Free surface vertical vortex prediction method based on liquid level drop rate bias distribution

Abstract

The application discloses a free surface vertical vortex prediction method based on liquid level drop rate deviation distribution, which is used for predicting whether a vertical fluid naturally flowing out of a water outlet at the bottom of a container under the action of gravity will form a vortex. Firstly, an irrotational theoretical curve is derived, which is a theoretically described target container liquid level height change curve with time; then, a ratio K of actual time to theoretical time at a certain liquid level height of the target container is calculated, and the ratio K is compared with an irrotational expected value to determine whether a vortex is generated; wherein, the ratio K is calculated based on measured container liquid level change data and the irrotational theoretical curve, or is calculated based on a hole diameter ratio D / d of the target container. The application can predict whether a vortex is generated by real-time monitoring of a free liquid surface drop rate or directly through a container hole diameter ratio, and realizes rapid prediction of free surface deformation of a cylindrical container drainage.

Description

Technical Field

[0001] This invention relates to the field of vortex prediction technology, and in particular to a method for predicting vertical vortices on free surfaces based on the distribution of liquid level drop rate deviation. Background Technology

[0002] Vortex motion is a common phenomenon of fluid mass rotation in nature. For example, during the drainage process of cylindrical containers, vertical vortices often form on the free surface due to the suction effect of the outlet. These vortices can entrain air, causing instability, vibration, and reduced transport efficiency during drainage. Currently, predictions for cylindrical containers mainly rely on experimental observations, semi-empirical formulas, or costly numerical simulations. A balance between prediction accuracy and efficiency is difficult to achieve; therefore, a fast and accurate vortex prediction method suitable for the drainage of cylindrical containers is urgently needed. Summary of the Invention

[0003] Purpose of the invention: In order to overcome the shortcomings of the existing technology, the present invention provides a method for predicting vertical vortices on free surfaces based on the distribution of liquid level drop rate deviation. This method can quickly predict the deformation of the free surface of a cylindrical container during drainage by real-time monitoring of the free liquid level drop rate or by directly predicting whether vortices are generated through the container aperture ratio.

[0004] Technical Solution: To achieve the above objective, the present invention provides a free surface vertical vortex prediction method based on the distribution of liquid level descent rate deviation. This method is used to predict whether a vertical fluid flowing naturally from the bottom outlet of a container under gravity will form a vortex. The method includes the following steps: S1. For the target container and its outlet specifications, a non-rotational theoretical curve is determined. This non-rotational theoretical curve is the theoretical curve of the liquid level height of the target container changing over time. S2. The ratio K of the actual time taken at a certain liquid level height in the target container to the theoretical time is calculated, and the ratio K is compared with the expected non-rotational value. The comparison is used to determine whether vortices are generated; or the Reynolds number Re is calculated and it is determined whether the obtained Reynolds number Re conforms to the Reynolds number range of turbulence to determine whether vortices are generated; wherein, the ratio K is calculated based on the measured container liquid level change data and the irrotational theoretical curve, or based on the orifice ratio D / d of the target container; the Reynolds number Re is calculated based on the measured short-time change of container liquid level and the orifice ratio D / d of the target container.

[0005] Further, in step S2, the change in the liquid level height of the target container over time is monitored in real time to obtain the actual curve; based on the actual curve and the irrotational theoretical curve, the ratio K of the actual time to the theoretical time at multiple liquid level heights is calculated and compared with the irrotational expected value. In comparison, based on multiple K values ​​relative to each other The distribution of the data helps determine whether vortices are generated.

[0006] Furthermore, the expression for the irrotational theoretical curve is:

[0007]

[0008] In the formula, g is the acceleration due to gravity, A1 is the area of ​​the free liquid surface, A2 is the area of ​​the outlet, ζ is the resistance coefficient of the outlet, ε is the contraction coefficient of the outlet, and the range of values ​​for ζ and ε is determined by the shape of the outlet; h0 is the initial liquid level height, h is the instantaneous height of the free liquid surface, and t is the theoretical time required for the free liquid surface to drop from height h0 to height h.

[0009] Furthermore, the specific prediction process includes the following steps:

[0010] S21. For each time the free liquid surface drops a fixed height ∆h, record the instantaneous height h of the free liquid surface and the corresponding actual time t. h .

[0011] S22. Based on the irrotational theory curve, obtain the theoretical time t at the instantaneous height h of each record, and calculate K(h) = t for each instantaneous height h. h / t.

