A steady-state prediction method for complex hydraulic systems with or without pressure mixing connection

Abstract

This invention provides a steady-state prediction method for complex hydraulic systems with both pressurized and unpressurized sections. It divides the main water conveyance structure of the water diversion system into pressurized and unpressurized structures, and quantifies the unpressurized sections as pressurized sections, cleverly avoiding the mathematical difficulties of directly solving the steady-state conditions of the unpressurized sections. This method greatly simplifies the complexity of steady-state numerical simulation of water diversion systems, making it possible to numerically simulate complex hydraulic systems with both pressurized and unpressurized sections. This invention quantifies the unpressurized sections as pressurized sections and then uses a matrix structure method for solving the problem. This calculation method has good iterative stability and high calculation accuracy. Furthermore, it has strong adaptability to changes in the layout of the water diversion system with both pressurized and unpressurized sections, greatly improving the applicability of numerical simulations for complex water diversion projects in later stages.

Description

Technical Field

[0001] This invention relates to a numerical simulation calculation method for hydraulic transient processes, and in particular to a steady-state prediction method for complex hydraulic systems with and without pressure, applicable to water conservancy and hydropower projects. Background Technology

[0002] Water diversion projects can be classified into pressurized water diversion, unpressurized water diversion, and combined pressurized and unpressurized water diversion according to the pressure state of their water pipelines. When the flow parameters (pressure, density, velocity, etc.) at each spatial point within a hydraulic system do not change with time, the hydraulic system can be considered to be in a steady state, or simply steady state.

[0003] Currently, most pressurized water conveyance projects and hydropower station water diversion projects adopt pressurized system structures. Calculation methods for the transient processes of pressurized systems are relatively mature, such as the method of characteristics and the structural matrix method. Extensive practical engineering testing has verified their high calculation accuracy, meeting the needs of these projects. However, due to the simplicity and lower cost of open channels, which help alleviate water hammer pressure in water conveyance systems, the structural methods of arbitrarily connecting open channels and pressurized pipelines are becoming increasingly common. For these complex hydraulic systems with both pressurized and unpressurized connections, numerical simulation of the transient processes is quite challenging.

[0004] Currently, most computational software programs require a specific water level at the inlet or outlet of the open channel as the starting point for calculating water diversion projects with open channel sections. This typically means the software requires the open channel to be directly connected to an upper or lower reservoir. However, it struggles to handle situations where the open channel is located arbitrarily within the water diversion project. This is because, unlike pressurized pipelines where head loss is an explicit function of flow rate, open channel flow head loss is an implicit function of flow rate and water depth, with water depth being a function of head loss. Therefore, methods effective for solving pressurized systems are not applicable to solving steady-state conditions for open channel flow.

[0005] For the reasons mentioned above, compared with the numerical simulation of pressurized systems, the research progress of numerical simulation of complex pressurized and unpressurized hybrid hydraulic systems is relatively slow and difficult to meet the needs of current engineering design. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of difficulty in solving the steady-state conditions of complex hydraulic systems with and without pressure in existing methods, and the low accuracy. This invention proposes a steady-state prediction method for complex hydraulic systems with and without pressure, which can perform steady-state simulation prediction for complex water diversion systems with different layouts, and has high calculation accuracy and fast iteration.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A steady-state prediction method for complex coupled and uncompressed hydraulic systems, characterized by the following steps:

[0009] Step (1) divides the main water conveyance structure of the water diversion and transmission system into pressurized structure and unpressurized structure;

[0010] Step (2) divide the unpressurized structure into sections and assume that the water level and flow rate at the end section of the unpressurized structure are its corresponding design water level and design flow rate;

[0011] Step (3): Using the water level and flow rate at the end section of the unpressurized structure as the starting point for calculation, the water level and flow rate at each section of the unpressurized structure are recursively calculated.

[0012] Step (4): Using the constraint that the average cross-sectional area and total head loss of the unpressurized section and the equivalent pressurized section are equal, the unpressurized section is equivalent to the pressurized section.

[0013] Step (5): Establish the structural matrix equation for the entire pressurized water supply system and solve for the hydraulic elements at the end of the pressure pipeline after quantization.

[0014] Step (6) converts the hydraulic elements at the end of the pressure pipeline into the water level and flow rate at the end section of the original unpressurized section;

[0015] Step (7): Compare the water level and flow rate of the end section obtained in the last iteration with the water level and flow rate of the end section obtained in the previous iteration. If the accuracy requirements are met, proceed to the next step; if the accuracy requirements are not met, take the water level and flow rate of the end section obtained in the last iteration as known values ​​and return to step (3).

