Method for determining the height of a rough sublayer boundary

Abstract

The application discloses a method for determining rough sublayer boundary height, comprising: performing flow measurement in a rough sublayer flow scene to obtain the along-water-depth distribution data of Reynolds stress in the rough sublayer, and determining the theoretical bed surface height and the water flow demarcation height of the rough sublayer according to the data; performing theoretical analysis and establishing a relational expression between the rough sublayer boundary height and the flow characteristic parameters; and substituting the rough sublayer boundary height, the theoretical bed surface height and the water flow demarcation height of the rough sublayer into the relational expression to obtain the value of the rough sublayer boundary height h o under the corresponding conditions. The method can help enrich the turbulence mechanics theory system and provide technical support for engineering application work related to fluid mechanics problems, such as fine river management and wind resource utilization.

Description

Technical Field

[0001] This invention belongs to the field of turbulent mechanics, specifically relating to a method for determining the boundary height of a rough sublayer. Background Technology

[0002] Under natural conditions, any surface with a fixed boundary possesses a certain degree of roughness, such as sand ripples on a riverbed, mountains and buildings on land, and wind turbines on the ocean. This roughness causes changes in the flow characteristics of fluids like water and air within a certain vertical range near the boundary, significantly impacting riverbed erosion and deposition, air pollutant transport, and wind turbine output. The range of these changes in flow characteristics is called the roughness sublayer, while sand ripples, mountains, buildings, and wind turbines are collectively referred to as rough elements. Generally, the boundary height of the roughness sublayer is several times greater than the height of the rough element. Determining the corresponding boundary height is of significant value for river management, air pollution control, and wind power generation.

[0003] Currently, there are two methods for determining the boundary height of the rough sublayer. Method one involves measuring the flow velocity at multiple locations along the vertical axis at intervals, and determining the critical height at which the velocity distribution pattern changes as the boundary height of the rough sublayer. Method two involves calculating the vertical distribution of turbulent kinetic energy generation and dissipation rates, and determining the critical height corresponding to their equality as the boundary height of the rough sublayer. Both methods have sufficient theoretical support; however, in practical applications, Method one has a certain degree of subjectivity, and Method two involves a large workload, making it difficult to obtain the target value quickly and accurately. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a method for determining the boundary height of a rough sublayer based on theoretical formula analysis.

[0005] Technical solution: The method for determining the boundary height of the rough sublayer according to the present invention includes the following steps:

[0006] Flow measurements were performed in a rough sub-layer flow scenario to obtain Reynolds stress distribution data along the water depth in the rough element layer, and the theoretical bed height and the water flow boundary height of the rough element layer were determined accordingly.

[0007] Theoretical analysis was performed to establish the relationship between the height of the rough sublayer boundary and the aforementioned flow characteristic parameters, i.e.

[0008] Among them, h p h is the water flow boundary height of the rough element layer. o Z0 is the boundary height of the rough sublayer, d is the theoretical bed height, and B is the coefficient.

[0009] The boundary height z0 of the rough element layer, the theoretical bed height d, and the water flow boundary height h of the rough element layer are defined. pSubstituting the values ​​into the relational formula, we obtain the corresponding roughness sublayer boundary height h under the given conditions. o The value of .

[0010] Furthermore, the rough sublayer flow scenario includes: using a rigid bar with a height of z0 to simulate a rough element, and arranging several rigid bars neatly at the bottom of the water tank to form a rough sublayer flow.

[0011] Furthermore, the formula for calculating the theoretical bed surface height d is:

[0012]

[0013] in, For Reynolds stress, Let z be the Reynolds stress gradient and z be the water depth.

[0014] Furthermore, data on the distribution of Reynolds stress along the water depth in the rough element layer were obtained, including:

[0015] For a given flow cross section, flow measurements are performed along the water depth direction using an acoustic Doppler current meter (ADV) or other flow measurement equipment, and the Reynolds stress at each measurement height of the rough element layer is obtained. Distribution data;

[0016] Furthermore, the Reynolds stress at adjacent measuring points... Dividing the difference by the spatial distance between the measuring points yields the Reynolds stress gradient. Values ​​were calculated, and the Reynolds stress gradient of the rough element layer was plotted. Scatter plot showing distribution along water depth.