[0012] S23. Based on the calculated multiple K(h) values ​​and their corresponding instantaneous heights h, obtain an image showing the change of K values ​​with the instantaneous height h. Multiple K value points in this image constitute a set of K values, and the image also includes labels representing... The baseline for the value.

[0013] S24. By calculating each K value relative to... The offset of the value is compared with the statistical distribution parameter multiple scale of the K value set. Based on the statistical characteristics of whether the offset falls within or outside the statistical distribution parameter multiple scale, the occurrence of the vortex is quantitatively characterized and determined.

[0014] Furthermore, the statistical distribution parameters of the K-value set include at least the standard deviation, and the relationship between each K-value and the standard deviation is calculated. The absolute value of the difference between the values ​​is then compared with a preset statistical distribution parameter multiple scale, which is the product of a preset multiple threshold and the standard deviation. Based on the comparison result, each K value is marked as falling into the interval or exceeding the interval. Based on the combination of K value states of falling into the interval and exceeding the interval, a determination result of whether a vortex has been generated is generated.

[0015] Furthermore, the irrotational expectation value The irrotation was calibrated using an irrotational experiment, which employed multiple sets of experimental apparatuses with different aperture ratios. The variation of the K value with instantaneous height h was obtained according to steps S21-S23. When most K values ​​fell within one standard deviation of the average of this set of K values, the average of this set of K values ​​was taken as the expected irrotational value. .

[0016] Furthermore, the experimental apparatus adopts a symmetrical cylindrical container (1), the aperture ratio of which is consistent with that of the target container; a gravity sensor (2) is set at the horizontal symmetry line of the cylindrical container (1) to monitor the change of the mass m of the liquid in the container; the change of the instantaneous height h of the free liquid surface is obtained based on the change of the measured mass m, and the conversion relationship is h=m / s.

[0017] Further, in step 2, the K value is calculated using the aperture ratio D / d of the target container:

[0018] K = 0.0156 × D / d + 0.5074

[0019] In the formula, D is the inner diameter of the container, and d is the diameter of the outlet.

[0020] Furthermore, when D / d is greater than or equal to the critical aperture ratio, the K value continuously approaches the irrotational desired value. Nearby oscillations indicate no vortex generation. When D / d is less than the critical aperture ratio, it is preliminarily determined that water vortices may be generated. The K value is then calculated based on D / d, and compared with the expected vortex-free value. The presence of vortices is determined by whether the distance is within a preset multiple of the standard deviation.

[0021] Furthermore, the formula for calculating the Reynolds number Re is as follows:

[0022] Re=ρvd / μ

[0023]

[0024] In the formula, D is the inner diameter of the container, d is the orifice diameter of the outlet, ρ is the fluid density, v is the fluid velocity, μ is the dynamic viscosity coefficient of the fluid at a certain temperature, Δt is an extremely short time interval, and Δh is the change in liquid level within that extremely short time interval.

[0025] Beneficial effects: The free surface vertical vortex prediction method based on the liquid level drop rate deviation distribution of the present invention is applicable to vortex prediction in the drainage of cylindrical containers. It can determine whether vortex flow can occur by giving a parameter K that can be calculated quickly, based on Gaussian distribution, or by calculating Reynolds number, given the inner diameter of the container, the outlet orifice diameter and the initial liquid level. Both methods require only simple calculations and achieve rapid prediction of whether vortex flow will occur. It has been verified to have high accuracy. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of a small-aperture water outlet.

[0027] Figure 2 The simulation-theoretical curves are shown for the four coefficient combinations: ζ=0.04, ε=0.62; ζ=0.04, ε=0.63; ζ=0.06, ε=0.62; and ζ=0.06, ε=0.63.

[0028] Figure 3 for Figure 2 A comparison diagram of the overlap of four simulated theoretical curves.

[0029] Figure 4 The figure shows a comparison of the irrotational theoretical curves for four aperture ratios: 100 / 3, 55 / 3, 100 / 6, and 55 / 6.

[0030] Figure 5 This is a schematic diagram of the experimental apparatus according to an embodiment of the present invention.

[0031] Figure 6 A comparison chart of experimental data points for a 100 / 3 aperture ratio with the irrotational theoretical curve, and a photograph of the fluid state.

[0032] Figure 7 This is a distribution diagram of K values ​​corresponding to a 100 / 3 aperture ratio.

