Device and method for measuring permeability and inertial coefficient of porous medium under vacuum condition

Abstract

The application discloses a measuring device and method for permeability coefficient and inertial coefficient of porous medium under vacuum state. The measuring device comprises a clamping mechanism and a vacuum generator. The clamping mechanism has a cavity for accommodating the porous medium, and the cavity has an inlet and an outlet at two ends. Air enters the inlet of the cavity through a throttle valve and a flow meter in sequence. The vacuum generator is connected with the outlet of the cavity and connected with an air source through a pressure reducing valve. A first pressure gauge is arranged at the inlet of the cavity for measuring the pressure upstream of the porous medium, and a second pressure gauge is arranged at the outlet of the cavity for measuring the pressure downstream of the porous medium. The application can obtain the permeability coefficient and the inertial coefficient of the flow characteristics of the porous medium under vacuum state.

Description

Technical Field

[0001] This invention relates to the detection of flow characteristic parameters of porous media, specifically to a device and method for measuring the permeability coefficient and inertia coefficient of porous media under vacuum conditions. Background Technology

[0002] Porous media (such as porous copper alloys and porous foamed metals) contain numerous micropores and possess advantages such as uniform adsorption, environmental friendliness, energy efficiency, and reusability. They are often used as flow-throttling elements in vacuum forming. During vacuum adsorption, the gas flow rate drawn into the porous media controls the stretching speed of the formed part, which directly affects the uniformity of the part's wall thickness. Therefore, understanding the flow characteristics of porous media under vacuum conditions is crucial.

[0003] Gas flow within porous media is typically described by the Darcy-Forchheimer law, in which permeability and inertia are two important characteristic parameters. CN212121706U discloses a device for measuring the permeability of porous media, and CN106932327A discloses a device and system for testing the permeability of porous media. Both only involve the measurement of the permeability coefficient of porous media, not the inertia coefficient, and the measurement pressure environment is positive pressure. However, both positive pressure and vacuum will produce pressure drops that cause gas flow. But during gas flow, positive pressure increases the pressure, while vacuum decreases the pressure. This causes different changes in the physical properties of the gas itself, such as density, during flow, thus affecting the determination of flow characteristic parameters. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide an apparatus and method for measuring the permeability coefficient and inertia coefficient of porous media under vacuum conditions.

[0005] Technical solution: The first aspect of the present invention provides a device for measuring the permeability coefficient and inertia coefficient of porous media under vacuum conditions, including a clamping mechanism and a vacuum generator. The clamping mechanism has a cavity for accommodating the porous media, with an inlet and an outlet at the two ends of the cavity, respectively. Air enters the cavity inlet after passing through a throttle valve and a flow meter in sequence. The vacuum generator is connected to the cavity outlet and is connected to a gas source through a pressure reducing valve. A first pressure gauge for measuring the upstream pressure of the porous media is provided at the cavity inlet, and a second pressure gauge for measuring the downstream pressure of the porous media is provided at the cavity outlet.

[0006] Furthermore, a silencer is installed on the vacuum generator.

[0007] Furthermore, the aforementioned measuring device also includes a container filled with copper wire and a vessel containing heat transfer oil, with the container immersed in the heat transfer oil; the vessel is equipped with a heating device for heating the heat transfer oil and a thermometer for measuring the temperature of the heat transfer oil; air enters the cavity inlet after passing through a throttle valve, a flow meter, and the container in sequence; the thermometer and the heating device are interlocked.

[0008] Furthermore, the heating device uses an electric heating wire.

[0009] A second aspect of the present invention provides a method for measuring the permeability and inertia coefficient of a porous medium under vacuum conditions, employing the aforementioned measuring device; the measuring method includes:

[0010] (1) Turn on the air source to make the vacuum generator generate negative pressure, and the air flows from the upstream to the downstream of the porous medium; adjust the pressure reducing valve to change the downstream pressure; within the pressure difference range of 0 to 100 kPa, record the upstream pressure P1 and the downstream pressure P2 every 5 kPa, and record the corresponding flow rate at the same time.

