A water pump flow field measurement method based on inertial guidance and a velocity measuring particle

Abstract

The application discloses a kind of water pump flow field measurement method and velocity measuring particle based on inertial guidance, it is related to water pump flow field measurement technical field.The method comprises: assembling and calibrating the velocity measuring particle of built-in IMU, releasing at water pump entrance, so that it enters water pump interior and records acceleration data itself, recycles particle at water pump in outlet, reads IMU data in particle, reconstructs particle motion track by zero offset calibration, attitude solution, gravity elimination, integral positioning, zero speed correction and other steps, reconstructs global velocity field using the trajectory of multiple particles by RBF interpolation, and then calculates flow, traces streamline and generates velocity nephogram.The application does not need to reconstruct the structure of water pump, is not limited by flow pattern and pipeline transparency, can simultaneously output high-precision flow and full flow field visualization result, provides a kind of new technical means for water pump operation monitoring and optimization design.

Description

Technical Field

[0001] This invention relates to the field of water pump flow field measurement technology, and more specifically, to a water pump flow field measurement method and velocity measuring particles based on inertial guidance, used for water pump flow measurement, streamline drawing and velocity cloud map generation. Background Technology

[0002] Pumping stations, as the core hub of fluid transport systems, are widely used in urban water supply and drainage, farmland irrigation, industrial production, and water conservancy projects. Flow measurement is a crucial link in the entire life cycle management of pumping stations, and its accuracy directly affects unit efficiency assessment, energy-saving scheduling, and safe operation. Currently, commonly used pump flow measurement methods typically employ ultrasonic flow meters, propeller flow meters, electromagnetic flow meters, Pitot tube flow meters, Venturi tube flow meters, and PIV (particle image velocimetry) technology commonly used in model pumps. However, these traditional flow meter structures all have the following drawbacks in practical engineering applications:

[0003] (i) It has strict requirements for flow patterns and is difficult to adapt to the complex flow field inside the water pump.

[0004] Traditional flow measurement methods generally rely on axisymmetric, fully developed, and stable flow fields as a prerequisite for measurement. For example, Pitot tubes and propeller flow meters require the installation axis to be strictly parallel to the pipe axis, and the incoming flow direction must be consistent with the measurement axis; ultrasonic flow meters require that the measured liquid does not contain a large number of air bubbles, and that there is no obvious turbulence or eddies at the measurement location; electromagnetic flow meters also require a uniform flow field distribution, otherwise nonlinear measurement errors will occur. However, the internal flow field of an actual water pump is extremely complex: the high-speed rotation of the impeller induces strong swirling and secondary flows, flow separation and wake regions exist within the impeller passage, and the flow near the pump outlet exhibits strong non-uniformity and pulsation. Under such complex flow conditions, the signal from traditional flow meters will be severely distorted, and the measurement error will increase significantly. To improve measurement conditions, engineering often requires the installation of flow straightening devices such as guide vanes, flow stabilizers, and float boxes, which not only increases additional head loss but also fails to fundamentally solve the measurement accuracy problem.

[0005] (ii) Installation location is limited, making it difficult to adapt to compact pump room environments.

[0006] Most traditional flow meters require strict upstream and downstream straight pipe length requirements (typically 5 to 10 times the pipe diameter) to ensure sufficient flow development. However, pump rooms generally suffer from dense pump units, compact pipe layouts, and limited space, resulting in strong flow field disturbances and significant vibrations near the pump inlet and outlet, making it difficult to provide adequate installation space. Furthermore, the installation of invasive measuring devices (such as Pitot tubes and paddlewheels) may interfere with the pump structure, valves, flanges, and other components, even altering the local flow field morphology and further affecting measurement accuracy. While non-invasive devices (such as ultrasonic flow meters) do not require openings, they are sensitive to pipe material, wall thickness, and scaling conditions, and face signal interference issues in complex electromagnetic environments.

[0007] (iii) Laboratory PIV technology cannot be directly applied to industrial prototype water pumps.

[0008] Particle image velocimetry (PIV) technology is widely used in flow field studies of transparent model pumps in the laboratory due to its high spatial resolution. However, PIV technology has the following inherent drawbacks, making it completely unsuitable for measuring the internal flow field of industrial-grade closed water pumps. PIV requires an optical window and laser light source, demanding complete transparency of the measured flow channel, while industrial water pumps are mostly opaque metal casings, making it impossible to observe the internal flow from the outside; PIV typically only measures the velocity distribution within a two-dimensional plane, failing to acquire three-dimensional flow field information across the entire flow channel; it is environmentally sensitive, with high requirements for vibration, ambient light, and water turbidity, making stable operation in industrial settings difficult; and it is costly, with high-speed cameras, dual-pulse lasers, and other equipment being expensive and requiring professional operation, making it unsuitable for routine inspections.

