WO1984001818A1 - Improvements in or relating to fluid handling apparatus - Google Patents

Improvements in or relating to fluid handling apparatus Download PDF

Info

Publication number
WO1984001818A1
WO1984001818A1 PCT/US1983/001635 US8301635W WO8401818A1 WO 1984001818 A1 WO1984001818 A1 WO 1984001818A1 US 8301635 W US8301635 W US 8301635W WO 8401818 A1 WO8401818 A1 WO 8401818A1
Authority
WO
WIPO (PCT)
Prior art keywords
fluid
interrupter
tube
elements
shell
Prior art date
Application number
PCT/US1983/001635
Other languages
English (en)
French (fr)
Inventor
Richard A Holl
Original Assignee
Vapor Corp
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 Vapor Corp filed Critical Vapor Corp
Priority to JP83503520A priority Critical patent/JPS59501991A/ja
Priority to DE8383903701T priority patent/DE3376449D1/de
Priority to AT83903701T priority patent/ATE33896T1/de
Priority to DE1983903701 priority patent/DE124584T1/de
Priority to BR8307596A priority patent/BR8307596A/pt
Priority to IN243/DEL/84A priority patent/IN160888B/en
Publication of WO1984001818A1 publication Critical patent/WO1984001818A1/en
Priority to DK318684A priority patent/DK318684D0/da

Links

Classifications

    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28HEAT EXCHANGE IN GENERAL
    • F28FDETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F13/00Arrangements for modifying heat-transfer, e.g. increasing, decreasing
    • F28F13/06Arrangements for modifying heat-transfer, e.g. increasing, decreasing by affecting the pattern of flow of the heat-exchange media
    • F28F13/12Arrangements for modifying heat-transfer, e.g. increasing, decreasing by affecting the pattern of flow of the heat-exchange media by creating turbulence, e.g. by stirring, by increasing the force of circulation
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28HEAT EXCHANGE IN GENERAL
    • F28FDETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F13/00Arrangements for modifying heat-transfer, e.g. increasing, decreasing
    • F28F13/02Arrangements for modifying heat-transfer, e.g. increasing, decreasing by influencing fluid boundary

