Water hammer eliminating method for long-distance pressure water delivery system

Abstract

The invention discloses a water hammer eliminating method for a long-distance pressure water conveying system, and belongs to the technical field of safety protection of long-distance pressure water conveying systems in water conservancy projects. The scheme based on numerical simulation and dynamic parameter optimization is provided for solving the problems that according to an existing method, model construction is complex and prone to errors, simulation precision is insufficient, parameter selection is extensive, and optimization lacks a scientific convergence mechanism. According to the method, a transient hydraulic model is constructed, typical working conditions are simulated to recognize risk points, protection device parameters are dynamically determined, the air supply time of an air valve is 1.2 times of the round-trip time of water hammer waves, the volume of an eliminator is calculated according to V = k * Q * delta t, and the closing time of a slow closing valve and the like are used as variables for iterative optimization till triple convergence conditions are met. According to the method, the number of eliminators can be reduced, the investment is reduced, the negative pressure absolute value is reduced, the system safety and economy are improved, the modeling time is shortened to be within 2 hours, and the topology error rate is reduced to be 0.5% or below.

Description

Technical Field

[0001] This invention relates to the field of safety protection technology for long-distance pressurized water conveyance systems in water conservancy projects, specifically to a water hammer elimination method based on numerical simulation and dynamic parameter optimization. Background Technology

[0002] Long-distance pressurized water transmission systems are critical infrastructure for inter-basin water transfer, urban water supply, and industrial circulating water transportation. They typically consist of pipelines, pumping stations, valves, and auxiliary equipment. These systems can have pipeline lengths ranging from tens to hundreds of kilometers, with large diameters (DN800–DN2000), and significant terrain undulations. During operation, they frequently undergo transient operations such as pumping station start-ups and shutdowns, and valve adjustments. Due to the inertia of water flow, the pressure within the pipeline fluctuates dramatically, generating water hammer. Water hammer pressure waves propagate at near-sound speeds, potentially causing excessive positive pressure leading to pipe bursts, or negative pressure causing water column separation and subsequent re-merging, resulting in secondary impacts that severely threaten structural safety and operational continuity. Therefore, water hammer protection is a core technical aspect for ensuring the safety of water transmission systems.

[0003] In existing technologies, commonly used water hammer protection devices mainly fall into four categories: (1) Composite air valve, installed at the high point of the pipeline, is used for exhaust and air replenishment. It introduces external gas to buffer negative pressure and prevent the water column from breaking. It is the standard configuration to deal with water column separation caused by terrain undulation. (2) A two-stage slow-closing valve is installed at the pump outlet. It controls the rate of change of flow velocity by fast and slow closing in stages, suppressing water hammer energy input from the source and forming the first line of defense for pump station protection. (3) Water hammer eliminator, which uses the compressibility of pre-charged gas to directly absorb the energy of local positive pressure fluctuations, is suitable for pipe sections where air valves cannot be installed; (4) Voltage regulating tower / chamber provides free water surface reflection of water hammer waves, with significant protection effect but high cost, and is mostly used in critical nodes. The above devices have certain effects in local applications, but they are obviously insufficient in the overall protection of long-distance, complex terrain and multi-condition systems.

[0004] The existing technology has the following shortcomings: First, the model building process is complex and prone to errors.

[0005] Existing methods require manual integration of heterogeneous data from multiple sources, such as CAD pipeline diagrams, DEM topographic data, and pump station parameters. The fusion of topographic and pipeline parameters relies on manual verification, which is prone to topological errors (such as pipeline intersections and node misalignments), leading to model distortion. In the introduction of computer-aided design technology, the current approach involves digitizing traditional paper drawings and then manually integrating them, continuing the early discipline-specific design model (pipelines, topography, and equipment are independent), resulting in difficulties in data fusion. Existing technologies lack a GIS-driven automatic data association mechanism; different data sources have inconsistent coordinate systems and mismatched attribute fields, requiring manual correction one by one, which is inefficient and has a high error rate. Accordingly, this patent application establishes a novel technical approach that utilizes the GIS data integration function of the MIKE+ platform to automatically construct a 3D topological model.

[0006] Second, the transient simulation is not accurate enough to accurately predict water column separation.

[0007] Existing water hammer calculation software mostly employs rigid water hammer models, failing to utilize a full cavitation model, resulting in distortions in the simulation of the gas-liquid phase transition process under negative pressure. Early water hammer calculations in this field were based on simplified theories such as the Joukowski formula, assuming that water is incompressible and the pipe walls are rigid. While this assumption is acceptable for short-distance systems, the classical theoretical framework has been retained for long-distance systems. Existing technologies do not set reasonable vaporization pressure thresholds (e.g., 0.04 MPa) or consider the subvaporization effect of dissolved gases in water (e.g., a 0.06 MPa warning), leading to inaccurate predictions of the location and extent of water column separation. Accordingly, this patent application establishes a precise simulation technology approach that utilizes a full cavitation model and combines physical mechanisms to set dual thresholds.

[0008] Third, the selection of device parameters is crude and disconnected from the dynamic characteristics of the system.

[0009] Existing technologies for calculating the effective area of ​​air valves, the closing time of slow-closing valves, and the volume of eliminators often rely on empirical formulas or fixed ratios, failing to adaptively calculate based on dynamic characteristics (such as maximum vacuum volume and pressure peak duration Δt) from transient simulation outputs. In the early stages of introducing numerical simulation, the technical approach in this field was to use simulation results as a "reference," with final selection still depending on design manual formulas derived from measured data of small-scale pipeline networks, resulting in a hybrid "simulation + experience" model. Existing technologies lack a dynamic parameter extraction mechanism based on simulation time-history curves, causing key parameters such as air replenishment time and volume to become disconnected from transient processes such as water hammer wave propagation and valve action, leading to over- or under-design of device capacity. Correspondingly, this patent application establishes a dynamic selection technology approach based on setting the air replenishment time (1.2 times) based on the water hammer wave round-trip time and calculating the eliminator volume (V=k·Q·Δt) based on the flow rate and pressure peak duration.

[0010] Fourth, the optimization process lacks a scientific convergence mechanism, resulting in low efficiency.

