnetic fields are produced by two magnetic yokes (with excitation windings) displaced from each other along the longitudinal axis of the pouring tube and electrically excited so that the resulting magnetic fields each have a significant component 90" out of phase with the other.
  • a magnetic shield is preferably positioned between the two magnetic yokes. 6.
  • the whole assembly may be designed as two fitting halves, into which it may be split for ease of assembly around the pouring tube.
  • the flow rate is adjusted simply by controlling the phase or amplitude of the current through one or more of the windings.
  • Figure 1 shows a diagrammatic perspective view of a valve apparatus of the invention
  • Figure 2 shows a diagrammatic perspective view of the pouring tube used in the Figure 1 valve, illustrating the direction of the magnetic fields and the flow of electric currents in the liquid;
  • Figures 3A & B show a preferred embodiment of a valve apparatus of the invention, similar to that of Figures 1 & 2, in elevation and plan views;
  • Figure 4 shows a diagrammatic perspective view of another configuration of valve apparatus according to the invention.
  • the valve apparatus shown in Figure 1 has a pouring tube (41) for liquid metal, magnetic yokes (42,43) for generating an alternating magnetic field across the liquid metal in a direction perpendicular to its direction of flow, and excitation windings (44,45) on the yokes.
  • the alternating electrical current supplied through the first excitation winding 44 is arranged to be 90° out of phase with that through the second excitation winding 45.
  • the first yoke 42 has poles (46, 47) which are positioned adjacent the pouring tube at opposite ends of its diameter; similarly, the second yoke 43 has poles (48,49) positioned adjacent the pouring tube at opposite ends of its diameter, and a little below the first yoke's poles 46,47.
  • the magnetic field 56 generated by the first coil and yoke assembly 42,44,46,47 will induce in the liquid metal an alternating electrical current flow as indicated by the dotted lines (58), which will be in phase with the alternating magnetic field 57. A part of this electrical current flow will interact with a part of the magnetic field 57 generated by the second coil and yoke assembly 43,45,48,49 to generate Lorenz forces in the liquid metal.
  • the magnetic field 57 generated by the second coil and yoke assembly 43,45,48,49 will induce in the liquid metal an alternating electrical current flow as indicated by the dotted lines (59), and a part of this electrical current flow will interact with a part of the magnetic field 56 generated by the first coil and yoke assembly 42,44,46,47 to generate Lorenz forces in the liquid metal, both sets of Lorenz forces acting in the same direction.
  • FIG. 1 shows elevation and plan views of a valve configured substantially as in Figure 1.
  • the valve is built around a ceramic pouring tube (61), around which the valve assembly is fitted.
  • Electromagnet assemblies (62,63) are wound on strip- wound laminated yokes whose pole faces are fitted closely to the pouring tube.
  • the laminations may be silicon iron, or for higher frequency applications, may be of other suitable material such as mumetal or radiometal.
  • the width of the lamination stack is conveniently the same as or slightly less than the diameter of the liquid metal stream, while the height of the stack may be equal to or greater than this.
  • Twin excitation coils 64,65 are fitted to the side limbs of the yokes as shown, since this arrangement generally results in a more efficient magnetic circuit than does the single coil arrangement shown in Figure 1.
  • the first electromagnet assembly 62 is supplied from one phase of an alternating electrical supply and the second electromagnet assembly 63 from another phase, the phase difference between the two phases being adjusted (by means not shown) to maximise the Lorenz forces opposing the downward flow of liquid metal through the pouring tube.
  • the vertical separation between the pole faces is kept small.
  • a small separation will result in the magnetic field from each assembly being diverted through the laminations of the other assembly so reducing the field through the liquid metal.
  • an electromagnetic shield (66) is fitted between the two laminated yokes in the region where they are close to each other. The thickness of the electromagnetic shield is as small as possible, but greater than the skin depth of magnetic fields in the shield material at the frequency of operation. For an operating frequency of 2.5kHz, a copper plate of 2-3mm thickness is satisfactory.
  • the pouring tube (73) is associated with electromagnets (71,72) disposed on opposite sides and staggered vertically so that the lower pole of magnet 71 is positioned midway between the upper and lower poles of magnet 72 (and, similarly, the upper pole of magnet 72 is midway between the two poles of magnet 71).
  • electromagnets 71,72
  • Electromagnet 71 may be powered from one phase of a normal three-phase current supply, while electromagnet 72 may be powered from another phase.
  • This embodiment has the advantage that the two electromagnets can readily be moved apart to accommodate different diameters of pouring tube.

