EP1306636B1 - Process and apparatus for uniform heating of a mixture of dust particles in a hot gas flow - Google Patents

Process and apparatus for uniform heating of a mixture of dust particles in a hot gas flow Download PDF

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EP1306636B1
EP1306636B1 EP20010123693 EP01123693A EP1306636B1 EP 1306636 B1 EP1306636 B1 EP 1306636B1 EP 20010123693 EP20010123693 EP 20010123693 EP 01123693 A EP01123693 A EP 01123693A EP 1306636 B1 EP1306636 B1 EP 1306636B1
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Prior art keywords
hot gas
gas flow
grains
grain
flow
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German (de)
French (fr)
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EP1306636A1 (en
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Fritz Dr.-Ing. Schoppe
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F26DRYING
    • F26BDRYING SOLID MATERIALS OR OBJECTS BY REMOVING LIQUID THEREFROM
    • F26B17/00Machines or apparatus for drying materials in loose, plastic, or fluidised form, e.g. granules, staple fibres, with progressive movement
    • F26B17/10Machines or apparatus for drying materials in loose, plastic, or fluidised form, e.g. granules, staple fibres, with progressive movement with movement performed by fluid currents, e.g. issuing from a nozzle, e.g. pneumatic, flash, vortex or entrainment dryers
    • F26B17/101Machines or apparatus for drying materials in loose, plastic, or fluidised form, e.g. granules, staple fibres, with progressive movement with movement performed by fluid currents, e.g. issuing from a nozzle, e.g. pneumatic, flash, vortex or entrainment dryers the drying enclosure having the shape of one or a plurality of shafts or ducts, e.g. with substantially straight and vertical axis
    • F26B17/102Machines or apparatus for drying materials in loose, plastic, or fluidised form, e.g. granules, staple fibres, with progressive movement with movement performed by fluid currents, e.g. issuing from a nozzle, e.g. pneumatic, flash, vortex or entrainment dryers the drying enclosure having the shape of one or a plurality of shafts or ducts, e.g. with substantially straight and vertical axis with material recirculation, classifying or disintegrating means
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F26DRYING
    • F26BDRYING SOLID MATERIALS OR OBJECTS BY REMOVING LIQUID THEREFROM
    • F26B17/00Machines or apparatus for drying materials in loose, plastic, or fluidised form, e.g. granules, staple fibres, with progressive movement
    • F26B17/10Machines or apparatus for drying materials in loose, plastic, or fluidised form, e.g. granules, staple fibres, with progressive movement with movement performed by fluid currents, e.g. issuing from a nozzle, e.g. pneumatic, flash, vortex or entrainment dryers
    • F26B17/107Machines or apparatus for drying materials in loose, plastic, or fluidised form, e.g. granules, staple fibres, with progressive movement with movement performed by fluid currents, e.g. issuing from a nozzle, e.g. pneumatic, flash, vortex or entrainment dryers pneumatically inducing within the drying enclosure a curved flow path, e.g. circular, spiral, helical; Cyclone or Vortex dryers
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28HEAT EXCHANGE IN GENERAL
    • F28CHEAT-EXCHANGE APPARATUS, NOT PROVIDED FOR IN ANOTHER SUBCLASS, IN WHICH THE HEAT-EXCHANGE MEDIA COME INTO DIRECT CONTACT WITHOUT CHEMICAL INTERACTION
    • F28C3/00Other direct-contact heat-exchange apparatus
    • F28C3/10Other direct-contact heat-exchange apparatus one heat-exchange medium at least being a fluent solid, e.g. a particulate material
    • F28C3/12Other direct-contact heat-exchange apparatus one heat-exchange medium at least being a fluent solid, e.g. a particulate material the heat-exchange medium being a particulate material and a gas, vapour, or liquid