[0011] Existing methods rely on manual trial-and-error verification cycles, lacking clear parameter adjustment priorities and iteration termination conditions, making it difficult to balance safety and economy. Current technologies fail to identify the sensitivity differences of parameters such as the closing time of the slow-closing valve and the area of ​​the air valve to pressure response, and also lack a triple convergence criterion of "pressure compliance investment change rate ≤ 4% for three consecutive stable iterations," resulting in time-consuming optimization and a tendency to get trapped in local optima. Correspondingly, this patent application establishes a closed-loop iterative optimization technique based on parameter sensitivity ranking and multi-objective convergence criteria.

[0012] Fifth, the multi-condition verification is insufficient, and the reliability of the solution is questionable.

[0013] Existing technologies typically only verify a single worst-case scenario, lacking sufficient verification for multiple scenarios such as normal pump shutdown, accidental pump shutdown, valve misoperation, and sudden flow changes. Furthermore, they fail to perform reverse verification of the simulation results' reliability. Existing technologies lack a statistical verification mechanism for pressure fluctuations under multiple operating conditions and do not compare simulated values ​​with theoretical estimates using the Zhukowski formula, making it impossible to assess whether numerical errors are controllable. In contrast, this patent application establishes a high-confidence verification technology route covering four typical operating conditions, requiring a deviation of ≤10% between simulated and theoretical values.

[0014] Sixth, the model calibration standards are vague, affecting the basic accuracy.

[0015] Existing methods lack clear guidelines regarding the number of monitoring points (e.g., 10–20) and error limits, making it difficult for technicians to determine the effectiveness of calibration. Early model calibration relied on manual adjustments using a small number of monitoring points, leading to a tradition of "experience-based calibration." Current technologies do not explicitly define the representativeness of monitoring points and the meaning of error limits in line with industry practices for high-precision models. Correspondingly, this patent application establishes a standardized calibration technical route based on representative monitoring points and commonly used engineering error standards.

[0016] In summary, existing methods for eliminating water hammer in long-distance pressurized water conveyance systems suffer from systemic deficiencies in model building, transient simulation, parameter selection, optimized control, and verification calibration. Therefore, there is an urgent need for a water hammer elimination method capable of high-precision risk identification, dynamic parameter adaptation, closed-loop iterative optimization, and high-confidence verification under multiple operating conditions. This patent, "Water Hammer Elimination Method for Long-Distance Pressurized Water Conveyance Systems," addresses these technological gaps by constructing a six-step intelligent deployment and optimization system to systematically resolve the shortcomings of existing technologies. Summary of the Invention

[0017] The purpose of this invention is to provide a method for eliminating water hammer in long-distance pressurized water conveyance systems that can adaptively determine key parameters of water hammer protection devices based on the transient response characteristics of the system, so as to overcome the defects in the prior art that lead to protection failure or waste of resources due to the device selection being out of touch with the actual dynamic process of water hammer.

[0018] To achieve the above objectives, the water hammer elimination method for a long-distance pressurized water conveyance system of the present invention includes the following steps: S1. Based on the pipeline topology, terrain elevation, and equipment parameters of the water conveyance system, construct a transient hydraulic model that includes pipeline nodes, pipe segments, and pump and valve equipment; S2. Apply various typical transient operating conditions to the transient hydraulic model to simulate and obtain the pressure time history response data of each node; S3. Based on the pressure time history response data, identify risk points, including: nodes where the positive pressure exceeds 120% of the design pressure, nodes where the pressure is below -0.04MPa, and nodes located at local high points with pressure below -0.06MPa; S4. Install water hammer protection devices at the identified risk points, and dynamically determine the key parameters of each device based on the pressure time history response data: For the air valve, the air replenishment time is set to 1.2 times the round-trip time of the water hammer wave; For water hammer eliminators, their volume is calculated using the formula V=k·Q·Δt, where Q is the design flow rate of the corresponding pipe section, Δt is the duration of the pressure peak, and k is the safety factor, ranging from 1.2 to 1.5. S5. Using the slow-closing valve closing time, the effective area of ​​the air valve, and the water hammer eliminator volume as optimization variables, adjust the parameters according to the sensitivity of each variable to the maximum system pressure, and iteratively execute steps S2 to S4 until the triple convergence condition is met: The maximum positive pressure of the system does not exceed 110% of the design pressure, and the minimum pressure is not lower than -0.05MPa. The relative change rate of the equipment procurement cost for two consecutive iterations is ≤4%, and the results are stable for three consecutive iterations. Execute S6 after the triple convergence condition is met; S6. The final scheme is verified under four operating conditions: normal pump shutdown, emergency pump shutdown, valve misoperation, and sudden flow change. The simulated maximum pressure is compared with the theoretical estimate based on the Rukowski formula ΔH=c·Δv / g. If the deviation is ≤10%, the scheme is confirmed to be effective. The scheme is then used to guide the selection, layout, and parameter setting of water hammer protection devices in long-distance pressurized water transmission systems to ensure pipeline operation safety.

[0019] In step S1, CAD pipeline diagrams, DEM terrain data, and equipment parameter tables are automatically imported through the GIS data integration function to construct a three-dimensional topology model and perform topology checks to correct pipeline intersections or isolated node errors.

[0020] In step S3, the "local high point" refers to a node in the pipeline whose elevation is more than 5 meters higher than its upstream and downstream adjacent pipe sections.

[0021] In step S4, the slow-closing valve is a two-stage slow-closing valve, whose closing process includes a rapid closing stage and a slow closing stage, which is used to suppress the initial water hammer wave and avoid secondary pressure rise.

[0022] In step S5, the sensitivity ranking is as follows: the closing time of the slow-closing valve has the most significant impact on the maximum system pressure, followed by the effective area of ​​the air valve, and then the volume of the water hammer eliminator.

[0023] In step S6, "valve misoperation" refers to the abnormal adjustment of the valve opening at a rate of 5% / s, and "flow mutation" refers to the instantaneous flow rate deviating from the design value by ±20%.

[0024] Before step S1, a model calibration step is also included: select 10 to 20 representative monitoring points, import their measured pressure data, and correct the friction coefficient so that the relative error between the simulated pressure and the measured pressure is ≤8%.

[0025] The water hammer protection device includes a composite air valve, a two-stage slow-closing valve, and a water hammer eliminator. The composite air valve is installed at the negative pressure risk point, the two-stage slow-closing valve is installed at the pump station outlet, and the water hammer eliminator is installed at the positive pressure risk point or a key node that needs to absorb local pressure fluctuations.

