DE102008010967A1 - Elongation flow generating method for use during e.g. extrusion, involves introducing medium into ring gap between outer wall of small cylinder and inner wall of large cylinder, and rotating cylinders with respective frequencies - Google Patents

Abstract

The method involves introducing a medium (4) into a ring gap between an outer wall of a small cylinder (1) and an inner wall of a large cylinder (2) that is arranged coaxial to the small cylinder. The cylinders are rotated around a common axis (3) with respective rotational frequencies and are connected with a control system (5), such that the frequencies are adjusted independent of each other. One frequency is reacted to another frequency as the square of an inner radius (R2) the large cylinder to the square of an outer radius (R1) of the small cylinder. An independent claim is also included for a device for executing a method for generating an elongation flow in a medium.

Description

The The present invention relates to a method and an apparatus for generating a pure expansion flow in liquids and the use of the method and / or the device for Carrying out rheological investigations on liquids under pure strain flow conditions.

Various devices are known from the prior art, with the aid of which a flow in liquids is generated in order to carry out rheological investigations, in particular the measurement of the viscosity. For example, show DE 34 90 625 T1 and US 3,803,903 Devices comprising an outer and an inner cylinder with an interposed, provided for receiving the medium to be examined annular gap. During the examination, at least one of the two cylinders is set in rotation and the torque required to maintain the flow generated in the medium, acting on the driven cylinder, is used to determine rheologically characteristic characteristics, such as the viscosity of the medium.

A similar device is from the DE 36 30 565 A1 become known, in which the outer cylinder is driven by a motor and, depending on the viscosity of the medium located in the annular gap between the two cylinders, the inner, freely rotatable cylinder in rotation. The rotational speed of the inner cylinder serves to determine the viscosity of the medium in the annular gap.

Alles These devices have in common that the currents generated in them have both a stretch and a rotation share. In numerous industrial processes - such as in fiber spinning, extrusion or injection molding - play however, pure strain currents often play a role or the currents are at least due to the expansion component dominated by the flow leading to a high degree of orientation and high voltages in complex fluids. So lead expansion flows in solutions high molecular weight linear polymers for extending the macromolecules, those with a flow-dominated flow associated with significantly increased viscosity.

The rheological properties determined with these known devices are therefore not very meaningful for such processes, because the influence of the rotation can not be easily compensated.

In addition to the classical rheometers individual devices are known from the prior art, with the help of targeted pure expansion flows are generated. That's how it describes DE 601 21 816 T2 a rheometer with intersecting inflow and outflow channels, in which an oscillating alternating current is generated. However, only in a stagnation point in the middle of the intersecting channels a pure strain flow is generated. Apart from this point, the flow is always superimposed on a rotation component.

From the US 5,357,784 a system is known in which the medium to be examined is passed through a channel with hyperbolic or semihyperbolic geometry and the expansion viscosity can be determined with the aid of the pressure difference occurring. However, this system is set to geometry-dependent strain rates, which can only be varied by changing the channel geometry.

Other systems, such as those from the FR 2 874 089 Although known devices are intended for the measurement of the extensional viscosity of polymer melts and elastomers, for measurements on liquids, however, completely unsuitable.

object In contrast, the present invention is a method and a device for generating a pure expansion flow and their use for determining the rheological properties a liquid.

Especially The invention aims at not only - such as known from the prior art - punctual, but spatially extended, pure expansion flow to generate, with the strain rates set freely and in time can be constant or variable.

This task is done by means of a Taylor Couette system, similar to that from the writings DE 34 90 625 T1 and US 3,803,903 known systems, solved. In contrast to the known from the prior art systems according to the invention, however, both cylinders are set in rotation about the common axis, with their rotational frequencies are coordinated so that in the annular gap between Both mediums located medium setting a rotation-free, homogeneous expansion flow.

By the measurement of the torque needed to control the flow To maintain the tension in the liquid and thus determine their viscosity.

in the The following is the invention with reference to an embodiment and the accompanying drawing explained in more detail become.

1 shows a Taylor Couette system with a first cylinder 1 and a second, hollow cylinder 2 both coaxial with the common axis 3 are aligned. In the annular gap between the two cylinders is the medium to be examined 4 in which an expansion flow is to be generated by means of the illustrated apparatus.

The first cylinder 1 has a drive shaft 11 , in turn, via a drive system with a gearbox 12 and a motor 13 is set in rotation. The second cylinder 2 is also powered by its drive shaft 21 from a drive system with a transmission 22 and a motor 23 set in rotation.