Definitions

  • the invention relates to the heating of a mixture of fine-grained Good different grain size using a hot gas flow and in particular relates to a method and an apparatus according to the preamble of claim 1 and 7, respectively.
  • a method according to the preamble of claim 1 is known from US-A-4 380 125.
  • This document describes a process for drying and preheating coking coal in a single flow tube, in which a hot gas stream entraining the bottom fed, ground, wet coal rises, and at the top of the air flow tube, all of the dried and preheated coal the gas stream is separated out.
  • the gas stream is divided into two streams by the larger gas volume is deflected as the first partial flow entraining the finer grain fractions from the original direction and leave the smaller amount of gas as the second partial flow entraining the coarser grain fraction initially in its direction, then deflected and with the first partial flow is reunited in approximately opposite direction to this.
  • this procedure divides the grain size mixture carried by the gas stream into only two fractions, within the fractions different treatment of the grains depending on their individual grain size is not possible.
  • Fine-grained material in particular that which has been produced by grinding, has a particle size distribution which can have a broad spectrum, ranging for example from 1 ⁇ m to 1000 ⁇ m. Also oversize from 2000 microns to 3000 microns is possible.
  • the invention is therefore based on the object to provide a method and an apparatus with which in a short time a heating of a grain mixture can be achieved at the same temperature.
  • the grain mixture is introduced into a flow of hot gases and undergoes a change in temperature during transport along the flow path of the hot gases due to the contact with the hot gases, according to the invention provided that the flow path which the single grain together with the hot Traps gases, is short for small grains and long for large grains, so that a longer heat-up time is available for the large grains.
  • the invention avoids these disadvantages in an elegant manner in that the grain mixture is introduced into an upward hot gas flow from above so that the large grains reach the hot gas flow at a lower altitude than the smaller grains, so that the larger grains are given a longer flow path becomes, as the small grains. As a result, despite a compact size of the required device uniform heating of the grains of all sizes is achieved.
  • the grain mixture is preferably introduced by means of a downward carrier gas flow in the upward hot gas flow, said two gas flows preferably in a contact surface, the length seen in the flow direction of the gases at least four times, preferably six times the thickness of the carrier gas flow, measured transversely to the contact surface of the two gas flows is.
  • Grains that do not enter the hot gas due to oversize are conveniently deposited so as not to disturb the process.
  • the hot gas flow is helical from bottom to top and the carrier gas is directed down the axis of this helix.
  • the helical flow can be guided from bottom to top widening in a conical jacket.
  • pressure conditions set along the axis of the helical flow which favor the downward flow of the carrier gas flow.
  • the apparatus of Fig. 1 consists of two substantially mutually parallel flow channels 1 and 2, of which the left channel 1 has a width B1 which is smaller than the width B2 of the channel 2.
  • the channels 1 and 2 are open to each other over a distance O, and close to the end of this open area, the flow channel 1 is closed, preferably by a cellular Z.
  • a hot air flow H is introduced from below into the flow channel 2 of greater width B2.
  • a conveying air flow F is introduced from above, which carries a grain mixture with it, consisting of small grains K1, medium grains K2 and oversize K3.
  • This flow of carrier gas and grain mixture is hereinafter referred to as F + K1 + K2 + K3.
  • all intermediate grain sizes may be included in the grain mixture.
  • the turbulence of the two flows F + K1 + K2 + K3 and H is characterized by components transverse to the main flow direction. These transverse components act on the grains, with the small grains K1 following the transverse components most easily.
  • the medium-sized grains K2 react later on the transverse components, while the oversize K3 completely falls down due to its larger mass, does not get into the hot air flow and can be deducted for example by the feeder Z.
  • the small grains K1 arrive earlier, i. above, in the upwardly directed hot air flow H, and the medium sized granules K2 reach further down in the upward flow H.
  • the medium granules K2 have thus, when they have reached the top, covered the longer flow path and therefore for that reason a longer one Residence time in the hot air flow H as the smaller grains.
  • larger grains K2 are carried in a known manner more slowly in a gas flow upward than smaller grains K1, resulting in an additional extension of the residence time for the medium-sized grains K2 in the hot air flow H.
  • a hot air flow is given here only as an example.
  • a hot gas another gas can also be used, for example an inert gas, if a chemical reaction of the grain mixture with the hot gas is to be avoided.
  • the device consists of a vertically standing, upwardly flared truncated cone 3 with a lower diameter D1, an upper diameter D2 and an axial length E.
  • a logarithmic spiral S of width B1 is concentrically attached , The spiral S is completely described by its angle ⁇ against the circumferential direction.
  • the desired separation effect has a clear optimum at angles ⁇ , which are approximately between 5 ° and about 12 °, with best values between 6 ° and 9 °. Below and above these angle values, the separation effect diminishes rapidly.
  • a discharge head C At the upper end of the truncated cone 3 is followed by a discharge head C, which has a diameter D3, to which the upper diameter D2 of the truncated cone 3 widens conically over a width B2.
  • the cylindrical portion of the discharge head C has a width B3 is arched by a dome.
  • the discharge head C is followed by a discharge line A outside.
  • the discharge head C is penetrated by a dip tube T of a diameter D T , which extends into the region of the transition between the discharge head C and the truncated cone 3 at the diameter D2.
  • the dip tube T ends at the level of the upper end of the truncated cone. 3
  • a cellular wheel Z Centrally connected to the lower end of the logarithmic spiral S is a cellular wheel Z which, on the one hand, constitutes a closure, but on the other hand permits the withdrawal of oversize particles.
  • a hot gas H of the logarithmic spiral S is fed, which initiates the hot gas H in the space enclosed by the truncated cone 3 chamber, where due to the helix angle ⁇ of the logarithmic S forms a wall-near upward flow W, which superimposes a circumferentially extending component is, which is not shown in the drawing and causes the hot gas flow to develop like a spiraling upwards from the bottom.
  • a feed gas stream F is introduced through the dip tube T, which carries with it a grain mixture containing grains K1, K2 and K3 different size, as described in the first example.
  • a grain mixture containing grains K1, K2 and K3 different size as described in the first example.
  • the carrier gas flow F emerging from the dip tube T with the entrained grains is set in rotation in the chamber enclosed by the truncated cone 3 by the peripheral component of the hot gas flow.
  • the small grains K1 follow this rotation rapidly, the larger K2s slower according to their larger mass and inertia, and the over grain K3 hardly ever.
  • the oversize K3 falls down and can be removed by the feeder Z.
  • the small grains K1 thus reach the wall-near flow W very quickly and are therefore fed quickly to the upper cone diameter D2.
  • the larger grains K2 fall deeper below and only further down in the chamber into the near-wall current W. They have a longer residence time in the chamber compared to the grains K1 for two reasons: their way in the wall-oriented, upward flow W is longer than that of the small grains K1 , and they are carried up more slowly than the small grains K1 because of their higher sink rate.
  • the spiral angle ⁇ of the logarithmic spiral S is of importance. It should be between 5 ° and 12 °, with best values between 6 ° and 9 °. Below and above these angle values, the separation effect in the chamber enclosed by the truncated cone 3 decreases rapidly.
  • the iron oxide (predominantly Fe 2 O 3 ) has ambient temperature and contains 10% moisture. It is designed with 2546 m 3 n / h hot gas (kiln exhaust) of 800 ° C heated to a temperature of 400 ° C and dried at the same time. The hot gas with the entrained iron oxide is blown through the dip tube T in the return flow R, which is established due to the forming in the chamber in a known manner pressure conditions. Of the 2546 m 3 n / h hot gas about 127 m 3 n / h are diverted before the logarithmic spiral S and used as 800 ° C hot medium F.
  • the dip tube T is intended to reach approximately to the diameter D2.
  • the pressure loss of the hot gas H as it flows through the chamber enclosed by the truncated cone is about 2200 Pa.
  • water or another suitable liquid may also be used as the carrier medium.
  • suitable liquid for grains heavier than water, water or another suitable liquid may also be used as the carrier medium.
  • the above considerations also apply to liquids as a medium instead of the aforementioned gases.

Description

Die Erfindung bezieht sich auf die Aufheizung eines Gemisches von feinkörnigem Gut unterschiedlicher Korngröße mit Hilfe einer Heißgasströmung und betrifft insbesondere ein Verfahren und eine Vorrichtung nach dem Oberbegriff des Anspruchs 1 bzw. 7.The invention relates to the heating of a mixture of fine-grained Good different grain size using a hot gas flow and in particular relates to a method and an apparatus according to the preamble of claim 1 and 7, respectively.

