Unsteady flow analysis method and system for characteristics of slurry in conveying pipeline

Abstract

The invention discloses an unsteady flow analysis method and system for characteristics of slurry in a conveying pipeline, and belongs to the technical field of slurry pipeline conveying, and the method comprises the following steps: S1, constructing a pipeline inlet slurry state sequence set by collecting slurry state parameters of a pipeline inlet at different moments; s2, according to the dynamic position of the slurry in the pipeline, establishing a density and flow velocity distribution model of the slurry in the full-length range of the pipeline at any moment; s3, the space-time step length is defined, discrete processing is conducted on the distribution condition of the slurry in the pipeline at any moment, and the flow velocity and density states of the slurry at different pipe section positions after discrete processing are obtained; s4, according to the discretized pipeline state, slurry density is introduced to serve as a key variable to modify a characteristic line equation, and the modified characteristic line equation is used for calculating the water hammer wave velocity of each discrete section and other fluid parameters influenced by the density; and S5, carrying out iterative calculation on the pipeline characteristics by using the transformed non-constant flow characteristic line theory to realize simulation of the hydraulic transition phenomenon in the slurry conveying process.

Description

Technical Field

[0001] This invention belongs to the field of mud pipeline transportation technology, and specifically relates to a method and system for analyzing the unsteady flow characteristics of mud in a transportation pipeline. Background Technology

[0002] In dredging projects and slurry transportation, hydraulic mud transport is a widely used technology. This technology typically relies on steady-state approximation calculations for design and analysis, assuming that the density, velocity, and other physical properties of the mud remain constant throughout the transport process. However, the real-world mud transport environment is far more complex than this assumption. Due to variations in factors such as inlet soil conditions, topography, and weather conditions, the density of the mud is actually a parameter that dynamically changes over time and space. This variation leads to non-constant flow characteristics within the pipeline, manifesting as transient water hammer, pressure and velocity fluctuations, which in turn cause a series of problems such as increased pipeline wear, increased pump cavitation risk, and decreased transport efficiency.

[0003] Currently, the analysis and calculation of mud transport systems are mainly limited to clear water conditions, neglecting the influence of mud density variations over time and space. Traditional calculation methods often employ steady-state analysis, assuming that the mud density is constant during transport. While this simplifies the calculation process to some extent, it also significantly limits the accuracy and applicability of the calculations. Especially when dealing with non-uniform density mud transport and rapidly changing operating conditions, existing steady-flow calculation theories and methods are inadequate, failing to reflect the complex fluid dynamics phenomena during mud transport in real time. Furthermore, the lack of effective dynamic simulation tools also limits the ability to optimize the design and operational control of transport systems, increasing operating costs and reducing operational efficiency.

[0004] In summary, current calculation methods for slurry transport pipeline systems have significant limitations and cannot meet the requirements for accurate analysis of dynamic changes in slurry density in modern dredging and slag transport projects. There is an urgent need for a new method that can consider the temporal and spatial changes in slurry density and perform full simulation calculations to improve the design and operation of slurry transport systems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for analyzing the unsteady flow characteristics of mud in conveying pipelines. By introducing mud density as a key feature, the invention modifies the calculation theory of unsteady flow under clear water conditions, enabling accurate calculation and simulation of the dynamic changes of non-uniform density mud in mud conveying pipeline systems.

[0006] The specific technical solution adopted in this invention is as follows: The primary objective of this patent is to provide a method for analyzing the unsteady flow characteristics of mud in a pipeline, including: S1. By collecting the mud state parameters at the pipeline inlet at different times, construct a mud state sequence set (ti, vi, ρi) at the pipeline inlet. S2. By analyzing the dynamic position of the mud in the pipeline, establish a model of the density and velocity distribution of the mud over the entire length of the pipeline at any given time. S3. After defining the time-space step, the distribution of mud in the pipeline at any time is discretized to obtain the flow velocity and density of the mud at different pipe sections. S4: Based on the discretized pipeline state, mud density is introduced as a key variable to modify the characteristic line equation. The modified characteristic line equation is used to calculate the water hammer wave velocity and other density-affected fluid parameters of each discrete segment. S5: Using the results of S4, the modified unsteady flow characteristic line theory is applied to iteratively calculate the pipeline characteristics, thereby simulating the hydraulic transition phenomenon during mud transportation.

[0007] Furthermore, in S2, define For inlet from pipeline i to pipeline j The length of the position, then: .

[0008] Furthermore, the formula for calculating the water hammer wave velocity is:

[0009] Where a is the water hammer wave velocity, and K is the elastic modulus of the medium being transported in the pipeline. Let D be the density of the medium being transported in the pipeline, b be the inner diameter of the pipeline, b be the pipe wall thickness, and E be the elastic modulus of the pipeline material.

[0010] Furthermore, the modified non-steady flow characteristic line theory is obtained as follows: the motion equations and continuity equations of the hydraulic transients of the clear water pipeline are modified, a key density term is introduced, the inertial force, viscous force, gravity and frictional resistance of the pipeline wall are considered, the non-steady flow process of the slurry is described by partial differential equations and the local and frictional resistance losses of the pipeline are considered, and the characteristic line method is used to discretize the slurry transport pipeline at any time, dividing the continuous pipeline into multiple pipe segments and nodes, and the slurry flow characteristics, including velocity, pressure and density, in each pipe segment are considered to be uniformly distributed.