[0033] Figure 8 A comparison chart of experimental data points for an 85 / 3 aperture ratio with the irrotational theoretical curve, and a photograph of the fluid state.

[0034] Figure 9 Distribution of K values ​​corresponding to an 85 / 3 aperture ratio

[0035] Figure 10 A comparison chart of experimental data points for a 55 / 3 aperture ratio with the irrotational theoretical curve, and a photograph of the fluid state.

[0036] Figure 11 Distribution of K values ​​corresponding to a 55 / 3 aperture ratio

[0037] Figure 12A comparison chart of experimental data points for a 55 / 6 aperture ratio with the irrotational theoretical curve, and a photograph of the fluid state.

[0038] Figure 13 Distribution of K values ​​corresponding to a 55 / 6 pore size ratio

[0039] Figure 14 A comparison chart of experimental data points for an 85 / 6 aperture ratio with the irrotational theoretical curve, and a photograph of the fluid state.

[0040] Figure 15 Distribution of K values ​​corresponding to an 85 / 6 pore size ratio

[0041] Figure 16 This is a graph showing the relationship between the mean K value and the aperture ratio.

[0042] Figure 17 A table showing the Reynolds number, Gaussian distribution, and fluid state for five aperture ratios: 100 / 3, 85 / 3, 55 / 3, 55 / 6, and 85 / 6. Detailed Implementation

[0043] The invention will now be further described with reference to the accompanying drawings.

[0044] As attached Figure 1-17 The free surface vertical vortex prediction method based on the distribution of liquid level drop rate deviation is used in this embodiment to predict whether a vortex will form under gravity when natural drainage occurs through a thin-walled hole at the bottom of a cylindrical container. The method specifically includes the following steps: S1. Based on the inner diameter of the target cylindrical container and the size of its outlet orifice, a non-rotational theoretical curve is proposed. This non-rotational theoretical curve is the curve showing the change of the liquid level height of the target container over time, as described in theory.

[0045] S11. Deriving the irrotational theory curve. Specifically, the Bernoulli equation is extended to the unsteady but incompressible flow in this scheme. In the inertial frame, the rotation of the fluid is negligible, so only a simple correction term needs to be added to obtain the Bernoulli equation for irrotational unsteady flow:

[0046] (1.1)

[0047] The equation is valid for unsteady, compressible, rotating, elastoviscoplastic flow measurements relative to a non-inertial coordinate system whose motion is known.

[0048] Let the free surface area inside the target container be A1, the free surface velocity be v1, the outlet area be A2, and the outlet flow velocity be v2. The free surface velocity is:

[0049] (1.2)

[0050] The continuity equation for fluids is:

[0051] v1A1=εv2A2 (1.3)

[0052] Substituting equations (1.2) and (1.3) into equation (1.1), we get:

[0053] (1.4)

[0054] (1.5)

[0055] Substituting equation (1.5) into equation (1.4) and simplifying, we get:

[0056] (1.6)

[0057] When the container drains water slowly, the acceleration of the free surface of the liquid is much less than the acceleration due to gravity:

[0058] (1.7)

[0059] Therefore, we get:

[0060] (1.8)

[0061] Let the initial liquid level in the container be h0. Assuming the liquid level drops from h0 to h, the theoretical time t required for the free liquid level to drop from h0 to h is derived from the following formula:

[0062] (1.9)

[0063] In the formula, g is the acceleration due to gravity, taken as 9.8 m / s². 2 A1 is the free liquid surface area, and A2 is the outlet area. Both can be calculated by measuring the inner diameter D of the container and the outlet diameter d, and then substituting them into the formula for the area of ​​a circle.

[0064] ζ is the resistance coefficient of the outlet, and ε is the contraction coefficient of the outlet. The values ​​of both ζ and ε are determined by the shape of the outlet. Figure 1 As shown, this embodiment takes a small edge hole as an example. The ratio of its hole length l to its hole diameter d is less than or equal to 0.5, its resistance coefficient ζ ranges from 0.04 to 0.06, and its shrinkage coefficient ε ranges from 0.62 to 0.63.