[0011] (2) Using the pressure difference data in the range of 20 to 100 kPa between the upstream and downstream pressure difference in step (1), calculate the average pressure P3 as the internal pressure of the porous medium (10);

[0012]

[0013] The density ρ inside the porous medium at different pressure differences is calculated according to equation (2):

[0014]

[0015] Where ρ0 is the air density under standard conditions, T0 is the air temperature under standard conditions, P0 is the air pressure under standard conditions, and T is the temperature at the time of measurement;

[0016] The flow velocity v inside the porous medium at different pressure differences is calculated according to equation (3):

[0017]

[0018] Among them G m Let A be the mass flow rate through the porous medium, and A be the cross-sectional area of ​​the porous medium. Porosity of porous media;

[0019] Calculate ρv at different pressure differences 2 The values ​​are then fitted to obtain the inflection point in the fitted curve. The range is expanded by ±10 kPa based on the pressure difference corresponding to the inflection point. This range is taken as the pressure difference range corresponding to the value of the inertia coefficient, denoted as P'.

[0020] (3) Take the flow data of different pressure differences in P' in step (2) and solve K′ and β′ using the Gauss-Newton least squares method according to formula (4). When the sum of squared residuals is the smallest, the solution is recorded as K′0 and β′0.

[0021]

[0022] Where μ is the air viscosity, K′ and β′ are fitting parameters, R is the gas constant, and L is the length of the porous medium;

[0023] (4) Expand the range of values ​​for β′0;

[0024] Based on the actual situation, two amplification parameters α1 and α2, both greater than 0, are introduced, with α1 being less than α2. The expanded range is α1·β′0~α2·β′0. Then, from the expanded range, selections are made every (α1·β′0~α2·β′0) / 10.

[0025] denoted as β1, β2, β3, ..., β 10 The obtained β1, β2, β3, ..., β 10 Then, using equation (4) to solve for K′ using the Gauss-Newton least squares method, we obtain K1, K2, K3, ..., K 10 ;

[0026] (5) Put K1, β1, K2, β2, K3, β3,…,K 10 β 10

[0027] Substituting these values ​​into equation (4) respectively, we can calculate the root mean square error between the theoretical flow rate and the measured actual flow rate under different pressure differences. The root mean square formula is as follows:

[0028]

[0029] Among them G 理论 The theoretical flow rate is calculated; at K1, β1, K2, β2, K3, β3, ..., K 10 β 10 middle,

[0030] Select combinations that satisfy E within 5% and remove those that do not.

[0031] (6) Using the actual flow rate measured in the pressure difference range of 0 to 10 kPa in step (1) and formula (6), K″ is linearly fitted. The obtained K″ is compared with the K′ value in the remaining combination in step (5) according to formula (7). The comparison result is recorded as E1.

[0032]

[0033]

[0034] Select the K′ and β′ combinations with E1 less than 2%, and substitute each selected K′ and β′ into equation (4) to calculate the theoretical flow rate of different pressure differences in the P' range in step (2). Further calculate the root mean square error of the theoretical flow rate and the actual flow rate according to equation (5), denoted as E2. The combination with the smallest E2 is identified as the final determined permeability coefficient and inertia coefficient.

[0035] If E1 does not meet the requirement of less than 2%, then reduce the error requirement and repeat the steps above for the root mean square error of the theoretical flow rate and actual flow rate for different pressure differences within the P' range.

[0036] Furthermore, the above measurement method also includes:

[0037] (7) Turn on the heating device. Heat is transferred to the container through the heat transfer oil. The temperature of the heat transfer oil measured by the thermometer is considered to be the temperature of the air flowing through the container. Record the temperature measured by the thermometer. Repeat steps (1) to (6) to obtain the flow characteristics parameters of the porous medium at different temperatures.

[0038] By heating the air, the flow characteristics parameters of porous media at different temperatures can be obtained, thus expanding the research scope beyond ambient temperature conditions.