[0011] A second objective of this invention is to provide a system for analyzing the unsteady flow characteristics of mud in a delivery pipeline, comprising: The basic data module collects mud state parameters at the pipeline inlet at different times to construct a sequence set of mud state data at the pipeline inlet. t i 、vi ρ i ); The distribution model analyzes the dynamic position of the mud in the pipeline to establish a model of the density and velocity distribution of the mud over the entire length of the pipeline at any given time. The discrete module defines the spatiotemporal step size and then discretizes the distribution of mud in the pipeline at any time to obtain the flow velocity and density of the mud at different pipe sections. The parameter calculation module, based on the discretized pipeline state, introduces mud density as a key variable to modify the characteristic line equation, and uses the modified characteristic line equation to calculate the water hammer wave velocity and other density-affected fluid parameters of each discrete segment. The execution module uses the results of parameter calculations and applies the modified unsteady flow characteristic line theory to iteratively calculate pipeline characteristics, thereby simulating the hydraulic transition phenomenon during mud transportation.

[0012] Furthermore, in the distribution model, we define Let i be the length from pipe inlet i to pipe position j, then: .

[0013] Furthermore, the formula for calculating the water hammer wave velocity is:

[0014] Where a is the water hammer wave velocity, and K is the elastic modulus of the medium being transported in the pipeline. Let D be the density of the medium being transported in the pipeline, b be the inner diameter of the pipeline, b be the pipe wall thickness, and E be the elastic modulus of the pipeline material.

[0015] Furthermore, the modified non-steady flow characteristic line theory is obtained as follows: the motion equations and continuity equations of the hydraulic transients of the clear water pipeline are modified, a key density term is introduced, the inertial force, viscous force, gravity and frictional resistance of the pipeline wall are considered, the non-steady flow process of the slurry is described by partial differential equations and the local and frictional resistance losses of the pipeline are considered, and the characteristic line method is used to discretize the slurry transport pipeline at any time, dividing the continuous pipeline into multiple pipe segments and nodes, and the slurry flow characteristics, including velocity, pressure and density, in each pipe segment are considered to be uniformly distributed.

[0016] A third objective of the present invention is to provide a computer program product, comprising a computer program, characterized in that the computer program is executed by a processor using the aforementioned method for analyzing the unsteady flow characteristics of mud in a delivery pipeline.

[0017] A fourth objective of the present invention is to provide a computer-readable storage medium including instructions that, when executed on a computer, cause the computer to perform the aforementioned method for analyzing the unsteady flow characteristics of mud in a delivery pipeline.

[0018] The advantages and positive effects of this invention are as follows: The technical solution of this invention effectively solves the problem that existing steady flow calculation theories under clear water conditions cannot accurately reflect the non-steady flow characteristics of density variations over time and space in slurry transport pipelines, thus hindering real-time dynamic simulation and optimization design. Specifically, in slurry transport systems, slurry, as a non-Newtonian fluid, exhibits significant time-varying and spatial heterogeneity due to particle settling, concentration gradients, and external factors affecting its density distribution. Existing theories assume a constant fluid density, neglecting these dynamic characteristics, leading to large deviations in simulation results and failing to guide practical engineering optimization. The aforementioned technical problems involve the dynamic non-steady flow phenomena in slurry transport processes, particularly the impact of spatiotemporal variations in slurry density on hydraulic transition processes in pipeline systems, including pressure fluctuations and flow velocity instability. For example, at pipe bends or diameter changes, density unevenness can trigger localized high pressure or cavitation risks, exacerbating system instability.

[0019] This invention can accurately simulate and predict the unsteady flow characteristics of non-uniformly distributed mud transport pipelines, providing a particularly in-depth understanding of the dynamic changes in key parameters such as water hammer velocity, velocity distribution, and density variation. By introducing water hammer velocity, it more accurately describes the propagation and attenuation laws of hydraulic shock waves and the evolution of velocity profiles, providing a reliable basis for design. The integration of the mud state prediction model and external data interface provides the system with real-time performance and predictive capabilities, enabling it to cope with complex and variable operating environments, such as severe weather and terrain conditions, ensuring the safety and continuity of mud transport operations.