Both engines 13 and 23 are there with a common tax system 5 connected, the rotational speeds of the motors and thus the rotational frequencies Ω ₁ and Ω _{2 of} the two cylinders 1 and 2 controls.

In this case, to achieve a rotation-free flow in the liquid 4 the rotational frequencies Ω ₁ and Ω _{2 are} matched to one another such that the rotational frequency Ω _{1 of} the first cylinder 1 to the rotational frequency Ω _{2 of} the second cylinder 2 behaves like the reciprocal of the square of its radii R ₁ and R ₂ . This relationship can be expressed in the following formula:

Evidence that the fulfillment of this condition for the formation of a strain-free flow in the medium 4 can be performed via Navier-Stokes equations for the velocity profile ν → between the cylinders of a Taylor-Couette cell.

In cylindrical coordinates (r, φ, z), the equation for the velocity profile ν → is as follows:

There exists only for the φ-direction a non-zero component. The velocity components in the direction of the axis of rotation 3 and in the direction of the radius r are constantly zero.

For the rotation of the flow in cylindrical coordinates, the following expression applies in the considered system:

As a result, the rotation rate of the flow is expressed by Ω. The velocity component of the flow can thus be decomposed into a rotation component and a strain component and the following applies:

• 1. Fall: Ω₁ = Ω₂ = Ω₀ ⇒ s = 0, Ω = Ω₀ Die Flüssigkeit rotiert in diesem Fall als „starrer Körper” mit der Drehfrequenz der Zylinder. Dabei besitzt die Strömung keinen Dehnungsanteil.
• 2. Fall:
  
  ⇒ Ω = 0 ⇒ rot(ν →) = 0 Die Strömung ist also in diesem der Erfindung zugrunde liegenden Fall rotationsfrei. Somit handelt es sich dabei um eine reine Dehnungsströmung.

There are two limiting cases for the movement of the liquid between the cylinders:

• 1st case: Ω ₁ = Ω ₂ = Ω ₀ ⇒ s = 0, Ω = Ω ₀ The liquid in this case rotates as a "rigid body" with the rotational frequency of the cylinders. The flow has no expansion component.
• 2nd case:
  
  ⇒ Ω = 0 ⇒ red (ν →) = 0 The flow is thus rotation-free in this case on which the invention is based. Thus, it is a pure expansion flow.

The gradient tensor of velocity in cylindrical coordinates is:

For the strain rate ε. (R) of the flow, the following applies as a function of the radius r:

The Strain rate of this flow is still of the radius r dependent, the maximum deviation from the mean of the strain rates over However, the annular gap can be about the ratio the cylinder radii are optimized.

The mean strain rate applies here

If the cylinder radii are selected, for example, with R ₁ = 19 mm and R ₂ = 20 mm, the following relationship results for the deviations from the mean value:

The Deviation is therefore a maximum of 5.3%.

For the generation of an expansion flow according to the invention Procedures are the two rotation frequencies for one predetermined mean strain rate according to equations (1) and (2) certainly.

In the embodiment shown in the figure, this is done automatically by the control device 5 into which only the strain rate is entered. Alternatively, however, it would also be conceivable for a rotational frequency to be set on the control device, and this then determines only the second rotational frequency by means of equation (1).

In any case, the control device gives 5 then a signal to the motors 13 and 23 so the two cylinders 1 and 2 with the corresponding rotational frequencies Ω ₁ and Ω _{2 are set} in rotation.

It it is obvious that the strain rate depends on the desired test conditions either constant or can be chosen as a function of time. For the latter case involves temporally periodic functions (sine function, Sawtooth function, ...), but also non-periodic functions in question.

In an advantageous embodiment, the control device is in this case 5 then configured such that the strain rate can be entered or programmed as a function of time in the control device.

In a further advantageous embodiment, the control device constantly collects information about the power consumption of the motors 13 and 23 , In this way it is possible to calculate by means of the torque constant of the drives the retroactive torque of the liquid on the lateral surface of the cylinder.

wobei τ_θr(R₁) die am ersten Zylinder wirkende Spannung und l die Höhe der Zylinder wirkenden Flüssigkeitssäule im System ist.For the torque M ₁ acting on the first cylinder, the following relationship applies:

where τ _θr (R ₁ ) is the voltage acting on the first cylinder and l is the height of the cylinder acting liquid _column in the system.

lässt sich also über das Drehmoment, die Geometrie der Vorrichtung und die Dehnungsrate unmittelbar die Dehnungsviskosität η_θ ermitteln.From this and the relationship for the strain viscosity η _θ

can therefore be on the torque, the geometry of the device and the strain rate directly determine the strain viscosity η _θ .

