RU2789667C1 - Inertia method for measuring the viscosity of non-newtonian fluids - Google Patents

Abstract

FIELD: measuring technology.

SUBSTANCE: invention relates to measuring technology and can be used to measure the coefficient of kinematic viscosity at different shear rates, temperature and pressure for non-Newtonian fluids that have the ability to reflect coherent radiation. The inertial method for measuring the viscosity of non-Newtonian fluids includes a smooth acceleration and a sharp stop of a closed transparent torus rotating around its axis, filled with a test liquid with light-reflecting properties, and determining the kinematic parameters of the inertial flow, namely, the shear strain rate on the flow surface and the volumetric flow rate, according to which from the simplified the Navier-Stokes equations numerically determine the kinematic viscosity of the fluid, while the kinematic characteristics are measured indirectly using a pre-trained convolutional neural network, which receives images of the fluid flow illuminated by coherent radiation at fixed times, obtained using a high-speed CMOS camera.

EFFECT: improving the accuracy of measuring the viscosity of non-Newtonian fluids.

1 cl, 1 dwg, 1 tbl

Description

The invention relates to measuring technology and can be used to measure the coefficient of kinematic viscosity at different shear rates, temperature and pressure for non-Newtonian fluids that have the ability to reflect coherent radiation.

There are known methods for measuring the coefficient of dynamic viscosity (hereinafter referred to as viscosity) of media, including determining the moment of friction force on the surface of a cylinder (cone, disk) immersed in the test medium at various shear strain rates, implemented in rotational viscometers. (Middleman S. The flow of polymers. Translated from English by Yu.N. Panov, edited by A.Ya. Malkin. - M .: Mir, 1971. - 360 p., Schramm G. Fundamentals of practical rheology and rheometry. Per. from English by I. A. Lavygina, Moscow: Kolos, 2003, 312 p.).

A known method includes pumping the test medium through a channel of known size and determining the stress and shear strain rate on the channel wall, implemented in capillary viscometers (SU patent No. 1716388, IPC G01N 11/04, publ. 1992).

A common disadvantage of these methods is the impossibility of creating conditions for the uniformity of fields of mechanical quantities on the surface of the spindle (for rotational viscometers) and in the volume of the channel (for capillary viscometers), which leads to an error in the calculation of shear stresses, shear strain rates and, as a consequence, viscosity.

The closest in terms of the physical conditions of the flow of the test medium and the technical implementation of the viscometer used is the method, which includes pumping the test medium through the channel of the torus mold under the action of time-varying forces of inertia and friction of the medium resulting from a sharp stop of the torus rotating around its axis, and determining the motion parameters medium, namely, shear stress and shear strain rate on the channel surface (patent RU No. 2589753, IPC G0lN l1/04, publ. 2016).

The disadvantages of this method are the assumption about the velocity profile in the channel, which introduces an additional error in the calculation of the shear strain rate, as well as the dimensions of the viscometer, and, as a result, the need for a large volume of the test liquid (300 ml).

The technical problem is to improve the accuracy of measuring viscosity as a function of shear strain rates, pressure and temperature for non-Newtonian fluids that have the ability to reflect coherent radiation, with a minimum number of measured parameters.

The technical problem is achieved by the fact that the inertial method for measuring the viscosity of non-Newtonian fluids includes a smooth acceleration and a sharp stop of a closed transparent torus rotating around its axis, filled with a test liquid with light-reflecting properties, and determining the kinematic parameters of the inertial flow, namely, the shear strain rate on the flow surface and volumetric flow rate, which are used to numerically determine the kinematic viscosity of the liquid from the simplified Navier-Stokes equation, while the kinematic characteristics are measured indirectly using a pre-trained convolutional neural network ResNetl8, to the input of which images of the fluid flow illuminated by coherent radiation are fed at fixed points in time, obtained using a high-speed CMOS camera, the values of the shear strain rate and volume flow are calculated in the output layer of the neural network.

