Spray nozzle apparatus for spray-drying applications

Abstract

The invention provides for an spray nozzle apparatus (1) for a spray drying apparatus comprising a nozzle provided with at least one nozzle orifice (26) for outputting spray droplets of a product to be dried and a least one inlet orifice (24) for transferring said product into a nozzle chamber (22), including an apparatus for adjusting the size of outputted droplets inline during the spray drying process.

Claims

1. A single phase spray nozzle apparatus for a spraying apparatus, the nozzle apparatus comprising: a nozzle provided with at least one nozzle orifice for outputting spray droplets of a product to be dried and at least one inlet orifice for transferring the product into a nozzle chamber, the nozzle chamber comprising walls defining a volume of the nozzle chamber, the nozzle chamber further comprising an apparatus for adjusting a size of the outputted spray droplets inline during a spray drying process, the apparatus comprises a plunger for adjusting the volume of the nozzle chamber based on spray drying process parameters and product parameters obtained inline during the spray drying process, the walls of the nozzle chamber do not have a turbulence generating surface, and the product to be dried has a viscosity between 1 and 1000 mPa.Math.s; an electric drive for adjusting geometry of the nozzle chamber, the electric drive controlled by a control device based on the spray drying process parameters and the product parameters obtained inline; and a connecting sleeve releasably fixed to the electrical drive and providing a longitudinal bore for rotatably accommodating a hollow shaft which transfers a rotating motion of an output shaft of the electrical drive to an adjusting pin driving the plunger into and out of the nozzle chamber, wherein the nozzle chamber is provided by a swirl chamber body inserted into an inner chamber of a nozzle body, the nozzle body releasably fixed to the connecting sleeve, the swirl chamber body is provided with an opening channel arranged in correspondence to the at least one inlet orifice for introducing the product into a swirl chamber of the swirl chamber body, the swirl chamber is provided with a helicoidal spiral-type tightening guiding face for accelerating the product into the direction of the at least one nozzle orifice.

2. The nozzle apparatus according to claim 1, wherein the plunger is movable into and out of the nozzle chamber by the electric drive, thereby adjusting a volume and a height of the nozzle chamber.

3. The nozzle apparatus according to claim 2, wherein the electric drive comprises an electric motor rotatably driving the output shaft, the rotation being transformed into a longitudinal motion of the plunger via a threaded engagement between the output shaft and the plunger.

4. The nozzle apparatus according to claim 1, wherein the plunger is axially movable, and the adjusting pin is provided with a longitudinally extending axial bore with an inner thread in engagement with an outer thread of the plunger such that a rotating motion of the adjusting pin is transformed into a longitudinal motion of the plunger.

5. The nozzle apparatus according to claim 1, wherein the at least one inlet orifice extends radially to the longitudinal axis of the nozzle such that the product is transferred to the nozzle via a tubing connected with the at least one inlet orifice.

6. The nozzle apparatus according to claim 1, wherein the at least one nozzle orifice is equipped with a releasably mounted orifice plate such that an opening diameter of the at least one nozzle orifice is variable by replacing the orifice plate by a different diameter orifice plate.

7. The nozzle apparatus according to claim 1, wherein a cone angle of a spray mist produced by the outputted spray droplets and the size of the outputted spray droplets are variable by axially moving the plunger relative to the nozzle chamber.