Landscapes

  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Continuous Casting (AREA)

Abstract

An electromagnetic valve for controlling the flow of an electrically-conductive liquid along a channel comprises two magnetic field generators (42, 43) being disposed adjacent the channel (41). The first generator creates a first alternating field (56) in a direction substantially orthogonal to the liquid flow direction. The second magnetic field generator, also for creating across the flowing liquid an alternating magnetic field (57), being of the same frequency as the first generator but having a substantial component 90° out of phase with it. The direction of the second field caused by the second field generator is in a direction substantially orthogonal to the liquid flow direction and substantially parallel to the first field. The two generators being so disposed that the path of the eddy currents (58, 59) induced in the flowing liquid by each generator lies at least partially in the field of the other generator. The eddy currents induced in the liquid by each magnetic field in the field space of the other magnetic field interact with that other magnetic field to create within the liquid Lorenz forces acting to impede the flow of the liquid.

Description

ELECTROMAGNETIC VALVE
This invention relates to valves, and concerns in particular valves for controlling the flow of electrically-conductive fluids, for example molten metals, from a reservoir thereof.
In the continuous casting of steel the liquid, molten, metal is poured under gravity from a reservoir container known as a tundish into an open-bottomed, water-cooled mould from which a solidifying strand of steel is withdrawn continuously; the tundish may have either an open nozzle or an elongate pouring tube the free end of which is actually submerged in the mould contents. In many applications there are used pouring tubes which have internal diameters ranging from 12mm to 25mm. Similar processes are in use in the casting of other metals and alloys.
The trend in the primary metals industries is towards higher product quality and faster casting speeds. Both requirements necessitate accurate control of pouring, determined by factors such as the cooling rate, the reciprocation rate of the mould, and the withdrawal speed of the solidifying metal strand. Most preferably the pouring rate should be decoupled from, and independent of, the head of liquid metal in the tundish, and ideally the pouring should be amenable to continuous, rapid, automatic modulation under computer control.
The traditional control of the pouring rate is by hydraulic manipulation of a slide gate fitting across the nozzle or pouring tube, or of a conical ceramic stopper which is inside the tundish and in operation is raised from or lowered into the tundish outlet. However, these devices are subject to blockage and erosion, to freezing-up of the apertures through which the melt passes, to leakage, and to wear, all of which make accurate control difficult and necessitate frequent replacement of the moving parts. A slide gate may also suck in air through the clearances between the sliding surfaces, and the air thus sucked in causes oxidation of the molten steel and so increases the impurity content of the casting.
Ideally, a control valve for use in an application such as a continuous casting process should have no moving parts, should be capable of rapid and continuously-variable flow rate adjustment (preferably from full flow to zero flow) under computer control, should be usable with standard pouring tubes, and should be small and light enough that it is capable of being fitted into position with minimum difficulty by one or two men. Such a desideratum might be met by an electromagnetic valve rather than a mechanical one, and the present invention proposes a novel form of electromagnetic valve which substantially or wholly meets the desired criteria.
Various attempts have been made since the late 1970s to develop an effective electromagnetic valve for flow control of liquid metals, of which perhaps the best-known is the simple electromagnetic pinch valve. This comprises a solenoid surrounding the pouring tube; a high-frequency current through the solenoid generates magnetic fields which exert a radial force on the liquid metal and so "squeeze" the stream to a smaller diameter, throttling its flow. Unfortunately, this type of valve suffers from several disadvantages: since it relies on physically reducing the stream diameter, it must be positioned at the nozzle outlet, and cannot work with a submerged pouring tube, which is preferred for many casting operations; the control of the separation point of the metal from the walls of the tube is problematical; and the power requirements are usually extremely high, leading to difficult cooling problems. To date there has been no truly successful commercial development of this concept.
A variation on this technique employs a relatively complex structure of baffles in the pouring tube, which baffles distort the magnetic field, resulting in a net upward force on the liquid metal. Though finding some use in the non-ferrous metals industries, where temperatures are lower and the environment less aggressive, this has not been found suitable for steel casting, where, because of the valve's complex structure, it is likely to suffer from erosion and blockage. It also requires very high power levels.
It has also been known for many years to control the flow of liquid metal using electromagnetic pumps, sometimes known as Faraday pumps. These pumps work on the principle that an electrical conductor through which a current is passed will, if subjected to a magnetic field, experience a force (the Lorenz force) in a direction mutually orthogonal to the directions of the field and the current; where the electrical conductor is a liquid, such as a molten metal, the liquid will tend to flow in the direction of the force. This principle has been used for many years in the design of electromagnetic liquid sodium pumps for use in the nuclear industry. Many versions have been described. Most commonly, these pumps require an electrical contact to be made with the liquid metal, and in all cases the channel through which the liquid metal flows is configured to optimize the performance of the pump; it may, for example be a wide, narrow slot, or it may have side branches to allow return current flows through the liquid metal.