Ein Verfahren nach dem Oberbegriff von Anspruch 1 ist aus US-A-4 380 125 bekannt. Diese Druckschrift beschriebt ein Verfahren zur Trocknung und Vorerhitzung von Kokskohle in einem einzigen Flugstromrohr, in dem ein heißer Gasstrom, der die am unteren Ende eingespeiste, gemahlene, feuchte Kohle mitreißt, aufsteigt, und am oberen Ende des Flugstromrohrs die gesamte getrocknete und vorerhitzte Kohle aus dem Gasstrom ausgesondert wird. Im Flugstromrohr wird der Gasstrom in zwei Teilströme aufgeteilt, indem die größere Gasmenge als erster Teilstrom unter Mitnahme der feineren Kornfraktionen aus der ursprünglichen Richtung abgelenkt wird und die kleineren Gasmenge als zweiter Teilstrom unter Mitnahme der gröberen Kornfraktion zunächst in seiner Richtung belassen, dann umgelenkt und mit dem ersten Teilstrom in annähernd entgegengesetzter Richtung zu diesem wieder vereint wird. Diese Verfahrensweise teilt also das Korngrößengemisch, das von dem Gasstrom mitgeführt wird, in nur zwei Fraktionen auf, innerhalb der Fraktionen ist eine unterschiedliche Behandlung der Körner in Abhängigkeit von ihrer individuellen Korngröße nicht möglich.A method according to the preamble of claim 1 is known from US-A-4 380 125. This document describes a process for drying and preheating coking coal in a single flow tube, in which a hot gas stream entraining the bottom fed, ground, wet coal rises, and at the top of the air flow tube, all of the dried and preheated coal the gas stream is separated out. In Flugstromrohr the gas stream is divided into two streams by the larger gas volume is deflected as the first partial flow entraining the finer grain fractions from the original direction and leave the smaller amount of gas as the second partial flow entraining the coarser grain fraction initially in its direction, then deflected and with the first partial flow is reunited in approximately opposite direction to this. Thus, this procedure divides the grain size mixture carried by the gas stream into only two fractions, within the fractions different treatment of the grains depending on their individual grain size is not possible.

Feinkörniges Gut, insbesondere solches, das durch Mahlen hergestellt worden ist, hat eine Korngrößenverteilung, die ein breites Spektrum aufweisen kann, das beispielsweise von 1 µm bis 1000 µm reicht. Auch ist Überkorn von 2000 µm bis 3000 µm möglich.Fine-grained material, in particular that which has been produced by grinding, has a particle size distribution which can have a broad spectrum, ranging for example from 1 μm to 1000 μm. Also oversize from 2000 microns to 3000 microns is possible.

Bei verschiedenen Prozessen, an denen ein Körnergemisch der vorgenannten Art teilnimmt, ist es erforderlich, das Körnergemisch gleichmäßig, d.h. auf gleiche Temperatur aller Körner, zu erhitzen. Die Geschwindigkeit des Temperaturanstieges hängt von der Korngröße ab, was es schwierig macht, die gleiche Temperatur in allen Körnern zu erreichen, wenn eine feste Aufheizzeit gewählt wird und diese nicht ausreichend lang ist, daß auch die großen Körner dieselbe Endtemperatur erreichen, wie die kleinen Körner.In various processes in which a grain mixture of the aforementioned type participates, it is necessary to use the grain mixture uniform, ie at the same temperature of all grains to heat. The rate of temperature increase depends on the grain size, which makes it difficult to reach the same temperature in all grains if a fixed heating time is chosen and it is not sufficiently long that the large grains will reach the same final temperature as the small grains ,

Der Erfindung liegt daher die Aufgabe zugrunde, ein Verfahren und eine Vorrichtung anzugeben, mit denen in kurzer Zeit eine Erwärmung eines Körnergemischs auf gleiche Temperatur erreicht werden kann.The invention is therefore based on the object to provide a method and an apparatus with which in a short time a heating of a grain mixture can be achieved at the same temperature.

Diese Aufgabe wird bezüglich des Verfahrens durch die im Anspruch 1 und bezüglich der Vorrichtung durch die im Anspruch 7 beschriebenen Merkmale gelöst. Vorteilhafte Ausgestaltungen davon sind Gegenstand der abhängigen Ansprüche.This object is achieved with respect to the method by the features described in claim 1 and with respect to the device by the features described in claim 7. Advantageous embodiments thereof are the subject of the dependent claims.

Gemäß der Erfindung wird das Körnergemisch in eine Strömung heißer Gase eingeführt und erfährt durch den Kontakt mit den heißen Gasen eine Temperaturänderung während des Transports längs des Strömungsweges der heißen Gase, wobei erfindungsgemäß vorgesehen ist, daß der Strömungsweg, den das einzelne Korn zusammen mit den heißen Gasen zurücklegt, bei kleinen Körnern kurz und bei großen Körnern lang ist, so daß für die großen Körner eine längere Aufheizzeit zur Verfügung steht.According to the invention, the grain mixture is introduced into a flow of hot gases and undergoes a change in temperature during transport along the flow path of the hot gases due to the contact with the hot gases, according to the invention provided that the flow path which the single grain together with the hot Traps gases, is short for small grains and long for large grains, so that a longer heat-up time is available for the large grains.

Verwendet man als Vorrichtung etwa ein horizontal angeordnetes, von den heißen Gasen durchströmtes Rohr, muß dieses so lang sein, daß auch die großen Körner die gewünschte Endtemperatur erreichen. Für die kleinen Körnern wäre das Rohr dann aber unnötig lang. Günstiger ist es daher, ein senkrecht angeordnetes Rohr zu verwenden, in dem die Heißgasströmung aufwärts geführt ist, ein sogenannter Stromtrockner, so daß die großen Körner in der Heißgasströmung etwas langsamer empor getragen werden, als die kleinen. Aber auch hier findet man am oberen Ende einen Austritt mit Vorrichtungen, etwa Zyklonen, die den Grobanteil der Körner, der noch nicht ganz durchgewärmt ist, abscheiden und zum nochmaligen Durchlauf durch die Vorrichtung an deren unteres Ende zurückführen, was wiederum mit einem entsprechenden apparativen Aufwand verbunden ist.Used as a device as a horizontally arranged, through which the hot gases flowed pipe, this must be so long that even the large grains reach the desired final temperature. For the small grains, the tube would be unnecessarily long. It is therefore more favorable to use a vertically arranged tube, in which the hot gas flow is guided upward, a so-called current dryer, so that the large grains are carried in the hot gas flow up a little slower than the small. But here you will find at the top of an outlet with devices such as cyclones, the coarse fraction of the grains, which is not quite warmed through, deposit and return to re-run through the device at the lower end, which in turn with a corresponding expenditure on equipment connected is.