[0009] In summary, existing technologies either have stringent requirements for flow conditions and equipment (such as ultrasonic and Pitot tubes), cannot be used on closed prototypes (such as PIV), or have excessive installation and modification costs (such as electromagnetic and Venturi tubes). There is still a lack of a measurement method that can simultaneously meet the requirements of adapting to complex flow conditions, being compatible with compact installation, being usable in non-transparent closed environments, and providing full-domain flow field output. Summary of the Invention

[0010] To address the aforementioned issues, this invention provides a method for measuring the flow field of a water pump based on inertial guidance and a velocity measuring particle. The aim is to achieve accurate measurement of the entire flow field in a closed pipe under complex flow conditions without shutting down the pump or modifying its structure. Simultaneously, it outputs flow rate, streamlines, and velocity cloud maps, providing technical support for water pump operation monitoring and optimization design.

[0011] To achieve the above objectives, the present invention adopts the following technical solution:

[0012] One aspect is a method for measuring the flow field of a water pump based on inertial guidance, the steps of which are as follows:

[0013] S1, Assemble and calibrate a set of velocity-measuring particles with a built-in inertial detection unit (IMU), including: IMU sensor, microcontroller, data storage module, battery and waterproof housing, wherein the particle density is adjusted to match the fluid to ensure that the particles have no relative motion with the fluid;

[0014] S2, obtain the geometric parameters of the target flow section of the water pump, establish a three-dimensional model of the water pump flow channel by measuring or reading the design drawings, and extract at least one flow section area and normal vector;

[0015] S3, under normal pump operation, rapidly release velocity-measuring particles at the pump inlet and record their initial spatial coordinates in the pump inlet pipe.

[0016] S4, recovers velocity-measuring particles at the outlet of the water pump;

[0017] S5 reads the raw data from the inertial sensor from the recovered velocimeters and performs the following calculations using a computer:

[0018] S51, Zero bias calibration: Before the experiment, the particle is placed at rest for 5 to 10 seconds, and the average value of the data during this rest period is taken as the zero bias calibration estimate of acceleration and angular velocity.

[0019] S52, Attitude calculation: The attitude quaternion is updated based on gyroscope data, and complementary filtering correction is performed using accelerometer data to obtain the particle's rotation matrix from the body coordinate system to the navigation coordinate system. ;

[0020] S53, the acceleration of the body coordinate system Switch to the navigation frame and subtract the gravity vector of the navigation frame. The actual acceleration of the particle in the navigation coordinate system is obtained. Then solve for the velocity and displacement; for Speed ​​is obtained by integrating over time. Integrating again yields the displacement trajectory. ,

[0021] S54, zero-velocity correction, uses data from the stationary phase after particle recovery to linearly correct integral drift:

[0022] S55, Full-field flow reconstruction: Using trajectory data of multiple particles, the velocity field inside the water pump is reconstructed through radial basis function (RBF) interpolation.

[0023] S56, Flow integral: The total volumetric flow rate passing through the inlet or outlet cross-section of a water pump per unit time is equal to the surface integral of the velocity along the normal direction of the cross-section, thus yielding the volumetric flow rate. ,unit :

[0024]

[0025] In the formula, This refers to the inlet / outlet cross-sectional area of ​​the water pump, in units of... , Let (x, y) be the velocity vector of a point (x, y) on the cross section, in units. , It is the unit normal vector of the cross section (pointing in the positive direction of flow). For the first Line number The velocity vector of the column grid is obtained by RBF interpolation. For the first Line number Area of ​​grid elements, unit ;

[0026] S57, Streamline and Velocity Cloud Map Generation: Based on the reconstructed velocity field, the fourth-order Runge-Kutta method is used to trace the streamlines. Starting from the seed point, the integral is performed along the velocity direction to map the velocity magnitude into a pseudo-color image.