[0026] The safety factor k is set to 1.3.

[0027] In step S5, "stable results of three consecutive iterations" means that the relative change rate of the maximum system pressure obtained in three consecutive iterations does not exceed 2%.

[0028] The present invention has the following advantages: This invention achieves high-precision identification of risk points through three thresholds (0.04MPa, 0.06MPa, and 120% of the design pressure), avoiding the missed detection of traditional single thresholds; The dynamic parameter formula V=k·Q·Δt enables precise matching between the canceller volume and transient energy, thereby reducing the volume configuration.

[0029] The air supply capacity of the air valve is checked by using 1.2 times the round-trip time of the water hammer wave as the time window. This ensures that sufficient air is injected into the cavity before the water column backflushs and closes. The compressibility of air is used to buffer the impact, thereby effectively suppressing the secondary pressure shock caused by the water hammer caused by the interruption and closure.

[0030] The triple convergence mechanism ensures that the scheme combines safety (stress compliance), economy (cost variation ≤4%), and numerical stability (consistent across three tests); multi-condition and theoretical deviation verification significantly improves the robustness of the scheme.

[0031] In typical long-distance pressurized water transmission systems (pipe length 100–200km, pipe diameter DN1400–DN1800), the number of water hammer eliminators can be reduced by 25%–35%, equipment investment can be reduced by about 30%, the absolute value of the maximum negative pressure of the system can be reduced by 50%–60%, and the peak positive pressure can be effectively controlled, significantly improving the safety and economy of the system.

[0032] The method automatically imports CAD pipeline maps and DEM topographic data through GIS data integration, and automatically checks and repairs them based on preset topology rules (including that pipelines must not intersect themselves, nodes must be connected, and there should be no isolated line segments), thus automating the modeling process. Compared with the traditional manual integration method, this method reduces data processing time from an average of 3 person-days to within 2 hours, and the topology error rate (defined as the proportion of nodes violating topology rules to the total number of nodes) from 12% to below 0.5%.

[0033] This invention combines elevation and negative pressure as dual criteria to accurately identify hidden high points where water column separation is likely to occur, avoiding misjudgments caused by relying solely on pressure thresholds.

[0034] Quick closing suppresses the initial water hammer wave, while slow closing avoids secondary pressure rise. Actual measurements show that it can reduce the peak pressure at the pump outlet by more than 25%.

[0035] In the optimization process, this invention prioritizes highly sensitive parameters based on their sensitivity to the system's maximum pressure (slow-closing valve closing time > air valve effective area > water hammer eliminator volume). Specifically, in each iteration, the slow-closing valve closing time is first adjusted until its influence on pressure approaches saturation, then the air valve area is adjusted, and finally, the eliminator volume is fine-tuned. Multi-condition testing on a 180km water conveyance system model showed that this strategy reduced the average number of iterations required to achieve triple convergence from 8 using the traditional disordered adjustment method to 4, resulting in a reduction of optimization time by approximately 50%.

[0036] After model calibration, under steady-state conditions, the maximum relative error between the simulated and measured pressures at each monitoring point does not exceed 3%; under typical transient conditions such as pump shutdown due to accidents, the maximum relative error is controlled within 7.5%. In contrast, the maximum relative error of the uncalibrated model under the same test conditions reaches 12%–18%.

[0037] In this invention, the three types of devices—composite air valve, two-stage slow-closing valve, and water hammer eliminator—work together to form a complete protection chain of "source control (slow-closing valve) — process buffer (air valve) — end absorption (eliminator)".

[0038] A value of k ranging from 1.2 to 1.5 can balance the protective effect with economy. Technicians can select the specific value within this range based on the pipe material, water quality conditions, and design specifications. Under the premise of ensuring the protective effect, the volume (V=k·Q·Δt) dynamically calculated by this invention can effectively avoid over-configuration in traditional empirical design, and significantly reduce the manufacturing cost and material consumption of water hammer eliminators.

[0039] This invention introduces multiple convergence criteria based on pressure fluctuation amplitude and device configuration stability (such as cost change rate ≤4% for two consecutive iterations and pressure fluctuation amplitude ≤2%) to avoid false convergence caused by numerical oscillations and ensure the reliability of the optimization results in terms of physical rationality and economy. Attached Figure Description

[0040] Figure 1 This is the MIKE+ model building flowchart (data preparation → model creation → parameter configuration → model calibration); MIKE+ is a comprehensive modeling and simulation software platform developed by the Danish Institute for Water and Environment (DHI) for urban water supply and drainage and pipeline systems. It adopts a GIS native integrated data organization and spatial modeling method to realize the model building, steady-state and unsteady-state (water hammer / transient) calculation, result visualization and scheme comparison and optimization of hydraulic systems such as pipelines / rivers in a unified environment. It also supports equipment condition analysis, parameter selection and multi-scenario verification through built-in professional modules and engineering toolkits for engineering planning, design and operation management decision-making.

[0041] Figure 2 This is a schematic diagram of the equipment layout (marking the locations of air valves, slow-closing valves, and water hammer eliminators). Figure 2 In the scheme shown, the volume of the water hammer eliminator is calculated according to V=k·Q·Δt, k=1.3, Q=3.0m³ / s, Δt=1.2s, resulting in V=4.68m³.

[0042] Figure 3 This is a technical flowchart for water hammer elimination schemes in GIS-driven long-distance pressurized water conveyance systems, demonstrating the complete technical process from model building, accurate simulation, parameter calculation to iterative optimization.

[0043] Figure 3 The “toolkit assistance” step in the process shown uses MIKE+ as an example, but it does not mean that the present invention is limited to this platform. Any software with the corresponding function can be applied.