[0039] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the provided measuring device can obtain the flow characteristic parameters of porous media under vacuum conditions; the provided measuring method can simultaneously and accurately obtain the permeability coefficient and inertia coefficient of porous media under vacuum conditions. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram of the structure of the device for measuring the permeability and inertia coefficient of porous media under vacuum conditions provided in the embodiments of this application;

[0042] Figure 2 This is the result of the actual air density ρ changing with pressure difference under vacuum conditions in the embodiments of this application;

[0043] Figure 3 This is the result of the actual air velocity v changing with pressure difference obtained under vacuum conditions in the embodiments of this application;

[0044] Figure 4 This embodiment of the application shows that ρv is actually obtained under vacuum conditions. 2 Results as a function of pressure differential;

[0045] Figure 5 This embodiment of the application expands ρv under vacuum conditions. 2 The result corresponds to the range of pressure differentials at the maximum value;

[0046] Figure 6 This is a comparison chart of theoretical and actual flow rates calculated using the permeability and inertia coefficients obtained under vacuum conditions in the embodiments of this application.

[0047] Figure 7 This is a flowchart of the method for measuring the permeability and inertia coefficient of porous media under vacuum conditions provided in the embodiments of this application;

[0048] Reference numerals: 1, air; 2, throttle valve; 3, flow meter; 4, thermometer; 5, container; 6, vessel; 7, heat transfer oil; 8, heating device; 9, first pressure gauge; 10, porous medium; 11, second pressure gauge; 12, silencer; 13, vacuum generator; 14, pressure reducing valve; 15, air source. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0050] Figure 1 The diagram shows a device for measuring the permeability and inertia coefficient of porous media under vacuum conditions, as provided in an embodiment of this application. The device includes a clamping mechanism, a container 5, a vessel 6, and a vacuum generator 13. The vessel 6 contains heat-conducting oil 7, and the container 5 is immersed in the oil 7, its interior filled with copper wire. The vessel 6 is equipped with a heating device 8 for heating the oil 7 and a thermometer 4 for measuring the temperature of the oil 7. The thermometer 4 is interlocked with the heating device 8, allowing the heat-conducting oil 7 to be heated to the desired temperature. In this embodiment, the heating device 8 uses an electric heating wire.

[0051] The clamping mechanism has a cavity for accommodating the porous medium 10. This cavity is a closed cavity with open ends, with the two ends being the inlet and outlet, respectively. Air 1 passes sequentially through a throttle valve 2, a flow meter 3, and a container 5. After being heated in the container 5, it enters the cavity inlet. The flow meter 3 is used to measure the flow rate through the porous medium 10. The throttle valve 2 is used to regulate the flow rate of the upstream gas. A vacuum generator 13 is connected to the cavity outlet and is connected to a gas source 15 via a pressure reducing valve 14. A silencer 12 is installed on the vacuum generator 13.

[0052] A first pressure gauge 9 is installed at the inlet of the cavity to measure the upstream pressure of the porous medium 10, and a second pressure gauge 11 is installed at the outlet of the cavity to measure the downstream pressure of the porous medium 10. When the upstream and downstream pressures change, the pressure can be recorded by the pressure gauges.

[0053] The porous medium 10 to be tested is a sintered metal porous medium with a diameter of 6 mm, a thickness of 2 mm, and a filtration accuracy of 2 μm.

[0054] Figure 7 The diagram shown is a flowchart of a method for measuring the permeability and inertia coefficient of porous media under vacuum conditions, provided in an embodiment of this application. The method uses the aforementioned measuring device and specifically includes the following steps.

[0055] (1) Open the air source 15 to generate negative pressure in the vacuum generator 13, and air 1 flows from the upstream to the downstream of the porous medium 10; adjust the pressure reducing valve 14 to change the downstream pressure; within the pressure difference range of 0 to 100 kPa, record the upstream pressure P1 and the downstream pressure P2 every 5 kPa, and record the corresponding flow rate at the same time; the upstream pressure P1 is measured by the first pressure gauge 9, the downstream pressure P2 is measured by the second pressure gauge 11, and the flow rate is measured by the flow meter 3.