[0020] In summary, this invention has significant application value and market prospects in the field of mud transportation engineering, and can effectively improve the safety, efficiency, and economic benefits of operations. It is widely applicable to the mining, dredging, and construction industries, achieving long-term cost savings and environmental benefits by reducing failure rates and optimizing resource utilization. Attached Figure Description

[0021] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a preferred embodiment of the present invention; Figure 2 This is another flowchart of a preferred embodiment of the present invention; Figure 3This is a schematic diagram of the discrete pipeline structure in a preferred embodiment of the present invention. Detailed Implementation

[0022] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0023] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of S or units is not necessarily limited to those S or units explicitly listed, but may include other S or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0024] Please see Figure 1 and Figure 2 This invention provides an unsteady flow analysis method for mud properties in conveying pipelines. By introducing mud density as a key parameter, the fluid theory of slurry pipeline transportation is derived, and the pipeline model is discretized using the method of characteristics to accurately simulate the water hammer transient behavior during transportation under different mud densities. This method not only considers the influence of the physical properties of mud on transient flow, but also improves the calculation accuracy and convergence stability through refined pipeline model discretization, enabling realistic prediction of the hydraulic transient process during mud transportation. This provides a scientific basis for the design, operation, maintenance, and control system development of mud transportation pipelines. Specifically, it includes: S1: By collecting mud state parameters at the pipeline inlet at different times, a sequence set of mud state parameters at the pipeline inlet is constructed. t i 、v i ρ i ); Firstly, density sensors and velocity sensors can be installed at the pipe inlet; Then, density and velocity sensors were used to collect mud flow rates at different times. v iand mud density ρ i ; Finally, a mud state sequence set is established by combining time ( t i 、v i ρ i ); This step can also construct a time distribution model of the mud state at the pipeline inlet location; as the mud conveying system changes with soil strength, terrain undulation, wind and wave flow, the mud density sucked in by the suction port is in a dynamic process. The mud state time distribution model is constructed by comprehensively considering parameters such as suction port tool shape, three-dimensional coordinate position change, mud entry thickness, and step.

[0025] S2: By analyzing the dynamic position of the mud in the pipeline, the sequence of the state of the mud along the pipeline at each time moment is obtained. Based on the sequence of the state of the mud along the pipeline at each time moment, a model of the density and velocity distribution of the mud at any time moment within the entire length of the pipeline is established. definition Let i be the length from pipe inlet i to pipe position j, then: ; if If the length equals the total length of the pipeline, then the mud transported to the pipe opening for that section is determined, and (establishment is made). t i ，t j The time pair indicates that the mud that enters the pipe at time i flows out of the pipe at time j.

[0026] Establish a sequence of the state of the slurry along the pipeline at each time point (time, pipe length, flow velocity, density); Based on the above analysis, if time k is less than i, it means the mud has not yet entered the pipe inlet; if k is greater than j, it means the mud sequence has been discharged from the pipe outlet; if k is greater than i and less than j, then the mud at time k is effective mud inside the pipe. The calculation... The value represents the position of the mud in the pipeline at time k, from which the mud density and velocity distribution along the entire pipeline at all times can be obtained.

[0027] Based on the time distribution of mud at the pipeline inlet and the pipeline flow velocity, this invention calculates the final time when the mud at the inlet reaches the pipeline outlet from the initial moment. Based on the inlet mud density, flow velocity, and other conditions in the section between the two moments, the distribution of mud in the pipeline at the final moment is obtained.

[0028] S3: After defining the time-space step, the distribution of mud in the pipeline at any time is discretized to obtain the discretized pipe segment position, flow velocity and density state. First, a spatiotemporal step size is defined for the calculation of unsteady slurry flow. Then, discrete interpolation is performed on the slurry in the pipe at any given time, for each case. Figure 3 As shown.

[0029] S4: Based on the discretized pipeline state, mud density is introduced as a key variable to modify the characteristic line equation. The modified characteristic line equation is used to calculate the water hammer wave velocity and other density-affected fluid parameters of each discrete segment. Establishment of a theoretical model for the characteristic lines of unsteady slurry flow: The motion and continuity equations for the hydraulic transients of the clear water pipeline are modified by introducing a key density term. The inertial force, viscous force, gravity, and frictional resistance of the pipeline wall are considered. Partial differential equations are used to describe the non-steady flow process of the slurry and the local and frictional losses of the pipeline are considered. The method of characteristics is used to discretize the slurry transport pipeline at any time, dividing the continuous pipeline into multiple small computational units (such as pipe segments and nodes). The slurry flow characteristics, including velocity, pressure, and density, within each micro-unit are considered to be uniformly distributed.

[0030] The basic theory of unsteady flow of clear water is as follows: Simplifying the equations of motion and continuity for the fluid flow, we obtain the following form: Momentum equation: (2-1-1) Continuity equation: (2-1-2) Let the eigenvalues ​​be , and after a series of transformations, we obtain the following two sets of equations by linearly combining the two equations above. Let each of them be represented by C. + and C - To name it, we have the characteristic line equation shown below: (2-1-3) (2-1-4) Divide a pipe into n segments, each with a length of Δx, and the above equation can be transformed into the following form. C + : (2-1-5) C - : (2-1-6) Among them: B=a / (gA); R=fΔx / (2gDA 2 ) The above two equations can be simplified into a simpler form. C + H pi =C p -BQpi (2-1-7) C - H pi =C M +BQ Pi (2-1-8) In the formula: C p、 C M Usually a known constant C P =H i-1 +BQ i-1 -RQ i-1 |Q i-1 |(2-1-9) C M =H i+1 -BQ i+1 +RQ i+1 |Q i+1 |(2-1-10) From equations (2-1-7) and (2-1-8), we get H Pi =(C P +C M ) / 2(2-1-11) Q Pi =(C P -C M ) / B(2-1-12) In the above formulas, the subscript P represents the cross section and i represents the time.

