Classifications

• • H—ELECTRICITY
  • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
  • H05B—ELECTRIC HEATING; ELECTRIC LIGHT SOURCES NOT OTHERWISE PROVIDED FOR; CIRCUIT ARRANGEMENTS FOR ELECTRIC LIGHT SOURCES, IN GENERAL
  • H05B3/00—Ohmic-resistance heating
  • H05B3/60—Heating arrangements wherein the heating current flows through granular powdered or fluid material, e.g. for salt-bath furnace, electrolytic heating
• • H—ELECTRICITY
  • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
  • H05B—ELECTRIC HEATING; ELECTRIC LIGHT SOURCES NOT OTHERWISE PROVIDED FOR; CIRCUIT ARRANGEMENTS FOR ELECTRIC LIGHT SOURCES, IN GENERAL
  • H05B1/00—Details of electric heating devices
  • H05B1/02—Automatic switching arrangements specially adapted to apparatus ; Control of heating devices
• • H—ELECTRICITY
  • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
  • H05B—ELECTRIC HEATING; ELECTRIC LIGHT SOURCES NOT OTHERWISE PROVIDED FOR; CIRCUIT ARRANGEMENTS FOR ELECTRIC LIGHT SOURCES, IN GENERAL
  • H05B3/00—Ohmic-resistance heating
  • H05B3/02—Details
  • H05B3/03—Electrodes
• • H—ELECTRICITY
  • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
  • H05B—ELECTRIC HEATING; ELECTRIC LIGHT SOURCES NOT OTHERWISE PROVIDED FOR; CIRCUIT ARRANGEMENTS FOR ELECTRIC LIGHT SOURCES, IN GENERAL
  • H05B2203/00—Aspects relating to Ohmic resistive heating covered by group H05B3/00
  • H05B2203/021—Heaters specially adapted for heating liquids

Definitions

• the present disclosure relates to ohmic fluid heating devices, and methods of heating a fluid.
• An ohmic fluid heater can be used to heat an electrically conductive fluid as, for example, potable water.
• Such a heater typically includes plural electrodes spaced apart from one another. The electrodes are contacted with the fluid to be heated so that the fluid fills the spaces between neighboring electrodes. Two or more of the electrodes are connected to a power supply so that different electrical potentials are applied to different ones of the electrodes.
• an ohmic heater is operated using normal AC utility power such as that obtainable from a household electric plug
• at least one of the electrodes is connected to one pole carrying an alternating potential
• at least one other electrode is connected to the opposite pole carrying a neutral or ground pole. Electricity passes between the electrodes through the fluid at least one space between the electrodes, and electrical energy is converted to heat by the electrical resistance of the fluid.
• the“heating rate”) in such a heater to achieve the desired temperature of the heated fluid. It has been proposed to vary the heating rate by mechanically moving electrodes closer relative to one another, thereby varying the electrical resistance between the electrodes. Such arrangements, however, require complex mechanical elements including moving parts exposed to the fluid. Moreover, it is difficult to make such mechanisms respond quickly to deal with rapidly changing conditions. For example, if an ohmic heater is used in an“instantaneous heating” arrangement to heat water supplied to a plumbing fixture such as a shower head, the water continually passes through the heater directly to the fixture while the fixture is in use. If the user suddenly increases the flow rate of the water, as by opening a valve on the fixture, the heater should react rapidly to increase the heating rate so as to maintain the water supplied to the fixture at a substantially constant temperature.
• an ohmic heater with a substantial number of electrodes and with power switches to selectively connect different ones of the electrodes to the poles of the power supply.
• an array of electrodes may be disposed in a linear arrangement with spaces between the electrodes.
• the array includes two electrodes at the extremes of the array and numerous intermediate electrodes between the two extreme electrodes. To provide a minimum heating rate, the extreme electrodes are connected to opposite poles of the power supply, and the intermediate electrodes are isolated from the poles.