Definitions

  • This invention is concerned with improvements in or relating to fluid handling apparatus, such as heat exchanger apparatus and fluid reactor apparatus. Review of the Prior Art
  • This structure consists of densely-packed convex sphere segments each arranged with a part of its convex surface touching or almost touching the heat transfer surface. Such a structure provides a very high coefficient of heat transfer without a disproportionate increase in the pumping power required to move the fluid through the apparatus.
  • an interrupter structure adapted for interruption of the boundary layer of a fluid flow at a surface or surfaces adjacent to the interrupter structure, the said structure comprising:
  • each interrupter element comprising a plurality of blade like members each of at least approximately spherical segment profile in side elevation, the members extending mutually radially outward relative to one another to touch or nearly touch the said surface or surfaces adjacent the element.
  • the structure comprises an axial core element to which the interrupter elements are connected and along which the interrupter elements are spaced.
  • the fluid handling apparatus may comprise heat exchange apparatus in which the interrupter elements are disposed adjacent the surface of a wall through which heat exchange takes place.
  • the fluid handling apparatus may comprise a fluid reactor in which the interrupter structure is coated with a material exhibiting reactive and/or catalytic properties toward the fluid.
  • an interrupter structure adapted for interruption of the boundary layer of a fluid flow at a surface or surfaces adjacent to the interrupter structure, the said structure comprising:
  • ⁇ _?MATO an elongated axial core element extending in the direction of fluid flow of the fluid, and a plurality of spaced spherical interrupter elements extending along the said core element, the spacing between the elements being such as to produce wake-interference flow in the fluid.
  • FIGURE 1 is a longitudinal section through a heat exchanger embodying the invention, taken on the line 1-1 of Figure 2, parts only of some of the tubes thereof being shown broken away and parts of structures being shown in phantom to avoid excessive detail;
  • FIGURE 2 is a part transverse section through the apparatus of Figure 1, taken on the line 2-2 of Figure 1, only the lower right quadrant being shown in full to avoid excessive detail;
  • FIGURE 3 is a transverse cross-section to an enlarged scale of an interrupter element of the apparatus of Figures 1 and 2;
  • FIGURES 4A, 4B and 4C are respective side elevations to an enlarged scale, and showing interrupter elements of different profiles;
  • FIGURE 5 is a longitudinal cross-section through a single tube illustrating the fluid flow therethrough past an interrupter element;
  • FIGURE 6 is a longitudinal section similar to Figure 1, showing an interrupter structure of another kind, and applied to fluid reaction apparatus of the invention.
  • FIGURE 7 is a plot of ranking of different heat exchanger surface, including a surface/structure combination of the invention. Description of the Preferred Embodiments
  • the heat exchanger of Figures 1 and 2 is of shell-and-tube type comprising a central shell member 10 having inlet 12 and outlet 14 for the fluid that is to pass in the shell around the outside of the tubes.
  • the two ends of the shell member 10 are closed by two respective tube sheet assemblies, each consisting of two spaced tube sheets 16 and 18 through which pass the ends of a plurality of parallel tubes 20 so as to be supported by the tube sheets.
  • the joints between the tubes and the apertures in the tube sheets through which . they pass, and also the joints between the tube sheet assemblies and the adjacent shell members, are sealed by specially shaped unitary gaskets 22 and 24. Any of the two fluids that leak through the gaskets enters the space between the tube sheets and can be vented to atmosphere without cross-contamination of the fluids.
  • the structure and functioning of such gaskets are more particularly described in my prior U.S. application
  • Two subsidiary like enS members 26 and 28 are mounted on the respective ends of the central shell member 10 abutting the respective tube sheet assemblies to form respective plenums for the fluid that enters and discharges from the interiors of the tubes 20, and are provided respectively with inlet 30 and outlet 32 for such fluid.
  • the ends of the shell end members 26 and 28 are closed by respective end plates 34 held to the members by respective encircling removable split rings 36 and tensioned band clamps 38.
  • the tube sheet assemblies and the subsidiary members are held assembled with the central shell 10 in similar manner by means of encircling split rings 40 and tensioned band clamps 42, the split rings having radially inwardly extending projections that engage in respective ⁇ ircumferenctial grooves in the shell members.
  • Each tube 20 has mounted therein a respective fluid flow interrupter structure 44 of the invention comprising a plurality of longitudinally spaced interrupter elements 46, which in this embodiment are mounted longitudinally spaced from one another along the length of the tube on an elongated axial core element rod 48.
  • the ends of this rod are free of the interrupter elements and extend out of the tubes 20 through the respective plenums into contact with the adjacent faces of the removable end plates 34, so that the interrupter structures are maintained in fixed longitudinal positions in the tubes.
  • each interrupter element 46 consists of a plurality of equal length blade like members 50 extending mutually radially outwards from the core rod 48 until they touch, or at least almost touch, the inside cylindrical wall of the respective tube.
  • each blade like member is of convex curvilinear profile as seen in side elevation, so that it has only effectively a point 52 of its circumference in contact with the tube inner wall, or immediately adjacent thereto.
  • a fluid flowing within a passage such as a tube 20
  • the boundary layer therefore reduces the heat transfer between the tube inner surface and the core layer.
  • an unobstructed boundary layer increases progressively in thickness in the direction of fluid flow, which will increase its insulating effect.
  • the boundary layer at the tube inner faces is interrupted in a "spot-wise" manner at - ⁇ - circu ferentially and longitudinally spaced spots by means of the fluid flow interrupter structure of the invention, while maintaining a non-turbulent fluid flow in the main body of the fluid constituted by the core layer.
  • both the inner and the outer surfaces of the tubes 20 may be polished to the desired degree of smoothness.
  • the disruption of the boundary layer at the multitude of spaced spots ensures that it stays thin, while the manner of its disruption ensures that turbulence is avoided that would cause unduly high friction drag.
  • the blade-like members of the interrupter elements are relatively thick at their root connections with the axial core rod and taper smoothly and progressively radially outwards until they terminate in a thin but smoothly rounded tip at or very closely adjacent to the tube inner surface. It will be understood by those skilled in the art that, because of usual manufacturing tolerances in the manufacture of the tubes and the interrupter structures, and also because of the need to be able easily to insert the structures into and remove them from the tubes, there may not always be positive contact at an interruption spot between the blade member and the tube interior wall, but the required effect will be obtained as long as the blade edge intrudes into the boundary layer. In a typical example of a small heat exchanger e.g.