[0056] (2) Determine the pressure difference range corresponding to the inertia coefficient value in the flow characteristic parameters of porous media.

[0057] Forchheimer's law is expressed as follows:

[0058]

[0059] Where μ is air viscosity, v is air velocity, ρ is air density, K is permeability coefficient, and β is inertia coefficient.

[0060] It can be seen that in Forchheimer's law, the density and flow velocity in the second term on the right side of the equation affect the determination of the inertial parameters.

[0061] In order to determine the influence of density and flow velocity, the average pressure P3 is calculated using the pressure difference data of the large range of upstream and downstream pressure difference in step (1), namely 20 to 100 kPa. P3 is considered to be the internal pressure of the porous medium 10 and is obtained according to equation (1).

[0062]

[0063] The density ρ inside the porous medium 10 at different pressure differences is calculated according to equation (2), and the calculation results are as follows: Figure 2 As shown;

[0064]

[0065] Where ρ0 is the air density under standard conditions, T0 is the air temperature under standard conditions, P0 is the air pressure under standard conditions, and T is the gas temperature at the time of measurement.

[0066] The flow velocity v inside the porous medium 10 at different pressure differences is calculated according to equation (3), and the calculation results are as follows: Figure 3 As shown;

[0067]

[0068] Among them G m Let A be the mass flow rate through the porous medium 10, and let A be the cross-sectional area of ​​the porous medium 10. Porosity of porous media;

[0069] Calculate ρv at different pressure differences 2 Value, ρv 2 The maximum value can be considered as the strongest inertial effect during gas flow, but it does not mean that the porous medium flow model established by Forchheimer's law can well represent the flow characteristics using the inertial coefficient corresponding to that pressure difference. ρv at different pressure differences... 2 Values ​​such as Figure 4 As shown.

[0070] Further analysis of the calculated different ρv 2 The values ​​are fitted to obtain the inflection point in the fitted curve. The range corresponding to this inflection point is then expanded by ±10 kPa. This pressure difference range is taken as the pressure difference range corresponding to the inertia coefficient value, denoted as P'. For example... Figure 5 The image shown is the fitted result, ρv 2 The pressure difference corresponding to the maximum value is 57.567 kPa, and the pressure difference at this moment is expanded to 47.567~67.567 kPa.

[0071] (3) Take the flow data of different pressure differences in the range of 47.567 to 67.567 kPa in step (2), and solve K′ and β′ using the Gauss-Newton least squares method according to formula (4). When the sum of squared residuals is the smallest, the solution K′0 is 1.36E-12 and β′0 is 0.694.

[0072]

[0073] Among them G m The mass flow rate through the porous medium is given by K′ and β′, where K′ and β′ are fitting parameters, R is the gas constant, and L is the length of the porous medium 10.

[0074] (4) Since the pressure difference of 47.567 to 67.567 kPa in step (2) is a range, multiple inertia coefficients can be calculated. Therefore, the value of β′0 in step (3) is expanded accordingly.

[0075] Introducing amplification parameters α1 and α2, where α1 is 0.8 and α2 is 1.2, we obtain an amplification range of 0.552 to 0.832. From this amplified range, values ​​are selected at intervals of 0.028, denoted as β1, β2, β3, ..., β 10 The selection results are shown in Table 1. The obtained β1, β2, β3, ..., β... 10 Each of these equations is then used to solve for K′ again using the Gauss-Newton least squares method, yielding K1, K2, K3, ..., K 10 The results are shown in Table 1.