The technical result consists in increasing the accuracy of measuring the viscosity of non-Newtonian fluids, depending on pressure, shear strain rates and temperature with a minimum number of measured parameters, which makes it possible to abandon the hypothesis of the velocity profile in the channel and the approximate calculation of the shear strain rate, as well as to abandon the measurement of torque . Instead, the shear strain rate is determined using a convolutional neural network pretrained on a labeled training set, which is a set of images of the flow in a thin transparent tube at each moment of time and analytically calculated values of the shear strain rate and volume flow.

To achieve a technical result, the following must be done.

The torus is smoothly accelerated and abruptly stopped, characterized by the radius of the generatrix of the circle r and the distance R from the center of the axis of symmetry of the torus to the center of the generatrix of the circle. A viscous medium is pumped into the torus under pressure p ₀ . The subject of investigation is the inertial motion of the fluid resulting from the abrupt stop of the torus. It is assumed that before the initial moment of time (the moment the torus stops), the circumferential velocity of all particles of the medium is V ₀ , after the torus stops, the medium continues to move under the action of inertia and friction forces. It is also assumed that in the time interval under study, the action of the gravitational force is insignificant, and the movement of the liquid occurs along stationary streamlines formed by a multitude of coaxial circles.

во-вторых, упростится форма записи граничных условий. А уравнение неразрывности примет тривиальный вид: ∂υ₂/∂β₂=0. Из последнего следует, что υ₂ не зависит от координаты β₂, т.е. υ₂=υ(β₁, β₃).The basic equations that describe this process are the Navier-Stokes, continuity and convective thermal conductivity equations (Loitsyansky, L.G. Mechanics of liquid and gas. M .: Drofa, 2003. - 870 p.). It is more convenient to write these equations in a toroidal coordinate system with Lame coefficients (G. Korn, T. Korn. Handbook of mathematics for scientists and engineers: Definitions. Theorems. Formulas. Per. I. G. Aramanovich. - 6. ed., Sr. - St. Petersburg: Lan, 2003. - 831 p.): H ₁ =1, H ₂ =β ₁ cos β ₃ +R, H ₃ =β ₁ . The transition to a curvilinear coordinate system allows us to significantly simplify the model, firstly, the velocity field will have one non-zero component

secondly, the form of writing the boundary conditions will be simplified. And the continuity equation will take a trivial form: ∂υ ₂ /∂β ₂ =0. It follows from the latter that υ ₂ does not depend on the coordinate β ₂ , i.e. υ ₂ \u003d υ (β ₁ , β ₃ ).

Since the medium is pumped into the torus under some constant pressure p ₀ , then, due to the symmetry of the flow region, the pressure is a function of two coordinates p(β ₁ , β ₃ ).

To determine the conditions for the homogeneity of pressure and temperature fields, the equations of the mathematical model are presented in a dimensionless form. The dimensionless quantities were chosen so that the dimensionless coordinates and functions varied in the range [0,1]. The method of non-dimensionalization is presented in the table.

The basic equations (Navier-Stokes and heat balance), describing the process under study in a dimensionless form in curvilinear coordinates β _i , taking into account the assumptions adopted in the formulation of the problem, will take the form:

- аналог критерия Эйлера (далее критерий Эйлера);Where

- an analogue of the Euler criterion (hereinafter, the Euler criterion);

- критерий Струхаля;

- Strouhal's criterion;

- критерий Рейнольдса;

- Reynolds criterion;

- критерий Прандтля;

- Prandtl criterion;

- критерий Эккерта;

- Eckert criterion;

- безразмерные геометрические критерий;

- dimensionless geometric criteria;

V0=ωR - characteristic velocity (maximum) of fluid flow;

t ₀ - the time of the inertial flow of the liquid to stop;

ΔT - change in liquid temperature;

η ₀ - characteristic kinematic viscosity of the investigated liquid;

ρ is the density of the investigated liquid.