[0027] Furthermore, the formulas for calculating the zero-bias calibration estimates of S51 acceleration and angular velocity are as follows:

[0028]

[0029]

[0030] Furthermore, in the formula, The zero-biased acceleration vector, in units. , The total number of samples in the static calibration section, N≥1000. For the static segment One acceleration sample, unit , Let be the initial static attitude rotation matrix. This is the zero bias vector of the gyroscope, in units. , For the static segment angular velocity samples, unit ; The initial attitude quaternion , This is the acceleration measurement value for the first frame of the stationary segment, in units of... , This is a function used to deduce the initial attitude from the gravity vector (the direction of acceleration should point to...). The navigation system is vertically downward.

[0031] Furthermore, in S52, the attitude quaternion update uses the first-order Runge-Kutta method (RK1) to integrate the quaternion differential equation:

[0032]

[0033] in, For the current quaternion, For sampling interval, in units , Let x be the differential of a quaternion, the function on the right-hand side, and y be the rate of change of the quaternion. normalize(x) represents normalizing the quaternion so that... To prevent numerical divergence, It is the transpose symbol;

[0034] The angular velocity error corrected by complementary filtering is:

[0035]

[0036]

[0037] In the formula, This is the angular velocity error vector, in units. , These are the three imaginary components of a quaternion. It is the transpose of the rotation matrix. The gravity vector of the navigation system ,unit , The measured acceleration values ​​of the system after zero bias compensation are in units. ; The angular velocity is input after PI correction, used for quaternion integration, unit , The value is the result after zero bias compensation; For proportional gain, Control the speed of error correction; Integral gain, eliminating steady-state error. This is the integral term of the angular velocity error, in units of... .

[0038] 4. Furthermore, .

[0039] Furthermore, S53 real motion acceleration The calculation method is as follows:

[0040]

[0041] In the formula, , This is the volume acceleration vector after zero-bias compensation, in units. , This is a physical value for acceleration, including a gravitational component, in units of... , The zero-biased acceleration vector, in units. , Let g be the gravity vector of the navigation system, in units. , This is the rotation matrix at the current moment.

[0042] Furthermore, the zero-speed correction described in S54 adopts a linear error allocation method:

[0043]

[0044]

[0045] In the formula, The corrected velocity vector at time i ( ),unit , The original integral velocity before correction, in units , , is the weighting coefficient for the static segment, which increases linearly from 0 to 1. The measured integral velocity at the end point k of the stationary segment, in units of... , The total duration of the static segment is expressed in seconds. Sampling interval time, in units , They are respectively End-of-shaft velocity drift, in units .

[0046] Furthermore, for S55, the full-field flow field reconstruction uses Gaussian radial basis functions:

[0047]

[0048] In the formula, For any point in the entire field after interpolation reconstruction velocity vector, unit , Let p be the RBF weight vector of the p-th particle, in units. , The total number of particles participating in the interpolation. For radial basis functions, ,unit , The three-dimensional coordinates of the trajectory point of the p-th particle, in units ;

[0049]

[0050] In the formula, For Gaussian radial basis functions, r is the Euclidean distance from the target point to the data point, in units. , For kernel bandwidth parameters, in units , , , where is the bandwidth scaling factor.

[0051] Furthermore, the tracing streamline described in S57 employs the fourth-order Runge-Kutta method:

[0052]

[0053] In the formula, For the coordinates of the next step on the streamline, Coordinates of the current streamline point Unit: m The arc length step for tracing along the streamline, in meters, Δs = 0.1~1m; These represent the first, second, third, and fourth slopes of RK4, respectively.

[0054] ,

[0055] , ,

[0056]

[0057] On the other hand, there is a velocity-measuring particle used in an inertial-guided water pump flow field measurement method. This particle can move with the flow and record data generated by its own IMU sensor, enabling streamline plotting and outputting the flow velocity at various points along the streamline, including:

[0058] An inertial measurement unit (IMU) integrates a three-axis accelerometer and a three-axis gyroscope to collect three-axis linear acceleration and three-axis angular velocity.

[0059] A microcontroller (MCU) is used to control data acquisition and storage;

[0060] A Flash data storage module is used to store the raw IMU data;

[0061] One power supply unit supplies power to all modules;

[0062] A waterproof outer shell encapsulates the above components into a sphere;

[0063] At least one replaceable counterweight is installed inside the housing to adjust the overall particle density to match the fluid being measured.

[0064] The IMU sensor, MCU processor, flash memory, counterweight, and battery are encapsulated inside a waterproof housing, forming a spherical shape.

[0065] The waterproof outer shell is covered with a rubber sleeve.