• the electric current passes from one extreme electrode through the fluid in a first space to the nearest one of the intermediate electrodes, then through fluid in the next space to the next isolated electrode and so on until it reaches the last intermediate electrode, and flows from the last intermediate electrode to the other extreme electrode.
• the fluid within all of the spaces is electrically connected in series between the two extreme electrodes.
• connection scheme provides minimum resistance between the poles.
• Intermediate heating rates may be achieved by connecting various combinations of electrodes to the poles of the power supply. For example, in one such connection scheme, two of the intermediate electrodes are connected to opposite poles of the power supply, and the remaining electrodes are electrically isolated from the poles of the power supply.
• the connected intermediate electrodes are separated from one another by a few other intermediate electrodes and a few spaces, so that fluid in only a few spaces is connected in series between the poles.
• This connection scheme provides a resistance between the poles that is higher than the resistance in the maximum heating rate scheme, but lower resistance than the resistance in the minimum heating rate scheme.
• different connection schemes will provide different resistances between the poles, and thus different heating rates. Because the resistance with a given connection scheme decreases as the conductivity increases, a parameter referred to herein as“specific resistance” is used in this disclosure to characterize a circuit or a part of a circuit having elements electrically connected by a fluid.
• the specific resistance is the ratio between the electrical resistance of the circuit or part of a circuit and the resistivity of the fluid in the circuit.
• the switches are electrically controllable switches such as semiconductor switching elements as, for example, thyristors.
• Ohmic heaters of this type can switch rapidly between connection schemes and thus switch rapidly between heating rates. Such heaters do not require any moving parts in contact with the fluid to control the heating rate.
• ohmic heaters of this type can only select from among the set of the specific resistances fixed by the physical configuration of the electrodes, and thus the heating rate, in steps. Under certain conditions, the available heating rates may not match the heating rate which produces the desired fluid temperature.
• providing electrodes in an arrangement with non-uniform specific resistances between pairs of neighboring electrodes as, for example, providing electrodes at non-uniform spacings can provide an ohmic heater suitable for operation under a wide range of conditions.
• the specific resistances between pairs of neighboring electrodes are selected so that, for a fluid of a given conductivity, the power levels available using different connection schemes include a series of non-redundant specific resistances extending over a very wide range.
• such a heater may provide 60 or more specific resistances in a substantially logarithmic series, i.e., a series of specific resistances such that a ratio between each specific resistance and the next lower specific resistance is substantially constant.
• a substantially logarithmic series i.e., a series of specific resistances such that a ratio between each specific resistance and the next lower specific resistance is substantially constant.
• the commercial implementations of heaters as disclosed in the aforementioned‘706 and‘943 Patents have used electrodes in the form of electrically-conductive plates which are disposed in a dielectric housing so that the plates subdivide the interior of the housing into channels.
• the housing includes passages which direct the fluid through these channels. While this arrangement works well for mass-produced heaters of modest size as, for example, domestic water heaters for private homes or individual apartments, it is not optimum for large-scale industrial and commercial heaters.
• Such heaters typically are built to order in a custom size to fit the application.
• the cost of designing and fabricating the complex dielectric housing to suit the particular arrangement of electrodes required for a customized arrangement can be significant.
• the components can be damaged if subjected to conditions such as extreme pressures and temperatures which may be encountered in industrial and commercial heaters, and may be difficult to repair or replace.
• Fig. 1 is a diagrammatic sectional view of a heater according to one embodiment of the invention.
• Fig. 2 is schematic view of an electrical circuit in the heater of Fig. 1.
• Fig. 3. is a diagrammatic perspective view of a heater according to a further embodiment of the invention.
• Fig. 4 is a fragmentary sectional view along line 4-4 in Fig. 3.
• Fig. 5 is a diagrammatic sectional view of a heater according to another embodiment of the invention.
• Fig. 6 is a diagrammatic sectional view of a heater according to yet another embodiment of the invention.