[0031] This is the basic difference equation for calculating unsteady flow of clean water, but it ignores the effect of density and cannot be used for mud transportation, especially for calculations where the mud in the pipeline is unevenly distributed over time and space.

[0032] Therefore, the influence of density is introduced into the theoretical re-derivation.

[0033] Influence of mud density on the characteristic equation Based on the motion equations and continuity equations of the original hydraulic transients of the pipeline, and using the medium density as the partial derivative with respect to time, the formula for calculating the positive water hammer wave velocity in a pipeline with homogeneous material freely supported at both ends, starting with pressurization, is as follows:

[0034] Where a: water hammer wave velocity, m / s; K: Elastic modulus of the medium transported in the pipeline, Pa; Density of the medium transported in the pipeline, kg / m³ 3 ; D: Pipe inner diameter, in meters; b: Pipe wall thickness, in meters; E: Elastic modulus of pipe material, Pa.

[0035] The above analysis shows that in the water hammer wave velocity variation model caused by different mud density distributions, water hammer wave velocity is a key parameter in the calculation of unsteady flow. When mud is transported in the pipeline, the water hammer wave velocity is not only related to the material, size, fixing method, elastic modulus, and wall thickness of the pipeline, but also closely related to the mud density. A water hammer wave velocity calculation equation that includes the slurry density is constructed, and the uneven distribution of mud density in the pipeline and its continuous change with time are considered. Using the method of characteristics, the characteristic coefficient B in the characteristic equation is discretized to obtain the change of water hammer wave velocity of different slurry densities with the elastic compression of the fluid.

[0036] S5: Using the results of S4, the modified unsteady flow characteristic line theory equations are applied to iteratively calculate the pipeline characteristics, thereby achieving accurate simulation of the hydraulic transition phenomenon during mud transportation. There is a progressive logical relationship between S1 and S5, which together constitute the complete process of the unsteady flow calculation method.

[0037] When slurry is transported in a pipeline, the water hammer wave velocity is related to the elastic modulus of the pipeline material, the density of the slurry, and its elastic modulus. The density distribution of the slurry transported in the pipeline is uneven and changes continuously over time. According to the method of characteristics, the calculation of the characteristic coefficient B in the characteristic equation is related to the water hammer wave velocity, and the calculation of the characteristic coefficient R is related to the slurry density. Therefore, based on the mesh discretization conditions of the method of characteristics, the water hammer wave velocity a, characteristic coefficient B, and characteristic coefficient R of the slurry transported in the pipeline are discretized in time and space, and a program is compiled to complete the relevant calculations.

[0038] By applying the technical solution of this embodiment, an unsteady flow analysis method for mud properties in a pipeline is realized, addressing the problem of inaccurate prediction and analysis of complex unsteady flow phenomena caused by density variations over time and space during mud transportation. By acquiring the mud state sequence at the pipeline inlet and determining the time from inlet to outlet, the relationship between the dynamic position of the mud and the density and velocity distribution throughout the pipeline is established. After defining the spatiotemporal step, the distribution state of the mud within the pipeline at any given time is discretized, obtaining the specific states of pipe segment position, velocity, and density. Based on this, mud density is introduced as a key variable to modify the characteristic line equation. The modified characteristic line equation is used to calculate water hammer wave velocity and evaluate other density-affected fluid parameters. Using the discretization results and the modified unsteady flow characteristic line equation, iterative calculations of pipeline characteristics are performed, achieving accurate simulation of hydraulic transition phenomena during mud transportation. This technical solution effectively improves the limitations of the existing steady flow calculation theory under clear water conditions. It can reflect the changes in mud density in the pipeline system with time and space in real time and dynamically, and improves the analysis capability and design accuracy of long-distance pipeline transportation in dredging projects, slurry transportation and other fields. It has important application value for predicting and mitigating water hammer effects, optimizing construction technology and improving control systems.

[0039] Furthermore, in this embodiment, the establishment of the pipeline mud state sequence in S2 includes real-time monitoring of the pressure, flow rate and density changes at the inlet of the mud delivery pipeline, and using numerical simulation methods to calculate the dynamic distribution of mud in the pipeline. The real-time monitoring can be carried out using a sensor array to cover multiple key parts of the pipeline inlet to obtain detailed mud state information.

[0040] In this embodiment, a sequence of mud state along the pipeline in S3 is established, and numerical simulation technology is used to accurately calculate the unsteady distribution of mud within the pipeline. By employing the method of characteristics, combined with discrete time and spatial units, this method can accurately capture the non-uniform changes in mud density over time and space, thereby deducing the dynamic distribution of mud within the pipeline. This combination of dynamic monitoring and simulation calculation not only provides in-depth insights into the transient behavior during mud transportation but also lays a solid data foundation for subsequent steps, ensuring the accuracy and reliability of the analysis of unsteady flow characteristics of mud. Furthermore, the dynamic calculation of water hammer wave velocity fully considers the influence of mud density and its distribution on wave velocity, further improving the calculation model for unsteady flow. Overall, the technical solution of this embodiment achieves comprehensive and high-precision simulation of the unsteady flow characteristics of mud transportation pipeline systems, providing strong support for engineering design and operation.