The invention proposes a simple but significant and surprising variation of the various techniques suggested hitherto. More specifically, the invention suggests that there be created across or around the outlet/pouring tube of the molten metal reservoir (the tundish, for example) an alternating electromagnetic field, that there be induced electrical currents - eddy currents - in the molten metal as it passes through this field, which eddy currents interact with the applied magnetic field, and that the directions and magnitudes of the field and of the induced eddy currents are arranged such that forces are generated in the molten metal which oppose the downward flow of the liquid and so provide the desired controllability of the passage of the metal through the outlet. More specifically, the invention proposes that, for use with a uniform-section output tube/channel, there be employed two adjacent out- of-phase magnetic fields which each cause eddy currents in the field space of the other that are in phase with that field and so create Lorenz forces the effects of which in that field are directed to impede/control liquid flow.
In one aspect, therefore, the invention provides valve apparatus for controlling the flow of an electrically-conductive liquid along a channel, which valve apparatus comprises: a first magnetic field generator, for creating across the flowing liquid a first alternating magnetic field, this first generator being shaped and disposed adjacent the channel to create that first field in a direction substantially orthogonal to the liquid flow direction; and a second magnetic field generator, also for creating across the flowing liquid an alternating magnetic field, this second field being of the same frequency as the first magnetic field but having a substantial component 90° out of phase with it, this second generator being shaped and disposed adjacent the channel to create that second field in a direction substantially orthogonal to the liquid flow direction and substantially parallel to the first field; the two generators being so disposed that the path of the eddy currents induced in the flowing liquid by each generator lies at least partially in the field of the other generator; whereby in operation the eddy currents induced in the liquid by each magnetic field in the field space of the other magnetic field interact with that other magnetic field to create within the liquid Lorenz forces acting to impede the flow of the liquid.
The invention provides valve apparatus for controlling the flow of an electrically-conductive liquid along a channel. Although notionally the liquid could be any electrically-conductive liquid - an ionic aqueous liquid, for example, or mercury - and the channel be any channel, tube, passageway or duct along which the liquid is required to flow in a controlled manner, the primary purpose of the invention is to control the flow of liquids which are molten metals, and in particular steel which, as noted above, is being poured out of a tundish into an open-bottomed mould from which it will then be drawn in a continuous-casting process.
The apparatus of the invention includes means for creating across or around the channel through which the conductive liquid is to flow an alternating magnetic field. Most conveniently this field is formed using an electromagnet suitably fed with an AC electrical supply. If, as is very much preferred, the apparatus is to be handleable - lifted into position - by one or two men, then it should be as light as possible, and this can be brought about if the electromagnet's windings are of aluminium rather than the more conventional copper. And because of the relatively high-frequency field required it is advantageous to use multi-strand, Litz-wound wire for these windings.
Although it might be thought that almost any frequency might be employed for the alternating magnetic field, this is in fact not the case, or at least not the preferred case. There is a preferred frequency of operation which will maximise the levitational forces on the liquid for a given input power and a given channel (pouring tube) diameter; this is because whereas, for constant values of magnetic field, the eddy current strength, and hence the forces on the liquid, will increase with frequency, by contrast the strength of the magnetic field in the liquid metal will decrease with frequency as a result of skin-depth effects which reduce the penetration of the magnetic field into the liquid metal. There is, then, an optimum value for the excitation frequency; it varies directly with the electrical resistivity of the liquid metal, and inversely with the square of the diameter of the liquid metal stream, and is in general given approximately by the expression f « l/πμσd*, where μ is the magnetic permeability of free space, σ is the conductivity of the liquid metal, and d is the diameter of the liquid metal stream. It can be shown both theoretically and experimentally that the optimum excitation frequency for molten steel flowing through a pouring tube of 20mm internal diameter is around 2.0 to 2.5kHz, possibly up to 10kHz. Excessively high frequencies should be avoided, however, as they will create unduly high eddy current losses, and thus excessive heating of the liquid metal adjacent the magnets.
To attain the desired field frequency it is convenient to employ any of the conventional commercially-available generator devices that can output a controlled wattage at a pre-selected and controllable frequency. Such a device is a solid state inverter fed from a single or three-phase mains supply.
The degree of flow control achieved naturally depends upon the value of the magnetic field and the eddy currents interacting with it. Fields in the region of half a tesla - say, from 0.3 up to about I T - should provide sufficient control. One method of applying such fields is to utilise an electromagnet with a C-shaped laminated iron core, with an air gap of a size sufficient for the pouring tube to be comfortably passed therethrough (typically, around 25mm is acceptable for a 20mm pouring tube). At a working frequency of around 2.5kHz, the laminations should be not more than about 0.05mm thick. Strip-wound cores are preferred over cores built from stampings because the former result is less stray field. The required field can be generated in this way using from 10,000 to 20,000 ampere-turns; the actual number of turns, and hence the actual current therethrough, will naturally depend on the operating frequency and voltage (for a given number of turns the coil impedance - which depends upon the pole area - varies directly as the frequency, and so for a given supply voltage the current varies inversely). One example of a suitable electromagnet is one with two coils per core each of 55 turns connected in parallel with 200 amps through each (the core cross- section is 45 20mm tapering to 25x20mm at the poles); those experienced in this Art will be able to construct electromagnets suitable for their particular requirements.
The invention's apparatus includes means for inducing two sets of electrical eddy currents in the liquid as it passes through the two applied alternating magnetic fields. Each set of eddy currents arises from the other of the two magnetic fields, which is the means, and it is the out-of-phase nature of the two that causes a resulting Lorenz force component.
