Method for identifying and predicting proportion of vortex region of karst pipeline

Abstract

The invention discloses a method for identifying and predicting the proportion of a karst pipeline vortex region, and relates to the technical field of hydrogeology. Comprising the following steps: selecting flow velocity, shape coefficient and relative roughness as main control factors from the angles of hydraulic conditions and pipeline structures, designing an artificial rough pipeline, and carrying out experiments and numerical simulation; calculating a vortex area proportion based on a numerical simulation flow field of the karst rough pipeline of the three main control factors; and constructing a quantitative relation between the vortex area proportion and different flow velocities, different shape coefficients and different relative roughness, and generating a prediction equation of the vortex area proportion by combining a multivariate statistical regression method. The method is convenient to operate and accurate in identification and test result, and accurate prediction of the eddy current area proportion can be realized under the condition of obtaining common field hydrogeological parameters.

Description

Technical Field

[0001] The present invention relates to the field of hydrogeological technology, and more particularly to a method for identifying and predicting the proportion of vortex areas in karst pipelines. Background Art

[0002] In recent years, karst conduits have become an effective seepage transmission tool in groundwater circulation, and more and more researchers have focused on this. Karst conduits are natural channels formed by carbonate karst erosion. Groundwater and pollutants move and migrate rapidly after entering karst conduits. They are the main storage place and runoff channel of karst groundwater in southern my country, and play a controlling role in the migration of pollutants.

[0003] Traditionally, non-Fickian transport phenomena such as the tailing of groundwater pollutant (tracer) penetration curves are attributed to adsorption analysis, bedrock water exchange, and branch pipeline effects. The pollutant concentration effect caused by eddy currents generated by irregular karst pipeline boundary conditions has not been taken seriously or even ignored.

[0004] Therefore, it is an urgent problem for those skilled in the art to propose a method for identifying and predicting the proportion of vortex areas in karst pipelines to solve the difficulties existing in the prior art. Summary of the invention

[0005] In view of this, the present invention provides a method for identifying and predicting the proportion of vortex areas in karst pipelines, which can achieve accurate prediction of the proportion of vortex areas under the condition of obtaining common hydrogeological parameters in the field.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for identifying and predicting the proportion of vortex areas in karst pipelines comprises the following steps:

[0008] S1. Select flow rate, shape coefficient and relative roughness as the main control factors from the perspective of hydraulic conditions and pipeline structure, design artificial rough pipelines and carry out experiments and numerical simulations;

[0009] S2, numerical simulation of flow field in karst rough pipe based on three main control factors, calculation of eddy current area proportion;

[0010] S3. Construct a quantitative relationship between the proportion of the eddy zone and different flow velocities, different shape coefficients, and different relative roughness, and generate a prediction equation for the proportion of the eddy zone using a multivariate statistical regression method.

[0011] In the above method, optionally, in S1, the designed artificial rough pipe is composed of protrusions of different sizes and shapes, including a semicircular rough unit karst pipe and a trapezoidal rough unit karst pipe with variable top and bottom lengths.

[0012] In the above method, optionally, the shape coefficient ε in S1 characterizes different types of trapezoidal rough units, where the short side of the trapezoid is L1 and the long side is L2. When the absolute roughness of the karst pipe is the same, the shape coefficient ε is defined as:

[0013]

[0014] When the shape coefficient ε = 0, the coarse element is a triangle;

[0015] The relative roughness η is the ratio of the roughness protrusion height Δ to the pipe diameter d:

[0016]

[0017] In the above method, optionally, in S1, the device for conducting the experiment and numerical simulation consists of a water supply device, an artificial karst pipeline experimental section, and a flow measurement device;

[0018] Water supply device: including a centrifugal pump, a water supply tank and a constant water head device. The centrifugal pump is used to pump water from the water supply tank to the constant water head device;

[0019] Flow measuring device: It consists of a water outlet pipeline, a flow measuring container and a pressure sensor. A pressure measuring hole is set on the side wall of the flow measuring container near the bottom. The water level in the container at different times during the experiment is automatically collected through the pressure sensor, and the water flow rate is calculated by the slope of the water level and time relationship curve.