• Fig. 7 is a schematic view of an electrical circuit in another embodiment of the invention.
• Fig. 8 is a diagrammatic sectional view depicting a heater used with the electrical circuit of Fig. 7.
• Figs 9, 10, 11 and 12 are diagrammatic views depicting certain connection patterns used in operation of the heater of Fig. 8.
• Fig. 13 is a diagrammatic view of an electrode array in a heater according to a further embodiment of the invention.
• a heater according to one embodiment of the invention includes a housing 20 and numerous rod-like electrodes extending within the housing in the plane of the drawing. These electrodes are disposed in an irregular two-dimensional array. As depicted in Fig. 1, the electrodes are circular cylinders and thus are circular as seen in cross-section in Fig. 1. In the irregular array, each of the electrodes has multiple neighboring electrodes. For example, electrodes 22a, 22b, 22c, and 22d are all neighbors of electrode 22e. Unless otherwise specified, the location of a rod-like or cylindrical electrode as used herein refers to the location of the axis of the electrode.
• Electrodes 22b, 22c, 22d, 22f and 22g are“outer electrodes” as referred to herein in that they cooperatively define the outer boundary 24 of the array.
• the outer boundary 24 of the array is the polygon formed by the shortest possible combination of imaginary straight lines extending in a plane perpendicular to the axes 26 of some of the electrodes 22 between the axes such the axes of all of the electrodes are either within or on the outer boundary.
• electrodes 22e, 22a and 22h are inner electrodes as referred to herein because their axes 26 lie within, but not on, the boundary 24.
• the electrodes lie at numerous different distances from one another.
• the array of Fig. 1 is irregular in two dimensions, in that the spacing between axes of the electrodes in both of the directions perpendicular to the axes of the electrodes, indicated by arrows X and Y in Fig. 1.
• the heater includes an electrical circuit (Fig. 2).
• the circuit includes a power supply 36 incorporating two poles in the form of conductors 38 and 40. These conductors are connected to source of electrical power such as utility power mains.
• the conductors are arranged so that in operation different electrical potentials are applied to poles 38 and 40.
• conductor 40 may be a neutral conductor which receives a neutral voltage, typically close to ground voltage
• conductor 38 may be a“hot conductor” which will receive an alternating voltage supplied by the utility power mains.
• This particular power supply is a single phase power supply in that only one alternating voltage is employed.
• Power switches 48 are connected between the electrodes 22 and power source 36.
• the power switches 48 are arranged so that each electrode may be connected to either one of poles 38 and 40 or may be left isolated from the poles.
• the term“switch” includes mechanical switches which may be manually actuated or actuated by devices such as relays or the like, and also includes solid state devices that can be actuated to switch between a non-conducting condition with very high impedance and a conducting condition with very low impedance. Examples of solid state switches include elements such as triacs, MOSFETs, thyristors, and IGBTs.
• an electrically conductive fluid as, for example, a conductive liquid such as potable water is passed through the housing 20 so that the fluid fills the space within the housing and contacts the surfaces of electrodes 22.
• One or more of the electrodes 22 are connected to the hot pole 38 by power switches 48, whereas one or more of the electrodes 22 are connected to the neutral pole 40 so that current flows between the different poles through the fluid contained in the housing.
• the current flow varies inversely with the resistance between the poles.
• the resistance between the poles depends on the specific resistances of all of the current paths through the fluid between pairs of the electrodes connected to different poles, conducting in parallel with one another.
• Electrodes 22e and 22h are disposed in the path of the flowing current, and these electrodes are electrically conductive, some of the current will pass through the these electrodes, and the specific resistance of the current path between electrodes 22c and 22b will differ appreciably from a hypothetical system in which electrodes 22e and 22h were absent. If only neighboring electrodes 22c and 22b are connected to opposite poles, current will flow between these electrodes.
• the current flows through all of the fluid in the chamber, but the predominant flow path of this flow lies near the straight line connecting the two electrodes.