According to the first and third equations of system (1), one can determine the condition of the pressure field homogeneity. The right sides of these equations are negligible compared to the pressure gradient components on the left side of the equations, provided:

с геометрическим параметром γ. Значение геометрического параметра определено размером конструкции устройства и имеет порядок γ~10¹. Из условия (2) можно определить условия для окружной скорости течения V₀ при фиксированных значениях геометрического параметра, характерного давления и плотности жидкости.Condition (2) determines the ratio of the analogue of the Euler criterion

with geometric parameter γ. The value of the geometric parameter is determined by the size of the device structure and has the order of γ~10 ¹ . From condition (2), it is possible to determine the conditions for the circumferential flow velocity V ₀ at fixed values of the geometric parameter, characteristic pressure, and fluid density.

The first term on the right side of the fourth equation of system (1) is responsible for the heat transfer from layer to layer of liquid. The order of this term depends on the Prandtl criterion Pr and the dimensionless geometric parameter γ. The second term on the right side of the fourth equation of system (1) characterizes the heat transfer due to forced convection. The order of this term depends on the Eckert criterion Ec. The order of magnitude of the left side of the fourth equation depends on the Strouhal criterion Sh and Reynolds Re. Thus, it is possible to achieve homogeneity of the temperature field in the channel by imposing the following condition on these criteria:

Expression (3) determines the conditions under which the terms on the right side of the fourth equation (1) are negligible compared to the left side of the equation. The order of the Reynolds number is determined from condition (3) for a fixed value of the torus radius r and characteristic viscosity η ₀ . The Prandtl criterion Pr is determined by the properties of the medium. The Eckert number Ec depends on the characteristic velocity, determined by condition (3), as well as on the value of ΔТ, therefore, when estimating its order, the condition of an insignificant temperature difference was taken into account [10 ^-1 ; ¹⁰⁰ ]. Condition (3) determines the order of magnitude of the characteristic time t ₀ of the inertial motion of the fluid in the channel under consideration.

Thus, it is possible to determine the conditions for the homogeneity of pressure and temperature fields from conditions (2), (3). It is possible to determine the values of the circumferential velocity of the torus V ₀ before stopping according to condition (2) and the time of fluid flow after stopping the torus according to condition (3), during which it is necessary to carry out measurements. In this case, the remaining parameters are fixed in advance.

Analyzing the terms of the second equation of system (1), taking into account the fulfillment of conditions (2), (3), we obtain a simplified equation, which for further calculations is more convenient to write in a dimensional form:

where υ=υ(β ₁ ) axial velocity component;

η is the coefficient of kinematic viscosity of the investigated liquid.

Equation (4) can be used to determine the kinematic viscosity for a given velocity field. To do this, it can be integrated over the channel thickness, taking into account the boundary condition

можно получить следующее выражение:After some transformations on the left side of the equation, replacing

you can get the following expression:

- значение скорости сдвига на поверхности течения; η_r - значение кинематической вязкой на поверхности течения (далее η), зависит от ξ_r; Q - объемный расход жидкости через сечение.Where

- the value of the shear rate on the surface of the flow; η _r - the value of the kinematic viscosity on the flow surface (hereinafter η), depends on ξ _r ; Q is the volumetric flow rate of liquid through the section.

The derivative on the left side of the equation can be replaced by a central finite difference. Then the kinematic viscosity can be determined in terms of the shear strain rate and the change in flow rate at each time t ^k :

where ξ ^k - values of the shear rate on the surface of the flow at each time t ^k ;

Q ^k+1 , Q ^k-1 - the value of the flow rate at the previous and next time step;

Δt=t ^k+1 -t ^k - time step, constant.