[0065] S12, Determining coefficients. For example... Figure 2As shown, the four images represent the simulated theoretical curves corresponding to four coefficient combinations: ζ=0.04, ε=0.62; ζ=0.04, ε=0.63; ζ=0.06, ε=0.62; and ζ=0.06, ε=0.63. Figure 3 As shown in the comparison diagram, the simulated theoretical curves of different coefficient combinations almost overlap. Therefore, the variation of ζ and ε within their respective value ranges has almost no effect on the irrotational theoretical curve. Thus, in actual prediction, when the outlet orifice type and size are determined, ζ and ε can be calculated using any predetermined parameter value within their respective value ranges. In this embodiment, ζ = 0.06 and ε = 0.63 are taken.

[0066] Therefore, given the inner diameter D of the target container, the size of its outlet orifice d, and the initial height h0 of the liquid level inside the container, the theoretical relationship curve between the drainage time t and the real-time height h of the liquid level can be obtained.

[0067] S13. Verification Curve. To verify whether the theoretical relationship curve between t and h derived above can be used as the theoretical irrotation curve for determining irrotation, multiple sets of experiments were conducted using a specially designed experimental setup. Different combinations of containers with different inner diameters and different outlet orifice diameters were used as control groups, such as... Figure 4 As shown in the figure, the four curves from top to bottom represent the simulated theoretical curves for four aperture ratios: 100 / 3, 55 / 3, 100 / 6, and 55 / 6. It can be seen from the figure that, with a fixed initial height h0, the larger the aperture ratio D / d of the cylindrical container, the steeper the theoretical curve, indicating a longer drainage time. This aligns with the varying water flow rates in the experiment. Therefore, the derived theoretical relationship curve between t and h can be used as the theoretical irrotation curve for determining irrotation. Furthermore, from... Figure 4 By comparison, we can preliminarily conclude that if multiple data points of a container with a certain aperture ratio coincide with the theoretical curve in actual measurement, it can be inferred that no vortex is generated. If multiple data points deviate from the theoretical curve, it can be inferred that vortex may be generated, and the greater the deviation, the more obvious the vortex.

[0068] S2. Define a parameter K, whose value characterizes the degree of deviation of the measured data points from the irrotational theoretical curve, and calibrate an irrotational expectation value. As a reference standard. The parameter K is the actual time t taken for the target container to descend to a certain instantaneous liquid level height h. h The ratio to the theoretical time t can be expressed as:

[0069] K(h) = t h / t

[0070] The ratio K is calculated and then compared with the irrotational expectation value. A comparison is made to determine whether a vortex has been generated. The ratio K can be calculated based on measured container liquid level change data and the irrotational theoretical curve.

[0071] The specific vortex prediction process includes the following steps:

[0072] S21. Monitor the liquid level in the target container. This can be done using a liquid level sensor or other common liquid level monitoring methods. Record the instantaneous height h of the free liquid level and the corresponding actual time t every time the free liquid level drops a fixed height ∆h. h .

[0073] S22. Obtain the theoretical time t at the instantaneous height h of each record based on the irrotational theory curve, and calculate K(h) = t for each instantaneous height h. h / t.

[0074] S23. Based on the calculated multiple K(h) values ​​and their corresponding instantaneous heights h, obtain a graph showing the change of K values ​​with instantaneous height h, such as... Figure 7 , 9 As shown in Figures 11, 13, and 15, multiple K-value points (such as...) in this image... Figure 7 , 9 The set of K values ​​is composed of multiple red asterisks (11, 13, 15), and the image also contains labels representing... The baseline of the value, such as Figure 7 , 9 The solid red lines in numbers 11, 13, and 15, along with the two dashed lines above and below them, represent the positions of the lines corresponding to the solid lines. The distance between values ​​is one standard deviation.

[0075] S24. By calculating each K value relative to... value offset ( The offset is compared with the statistical distribution parameter multiple scale of the K value set, and the occurrence of the vortex is quantitatively characterized and determined based on the statistical characteristics of whether the offset falls within or outside the statistical distribution parameter multiple scale.

[0076] The statistical distribution parameters of the set of K values ​​include at least the standard deviation σ. The relationship between each K value and the set of K values ​​is calculated. absolute value of the difference Then, the absolute value of the difference The K value is compared with a preset statistical distribution parameter multiple scale, which is the product of a preset multiple threshold x and the standard deviation σ. Based on the comparison result, each K value is marked as falling into the interval or exceeding the interval. Based on the combination of K value states of falling into the interval and exceeding the interval, a determination result of whether a vortex is generated is generated.