[0044] Appendix Figure 1 The specific steps of model construction and calibration are described in detail (corresponding to claims 2 and 7); Appendix Figure 2 Showcase the final installation layout plan; Attached Figure 3 As an overall technical process framework diagram, it summarizes the macro-path from model building to solution output. Detailed Implementation

[0045] The method for calculating parameters of the water hammer protection device involved in this invention can be implemented based on a general water hammer simulation platform with functions such as GIS data integration, transient flow simulation, complete cavitation model and parameter sensitivity analysis. Figure 1 The MIKE+ platform shown and Figure 3 The "MIKE+ built-in air valve selection, valve dynamic testing, and other tools" mentioned in the process are merely exemplary implementation methods used to illustrate that the present invention can complete parameter calculations with the assistance of existing mature software tools, and do not constitute a limitation on the present invention. The core innovation of the present invention lies in the adaptive parameter determination logic and iterative optimization mechanism based on the transient response characteristics of the system, rather than relying on a specific software toolkit; other platforms with equivalent functions (such as WaterGEMS, EPANETMSX, HazenWilliams, etc.) can also implement the method described in the present invention.

[0046] like Figures 1 to 3 As shown, a method for eliminating water hammer in a long-distance pressurized water conveyance system according to the present invention includes the following steps: S1. Based on the pipeline topology, terrain elevation, and equipment parameters of the water conveyance system, construct a transient hydraulic model that includes pipeline nodes, pipe segments, and pump and valve equipment; S2. The transient hydraulic model is enabled with a full cavitation model. Multiple typical transient conditions are applied for simulation. Pressure time history response data of each node are obtained, and discrete sequences of pressure changes over time are generated for each node, i.e., pressure time history curves.

[0047] S3. Based on the pressure time history response data, identify risk points, including: nodes with positive pressure exceeding 120% of the design pressure, nodes with pressure below -0.04 MPa (megapascals, the vaporization pressure of water at room temperature), and nodes located at local high points with pressure below -0.06 MPa (the subvaporization warning threshold considering the precipitation of dissolved gases in water); if the pressure of a node is below -0.04 MPa, it is marked as a general risk point; if the node is also located at a local high point in the pipeline with pressure below -0.06 MPa, it is marked as a high-risk point.

[0048] S4. Install water hammer protection devices at the identified risk points, and dynamically determine the key parameters of each device based on the pressure time history response data: For the air valve, the air replenishment time is set to 1.2 times the round-trip time of the water hammer wave, i.e., t 补=1.2×L / c, where L is the distance from the risk point to the nearest boundary; c is the water hammer wave velocity, in m / s (meters per second). Water hammer waves will be reflected when they encounter impedance abrupt changes (such as pumps, valves, surge tanks, and reservoirs) during propagation; these locations are called "hydraulic boundaries." The "nearest boundary" refers to the water hammer wave propagating from the risk point along all connected pipeline paths in both upstream and downstream directions, calculating the propagation time t = L / c to each impedance abrupt change boundary (including pump stations, surge tanks, reservoirs, closed ends, or fully closed valves), where L is the total length of the pipeline segment, and c is the water hammer wave velocity of the corresponding segment; the boundary corresponding to the path with the shortest propagation time is taken as the "nearest boundary."

[0049] For water hammer eliminators, their volume is calculated using the formula V=k·Q·Δt, where Q is the design flow rate of the corresponding pipe section, in m³ / s (cubic meters per second); Δt is the duration of the pressure peak, in seconds (s), defined as the length of the time interval in the pressure time history curve from the peak pressure rising to 10% of the peak pressure, then falling back to 10% of the peak pressure. This can be automatically extracted from the pressure-time series output by the transient simulation using the post-processing module of hydraulic simulation software or general data processing tools (such as Python or MATLAB). k is the safety factor, ranging from 1.2 to 1.5. S5. Using the slow-closing valve closing time, the effective area of ​​the air valve, and the water hammer eliminator volume as optimization variables, adjust the parameters according to the sensitivity of each variable to the maximum system pressure, and iteratively execute steps S2 to S4 until the triple convergence condition is met: The maximum positive pressure of the system does not exceed 110% of the design pressure, and the minimum pressure is not lower than -0.05MPa. The relative change rate of the equipment procurement cost for two consecutive iterations is ≤4%, and the results are stable for three consecutive iterations. After the triple convergence conditions are met, proceed to step S6. The risk identification thresholds (-0.04MPa, -0.06MPa) in step S3 are used to trigger the deployment of protective measures, while the convergence target (≥-0.05MPa) in step S5 is the bottom line for the safe operation of the optimized system. The two have different purposes; the former is more sensitive to ensure full coverage, while the latter is more lenient to reflect economy.

[0050] S6. The final scheme is verified under four operating conditions: normal pump shutdown, emergency pump shutdown, valve misoperation, and sudden flow change. The simulated maximum pressure is compared with the theoretical estimate based on the Rukowski formula ΔH=c·Δv / g. If the deviation is ≤10%, the scheme is confirmed to be effective. The scheme is then used to guide the selection, layout, and parameter setting of water hammer protection devices in long-distance pressurized water transmission systems to ensure pipeline operation safety.

[0051] The transient hydraulic model uses a full cavitation model, with an air release coefficient of 0.15 and an air dissolution coefficient of 0.02; the CAD pipeline diagram includes pipe section diameter, material, wall thickness, and node coordinate information; the DEM terrain data resolution is 30m; the equipment parameter table includes the pump's QH curve, rated power, and valve opening and closing characteristic curves. The "round-trip time of water hammer wave" is calculated using the formula L / c, where L is the length of the pipe section from the risk point to the nearest boundary (such as a pumping station or surge tank) (unit: m, i.e., meters), and c is the water hammer wave velocity (unit: m / s, i.e., meters per second). c is calculated using the formula c=√(K / ρ) / √(1+(K·D) / (E·δ)) (i.e., c=(K / ρ)). 0.5 / [1+(K·D) / (E·δ)] 0.5 ), where K=2.2GPa (water bulk modulus), ρ=1000kg / m³ (water density), D is the pipe diameter (unit: m), δ is the pipe wall thickness (unit: m), and E is the pipe material elastic modulus (210GPa for steel pipes and 35GPa for prestressed steel cylinder concrete pipes).

[0052] The “equipment procurement cost” includes the equipment purchase cost of air valves, slow-closing valves, and water hammer eliminators, which is calculated by multiplying the market unit price by the quantity. In the Rukowski formula, ΔH is the maximum water hammer head increment caused by water hammer (unit: meters of water column, mH2O), which is the increase in pressure head in the pipeline relative to the initial steady-state operating head when the valve is instantaneously closed; c is the water hammer wave velocity (unit: m / s), which is the propagation speed of the pressure wave in the pipeline; Δv is the absolute value of the sudden change in flow velocity (unit: m / s), which usually refers to the change in flow velocity caused by the sudden closure of the valve or the sudden shutdown of the water pump, i.e., Δv=v0; g=9.81m / s² is the acceleration due to gravity.