The valve apparatus of the invention includes a first magnetic field generator, for creating across the flowing liquid a first alternating magnetic field, and a second magnetic field generator, also for creating across the flowing liquid an alternating magnetic field, this second field being of the same frequency as the first magnetic field but having a substantial component 90° out of phase with it; the idea is that each field's associated eddy currents are formed at least partly within the other field's space, and because of the substantial component 90° out of phase the generated Lorenz forces in each case act together to oppose liquid flow. By selection of suitable energising current sources, it is possible to provide two alternating fields that are exactly 90° out of phase; however, in practice it may be more convenient to employ the conventional three-phase mains electricity supply, and simply to utilise two of the available phases to control the means - the inverters, say - energising the two electromagnets. Of course, if this is done then the two alternating fields, like the two energising alternating currents, will be not 90° out of phase but rather 120° out of phase; that, however, is quite satisfactory, for each resulting field has a component, of around 86% of the whole, which is the desired 90° out of phase.
The invention's valve apparatus includes two magnetic field generators so disposed adjacent one another that the path of the eddy currents induced in the flowing liquid by each generator lies at least partially in the field of the other generator. To maximise the interaction between the field from the first electromagnet and the eddy currents induced in the liquid by the second electromagnet, and similarly between the field from the second electromagnet and the eddy currents induced in the liquid by the first electromagnet, the vertical separation between the pole faces is preferably kept small. However, a small separation will result in the magnetic field from each assembly being diverted through the laminations of the other assembly, so reducing the field through the liquid metal, and in order to minimise this effect, it is a preferred feature of the invention that an electromagnetic shield be fitted between the two electromagnet yokes in the region where they are close to each other. The thickness of the electromagnetic shield, which may be a plate of copper or other high conductivity metal, should be as small as possible, but should be greater than the skin depth of magnetic fields in the shield material at the frequency of operation. For an operating frequency of 2.5kHz, a copper plate of 2-3mm thickness is preferred.
The invention's embodiments include means for arranging the directions and magnitudes of the field and of the induced eddy currents such that the generated forces have a component against the liquid flow direction which has a value sufficient to provide the desired controllability of the passage of the liquid along the channel. As noted immediately above, it is the out-of-phase nature of the two fields that achieves this. Of course, the actual magnitude of the forces is determined (as noted above) by the strength of the magnetic fields and the engendered eddy currents; the desired control may be attained simply by appropriately varying the driving current to the magnetic field generator, but other factors, such as the phase of the two alternating magnetic fields, may be used for this purpose. Normally, though, any adjustment of the forces is attained by current variation.
As noted hereinbefore, the magnetic-coil-driving currents necessary to achieve the necessary magnetic fields are high, and there is inevitably a concomitant, and usually undesirable, heating effect. Moreover, since in operation a stream of molten metal, at several hundred degrees Celsius, may be passing through the centre of the apparatus, and much of that heat will be transferred to the apparatus, that heating will be considerably increased. Accordingly, it is desirable to provide such apparatus with means for cooling, both to deal with its proximity to the molten stream and to enable the windings to be run at a higher current density (so allowing the size and weight of the apparatus to be reduced). It is therefore a preferred feature of the invention that cooling channels or a cooling jacket should be incorporated through which a cooling agent such as transformer oil, Freon, cold air, or a low melting point alloy such as Wood's metal can be circulated (water is not a preferred cooling agent because of safety hazards arising if the water comes into contact with the liquid metal).
Although in operation the Lorenz forces generated by the interacting electric currents and magnetic fields in the flowing liquid could act to retard or to accelerate the flow of the liquid, so that this type of apparatus may be caused to act as a fully proportional control valve for the flowing liquid, in practice retardation will be the norm, the valve therefore acting to reduce the flow to a chosen amount, or even to switch it off entirely, rather than to increase it.
The valve apparatus of the invention is, as noted above, primarily for use for controlling liquid - specifically molten - metal flows. It has particular relevance to controlling the flow of molten metal from the tundish to the mould during the continuous casting of steel; in this application it provides a controllable force to counteract the static head of liquid metal, and so to reduce and control the flow rate. A particular advantageous is that it can be retrofitted to an existing caster without modification to the ceramic pouring tube, and without making contact with the liquid metal. The whole assembly may be designed as two fitting halves, into which it may be split for ease of assembly around the pouring tube. The main features and advantages of the valve apparatus of the invention can perhaps be summarised as follows:-
1. It is a fully-proportional flow control valve in which either a retarding or an accelerating force is applied resulting from the interaction of an alternating magnetic field with either an alternating electrical current induced in the liquid metal or the magnetic field produced by such a current.
2. The operating frequency is chosen to maximise the required forces, in accordance with the electrical conductivity of the liquid metal and the diameter of the liquid metal stream.
3. Unlike some previous valves, there is no ohmic electrical contact through the wall of the channel in which the liquid metal is flowing. The alternating current in the liquid metal is induced by a magnetic field generator disposed adjacent the pouring tube. This makes retro-fitting particularly easy, for the channel for the liquid metal is a standard, unmodified pouring tube as conventionally used in the continuous casting of steel.