[0066] Furthermore, the particle diameter is ≤2cm, and the density and fluid matching error is ≤±5% to ensure that the particles have no relative motion with the fluid.

[0067] Beneficial effects of this invention:

[0068] Disturbance-free measurement: Particle density matches the fluid, has good tracking performance, and does not interfere with the flow field.

[0069] Good applicability: It has low requirements for actual on-site installation conditions, is easy to operate, and the IMU-sensing particle flow measurement method does not require the addition of equipment to the original unit, transparent pipes, straight pipe sections before and after, or shutdown. It can be directly used for prototype water pumps. IMU-sensing particles can be released from the unit inlet or maintenance gate well, and the measurement can be completed by recovering the IMU-sensing particles at the outlet.

[0070] Compared to traditional flow meters, IMU-sensing particle flow measurement covers a wider measurement range and a larger measurement area: the entire flow path from the unit inlet to the unit outlet is measured, which is a larger measurement range than traditional flow meters that can only measure a surface or a region.

[0071] Controllable accuracy: Through zero-speed correction and complementary filtering algorithms, the integral drift problem of inertial navigation is effectively suppressed.

[0072] Strong data visualization: The IMU-sensing particle flow measurement method outputs acceleration and angular velocity data measured by each sensor. After post-processing, streamlines of the entire flow field and velocity vectors at points along each streamline can be obtained. The flow rate through each surface in the flow channel can be calculated using the facet averaging method. Detailed Implementation

[0073] This invention proposes a method for measuring the flow field of a water pump based on inertial guidance, the steps of which are as follows:

[0074] Step 1. Assemble and calibrate a set of velocity-measuring particles with a built-in inertial detection unit (IMU), including: an IMU sensor, a microcontroller, a data storage module, a battery, and a waterproof housing. The particle density is adjusted to match the fluid to ensure that the particles have no relative motion with the fluid.

[0075] After assembling the above components, adjust the particle density by changing the counterweight to be slightly less than that of the liquid being tested. Then, write the operating system to the development board and test whether the particles can run normally. If they run normally, repeat the process to create more than 10 particles.

[0076] Step 2: Obtain the geometric parameters of the target flow section of the water pump. The required cross-sectional area can be measured by using a coordinate measuring machine, total station, or laser rangefinder after the unit is shut down. Alternatively, it can be obtained by modeling the unit's design drawings in software, establishing a three-dimensional model of the water pump flow channel, and extracting at least one flow cross-sectional area and normal vector.

[0077] Step 3: Under normal operating conditions of the water pump, rapidly release velocity-measuring particles at the water pump inlet and record their initial spatial coordinates in the water pump inlet pipe.

[0078] Release method: Load the IMU sensor particles into the launcher cartridge, and insert the transmitter's launch port into the water, reaching the water pump inlet. Purge the transmitter with high-pressure gas, causing the IMU sensor particles to be launched sequentially and rapidly towards the water pump inlet.

[0079] Before unit operation, place the prepared particles and remote release device near the unit's inlet. If the particles are equipped with Hall sensors, install electromagnets at both the inlet and outlet. Calibrate the IMU sensor before release. After the unit has been running normally for a period of time, release the sensor and record the release time. If the particles are equipped with Hall sensors, use the particle entry and exit times recorded by the Hall sensors. To ensure that the inertial navigation sensor error is within a controllable range, the particle entry and exit time should be less than 10 seconds.

[0080] Step 4: Recover the velocity-measuring particles downstream of the water pump outlet. Since the particle density is slightly less than that of the liquid being measured, they will not sink in water. As the water flow velocity decreases, they will gradually float to the surface. A net can be installed in the channel downstream of the water pump outlet to intercept the washed-out particles.

[0081] Step 5: Read the raw data from the inertial sensor from the recovered velocity-measuring particles and perform calculations using a computer.

[0082] After completing one pass, the particle is retrieved and the Flash data is exported to the host computer via USB / wireless interface to complete the following calculation process:

[0083] (1) Acceleration zero-bias calibration and angular velocity zero-bias calibration

[0084] Particle stationary calibration uses acceleration and angular velocity data from the stationary phases of the particles before and after the experiment to estimate the sensor's zero bias. Before each experiment, the particles are placed at rest for 5–10 seconds, and the average value of the data during this stationary phase is taken as the zero bias estimate.