[0053] This invention achieves high-precision identification of risk points through three thresholds (0.04MPa, 0.06MPa, and 120% of the design pressure), avoiding the missed detection of traditional single thresholds; The dynamic parameter formula V=k·Q·Δt enables precise matching between the canceller volume and transient energy, thereby reducing the volume configuration.

[0054] The air supply capacity of the air valve is checked by using 1.2 times the round-trip time of the water hammer wave as the time window. This ensures that sufficient air is injected into the cavity before the water column backflushs and closes. The compressibility of air is used to buffer the impact, thereby effectively suppressing the secondary pressure shock caused by the water hammer caused by the interruption and closure.

[0055] The triple convergence mechanism ensures that the scheme combines safety (stress compliance), economy (cost variation ≤4%), and numerical stability (consistent across three tests); multi-condition and theoretical deviation verification significantly improves the robustness of the scheme.

[0056] This method is applicable to pressurized water conveyance systems with pipe diameters of DN800–DN2000 and lengths of 20–500 km; the full cavitation model must be explicitly enabled in the simulation software, otherwise water column separation cannot be accurately predicted; sensitivity ranking can be obtained through analysis of variance, Sobol index or platform built-in tools, without relying on a specific algorithm.

[0057] The 0.06MPa warning threshold is based on the physical mechanism of Henry's Law: when local negative pressure causes dissolved gas in water to become supersaturated, microscopic gas nuclei are released, which becomes the induction point for water column separation. This can identify risks earlier than the vaporization pressure (0.04MPa). In engineering, 0.06MPa is used as the warning threshold, providing a safety margin of about 0.02MPa.

[0058] The safety factor k typically ranges from 1.2 to 1.5. This range comprehensively considers both the reliability and economic efficiency of water hammer protection: when k < 1.2, the device volume is too small, making it difficult to effectively suppress pressure fluctuations under extreme conditions; when k > 1.5, the device size is too large, leading to a significant increase in investment costs. This range conforms to the general principles of safety factor design in hydraulic engineering. Those skilled in the art can optimize the value within this range based on the technology disclosed in this invention and the specific engineering conditions.

[0059] In typical long-distance pressurized water transmission systems (pipe length 100–200km, pipe diameter DN1400–DN1800), the number of water hammer eliminators can be reduced by 25%–35%, equipment investment can be reduced by about 30%, the absolute value of the maximum negative pressure of the system can be reduced by 50%–60%, and the peak positive pressure can be effectively controlled, significantly improving the safety and economy of the system.

[0060] The complete cavitation model refers to a physical sub-model used in transient hydraulic simulations to simulate the phase change (liquid → gas) of a liquid due to local pressure falling below the vaporization pressure threshold, forming compressible bubbles and affecting the fluid continuity equation. This model requires setting the following key parameters: vaporization pressure threshold of water: 0.04 MPa (absolute pressure, corresponding to an engineering approximation at 20°C); air release coefficient: 0.15 (dimensionless, characterizing the relative rate of dissolved gas release under negative pressure); air dissolution coefficient: 0.02 (dimensionless, characterizing the relative rate of gas redissolution under positive pressure); effective bulk modulus of the gas phase: 15 kPa (characterizing the compressibility of the gas-liquid mixture, typically ranging from 10–50 kPa). It can be implemented by enabling the "VaporCavitation" option in the MIKE+ software, or by introducing a gas-liquid phase change source term into the governing equations based on the method of characteristics (MOC) to couple the dynamic evolution of pressure, velocity, and gas phase volume fraction.

[0061] Based on the 180km water conveyance system model described in Example 1, the technical effects of the core features of this invention were verified through ablation experiments: when the complete cavitation model was closed, the prediction error of the water column separation position reached ±3.2km, which is 10.7 times larger than the error when the model was enabled; when the dynamic air replenishment time (set as 1.2 times the characteristic propagation time of water hammer wave, i.e. 1.2×L / c) was replaced with the traditional fixed value of 30s, the occurrence rate of secondary water hammer increased from 5% to 45%, an increase of 40 percentage points.

[0062] In step S1, CAD pipeline diagrams, DEM terrain data, and equipment parameter tables are automatically imported through the GIS data integration function to construct a three-dimensional topology model and perform topology checks to correct pipeline intersections or isolated node errors.

[0063] Convert CAD pipeline diagrams to Shapefile format, which includes line features (pipe segments) and point features (nodes). The DEM is a topographic elevation dataset stored with a nominal spatial resolution of 30 meters (1 arcsecond). Each raster value represents the orthographic elevation (i.e., altitude, in meters) at that location. The elevation datum is defined with reference to the EGM96 geoid model, forming the topographic skeleton for constructing the 3D model of the water conveyance system. The DEM topographic data is stored in GeoTIFF format and uses the UTMZone50N projection coordinate system (EPSG:32650) based on the WGS84 datum ellipsoid to ensure accurate alignment with the CAD pipeline map, which also uses projection coordinates, in planar positions. Data Sources: This invention prioritizes the use of freely available SRTM or ASTERGDEM global elevation data. ASTERGDEM already provides orthographic elevation data based on the EGM96 geoid model; SRTM raw data is ellipsoidal height and needs to be converted to orthographic elevation using the EGM96 model before use. It is automatically imported using the GIS data integration function of MIKE+, and elevation datum consistency is verified before model construction.

[0064] Topology checks include automatically detecting pipeline self-intersections, disconnected endpoints, and duplicate nodes, and generating a log of repair suggestions.

[0065] The method automatically imports CAD pipeline maps and DEM topographic data through GIS data integration, and automatically checks and repairs them based on preset topology rules (including that pipelines must not intersect themselves, nodes must be connected, and there should be no isolated line segments), thus automating the modeling process. Compared with the traditional manual integration method, this method reduces data processing time from an average of 3 person-days to within 2 hours, and the topology error rate (defined as the proportion of nodes violating topology rules to the total number of nodes) from 12% to below 0.5%.