  • each interrupter element i.e. where the roots of the blades meet the core rod, there is a maximum of blade surface area relative to the path cross-sectional area for fluid flow through the element, so that the friction drag is at a maximum.
  • the amount of blade material has become substantially zero, so that the friction drag is reduced in relation to the cross sectional area.
  • OMPI &?NAT1 such wake interference flow providing the highest mixing and heat transfer efficiency with lowest required pumping power.
  • the general direction of flow of the fluid in a tube is indicated in Figure 5 by arrows 54 and it will be seen that the flow interrupter structure causes the production of flow eddies 56 of shape and rotational frequency that, as described above, depend upon the geometry of the structure.
  • Wake eddies will be produced around the spots 52 of interruption downstream of the flow, while advance eddies will be produced upstream of the flow. If the spacing of the interruption spots 52 is made such that the advance and wake eddies of immediately successive spots coincide, then the desired wake interference flow is obtained with its very efficient non turbulent mixing between the interrupted boundary layers and the adjacent core layer.
  • a turbulent flow, which is to be avoided, may be distinguished from a vortex or eddy in that the former is irregular and there
  • RNA ⁇ is no observable pattern as witn a vortex. Vortices, eddies and swirls therefore do not constitute turbulence.
  • the conditions for maintenance of non turbulent flow with a particular structure can be observed for example by providing suitable windows in an experimental structure and adding visible fluids to the fluid flow if required.
  • the interrupter structure may readily be produced relatively inexpensively as a cast or moulded integral element of required diameter, element spacing and element free end length.
  • a variety of different materials can be used, such as metals, non-metallic materials such as plastics materials, and refractory materials such as alumina and cements. Because of its relatively large surface area and its efficient surface contact with the mixing flowing fluid the interruption structure is particularly suited as a support for material with which the fluid is to be contacted, such as a catalytic material.
  • the interrupter structure itself can be made of the contact and/or catalytic material, and alumina is a specific example of such a material, having this dual property.
  • FIG. 4a shows in side elevation part of a structure in which the profile of the element is spherical; the profile is of course a circle. Other profiles can be used and should be such as to present smoothly contoured edges to the fluid flow, so as to reduce friction losses to a minimum and also to ensure the maintenance of non turbulent flow.
  • Figure 4b shows for example elements of an ellipsoidal profile, while Figure 4c shows elements of an egg or drop shaped profile.; in the latter two profiles the edge of largest radius faces upstream.
  • the fluid is very viscous, such as a viscous oil that is to be heated.
  • a fluid is usually of low thermal conductivity and a thermal boundary layer will be established immediately adjacent to the heat transfer surface that is much thinner than the flow boundary layer.
  • the interrupting structure must be arranged to interrupt this thinner thermal boundary layer irrespective of the thickness of the flow boundary layer.
  • the principal factor in the determination of the thickness of the thermal boundary layer is the Prandtl number, which is high when the viscosity is high and the thermal conductivity is low.
  • Figure 7 is a plot of the ranking of surfaces in accordance with this method, comparing surfaces provided with an interrupter structure of the invention with a surface constitsuted by a tube of 1.2 cm diameter and a plate heat
  • the test fluid was water and the lowest line A is for heat transfer in a plain tube of 1.2 cm diameter, using data obtained from the above-mentioned paper of Soland, Mack and Rohsenow.
  • the line B is for an "APV” plate heat exchanger of 0.5 cm plate pitch, using data obtained from the "APV Heat Transfer Handbook, 2nd Edition, published by APV Inc. of Tonawanda, New York, U.S.A.”. It will be seen that line B represents an improvement of 28% in performance over line A.
  • the lower line C plots the performance of a shell and tube heat exschanger of the invention employing seven tubes of 1.25 cm diameter and equipped internally with radially bladed interrupter structures and externally with sphere rods on the shell side with a sphere diameter of 1 cm.
  • the higher line D plots the maximum performance so far obtained with a heat exchanger of the invention. It will be seen that line C represents an improvement of respectively 250% and 200% of lines A and B, while line D represents an improvement of respectively 515% and 400%.
  • FIG. 1 to 3 employs a different form of interrupter structure in the fluid path constituted by the space between the shell interior and the tube exteriors.
  • This different structure also consists of a core rod 54, but the longitudinally spaced interrupter elements consist of solid spheres 56 mounted on the rod at the spacing required to provide wake interference fluid flow.
  • These sphere carrying rods for convenience called sphere rods, are disposed around the tube exteriors with these longitudinal axes parallel to the tube axes and with their spherical surfaces in point contact with the adjacent tube surfaces; . at some locations the spheres may also touch one another.
  • the spheres have the same effect of point interruption of the boundary layers and production of mixing vortices that increase the heat transfer from the exterior tube surfaces to the fluid.
  • the ends of the sphere rod cores are free of spheres and are in end engagement with the tube sheets 16, so that they can be located accurately longitudinally; by changing the length of the sphere free ends the spheres of one rod can therefore be arranged to be opposite to the spaces between the spheres on the immediately adjacent rods to ensure the maximum fluid flow capacity in the, path, and minimize the pressure drop of the fluid through the shell.
  • the rod ends are also made free of spheres to provide fluid flow plenum spaces of adequate flow capacity in the shell adjacent the inlet and outlet to the shell.
  • Figure 6 illustrates in cross section a reactor apparatus employing a sphere rod interrupter structure of the invention inside each tube 25.
  • a sphere rod structure usually is somewhat less expensive to make than the bladed interrupter structure, and is also somewhat more robust.
  • a bladed structure may however be employed if the additional surface area which it provides is advantageous.
  • the sphere. rod core element should rest on the bottom of the horizontal tube interior so that its spherical structure elements will each penetrate at least at one point each the interior boundary layer of the tube and interrupt it there.
  • the external sphere diameter should be between 50% and 80% of the tube internal diameter.
  • the elements are referred to as spheres they also can be of ellipsoidal, egg or
  • OMFX drop shape and an egg shaped element structure is illustrated to the right of Figure 6.
  • Spheres of 80% or less of tube internal diameter permit adequate fluid flow, while spheres of 50% or more of tube internal diameter are required for adequate performance in both boundary layer disruption and vortex generation.