[0020] In the above method, optionally, in S2, between the rough units, the streamlines will bend, and the streamlines will swirl to form eddy regions;

[0021] The pores between two adjacent rough units are the ABC region;

[0022] Project the side wall AC along the y-axis into a straight line Y1Y2. The velocity components in the x and y directions of the straight line AC intersect with the y-axis at point M. The velocity components in the x and y directions of point M are both 0, which is the turning point of the flow velocity direction. Along the Y1Y2 direction, the velocity component in the x direction changes from negative to positive, and the velocity component in the y direction changes from positive to negative. Point M is the boundary between the vortex area and the mainstream channel.

[0023] Project the straight line AC along the x-axis to the straight line X1X2, plot the magnitudes of the x- and y-direction velocity components along the AC section on X1X2, and find the dividing point H;

[0024] The horizontal coordinate of point F is the x coordinate of point H, and the vertical coordinate is the y coordinate of point M;

[0025] In the flow field space, there is only one streamline passing through point F, and the boundary line EF of the eddy zone is obtained;

[0026] Project the straight line AB along the y-axis to Y3Y4, and draw the x- and y-direction velocity component curves of the AB section on Y3Y4, and you can get the dividing point G on the straight line X1X2 and the dividing point L on the straight line Y3Y4;

[0027] The straight lines GH and JI are the central axes of the two corresponding rough units, HI is the central axis of the karst pipeline in the x direction, and the total eddy area ratio is the area of ​​polygon ABC divided by the area of ​​polygon AGHIJ:

[0028]

[0029] Where ω is the total eddy zone ratio, Sr is the total eddy zone area in the karst pipeline, that is, the area of ​​polygon ABC, and the unit is m 2 ; Sz is the total area of ​​pore space in the karst pipe, that is, the area of ​​polygon AGHIJ, the unit is m 2 .

[0030] In the above method, optionally, in S3, the equation for predicting the proportion of the eddy current area is as follows:

[0031] ω=-18.325·ε+142.901·η+5.012·ln(v)+2.312

[0032] Among them, ω is the proportion of the total eddy area, ε is the shape coefficient, η represents the relative roughness, and v represents the flow velocity in m / s.

[0033] It can be seen from the above technical solutions that, compared with the prior art, the present invention provides a method for identifying and predicting the proportion of vortex areas in karst pipelines, and its beneficial effects are:

[0034] A method for quantitatively characterizing the size of the eddy zone proportion is proposed, which clarifies the quantitative relationship between different flow velocities, different shape coefficients and different relative roughness and the size of the eddy zone proportion, and constructs a predictive relationship between the three main controlling factors and the eddy zone proportion; the method of the present invention is easy to operate and the prediction result is accurate; it can achieve accurate prediction of the eddy zone proportion under the condition of obtaining hydrogeological parameters that are common and relatively easy to obtain in the field; this method is of great significance to the fields of water disasters in karst areas, pollutant prevention and control, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0036] Figure 1 A flow chart of a method for identifying and predicting the proportion of vortex areas in karst pipelines provided by the present invention;

[0037] Figure 2a A schematic diagram of a triangular rough unit karst pipeline of the present invention;

[0038] Figure 2b It is a schematic diagram of a trapezoidal rough unit karst pipeline of the present invention;

[0039] Figure 2c It is a schematic diagram of a semicircular rough unit karst pipeline of the present invention;

[0040] Figure 3 It is a schematic diagram of the experimental device of the present invention;

[0041] Figure 4 It is the karst pipeline eddy flow area identification map of the present invention;

[0042] Figure 5a It is a schematic diagram of the proportion of the vortex area of ​​the semicircular rough unit karst pipeline of the present invention;

[0043] Figure 5b It is a schematic diagram of the proportion of the vortex area of ​​the triangular rough unit karst pipeline of the present invention;

[0044] Figure 5c It is a schematic diagram of the proportion of the vortex area of ​​the trapezoidal rough unit karst pipeline of the present invention;

[0045] Figure 6 The graph of the area ratio of the eddy flow zone of different types of karst pipelines according to the present invention varies with different flow rates;

[0046] Figure 7 The graph of the area ratio of the eddy flow area of ​​different types of karst pipelines according to the present invention and the shape coefficient;

[0047] Figure 8 The graph of the area ratio of the eddy flow zone of different types of karst pipelines according to the present invention varies with different relative roughness;