[0066] GIS data can originate from Shapefile or GeoTIFF formats output by platforms such as ArcGIS and QGIS, and be imported and processed by hydraulic simulation software such as MIKE+.

[0067] In step S3, the "local high point" refers to a node in the pipeline whose elevation is more than 5 meters higher than its upstream and downstream adjacent pipe sections. The "upstream and downstream adjacent pipe sections" typically refer to the average elevation of pipe sections within a 1-2 km radius before and after this node. This 5m threshold comprehensively considers terrain undulations and negative pressure development characteristics, effectively identifying areas at risk of water column separation. Local high points usually appear on ridges, the tops of bridges and culverts, or on uphill sections after pump station outlets.

[0068] This invention combines elevation and negative pressure as dual criteria to accurately identify hidden high points where water column separation is likely to occur, avoiding misjudgments caused by relying solely on pressure thresholds.

[0069] In step S4, the slow-closing valve is a two-stage slow-closing valve, whose closing process includes a rapid closing stage and a slow closing stage, which is used to suppress the initial water hammer wave and avoid secondary pressure rise.

[0070] Rapid closing phase: closing to 80% opening within 0–2 seconds; slow closing phase: closing from 80% opening to 0% opening within 2–60 seconds; among which, Figure 2 The embodiment shown uses a specific configuration of 2s fast shutdown + 45s slow shutdown.

[0071] The slow-closing valve uses a programmable actuator, and its closing time can be set to a segmented linear mode (e.g., fast closing to 80% in 2 seconds, then slow closing to 0% in 45 seconds), or it can be configured to linear, exponential, or other smooth closing patterns. Fast closing suppresses the initial water hammer wave, and slow closing avoids secondary pressure rise. Actual measurements show that it can reduce the peak pressure at the pump outlet by more than 25%.

[0072] In step S5, the sensitivity ranking is as follows: the closing time of the slow-closing valve has the most significant impact on the maximum system pressure, followed by the effective area of ​​the air valve, and then the volume of the water hammer eliminator.

[0073] Sensitivity ranking can be obtained through global sensitivity analysis methods (such as the Sobol index) or parameter impact assessment tools built into the hydraulic simulation platform. For example, it can be calculated using the "ParameterSensitivity" module of the MIKE+ platform, outputting the standardized regression coefficients of each parameter with respect to maximum pressure. Those skilled in the art can determine the relative importance of each parameter based on the software output results without pre-setting specific weight values.

[0074] In the optimization process, this invention prioritizes highly sensitive parameters based on their sensitivity to the system's maximum pressure (slow-closing valve closing time > air valve effective area > water hammer eliminator volume). Specifically, in each iteration, the slow-closing valve closing time is first adjusted until its influence on pressure approaches saturation, then the air valve area is adjusted, and finally, the eliminator volume is fine-tuned. Multi-condition testing on a 180km water conveyance system model showed that this strategy reduced the average number of iterations required to achieve triple convergence from 8 using the traditional disordered adjustment method to 4, resulting in a reduction of optimization time by approximately 50%.

[0075] In step S6, "valve misoperation" refers to the abnormal adjustment of the valve opening at a rate of 5% / s, and "flow mutation" refers to the instantaneous flow rate deviating from the design value by ±20%.

[0076] Valve malfunction simulation: A faulty electric actuator causes the valve opening to decrease from 100% to 0% at a rate of 5% / s. Simulation of sudden flow change: The upstream reservoir gate suddenly opens, causing the inflow to increase from Q_design to 1.2·Q_design.

[0077] "Valve misoperation" and "flow mutation" cover the two most common types of human / equipment failures in actual operation, verifying the robustness of the solution under non-design conditions.

[0078] Before step S1, a model calibration step is also included: select 10 to 20 representative monitoring points, import their measured pressure data, and correct the friction coefficient so that the relative error between the simulated pressure and the measured pressure is ≤8%.

[0079] Monitoring points are evenly distributed along the pipeline, covering the highest and lowest elevation points, pump station inlets and outlets, and end users; the sampling frequency of measured data is ≥1Hz, including steady-state and transient conditions; the friction coefficient correction is achieved using a nonlinear least squares method, such as the Levenberg-Marquardt nonlinear least squares method.

[0080] After model calibration, under steady-state conditions, the maximum relative error between simulated and measured pressures at each monitoring point does not exceed 3%; under typical transient conditions such as pump shutdown due to accidents, the maximum relative error is controlled within 7.5%. In contrast, the maximum relative error of the uncalibrated model under the same test conditions reaches 12%–18%. This error is calculated based on 10–20 representative monitoring points evenly distributed along the pipeline (including the highest and lowest elevation points, pump station inlets and outlets, and the pipeline end), and is defined as: Relative Error = (P... sim -P meas ) / P_meas×100%. Where P meas P represents the measured pressure. sim This represents simulated pressure.

[0081] The water hammer protection device includes a composite air valve, a two-stage slow-closing valve, and a water hammer eliminator. The composite air valve is installed at the negative pressure risk point, the two-stage slow-closing valve is installed at the pump station outlet, and the water hammer eliminator is installed at the positive pressure risk point or a key node that needs to absorb local pressure fluctuations.

[0082] The composite air valve has dual functions of high-speed exhaust and micro-volume air replenishment; the two-stage slow-closing valve supports segmented control of fast and slow closing; the water hammer eliminator uses pre-charged gas to absorb pressure fluctuation energy. In a typical implementation, the pre-charged nitrogen pressure can be selected as 0.6 MPa, and the maximum working pressure is 2.5 MPa, but the invention is not limited to these.

[0083] In this invention, the three types of devices—composite air valve, two-stage slow-closing valve, and water hammer eliminator—work together to form a complete protection chain of "source control (slow-closing valve) — process buffer (air valve) — end absorption (eliminator)".

[0084] A value of k ranging from 1.2 to 1.5 can balance the protective effect with economy. Technicians can select the specific value within this range based on the pipe material, water quality conditions, and design specifications. Under the premise of ensuring the protective effect, the volume (V=k·Q·Δt) dynamically calculated by this invention can effectively avoid the over-configuration problem of "better too large than too small" in traditional empirical design, and significantly reduce the manufacturing cost and material consumption of water hammer eliminators.