8. A spray-drying apparatus comprising: a nozzle having at least one nozzle orifice for outputting spray droplets of a product to be dried and at least one inlet orifice for transferring the product into a nozzle chamber, the nozzle chamber comprising walls defining a volume of the nozzle chamber, the nozzle chamber further comprising an apparatus for adjusting a size of the outputted spray droplets inline during a spray drying process, the apparatus comprises a plunger for adjusting the volume of the nozzle chamber based on spray drying process parameters and product parameters obtained inline during the spray drying process, the walls of the nozzle chamber do not have a turbulence generating surface, and the product to be dried has a viscosity between 1 and 1000 mPa.Math.s; an electric drive for adjusting geometry of the nozzle chamber, the electric drive controlled by a control device based on the spray drying process parameters and the product parameters obtained inline; and a connecting sleeve releasably fixed to the electrical drive and providing a longitudinal bore for rotatably accommodating a hollow shaft which transfers a rotating motion of an output shaft of the electrical drive to an adjusting pin driving the plunger into and out of the nozzle chamber, wherein the nozzle chamber is provided by a swirl chamber body inserted into an inner chamber of a nozzle body, the nozzle body releasably fixed to the connecting sleeve, the swirl chamber body is provided with an opening channel arranged in correspondence to the at least one inlet orifice for introducing the product into a swirl chamber of the swirl chamber body, the swirl chamber is provided with a helicoidal spiral-type tightening guiding face for accelerating the product into the direction of the at least one nozzle orifice.

9. The spray-drying apparatus according to claim 8, wherein the product is a paste, and the apparatus comprises an inline differential pressure drop measuring apparatus for continuous determination of a shear viscosity of the paste, the inline differential pressure drop measuring apparatus provided in a bypass to a processing line upstream of the nozzle.

10. The spray-drying apparatus according to claim 9, wherein the bypass comprises a pump, a flow meter, and a differential pressure tube.

11. A spray-drying process comprising: spraying a paste of a product using a spray nozzle provided with at least one nozzle orifice for outputting spray droplets of a product to be dried and at least one inlet orifice for transferring the product into a nozzle chamber, the nozzle chamber comprising walls defining a volume of the nozzle chamber, the nozzle chamber further comprising an apparatus for adjusting a size of the outputted spray droplets inline during the spray drying process, the apparatus comprises a plunger for adjusting the volume of the nozzle chamber based on spray drying process parameters and product parameters obtained inline during the spray drying process, the walls of the nozzle chamber do not have a turbulence generating surface, and the product to be dried has a viscosity between 1 and 1000 mPa.Math.s, the product is sprayed into a drying chamber; adjusting geometry of the nozzle chamber using an electric drive controlled by a control device based on the spray drying process parameters and the product parameters obtained inline, wherein the adjusting of the geometry of the nozzle chamber comprises transferring a rotating motion of an output shaft of the electrical drive to an adjusting pin driving the plunger into and out of the nozzle chamber, wherein a connecting sleeve is releasably fixed to the electrical drive and provides a longitudinal bore for rotatably accommodating a hollow shaft which transfers the rotating motion, and the nozzle chamber is provided by a swirl chamber body inserted into an inner chamber of a nozzle body, the nozzle body releasably fixed to the connecting sleeve, the swirl chamber body is provided with an opening channel arranged in correspondence to the at least one inlet orifice for introducing the product into a swirl chamber of the swirl chamber body, the swirl chamber is provided with a helicoidal spiral-type tightening guiding face for accelerating the product into the direction of the at least one nozzle orifice and providing hot gas to the drying chamber to dry the paste to a powder.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) In the following the invention will be described in further detail by means of an embodiment thereof and the appended drawings.

(2) FIG. 1 shows a partial sectional side view of an embodiment of a spray nozzle apparatus according to the invention;

(3) FIG. 2 shows a cross sectional view of a hollow shaft of the spray nozzle apparatus of FIG. 1;

(4) FIG. 3 shows a partial sectional view of an adjusting pin;

(5) FIG. 4 shows a front view of the swirl chamber body of the spray nozzle apparatus of FIG. 1; and

(6) FIGS. 5 and 5A depict a side view and a front view (in the direction of arrow A) of the plunger of the spray nozzle apparatus of FIG. 1.

(7) FIG. 6 is a flow chart of a process for controlling the spray droplet size of a spray nozzle apparatus of the invention;

(8) FIG. 7 is a flow chart of a differential pressure drop method that can be carried out with the differential pressure drop measuring apparatus as used in a preferred embodiment of the present invention;

(9) FIG. 8 shows a principle of a differential pressure drop measuring apparatus as used in a preferred embodiment of the present invention.

