CN115791520A - Determination method of viscosity calculation model and powder apparent viscosity measurement system - Google Patents
Determination method of viscosity calculation model and powder apparent viscosity measurement system Download PDFInfo
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Abstract
The invention discloses a determination method of a viscosity calculation model and a powder apparent viscosity measurement system, wherein the system comprises the following steps: a storage bin; the gas source gas supply device is connected with the storage bin and is used for injecting gas into the storage bin so as to enable powder in the storage bin to be discharged from a storage bin outlet of the storage bin; the weighing module is positioned below the outlet of the storage bin and used for weighing the powder mass discharged from the storage bin; the pressure detection module is used for detecting the pressure in the storage bin; the processor is respectively electrically connected with the weighing module and the pressure detection module, and is used for determining the blanking mass flow rate according to the mass change of the powder and determining the apparent viscosity of the powder according to the blanking mass flow rate, the pressure and the viscosity calculation model; the viscosity calculation model represents the corresponding relation between the blanking mass flow rate, the pressure in the storage bin and the apparent viscosity. The invention can quickly and accurately measure the apparent viscosity of the powder, is suitable for measuring the apparent viscosity of various flowable powders and has simple operation.
Description
Technical Field
The invention relates to the technical field of powder viscosity measurement, in particular to a determination method of a viscosity calculation model and a powder apparent viscosity measurement system.
Background
At present, the measurement and characterization of apparent viscosity of powder mainly depend on the principle of a rotational viscometer, a shear characteristic curve of a sample is obtained by shearing a powder bed layer, and the mutual relation between shear stress and strain of the powder is analyzed, so that the apparent viscosity of the powder is obtained. However, the method is applicable to fluid, the method for measuring the powder has a lot of uncertainty, is influenced by instrument parameters and experimental operation, has a certain distance from perfection, has greatly different properties of the fluid and the powder, has more influencing factors during detection of the powder, needs to be professional in operation, and has no mature instrument for measuring the apparent viscosity of the powder.
Disclosure of Invention
The invention aims to overcome the defect of inaccurate measurement of the apparent viscosity of powder in the prior art, and provides a determination method of a viscosity calculation model and a powder apparent viscosity measurement system.
The invention solves the technical problems through the following technical scheme:
in a first aspect, a powder apparent viscosity measurement system is provided, which includes:
a storage bin;
the gas source air supply device is connected with the stock bin and used for injecting gas into the stock bin so as to enable powder in the stock bin to be discharged from a stock bin outlet of the stock bin;
the weighing module is positioned below the outlet of the stock bin and is used for weighing the powder mass discharged by the stock bin;
the pressure detection module is used for detecting the pressure in the storage bin;
the processor is respectively electrically connected with the weighing module and the pressure detection module, and is used for determining the blanking mass flow rate according to the mass change of the powder and determining the apparent viscosity of the powder according to the blanking mass flow rate, the pressure and viscosity calculation model; and the viscosity calculation model represents the corresponding relation between the blanking mass flow rate, the pressure in the stock bin and the apparent viscosity.
Optionally, the gas supply device comprises a pipeline, and a needle valve and a flow meter arranged on the pipeline;
one end of the pipeline is used for inputting external air supply equipment, and the other end of the pipeline is connected with the stock bin;
the flowmeter is used for measuring the gas flow in the pipeline;
the processor is also electrically connected with the needle valve and the flowmeter respectively, and is used for adjusting the opening of the needle valve according to the gas flow so that the gas flow injected into the storage bin by the gas supply device reaches a target flow.
Optionally, the gas source supply device comprises a cold dryer, the cold dryer is arranged on the pipeline, and the cold dryer is used for removing moisture and impurities in the gas.
Optionally, the gas source gas supply device further comprises a gas storage tank, the gas storage tank is arranged on the pipeline, and the gas storage tank is used for storing and buffering gas.
Optionally, the storage bin further comprises a pressure relief valve, the pressure relief valve is arranged at the top of the storage bin, and the pressure relief valve is electrically connected with the processor;
the processor is further used for opening the pressure relief valve when the pressure in the storage bin is larger than the upper limit value of the safety pressure range, so that the pressure in the storage bin is in the safety pressure range.
In a second aspect, a method for determining a viscosity calculation model is provided, including:
determining a corresponding relation between a feeding mass flow rate and a first pressure difference by using the powder apparent viscosity measurement system of the first aspect; the first pressure difference is the difference between the pressure in the storage bin and the atmospheric pressure;
according to the stress analysis of the powder in the storage bin, a force balance equation representing the powder infinitesimal is obtained;
correcting the Poiseup equation according to the force balance equation to obtain a corrected Poiseup equation suitable for describing the blanking process of the stock bin;
and constructing a viscosity calculation model according to the corresponding relation and the correction Poiseuille equation.