[0016] Step (8): For the unpressurized section, the water level and flow rate at the end section obtained in the last iteration are used to recursively calculate the steady state of each section in the unpressurized section. For the pressurized section, the water level and flow rate obtained in the last iteration are used as the steady state of each hydraulic node.

[0017] Specifically, in step (1), the pressureless structure refers to a structure in which the fluid is in direct contact with the atmosphere during its movement, while the pressurized structure refers to a structure in which the fluid is not in direct contact with the atmosphere during its movement.

[0018] Specifically, in step (2), the unpressurized section can be divided into M segments, and the segment nodes can be marked as 1, 2, ..., m+1. Meanwhile, the water level corresponding to the cross-section where the (m+1)th node of the unpressurized section is located is assumed to be the design water level, and the corresponding flow rate is assumed to be the design flow rate, as shown in the following formula:

[0019] Z m+1 (k)=Z m+1，P (1)

[0020] Qi (k)=Q m+1,p i = 1, 2, 3, ..., m+1 (2)

[0021] In the formula: k is the number of iterations; Z m+1，P Z represents the design water level corresponding to the cross-section where the (m+1)th node is located; m+1 (k) represents the water level obtained by the cross-section where the (m+1)th node is located in the kth iteration; Q m+1，P Q represents the design flow rate corresponding to the cross-section where the (m+1)th node is located; i (k) represents the flow rate of the section containing node i in the kth iteration; since it is under steady-state conditions, the flow rate of each section in the unpressurized section is equal everywhere.

[0022] Specifically, in step (3), the recursive calculation of water level and flow rate at each section of the unpressurized structure refers to taking the section where the (m+1)th node of the unpressurized section is located as the starting point of the calculation, using the energy conservation equation, and taking the hydraulic elements at the (m+1)th node as known quantities, to calculate up to the section where the mth node is located, and then from the section where the mth node is located to the (m-1)th node, and so on, until the inlet section of the unpressurized section, i.e., the section where the first node is located. The recursive formula is as follows:

[0023]

[0024] In the formula: Z i (k) represents the water level obtained by the cross-section where the i-th node is located in the k-th iteration; B i Z is the average cross-sectional width of the section containing the i-th node; i，d ζ is the bottom elevation of the section containing the i-th node; i Let Z be the head loss coefficient at the section where the i-th node is located. The recursive equation contains the unknown Z on the right-hand side. i (k) can be obtained through iterative calculation to obtain its numerical solution.

[0025] Specifically, in step (4), quantifying the unpressurized section as a pressurized section means replacing the average cross-section of all sections of the unpressurized section with the equivalent cross-section of the pressurized structure, and ensuring that the total head loss of both is equal. Using these two conditions as constraints, all unpressurized structures are quantified as their corresponding pressurized structures. The calculation formula is as follows:

[0026]

[0027]

[0028] In the formula, λ is the friction head loss coefficient. This formula can be used to quantify the unpressurized section into an area A in the k-th iteration. eq (k), with length L eq (k) is a pressurized pipeline.

[0029] Specifically, step (5) involves the structural matrix equations of the pressure-driven water conveyance system, as shown below:

[0030]

[0031] In the formula: [A] is the overall matrix of the entire water diversion and conveyance system; This is the pressure head vector of the entire water diversion and conveyance system; Let be the flow vector of the entire water supply system. It is worth noting that during the matrix structure method solution, one iterative calculation of the equivalent pressurized pipeline has already been completed.

[0032] Specifically, in step (6), the hydraulic elements at the end of the pressure pipeline are converted into the water level and flow rate at the end of the unpressurized section. The conversion formula is as follows:

[0033] Z m+1 (k+1)=h m+1 (k+1)+Z m+1，d (7)

[0034] Q m+1 (k+1)=q m+1 (k+1) (8)

[0035] Specifically, in step (7), the water level and flow rate at the end section obtained in the last iteration are compared with those obtained in the previous iteration, and the judgment formula is as follows:

[0036] |Z m+1 (k+1)-Z m+1 (k)|<ξ1 (9)

[0037] |Q m+1 (k+1)-Q m+1 (k)|<ξ2 (10)

[0038] In the formula: ξ1 and ξ2 are the allowable error of water level and the allowable error of flow rate, respectively.

[0039] Specifically, in step (8), the water level and flow rate of the last cross-section obtained in the last iteration are used to recursively deduce the first cross-section as the stable state of each cross-section in the unpressurized section. The deduction formula is as follows:

[0040]

[0041] In a second aspect of the present invention, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the above-described steady-state prediction method for complex coupled hydraulic systems with and without pressure.