(10) The spray nozzle apparatus 1 according to FIG. 1 comprises an electric drive 2 provided with an interface (such as a Profibus interface or Ethernet/IP interface) and a power supply (such as a 24V-DC power supply) at 3 and an electric motor 4 including a transmission connected with 3.

(11) The electric motor 4 drives an output shaft 5 in a rotating manner. The output shaft 5 extends into a longitudinally extending inner bore 6 of a hollow shaft 7 which is depicted in more detail in FIG. 2.

(12) The hollow shaft 7 is rotatably accommodated in a longitudinally extending inner bore 8 of a connecting sleeve 9 which can be fixed to the housing of transmission 4 by bolts 10.

(13) The inner bore 6 of the hollow shaft 7 is equipped with an inner thread 11 which can be brought into a threaded engagement with an outer thread 12 provided on an end piece of an adjusting pin 13shown in more detail in FIG. 3which can be inserted into the inner bore 6 of the hollow shaft 7.

(14) Opposite to the threaded terminal end 12 of the adjusting pin 13 there is provided a receiving section of the adjusting pin 13, which is formed with an inner bore 14 equipped with an inner thread 15.

(15) The inner thread 15 of the adjusting pin 13 serves to be brought into a threaded engagement with an outer thread 16 of a plunger 17 more clearly shown in FIGS. 5 and 5A.

(16) As can be seen from FIGS. 5 and 5A, the plunger 17 comprises an outer circumferential surface section 18 with a helicoidally shaped cross section corresponding to the shape and size of a receiving section 19 of a swirl chamber body 20 accommodated in a nozzle body 23 which is mounted to the connecting sleeve 9 as shown in FIG. 4.

(17) The swirl chamber body 20 comprises a lateral or tangential inlet channel 21 for introducing paste material or the like into the swirl chamber 22 of the swirl chamber body 20.

(18) Material to be transported through the inlet channel 21 into the swirl chamber 22 can enter the nozzle body 23 via a first orifice 24 or inlet orifice which extends radially to the common longitudinal axis 28 of the nozzle body 23 and the connecting sleeve 9. To this end there is a tube 25 connected to the first orifice 24 of the nozzle body 23 defining an inlet opening of the apparatus 1.

(19) Paste or paste like material delivered to the nozzle body 23 via the tube 25 enters the nozzle body 23 via the first orifice 24 and enters the swirl chamber 22 via the inlet channel 21.

(20) The swirl chamber 22 is equipped with an axially extending through hole having an inner circumferential surface section with a helicoidally shaped cross section, thus forming a helicoidal, spiral type guiding face that serves to accelerate the material into the direction of a second orifice 26 or nozzle orifice of the nozzle body 23 defining an outlet opening of the apparatus 1. There is an orifice plate 27 provided between the axial outlet of the swirl chamber 22 and the second orifice 26 by which orifice plate 27 the opening angle of the spray cone can be adjusted.

(21) FIG. 1 shows the plunger 17 closing the first orifice 24. Driving the motor 3 makes the hollow shaft 7 rotate and thus also makes the adjusting pin 13 rotate about its longitudinal axis. The plunger 17 is connected to the inner thread 15 of the adjusting pin 13 via the outer thread 16 and can only execute a movement relative to the swirl chamber body 20 along the longitudinal axis of the plunger 17 but can not rotate relative to the swirl chamber body 20. Thus a rotation of the adjusting pin 13 is transformed into an axial movement of the plunger 19 relative to the swirl chamber body 20.

(22) By this movement of the plunger 18 the axial width of the first orifice 24 and the geometry of the swirl chamber 22 and thus the nozzle chamber can be modified. Since the electric drive 2 is controlled by process and product parameters which in turn are obtained or evaluated inline during the manufacturing process of the powder to be achieved, the control takes place inline with the manufacturing process of the powder. To achieve this, the control circuit provides the electric drive 2 with signals such that the plunger 17 is being moved axially in the direction of the longitudinal axis 28 as shown in FIG. 1. By this movement of the plunger 17 the spray droplet size of the material to be atomized can be adjusted towards the minimum Sauter diameter possible for a given set of input parameters.