и значения расхода Q^k в каждый момент времени t^k определяется с помощью программы расчета, в основу которой заложена предварительно обученная сверточная нейронная сеть. Изображения течения жидкости, полученные через равные промежутки времени Δt, подаются на вход нейронной сети, сверточные слои которой преобразуют эти изображения и передают на слои аппроксиматора, выходной слой сети содержит два нейрона (для скорости сдвиговой деформации и объемного расхода). Таким образом, за время измерений t₀ (время инерционного течения в торе) определяется массив значений скорости сдвига и объемного расхода, по которым с помощью итерационной формулы (5), полученной из уравнения Навье-Стокса, рассчитываются соответствующие значения кинематической вязкости.Surface shear rates

and the flow rate Q ^k at each time t ^k is determined using the calculation program, which is based on a pre-trained convolutional neural network. Fluid flow images obtained at equal time intervals Δt are fed to the input of a neural network, the convolutional layers of which transform these images and transmit them to the approximator layers, the output layer of the network contains two neurons (for shear strain rate and volume flow). Thus, during the measurement time t ₀ (the time of the inertial flow in the torus), an array of values of the shear rate and volume flow is determined, from which, using the iterative formula (5) obtained from the Navier-Stokes equation, the corresponding values of the kinematic viscosity are calculated.

To implement the method, a device was used, containing a support 1, on which a stand 2, a brake mechanism 3 and a stepper motor 4 are installed. A disk 5 is mounted on the stepper motor 4. A torus 6 is fixed on the disk 5. A CMOS camera 7 and a source 8 are fixed on the stand 2 coherent radiation. The stepper motor 4, the brake mechanism 3, the source 8 of coherent radiation and the CMOS camera 7 are connected to the information processing unit 9. The information processing unit 9 is connected to the information display unit 10 .

The method is carried out as follows.

и объемного расхода Qfe4epe3 равные промежутки времени Δt. Затем по полученным значениям кинематических характеристик с помощью итерационной формулы, полученной из уравнения Навье-Стокса, вычисляют значения кинематической вязкости испытуемой жидкости для каждого значения скорости сдвиговой деформации. Полученные данные передают на блок 10 отображения информации.In the torus 6, mounted on the disk 5, under pressure p ₀ , the test liquid with light-reflecting properties is pumped. The stepper motor 4 is turned on. The disk 5 with the torus 6 mounted on it is smoothly accelerated to peripheral speed V ₀ , then the stepper motor 4 is turned off and the brake mechanism 3 is turned on, while the disk 5 with the torus 6 stops abruptly. After the torus 6 stops, the liquid makes an inertial motion. During the time of inertial motion, with the help of a vision system, which includes a CMOS camera 7 and a source 8 of coherent radiation, images of the fluid flow at point A are captured. CUDA cores, where it is processed indirectly using a pretrained convolutional neural network, and based on the results of the processing, the kinematic characteristics of the fluid are calculated: the shear strain rate on the flow surface

and volume flow Qfe4epe3 equal time intervals Δt. Then, according to the obtained values of the kinematic characteristics, using the iterative formula obtained from the Navier-Stokes equation, the values of the kinematic viscosity of the test fluid are calculated for each value of the shear strain rate. The received data is transmitted to the information display unit 10 .

The proposed method for measuring viscosity makes it possible to investigate the viscosity of media with complex rheological properties that simultaneously depend on shear strain rates, pressure and temperature in a wide range of the above parameters, and, unlike the prototype, has a higher accuracy in determining the shear strain rate due to the use of ultra-precise neural networks, which improves the accuracy of the calculation of the viscosity itself.

Claims (1)

An inertial method for measuring the viscosity of non-Newtonian fluids, which includes a smooth acceleration and a sharp stop of a closed transparent torus rotating around its axis, filled with a test fluid with light-reflecting properties, and determining the kinematic parameters of the inertial flow, namely, the shear strain rate on the flow surface and volume flow, by which the simplified Navier-Stokes equation, the kinematic viscosity of the liquid is numerically determined, while the kinematic characteristics are measured indirectly using a pre-trained convolutional neural network, the input of which is images of the fluid flow illuminated by coherent radiation at fixed times, obtained using a high-speed CMOS camera .

Images