[0076] Table 1

[0077] K β error <![CDATA[K1-β1]]> 1.51E-12 0.594 7.34％ <![CDATA[K2-β2]]> 1.40E-12 0.614 6.98％ <![CDATA[K3-β3]]> 1.29E-12 0.634 4.52％ <![CDATA[K4-β4]]> 1.35E-12 0.654 4.03％ <![CDATA[K5-β5]]> 1.39E-12 0.674 4.24％ <![CDATA[K6-β6]]> 1.37E-12 0.714 5.04％ <![CDATA[K7-β7]]> 1.42E-12 0.734 7.36％ <![CDATA[K8-β8]]> 1.46E-12 0.754 7.21％ <![CDATA[K9-β9]]> 1.47E-12 0.774 8.11％ <![CDATA[K 10 -b 10 ]]> 1.54E-12 0.794 7.69％

[0078] (5) Replace K1, β1, K2, β2, K3, β3, ..., K in Table 1. 10 β 10 Substituting these values ​​into equation (4) respectively, we can calculate the root mean square error between the theoretical flow rate and the measured actual flow rate under different pressure differences. The root mean square formula is as follows:

[0079]

[0080] Among them G 理论 The theoretical flow rate is calculated; at K1, β1, K2, β2, K3, β3, ..., K 10 β 10 In the selection, combinations that satisfy E within 5% are chosen, and those that do not are removed; Table 2 shows the calculated E for each group, where the remaining ones are K3, β3, K4, β4, K5, and β5.

[0081] (6) Using the actual flow rate measured in the pressure difference range of 0 to 10 kPa in step (1) and equation (6), K″ is linearly fitted. The obtained K″ is compared with K3, K4 and K5 according to equation (7). The comparison result is recorded as E1, as shown in Table 2.

[0082]

[0083]

[0084] The combinations of K′ and β′ with E1 less than 2% were selected, and the results are shown in Table 2. Substituting K4 and K5 into equation (4), the theoretical flow rates for different pressure differences within the P′ range in step (2) were calculated respectively. The root mean square error (RMSE) of the theoretical and actual flow rates was further calculated according to equation (5), denoted as E2, and the results are shown in Table 2. As shown in Table 2, K4 and β4 yielded the smallest error and were considered the final determined permeability coefficient and inertia coefficient. These permeability coefficients and inertia coefficients were then substituted into equation (4) to calculate the theoretical and actual flow rates for different pressure differences. Figure 6 As shown, the comparison results are quite consistent.

[0085] Table 2

[0086] <![CDATA[E1]]> <![CDATA[E2]]> <![CDATA[K3-β3]]> 2.42％ <![CDATA[K4-β4]]> 1.75％ 2.03％ <![CDATA[K5-β5]]> 1.98％ 2.92％

[0087] (7) Turn on the heating device 8. Heat is transferred to the container tank 5 through the heat transfer oil 7. The container tank 5 filled with copper wire is heated, which causes the temperature of the air 1 flowing through it to rise. The temperature of the heat transfer oil 7 measured by the thermometer 4 can be regarded as the temperature of the air 1 flowing through the container tank 5. Record the temperature measured by the thermometer 4. Repeat steps (1) to (6) to obtain the permeability coefficient and inertia coefficient of the porous medium flow characteristics at different temperatures.