[0085] In water conveyance systems with high sediment content (>50 mg / L), increased pipe wall roughness and friction coefficient due to sediment erosion lead to a decreased velocity decay rate during transient processes, potentially resulting in a longer pressure peak duration Δt compared to clean water conditions. In this case, the k value can be appropriately increased within the range of 1.2–1.5 (e.g., to 1.4 or 1.5) to compensate for insufficient protection margin caused by changes in energy dissipation characteristics. The optimal value is determined by using a numerical model capable of simultaneously simulating the transient process of water flow and the impact of sediment transport on pipe friction (e.g., mature water-sediment coupling tools such as Delft3D, MIKE+Sediment module, or HEC-RAS sediment module) for transient simulation, and then based on the simulated pressure peak duration Δt.

[0086] In step S5, "stable results of three consecutive iterations" means that the relative change rate of the maximum system pressure obtained in three consecutive iterations does not exceed 2%.

[0087] This invention introduces multiple convergence criteria based on pressure fluctuation amplitude and device configuration stability (such as cost change rate ≤4% for two consecutive iterations and pressure fluctuation amplitude ≤2%) to avoid false convergence caused by numerical oscillations and ensure the reliability of the optimization results in terms of physical rationality and economy.

[0088] Example 1: Simulation Verification of Optimized Water Hammer Protection for Long-Distance Water Conveyance Systems 1. Model Building A transient hydraulic model of a typical long-distance pressurized water conveyance system is constructed, with the following parameters: The pipeline is 180km long, with a diameter of DN1600, a wall thickness of 20mm, and is made of PCCP (E=35GPa). Roughness 0.05mm, design flow rate 3.0m³ / s. Import 30m resolution DEM terrain data into MIKE+. Automatically identify 3 local high points (the elevation is ≥5m higher than the average elevation within a 500m range upstream and downstream). Set up 10 pumping stations (QH curve input), with an upstream water level of 60m and a downstream pressure ≥0.2MPa boundary.

[0089] During the model building phase, the GIS integration function of the hydraulic simulation platform is used to automatically fuse pipeline, terrain, and equipment data. Taking the MIKE+ platform as an example, its "Topology Inspector" module is enabled, and the following basic topology rules are configured: (1) Pipeline elements must not intersect each other; (2) All pipe segment endpoints must be connected to nodes; (3) Unclosed hanging segments are prohibited.

[0090] The system automatically marks violation locations and provides a one-click repair option, significantly improving modeling efficiency and data quality. Testing of the 180km water conveyance system model described in this embodiment showed that traditional manual modeling took an average of about 3 person-days, with a topology error rate (defined as the proportion of nodes violating the above rules to the total number of nodes) of 12%. After adopting the automated process described in this invention, the modeling time was reduced to within 2 hours, and the topology error rate was reduced to 0.47%.

[0091] It should be noted that the MIKE+ platform is only an exemplary implementation tool. Those skilled in the art can choose other general platforms with similar GIS topology inspection functions (such as ArcGIS, QGIS or WaterGEMS) to implement the same automatic data verification and repair process.

[0092] 2. Initial Plan Based on traditional experience, 28 water hammer eliminators (5m³ / unit) were installed, evenly distributed at high points and pump station outlets.

[0093] 3. Optimization process Run the transient flow module with a time step of 0.05s and a simulation duration of 900s, and enable the water cave model.

[0094] The "Water Hammer Analysis Toolkit" is invoked to automatically mark risk points (positive pressure > 2.2 MPa or negative pressure < -0.06 MPa). The Water Hammer Analysis Toolkit refers to a post-processing module that automatically filters nodes meeting any of the following conditions as high-risk points by reading the pressure time-history data output from transient simulations: (1) the peak positive pressure exceeds a set threshold; (2) the pressure is lower than the cavitation occurrence criterion (e.g., < 0.06 MPa). This module can be implemented using a general scripting language (e.g., Python, Tcl) or the built-in result analysis function of commercial hydraulic software. In this embodiment, seven risk points are marked.

[0095] Using the formula V=k·Q·Δt, Δt=1.2s was extracted from the pressure time history curve, and k was taken as 1.3 after sensitivity analysis, resulting in a single unit volume V=4.68m³. A total of 19 water hammer eliminators (total volume 88.92m³) were ultimately deployed. Typical deployment locations at local high points and pump station outlets are shown in the attached diagram. Figure 2 It should be noted that the appendix... Figure 2This is a schematic diagram of the device layout, illustrating only the types and typical layout logic of the composite air valve, two-stage slow-closing valve, and water hammer eliminator. The specific number and location of the devices in actual engineering projects need to be dynamically determined based on transient simulation results. Those skilled in the art can refer to the diagram for further information. Figure 2 The logic shown combines the risk point coordinates output by the simulation to automatically generate a deployment plan, eliminating the need to rely on attached diagrams to determine the exact location of each device.

[0096] The value of k was determined through Sobol global sensitivity analysis. Within the range of k=1.2–1.5, the optimal combination of protection effect and economy was achieved when k=1.3 in this embodiment. Traditional methods adjust parameters in a random or fixed order, requiring an average of 8 iterations to meet the convergence condition; while this invention, based on the results of Sobol sensitivity analysis, optimizes sequentially in the order of "slow-closing valve → air valve → eliminator," achieving convergence in only 4 iterations, significantly improving optimization efficiency.

[0097] During the optimization process, a triple convergence condition is used to determine whether the iteration terminates. This condition simultaneously ensures system safety, economy, and numerical stability, and specifically includes: (1) Safety conditions: The maximum positive pressure of the system shall not exceed 110% of the pipeline design pressure, and the minimum pressure shall not be lower than -0.05MPa; (2) Economic conditions: The relative change rate of the equipment procurement cost for two consecutive iterations is ≤4% (mainly reflected in the total volume change rate of the water hammer eliminator ≤5%, and the number and layout of air valves and slow-closing valves remain unchanged). (3) Stability condition: The relative change rate of the maximum system pressure obtained in three consecutive iterations does not exceed 2%, that is, it satisfies |(Pn-Pn-1) / Pn-1|×100%≤2%, and Pn≤safety threshold. Where Pn is the maximum pressure obtained in the nth iteration, and the safety threshold is taken as 110% of the pipeline design pressure (corresponding to the design pressure of 2.0MPa).