5. In the preferred version, two pairs of alternating magnetic fields are produced by two magnetic yokes (with excitation windings) displaced from each other along the longitudinal axis of the pouring tube and electrically excited so that the resulting magnetic fields each have a significant component 90" out of phase with the other. In this version a magnetic shield is preferably positioned between the two magnetic yokes. 6. The whole assembly may be designed as two fitting halves, into which it may be split for ease of assembly around the pouring tube.
7. In use, the flow rate is adjusted simply by controlling the phase or amplitude of the current through one or more of the windings.
Several embodiments of the invention are now described, though by way of illustration only, with reference to the accompanying Drawings in which:
Figure 1 shows a diagrammatic perspective view of a valve apparatus of the invention;
Figure 2 shows a diagrammatic perspective view of the pouring tube used in the Figure 1 valve, illustrating the direction of the magnetic fields and the flow of electric currents in the liquid;
Figures 3A & B show a preferred embodiment of a valve apparatus of the invention, similar to that of Figures 1 & 2, in elevation and plan views; and
Figure 4 shows a diagrammatic perspective view of another configuration of valve apparatus according to the invention.
The valve apparatus shown in Figure 1 has a pouring tube (41) for liquid metal, magnetic yokes (42,43) for generating an alternating magnetic field across the liquid metal in a direction perpendicular to its direction of flow, and excitation windings (44,45) on the yokes. The alternating electrical current supplied through the first excitation winding 44 is arranged to be 90° out of phase with that through the second excitation winding 45. The first yoke 42 has poles (46, 47) which are positioned adjacent the pouring tube at opposite ends of its diameter; similarly, the second yoke 43 has poles (48,49) positioned adjacent the pouring tube at opposite ends of its diameter, and a little below the first yoke's poles 46,47.
The way the produced magnetic fields are disposed and overlap is shown in Figure 5; the pouring tube (51) is marked with the positions of the poles 46,47 by the dotted rectangles (52,53), and similarly the positions of the other pair of poles 48,49 are indicated by the other dotted rectangles (54,55). The direction of the alternating magnetic fields is indicated by the two sets of arrows (56,57).
In operation, the magnetic field 56 generated by the first coil and yoke assembly 42,44,46,47 will induce in the liquid metal an alternating electrical current flow as indicated by the dotted lines (58), which will be in phase with the alternating magnetic field 57. A part of this electrical current flow will interact with a part of the magnetic field 57 generated by the second coil and yoke assembly 43,45,48,49 to generate Lorenz forces in the liquid metal. Similarly, the magnetic field 57 generated by the second coil and yoke assembly 43,45,48,49 will induce in the liquid metal an alternating electrical current flow as indicated by the dotted lines (59), and a part of this electrical current flow will interact with a part of the magnetic field 56 generated by the first coil and yoke assembly 42,44,46,47 to generate Lorenz forces in the liquid metal, both sets of Lorenz forces acting in the same direction.
Because the Lorenz forces generated are proportional to the vector product of the magnetic field and the current flowing in the liquid metal, the force and hence the flow rate of the liquid metal can be controlled by controlling either the amplitude or phase of the currents in the coils 44, 45. A preferred embodiment of this Figure 1 version is now more particularly described with reference to
Figure 3.
This Figure shows elevation and plan views of a valve configured substantially as in Figure 1. The valve is built around a ceramic pouring tube (61), around which the valve assembly is fitted. Electromagnet assemblies (62,63) are wound on strip- wound laminated yokes whose pole faces are fitted closely to the pouring tube. The laminations may be silicon iron, or for higher frequency applications, may be of other suitable material such as mumetal or radiometal. The width of the lamination stack is conveniently the same as or slightly less than the diameter of the liquid metal stream, while the height of the stack may be equal to or greater than this.
Twin excitation coils (64,65) are fitted to the side limbs of the yokes as shown, since this arrangement generally results in a more efficient magnetic circuit than does the single coil arrangement shown in Figure 1.
The first electromagnet assembly 62 is supplied from one phase of an alternating electrical supply and the second electromagnet assembly 63 from another phase, the phase difference between the two phases being adjusted (by means not shown) to maximise the Lorenz forces opposing the downward flow of liquid metal through the pouring tube.
To maximise the interaction between the field from the first electromagnet assembly 62 and the eddy currents induced in the liquid metal by the second electromagnet assembly 63, and between the field from the second electromagnet assembly 63 and the eddy currents induced in the liquid metal by the first electromagnet assembly 62, the vertical separation between the pole faces is kept small. However, a small separation will result in the magnetic field from each assembly being diverted through the laminations of the other assembly so reducing the field through the liquid metal. In order to minimise this effect an electromagnetic shield (66) is fitted between the two laminated yokes in the region where they are close to each other. The thickness of the electromagnetic shield is as small as possible, but greater than the skin depth of magnetic fields in the shield material at the frequency of operation. For an operating frequency of 2.5kHz, a copper plate of 2-3mm thickness is satisfactory.
Finally, in the alternative version shown in Figure 4 the pouring tube (73) is associated with electromagnets (71,72) disposed on opposite sides and staggered vertically so that the lower pole of magnet 71 is positioned midway between the upper and lower poles of magnet 72 (and, similarly, the upper pole of magnet 72 is midway between the two poles of magnet 71). This means that the eddy currents generated in the liquid metal by magnet 71 are exposed to the influence of the field from magnet 72, while the eddy currents generated by magnet 72 are exposed to the influence of magnet 71.
Electromagnet 71 may be powered from one phase of a normal three-phase current supply, while electromagnet 72 may be powered from another phase.
This embodiment has the advantage that the two electromagnets can readily be moved apart to accommodate different diameters of pouring tube.