Die Erfindung vermeidet diese Nachteile in eleganter Weise dadurch, daß das Körnergemisch in eine aufwärts geführte Heißgasströmung von oben so eingeleitet wird, daß die großen Körner in tieferer Höhenlage in die Heißgasströmung gelangen, als die kleineren Körner, so daß den größeren Körnern ein längerer Strömungsweg zugeteilt wird, als den kleinen Körnern. Dadurch durch wird trotz kompakter Größe der dafür benötigten Vorrichtung eine gleichmäßige Erwärmung der Körner aller Größen erreicht.The invention avoids these disadvantages in an elegant manner in that the grain mixture is introduced into an upward hot gas flow from above so that the large grains reach the hot gas flow at a lower altitude than the smaller grains, so that the larger grains are given a longer flow path becomes, as the small grains. As a result, despite a compact size of the required device uniform heating of the grains of all sizes is achieved.

Das Körnergemisch wird dabei vorzugsweise mit Hilfe einer abwärts gerichteten Trägergasströmung in die aufwärts gerichtete Heißgasströmung eingebracht, wobei diese beiden Gasströmungen sich vorzugsweise in einer Berührungsfläche berühren, deren Länge in Strömungsrichtung der Gase gesehen wenigstens das Vierfache, vorzugsweise das Sechsfache der Dicke der Trägergasströmung, gemessen quer zur Berührungsfläche der beiden Gasströmungen, beträgt.The grain mixture is preferably introduced by means of a downward carrier gas flow in the upward hot gas flow, said two gas flows preferably in a contact surface, the length seen in the flow direction of the gases at least four times, preferably six times the thickness of the carrier gas flow, measured transversely to the contact surface of the two gas flows is.

Körner, die infolge Übergröße nicht in das Heißgas gelangen, werden zweckmäßigerweise abgeschieden, um den Prozeß nicht zu stören.Grains that do not enter the hot gas due to oversize are conveniently deposited so as not to disturb the process.

Vorzugsweise verläuft die Heißgasströmung schraubenlinienförmig von unten nach oben, und das Trägergas wird in der Achse dieser Schraubenlinie abwärts geführt. Es ergeben sich dadurch stabile Strömungsverhältnisse. Dabei kann die schraubenlinienförmige Strömung sich von unten nach oben erweiternd in einem Kegelmantel geführt sein. Dadurch stellen sich Druckverhältnisse längs der Achse der schraubenlinienförmigen Strömung ein, die das Abwärtsströmen der Trägergasströmung begünstigen.Preferably, the hot gas flow is helical from bottom to top and the carrier gas is directed down the axis of this helix. This results in stable flow conditions. In this case, the helical flow can be guided from bottom to top widening in a conical jacket. As a result, pressure conditions set along the axis of the helical flow, which favor the downward flow of the carrier gas flow.

Die Erfindung wird nachfolgend und unter Bezugnahme auf die Zeichnungen näher erläutert. Es zeigt:

  • Fig. 1 im Längsschnitt ein vereinfachtes Schema eines zur Ausführung der Erfindung modifizierten Stromtrockners, und
  • Fig. 2 einen Längsschnitt durch eine zweite Ausführungsform einer erfindungsgemäßen Vorrichtung, in der die Heißgasströmung in einer sich von unten nach oben erweiternden Spirale geführt ist.
The invention is explained in more detail below and with reference to the drawings. It shows:
  • Figure 1 is a longitudinal sectional view of a simplified scheme of modified for carrying out the invention current dryer, and
  • Fig. 2 is a longitudinal section through a second embodiment of a device according to the invention, in which the hot gas flow is guided in a widening from bottom to top spiral.

Die Vorrichtung nach Fig. 1 besteht aus zwei im wesentlichen parallel zueinander angeordneten Strömungskanälen 1 und 2, von denen der linke Kanal 1 eine Breite B1 hat, die kleiner als die Breite B2 des Kanals 2 ist. Die Kanäle 1 und 2 sind auf einer Strecke O zueinander offen, und dicht unterhalb des Endes dieses offenen Bereiches ist der Strömungskanal 1 geschlossen, vorzugsweise durch ein Zellenrad Z.The apparatus of Fig. 1 consists of two substantially mutually parallel flow channels 1 and 2, of which the left channel 1 has a width B1 which is smaller than the width B2 of the channel 2. The channels 1 and 2 are open to each other over a distance O, and close to the end of this open area, the flow channel 1 is closed, preferably by a cellular Z.

Zum Betrieb der Vorrichtung wird in den Strömungskanal 2 größerer Breite B2 von unten eine Heißluftströmung H eingeleitet. In den linken Strömungskanal 1 geringerer Breite B1 wird von oben eine Förderluftströmung F eingeleitet, die ein Körnergemisch mit sich führt, bestehend aus kleinen Körner K1, mittelgroßen Körner K2 und Überkorn K3. Diese Strömung aus Trägergas und Körnergemisch wird nachfolgend mit F+K1+K2+K3 bezeichnet. Selbstverständlich, und in der Praxis in der Regel vorkommend, können auch alle Kornzwischengrößen in dem Körnergemisch enthalten sein.To operate the device, a hot air flow H is introduced from below into the flow channel 2 of greater width B2. In the left flow channel 1 lesser width B1, a conveying air flow F is introduced from above, which carries a grain mixture with it, consisting of small grains K1, medium grains K2 and oversize K3. This flow of carrier gas and grain mixture is hereinafter referred to as F + K1 + K2 + K3. Of course, and usually occurring in practice, all intermediate grain sizes may be included in the grain mixture.

Zwischen den Strömungen F+K1+K2+K3 und H bildet sich nach den Lehren der freien Turbulenz entlang einer gedachten Linie L, die in der Zeichnung gestrichelt angedeutet ist, und von dieser ausgehend nach außen eine Zone der Verwirbelung aus, die von einem Punkt P1 am oberen Ende bis zu einem Punkt P2 am unteren Ende der Linie L reicht, deren Distanz etwa der Länge O der Öffnung zwischen beiden Strömungskanälen 1 und 2 entspricht. Dabei bildet die Linie L mit der Hauptströmungsrichtung einen Winkel von 10° bis 15°, so daß der Abstand der Punkte P1 und P2 etwa das Vier- bis Sechsfache der Breite B1 des Strömungskanals 1 entspricht. Mindestens auf dieser Länge müssen sich die beiden Strömungen F+K1+K2+K3 und H einander berühren.Between the flows F + K1 + K2 + K3 and H forms according to the teachings of the free turbulence along an imaginary line L, which is indicated by dashed lines in the drawing, and from this outward a zone of turbulence, from a point P1 at the upper end extends to a point P2 at the lower end of the line L, whose distance corresponds approximately to the length O of the opening between the two flow channels 1 and 2. In this case, the line L with the main flow direction forms an angle of 10 ° to 15 °, so that the distance of the points P1 and P2 corresponds to about four to six times the width B1 of the flow channel 1. At least on this length, the two flows F + K1 + K2 + K3 and H must touch each other.