[0042] In a third aspect of the present invention, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the program, implements the aforementioned steady-state prediction method for complex coupled hydraulic systems with and without pressure.

[0043] This invention provides a steady-state prediction method for complex coupled hydraulic systems with and without pressure, which has the following advantages:

[0044] 1) The idea of ​​equating the unpressurized section with the pressurized section proposed in this invention cleverly avoids the mathematical difficulties of directly solving the steady-state conditions of the unpressurized section. This method can greatly simplify the complexity of steady-state numerical simulation of water diversion and conveyance system, making it possible to numerically simulate complex hydraulic systems with and without pressurization.

[0045] 2) The numerical simulation method for complex hydraulic systems with and without pressure proposed in this invention, by treating the unpressurized section as a pressurized section in the steady-state solution process—the most challenging part of numerical simulation—and then using the matrix structure method for solution, exhibits good iterative stability and high calculation accuracy. Furthermore, it demonstrates strong adaptability to variations in the layout of water diversion and conveyance systems with and without pressure, significantly improving the applicability of numerical simulations for complex water diversion and conveyance projects in later stages. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the typical complex pressurized and unpressurized hybrid hydraulic system of the present invention.

[0047] Figure 2 This is a schematic diagram illustrating the principle of converting the pressureless section into a pressure section according to the present invention.

[0048] Figure 3 This is a steady-state energy head distribution diagram of the complex pressurized and unpressurized hybrid hydraulic system of the present invention.

[0049] Figure 4 This is a schematic diagram illustrating the steady-state solution principle of the complex pressurized and unpressurized hybrid hydraulic system of the present invention. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0051] A schematic diagram of the typical complex pressurized and unpressurized hybrid hydraulic system layout of the present invention is shown below. Figure 1 As shown in the figure. The figure shows: upstream reservoir 1, upstream reservoir side flow regulating valve 21, upstream pressure pipeline 31, open channel upstream side flow regulating valve 22, open channel 4, open channel downstream side valve 23, downstream pressure pipeline 32, downstream reservoir side valve 24, and downstream reservoir 5.

[0052] In this embodiment, the upstream reservoir's design water level is 1046.00m, and the valve's flow area is 10.18m². 2 The open channel is 3818.00m long, and the downstream reservoir has a design water level of 750.00m. The parameters of the pressurized pipeline and the open channel are shown in Table 1-2.

[0053] Table 1 Pipeline Parameters

[0054] Pipeline section number Length (m) <![CDATA[Area (m 2 )]]> Manning roughness coefficient Wave speed (m / s) 31 1000 10.18 0.014 900 32 1500 3.14 0.012 1200

[0055] Table 2 Open Channel Parameters

[0056]

[0057] Taking this embodiment as an example, the steps of a steady-state prediction method for a complex coupled hydraulic system with and without pressure are as follows:

[0058] Step (1) divides the main water conveyance structure of the water diversion and transmission system into a pressurized structure and an unpressurized structure; in this embodiment, the water conveyance structure can be divided into an unpressurized structure (open channel 4) and a pressurized structure (upstream pressure pipeline 31, downstream pressure pipeline 32);

[0059] Step (2) involves segmenting the unpressurized structure and assuming that the water level and flow rate at the end section of the unpressurized structure correspond to its design water level and design flow rate. In this embodiment, the open channel section is divided into 40 segments, with node 1 marking the first section and node m+1 marking the last section. It is assumed that the water level at the end of open channel 4 is the design water level of 834.62m and the flow rate at the end is the design flow rate of 72.06m³. 3 / s;

[0060] Step (3) uses the water level and flow rate at the end section of the unpressurized structure as the starting point for calculation, and recursively calculates the water level and flow rate at each section of the unpressurized structure. In this embodiment, the algorithm in equation (3) is used, with the end water level of open channel 4 being 834.62m and the end flow rate being 72.06m. 3 The water level and flow rate of the first 40 cross-sections were calculated using a / s method. Since this was under steady-state conditions, the flow rate of the first 20 cross-sections in the unpressurized section was constant at 72.06 m³ / s. 3 / s, with water levels of 835.07m, 837.98m, ..., 1030.01m respectively.