[0041] Furthermore, in this embodiment, the selection of the spatiotemporal step size in the discretization of the pipeline model needs to be based on the hydrodynamic stability condition to ensure that the discretization process does not lead to the divergence of the numerical solution. In particular, the influence of the change in slurry density on the discretization step size is considered to ensure the accuracy and effectiveness of the calculation results.

[0042] In this embodiment, the selection and determination of the spatiotemporal step size are based on the fluid dynamics stability condition to ensure that the discretization process does not lead to the divergence of the numerical solution. Particular emphasis is placed on the influence of slurry density changes on the discrete step size to maintain the accuracy and reliability of the calculation results. A reasonable setting of the discrete step size is crucial for the application of the characteristic line algorithm in pipeline models. It directly relates to the correct implementation and application effect of the unsteady flow calculation theory for pipeline slurry transportation, enabling the algorithm to maintain good computational performance and convergence characteristics even when dealing with complex situations where slurry density dynamically changes over time and space. This method enables the calculation of unsteady flow characteristics of pipelines with non-uniform slurry distribution, not only improving computational accuracy but also enhancing the model's adaptability and generalization ability in practical engineering applications. It has significant practical value for guiding the adjustment of construction process parameters, predicting maximum discharge pressure and flow rate, and improving control systems.

[0043] Furthermore, in this embodiment, the dynamic calculation of water hammer wave velocity includes a comparative analysis of the water hammer wave velocity of mud with different densities under the same pipeline conditions, in order to assess the degree of influence of mud density changes on the hydraulic transition process.

[0044] In this embodiment, the unsteady flow analysis method for mud properties in the pipeline accurately calculates the dynamic changes in water hammer velocity. Specifically, by comparing and analyzing the water hammer velocity of mud with different densities under the same pipeline conditions, the influence of mud density variation on the hydraulic transition process is evaluated. This technical solution utilizes a discrete time and space approach, establishing a correlation between the dynamic distribution and flow characteristics of the slurry in the pipeline based on the time distribution model of mud density at the pipeline inlet and the spatial distribution model along the pipeline, thereby accurately capturing the subtle changes in water hammer velocity with mud density fluctuations. By discretizing the pipeline using the method of characteristics and combining it with the water hammer velocity change model caused by different mud density distributions, this embodiment can quickly and effectively predict and analyze the transient behavior of the pipeline under unsteady flow conditions, providing strong data support for optimized design and operation control. Furthermore, by comprehensively applying the aforementioned discretization results and density influence to the improved hydraulic transition process calculation formula, the coherence and accuracy of the entire calculation system are ensured, making the transient flow analysis of the pipeline system closer to actual working conditions and enhancing the application value and practicality of the calculation method.

[0045] Furthermore, in this embodiment, the calculation method also includes establishing a mud state prediction model to predict the state of the mud inlet at future times, including parameters such as density and flow rate, so as to adjust the control strategy in the pipeline system.

[0046] In this embodiment, the calculation method further includes the establishment of a mud state prediction model to estimate the state of the mud inlet at future moments, including but not limited to key parameters such as mud density and flow velocity. This prediction model, based on historical data and current operating conditions, utilizes mathematical statistical methods or machine learning algorithms to predict potential density and flow velocity changes at the mud inlet in advance. By integrating prediction functions, the pipeline system can pre-adjust its control strategy to cope with transient changes that may occur during mud transport, achieving more precise and efficient system operation. The combination of the prediction model and the mud non-uniform distribution calculation method not only improves the safety of the slurry transport process but also optimizes transport efficiency, reduces energy consumption and equipment wear caused by non-steady flow, provides technical support for real-time monitoring and intelligent control, and thus improves the stability and economy of the entire system. Of course, in other embodiments not shown in the figure, the input parameters of the prediction model can also be dynamically updated through real-time monitoring and feedback mechanisms to enhance the accuracy and adaptability of the prediction.

[0047] Furthermore, in this embodiment, the calculation of the time tj for the mud to reach the outlet from the inlet can be based not only on the flow velocity parameter, but also on factors such as the inclination of the pipeline, the roughness of the pipe wall, and the viscosity of the mud, in order to achieve a more accurate time estimation.

[0048] In this embodiment, the calculation of the time tj for the mud to travel from the inlet to the outlet is based not only on the flow velocity parameter but also comprehensively considers factors such as the inclination of the pipeline, the roughness of the pipe wall, and the viscosity of the mud, achieving a more accurate time estimation. This method, by introducing these additional factors, enhances the complexity and accuracy of the time estimation model, ensuring that the transient characteristics of the hydraulic transition during mud transport are fully considered. Specifically, the inclination of the pipeline affects the flow characteristics of the mud under gravity, the roughness of the pipe wall affects the frictional resistance, which in turn affects the flow velocity, and the viscosity of the mud determines the magnitude of its flow resistance. The comprehensive consideration of these factors allows the time estimation to more closely approximate actual working conditions, thereby improving the reliability of the mud transport pipeline characteristic calculation. This time calculation method, which comprehensively considers key parameters, can more accurately predict the dynamic distribution of mud in the pipeline, providing an accurate time basis for unsteady flow calculations and enhancing the accuracy and applicability of the calculation results. In other embodiments not shown in the figure, these parameters can be dynamically adjusted to further optimize the calculation model and improve the simulation accuracy of the mud transport process.