[0077] In this embodiment, a preset multiple threshold x=5 is obtained based on Gaussian distribution statistics, that is, when When, the corresponding K value is marked as falling into the interval state, when When the K value is outside the range, the corresponding K value is marked as being outside the range. When most K values ​​are within the range, it is determined that no vortex is generated. When most K values ​​are outside the range, it is determined that a vortex is generated.

[0078] The expected value of irrotation The irrotation was calibrated using an irrotational experiment, which employed multiple sets of experimental apparatuses with different aperture ratios. The variation of the K value with instantaneous height h was obtained according to steps S21-S23. When most K values ​​fell within one standard deviation of the average of this set of K values, the average of this set of K values ​​was taken as the expected irrotational value. .

[0079] like Figure 5 As shown, the experimental setup uses a symmetrical cylindrical container 1. Water is added to the container to a preset initial height, such as 100mm. After the liquid surface becomes still, the water is allowed to fall freely through a small hole at the bottom, and timing and high-speed camera recording of the water flow are started simultaneously. Every time the liquid level drops by 10mm, the instantaneous height h and corresponding time t are recorded. The irrotational theoretical curve of the container is simulated using MATLAB, and the experimental data processing method is used to obtain a comparison graph between discrete experimental data points and the irrotational theoretical curve. The generated comparison graph is then visually compared with the corresponding fluid state captured in the video. The average value of the K-value set corresponding to each aperture ratio experiment is calculated.

[0080] This embodiment uses cylindrical containers with five different pore sizes: 100 / 3, 85 / 3, 55 / 3, 55 / 6, and 85 / 6. In each experiment, water of the same height and temperature was injected into the cylinder to ensure a constant temperature and water concentration. Each pore size ratio was measured five times, with time data recorded for every 10 mm decrease in height. The mean and standard deviation of the five measurements were then calculated for further plotting and data analysis.

[0081] like Figure 6 , 8 As shown in figures 10, 12, and 14, the fluid states observed in the photographs indicate that the water flow generated by the containers with aperture ratios of 100 / 3 and 85 / 3 is irrotational direct current, and the corresponding experimental data points all lie on the theoretical curve, verifying the reliability of the irrotational theoretical curve. Specifically, the average value of the K-value set corresponding to the 100 / 3 aperture ratio is 1.0017, and the average value of the K-value set corresponding to the 85 / 3 aperture ratio is 0.9596.

[0082] like Figure 7As shown in the K-value distribution map corresponding to a 100 / 3 aperture ratio, most K-value points fall within one standard deviation of its average value of 1.0017. Therefore, its average K-value of 1.0017 can be used as the expected value of irrotation. .like Figure 9 As shown, when 1.0017 is the expected irrotation value, in the K-value distribution map corresponding to the 85 / 3 aperture ratio, the distance between all K-value points and the expected irrotation value of 1.0017 is less than 3 times the standard deviation, theoretically indicating that no vortices are generated, which is consistent with the fluid state observed in the photograph. Therefore, the K-value distribution maps corresponding to the other three aperture ratios (such as...) Figure 11 , 13 Both 1 and 15 have an irrotational expected value of 1.0017.

[0083] like Figure 11 As shown, all K-values ​​are more than 5 times the standard deviation from the irrotational expected value of 1.0017, which theoretically indicates the presence of vortices. Figure 10 The fluid state diagram shown verifies the generation of a slight vortex flow.

[0084] like Figure 13 As shown, all K-values ​​are more than 13 times the standard deviation from the irrotational expected value of 1.0017, which theoretically indicates the existence of vortices. Figure 12 The fluid state diagram shown verifies the generation of large vortex flow.

[0085] like Figure 15 As shown, all K-values ​​are more than 9 times the standard deviation from the irrotational expected value of 1.0017, which theoretically suggests the presence of vortices. Figure 14 The fluid state diagram shown verifies the generation of a large vortex flow.

[0086] The above three sets of experiments further verified that vortex flow can indeed be generated when the experimental data points do not match the irrotational theoretical curve.

[0087] The cylindrical container 1 is mounted on a base 3, which is supported at the horizontal line of symmetry of the cylindrical container 1. A gravity sensor 2 is installed on the support surface to monitor the change in the mass m of the liquid inside the container. This scheme obtains the change in the instantaneous height h of the free liquid surface based on the measured change in mass m, and the conversion relationship is 0.001kg = 1ml = 1cm. 3 m=V=hπr 2 That is, h = m / s. This can reduce errors caused by human factors when reading the liquid level.