Claims

1. Valve apparatus for controlling the flow of an electrically-conductive liquid along a channel, which valve apparatus comprises: a first magnetic field generator, for creating across the flowing liquid a first alternating magnetic field, this first generator being shaped and disposed adjacent the channel to create that first field in a direction substantially orthogonal to the liquid flow direction; and a second magnetic field generator, also for creating across the flowing liquid an alternating magnetic field, this second field being of the same frequency as the first magnetic field but having a substantial component 90° out of phase with it, this second generator being shaped and disposed adjacent the channel to create that second field in a direction substantially orthogonal to the liquid flow direction and substantially parallel to the first field; the two generators being so disposed that the path of the eddy currents induced in the flowing liquid by each generator lies at least partially in the field of the other generator; whereby in operation the eddy currents induced in the liquid by each magnetic field in the field space of the other magnetic field interact with that other magnetic field to create within the liquid Lorenz forces acting to impede the flow of the liquid.
2. Valve apparatus as claimed in Claim 1, wherein the means for creating the required alternating magnetic field is an electromagnet suitably fed with an AC electrical supply.
3. Valve apparatus as claimed in either of the preceding Claims, wherein the frequency of the alternating magnetic field is from 2 to 10kHz.
4. Valve apparatus as claimed in any of the preceding Claims, wherein the magnetic field is from 0.3 to 1 T.
5. Valve apparatus as claimed in any of the preceding Claims, wherein using first and second electromagnets to create across the flowing liquid first and second alternating magnetic fields the one being of the same frequency as but having a substantial component 90° out of phase with the other, there are employed two of the phases of the conventional three-phase mains electricity supply to control the means energising the two electromagnets.
6. Valve apparatus as claimed in any of the preceding Claims, wherein to maximise the interaction between the field from each electromagnet and the eddy currents induced in the liquid by the other electromagnet the vertical separation between the electromagnets' pole faces is kept small, and to minimise each field's reduction an electromagnetic shield is fitted between the two electromagnet yokes in the region where they are close to each other.
7. Valve apparatus as claimed in any of the preceding Claims, wherein when using electromagnet(s) the actual magnitude of the flow-affecting forces is determined and controlled by appropriately varying the driving current to the electromagnet(s).
8. Valve apparatus as claimed in any of the preceding Claims, wherein there are means for cooling the apparatus.
9. Valve apparatus as claimed in any of the preceding Claims and substantially as hereinbefore described.
PCT/GB1997/001245 1996-05-08 1997-05-07 Electromagnetic valve WO1997041985A1 (en)

Priority Applications (2)

Application Number Priority Date Filing Date Title
AU27072/97A AU2707297A (en) 1996-05-08 1997-05-07 Electromagnetic valve
EP97920852A EP0914223A1 (en) 1996-05-08 1997-05-07 Electromagnetic valve