(23) Measuring these input parameters inline with the production process of the powder enables it to adjust the droplet size towards the minimum Sauter diameter possible inline and thus makes it possible to consider the complete range of spray viscosities during the production process of the powder to be produced.

(24) In a particularly preferred embodiment of the present invention, the input parameters which are measured inline with the production process are as follows: flow rate of the product into the spraying apparatus pipes towards the nozzle, pressure of the product into the pipes towards the nozzle, viscosity of the product measured in the pipes towards the nozzle, and/or finally density of the product, that is also measured in the pipes of the apparatus leading to the nozzle.

(25) The product paste entering the swirl chamber through the inlet channel 21 follows a helicoidal and spiral way due to the spiral-type cross section design of the swirl chamber in a combined circumferential and axial direction towards the nozzle orifice 26. This design accelerates the traveling speed of the product paste flow in the swirl chamber, provided that the mass flow of the product paste is constant. The product paste is exiting the spray nozzle through the orifice plate 27 and the nozzle orifice 26 as a cone-shaped film 29 with a cone tip angle wherein the film 29 atomizes into droplets forming a spray mist. The cone tip angle is directly proportional to the traveling speed of the product paste in the nozzle orifice 26, i.e. the higher the traveling speed is, the larger the cone tip angle becomes and the smaller the droplets size.

(26) A cone tip angle of 0 generates no atomization and, in a realized example, a cone tip angle of 100 generates droplets having a Sauter-diameter of D.sub.32=30 m. The wider the cone tip angle is, the smaller the droplets become so that the droplet size can be controlled by the cone tip angle and thus by the traveling speed of the product paste in the nozzle orifice 26. The invention should not be regarded as being limited to the embodiment shown and described in the above but various modifications and combinations of features may be carried out without departing from the scope of the following claims.

(27) FIG. 6 is a flowchart of a process for controlling the spray droplet size of an agglomeration spray nozzle apparatus of the invention, when the processing line is provided with an inline differential pressure drop measuring apparatus. The product paste in FIG. 6 indicated as concentrate is delivered to a dosing point 30, which leads a part of the product paste stream into a bypass line 32. The majority of the product paste stream is directed into a main product paste line 34. The bypass line 32 is redirected into the main product paste line 34 at a line junction 36 downstream of a differential pressure drop measuring apparatus 38 provided in the bypass line 32.

(28) Downstream of the line junction 36 a mass flow meter 40, a density meter 42 and a spray pressure probe 44 are provided in the main product paste line. Downstream of the spray pressure probe 44 the main product paste line 34 enters a spray nozzle apparatus 1 through tube 25. The product paste delivered to the spray nozzle apparatus 1 is then sprayed into a spray drying chamber 46.

(29) The differential pressure drop measuring apparatus 38 determines the shear rate and the shear viscosity of the product paste delivered to the spray nozzle, according to one preferred embodiment of the invention. The data of the shear rate and shear viscosity are delivered from the differential pressure drop measuring apparatus 38 to a control device (SPS-control) 48. In the same manner, the product paste mass flow rate Q.sub.m determined in the mass flow meter 40, the product paste density determined in the density meter 42 and the spray pressure P of the product paste determined in the spray pressure probe 44 are also delivered to the control device 48. The shear rate has to be greater than 1000 s.sup.1.

(30) Control device 48 comprises a computer which calculates an output control parameter based on the above data delivered to the control device 48 and on the basis of known spray nozzle geometry parameters stored in a memory of the control device 48. The output control parameter is delivered to the spray nozzle apparatus 1 in order to adjust the swirl chamber piston 17 (plunger) to a calculated position in order to obtain a desired swirl chamber volume.

(31) The following equations 1-7 describe the solving procedure how to control the plunger position (given with h.sub.sc) based on a change in the paste shear viscosity .