[0049] Furthermore, in this embodiment, the mud settling rate is introduced as an additional parameter in the establishment of the mud state sequence along the pipeline, which is used to more accurately describe the change of mud density in the pipeline length direction, thereby improving the accuracy of pipeline characteristic simulation.

[0050] In this embodiment, considering the influence of the time-varying mud density at the pipeline inlet and the mud settling rate, a mud state sequence along the pipeline is established. Through a detailed description of the mud density and its temporal distribution at the pipeline inlet, combined with the mud flow velocity and settling characteristics within the pipeline, this invention achieves accurate modeling of the dynamic distribution of mud density within the pipeline at any given time. This model serves as the basis for calculating the continuous distribution of micro-units, further improving the accuracy and reliability of pipeline characteristic simulation. During the calculation process, the pipeline is discretized in time and space using the method of characteristics. Considering the dynamic changes in mud density and flow velocity, the characteristic coefficients B and R are accurately solved. Combined with the changes in water hammer wave velocity, the transient simulation of mud pipeline characteristics under non-uniform density conditions is completed. Through this series of improvements and innovations, the calculation method of this invention can more accurately reflect the hydraulic transient process under actual working conditions. This is of great significance for guiding the adjustment of construction process parameters, predicting maximum discharge pressure and flow rate, improving control systems, and training technical personnel, thereby promoting the development and progress of dredging engineering and slag transportation technology.

[0051] Furthermore, in this embodiment, the characteristic calculation equation application also includes the function of visualizing the calculation results, enabling users to intuitively understand the hydraulic transition phenomenon during mud transportation and the impact of changes in various parameters on pipeline characteristics.

[0052] In this embodiment, the application of the characteristic calculation equation is further extended to the visualization of the calculation results. This function aims to intuitively present the impact of hydraulic transition phenomena and parameter changes during mud transportation on pipeline characteristics to the user. Through a graphical interface, users can clearly observe the spatiotemporal evolution of key parameters such as mud density, flow velocity, and pressure, and how these parameters affect changes in water hammer velocity and characteristic coefficients. The implementation effect is enhanced user understanding of the mud transportation process, which helps to more accurately control and adjust construction process parameters, predict maximum discharge pressure and flow rate under extreme conditions, and provides strong support for improving control systems and training technical personnel. Simultaneously, the design and implementation of the visualization function in this embodiment improves the interactivity and practicality of mud transportation calculations, enabling theoretical calculation results to be more effectively transformed into decision-making basis in engineering practice.

[0053] Furthermore, in this embodiment, the establishment of the mud state prediction model also includes an interaction interface with an external database to obtain real-time mud parameters and environmental data, including weather conditions, terrain features, etc., in order to enhance the real-time performance and prediction capabilities of the system.

[0054] In this embodiment, the mud state prediction model, through interaction with an external real-time database, can acquire environmental data, including weather conditions and terrain features, as well as the latest mud parameters. This provides a basis for dynamic adjustment of the calculation model, enhancing the system's real-time response capability and prediction accuracy. By integrating real-time data, the system can update the calculation results instantly when key parameters such as mud density and flow velocity change, reflecting the actual distribution of mud in the pipeline. This allows for more accurate prediction of unsteady flow characteristics such as pressure fluctuations and flow velocity changes during the hydraulic transition process. This design enables the calculation of mud transport pipeline characteristics to be no longer limited to static conditions but can adapt to the changing environmental factors at the work site. It provides more accurate data support for pipeline system design, operation monitoring, and fault diagnosis in dredging projects, slag transport, and other fields, helping to improve transport efficiency and reduce energy consumption and maintenance costs. Of course, in other embodiments not explicitly shown in this example, the performance of the mud state prediction model can be further optimized through different data acquisition and processing strategies. For example, machine learning algorithms can be used to automatically identify and filter irrelevant noise to improve the quality of input data, or multi-source data fusion theory can be used to enhance the robustness and generalization ability of the model to cope with more complex and variable working conditions. In other embodiments not shown in the figure, the mud state prediction model can also be linked with a remote monitoring system to achieve remote real-time monitoring and intelligent control, further improving the safety and economy of operation.

[0055] This invention provides a method for constructing an unsteady flow calculation system for the characteristics of a non-uniformly distributed mud transport pipeline, comprising: S1: inputting basic parameters, receiving the inlet mud state sequence set (ti, vi, ρi) and pipeline geometric parameters of the mud transport pipeline; S2: based on the state sequence set, calculating the propagation position and time of the mud in the pipeline at each moment; S3: after defining the spatiotemporal step size, discretizing the pipeline using the characteristic line method to form multiple calculation units; S4: for the discretized model, developing an algorithm to solve the water hammer wave velocity and other density-affected parameters in the modified characteristic line equation; S5: integrating the modules from S1 to S4 to create a simulation system capable of real-time feedback of the transient water hammer behavior of the mud transport pipeline, wherein there is a progressive logical relationship between S1 to S5, which together constitute the construction process of the calculation system.