[0088] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for measuring the permeability and inertia coefficient of porous media under vacuum conditions, characterized in that, A device for measuring the permeability and inertia coefficient of porous media under vacuum is used. The device includes a clamping mechanism and a vacuum generator (13). The clamping mechanism has a cavity for accommodating the porous media (10), with an inlet and an outlet at each end. Air (1) enters the cavity inlet after passing through a throttle valve (2) and a flow meter (3) in sequence. The vacuum generator (13) is connected to the cavity outlet and is connected to a gas source (15) through a pressure reducing valve (14). A first pressure gauge (9) for measuring the upstream pressure of the porous media (10) is provided at the cavity inlet, and a pressure gauge (9) for measuring the upstream pressure of the porous media (10) is provided at the cavity outlet. A second pressure gauge (11) is provided to measure the downstream pressure of the porous medium (10); the measuring device also includes a container (5) filled with copper wire and a vessel (6) containing heat transfer oil (7), the container (5) being immersed in the heat transfer oil (7); the vessel (6) is provided with a heating device (8) for heating the heat transfer oil (7) and a thermometer (4) for measuring the temperature of the heat transfer oil (7); air (1) enters the cavity inlet after passing through a throttle valve (2), a flow meter (3), and the container (5) in sequence; the thermometer (4) is interlocked with the heating device (8); The measurement method includes: (1) Turn on the air source (15) to generate negative pressure in the vacuum generator (13), and the air (1) flows from the upstream to the downstream of the porous medium (10); adjust the pressure reducing valve (14) to change the downstream pressure; record the upstream pressure every 5 kPa within the pressure difference range of 0~100 kPa between the upstream and downstream. Downstream pressure At the same time, the corresponding traffic is recorded; (2) Using the pressure difference data within the range of 20~100kPa between upstream and downstream pressure difference in step (1), calculate the average pressure. , as the internal pressure of the porous medium (10); （1） Density of porous media (10) under different pressure differences Calculate according to formula (2): （2） in The density of air under standard conditions. The air temperature under standard conditions. This refers to the air pressure under standard conditions. The gas temperature at the time of measurement; Flow velocity at different pressure differences inside porous medium (10) Calculate according to formula (3): （3） in The mass flow rate through the porous medium (10), The cross-sectional area of ​​the porous medium (10) is the flow cross-section. Porosity of porous media; Calculate the pressure difference at different times The values ​​are then fitted to obtain the inflection point in the fitted curve. The pressure difference corresponding to this inflection point is then expanded within a range of ±10 kPa. This range is taken as the pressure difference range corresponding to the inertia coefficient value, denoted as [missing value]. ; (3) In step (2) Flow data with different internal pressure differentials are processed according to equation (4). , When solving using the Gauss-Newton least squares method, the result that minimizes the sum of squared residuals is denoted as... and ; （4） in air viscosity, and For the fitting parameters, The gas constant is The length of the porous medium (10); (4) The range of values ​​is expanded; Based on the actual situation, two amplification parameters, both greater than 0, are introduced. and , Less than The expanded range is Furthermore, from the expanded scope, it is stipulated that every [period] Select, denoted as ; will be obtained Reuse equation (4) separately for Solving using the Gauss-Newton least squares method yields the following results: ; (5) Substituting these values ​​into equation (4), we can calculate the root mean square error between the theoretical flow rate and the measured actual flow rate under different pressure differences. The root mean square formula is as follows: （5） in The theoretical flow rate is calculated; Among them, select those that satisfy For combinations within 5%, remove those that do not meet the requirements; (6) Using the actual flow rate measured in step (1) within the pressure difference range of 0~10 kPa and formula (6) to... Perform linear fitting to obtain Each of the remaining combinations in step (5) The values ​​are compared for linearity according to equation (7), and the comparison result is denoted as . ; （6） （7） Will Less than 2% , Select the combinations and then select each group. , Substitute into equation (4) and calculate the values ​​in step (2) respectively. The theoretical flow rate for different pressure differentials within the range is further calculated using equation (5), and the root mean square error between the theoretical flow rate and the actual flow rate is denoted as... , will get The smallest combination is determined as the final permeability coefficient and inertia coefficient; if If no combination meets the requirement of less than 2%, then lower the error requirement and repeat the above steps. The steps for calculating the root mean square error of theoretical and actual flow rates within a range of different pressure differentials; (7) Turn on the heating device (8), and heat is transferred to the container (5) through the heat transfer oil (7). The temperature of the heat transfer oil (7) measured by the thermometer (4) is considered to be the temperature of the air (1) flowing through the container (5). Record the temperature measured by the thermometer (4). Repeat steps (1) to (6) to obtain the flow characteristics parameters of the porous medium at different temperatures.

2. The method for measuring the permeability and inertia coefficient of porous media under vacuum conditions according to claim 1, characterized in that, The vacuum generator (13) is equipped with a silencer (12).

3. The method for measuring the permeability and inertia coefficient of porous media under vacuum conditions according to claim 1, characterized in that, The heating device (8) uses an electric heating wire.

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