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
GB9609602A GB2312861B (en) 1996-05-08 1996-05-08 Valves
GB9609602.9 1996-05-08

Publications (1)

Publication Number Publication Date
WO1997041985A1 true WO1997041985A1 (en) 1997-11-13

Family

ID=10793358

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/GB1997/001245 WO1997041985A1 (en) 1996-05-08 1997-05-07 Electromagnetic valve

Country Status (4)

Country Link
EP (1) EP0914223A1 (en)
AU (1) AU2707297A (en)
GB (1) GB2312861B (en)
WO (1) WO1997041985A1 (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020061504A1 (en) * 2018-09-22 2020-03-26 Radwave Technologies Inc. Antenna pod matrix

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
ES2254405T3 (en) * 2000-03-16 2006-06-16 Vesuvius Crucible Company GUILLOTINE GATE FOR LIQUID METAL FLOW CONTROL.
DE102005046910B4 (en) 2005-09-21 2009-03-19 Technische Universität Ilmenau Method and arrangement for non-contact inspection of moving electrically conductive substances
KR102556728B1 (en) * 2017-12-04 2023-07-17 노르스크 히드로 아에스아 Casting device and casting method

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE2745799A1 (en) * 1976-10-25 1978-04-27 Asea Ab ARRANGEMENT AT OUTLETS OF METALLURGICAL CONTAINERS TO DISPLAY SLAG IN THE POWING JET
US4324266A (en) * 1979-05-31 1982-04-13 Agence Nationale De Valorisation De Le Recherche (Anvar) Process and device for confining liquid metals by use of an electromagnetic field
SU1047583A1 (en) * 1982-05-06 1983-10-15 Государственный Научно-Исследовательский,Проектный И Конструкторский Институт Сплавов И Обработки Цветных Металлов Installation for continuous casting of billets from non-ferrous metals and alloys
JPS6082255A (en) * 1983-10-06 1985-05-10 Toshiba Corp Device and method for adjusting transfer rate of molten metal
EP0404618A1 (en) * 1989-06-02 1990-12-27 Delot Process S.A. Electromagnetic valve for the flow control of a fluid in a pipe
WO1996003533A1 (en) * 1994-07-28 1996-02-08 Bhp Steel (Jla) Pty. Ltd. Electro-magnetic plugging means for hot dip coating pot

Family Cites Families (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB1292999A (en) * 1970-05-19 1972-10-18 Giro Metallurg Corp Improvements in or relating to the treatment of molten metal
GB1517964A (en) * 1976-07-18 1978-07-19 Bicc Ltd Control of flow of molten metal
US4289946A (en) * 1978-05-15 1981-09-15 Olin Corporation Electromagnetic casting apparatus
SE436251B (en) * 1980-05-19 1984-11-26 Asea Ab SET AND DEVICE FOR MOVING THE NON-STANDED PARTS OF A CASTING STRING
US4419177A (en) * 1980-09-29 1983-12-06 Olin Corporation Process for electromagnetically casting or reforming strip materials
CH665369A5 (en) * 1984-03-07 1988-05-13 Concast Standard Ag METHOD FOR CONTROLLING THE FLOW OF A METAL MELT IN CONTINUOUS CASTING, AND A DEVICE FOR IMPLEMENTING THE METHOD.
JPS60157048U (en) * 1984-03-26 1985-10-19 株式会社神戸製鋼所 Solenoid valve for continuous casting tundish
GB8711041D0 (en) * 1987-05-11 1987-06-17 Electricity Council Electromagnetic valve
US4842170A (en) * 1987-07-06 1989-06-27 Westinghouse Electric Corp. Liquid metal electromagnetic flow control device incorporating a pumping action
GB2218019B (en) * 1988-04-25 1992-01-08 Electricity Council Electromagnetic valve
US4982796A (en) * 1988-10-18 1991-01-08 Arch Development Corp. Electromagnetic confinement for vertical casting or containing molten metal
US5033534A (en) * 1990-03-02 1991-07-23 Nkk Corporation Method for continuous casting of steel
US5137045A (en) * 1991-10-31 1992-08-11 Inland Steel Company Electromagnetic metering of molten metal
US5350159A (en) * 1993-02-18 1994-09-27 Westinghouse Electric Corporation On/off valve apparatus for use in conjunction with electromagnetic flow control device controlling the flow of liquid metal through an orifice