[0056] By applying the technical solution of this embodiment, accurate calculations of pipeline characteristics under non-steady flow conditions are achieved by receiving the inlet mud state sequence set and pipeline geometric parameters of the mud conveying pipeline. First, based on the mud state sequence set, the propagation position and time of the mud in the pipeline are accurately calculated. This step considers the dynamic changes in mud density with time and space, providing important basic data for subsequent calculations. Next, a spatiotemporal step size is defined, and the pipeline is discretized using the method of characteristics to form multiple computational units. This method can adapt to the non-uniform distribution of mud density, improving the accuracy of the calculation. Then, for the discretized model, an algorithm is developed to solve the water hammer wave velocity and other density-affected parameters in the modified characteristic line equation. This process considers the influence of mud density on the water hammer wave velocity, making the calculation results closer to reality. Finally, by integrating the above steps, a simulation system capable of providing real-time feedback on the transient behavior of water hammer in slurry transport pipelines was created. This system enables dynamic simulation and analysis of pipeline system characteristics under non-uniform density conditions, improving the scientific rigor and safety of slurry transport system design and operation. It also overcomes the limitations of traditional steady-flow algorithms in handling dynamically changing slurry densities, enhancing the predictive ability for non-steady-flow phenomena and its engineering application value.

[0057] Furthermore, in this embodiment, the construction method also includes a real-time data processing module, which is used to receive and analyze real-time data in the pipeline state sequence set to dynamically adjust the calculation parameters and ensure the consistency between the calculation results and the actual pipeline characteristics.

[0058] In this embodiment, the introduction of a real-time data processing module enables the calculation method to dynamically adjust calculation parameters based on field data from the pipeline state sequence set, ensuring that the calculation results reflect the actual operating characteristics of the pipeline in real time. This module receives real-time measurements such as flow velocity and mud density from the sensor network, compares them with a preset pipeline model, automatically identifies deviations from theoretical expectations, and updates key coefficients in the characteristic line equation, such as water hammer velocity and characteristic coefficients B and R, to adapt to the uneven distribution and time-varying changes in mud density within the pipeline. In this way, the calculation model can quickly respond to any changes in pipeline operating conditions, improving prediction accuracy. Especially when dealing with non-steady flow and complex hydraulic transition processes, it can better simulate the dynamic behavior of real mud transportation processes, providing data support for real-time system monitoring, fault diagnosis, and optimized operation, thereby enhancing the reliability and efficiency of the pipeline transportation system.

[0059] An unsteady flow analysis system for mud properties in a delivery pipeline includes: The basic data module collects the mud state parameters at the pipeline inlet at different times to construct a set of mud state sequences (ti, vi, ρi) at the pipeline inlet. The distribution model analyzes the dynamic position of the mud in the pipeline to establish a model of the density and velocity distribution of the mud over the entire length of the pipeline at any given time. The discrete module defines the spatiotemporal step size and then discretizes the distribution of mud in the pipeline at any time to obtain the flow velocity and density of the mud at different pipe sections. The parameter calculation module, based on the discretized pipeline state, introduces mud density as a key variable to modify the characteristic line equation, and uses the modified characteristic line equation to calculate the water hammer wave velocity and other density-affected fluid parameters of each discrete segment. The execution module uses the results of parameter calculations and applies the modified unsteady flow characteristic line theory to iteratively calculate pipeline characteristics, thereby simulating the hydraulic transition phenomenon during mud transportation.

[0060] In the distribution model, the definition is... Let i be the length from pipe inlet i to pipe position j, then: .

[0061] The formula for calculating the water hammer wave velocity is:

[0062] Where a is the water hammer wave velocity, and K is the elastic modulus of the medium being transported in the pipeline. Let D be the density of the medium being transported in the pipeline, b be the inner diameter of the pipeline, b be the pipe wall thickness, and E be the elastic modulus of the pipeline material.

[0063] Furthermore, the modified non-steady flow characteristic line theory is obtained as follows: the motion equations and continuity equations of the hydraulic transients of the clear water pipeline are modified, a key density term is introduced, the inertial force, viscous force, gravity and frictional resistance of the pipeline wall are considered, the non-steady flow process of the slurry is described by partial differential equations and the local and frictional resistance losses of the pipeline are considered, and the characteristic line method is used to discretize the slurry transport pipeline at any time, dividing the continuous pipeline into multiple pipe segments and nodes, and the slurry flow characteristics, including velocity, pressure and density, in each pipe segment are considered to be uniformly distributed.

[0064] A computer program product includes a computer program, characterized in that the computer program is executed by a processor using the aforementioned method for analyzing the unsteady flow characteristics of mud in a delivery pipeline.

[0065] A computer-readable storage medium includes instructions that, when executed on a computer, cause the computer to perform the aforementioned method for analyzing the unsteady flow characteristics of mud in a delivery pipeline.