[0085] The formulas for calculating the zero-bias calibration estimates of acceleration and angular velocity are as follows:

[0086]

[0087]

[0088] In the formula, The zero-biased acceleration vector, in units. , The total number of samples in the static calibration section, N≥1000. For the static segment One acceleration sample, unit , Let be the initial static attitude rotation matrix. This is the zero bias vector of the gyroscope, in units. , For the static segment angular velocity samples, unit ; The initial attitude quaternion , This is the acceleration measurement value for the first frame of the stationary segment, in units of... , This is a function used to deduce the initial attitude from the gravity vector (the direction of acceleration should point to...). The navigation system is vertically downward.

[0089] (2) Quadruple attitude integral

[0090] The attitude quaternion is updated based on gyroscope data, and complementary filtering correction is performed using accelerometer data to obtain the particle's rotation matrix from the body coordinate system to the navigation coordinate system. .

[0091] The quaternion differential equation is integrated using the first-order Runge-Kutta method (RK1):

[0092]

[0093] in, ; For the current quaternion, For sampling interval, in units , Let x be the differential of a quaternion, the function on the right-hand side, and y be the rate of change of the quaternion. normalize(x) represents normalizing the quaternion so that... To prevent numerical divergence, It is the transpose symbol;

[0094] To suppress attitude drift caused by the pure integration method, the Mahony complementary filtering algorithm is used to correct the gyroscope integration results with the accelerometer as a reference. The angular velocity error corrected by the complementary filtering is:

[0095]

[0096]

[0097] In the formula, This is the angular velocity error vector, in units. , These are the three imaginary components of a quaternion. It is the transpose of the rotation matrix. The gravity vector of the navigation system ,unit , g, unit ; The angular velocity is input after PI correction, used for quaternion integration, unit , The result is the original angular velocity measurement after zero bias compensation; For proportional gain, Control the speed of error correction; Integral gain, eliminating steady-state error. This is the integral term of the angular velocity error, in units of... .

[0098] (3) Rotation matrix calculation

[0099] The conversion relationship between quaternions and direction cosine matrices is as follows:

[0100] ,

[0101] [ ],

[0102] ]

[0103] In the formula, R(q) represents a 3×3 rotation matrix (system → navigation system, denoted as (q)). ,satisfy , These represent the four components of the normalized quaternion at the current moment. The three lines of the above equation represent the system... axis, axis, The direction cosine of the axis in the navigation system.

[0104] (4) Gravitational acceleration elimination

[0105] The IMU is fixed to the particle and moves with it. The acceleration it measures consists of two parts: the actual motion acceleration and the gravitational acceleration. After converting the volume coordinate acceleration to the navigation frame, subtracting the gravity vector of the navigation frame yields the particle's actual motion acceleration.

[0106] Acceleration of the body coordinate system Switch to the navigation frame and subtract the gravity vector of the navigation frame. The actual acceleration of the particle in the navigation coordinate system is obtained. Then solve for the velocity and displacement; for Speed ​​is obtained by integrating over time. Integrating again yields the displacement trajectory. :

[0107] Real motion acceleration The calculation method is as follows:

[0108]

[0109] In the formula, , This is the volume acceleration vector after zero-bias compensation, in units. , This is a physical value for acceleration, including a gravitational component, in units of... , The zero-biased acceleration vector, in units. , Let g be the gravity vector of the navigation system, in units. , This is the rotation matrix at the current moment.

[0110] (5) Velocity-displacement integral

[0111] Given the acceleration of the navigation system, solve for the velocity and displacement step by step:

[0112]

[0113]

[0114] In the formula, For the first The navigation system velocity vector at each time step [ , ] T ,unit , For the first The navigation system velocity vector at each time step, in units. , For time intervals, in units , For the first The acceleration of the navigation system at each time step, in units , For the first The navigation system displacement vector at each time step [ , ] T ,unit , For the first The navigation system displacement vector at each time step, in units. , For the first The navigation system speed at each time step, in units .

[0115] (6) Zero speed correction

[0116] Linear correction of integral drift is performed using the static segment data after particle recovery. Zero-rate update is the core method for suppressing integral drift. Let the particle static segment be... The speed should be zero, achieved by applying a linear speed correction at the end of the stationary segment:

[0117]

[0118]

[0119] In the formula, The corrected velocity vector at time i ( ),unit , The original integral velocity before correction, in units , , is the weighting coefficient for the static segment, which increases linearly from 0 to 1. The measured integral velocity at the end point k of the stationary segment, in units of... , The total duration of the static segment is expressed in seconds. Sampling interval time, in units , They are respectively End-of-shaft velocity drift, in units .