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Thermal Sciences (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Heat-Exchange Devices With Radiators And Conduit Assemblies (AREA)
  • Electrical Discharge Machining, Electrochemical Machining, And Combined Machining (AREA)
  • Devices And Processes Conducted In The Presence Of Fluids And Solid Particles (AREA)
  • Compression-Type Refrigeration Machines With Reversible Cycles (AREA)
PCT/US1983/001635 1982-11-01 1983-10-18 Improvements in or relating to fluid handling apparatus WO1984001818A1 (en)

Priority Applications (7)

Application Number Priority Date Filing Date Title
JP83503520A JPS59501991A (ja) 1982-11-01 1983-10-18 流体処理装置の改良乃至それに関する改良
DE8383903701T DE3376449D1 (en) 1982-11-01 1983-10-18 Improvements in or relating to fluid handling apparatus
AT83903701T ATE33896T1 (de) 1982-11-01 1983-10-18 Verbesserungen an oder betreffend fluidabehandlungsvorrichtungen.
DE1983903701 DE124584T1 (de) 1982-11-01 1983-10-18 Verbesserungen an oder betreffend fluidabehandlungsvorrichtungen.
BR8307596A BR8307596A (pt) 1982-11-01 1983-10-18 Aperfeicoamento em aparelho de manuseio de fluido ou relacionados ao mesmo
IN243/DEL/84A IN160888B (xx) 1982-11-01 1984-03-19
DK318684A DK318684D0 (da) 1982-11-01 1984-06-28 Fluidumbehandlingsapparat