[0017] Furthermore, the formula for calculating the water flow boundary height of the rough element layer is:

[0018] h p =Ct+Dd (2)

[0019] Among them, h p denoted as the water flow boundary height of the rough element layer, t is the height at which the Reynolds stress gradient abruptly changes along the water depth, d is the theoretical bed height, and C and D are coefficients.

[0020] Furthermore, the method for establishing the relationship between the rough sub-layer boundary height and the aforementioned flow characteristic parameters is as follows:

[0021] (1) Divide the water flow along the water depth direction into four regions: I, II, III, and IV. Regions I and II form the rough element layer, and regions I, II, and III form the rough sublayer. Then, the upper boundary h of region III is... o That is, the boundary height of the rough sublayer;

[0022] (2) The formulas for the vertical distribution of the flow velocity U in each region are as follows:

[0023]

[0024]

[0025] Where a and b are constants, U z0 Let z0 be the flow velocity at the boundary height of the rough element layer. h is the water flow boundary height of the rough element layer. p Flow velocity at that point The height h of the rough sub-layer boundary o The flow velocity at point H is the water depth in the tank, z is the water depth, and u is the flow velocity at point H. * κ is the frictional velocity, and κ is the Karman constant.

[0026] (3) Differentiating equations (4) and (5) respectively, we get:

[0027]

[0028] For the top of the rough element z = z0, combining equations (7) and (8) yields:

[0029]

[0030] definition Then the above formula becomes:

[0031]

[0032] (4) For the upper boundary of region III, z = h o From equation (8), we get:

[0033]

[0034] Differentiating equation (6), we get:

[0035]

[0036] Combining equations (11) and (12), we get:

[0037]

[0038] (5) For the upper boundary of region I, z = h p Then, in formula (3), U corresponds to Therefore, from equation (3), we get:

[0039]

[0040] Combining equations (14) and (15), we get:

[0041]

[0042] At the same time, from equation (7), for z = h p ,have:

[0043]

[0044] Combining equation (17) with equations (10) and (13), we get:

[0045]

[0046] Combining equations (18) and (16), we get:

[0047]

[0048] (6) For the upper boundary of region III, z = h o From equation (6), we get:

[0049]

[0050] Combining equations (10) and (13), we get:

[0051]

[0052] Combining equation (21) with equations (19) and (20), we get:

[0053]

[0054] Where B = cosh 2 (1)·tanh(1).

[0055] The present invention also provides a system for determining the boundary height of the rough sub-layer corresponding to the method described above, comprising:

[0056] The measurement and calculation unit is used to perform flow measurements in a rough sublayer flow scenario to obtain Reynolds stress distribution data along the water depth in the rough element layer, thereby determining the theoretical bed height and the water flow boundary height of the rough element layer.

[0057] The formula analysis unit is used to perform theoretical analysis and establish the relationship between the height of the rough sub-layer boundary and the aforementioned flow characteristic parameters, i.e.

[0058] Among them, h p h is the water flow boundary height of the rough element layer. o Z0 is the boundary height of the rough sublayer, d is the theoretical bed height, and B is the coefficient.

[0059] The rough element layer boundary height determination element is used to determine the rough element layer boundary height z0, the theoretical bed height d, and the water flow boundary height h of the rough element layer.p Substitute the values into the relational expression to obtain the roughness sublayer boundary height h corresponding to the corresponding condition o value.

[0060] The present invention further provides an electronic device, comprising a memory and a processor, wherein:

[0061] the memory is configured to store a computer program capable of running on the processor;

[0062] the processor is configured to, when running the computer program, execute the steps of the method for determining the roughness sublayer boundary height.

[0063] The present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer instructions, and when invoked, the computer instructions are configured to execute the steps of the method for determining the roughness sublayer boundary height.

[0064] The present invention further provides a computer program product, comprising computer programs / instructions, which when executed by a processor implement the steps of the method for determining the roughness sublayer boundary height.