Die Verwirbelung der beiden Strömungen F+K1+K2+K3 und H ist durch Komponenten quer zur Hauptströmungsrichtung gekennzeichnet. Diese Querkomponenten wirken auf die Körner ein, wobei die kleinen Körner K1 den Querkomponenten am leichtesten folgen. Die mittelgroßen Körner K2 reagieren später auf die Querkomponenten, während das Überkorn K3 wegen seiner größeren Masse nach unten vollständig durchfällt, nicht in die Heißluftströmung gelangt und beispielsweise durch das Zellenrad Z abgezogen werden kann.The turbulence of the two flows F + K1 + K2 + K3 and H is characterized by components transverse to the main flow direction. These transverse components act on the grains, with the small grains K1 following the transverse components most easily. The medium-sized grains K2 react later on the transverse components, while the oversize K3 completely falls down due to its larger mass, does not get into the hot air flow and can be deducted for example by the feeder Z.

Aufgrund dieser Tatsache gelangen die kleinen Körner K1 früher, d.h. weiter oben, in die aufwärts gerichtete Heißluftströmung H, und die mittelgroßen Körner K2 gelangen weiter unten in die aufwärts gerichtete Strömung H. Die mittelgroßen Körner K2 haben also, wenn sie oben angekommen sind, den längeren Strömungsweg zurückgelegt und daher schon aus diesem Grunde eine längere Verweilzeit in der Heißluftströmung H als die kleineren Körner. Hinzu kommt, daß größere Körner K2 in bekannter Weise langsamer in einer Gasströmung nach oben getragen werden, als kleinere Körner K1, woraus sich eine zusätzliche Verlängerung der Verweilzeit für die mittelgroßen Körner K2 in der Heißluftströmung H ergibt.Due to this fact, the small grains K1 arrive earlier, i. above, in the upwardly directed hot air flow H, and the medium sized granules K2 reach further down in the upward flow H. The medium granules K2 have thus, when they have reached the top, covered the longer flow path and therefore for that reason a longer one Residence time in the hot air flow H as the smaller grains. In addition, larger grains K2 are carried in a known manner more slowly in a gas flow upward than smaller grains K1, resulting in an additional extension of the residence time for the medium-sized grains K2 in the hot air flow H.

Das von der Erfindung angestrebte Ziel ist damit erreicht. Allerdings sind die Trennvorgänge, die durch die genannten Strömungsquerkomponenten geschaffen werden, noch durch eine bekannte Unschärfe gekennzeichnet, so daß diese Ausführungsform der Erfindung nur einfachen Anwendungen genügt.The goal sought by the invention is thus achieved. However, the separation processes provided by the aforementioned flow cross components are still characterized by a known blurring, so that this embodiment of the invention only satisfies simple applications.

Es sei an dieser Stelle erwähnt, daß eine Heißluftströmung hier nur als Beispiel angegeben ist. Als Heißgas kann auch ein anderes Gas in Frage kommen, beispielsweise ein inertes Gas, wenn eine chemische Reaktion des Körnergemisches mit dem Heißgas vermieden werden soll.It should be mentioned at this point that a hot air flow is given here only as an example. As a hot gas, another gas can also be used, for example an inert gas, if a chemical reaction of the grain mixture with the hot gas is to be avoided.

Für höhere Ansprüche an die Trennschärfe wird die aufwärts gerichtete Strömung nach Art eines Zyklons geführt, woraus sich eine abgewandelte und dem vorliegenden. Zweck in besonderer Weise angepaßte Bauform einer an sich bekannten Mischkammer ergibt. Diese ist in Fig. 2 dargestellt.For higher demands on the selectivity of the upward flow is performed in the manner of a cyclone, resulting in a modified and the present. Purpose specially adapted design of a known mixing chamber results. This is shown in Fig. 2.

Gemäß Fig. 2 besteht die Vorrichtung aus einem vertikal stehenden, sich nach oben erweiternden Kegelstumpf 3 mit einem unteren Durchmesser D1, einem oberen Durchmesser D2 und einer axialen Länge E. Am unteren Ende des Kegelstumpfes 3 ist konzentrisch eine logarithmische Spirale S der Breite B1 angebracht. Die Spirale S ist durch ihren Winkel α gegen die Umfangsrichtung vollständig beschrieben. Der angestrebte Trenneffekt hat ein deutliches Optimum bei Winkeln α, die etwa zwischen 5° und etwa 12° liegen, mit Bestwerten zwischen 6° und 9°. Unterhalb und oberhalb dieser Winkelwerte läßt der Trenneffekt rasch nach.According to Fig. 2, the device consists of a vertically standing, upwardly flared truncated cone 3 with a lower diameter D1, an upper diameter D2 and an axial length E. At the lower end of the truncated cone 3, a logarithmic spiral S of width B1 is concentrically attached , The spiral S is completely described by its angle α against the circumferential direction. The desired separation effect has a clear optimum at angles α, which are approximately between 5 ° and about 12 °, with best values between 6 ° and 9 °. Below and above these angle values, the separation effect diminishes rapidly.

An das obere Ende des Kegelstumpfes 3 schließt sich ein Austragekopf C an, der einen Durchmesser D3 hat, auf den sich der obere Durchmesser D2 des Kegelstumpfes 3 über eine Breite B2 konisch erweitert. Der zylindrische Abschnitt des Austragekopfes C hat eine Breite B3 ist von einer Kuppel überwölbt.At the upper end of the truncated cone 3 is followed by a discharge head C, which has a diameter D3, to which the upper diameter D2 of the truncated cone 3 widens conically over a width B2. The cylindrical portion of the discharge head C has a width B3 is arched by a dome.