Optionally, fitting parameters in the corresponding relationship are obtained by performing nonlinear fitting on the data of the first pressure difference and the data of the blanking mass flow rate; and the data of the blanking mass flow rate is determined according to the mass of the powder and the blanking time.
Optionally, the modified poiseuille equation is obtained by analyzing the adhesion, gravity and second pressure difference of the powder microelements and the flow velocity of the powder microelements in the silo; the second pressure difference is the pressure difference between the lower surface and the upper surface of the powder micro element.
The positive progress effects of the invention are as follows: the invention can quickly and accurately measure the apparent viscosity of the powder, is suitable for measuring the apparent viscosity of various flowable powders and has simple operation.
Drawings
Fig. 1 is a schematic structural diagram of a powder apparent viscosity measurement system according to an exemplary embodiment of the present invention;
FIG. 2 is a schematic diagram of a infinitesimal force analysis involved in the derivation of a modified Poiseuille equation according to an exemplary embodiment of the present invention;
FIG. 3 is a flow chart of a method for determining a viscosity calculation model according to an exemplary embodiment of the present invention;
FIG. 4 is a graph illustrating the apparent viscosity measurement of a non-sticky powder provided by experiment one in an exemplary embodiment of the invention;
fig. 5 is a result of an experiment of blanking the viscous powder silo according to the second experiment in the first exemplary embodiment of the present invention;
FIG. 6 is a measurement result of apparent viscosity of viscous powder provided in experiment two in an exemplary embodiment of the invention;
fig. 7 is a graph showing the results of experiment one and experiment two compared with the viscosity measurement results of the conventional method in an exemplary embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples, which are not intended to limit the invention thereto.
Fig. 1 is a schematic diagram of a powder apparent viscosity measurement system according to an embodiment of the present invention, where the powder apparent viscosity measurement system includes an air supply device, a storage bin 17, a pressure detection module 18, a processor 19, and a weighing module 110; the gas source gas supply device is connected with the bin 17 through a pipeline 14 and used for injecting gas into the bin 17 so as to enable powder in the bin 17 to be discharged from a bin outlet of the bin 17, the weighing module 110 is located below the bin outlet of the bin 17 and used for weighing the powder mass discharged from the bin 17, the pressure detection module 18 is used for detecting the pressure in the bin 17, the processor 19 is electrically connected with the weighing module 110 and the pressure detection module 18 and used for determining the discharging mass flow rate according to the mass change of the powder and determining the apparent viscosity of the powder according to the discharging mass flow rate, the pressure and the viscosity calculation model, and the viscosity calculation model represents the discharging mass flow rate and the corresponding relation between the pressure in the bin 17 and the apparent viscosity.
In one embodiment, the silo 17 is composed of a conical hopper and a cylindrical silo, wherein the silo 17 can be a conical silo or a silo, and the preferred structure is the conical silo; the gas injected by the gas supply device can be compressed gas from a compressor or a steel cylinder, and is preferably inert gas such as nitrogen, carbon dioxide and the like.
In one embodiment, the gas supply device comprises a pipeline 14, and a needle valve 13 and a flow meter 15 which are arranged on the pipeline 14, one end of the pipeline 14 is used for inputting an external gas supply device, the other end of the pipeline 14 is connected with the bin 17, the flow meter 15 is used for measuring the gas flow in the pipeline 14, and the processor 19 is also electrically connected with the needle valve 13 and the flow meter 15 respectively and used for adjusting the opening degree of the needle valve 13 according to the gas flow in the pipeline 14 so that the gas flow injected into the bin 17 by the gas supply device reaches a target flow. Wherein, the target flow is set according to the actual situation. The target flow rate can maintain smooth powder blanking, the range of the target flow rate is preferably such that the lower limit of the gas speed in the storage bin exceeds the critical arch breaking gas speed, and the upper limit does not exceed the powder escape speed, wherein the escape speed is the minimum speed of the powder leaving the storage bin.
In the embodiment of the invention, the air pressure in the stock bin 17 can be kept constant under the condition of determined air flow, so that the powder is fed at a constant speed, and the measurement result of the apparent viscosity of the powder is more accurate.