[0088] Through the above-mentioned multiple sets of experiments, it was further discovered that there is a certain relationship between the K value and the pore size ratio D / d. Therefore, by calculating the pore size ratio D / d and fitting a graph showing the relationship between the mean K value and the pore size ratio D / d, as shown... Figure 16 As shown;

[0089] The K value is calculated using the aperture ratio D / d of the target container:

[0090] K = 0.0156 × D / d + 0.5074

[0091] In the formula, D is the inner diameter of the container, and d is the diameter of the outlet.

[0092] Therefore, the K value can be directly calculated based on the pore size ratio D / d of the target container. It can also be seen that within a certain range, K increases with the increase of the pore size ratio. In this embodiment, when D / d is greater than or equal to the critical pore size ratio of 100 / 3, the K value continuously approaches the irrotational expected value. Oscillations around 1.0017 indicate no vortex generation. When D / d is less than the critical aperture ratio of 100 / 3, it is preliminarily determined that water vortices may be generated. The K value is then calculated based on D / d and further assessed. The presence of vortices is determined by whether the value is greater than or equal to 5σ. This allows for direct determination of vortex flow based on the target container aperture ratio D / d.

[0093] In another embodiment of this scheme, given the inner diameter D of the target container and the orifice diameter d of the outlet, the Reynolds number Re is calculated, and it is determined whether the obtained Reynolds number Re conforms to the Reynolds number range of turbulence to determine whether vortices are generated; the Reynolds number Re is calculated based on the measured container liquid level change data and the orifice diameter ratio D / d of the target container, and its calculation formula is as follows:

[0094] Re=ρvd / μ

[0095]

[0096] In the formula, D is the inner diameter of the container, d is the orifice diameter of the water outlet, both in meters; ρ is the fluid density, and in this embodiment, the density of the water is 998.2 kg / m³. 3 v represents the fluid velocity in m / s; μ represents the dynamic viscosity coefficient of the fluid at a certain temperature. In this embodiment, the dynamic viscosity coefficient of water at 15℃ is taken as 1.1404 × 10⁻⁶. -2 pa∙s.

[0097] Δt is an extremely short time interval, such as 0.1-0.5 s, Δh t This represents the change in liquid level within this extremely short time interval.

[0098] The Reynolds number is also a basis for judging flow characteristics. When the Reynolds number is less than 2300, the fluid flow is laminar; when the Reynolds number is greater than 2300 but less than 4000, it is transitional flow; and when the Reynolds number is greater than 4000, it is turbulent flow. A water helix can also be considered a flow pattern, and its degree of twisting can be approximated by transitional or turbulent flow. Laminar flow, also called sheet flow, refers to low-velocity flow where the fluid flows in layers without mixing. As the velocity gradually increases, the streamlines begin to exhibit wavy oscillations, with the frequency and amplitude of the oscillations increasing with the velocity. This flow condition is called transitional flow. When the velocity increases to a very high level, the streamlines are no longer clearly distinguishable, and many small vortices appear in the flow field; this is called turbulent flow, also known as disturbance flow, disturbance flow, or turbulent flow.

[0099] By calculating the Reynolds number, we can obtain the following... Figure 17 The results are shown.

[0100] The Reynolds number corresponding to a 100 / 3 aperture ratio container is less than 2317.8709, which falls within the Reynolds number range for laminar flow. No spiral phenomenon was observed, and there were no depressions. This is consistent with the experiments in this paper.

[0101] The Reynolds number corresponding to the 85 / 3 aperture ratio container is less than 4000, which is within the Reynolds number range of the transition flow. No spiral phenomenon was observed, and there were no depressions.

[0102] The Reynolds number corresponding to the 55 / 3 aperture ratio container is between 2575.68 and 3710.803, which is within the Reynolds number range of the transition flow. It is a small spiral with no obvious indentation.

[0103] The Reynolds number corresponding to the 85 / 6 aperture ratio container is between 4539 and 5965, which is within the Reynolds number range of turbulent flow. This is exactly the large spiral we see, with obvious depressions on the liquid surface.

[0104] The Reynolds number corresponding to the 55 / 6 aperture ratio container is between 9877.0607 and 6990.178885, which is consistent with the Reynolds number range of turbulent flow. This is exactly the large spiral we see, with obvious depressions on the liquid surface.

[0105] In summary, once the aperture ratio is determined, a Reynolds number greater than 4000 indicates the presence of vortex flow.