• the presence of other electrodes, such as electrode 26e will affect the current flow to some extent, but this effect is small in comparison to the effect of electrodes 22e and 22h in the preceding example.
• the specific resistances between different pairs of two electrodes differ from one another.
• the interior electrodes help to provide a wide range of specific resistances between poles 38 and 40 which can be formed by connecting different electrodes to the poles, so that the heater can provide a wide range of heating rates and a large number of distinct heating rates within this range.
• the assembly may be compact in the dimensions transverse to the axes of the electrodes. This is particularly desirable where the liquid to be heated is under pressure so that the housing holding the electrodes must be a pressure vessel.
• the cost and weight of the walls of a pressure vessel required to withstand a given pressure increase as the cross-sectional dimensions of the vessel increase.
• the heater discussed above further includes an optional control circuit 56 (Fig. 2).
• the particular control circuit of 56 includes a control processing unit 58 and one or more sensors for sensing the one or more operating parameters of the heater.
• the one or more sensors may include only an outlet temperature sensor (not shown) which is physically mounted in or near the outlet of housing 20 to detect the temperature of fluid discharged from the heater.
• the temperature sensor may include conventional elements as, for example, one or more thermocouples, thermistors and resistance elements having electrical resistance which varies with temperature.
• the control processing unit 58 is linked to power switches 48 so that the control processing unit can actuate the switches to provide various connection schemes as discussed.
• the control processing unit may include a memory 70 such as a non-volatile memory, random access memory or other conventional storage element.
• the memory desirably stores data for least some of the various connection schemes attainable by operation of the switches.
• the data in the table for each connection scheme may include the settings for each of the power switches 48 to form a particular connection scheme, as well as data specifying, either explicitly or implicitly, a ranking of the stored connection schemes in order of their specific resistances.
• the data for each connection scheme may include the specific resistance between the poles for that connection scheme, or equivalent data such as values of resistance or conductivity for the various connection schemes all measured or calculated for the case where the spaces are filled with a fluid of a given conductivity.
• the explicit data may be simply an ordinal number for each connection scheme.
• the data specifying switch settings for each connection scheme may be stored at addresses within the memory, such that the data at a lowest address specifies the switch settings for a connection scheme with the lowest specific resistance, the data at the next lowest address specifies the data for the connection scheme with the next lowest specific resistance, and so on.
• Control processing unit 58 further includes a logic unit 72 connected to memory 70.
• the logic unit has one or more outputs connected to the power switches 48 as, for example, by conventional driver circuits (not shown) arranged to translate signals supplied by the logic unit to appropriate voltages or currents to actuate the switches.
• the logic unit may include a general-purpose processor programmed to perform the operations discussed herein, a hard wired logic circuit, a programmable gate array, or any other logic element capable of performing the operations discussed herein. Although the term“unit” is used herein, this does not require that the elements constituting the unit be disposed in a single location. For example, parts of the control processing unit, or parts of the logic unit, may be disposed at physically separate locations, and may be operatively connected to one another through any communications medium.
• the control unit may start the heater in operation by retrieving the switch setting data for the connection scheme with the highest specific resistance (lowest heating rate) and setting the switches accordingly, so that this connection scheme is set as the first connection scheme in use.
• the control unit periodically compares the outlet temperature of the fluid, as determined by the outlet temperature sensor, with a setpoint temperature. If the outlet temperature is below a setpoint temperature by more than a predetermined tolerance, the control unit retrieves the switch setting data for a connection scheme having specific resistance one step lower than the connection scheme then in use to provide a greater heating rate, and sets the switches accordingly. This process is repeated cyclically until the outlet temperature reaches the setpoint.
• the control unit selects a connection scheme with a specific resistance one step higher on the next cycle so as to reduce the heating rate. In this way, the control circuit will ultimately settle at a heating rate which brings the fluid to the desired output temperature.