(32) Accordingly the solving procedure is applied for a change in mass flow rate Qm and paste density .

(33) Universal Massflow-Characterisation of Pressure Swirl Nozzle Flows:

(34) $\begin{array}{cc}\frac{\mathrm{Qm}}{d_{\mathrm{sc}}}=2.1844{\left(\frac{d_{\mathrm{or}}}{d_{\mathrm{sc}}}\right)}^{1.2859}{\left(\frac{h_{\mathrm{sc}}}{d_{\mathrm{sc}}}\right)}^{0.4611}{\left(\frac{\sqrt{P}{d}_{\mathrm{sc}}}{}\right)}^{0.9140}& \left(1\right)\end{array}$
The relation between spray pressure P and axial position of the plunger (given with h.sub.sc) is derived for the example of a shear viscosity change from .sub.old to .sub.new:

(35) $\begin{array}{cc}\frac{{}_{\mathrm{new}}}{{}_{\mathrm{old}}}={\left(\frac{h_{\mathrm{sc},\mathrm{old}}}{h_{\mathrm{sc},\mathrm{new}}}\right)}^{0.4611}{\left(\frac{{}_{\mathrm{new}}}{{}_{\mathrm{old}}}\right)}^{0.9140}{\left(\frac{P_{\mathrm{old}}}{P_{\mathrm{new}}}\right)}^{\frac{0.9140}{2}}& \left(2\right)\end{array}$
Solved for the spray pressure ratio:

(36) $\begin{array}{cc}\frac{P_{\mathrm{old}}}{P_{\mathrm{new}}}={\left(\frac{{}_{\mathrm{new}}}{{}_{\mathrm{old}}}\right)}^{\frac{1-0.9140}{0.4570}}{\left(\frac{h_{\mathrm{sc},\mathrm{old}}}{h_{\mathrm{sc},\mathrm{new}}}\right)}^{\frac{-0.4611}{0.4570}}& \left(3\right)\end{array}$
In order to find a direct relation between plunger position h.sub.sc and shear viscosity , the spray pressure ratio has to be found from another equation, see equations 4-6 below:
Universal Spray Droplet Size Characterisation of Pressure Swirl Nozzle Sprays:

(37) $\begin{array}{cc}\frac{D_{32,\mathrm{globaal}}}{d_{\mathrm{sc}}}=1.0798{\mathrm{Re}}^{-0.2987}{{\mathrm{We}}^{-0.1709}\left(\frac{h_{\mathrm{sc}}}{d_{\mathrm{sc}}}\right)}^{-0.0772}{\left(\frac{d_{\mathrm{or}}}{d_{\mathrm{sc}}}\right)}^{0.9534}& \left(4\right)\end{array}$
Again, one can derive the Spray Pressure Ratio with the consistency conditions that D.sub.32-global-old and D.sub.32-global-new remain constant:

(38) $\begin{array}{cc}\frac{D_{32,\mathrm{global},\mathrm{old}}}{D_{32,\mathrm{global},\mathrm{new}}}=1={\left(\frac{{\mathrm{Re}}_{\mathrm{old}}}{{\mathrm{Re}}_{\mathrm{new}}}\right)}^{-0.2987}{\left(\frac{{\mathrm{We}}_{\mathrm{old}}}{{\mathrm{We}}_{\mathrm{new}}}\right)}^{-0.1709}{\left(\frac{h_{\mathrm{sc},\mathrm{old}}}{h_{\mathrm{sc},\mathrm{new}}}\right)}^{-0.0772}={\left(\frac{h_{\mathrm{sc},\mathrm{old}}}{h_{\mathrm{sc},\mathrm{new}}}\right)}^{-0.2987}{\left(\frac{{}_{\mathrm{old}}}{{}_{\mathrm{new}}}\right)}^{0.2987}{\left(\frac{h_{\mathrm{sc},\mathrm{old}}}{h_{\mathrm{sc},\mathrm{new}}}\right)}^{0.2987}{\left(\frac{h_{\mathrm{sc},\mathrm{old}}}{h_{\mathrm{sc},\mathrm{new}}}\right)}^{0.1709.Math.2}{\left(\frac{h_{\mathrm{sc},\mathrm{old}}}{h_{\mathrm{sc},\mathrm{new}}}\right)}^{-0.0772}& \left(5\right)\end{array}$
And hence the solution, how to control the plunger height h.sub.sc,new based on a current position h.sub.sc,old:

(39) $\begin{array}{cc}\left(\frac{h_{\mathrm{sc},\mathrm{new}}}{h_{\mathrm{sc},\mathrm{old}}}\right)={\left(\frac{{}_{\mathrm{new}}}{{}_{\mathrm{old}}}\right)}^{-1.1289}& \left(6\right)\end{array}$
Combining equations 3 and 6 one receives the solution, how to control the spray pressure:

(40) $\begin{array}{cc}\frac{P_{\mathrm{new}}}{P_{\mathrm{old}}}={\left(\frac{{}_{\mathrm{new}}}{{}_{\mathrm{old}}}\right)}^{0.9508}& \left(7\right)\end{array}$

(41) FIG. 7 is a flowchart of the differential pressure drop method that can be applied with the inline differential pressure drop measuring apparatus 38. A feed pump 50 is provided in the bypass line 32 downstream of dosing point 30. The feed pump 50 ensures a constant feed-flow-rate in the differential pressure drop measuring apparatus 38 to enable shear rates which cover the second Newtonian viscosity plateau. Downstream of the feed pump 50 a mass flow meter 52 is provided through which the product paste in the bypass line 32 is directed into a pressure drop meter 54. The shear viscosity () of the product paste in the bypass line 32 is calculated from the mass flow measured in the mass flow meter 52, the known product density of the product paste and the pressure drop measured in the pressure drop meter 54. This calculation is either made in a computer (not shown) of the differential pressure drop measuring apparatus 38 or, the respective data are delivered to the control device 48 and the shear viscosity is calculated in the computer of the control device 48. In order to consider the fact that the pressure drop is measured in a bypass line 32 the bypass mass flowrate is adjusted by the feed pump 50 until the shear-rate is above 1000 s.sup.1, so that the second Newtonian plateau viscosity can be measured by the pressure drop-meter 54 within laminar flow conditions.

(42) A pulsation damper is also preferably provided in the bypass to reduce the noise in the pressure determination.

(43) In the present example the dosing point 30 regulates the bypass flow rate to keep the bypass flow pressure <20 bar at laminar flow conditions, with a Reynolds number below 2300.

(44) FIG. 8 shows the principle of an inline differential pressure drop measuring apparatus (pressure drop meter) that can advantageously be provided upstream of the nozzle of the invention.

(45) The pressure drop meter 100 comprises a tube having a fluid inlet section 102 and a fluid outlet section 104 and three pressure drop measuring sections 106, 108, 110 provided between the inlet section 102 and the outlet section 104. The first pressure drop measuring section 106 which is close to the inlet section 102 has a first internal diameter d.sub.1 and a first axial length l.sub.1. A first differential pressure meter 112 measuring a first pressure drop p.sub.1 is connected to the first pressure drop measuring section 106 in a commonly known matter wherein the axial distance L.sub.1 between the two static pressure measuring openings in the wall of the first pressure drop measuring section 106 is substantially equal to the length l.sub.1 of the first pressure drop measuring section 106.

(46) The second pressure drop measuring section 108 is provided downstream of the first pressure drop measuring section 106. The internal diameter d.sub.2 of the second pressure drop measuring section 108 is smaller than the diameter d.sub.1 of the first pressure drop measuring section. The length l.sub.2 of the second pressure drop measuring section 108 is shorter than the length of the first pressure drop measuring section 106. The second pressure drop measuring section 108 comprises a second differential pressure meter 114 measuring a second pressure drop p.sub.2 wherein the distance L.sub.2 between the two static pressure measuring openings in the wall of the second pressure drop measuring section 108 is shorter than the distance L.sub.1 of the first differential pressure meter 112.