[0106] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the above principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation, characterized in that, To predict whether a vertical fluid flowing naturally from the bottom outlet of a container under gravity will form a vortex, the following steps are included: S1. For the target container and its outlet specifications, formulate an irrotational theoretical curve, which is the theoretical curve of the change of the liquid level height of the target container over time. S2. Calculate the ratio K of the actual time taken to the theoretical time at a certain liquid level in the target container, and then compare the ratio K with the irrotational expected value. Compare the results to determine whether a vortex has been generated; The ratio K is calculated based on the measured container liquid level change data and the irrotational theoretical curve, or it is calculated based on the pore size ratio D / d of the target container.

2. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 1, characterized in that: In step S2, the change in the liquid level height of the target container over time is monitored in real time to obtain the actual curve; based on the actual curve and the irrotational theoretical curve, the ratio K of the actual time to the theoretical time at multiple liquid level heights is calculated and compared with the irrotational expected value. In comparison, based on multiple K values ​​relative to each other The distribution of the data helps determine whether vortices are generated.

3. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 2, characterized in that, The expression for the irrotational theory curve is: In the formula, g is the acceleration due to gravity, A1 is the free liquid surface area, A2 is the area of ​​the outlet, ζ is the resistance coefficient of the outlet, and ε is the contraction coefficient of the outlet. The range of values ​​for ζ and ε is determined by the shape of the outlet. h0 is the initial liquid level height, h is the instantaneous height of the free liquid level, and t is the theoretical time required for the free liquid level to drop from height h0 to height h.

4. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 3, characterized in that, The specific prediction process includes the following steps: S21. For each fixed height Δh that the free liquid surface descends, record the instantaneous height h of the free liquid surface and the corresponding actual time t. h ; S22. Based on the irrotational theory curve, obtain the theoretical time t at the instantaneous height h of each record, and calculate K(h) = t for each instantaneous height h. h / t; S23. Based on the calculated multiple K(h) values ​​and their corresponding instantaneous heights h, obtain an image showing the change of K values ​​with the instantaneous height h. Multiple K value points in this image constitute a set of K values, and the image also includes labels representing... The baseline for the value; S24. By calculating each K value relative to... The offset of the value is compared with the statistical distribution parameter multiple scale of the K value set. Based on the statistical characteristics of whether the offset falls within or outside the statistical distribution parameter multiple scale, the occurrence of the vortex is quantitatively characterized and determined.

5. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 4, characterized in that: The statistical distribution parameters of the set of K values ​​include at least the standard deviation. The relationship between each K value and the standard deviation is calculated. The absolute value of the difference between the values ​​is then compared with a preset statistical distribution parameter multiple scale, which is the product of a preset multiple threshold and the standard deviation. Based on the comparison result, each K value is marked as falling into the interval or exceeding the interval. Based on the combination of K value states of falling into the interval and exceeding the interval, a determination result of whether a vortex has been generated is generated.

6. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 5, characterized in that: The expected value of irrotation The irrotation was calibrated using an irrotational experiment, which employed multiple sets of experimental apparatuses with different aperture ratios. The variation of the K value with instantaneous height h was obtained according to steps S21-S23. When most K values ​​fell within one standard deviation of the average of this set of K values, the average of this set of K values ​​was taken as the expected irrotational value. .

7. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 6, characterized in that: The experimental setup uses a symmetrical cylindrical container (1) with the same aperture ratio as the target container. A gravity sensor (2) is installed at the horizontal symmetry line of the cylindrical container (1) to monitor the change in the mass m of the liquid inside the container. The change in the instantaneous height h of the free liquid surface is obtained based on the change in the measured mass m, and the conversion relationship is h = m / s.

8. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 1, characterized in that: In step 2, the K value is calculated using the aperture ratio D / d of the target container: K = 0.0156 × D / d + 0.5074 In the formula, D is the inner diameter of the container, and d is the diameter of the outlet.

9. The method for predicting vertical vortices on a free surface based on the distribution of liquid level descent rate deviation according to claim 8, characterized in that: When D / d is greater than or equal to the critical aperture ratio, the K value continuously approaches the irrotational desired value. Nearby oscillations indicate no vortex generation. When D / d is less than the critical aperture ratio, it is preliminarily determined that water vortices may be generated. The K value is then calculated based on D / d, and compared with the expected vortex-free value. The presence of vortices is determined by whether the distance is within a preset multiple of the standard deviation.

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