In one embodiment, the gas supply device includes a freeze dryer 11, and the freeze dryer 11 is disposed on the pipeline 14 and is configured to remove moisture and impurities from the gas, so that the gas filled in the storage bin 17 is clean and does not affect the measurement of the apparent viscosity of the powder.
In one embodiment, the gas supply device comprises a gas storage tank 12, and the gas storage tank 12 is disposed on the pipeline 14 and is used for storing and buffering gas, so that the first pressure difference in the storage bin 17 is kept constant, the powder is discharged and flows under the condition of the constant first pressure difference, and the accuracy of the apparent viscosity measurement of the powder is improved.
In one embodiment, the storage bin comprises a pressure relief valve 16, the pressure relief valve 16 is arranged at the top of the storage bin 17 and electrically connected with the processor 19, and the processor 19 opens the pressure relief valve 16 when the pressure in the storage bin 17 is greater than the upper limit value of the safety pressure range (110% of the storage bin design pressure value), so that the pressure in the storage bin 17 is within the safety pressure range, the pressure in the storage bin 17 is prevented from being too large, and the safety operation in the storage bin 17 is ensured.
Wherein, the safe pressure scope sets up according to actual conditions by oneself.
The working principle of the powder apparent viscosity measurement system is further explained with reference to fig. 1:
after powder with a certain material level is added into a bin 17, gas is introduced into a gas source gas supply device from a ventilation position, the gas flows through a freeze drying machine 11 for drying and impurity removal and then enters a gas storage tank 12, then flows into the bin 17 through a pipeline 14, a flow meter 15 measures the gas flow in the pipeline 14 during the gas flow, the opening degree of a needle valve 13 is reduced when the gas flow reaches a target flow value, the gas flow entering the bin 17 is controlled to be the target flow value through the needle valve 13 and the flow meter 15, the powder is discharged and flows after the pressure in the bin 17 reaches a specified pressure, the powder is discharged from a bin outlet of the bin 17 and gathered in a weighing module 110, the mass of the discharged powder is weighed by the weighing module 110 and is conveyed to a processor 19, the processor 19 obtains the numerical values of the weighing module 110 and a pressure detection module 18, the discharge mass flow rate is calculated according to the change of the powder mass along with time, and the apparent viscosity of the powder is determined according to a discharge mass, pressure and viscosity calculation model.
In order to calculate the apparent viscosity of the powder, an embodiment of the present invention provides a method for determining a viscosity calculation model based on a powder apparent viscosity measurement system, and as shown in fig. 3, the method for determining the viscosity calculation model includes the following steps:
and 301, determining the corresponding relation between the feeding mass flow rate and the first pressure difference by using a powder apparent viscosity measurement system.
Wherein, the apparent viscosity measurement system of powder is the system that any one of the above-mentioned embodiments provided.
In one embodiment, fitting parameters in the corresponding relation are obtained by performing nonlinear fitting on the data of the first pressure difference and the data of the blanking mass flow rate, the fitting result can be more ideal by increasing the data amount of data fitting, and the data of the blanking mass flow rate is determined according to the powder mass and the blanking duration.
The specific steps for determining the correspondence are described below:
adding powder into a bin, filling gas into the bin to increase the pressure in the bin, opening a blanking valve at a specified pressure P, and blanking the powder to flow under a constant first pressure difference delta P, wherein the first pressure difference is the difference between the pressure in the bin and the atmospheric pressure; collecting the blanking mass M of the powder, calculating the blanking mass flow rate by recording the blanking duration, and determining that the corresponding relation between the blanking mass flow rate and the first pressure difference is as follows:
W＝αΔP β ，
wherein W is the blanking mass flow rate of the powder, the blanking mass of the powder in unit time is represented, and alpha and beta are fitting parameters;
and 302, carrying out stress analysis on the powder in the storage bin to obtain a force balance equation representing the powder infinitesimal.
The specific steps of step 302 are:
taking the bin shown in fig. 2 as an example, taking the powder infinitesimal to perform stress analysis, and obtaining an expression of the adhesive force of the powder infinitesimal as follows:
wherein pi is a circumferential ratio, r is an integral variable used in derivation, wherein the integral variable is any distance between a central point of the stock bin and the wall surface of the stock bin, eta is the apparent viscosity of fluid flowing in a laminar flow manner in the stock bin, l is the height of a powder bed layer in the stock bin, namely the height of powder accumulated in the stock bin, v is the powder infinitesimal flow velocity, f is the powder infinitesimal flow velocity r And f r+dr The powder microelements have the adhesive force at r and r + dr respectively.