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US43830082A 1982-11-01 1982-11-01

Publications (1)

Publication Number Publication Date
WO1984001818A1 true WO1984001818A1 (en) 1984-05-10

Family

ID=23740091

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US1983/001635 WO1984001818A1 (en) 1982-11-01 1983-10-18 Improvements in or relating to fluid handling apparatus

Country Status (12)

Country Link
EP (1) EP0124584B1 (xx)
JP (1) JPS59501991A (xx)
AU (1) AU574339B2 (xx)
CA (1) CA1217763A (xx)
DE (1) DE3376449D1 (xx)
DK (1) DK318684D0 (xx)
IN (1) IN160888B (xx)
IT (1) IT1203715B (xx)
MX (1) MX159117A (xx)
NO (1) NO842342L (xx)
WO (1) WO1984001818A1 (xx)
ZA (1) ZA838057B (xx)

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4545426A (en) * 1984-08-31 1985-10-08 Mobil Oil Corporation Reversing turbulators for heat exchangers
FR2740210A1 (fr) * 1995-10-20 1997-04-25 Peugeot Ensemble pour echangeur de chaleur tubulaire comportant des elements de creation de turbulence et installation d'echange urs de chaleur comprenant cet ensemble
CN102798300A (zh) * 2011-05-24 2012-11-28 哈尔滨工大金涛科技股份有限公司 腰鼓流道式污水换热器
WO2012161949A1 (en) * 2011-05-25 2012-11-29 Saudi Arabian Oil Company Turbulence-inducing devices for tubular heat exchangers
CN104567523A (zh) * 2014-12-30 2015-04-29 湘潭大学 一种管内插椭球体强化循环粒子除垢防垢与传热装置
CN112710170A (zh) * 2020-12-30 2021-04-27 佛山科学技术学院 一种管壳式换热器
CN112728990A (zh) * 2020-12-30 2021-04-30 佛山科学技术学院 一种内插球体换热管
CN112815762A (zh) * 2021-01-19 2021-05-18 珠海格力电器股份有限公司 换热管结构、换热管组件和换热器

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE29516927U1 (de) * 1995-10-26 1996-02-01 SGL Technik GmbH, 86405 Meitingen Rohr für Wärmeaustauscher mit wirbelerzeugenden Stromstörungselementen

Citations (9)

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Publication number Priority date Publication date Assignee Title
US155936A (en) * 1874-10-13 Improvement in tubes for underground-telegraph lines
US1283550A (en) * 1918-04-23 1918-11-05 Thomas T Parker Steam-superheater.
US1313624A (en) * 1919-08-19 Planoqrapii co
US2034822A (en) * 1935-05-13 1936-03-24 Hotstream Heater Co Heat transfer means
US2070427A (en) * 1935-05-22 1937-02-09 Faunce Benjamin Rice Heat extractor
US2709128A (en) * 1952-10-09 1955-05-24 Gas Machinery Co Packing or filling element
GB730375A (en) * 1949-06-07 1955-05-25 Hoechst Ag Improved heat exchange apparatus
FR1249001A (fr) * 1959-02-24 1960-12-23 Maschf Augsburg Nuernberg Ag échangeur de chaleur tubulaire pour supports de chaleur coûteux
US4211277A (en) * 1977-05-31 1980-07-08 Sulzer Brothers Ltd. Heat exchanger having internal fittings