[0061] Step (4) uses the constraint that the average cross-sectional area and total head loss of the unpressurized section and the equivalent pressurized section are equal to be equal, and then the unpressurized section is equivalently converted into a pressurized section; in this embodiment, it can be deduced from equations (4) and (5) that the open channel 4 can be equivalently converted into an area of ​​37.90m². 2 A pressurized pipeline with a length of 784,545.13m;

[0062] Step (5): Establish the structural matrix equation for the entire pressurized water supply system and solve for the hydraulic elements at the end of the pressure pipeline after quantification. In this embodiment, after solving, the internal water pressure at the end of the pressure pipeline is -188.96m (this value is only a calculation process value and has no physical meaning), and the flow rate is 72.05m³. 3 / s;

[0063] Step (6) converts the hydraulic elements at the end of the pressure pipeline into the water level and flow rate at the end section of the original unpressurized section. In this embodiment, the center elevation of the pipeline end is 1023.40m. From equations (7) and (8), the water level at the original end section can be calculated to be 834.44m and the flow rate to be 72.05m³. 3 / s;

[0064] Step (7): Compare the water level and flow rate of the terminal section obtained in the last iteration with those obtained in the previous iteration. If the accuracy requirements are met, proceed to the next step; if the accuracy requirements are not met, use the water level and flow rate of the terminal section obtained in the last iteration as known values ​​and return to step (3). In this embodiment, the allowable error ξ1 for water level is 1×10⁻⁶. -6 m, the allowable error of flow rate ξ2 is 1×10 -8 m 3 / s. The water level at the final cross-section obtained from the last iteration was 834.44m, and the flow rate was 72.05m³ / s. 3 / s. The water level and flow rate at the last calculated terminal section were 834.62 m and 72.06 m³, respectively. 3 If the values ​​per second are all greater than the allowable error, then the final water level of 834.44 m and the final flow rate of 72.05 m³ / s obtained from the last iteration should be used. 3 / s is taken as a known value, and the process returns to step (3) to recalculate until the allowable error is met, and then proceeds to the next step;

[0065] Step (8): For the unpressurized section, the water level and flow rate at the end section obtained from the last iteration are used to advance to the beginning section as the stable state of each section in the unpressurized section. For the pressurized section, the water level and flow rate obtained from the last iteration are used as the stable state of each hydraulic node. In this embodiment, the water level of each hydraulic node can be calculated from equation (11). The water levels at the beginning and end of the upstream pressure pipeline 31 are 1045.18 and 1030.79 m, respectively; the water levels at the beginning and end of the open channel are 1030.19 and 834.80 m, respectively; and the water levels at the beginning and end of the downstream pressure pipeline 32 are 834.21 and 752.25 m, respectively.

[0066] In this embodiment, the steady-state energy head distribution of the unpressurized hybrid hydraulic system is as follows: Figure 3 As shown in the figure, it can be seen that the above method is feasible.

[0067] From the above description of the embodiments, those skilled in the art will clearly understand that the facilities of the present invention can be implemented using software plus necessary general-purpose hardware platforms. Embodiments of the present invention can be implemented using existing processors, or by dedicated processors used for this or other purposes for suitable systems, or by hardwired systems. Embodiments of the present invention also include non-transitory computer-readable storage media, comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon; such machine-readable media can be any available medium accessible by a general-purpose or special-purpose computer or other machine with a processor. For example, such machine-readable media can include RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disc storage, disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the required program code in the form of machine-executable instructions or data structures and is accessible by a general-purpose or special-purpose computer or other machine with a processor. When information is transmitted or provided to a machine via a network or other communication connection (hardwired, wireless, or a combination of hardwired and wireless), that connection is also considered a machine-readable medium.

[0068] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A steady state prediction method of a complex hydraulic system with or without pressure mixing and connection, characterized in that Includes the following steps: Step (1) divides the main water conveyance structure of the water diversion and transmission system into pressurized structure and unpressurized structure; Step (2): Divide the unpressurized structure into sections, and assume that the water level and flow rate at the end section of the unpressurized structure are its corresponding design water level and design flow rate; Step (3): Using the water level and flow rate at the end section of the unpressurized structure as the starting point for calculation, the water level and flow rate at each section of the unpressurized structure are recursively calculated. Step (4): Using the constraint that the average cross-sectional area and total head loss of the unpressurized section and the equivalent pressurized section are equal, the unpressurized section is equivalent to the pressurized section. Step (5): Establish the structural matrix equation for the entire pressurized water supply system and solve for the hydraulic elements at the end of the pressure pipeline after quantization. Step (6) converts the hydraulic elements at the end of the pressure pipeline into the water level and flow rate at the end section of the original unpressurized section; Step (7): Compare the water level and flow rate of the end section obtained in the last iteration with the water level and flow rate of the end section obtained in the previous iteration. If the accuracy requirements are met, proceed to the next step; if the accuracy requirements are not met, take the water level and flow rate of the end section obtained in the last iteration as known values ​​and return to step (3). Step (8): For the unpressurized section, the water level and flow rate of the last end section obtained in the last iteration are used to advance to the first end section as the stable state of each section of the unpressurized section; for the pressurized section, the water level and flow rate obtained in the last iteration are used as the stable state of each hydraulic node. The pressureless structure in step (1) specifically refers to a structure in which the fluid is in direct contact with the atmosphere during its movement, while the pressurized structure specifically refers to a structure in which the fluid is not in direct contact with the atmosphere during its movement.