[0048] Fig. 9 It is a comparison chart of the experimental value and the predicted value of the eddy current area ratio of the present invention. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] See also Figure 1As shown, a method for identifying and predicting the proportion of vortex areas in karst pipelines includes the following steps:

[0051] S1. Select flow rate, shape coefficient and relative roughness as the main control factors from the perspective of hydraulic conditions and pipeline structure, design artificial rough pipelines and carry out experiments and numerical simulations;

[0052] S2, numerical simulation of flow field in karst rough pipe based on three main control factors, calculation of eddy current area proportion;

[0053] S3. Construct a quantitative relationship between the proportion of the eddy zone and different flow velocities, different shape coefficients, and different relative roughness, and generate a prediction equation for the proportion of the eddy zone using a multivariate statistical regression method.

[0054] Furthermore, in previous studies, it was found that the flow conditions and the structure of the karst pipeline seriously affect the motion state of the fluid in the pipeline, so the flow rate, shape coefficient, and relative roughness were selected as the main controlling factors;

[0055] Further, refer to Figure 2a , Figure 2b , Figure 2c As shown, a series of karst pipes are designed. The karst pipes are composed of protrusions of different sizes and shapes. In addition to the semicircular rough unit karst pipes, a series of trapezoidal rough unit karst pipes with variable top and bottom lengths are also constructed.

[0056] Furthermore, the shape coefficient ε in S1 characterizes different types of trapezoidal roughness units, where the short side of the trapezoid is L1 and the long side is L2. When the absolute roughness of the karst pipe is the same, the shape coefficient ε is defined as:

[0057]

[0058] When the shape coefficient ε = 0, the coarse element is a triangle;

[0059] In this study, four different rough units (ε=0, ε=1 / 4, ε=1 / 2, ε=3 / 4) were designed to explore the effect of shape coefficient on the eddy current zone;

[0060] The protrusion height of the roughness unit also affects the movement of the fluid, so four relative roughnesses (η) of 1 / 3, 1 / 3.62, 1 / 4.22, and 1 / 4.86 are designed;

[0061] The relative roughness η is the ratio of the roughness protrusion height Δ to the pipe diameter d:

[0062]

[0063] Further, see Figure 3As shown, in S1, the device for conducting experiments and numerical simulations consists of a water supply device, an artificial karst pipeline experimental section, and a flow measurement device;

[0064] Water supply device: including a centrifugal pump, a water supply tank and a constant water head device. The centrifugal pump is used to pump water from the water supply tank to the constant water head device;

[0065] Flow measuring device: It consists of a water outlet pipeline, a flow measuring container and a pressure sensor. A pressure measuring hole is set on the side wall of the flow measuring container near the bottom. The water level in the container at different times during the experiment is automatically collected through the pressure sensor, and the water flow rate is calculated by the slope of the water level and time relationship curve.

[0066] Furthermore, in S2, the karst conduit flow field shows that between the rough units, the streamlines always have certain bends, and under certain conditions, the streamlines swirl to form eddy zones;

[0067] Further, refer to Figure 4 As shown, taking a trapezoidal (ε=1 / 4, η=1 / 3) karst pipe with a flow rate of 0.04 m / s as an example,

[0068] The ABC region is the gap between two adjacent rough units. The blue arrow only indicates the velocity direction. The x-direction velocity component of the side walls AB and AC is represented by the red curve, and the y-direction velocity component is represented by the blue line.

[0069] Project the side wall AC along the y-axis into a straight line Y1Y2. The velocity components in the x and y directions of the straight line AC intersect with the y-axis at point M. The velocity components in the x and y directions at point M are both 0, which is the turning point of the flow velocity direction. Along the Y1Y2 direction, the velocity component in the x direction just changes from negative to positive, and the velocity component in the y direction changes from positive to negative. Point M is the boundary point between the eddy zone and the mainstream channel.