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR367584A (fr) * 1905-07-01 1906-11-05 Arthur Wilfred Brewtnall Perfectionnements apportés aux appareils pour refroidir ou pour chauffer des liquides, des vapeurs et autres fluides
GB191116948A (en) * 1911-07-24 1912-07-18 Charles Algernon Parsons Improvements in and relating to Means for the Heating or Cooling of Fluids.
DE3005751A1 (de) * 1980-02-15 1981-08-20 Küba Kühlerfabrik Baierbrunn H.W.Schmitz GmbH & Co KG, 8021 Baierbrunn Verfahren und vorrichtung zur erhoehung der waermeleistung von verdampfern
EP0042613A3 (en) * 1980-06-24 1982-08-11 Richard Adolf Holl Apparatus and process for heat transfer

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US155936A (en) * 1874-10-13 Improvement in tubes for underground-telegraph lines
US1313624A (en) * 1919-08-19 Planoqrapii co
US1283550A (en) * 1918-04-23 1918-11-05 Thomas T Parker Steam-superheater.
US2034822A (en) * 1935-05-13 1936-03-24 Hotstream Heater Co Heat transfer means
US2070427A (en) * 1935-05-22 1937-02-09 Faunce Benjamin Rice Heat extractor
GB730375A (en) * 1949-06-07 1955-05-25 Hoechst Ag Improved heat exchange apparatus
US2709128A (en) * 1952-10-09 1955-05-24 Gas Machinery Co Packing or filling element
FR1249001A (fr) * 1959-02-24 1960-12-23 Maschf Augsburg Nuernberg Ag échangeur de chaleur tubulaire pour supports de chaleur coûteux
US4211277A (en) * 1977-05-31 1980-07-08 Sulzer Brothers Ltd. Heat exchanger having internal fittings

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4545426A (en) * 1984-08-31 1985-10-08 Mobil Oil Corporation Reversing turbulators for heat exchangers
EP0173468A2 (en) * 1984-08-31 1986-03-05 Mobil Oil Corporation Reversing turbulators and heat exchangers containing same
EP0173468A3 (en) * 1984-08-31 1986-04-23 Mobil Oil Corporation Reversing turbulators and heat exchangers containing same
AU581242B2 (en) * 1984-08-31 1989-02-16 Mobil Oil Corporation Reversing turbulators for heat exchangers
FR2740210A1 (fr) * 1995-10-20 1997-04-25 Peugeot Ensemble pour echangeur de chaleur tubulaire comportant des elements de creation de turbulence et installation d'echange urs de chaleur comprenant cet ensemble
CN102798300A (zh) * 2011-05-24 2012-11-28 哈尔滨工大金涛科技股份有限公司 腰鼓流道式污水换热器
WO2012161949A1 (en) * 2011-05-25 2012-11-29 Saudi Arabian Oil Company Turbulence-inducing devices for tubular heat exchangers
US9605913B2 (en) 2011-05-25 2017-03-28 Saudi Arabian Oil Company Turbulence-inducing devices for tubular heat exchangers
CN104567523A (zh) * 2014-12-30 2015-04-29 湘潭大学 一种管内插椭球体强化循环粒子除垢防垢与传热装置
CN112710170A (zh) * 2020-12-30 2021-04-27 佛山科学技术学院 一种管壳式换热器
CN112728990A (zh) * 2020-12-30 2021-04-30 佛山科学技术学院 一种内插球体换热管
CN112710170B (zh) * 2020-12-30 2022-07-15 佛山科学技术学院 一种管壳式换热器
CN112815762A (zh) * 2021-01-19 2021-05-18 珠海格力电器股份有限公司 换热管结构、换热管组件和换热器

Also Published As

Publication number Publication date
EP0124584A1 (en) 1984-11-14
DE3376449D1 (en) 1988-06-01
AU574339B2 (en) 1988-07-07
IN160888B (xx) 1987-08-15
JPS59501991A (ja) 1984-11-29
CA1217763A (en) 1987-02-10
DK318684A (da) 1984-06-28
IT8323565A0 (it) 1983-11-02
EP0124584B1 (en) 1988-04-27
AU2200883A (en) 1984-05-22
MX159117A (es) 1989-04-21
DK318684D0 (da) 1984-06-28
IT1203715B (it) 1989-02-23
EP0124584A4 (en) 1985-04-25
NO842342L (no) 1984-06-12
ZA838057B (en) 1984-06-27

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