[0065] Beneficial effects: Compared with the prior art, the remarkable technical effect of the present invention is: performing flow measurement in a rough sublayer flow environment to obtain water depth distribution data of Reynolds stress in the roughness element layer (0<z<z0), and determining the theoretical bed height d, the height t at which the Reynolds stress gradient mutates along the water depth, and the flow boundary height h of the roughness element layer p and other flow characteristic parameters, wherein h p =0.38t+0.62d; carrying out theoretical analysis and establishing a relational expression between the roughness sublayer boundary height h o and the above flow characteristic parameters, that is substituting the values of z0, d and h p into the relational expression, the roughness sublayer boundary height h corresponding to the corresponding condition can be obtained o ; the determination idea and calculation method of the roughness sublayer boundary height proposed by the present invention effectively overcome the deficiencies of the prior art in terms of calculation efficiency or accuracy, can obtain the boundary height of the roughness sublayer relatively quickly and accurately, and help to enrich the turbulent mechanics theoretical system and provide technical support for engineering applications involving fluid mechanics problems such as refined river management and wind resource utilization. Description of Drawings

[0066] Figure 1 is a flow chart of the method of the present invention;

[0067] Figure 2 is a schematic diagram of roughness sublayer flow and related zoning;

[0068] Figure 3 is the Reynolds stress in the roughness element layer is a scatter plot distributed along water depth;

[0069] Figure 4 is the Reynolds stress gradient in the roughness element layer is a scatter plot distributed along water depth. DETAILED DESCRIPTION OF EMBODIMENTS

[0070] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0071] As shown in Figure 1 , the method for determining the boundary height of the roughness sublayer according to the present invention comprises the following steps:

[0072] S1, simulating roughness elements by using rigid rods with a height of z0, arranging a plurality of rigid rods neatly on the bottom of a water flume, and constructing a device for roughness sublayer flow to simulate roughness sublayer flow; specifically:

[0073] Referring to Figure 2 , in one embodiment, the device for forming roughness sublayer flow comprises a plurality of rigid rods with a height of 6 cm (i.e., z0=6 cm) for simulating roughness elements, a 12 m long and 0.6 m wide variable-slope circulating straight flume system, water pools connected to the head and tail of the flume, a water pump for supplying water from the water pools to the flume, and a device for measuring Reynolds stress in the roughness element layer distribution data (such as ADV). On this basis, a group of rigid rods are inserted straight into the bottom plate of the flume, and all rigid rods are ensured to be arranged uniformly and neatly on the entire bottom plate (one rigid rod is distributed every 10 cm 2 ); a water pump is used to continuously input water flow with a constant flow rate from the inlet of the flume; a tail gate at the outlet of the flume is used to control the water depth so that the roughness elements are submerged, and the slope at the bottom of the flume is adjusted to ensure that the water depth H in the flume remains unchanged along the path. At this time, the water flow motion is divided into four regions I, II, III and IV along the water depth direction, wherein the roughness element layer is composed of region I and region II, and the roughness sublayer is composed of region I, region II and region III, then the upper boundary h of region III o is the boundary height of the roughness sublayer.

[0074] S2, measuring the flow characteristics of the roughness element layer along a measuring line to obtain the water depth distribution data of Reynolds stress in the roughness element layer (0<z<z0), and determining the magnitudes of flow characteristic parameters such as the theoretical bed surface height d, the height t at which the Reynolds stress gradient mutates along water depth, and the flow boundary height h of the roughness element layer p ;

[0075] Select a flow cross-section 5m downstream of the flume inlet, and select the centerline of this cross-section (i.e., the line equidistant from both side walls of the flume) as the measurement line. Use an Acoustic Doppler Velocimeter (ADV) or other flow measuring equipment to measure the flow characteristics in the roughness element layer (i.e., 0<z<6cm) along this measurement line (i.e., along the water depth direction), and obtain the Reynolds stress at each measurement height values, so as to plot scattered points of Reynolds stress in the roughness element layer distributed along water depth, as shown in Figure 3 . Further, dividing the difference between adjacent measuring points by the spatial distance between the measuring points can obtain the Reynolds stress gradient values, and plot a scatter diagram of Reynolds stress gradient in the roughness element layer distributed along water depth, as shown in . Figure 4 .