[0070] Project the straight line AC along the x-axis to the straight line X1X2, and plot the magnitudes of the x- and y-direction velocity components along the AC section on X1X2, and the dividing point H can be found;

[0071] The horizontal coordinate of point F is the x coordinate of point H, and the vertical coordinate is the y coordinate of point M;

[0072] In the flow field space, there is only one streamline passing through point F, and the boundary line EF of the eddy zone can be obtained;

[0073] Project the straight line AB along the y-axis to Y3Y4, and draw the x- and y-direction velocity component curves of the AB section on Y3Y4, and you can get the dividing point G on the straight line X1X2 and the dividing point L on the straight line Y3Y4;

[0074] The x-coordinate corresponding to point L and the y-coordinate corresponding to point G are reversely projected back to straight line AB, and the streamline passing through the point is drawn, which coincides with the streamline EF. This proves that the method is feasible. It has been verified that all eddy current zones near the middle of the same rough circular tube have the same shape and equal area, and the same is true in semicircular karst pipes.

[0075] Further, refer to Figure 5a , Figure 5b , Figure 5c As shown, the green area is the eddy area, the yellow area is the mainstream channel, the straight lines GH and JI are the central axes of the two corresponding rough units, HI is the central axis of the karst pipeline in the x direction, and the total eddy area ratio is the area of ​​polygon ABC divided by the area of ​​polygon AGHIJ:

[0076]

[0077] Where ω is the total eddy zone ratio, Sr is the total eddy zone area in the karst pipeline, that is, the area of ​​polygon ABC, and the unit is m 2 ; Sz is the total area of ​​pore space in the karst pipe, that is, the area of ​​polygon AGHIJ, in m 2 .

[0078] Furthermore, in S3,

[0079] Reference Figure 6 As shown in the figure, the relationship between the proportion of the eddy area and the flow velocity: taking the flow velocities of 0.001, 0.01, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, and 0.4 m / s as examples, the eddy area continues to increase with the increase of the flow velocity, but eventually tends to a fixed value and a1;

[0080] Finally, the relationship between the flow velocity and the proportion of the eddy current area under the rough shapes of triangle, trapezoid (1 / 4), trapezoid (1 / 2), trapezoid (3 / 4), and circle is obtained. The two are exactly in a logarithmic relationship, and the following expression exists:

[0081] ω=a1-b1lnv;

[0082] Reference Figure 7 As shown in the figure, the relationship between the proportion of the eddy current area and the shape coefficient: Taking four shape coefficients (ε=0, ε=1 / 4, ε=1 / 2, ε=3 / 4) as an example, it is found that ω decreases as the shape coefficient increases, and there is a linear decreasing law between the two. The fitting can obtain the following equation:

[0083] ω=b2-a2·ε;

[0084] Reference Figure 8As shown in the figure, the relationship between the proportion of eddy current zone and roughness: Taking four relative roughnesses of 1 / 3, 1 / 3.62, 1.4.22, and 1 / 4.86 as examples, the relationship between relative roughness and the proportion of eddy current zone is established; there is an obvious linear relationship between the two in the karst pipelines of the five rough units, and the relationship between the two can be expressed by the following equation:

[0085] ω=b3+a3·η

[0086] The total eddy current area ratio ω has a linear relationship with the shape coefficient ε and the relative roughness η, and a logarithmic relationship with the flow velocity v. Spass software was used to perform mathematical statistical regression analysis on the existing 70 eddy current area ratio data. The analysis results showed that the R2 of the model was 0.852, and all indicators passed the regression analysis test. The regression model was successfully established, and the regression model equation shown below was obtained. The equation for measuring the eddy current area ratio is as follows:

[0087] ω=-18.325·ε+142.901·η+5.012·ln(v)+2.312

[0088] Among them, ω is the proportion of the total eddy area, ε is the shape coefficient, η represents the relative roughness, and v represents the flow velocity in m / s.

[0089] In a specific embodiment, in order to verify the accuracy of the model, another 60 sets of data were selected for verification. Fig. 9 As shown, the horizontal axis is the true value detected, and the vertical axis is the predicted value calculated using the regression model equation; the red line in the figure is the standard curve with a slope of 1 and an intercept of 0, and the green area is the 85% prediction interval;

[0090] from Fig. 9 It can be seen that some blue points fall on the red line, and the rest are evenly distributed near the red line, which shows that the model can well predict the proportion of the total eddy flow area in the two-dimensional karst pipeline.