• the control system actuates the switches to change the control scheme at times when the alternating voltage applied to the hot pole 38 of the power supply is at or near zero. Such zero crossing times occur twice during each cycle of a conventional AC waveform. This arrangement minimizes switching transients and electrical noise generation.
• control logic may use measured current flow between the poles and measured flow rate of the liquid to determine a predicted temperature rise within the heater, and add the predicted temperature rise to a measured inlet temperature of liquid entering the heater to arrive at a predicted outlet temperature. If the predicted outlet temperature is below the setpoint temperature by more than the tolerance, the control logic switches to a connection scheme having a lower specific resistance to increase the current flow. The control logic takes the reverse action if the predicted outlet temperature is above the setpoint temperature.
• the electrical circuit of the heater may optionally include one or more shunting busses 52 and shunting switches 50 operable to connect each electrode to the shunting bus or busses and to disconnect each electrode from the shunting bus or busses.
• Each shunting bus can be used to establish a low resistance conductive path between any two electrodes which are not connected to the poles. In the example above where only electrodes 22c and 22g are connected to opposite poles of the power supply and the other electrodes are disconnected from the poles of the power supply and also are disconnected from the shunting bus, the specific resistance of the current path is relatively high.
• the conductive path will be a composite of two paths in parallel, i.e., a first path from electrode 22c directly to the electrode 22g as discussed above, and a second path from electrode 22c to electrode 22e, through the shunting bus to electrode 22h and from electrode 22h to electrode 22g. Because the shunting switches 50 and shunting bus 52 have very low impedance, the path through electrodes 22e and 22h and the shunting bus will predominate. In this instance, the specific resistance between electrodes 22c and 22g will be much lower. Where the shunting bus is included, it provides additional connection schemes having further different specific resistances.
• connection schemes are included in the data specifying the various connection schemes and the specific resistances of the various connection schemes stored in the memory 70 of the control unit 56, and the control unit is linked to the shunting switches 52 so that the control unit can open and close the shunting switches as needed.
• the housing may be an elongated hollow body 102 having a pair of end walls 104 and 106.
• Cylindrical electrodes 122 extend through holes 108 (Fig. 4) in end wall 104.
• the electrode array desirably includes numerous electrodes extending parallel with one another and parallel to the axis of elongation 110 of body 102.
• the electrodes may be positioned in any desired array simply by forming the holes 108 in the desired configuration, which facilitates customization of the heater for a particular application.
• the end walls of the hollow body may be formed from a dielectric material such as a polymer, or else may be formed from a conductive material such as a metal and equipped with dielectric sleeves (not shown) within holes 108.
• the exposed ends 125 of the electrodes can be readily connected to the electrical circuit.
• the individual electrodes passing through the end wall can be secured in place and sealed to the end wall by any of the well-known techniques commonly used to secure elements such as tubes passing through a wall.
• a seal may be formed by an O- ring 126 seated in a groove 128 on the electrode, and may be secured in place by screw threads (not shown) on the electrode engaged with corresponding screw threads (not shown) in holes 108.
• the electrodes can be readily removed and serviced or replaced as needed.
• An inlet (now shown) and an outlet (not shown) are provided in opposite ends walls 104 and 106 to pass fluid through the interior of the heater.
• a heater according to a further embodiment of the invention also includes an array of rod-like electrodes 322 extending parallel to one another, in the directions into and out of the plane of the drawing as seen in Fig. 5.
• the array is partially regular and partially irregular.
• the electrodes are disposed in columns 301 extending in the direction denoted by arrow “Y” and in rows extending in the direction denoted by arrow “X”, perpendicular to direction Y, both of these directions being perpendicular to the axes of the electrodes.
• electrodes 322aa, 322ab, and 322ac constitute column 301a
• electrodes 322aa, 322ba, 322ca, 322da and 322ea constitute row 303a.
• the electrodes within each row are disposed at the same location in the Y direction.