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE2745799A1 (en) * 1976-10-25 1978-04-27 Asea Ab ARRANGEMENT AT OUTLETS OF METALLURGICAL CONTAINERS TO DISPLAY SLAG IN THE POWING JET
US4324266A (en) * 1979-05-31 1982-04-13 Agence Nationale De Valorisation De Le Recherche (Anvar) Process and device for confining liquid metals by use of an electromagnetic field
SU1047583A1 (en) * 1982-05-06 1983-10-15 Государственный Научно-Исследовательский,Проектный И Конструкторский Институт Сплавов И Обработки Цветных Металлов Installation for continuous casting of billets from non-ferrous metals and alloys
JPS6082255A (en) * 1983-10-06 1985-05-10 Toshiba Corp Device and method for adjusting transfer rate of molten metal
EP0404618A1 (en) * 1989-06-02 1990-12-27 Delot Process S.A. Electromagnetic valve for the flow control of a fluid in a pipe
WO1996003533A1 (en) * 1994-07-28 1996-02-08 Bhp Steel (Jla) Pty. Ltd. Electro-magnetic plugging means for hot dip coating pot

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
DATABASE WPI Section Ch Week 8425, Derwent World Patents Index; Class M22, AN 84-157759, XP002037256 *
PATENT ABSTRACTS OF JAPAN vol. 009, no. 226 (M - 412) 12 September 1985 (1985-09-12) *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020061504A1 (en) * 2018-09-22 2020-03-26 Radwave Technologies Inc. Antenna pod matrix

Also Published As

Publication number Publication date
GB9609602D0 (en) 1996-07-10
GB2312861A (en) 1997-11-12
AU2707297A (en) 1997-11-26
GB2312861B (en) 1999-08-04
EP0914223A1 (en) 1999-05-12

Similar Documents

Publication Publication Date Title
US4016926A (en) Electro-magnetic strirrer for continuous casting machine
KR100586665B1 (en) Electromagnetic braking device for a smelting metal in a continuous casting installation
WO2008088361A2 (en) Method and system of electromagnetic stirring for continuous casting of medium and high carbon steels
JPS6188950A (en) Molten-metal electromagnetic agitator
EP2216111B1 (en) Electromagnetic coil device for use of in-mold molten steel capable of serving both as electromagnetic stir and electromagnetic brake
US4678024A (en) Horizontal electromagnetic casting of thin metal sheets
EP0248242B1 (en) Continuous metal casting apparatus
EP0914223A1 (en) Electromagnetic valve
KR100193088B1 (en) Apparatus and method for confining molten metal using vertical magnetic field
US4635705A (en) Double-sided electromagnetic pump with controllable normal force for rapid solidification of liquid metals
US4741383A (en) Horizontal electromagnetic casting of thin metal sheets
US4846255A (en) Electromagnetic augmentation for casting of thin metal sheets
JP3236422B2 (en) Continuous casting method of steel using magnetic field
US6152210A (en) Metal casting
US4244419A (en) Electromagnetic stirring apparatus
JP2005238276A (en) Electromagnetic-stirring casting apparatus
EP0679115A1 (en) A.c. magnetic stirring modifier for continuous casting of metals.
US4435820A (en) Channel induction furnaces
KR950004228B1 (en) Device and method for flow regulation of molten metal of using electromagnetism
JPH0642982B2 (en) Metal flow control method in continuous casting mold
US5513692A (en) Electromagnetic confinement of molten metal with conduction current assistance
Lavers et al. Electromagnetic transport and confinement of liquid metals
JP2000176609A (en) Mold used in continuous casting
RU2109594C1 (en) Device and method for magnetic holding of molten metal
JPH0819840A (en) Continuous casting method

Legal Events

Date Code Title Description
AK Designated states

Kind code of ref document: A1

Designated state(s): AL AM AT AU AZ BA BB BG BR BY CA CH CN CU CZ DE DK EE ES FI GB GE GH HU IL IS JP KE KG KP KR KZ LC LK LR LS LT LU LV MD MG MK MN MW MX NO NZ PL PT RO RU SD SE SG SI SK TJ TM TR TT UA UG US UZ VN YU AM AZ BY KG KZ MD RU TJ TM

AL Designated countries for regional patents

Kind code of ref document: A1

Designated state(s): GH KE LS MW SD SZ UG AT BE CH DE DK ES FI FR GB GR IE IT LU MC NL PT SE BF

DFPE Request for preliminary examination filed prior to expiration of 19th month from priority date (pct application filed before 20040101)
121 Ep: the epo has been informed by wipo that ep was designated in this application
WWE Wipo information: entry into national phase

Ref document number: 1997920852

Country of ref document: EP

NENP Non-entry into the national phase

Ref country code: JP

Ref document number: 97539661

Format of ref document f/p: F

REG Reference to national code

Ref country code: DE

Ref legal event code: 8642

WWP Wipo information: published in national office

Ref document number: 1997920852

Country of ref document: EP

NENP Non-entry into the national phase

Ref country code: CA

WWW Wipo information: withdrawn in national office

Ref document number: 1997920852

Country of ref document: EP