[0076] On this basis, calculate the theoretical bed height d, the formula is:

[0077]

[0078] wherein, z0 is the boundary height of the roughness element layer, and z is the water depth.

[0079] The d value corresponding to this embodiment is obtained as 41.7mm.

[0080] Meanwhile, according to the corresponding roughness element layer scattered points distributed along water depth Figure 3 , the height t value where mutation occurs is obtained as 41mm.

[0081] On this basis, calculate the flow boundary height h of the roughness element layer p , the calculation formula is:

[0082] h p =Ct+Dd (2)

[0083] In this embodiment, C=0.38, D=0.62, and then the h p value corresponding to this embodiment is obtained as 41.4mm.

[0084] S3, performing theoretical analysis and establishing a relational expression between the roughness sublayer boundary height h o and the flow characteristic parameters z0, d, h p , specifically comprising the following steps:

[0085] S31, it is known that the vertical distribution formula of flow velocity U corresponding to each region is as follows:

[0086]

[0087] wherein, a and b are constants, Let z0 be the flow velocity at the boundary height of the rough element layer. h is the water flow boundary height of the rough element layer. p Flow velocity at that point The height h of the rough sub-layer boundary o The flow velocity at the location, H is the water depth in the tank, and u * κ represents the frictional flow velocity, and κ is the Karman constant. In this embodiment, κ = 0.4.

[0088] S32. Differentiating equations (4) and (5) respectively, we get:

[0089]

[0090] For the top of the rough element (z = z0), combining equations (7) and (8) yields:

[0091]

[0092] definition Then the above formula becomes:

[0093]

[0094] S33, For the upper boundary of region III (z = h) o From equation (8), we get:

[0095]

[0096] Differentiating equation (6), we get:

[0097]

[0098] Combining equations (11) and (12), we get:

[0099]

[0100] S34. For the upper boundary of region I (z = h) p ), then in formula (3) U corresponds to U hp Therefore, from equation (3), we get:

[0101]

[0102] Combining equations (14) and (15), we get:

[0103]

[0104] At the same time, from equation (7), for z = h p ,have:

[0105]

[0106] Combining equation (17) with equations (10) and (13), we get:

[0107]

[0108] Combining equations (18) and (16), we get:

[0109]

[0110] S35. For the upper boundary of region III (z = h) o From equation (6), we get:

[0111]

[0112] Combining equations (10) and (13), we get:

[0113]

[0114] Combining equation (21) with equations (19) and (20), we get:

[0115]

[0116] Right now:

[0117]

[0118] S4. The z0, d, and h measured in step S2 p Substituting the value into relation (23), the corresponding roughness sublayer boundary height h can be obtained. o The value of .

[0119] In this embodiment, z0 = 0.06m, d = 0.0417m, and h are... p Substituting =0.0414m into equation (23), the corresponding rough sub-layer boundary height h can be obtained through trial calculation. o =0.4482m.

[0120] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for determining the boundary height of a rough sublayer, characterized in that, Includes the following steps: Flow measurements were performed in a rough sub-layer flow scenario to obtain Reynolds stress distribution data along the water depth in the rough element layer, and the theoretical bed height and the water flow boundary height of the rough element layer were determined accordingly. Theoretical analysis was performed to establish the relationship between the height of the rough sublayer boundary and the aforementioned flow characteristic parameters, i.e. Among them, h p h is the water flow boundary height of the rough element layer. o Z0 is the boundary height of the rough sublayer, d is the theoretical bed height, and B is the coefficient. The boundary height z0 of the rough element layer, the theoretical bed height d, and the water flow boundary height h of the rough element layer are defined. p Substituting the values ​​into the relational formula, we obtain the corresponding roughness sublayer boundary height h under the given conditions. o The value of .

2. The method for determining the boundary height of the rough sub-layer according to claim 1, characterized in that, The rough sublayer flow scenario includes: using a rigid bar with height z0 to simulate a rough element, and arranging several rigid bars neatly at the bottom of a water tank to form a rough sublayer flow.

3. The method for determining the boundary height of the rough sub-layer according to claim 1, characterized in that, The formula for calculating the theoretical bed surface height d is: in,- For Reynolds stress, Let z be the Reynolds stress gradient and z be the water depth.