• the electrodes are regularly spaced from one another in the Y direction, so that the distances in the Y direction between adjacent rows 303 are equal.
• the electrodes within each column are disposed at the same location in the X direction. However, the distances C between mutually-adjacent columns are unequal to one another, so that the columns are irregularly spaced from one another in the X direction.
• distance C ab between columns 301a and 301b is larger than distance C bc between columns 301b and 301c.
• those electrodes which are disposed in the outer columns 301a and 301e, and those electrodes disposed in outer rows 301a and 301c constitute the outer electrodes and define the boundary of the array, whereas those electrodes which are disposed neither in an outer row nor in an outer column (electrodes 322bb, 322cb and 322 db) constitute the inner electrodes disposed within the boundary.
• the array of Fig. 5 is disposed in a housing 320 having dielectric walls.
• the housing is arranged so that liquid passing through the heater flows predominantly in a direction transverse to the axes of the electrodes, in this case the X direction, through the array from inlet 307 to an outlet 309.
• the flow may be directed generally in directions parallel to the axes of the electrodes.
• the electrodes 322 an connected to a power supply similar to that discussed above, so that each electrode can be connected to one or the other pole of the power supply, or may be left disconnected.
• the power supply includes a shunting bus as discussed above, the power supply can connect two or more of the electrodes which are disconnected from the poles to the shunting bus as discussed above.
• An array of this type can provide numerous combinations of current paths which provide numerous different specific resistances between the poles of the power supply.
• some or even all of the spacings between columns may be equal to one another.
• the array is a completely regular array.
• a substantial number of conduction schemes having different specific resistances can be provided.
• the specific resistance between a given pair of electrodes connected to different poles of the power supply will be affected by other electrodes, and this effect varies with the location of the other electrodes relative to the pair of connected electrodes. This effect increases the number of different conduction schemes which can be provided by the array. For example, in the array of Fig.
• the specific resistance between electrodes 322aa and 322ab will differ from the specific resistance between electrodes 322ba and 322bb.
• the latter electrode pair (322ba and 322bb) has four other electrodes in close proximity, whereas the former electrode pair (322aa and 322bb) has only two other electrodes in close proximity.
• the specific resistance between a pair of outer electrodes disposed at a given distance from one another will differ from the specific resistance between a pair of electrodes disposed at the same distance from one another which pair includes one or more inner electrodes. This effect is greater in a compact array with relatively small distances between electrodes.
• One measure of compactness is the mean distance between neighboring electrodes.
• the mean distance may be less than five times the mean diameter of the individual electrodes, more desirably less than 3 times the mean diameter of the individual electrodes, and still more desirably less than 2 times the mean diameter of the individual electrodes.
• a heater according to a further embodiment of the invention includes a housing 420 and an array of rod-like electrodes 422 having outer electrodes disposed at locations on an outer circle 401 having a radius Ro around a central axis 410.
• the array further includes six inner rod-like electrodes 423 disposed at regular circumferential intervals of 2a on an inner circle 403, concentric with the outer circle and with central axis 410.
• the radius Ri of the inner circle is smaller than Ro-
• a first one 423a of the inner electrodes is offset in the circumferential direction around central axis 410 from a first one 422a of the outer electrodes by a/2 degrees.
• every other one of the inner electrodes 423 also lies at a circumferential location midway between the circumferential locations of the two closest outer electrodes. All of the electrodes extend parallel to one another and parallel to the central axis 410.
• each of the electrodes can be connected to either pole of the power supply, or left disconnected from the power supply.
• electrodes which are disconnected from the power supply can be connected to the shunting bus.
• this array of electrodes has some degree of regularity, it provides a substantial number of unique specific resistances between various combinations of electrodes.
• the circumferential spacings between inner electrodes 423, the circumferential spacings between outer electrodes 442, or both may be wholly or partially irregular.
• further electrodes may be added within the array, and those electrodes may be disposed at locations on further circles.