[0098] When all three conditions are met, the optimization is considered to have converged, and the final solution is output.

[0099] In this embodiment, the selected water hammer eliminator is pre-charged with nitrogen at a pressure of 0.6 MPa, has a maximum operating pressure of 2.5 MPa, and its volume is calculated using V = 1.3 × Q × Δt. It should be noted that the pre-charge pressure can be adjusted according to the pipeline operating pressure, typically taking 50%–70% of the system steady-state pressure; however, this invention is not limited to this specific value.

[0100] 4. Working condition simulation Simulate four types of working conditions in sequence: Single pump trip: Pump #1 loses power at t=5s; Power outage across the entire line: All pumps stop at t=10s; Valve misoperation: Opening degree changes from 100% to 0% within 10 seconds (change rate 5% / s); Flow change: Upstream flow jump of ±20% at t=60s; For each operating condition, 20 key points are monitored, and pressure time-series data are recorded.

[0101] 5. Results Analysis The extreme pressure values ​​at each monitoring point were extracted, and the minimum system pressure was increased from -0.08MPa to -0.035MPa.

[0102] The maximum positive pressure decreased from 2.5MPa to 1.95MPa. The total investment was calculated based on a unit price of 150,000 yuan per unit (including valves, installation, and commissioning), decreasing from 28 units × 150,000 yuan = 4.2 million yuan to 19 units × 150,000 yuan = 2.85 million yuan, a reduction of 32% (Note: In the example, 12.7% refers to the total cost including civil engineering, while this refers to the equipment investment).

[0103] The above embodiments are only used to illustrate and not limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention without departing from the spirit and scope of the present invention. Any modifications or partial substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for eliminating water hammer in a long-distance pressurized water conveyance system, characterized in that: Includes the following steps: S1. Based on the pipeline topology, terrain elevation, and equipment parameters of the water conveyance system, construct a transient hydraulic model that includes pipeline nodes, pipe segments, and pump and valve equipment; S2. Apply various typical transient operating conditions to the transient hydraulic model to simulate and obtain the pressure time history response data of each node; S3. Based on the pressure time history response data, identify risk points, including: nodes where the positive pressure exceeds 120% of the design pressure, nodes where the pressure is below -0.04MPa, and nodes located at local high points with pressure below -0.06MPa; S4. Install water hammer protection devices at the identified risk points, and dynamically determine the key parameters of each device based on the pressure time history response data: For the air valve, the air replenishment time is set to 1.2 times the round-trip time of the water hammer wave; For water hammer eliminators, their volume is calculated using the formula V=k·Q·Δt, where Q is the design flow rate of the corresponding pipe section, Δt is the duration of the pressure peak, and k is the safety factor, ranging from 1.2 to 1.

5. S5. Using the slow-closing valve closing time, the effective area of ​​the air valve, and the water hammer eliminator volume as optimization variables, adjust the parameters according to the sensitivity of each variable to the maximum system pressure, and iteratively execute steps S2 to S4 until the triple convergence condition is met: The maximum positive pressure of the system does not exceed 110% of the design pressure, and the minimum pressure is not lower than -0.05MPa. The relative change rate of the equipment procurement cost for two consecutive iterations is ≤4%, and the results are stable for three consecutive iterations. Execute S6 after the triple convergence condition is met; S6. The final scheme is verified under four operating conditions: normal pump shutdown, emergency pump shutdown, valve misoperation, and sudden flow change. The simulated maximum pressure is compared with the theoretical estimate based on the Rukowski formula ΔH=c·Δv / g. If the deviation is ≤10%, the scheme is confirmed to be effective. The scheme is then used to guide the selection, layout, and parameter setting of water hammer protection devices in long-distance pressurized water transmission systems to ensure pipeline operation safety.

2. The water hammer elimination method for a long-distance pressurized water conveyance system according to claim 1, characterized in that: In step S1, CAD pipeline diagrams, DEM terrain data, and equipment parameter tables are automatically imported through the GIS data integration function to construct a three-dimensional topology model and perform topology checks to correct pipeline intersections or isolated node errors.

3. The water hammer elimination method for a long-distance pressurized water conveyance system according to claim 1, characterized in that: In step S3, the "local high point" refers to a node in the pipeline whose elevation is more than 5 meters higher than its upstream and downstream adjacent pipe sections.

4. The water hammer elimination method for a long-distance pressurized water conveyance system according to claim 1, characterized in that: In step S4, the slow-closing valve is a two-stage slow-closing valve, whose closing process includes a rapid closing stage and a slow closing stage, which is used to suppress the initial water hammer wave and avoid secondary pressure rise.

5. The water hammer elimination method for a long-distance pressurized water conveyance system according to claim 1, characterized in that: In step S5, the sensitivity ranking is as follows: the closing time of the slow-closing valve has the most significant impact on the maximum system pressure, followed by the effective area of ​​the air valve, and then the volume of the water hammer eliminator.

6. The method for eliminating water hammer in a long-distance pressurized water conveyance system according to claim 1, characterized in that: In step S6, "valve misoperation" refers to the abnormal adjustment of the valve opening at a rate of 5% / s, and "flow mutation" refers to the instantaneous flow rate deviating from the design value by ±20%.

7. The water hammer elimination method for a long-distance pressurized water conveyance system according to claim 1, characterized in that: Before step S1, a model calibration step is also included: select 10 to 20 representative monitoring points, import their measured pressure data, and correct the friction coefficient so that the relative error between the simulated pressure and the measured pressure is ≤8%.

8. The method for eliminating water hammer in a long-distance pressurized water conveyance system according to claim 1, characterized in that: The water hammer protection device includes a composite air valve, a two-stage slow-closing valve, and a water hammer eliminator. The composite air valve is installed at the negative pressure risk point, the two-stage slow-closing valve is installed at the pump station outlet, and the water hammer eliminator is installed at the positive pressure risk point or a key node that needs to absorb local pressure fluctuations.

9. The method for eliminating water hammer in a long-distance pressurized water conveyance system according to claim 1, characterized in that: The safety factor k is set to 1.

3.

10. The method for eliminating water hammer in a long-distance pressurized water conveyance system according to claim 1, characterized in that: In step S5, "stable results of three consecutive iterations" means that the relative change rate of the maximum system pressure obtained in three consecutive iterations does not exceed 2%.

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