4. The method for determining the boundary height of the rough sub-layer according to claim 1, characterized in that, Data on the distribution of Reynolds stress along water depth in the rough element layer were obtained, including: For a given flow cross section, flow measurements are performed along the water depth direction using an acoustic Doppler current meter (ADV) or other flow measurement equipment, and the Reynolds stress at each measurement height of the rough element layer is obtained. Distribution data; Furthermore, the Reynolds stress at adjacent measuring points is... Dividing the difference by the spatial distance between the measuring points yields the Reynolds stress gradient. The dz value was calculated, and the Reynolds stress gradient of the rough element layer was plotted. A scatter plot showing the distribution of dz along water depth.

5. The method for determining the boundary height of the rough sub-layer according to claim 1, characterized in that, The formula for calculating the water flow boundary height of the rough element layer is: h p =Ct+F (2) Among them, h p denoted as the water flow boundary height of the rough element layer, t is the height at which the Reynolds stress gradient abruptly changes along the water depth, d is the theoretical bed height, and C and D are coefficients.

6. The method for determining the boundary height of the rough sub-layer according to claim 1, characterized in that, The method for establishing the relationship between the rough sub-layer boundary height and the above-mentioned flow characteristic parameters is as follows: (1) Divide the water flow along the water depth direction into four regions: I, II, III, and IV. Regions I and II form the rough element layer, and regions I, II, and III form the rough sublayer. Then, the upper boundary h of region III is... o That is, the boundary height of the rough sublayer; (2) The formulas for the vertical distribution of the flow velocity U in each region are as follows: Where a and b are constants, U z0 Let z0 be the flow velocity at the boundary height of the rough element layer. h is the water flow boundary height of the rough element layer. p Flow velocity at that point The height h of the rough sub-layer boundary o The flow velocity at point H is the water depth in the tank, z is the water depth, and u is the flow velocity at point H. * κ is the frictional velocity, and κ is the Karman constant. (3) Differentiating equations (4) and (5) respectively, we get: For the top of the rough element z = z0, combining equations (7) and (8) yields: definition Then the above formula becomes: (4) For the upper boundary of region III, z = h o From equation (8), we get: Differentiating equation (6), we get: Combining equations (11) and (12), we get: (5) For the upper boundary of region I, z = h p Then, in formula (3), U corresponds to U hp Therefore, from equation (3), we get: Combining equations (14) and (15), we get: At the same time, from equation (7), for z = hp, we have: Combining equation (17) with equations (10) and (13), we get: Combining equations (18) and (16), we get: (6) For the upper boundary z = ho of region III, we get from equation (6): Combining equations (10) and (13), we get: Combining equation (21) with equations (19) and (20), we get: Right now: Where B = cosh 2 (1)·tanh(1).

7. A system for determining the height of a rough sub-layer boundary, characterized in that, include: The measurement and calculation unit is used to perform flow measurements in a rough sublayer flow scenario to obtain Reynolds stress distribution data along the water depth in the rough element layer, thereby determining the theoretical bed height and the water flow boundary height of the rough element layer. The formula analysis unit is used to perform theoretical analysis and establish the relationship between the height of the rough sub-layer boundary and the aforementioned flow characteristic parameters, i.e. Among them, h p h is the water flow boundary height of the rough element layer. o Z0 is the boundary height of the rough sublayer, d is the theoretical bed height, and B is the coefficient. The rough element layer boundary height determination element is used to determine the rough element layer boundary height z0, the theoretical bed height d, and the water flow boundary height h of the rough element layer. p Substituting the values ​​into the relational formula, we obtain the corresponding roughness sublayer boundary height h under the given conditions. o The value of .

8. An electronic device, characterized in that, Includes memory and processor, wherein: Memory is used to store computer programs that can run on a processor; A processor, configured to, while running the computer program, perform the steps of the method for determining the height of the rough sublayer boundary as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when invoked, are used to perform the steps of the method for determining the boundary height of the rough sub-layer as described in any one of claims 1-6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method for determining the boundary height of the rough sub-layer according to any one of claims 1-6.

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