An den Austragekopf C schließt sich außen eine Austrageleitung A an. Zentrisch ist der Austragekopf C von einem Tauchrohr T eines Durchmesser DT durchdrungen, das bis in den Bereich des Übergangs zwischen dem Austragekopf C und den Kegelstumpf 3 beim Durchmesser D2 reicht. Vorzugsweise endet das Tauchrohr T in Höhe des oberen Endes des Kegelstumpfs 3.At the discharge head C is followed by a discharge line A outside. Centrally, the discharge head C is penetrated by a dip tube T of a diameter D T , which extends into the region of the transition between the discharge head C and the truncated cone 3 at the diameter D2. Preferably, the dip tube T ends at the level of the upper end of the truncated cone. 3

An das untere Ende der logarithmischen Spirale S schließt sich zentrisch ein Zellenrad Z an, das einerseits einen Verschluß darstellt, andererseits aber den Abzug von Überkorn erlaubt.Centrally connected to the lower end of the logarithmic spiral S is a cellular wheel Z which, on the one hand, constitutes a closure, but on the other hand permits the withdrawal of oversize particles.

Im Betrieb dieser Vorrichtung wird ein Heißgas H der logarithmischen Spirale S zugeführt, die das Heißgas H in die von dem Kegelstumpf 3 umschlossene Kammer einleitet, wo sich aufgrund des Spiralwinkels α der logarithmischen S eine wandnahe Aufwärtsströmung W ausbildet, der eine in Umfangsrichtung verlaufende Komponente überlagert ist, die in der Zeichnung nicht dargestellt ist und dazu führt, daß die Heißgasströmung sich wie eine von unten nach oben erweiternde Spirale entwickelt.In operation of this device, a hot gas H of the logarithmic spiral S is fed, which initiates the hot gas H in the space enclosed by the truncated cone 3 chamber, where due to the helix angle α of the logarithmic S forms a wall-near upward flow W, which superimposes a circumferentially extending component is, which is not shown in the drawing and causes the hot gas flow to develop like a spiraling upwards from the bottom.

Von oben wird durch das Tauchrohr T ein Fördergasstrom F eingeleitet, der ein Körnergemisch mit sich führt, das Körner K1, K2 und K3 unterschiedlicher Größe, wie im ersten Beispiel beschrieben enthält. Aus Gründen der Vereinfachung sei hier wieder nur von kleinen Körnern K1, größeren Körnern K2 und Überkorn K3 die Rede.From above a feed gas stream F is introduced through the dip tube T, which carries with it a grain mixture containing grains K1, K2 and K3 different size, as described in the first example. For reasons of simplification, here again only small grains K1, larger grains K2 and oversize K3 are mentioned.

Die aus dem Tauchrohr T austretende Trägergasströmung F mit den mitgeführten Körnern, wieder insgesamt mit F+K1+K2+K2 bezeichnet, wird in der von dem Kegelstumpf 3 umschlossenen Kammer durch die Umfangskomponente der Heißgasströmung in Rotation versetzt. Dieser Rotation folgen die kleinen Körner K1 schnell, die größeren K2 entsprechend ihrer größeren Masse und Trägheit langsamer, und das Überkorn K3 fast gar nicht. Das Überkorn K3 fällt nach unten durch und kann durch das Zellenrad Z abgezogen werden.The carrier gas flow F emerging from the dip tube T with the entrained grains, again denoted overall by F + K1 + K2 + K2, is set in rotation in the chamber enclosed by the truncated cone 3 by the peripheral component of the hot gas flow. The small grains K1 follow this rotation rapidly, the larger K2s slower according to their larger mass and inertia, and the over grain K3 hardly ever. The oversize K3 falls down and can be removed by the feeder Z.

Die kleinen Körner K1 gelangen somit sehr schnell in die wandnahe Strömung W und werden daher schnell dem oberen Kegeldurchmesser D2 zugeführt. Die größeren Körner K2 fallen tiefer nach unten durch und gelangen erst weiter unten in der Kammer in die wandnahe Strömung W. Sie haben gegenüber den Körnern K1 aus zwei Gründen eine längere Verweilzeit in der Kammer: Ihr Weg in der wandnahen, aufwärts gerichteten Strömung W ist länger als der der kleinen Körner K1, und sie werden wegen ihrer größeren Sinkgeschwindigkeit langsamer nach oben getragen, als die kleinen Körner K1.The small grains K1 thus reach the wall-near flow W very quickly and are therefore fed quickly to the upper cone diameter D2. The larger grains K2 fall deeper below and only further down in the chamber into the near-wall current W. They have a longer residence time in the chamber compared to the grains K1 for two reasons: their way in the wall-oriented, upward flow W is longer than that of the small grains K1 , and they are carried up more slowly than the small grains K1 because of their higher sink rate.

Wenn die Körner K1 und K2 in den Austragekopf C gelangen, werden sie dort durch die Austrageleitung A aus der Vorrichtung entlassen. Die Gasströmungen H und F und die kleinen und mittleren Körner K1 und K2 haben sich addiert, was in der Zeichnung entsprechend mit F+H+K1+K2 dargestellt ist.When the grains K1 and K2 enter the discharge head C, they are discharged there from the device through the discharge line A. The gas flows H and F and the small and medium grains K1 and K2 have added up, which is represented in the drawing as corresponding to F + H + K1 + K2.

Für die Trennung der kleinen Körner K1 von den größeren Körnern K2, und natürlich für die Trennung aller Kornzwischengrößen, ist der Spiralwinkel α der logarithmischen Spirale S von Wichtigkeit. Er sollte zwischen 5° und 12° liegen, mit Bestwerten zwischen 6° und 9°. Unterhalb und oberhalb dieser Winkelwerte läßt der Trenneffekt in der vom Kegelstumpf 3 umschlossenen Kammer rasch nach.For the separation of the small grains K1 from the larger grains K2, and of course for the separation of all intermediate grain sizes, the spiral angle α of the logarithmic spiral S is of importance. It should be between 5 ° and 12 °, with best values between 6 ° and 9 °. Below and above these angle values, the separation effect in the chamber enclosed by the truncated cone 3 decreases rapidly.

Bei einer Vorrichtung nach Fig. 2 ist die Einhaltung bestimmter Abmessungen wichtig. Bei Abweichung nach unten oder oben läßt entweder die angestrebte Wirkung nach, oder das Strömungsbild schlägt ganz um und wird völlig unbrauchbar.In a device according to Fig. 2, compliance with certain dimensions is important. In case of deviation downwards or upwards either the desired effect diminishes, or the flow pattern beats completely and becomes completely useless.