[0091] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0092] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for identifying and predicting the proportion of vortex areas in karst pipelines, It is characterized in that The following steps are involved: S1. Select flow rate, shape coefficient and relative roughness as the main control factors from the perspective of hydraulic conditions and pipeline structure, design artificial rough pipelines and carry out experiments and numerical simulations; S2, numerical simulation of flow field in karst rough pipe based on three main control factors, calculation of eddy current area proportion; S3. Construct a quantitative relationship between the proportion of the eddy zone and different flow velocities, different shape coefficients, and different relative roughness, and generate a prediction equation for the proportion of the eddy zone using a multivariate statistical regression method.

2. A method for identifying and predicting the proportion of vortex areas in karst pipelines according to claim 1, It is characterized in that In S1, the designed artificial rough pipes are composed of protrusions of different sizes and shapes, including semicircular rough unit karst pipes and trapezoidal rough unit karst pipes with variable lengths at the top and bottom.

3. A method for identifying and predicting the proportion of vortex areas in karst pipelines according to claim 2, It is characterized in that The shape coefficient ε in S1 characterizes different types of trapezoidal rough elements, and the short side of the trapezoid is L 1 , the long side is L 2 , when the absolute roughness of the karst pipe is the same, the shape coefficient ε is defined as: When the shape coefficient ε = 0, the coarse element is a triangle; The relative roughness η is the ratio of the roughness protrusion height Δ to the pipe diameter d:

4. A method for identifying and predicting the proportion of vortex areas in karst pipelines according to claim 1, It is characterized in that In S1, the device for conducting experiments and numerical simulations consists of a water supply device, an artificial karst pipeline experimental section, and a flow measurement device; The water supply device includes: a centrifugal pump, a water supply tank and a water head setting device, and the centrifugal pump is used to pump water from the water supply tank to the water head setting device; The flow measuring device consists of a water outlet pipeline, a flow measuring container and a pressure sensor. A pressure measuring hole is provided on the side wall of the flow measuring container near the bottom. The water level in the container at different times during the experiment is automatically collected through the pressure sensor, and the water flow rate is calculated based on the slope of the water level-time relationship curve.

5. A method for identifying and predicting the proportion of vortex areas in karst pipelines according to claim 1, It is characterized in that In S2, between the rough units, the streamlines will bend, and the streamlines will swirl to form eddy zones; The pores between two adjacent rough units are the ABC region; Project the wall AC along the y-axis into a straight line Y 1 Y 2 The velocity components of the x and y directions of the straight line AC intersect the y axis at point M. The velocity components of the x and y directions of point M are both 0, which is the turning point of the flow velocity direction. 1 Y 2 Direction, the velocity component in the x direction changes from negative to positive, and the velocity component in the y direction changes from positive to negative. Point M is the boundary between the eddy current zone and the mainstream channel. Project the line AC along the x-axis to the line X 1 X 2 , draw X 1 X 2 Calculate the magnitude of the x- and y-direction velocity components along the AC section line and find the dividing point H; The horizontal coordinate of point F is the x coordinate of point H, and the vertical coordinate is the y coordinate of point M; In the flow field space, there is only one streamline passing through point F, and the boundary line EF of the eddy zone is obtained; Project the line AB along the y-axis to Y 3 Y 4 , also in Y 3 Y 4 Plotting the x and y direction velocity component curves of the AB section on the surface, we can get the straight line X 1 X 2 The dividing point G on the straight line Y 3 Y 4 Upper dividing point L; The straight lines GH and JI are the central axes of the two corresponding rough units, HI is the central axis of the karst pipeline in the x direction, and the total eddy area ratio is the area of ​​polygon ABC divided by the area of ​​polygon AGHIJ: Where ω is the total eddy zone ratio, Sr is the total eddy zone area in the karst pipeline, that is, the area of ​​polygon ABC, and the unit is m 2 ; Sz is the total area of ​​pore space in the karst pipe, that is, the area of ​​polygon AGHIJ, in m 2 .

6. A method for identifying and predicting the proportion of vortex areas in karst pipelines according to claim 1, It is characterized in that In S3, the equation for predicting the proportion of the eddy current area is as follows: ω=-18.325·ε+142.901·η+5.012·ln(v)+2.312 Among them, ω is the proportion of the total eddy area, ε is the shape coefficient, η represents the relative roughness, and v represents the flow velocity in m / s.

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