• the inner electrodes may be disposed on an inner circle which is not concentric with the outer circle.
• a power supply 536 for use with three-phase power includes three poles 540, 542 and 546 which are connectable to a three-phase utility circuit (not shown) to receive alternating potentials of equal magnitude offset by 120° in phase from one another, i.e., at phase angles of 0°, 120°, and 240°.
• power switches 548 are provided for selectively connecting each of the electrodes to one of the poles. Only two of the electrodes 522 are depicted in Fig. 7 for clarity of illustration; the same arrangement of power switches 548 typically is provided for every one of the electrodes.
• the power switches may include only a single switch for each electrode, so that a given electrode may be connected to one of the poles or left disconnected.
• the power switches associated with different electrodes are arranged to connect different ones of the electrodes to different poles.
• one or more shunting busses 552 and shunting switches 550 also may be provided. In three-phase operation, current flows through the electrodes and through current paths in the fluid between each pair of poles, i.e., between poles 540 and 542; between pole 540 and 544; and between poles 542 and 544.
• the electrical resistances between each pair of poles desirably is equal to the electrical resistance between each other pair of poles. Assuming that the electrical resistivity of the fluid in contact with the electrodes is the same along each current path in the fluid, the specific resistance between each pair of poles should be equal.
• the heater includes electrodes 522 disposed in a dielectric housing 520.
• the electrodes desirably are arranged at locations of a hexagonal lattice as depicted in Fig. 8.
• all of the electrodes 522 are rod-like and extend parallel to one another, into and out of the plane of the drawing.
• the electrodes are disposed in rows having row directions at angles of 60° from one another, with the centers of the electrodes in each row disposed on row axes (denoted A, B and C in Fig. 9) extending in the row directions.
• row axes denoted A, B and C in Fig. 9
• the row axes parallel to one another are disposed at identical spacings from one another so as to define intersections at vertices of numerous equilateral triangles, and the axes of the array are disposed at least some of the vertices.
• the array includes outer electrodes which in this embodiment define an outer regular hexagon, and inner electrodes which define an inner hexagon.
• the row axes also define a central vertex 510.
• a central axis extends parallel to the axes of the electrodes through the central vertex, and the array has six-fold symmetry about the central axis.
• the same array can also be described as an arrangement of electrodes disposed on concentric circles, where all of the electrodes disposed on the inner hexagon lie on an inner circle (not shown) of radius Ri around the central vertex; the electrodes disposed at the comers of the outer hexagon lying on an outermost circle (not shown) of radius Ro concentric with the inner circle and central vertex 510; and the electrodes on the sides of the outer hexagon, shown shaded in Fig. 9, are disposed on an intermediate circle (not shown) of radius R INT concentric with the inner and outer circles, where Ri ⁇ R INT ⁇ Ro.
• the power supply is arranged to connect at least some of the electrodes to the poles of the power supply in connection schemes such that the connected electrodes include three sets of electrodes connected to different ones of the poles 540, 542 and 544 of the power supply (Fig. 7).
• connection schemes such that the connected electrodes include three sets of electrodes connected to different ones of the poles 540, 542 and 544 of the power supply (Fig. 7).
• One such of connection scheme is depicted in Fig. 9, with the electrodes 522a of a first set, 522b of a second set and 522c of a third set shown with different cross-hatchings.
• all of the electrodes 522 of the array are connected to the poles to provide low specific resistances between the poles.
• FIG. 9 One such of connection scheme is depicted in Fig. 9, with the electrodes 522a of a first set, 522b of a second set and 522c of a third set shown with different cross-hatchings. In this particular scheme, all of the
• each set of electrodes 522a, 522b, 522c includes only one electrode, and these electrodes are outer electrodes at the corners of the hexagonal array to provide very high specific resistance between the poles, and thus provide the minimum heating rate. In this pattern, the remaining electrodes are disconnected from the poles of the power supply. Numerous intermediate schemes to provide numerous different specific resistances between the poles can be formed; one such intermediate scheme is shown in Fig. 11. In each of the connection schemes discussed above, each connected electrode and the corresponding electrodes of the other two sets are disposed at vertices of an equilateral triangle having its center at the central axis of the array. For example, in Fig.