[0066] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing devices. They can be centralized on a single computing device or distributed across a network of multiple computing devices. They can be implemented using computer-executable program code, and thus can be stored in a storage device for execution by a computing device. In some cases, the steps shown or described can be performed in a different order than those described herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0067] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the unsteady flow characteristics of mud in a conveying pipeline, characterized in that, include: S1. By collecting mud state parameters at the pipeline inlet at different times, a sequence set of mud state parameters at the pipeline inlet is constructed. t i 、 v i ρ i ); S2. By analyzing the dynamic position of the mud in the pipeline, establish a model of the density and velocity distribution of the mud over the entire length of the pipeline at any given time. S3. After defining the time-space step, the distribution of mud in the pipeline at any time is discretized to obtain the flow velocity and density of the mud at different pipe sections. S4: Based on the discretized pipeline state, mud density is introduced as a key variable to modify the characteristic line equation. The modified characteristic line equation is used to calculate the water hammer wave velocity and other density-affected fluid parameters of each discrete segment. S5: Using the results of S4, the modified unsteady flow characteristic line theory is applied to iteratively calculate the pipeline characteristics, thereby simulating the hydraulic transition phenomenon during mud transportation.

2. The method for analyzing the unsteady flow characteristics of mud in a conveying pipeline according to claim 1, characterized in that, In S2, define For inlet from pipeline i to pipeline j The length of the position, then: 。 3. The method for analyzing the unsteady flow characteristics of mud in a conveying pipeline according to claim 1 or 2, characterized in that, The formula for calculating the water hammer wave velocity is: Where a is the water hammer wave velocity, and K is the elastic modulus of the medium being transported in the pipeline. Let D be the density of the medium being transported in the pipeline, b be the inner diameter of the pipeline, b be the pipe wall thickness, and E be the elastic modulus of the pipeline material.

4. The method for analyzing the unsteady flow characteristics of mud in a conveying pipeline according to claim 1, characterized in that, The modified method for obtaining the characteristic line theory of unsteady flow is as follows: the motion equations and continuity equations of the hydraulic transients of the clear water pipeline are modified, a key density term is introduced, and the inertial force, viscous force, gravity and frictional resistance of the pipeline wall are considered. Partial differential equations are used to describe the unsteady flow process of the slurry and the local and frictional resistance losses of the pipeline are considered. The characteristic line method is used to discretize the slurry transport pipeline at any time, and the continuous pipeline is divided into multiple pipe segments and nodes. The slurry flow characteristics, including velocity, pressure and density, in each pipe segment are considered to be uniformly distributed.

5. A system for analyzing the unsteady flow characteristics of mud in a pipeline, characterized in that, include: The basic data module collects mud state parameters at the pipeline inlet at different times to construct a sequence set of mud state data at the pipeline inlet. t i 、v i ρ i ); The distribution model analyzes the dynamic position of the mud in the pipeline to establish a model of the density and velocity distribution of the mud over the entire length of the pipeline at any given time. The discrete module defines the spatiotemporal step size and then discretizes the distribution of mud in the pipeline at any time to obtain the flow velocity and density of the mud at different pipe sections. The parameter calculation module, based on the discretized pipeline state, introduces mud density as a key variable to modify the characteristic line equation, and uses the modified characteristic line equation to calculate the water hammer wave velocity and other density-affected fluid parameters of each discrete segment. The execution module uses the results of parameter calculations and applies the modified unsteady flow characteristic line theory to iteratively calculate pipeline characteristics, thereby simulating the hydraulic transition phenomenon during mud transportation.

6. The unsteady flow analysis system for mud properties in a delivery pipeline according to claim 5, characterized in that, In the distribution model, the definition is... For inlet from pipeline i to pipeline j The length of the position, then: 。 7. The unsteady flow analysis system for mud properties in a delivery pipeline according to claim 6, characterized in that, The formula for calculating the water hammer wave velocity is: Where a is the water hammer wave velocity, and K is the elastic modulus of the medium being transported in the pipeline. Let D be the density of the medium being transported in the pipeline, b be the inner diameter of the pipeline, b be the pipe wall thickness, and E be the elastic modulus of the pipeline material.

8. The unsteady flow analysis system for mud properties in a delivery pipeline according to claim 6, characterized in that, The modified method for obtaining the characteristic line theory of unsteady flow is as follows: the motion equations and continuity equations of the hydraulic transients of the clear water pipeline are modified, a key density term is introduced, and the inertial force, viscous force, gravity and frictional resistance of the pipeline wall are considered. Partial differential equations are used to describe the unsteady flow process of the slurry and the local and frictional resistance losses of the pipeline are considered. The characteristic line method is used to discretize the slurry transport pipeline at any time, and the continuous pipeline is divided into multiple pipe segments and nodes. The slurry flow characteristics, including velocity, pressure and density, in each pipe segment are considered to be uniformly distributed.

9. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program is a method for analyzing the unsteady flow characteristics of mud in a delivery pipeline as described in any one of claims 1-4.

10. A computer-readable storage medium comprising instructions, when executed on a computer, causing the computer to perform the unsteady flow analysis method for mud properties in a delivery pipeline as described in any one of claims 1-4.

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