2. The steady state prediction method of a complex hydraulic system with or without pressure mixing according to claim 1, characterized in that: In step (2), the unpressurized section is divided into M segments, and the segment nodes can be marked as 1, 2, ..., m+1; at the same time, the water level corresponding to the cross section where the m+1 node of the unpressurized section is located is assumed to be the design water level, and the corresponding flow rate is assumed to be the design flow rate, as shown in the following formula: （1） （2） In the formula: k is the number of iterations; This represents the design water level corresponding to the cross-section where the (m+1)th node is located. This is the water level obtained by the cross section where the (m+1)th node is located in the kth iteration; This represents the design flow rate corresponding to the cross section where the (m+1)th node is located. Let be the flow rate of the section containing node i in the kth iteration; since it is under steady-state conditions, the flow rate of each section in the unpressurized section is equal everywhere.

3. The steady-state prediction method for a complex coupled hydraulic system with and without pressure as described in claim 1, characterized in that: In step (3), the recursive calculation of water level and flow rate at each section of the unpressurized structure refers to taking the section where the (m+1)th node of the unpressurized section is located as the starting point of the calculation, using the energy conservation equation, and taking the hydraulic elements at the (m+1)th node as known quantities, to calculate up to the section where the mth node is located, and then from the section where the mth node is located to the (m-1)th node, and so on, until the inlet section of the unpressurized section, i.e., the section where the first node is located; the recursive formula is as follows: （3） In the formula: Let be the water level obtained by the cross section where the i-th node is located in the k-th iteration; is the average cross-sectional width of the section where the i-th node is located; Let be the bottom elevation of the section where the i-th node is located; Let be the head loss coefficient of the section where the i-th node is located; the recursive formula contains an unknown on the right side of the equation. The numerical solution can be obtained through iterative calculation.

4. The steady-state prediction method for a complex coupled hydraulic system with and without pressure as described in claim 1, characterized in that: In step (4), quantifying the unpressurized section as a pressurized section means replacing the average cross-section of all sections of the unpressurized section with the equivalent cross-section of the pressurized structure, and ensuring that the total head loss of the two is equal. Using these two conditions as constraints, all unpressurized structures are quantified as their corresponding pressurized structures. The calculation formula is as follows: （4） （5） In the formula: This is the head loss coefficient along the friction length; using this formula, the unpressurized section is equivalently quantified into area in the k-th iteration. , length is Pressurized pipelines.

5. The steady-state prediction method for a complex coupled hydraulic system with and without pressure as described in claim 1, characterized in that: The structural matrix equation for the pressurized water conveyance system in step (5) is shown below: （6） In the formula: This is the overall matrix of the entire water diversion and conveyance system; This is the pressure head vector of the entire water diversion and conveyance system; This is the flow vector for the entire water diversion and conveyance system.

6. The steady-state prediction method for a complex coupled hydraulic system with and without pressure as described in claim 1, characterized in that: In step (6), the hydraulic elements at the end of the pressure pipeline are converted into the water level and flow rate at the end of the unpressurized section. The conversion formula is as follows: （7） （8）。 7. The steady-state prediction method for a complex coupled hydraulic system with and without pressure as described in claim 1, characterized in that: In step (7), the water level and flow rate at the end section obtained in the last iteration are compared with those obtained in the previous iteration. The judgment formula is as follows: （9） （10） In the formula: , These are the allowable errors for water level and flow rate, respectively. In step (8), the water level and flow rate at the end section obtained from the last iteration are used to extrapolate to the beginning section, which serves as the stable state of each section in the unpressurized section. The calculation formula is as follows: （11）。 8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steady-state prediction method for complex coupled hydraulic systems with and without pressure as described in any one of claims 1 to 7.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steady-state prediction method for complex coupled hydraulic systems with and without pressure as described in any one of claims 1 to 7.

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