• electrodes 522al, 522b 1 and 522c 1 are disposed at the vertices of one equilateral triangle, whereas electrodes 522a2, 522b2 and 522c2 are disposed at the vertices of another equilateral triangle.
• the connected electrodes of each are disposed at locations of the connected electrodes of the other sets rotated 120° about the central axis 510 from the locations of another set.
• the electrode sets have three-fold symmetry about the central axis.
• connection schemes therefore provide substantially equal specific resistances between the poles.
• the connected electrodes 522a, 522b and 522c are disposed at vertices of an equilateral triangle which is not centered at central axis 512.
• the conduction paths are of equal lengths and will have equal specific resistances apart from any differences which may be caused by differences in the effects of neighboring electrodes.
• connection schemes can include one or more electrodes connected to one or two of the poles in such a way as to cause inequality.
• electrodes which cause unequal current flows can be connected cyclically.
• an electrode which causes unequal current flows with a greatest current through one pole is connected for a period and then disconnected and replaced by a second electrode which causes a corresponding unequal flow with a maximum current directed through a second pole, and the second electrode is then disconnected and replaced by a third electrode which causes a corresponding unequal current flow with the maximum current through the third pole.
• the third electrode is disconnected and replaced by the first electrode at the beginning of the next cycle. In this manner, the unequal current flows rotate among the poles, which distribute the effects of the excess current among the phases.
• the array of electrodes shown in Fig. 13 includes three groups of electrodes 622a, 622b and 622c.
• the electrodes within each group are shown with the same shading.
• the electrodes within each group are disposed at irregular radii from a central axis 610, and at irregular intervals in the circumferential direction around the axis.
• the groups are congruent with one another but each group is rotated 120° from the position of another group.
• the power supply is arranged to connect sets of electrodes so that the connected electrodes include corresponding electrodes from all three groups.
• the array has three-fold symmetry about the central axis, and thus the electrodes lie on vertices of equilateral triangles having centers at the central axis 610.
• shunting busses are used with an array having three-fold symmetry about an axis
• three shunting busses may be used so that the set of electrodes connected to one another by each bus each bus is congruent with the set of electrodes connected by another bus, but is rotated 120° from the position of such other set.
• vanes may be provided within the housing to induce rotational flow around the axis of the housing, so that the liquid follows a generally helical path.
• the same effect may be achieved by configuring the inlet, outlet or both so that the flow of fluid into housing, out of the housing or both will induce rotational flow around the axis of the housing.
• the rod-like electrodes are in the form of right circular cylinders.
• the rod-like elements may by tapered.
• the rod-like electrodes may have non-circular cross-sectional shapes in the regions of the electrodes which are exposed to the liquid. These electrodes may be generally cylindrical or conical to provide a circular cross-sectional shape in the regions of the electrodes which penetrate the walls of the housing.
• the electrodes are of equal diameter.
• the diameters of the electrodes may be unequal.
• the lattice arrangement as depicted in Fig. 8 has all of the electrodes disposed at equal spacings. This arrangement may be varied somewhat.
• the diameter of the intermediate circle may be increased slightly to move the electrodes on the intermediate circle away from the central axis.
• the smaller triangular sets of three connected electrodes as depicted in Fig. 12 will not have equal distances between the connected electrodes, and therefore may induce some phase inequality, but there will be additional unique specific resistances.
• the array of Fig. 8 is just one example of an array where the entire array has N-fold symmetry about a central axis where N is 3 or a multiple of 3.
• the array of Fig. 8 includes subgroups of electrodes having N-fold symmetry about other axes. Other arrays having either or both of these properties can be used to provide three-phase balance.

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