Nachstehend werden Abmessungen angegeben, die insbesondere für den genannten Trenneffekt optimal sind. Sie werden dargestellt am Beispiel einer Erwärmung von 2200 kg/h Eisenoxid vom Korngrößenbereich 96% unter 74 µm, mit Überkorn bis ca. 1 mm. Das Eisenoxid (überwiegend Fe2O3) hat Umgebungstemperatur und enthält 10% Feuchte. Es soll mit 2546 m3 n/h Heißgas (Ofenabgas) von 800°C auf eine Temperatur von 400°C aufgeheizt und zugleich getrocknet werden. Das Heißgas mit dem mitgeführten Eisenoxid wird durch das Tauchrohr T in die Rückströmung R eingeblasen, die sich aufgrund der sich in der Kammer in bekannter Weise ausbildenden Druckverhältnisse einstellt. Von den 2546 m3 n/h Heißgas werden vor der logarithmischen Spirale S etwa 127 m3 n/h abgezweigt und als 800°C heißes Fördermedium F verwendet.Below dimensions are given, which are optimal in particular for the said separation effect. They are illustrated by the example of a heating of 2200 kg / h of iron oxide of a particle size range of 96% below 74 μm, with oversize to approx. 1 mm. The iron oxide (predominantly Fe 2 O 3 ) has ambient temperature and contains 10% moisture. It is designed with 2546 m 3 n / h hot gas (kiln exhaust) of 800 ° C heated to a temperature of 400 ° C and dried at the same time. The hot gas with the entrained iron oxide is blown through the dip tube T in the return flow R, which is established due to the forming in the chamber in a known manner pressure conditions. Of the 2546 m 3 n / h hot gas about 127 m 3 n / h are diverted before the logarithmic spiral S and used as 800 ° C hot medium F.

Nach Vorversuchen ergab sich ein optimaler Trenneffekt bei folgenden Abmessungen: α = 6,85° B1 = 225 mm D1 = 385 mm E = 1.668 mm D2 = 770 mm B3 = 500 mm D3 = 1.300 mm A = 250 mm DT = 200 mm After preliminary tests, an optimal separation effect resulted for the following dimensions: α = 6.85 ° B1 = 225 mm D1 = 385 mm E = 1,668 mm D2 = 770 mm B3 = 500 mm D3 = 1,300 mm A = 250 mm D T = 200 mm

Das Tauchrohr T soll näherungsweise bis zum Durchmesser D2 reichen.The dip tube T is intended to reach approximately to the diameter D2.

Im vorliegenden Falle war der Mengananteil Überkorns K3, der mangels Verweilzeit der Körner K3 nicht hinreichend aufgeheizt werden konnte: K 3 : K 1 + K 2 + K 3 = 0 , 02

Figure imgb0001
In the present case, the amount of oversize K3 which could not be heated sufficiently due to the lack of residence time of the grains K3 was: K 3 : K 1 + K 2 + K 3 = 0 . 02
Figure imgb0001

Bei den genannten Durchsatzdaten ist der Druckverlust des Heißgases H beim Durchströmen der vom Kegelstumpf umschlossenen Kammer etwa 2200 Pa.In the above-mentioned flow rate data, the pressure loss of the hot gas H as it flows through the chamber enclosed by the truncated cone is about 2200 Pa.

Die zulässigen Variationsbreiten der genannten Abmessungen sind:The permitted variation widths of the mentioned dimensions are:

a) Spiralwinkel αa) spiral angle α

Zwischen 6° und 9° wurde kein Einfluß des Winkels auf den Trenneffekt gefunden. Unter 5° steigt der Druckverlust nutzlos an; über 12° steigt der Bauaufwand der Spirale.Between 6 ° and 9 ° no influence of the angle on the separation effect was found. Below 5 °, the pressure loss increases useless; over 12 ° increases the construction cost of the spiral.

b) Spiralabmessungen D1 und B1b) Spiral dimensions D1 and B1

Bis ca. 10° Abweichung läßt die Effektivität der Durchmischung der Körner K1 und K2 mit dem Heißgas H langsam nach. Der Druckverlust entwickelt sich umgekehrt dem Quadrat der Abmessungen. In den Grenzen von ca. 20% kann eine Vergrößerung von D1 durch Verkleinerung von B1 kompensiert werden, gilt also B1 x D1 = konstant. Bei weiterem Verkleinern von D1 und B1 steigt der Druckverlust quadratisch, aber nutzlos an. Bei weiterem Vergrößern läßt die genannte Mischleistung nach.Up to about 10 ° deviation, the effectiveness of the mixing of the grains K1 and K2 with the hot gas H decreases slowly. The pressure loss develops inversely the square of the dimensions. Within the limits of approx. 20%, an enlargement of D1 can be compensated by reducing B1, so B1 x D1 = constant. As D1 and B1 further decrease, the pressure loss increases quadratically, but uselessly. Upon further enlargement, said mixing performance diminishes.

c) Länge Ec) length E

Bei Verkleinerung auf ca. 1350' mm sinken die Verweilzeit und damit die aufheizbare Korngröße. Unter einer Länge E von 1350 mm wird die Strömung in der Kammer instabil.When reducing to about 1350 'mm, the residence time and thus the heatable grain size decrease. At a length E of 1350 mm, the flow in the chamber becomes unstable.

d) Durchmesser D2d) diameter D2

Unter ca. 740 mm läßt die genannte Mischleistung nach. Eine Vergrößerung über 770 mm bis ca. 900 mm erhöht nur den Bauaufwand, bringt aber keinen Nutzen. Oberhalb von ca. 1000 mm wird die Strömung instabil.Below approx. 740 mm, the mentioned mixing performance diminishes. An enlargement over 770 mm to approx. 900 mm only increases the construction costs, but brings no benefit. Above about 1000 mm, the flow becomes unstable.

e) Kopfabmessungen D3 und B3e) Head dimensions D3 and B3

Diese Werte sind unkritisch und brauchten daher nicht näher untersucht zu werden. Hier gelten die Regeln der Technik.These values are not critical and therefore need not be investigated further. Here the rules of technology apply.