Obtaining the resultant force acting on the powder infinitesimal according to an adhesion expression, wherein the expression of the resultant force is as follows:
wherein G is the gravity borne by the powder infinitesimal, and f is the resultant force borne by the powder infinitesimal;
in the stable feeding stage, the flow of the powder infinitesimal is regarded as an equilibrium state, namely the resultant force f borne by the powder infinitesimal is balanced with the second differential pressure acting on the powder infinitesimal, and the force balance equation is as follows:
wherein p is a The pressure, p, on the upper surface of the powder micro-element b The pressure applied to the lower surface of the powder micro element;
and 303, correcting the Poiseup equation according to the force balance equation to obtain a corrected Poiseup equation suitable for blanking of the bin.
In one embodiment, the modified Poiseuille equation is obtained by analyzing the powder infinitesimal stress and the flow field parameters in the silo.
The method comprises the following specific steps:
carrying out stress analysis on the powder infinitesimal to obtain the gravity borne by the powder infinitesimal under the compression action, wherein the gravity expression is as follows:
G＝-ρg2πrldr，
wherein rho is the bulk density, and g is the acceleration of gravity;
simplifying a force balance equation and a gravity expression to obtain an expression as follows:
and integrating the expression to obtain a mathematical relationship between the apparent viscosity and the second pressure difference, wherein the mathematical relationship expression is as follows:
wherein R is the upper limit of integral, namely the inner diameter of a silo of the silo, R 0 The lower integration limit, i.e., the bin outlet inner diameter. v. of R The flow velocity at the wall of the silo inner wall can be considered as zero.
The flow velocity at the center in the silo can be obtained through a continuity equation,
the expression is as follows:
due to the fact that
R 2 -r 0 2 ≈R 2 。p a -p b ＝ΔP。
By substituting the above equations into the integrated equation, a modified poisson equation can be obtained:
and step 304, substituting the corresponding relation between the blanking mass flow rate and the first pressure difference into a corrected Poiseuille equation to construct a viscosity calculation model.
Constructing a viscosity calculation model according to the corresponding relation between the blanking mass flow rate and the first pressure difference obtained in the step 301 and the corrected Poiseuille equation obtained in the step 303 as follows:
the viscosity calculation model is used for calculating the apparent viscosity of the powder infinitesimal substances, so that the apparent viscosity of the powder with a motion law different from that of solid, liquid and gas substances is accurately measured and calculated, measurement means of powder rheological parameters are enriched, and a new thought is provided for the measurement of the powder rheological parameters.
The effect of the powder apparent viscosity measurement system and the viscosity calculation model is further explained by combining experimental data as follows:
experiment one, selecting non-sticky glass microsphere powder GB with an average particle size of about 51 mu m, wherein the inner diameter of a cylindrical silo of a silo is 150mm, the diameter of an outlet of a conical silo is 10mm, and the half cone angle is 15 degrees.
Developing a stock bin blanking experiment, comprising the following specific steps:
powder is added into a stock bin, the height corresponding to a powder bed layer is 285mm, gas is introduced into the stock bin to ensure that the first pressure difference in the stock bin is in the range of 0-20kPa, the powder is discharged and flows under constant first pressure difference, the experimental results of the first pressure difference and the discharge mass flow rate are obtained, the obtained data are substituted into the corresponding relation to obtain the numerical values of fitting parameters alpha and beta, and then the alpha, beta, the physical parameters of the powder and the structural parameters of the stock bin are substituted into a viscosity calculation model to obtain the corresponding apparent viscosities of the powder under different discharge mass flow rates, which are shown in table 1.
TABLE 1
The shear rate (gamma) of the powder micro-element flow can be further converted by the powder micro-element flow velocity, and the conversion relation is as follows:
thus, the apparent viscosity of the powder was changed depending on the shear rate, and the result is shown in FIG. 4.
Experiment two, selecting a viscous powder alumina Al with the average grain diameter of about 5 mu m 2 O 3 Bulk density of 518kg/m 3 The structural parameters of the storage bin and the parameters such as the height of the powder bed layer are the same as those in the first experiment.
A bin blanking experiment is carried out as shown in experiment one, the relation between the first pressure difference and the mass blanking flow rate is obtained as shown in fig. 5, wherein fitting parameters alpha and beta are 0.656 and 2.03 respectively, and the apparent viscosity measurement result of the powder obtained through calculation of the viscosity calculation model is shown in fig. 6.
Comparing the apparent viscosity of the powder obtained in the first experiment and the second experiment with the measurement result of the FT4 powder Rheometer, the result is shown in FIG. 7, wherein Silo is data obtained by performing a bin blanking experiment, and the Rheometer is data obtained by the powder Rheometer.