(47) A third pressure drop measuring section 110 is provided downstream of the second pressure drop measuring section 108 and the third pressure drop measuring section 110 opens into the outlet section 104. The internal diameter d.sub.3 of the third pressure drop measuring section 110 is smaller than the diameter d.sub.2 of the second pressure drop measuring section 108 and the length l.sub.3 of the third pressure drop measuring section is shorter than the length l.sub.2 of the second pressure drop measuring section. The third pressure drop measuring section 110 comprises in a commonly known manner a third differential pressure meter 116 measuring a third pressure drop p.sub.3. The distance L.sub.3 between the two static pressure measuring openings in the wall of the third pressure drop measuring section 110 is shorter than the distance L.sub.2 of the second differential pressure meter 114.

(48) The differential pressure drop meter 100 allows the measurement of three independent pressure drop recordings of the first, the second and the third differential pressure drop meters. Utilizing these three differential pressure drop probes in series, a single mass flow rate causes three increasing wall shear rates with the decreasing tube diameter.

(49) The following equation 8 is used to calculate the shear viscosity for laminar tube flows (Re<2300), applied to all 3 differential pressures p.sub.1, p.sub.2 and p.sub.3 (respectively measured at 112, 114 and 116, FIG. 8), by replacing p.sub.i and the corresponding tube dimensions (R.sub.i and L.sub.i) in equation 8:

(50) Only, if the shear viscosity .sub.i is equal (.sub.1=.sub.2=.sub.3) between the 3 differential pressures, the 2.sup.nd Newtonian shear viscosity is found and used e.g. in equation 1 and 7, etc.

(51) $\begin{array}{cc}{}_i=\frac{.Math.R_i^4.Math.p_i.Math.}{8.Math.\mathrm{Qm}.Math.L_i}& \left(8\right)\end{array}$
with following definitions of symbols:
R.sub.i: tube radius (R.sub.1, R.sub.2 and R.sub.3) in [m]
p.sub.i: tube pressure drop (p.sub.1, p.sub.2 and p.sub.3) in [Pa]
: product density in [kg/m3]
Qm: mass flow rate in [kg/s]
L.sub.i: tube length (distance L.sub.1, L.sub.2 and L.sub.3) in [m]

(52) TABLE-US-00001 TABLE 1 Abbreviations and formula Symbol, Abbreviation Description Units D.sub.32,global Global Sauter diameter as found [m] from PDA measurements of spray d.sub.sc Swirl chamber diameter [m] (smallest diameter of swirl chamber spiral) h.sub.sc Swirl chamber height [m] (axial height of swirl chamber) d.sub.or Orifice diameter [m] (diameter of opening made in orifice plate) b.sub.ch Width of swirl chamber inlet [m] channel (smallest width of inlet channel which leads into the swirl chamber) We Weber number $\mathrm{We}=\frac{{}_{\mathrm{liquid}}{u}_{\mathrm{bulk}}^2{d}_{\mathrm{orifice}}}{{}_{\mathrm{liquid}}}$ Eu Euler number 0$\mathrm{Eu}=\frac{P}{{}_{\mathrm{liquid}}{u}_{\mathrm{bulk}}^2}$ Re Reynolds number $\mathrm{Re}=\frac{{}_{\mathrm{liquid}}{u}_{\mathrm{bulk}}{h}_{\mathrm{sc}}}{}$ u.sub.bulk Bulk velocity at swirl chamber inlet $u_{\mathrm{bulk}}=\frac{\mathrm{Qm}}{{}_{\mathrm{liquid}}{h}_{\mathrm{sc}}{b}_{\mathrm{ch}}}$ [m/s] Qm Mass flow rate [kg/s] P Spray pressure [Pa] .sub.liquid Liquid density [kg/m.sup.3] .sub.liquid Liquid shear viscosity [Pa .Math. s] .sub.liquid Surface tension [N/m] PDA Phase-Doppler Anemometry