Alle Untersuchungsergebnisse setzen eine ungestörte Zuströmung des Heißgases H zur Spirale S voraus.All test results assume an undisturbed inflow of the hot gas H to the spiral S.

Da das Strömungsbild in der Kammer nicht von der Reynoldszahl abhängt, gelten hier die einfachen Modellgesetze der Strömungsbilder der freien Turbulenz:

  • Alle Abmessungen können ähnlich vergrößert oder verkleinert werden, ausgenommen natürlich der Spiralwinkel α. Die Durchsätze gehen dann mit dem Quadrat der Abmessungen. Der Heißgasdurchsatz kann erhöht oder verringert werden. Der Druckverlust geht dann mit dem Quadrat des Durchsatzes. Die Heißgaseintrittstemperatur kann bei gleichem Heißgasdurchsatz variiert werden. Der Druckverlust geht dann mit der absoluten Eintrittstemperatur.
Since the flow pattern in the chamber does not depend on the Reynolds number, the simple model laws of the flow patterns of free turbulence apply here:
  • All dimensions can be similarly enlarged or reduced, except, of course, the spiral angle α. The throughputs then go with the square of the dimensions. The hot gas flow rate can be increased or decreased. The pressure loss then goes with the square of the throughput. The hot gas inlet temperature can be varied at the same hot gas flow rate. The pressure loss then goes with the absolute inlet temperature.

Die Grenzen des Heißgasdurchsatzes bei gegebener Baugröße sind folgende:

  • Für die untere Grenze gilt, daß der Druckverlust ausreichen muß, um auch die mittleren Körner K2 auszutragen, nicht aber die Körner K3. Näherungsweise gilt für den Mindestdruckverlust: Δp min = 13 × γ k × d k ( mbar ) ,
    Figure imgb0002
    wobei γk (kg/m3) die Dichte des Korns und dK(m) die Abmessung des Korns ist.
The limits of the hot gas flow rate for a given size are the following:
  • For the lower limit applies that the pressure loss must be sufficient to discharge the average grains K2, but not the grains K3. As an approximation applies to the minimum pressure loss: Ap min = 13 × γ k × d k ( mbar ) .
    Figure imgb0002
    where γ k (kg / m 3) is the density of the grain and d K (m) is the dimension of the grain.

Für die obere Grenze gilt, daß die Verweilzeit und der Wärmeübergang in bekannter Weise für die Aufheizung der mittleren Körner K2 ausreichen müssen.For the upper limit applies that the residence time and the heat transfer must be sufficient in a known manner for the heating of the average grains K2.

Für Körner, die schwerer als Wasser sind, kann als Trägermedium auch Wasser oder eine geeignete andere Flüssigkeit verwendet werden. Die vorstehenden Überlegungen gelten auch für Flüssigkeiten als Medium anstelle der vorgenannten Gase.For grains heavier than water, water or another suitable liquid may also be used as the carrier medium. The above considerations also apply to liquids as a medium instead of the aforementioned gases.

Claims (13)

  1. A method for uniformly heating a mixture composed of coarse and fine grains by means of a hot gas flow within which said grains of different size have different dwelling times, characterized in that said grains are introduced into said hot gas flow depending on their size at different locations so that said grains cover a distance together with the hot gas which increases in length if grain size increases.
  2. The method of claim 1, characterized in that the grain mixture is introduced into an upwardly directed hot gas flow by means of a carrier gas flow directed downwards, so that a segregation of the grain mixture in dependency of the grain size takes place before said grains enter into the hot gas flow, so that the small grains enter into the hot gas flow at a position located higher than that where the larger grains enter into the hot gas flow.
  3. The method of claim 2, characterized in that the carrier gas flow directed downwards and comprising said grain mixture and the hot gas flow directed upwardly contact one another at an interface the length in which extending in flow direction of the gases is at least four times, preferably six times, the thickness of the carrier gas flow as measured transversely to the interface of the gas flows.
  4. The method of claim 2 or 3, characterized in that grains are separated which due to oversize do not enter into the hot gas.
  5. The method of on of the claims 2 to 4, characterized in that the hot gas flow extends in a helical path and the carrier gas along with the grain mixture is flowing downwards in the axis of said helical path.
  6. The method of claim 5, characterized in that said helical hot gas flow is conducted from below to the top in a conical surface.
  7. An apparatus for carrying out the method of one of the preceding claims, characterized by a reaction chamber which enlarges from the bottom to the top in the manner of a truncated cone and comprises an inlet guide helix (S) for the hot gas (H) at its bottom end and an outlet head (C) at its top end, and a feed tube (T) penetrating the latter and having a centrally disposed and axially directed outlet for the infeed of the carrier gas (F) and the grain mixture (K1+K2+K3) entrained therewith, said reaction chamber having the following parameters related to a hot gas throughput of 2.546 mn 3/h at a temperature of 800°C and approximately atmospheric pressure: Helix angle of the inlet guide helix S: α = 6°-9° Height of the inlet guide helix S: B1 = 225 mm Diameter of the reaction chamber at its bottom D1 = 385 mm Axial length of the reaction chamber E = 1.668 mm Diameter of the reaction chamber at its top: D2 = 770 mm Height of the outlet head: B3 = 500 mm
  8. The apparatus of claim 7, characterized in that the helix angle α of the inlet guide helix S is 6,85°.
  9. The apparatus of claim 7 or 8, characterized in that a transition piece is disposed between the upper end of the reaction chamber and the outlet head (C), said transition piece enlarging on a length B2 of about 135 mm to the diameter D3 = 1.300mm of the outlet head (C).
  10. The apparatus of claim 7 or 9, characterized in that with a hot gas throughput varied with respect to 2.546 mn 3/h by a factor, the linear dimensions of the apparatus are varied by the square root of said factor with respect to the dimensions given in claims 7 and 9, respectively.
  11. The apparatus of one of claims 7 to 10, characterized by a branching-off means by which a portion of the hot gas flow (H) is branched-off as a carrier gas flow for the grain mixture (K1+K2+K3) before its entry into the inlet guide helix (S).
  12. The apparatus of one of claims 7 to 10, characterized in that a drain (Z) is provided in the centre of the inlet guide helix (S) for the discharge of oversized grain (K3).
  13. The apparatus of one of the claims 7 to 12, characterized in that the dimensions D1 and B1 are varied within +/- 20% with respect to those given in claim 7, keeping the product B1 x D1 constant.
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