The apparent viscosity calculation method taking the rheometer as a characterization means comprises the following steps:
where A is the device calibration coefficient, which can be obtained by calibrating a fluid of known viscosity. D is the diameter of the blade, N r Is the angular velocity of rotation of the blade, T isThe torque applied to the paddle can be obtained by measuring the parameters through a flow energy testing module of the powder rheometer. The shear rates of the blades were:
h is the depth of penetration of the blade, again obtained by rheometer measurements.
The results of the bin blanking experiment and the rheometer experiment for representing the apparent viscosity of the powder are similar, and the method provided by the embodiment of the invention can be considered to effectively represent the apparent viscosity of the powder. Compared with a rheometer, the method provided by the embodiment of the invention has the characteristics of simple operation, simple principle, simple instrument and the like, and provides better alternative equipment and method.
While specific embodiments of the invention have been described above, it will be appreciated by those skilled in the art that this is by way of example only, and that the scope of the invention is defined by the appended claims. Various changes and modifications to these embodiments may be made by those skilled in the art without departing from the spirit and scope of the invention, and these changes and modifications are within the scope of the invention.
Claims (8)
1. A powder apparent viscosity measurement system is characterized by comprising:
a storage bin;
the gas source air supply device is connected with the stock bin and used for injecting gas into the stock bin so as to enable powder in the stock bin to be discharged from a stock bin outlet of the stock bin;
the weighing module is positioned below the outlet of the storage bin and used for weighing the powder mass discharged from the storage bin;
the pressure detection module is used for detecting the pressure in the storage bin;
the processor is respectively electrically connected with the weighing module and the pressure detection module, and is used for determining the blanking mass flow rate according to the mass change of the powder and determining the apparent viscosity of the powder according to the blanking mass flow rate, the pressure and viscosity calculation model; wherein the viscosity calculation model represents the corresponding relation between the blanking mass flow rate, the pressure in the storage bin and the apparent viscosity.
2. The powder apparent viscosity measurement system of claim 1, wherein the gas supply device comprises a pipeline, and a needle valve and a flow meter arranged on the pipeline;
one end of the pipeline is used for inputting external air supply equipment, and the other end of the pipeline is connected with the storage bin;
the flowmeter is used for measuring the gas flow in the pipeline;
the processor is also electrically connected with the needle valve and the flowmeter respectively, and is used for adjusting the opening of the needle valve according to the gas flow so that the gas flow injected into the storage bin by the gas supply device reaches a target flow.
3. The powder apparent viscosity measurement system of claim 2, wherein the gas supply device comprises a freeze dryer, the freeze dryer is arranged on the pipeline, and the freeze dryer is used for removing moisture and impurities in the gas.
4. The powder apparent viscosity measurement system of claim 2 or 3, wherein the gas supply device further comprises a gas storage tank disposed on the pipeline, the gas storage tank being configured to store and buffer gas.
5. The powder apparent viscosity measurement system of claim 2 or 3, wherein the bin further comprises a pressure relief valve, the pressure relief valve is arranged at the top of the bin, and the pressure relief valve is electrically connected with the processor;
the processor is further used for opening the pressure relief valve when the pressure in the storage bin is larger than the upper limit value of the safety pressure range, so that the pressure in the storage bin is in the safety pressure range.
6. A method for determining a viscosity calculation model, comprising:
determining a corresponding relation between a feeding mass flow rate and a first pressure difference by using the powder apparent viscosity measurement system of any one of claims 1-5; the first pressure difference is the difference between the pressure in the storage bin and the atmospheric pressure;
according to the stress analysis of the powder in the storage bin, a force balance equation representing the powder infinitesimal is obtained;
correcting the Poiseup equation according to the force balance equation to obtain a corrected Poiseup equation suitable for describing the blanking process of the stock bin;
and constructing a viscosity calculation model according to the corresponding relation and the correction Poiseuille equation.
7. The method for determining a viscosity calculation model according to claim 6, wherein the fitting parameters in the correspondence are obtained by non-linear fitting of the data of the first pressure difference and the data of the blanking mass flow rate; and the data of the blanking mass flow rate is determined according to the mass of the powder and the blanking time.
8. The method for determining a viscosity calculation model according to claim 6, wherein the modified Poiseuille equation is obtained by analyzing the adhesion, gravity and a second pressure difference of the powder micro-elements and the flow velocity of the powder micro-elements in the silo; the second pressure difference is the pressure difference between the lower surface and the upper surface of the powder micro element.
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