In a preferred embodiment of the device shown in the figure, this is done in one in the control device 5 intended evaluation unit 6 ,

Since the ratio of the rotational frequencies Ω ₁ and Ω _2, which is necessary for generating the pure expansion flow, depends solely on the ratio of the radii of the cylinders, it is also possible, in deviation from the embodiment of the device shown in the drawing, to use both a cylinder and a transmission To drive an engine comprehensive drive system. In this case, the ratio of the rotational frequencies is set by the mechanical configuration of the then necessary two outputs of the transmission, so that the variable speed of the engine is converted into only two mutually fixed output speeds.

QUOTES INCLUDE IN THE DESCRIPTION

This list The documents listed by the applicant have been automated generated and is solely for better information recorded by the reader. The list is not part of the German Patent or utility model application. The DPMA takes over no liability for any errors or omissions.

Cited patent literature

• - DE 3490625 T1 [0002, 0011]
• - US 3803903 [0002, 0011]
• - DE 3630565 A1 [0003]
• - DE 60121816 T2 [0006]
• US 5357784 [0007]
• FR 2874089 [0008]

Claims (12)

Method for generating an expansion flow of a fluid ( 4 ) at a predetermined rate of expansion at which the fluid ( 4 ) in the annular gap between the outer wall of a first, smaller cylinder ( 1 ) and the inner wall of a first cylinder ( 1 ) coaxial, second, larger cylinder ( 2 ), the first cylinder ( 1 ) with a first rotational frequency (Ω ₁ ) about the common axis ( 3 ) is rotated, the second cylinder ( 2 ) with a second rotational frequency (Ω ₂ ) about the common axis ( 3 ) is rotated, and the first rotational frequency (Ω ₁ ) to the second rotational frequency (Ω ₂ ) behaves as the square of the inner radius (R ₂ ) of the second cylinder ( 2 ) to the square of the outer radius (R ₁ ) of the first cylinder ( 1 ). Method according to Claim 1, in which the rotational frequencies are kept constant in time (Ω ₁ , Ω ₂ ). The method of claim 1, wherein the rotational frequencies (Ω ₁ , Ω ₂ ) are a function of time. Method according to Claim 3, in which the rotational frequencies (Ω ₁ , Q ₂ ) follow a time-periodic function. Device for generating an expansion flow, in particular for carrying out the method according to one of the preceding claims, comprising a first cylinder ( 1 ) with an outer radius (R ₁ ), a second, to the first cylinder ( 1 ) coaxially about a common axis ( 3 ) arranged hollow cylinder ( 2 ) with one compared to the outer radius (R ₁ ) of the first cylinder ( 1 ) larger inner radius (R ₂ ), both cylinders ( 1 . 2 ) for rotation about the common axis ( 3 ) and with a drive system ( 12 . 13 . 22 . 23 ) and an associated tax system ( 5 ) are connected such that the rotational frequencies (Ω ₁ , Ω ₂ ) of the two cylinders ( 1 . 2 ) are adjustable depending on each other. Device according to Claim 5, in which the drive system ( 12 . 13 . 22 . 23 ) consists of two engine-gearbox combinations each driving a cylinder, which are controlled by the control system ( 5 ). Device according to Claim 5, in which the drive system ( 12 . 13 . 22 . 23 ) consists of a common engine-gearbox combination driving both cylinders, which is controlled by the control system ( 5 ) is driven. Device according to one of Claims 5 to 7, in which the control system ( 5 ) is designed such that, from an input strain rate or an entered time profile of the strain rate, the rotational frequencies (Ω ₁ , Ω ₂ ) of the two cylinders ( 1 . 2 ) and a corresponding control signal to the drive system ( 12 . 13 . 22 . 23 ) passes on. Device according to one of Claims 5 to 8, in which the control system ( 5 ) is designed such that it is suitable for at least one of the two cylinders ( 1 . 2 ) that detects this retroactive torque or a characteristic physical quantity. Apparatus according to claim 9, wherein in the control system ( 5 ) additionally an evaluation unit ( 6 ) and is designed such that, with the aid of the torque or a physical variable characteristic of it, the viscosity of the medium ( 4 ). Use of the method according to one of the claims 1 to 4 and / or the device according to one of the claims 5 to 10 for determining a rheological parameter a medium. Use of the method according to one of the claims 1 to 4 and / or the device according to one of the claims 5 to 10 for determining the viscosity of a medium.