[0120] (7) Interface flow integral

[0121] At the inlet or outlet section of a water pump, the total volumetric flow rate per unit time is equal to the surface integral of the velocity along the normal direction of the section, thus yielding the volumetric flow rate. ,unit :

[0122]

[0123] In the formula, This refers to the inlet / outlet cross-sectional area of ​​the water pump, in units of... , Let (x, y) be the velocity vector of a point (x, y) on the cross section, in units. , It is the unit normal vector of the cross section (pointing in the positive direction of flow). For the first Line number The velocity vector of the column grid is obtained by RBF interpolation. For the first Line number Area of ​​grid elements, unit .

[0124] = , = , = ; Indicates the first OK Area of ​​a grid element, in units , Indicates the first Row grid width, unit , express Column grid height, in units , Pipe radius, unit , The optimal number of grid divisions in the x / y directions is [not specified]. .

[0125] (8) Streamline generation

[0126] Due to the limited number of velocities and sparse spatial sampling points, interpolation is used to reconstruct the discrete particle trajectory data into a continuous velocity distribution across the entire field.

[0127]

[0128] In the formula, For any point in the entire field after interpolation reconstruction velocity vector, unit , Let p be the RBF weight vector of the p-th particle, in units. , The total number of particles participating in the interpolation. For radial basis functions, ,unit , The three-dimensional coordinates of the trajectory point of the p-th particle, in units ;

[0129]

[0130] In the formula, For Gaussian radial basis functions, r is the Euclidean distance from the target point to the data point, in units. , For kernel bandwidth parameters, in units , , , where is the bandwidth scaling factor.

[0131] (9) Streamline tracing

[0132] Based on the reconstructed velocity field, the fourth-order Runge-Kutta method is used to trace the streamlines, integrating along the velocity direction starting from the seed point:

[0133]

[0134] / ds is the velocity direction vector along the streamline arc length s. The three-dimensional coordinates of a point on a streamline, in units , The velocity vector at that point, in units. , The magnitude of the velocity scalar at that point, in units .

[0135]

[0136] In the formula, For the coordinates of the next step on the streamline, Coordinates of the current streamline point Unit: m The arc length step is the distance along the streamline, in meters, Δs = 0.1~1m.

[0137] ,

[0138] , ,

[0139]

[0140] These represent the first, second, third, and fourth slopes of RK4, respectively.

[0141] (10) Velocity cloud map rendering

[0142] Map the full-field velocity scalar distribution (velocity magnitude) obtained by RBF interpolation to a pseudo-color image:

[0143]

[0144] In the formula, Speed ​​magnitude (scalar, used for cloud map color mapping), unit , For the three velocity components in the navigation system, in units .

[0145] A second aspect of the present invention provides a velocity-measuring particle for a water pump flow field measurement method based on inertial guidance. The particle can move with the flow and record data generated by its own IMU sensor, enabling streamline plotting and outputting the flow velocity at each point on the streamline, including:

[0146] An inertial measurement unit (IMU) integrating a three-axis accelerometer and a three-axis gyroscope is used to acquire three-axis acceleration and three-axis angular velocity. A microcontroller (MCU) is used to control data acquisition and storage. A flash memory module is used to store the IMU's raw data. A power supply unit powers all modules. A waterproof housing encapsulates the above components into a sphere. At least one replaceable counterweight is installed inside the housing to adjust the overall particle density to match the measured fluid. The IMU sensor, MCU processor, flash memory, counterweight, and battery are encapsulated within the waterproof housing, forming a spherical shape. The waterproof housing is covered with a rubber sleeve. The particle diameter is ≤2cm, and the density matching error with the fluid is ≤±5% to ensure that the particles have no relative motion with the fluid.

[0147] Addressing the challenges of installing traditional fixed flow measurement equipment on-site and the inapplicability of PIV particles in prototypes, this invention proposes a design that encapsulates an IMU module, MCU module, FLASH module, and power supply unit within a small sphere. The core components of the IMU-sensing particle require high integration, ensuring the overall particle diameter does not exceed 2cm. The spherical shell is constructed from pressure-resistant material and an outermost rubber layer, guaranteeing absolute waterproofing under water pressure. Simultaneously, the particle's interior provides space for a counterweight, allowing for adjustments to density to achieve measurements within different devices. This IMU-sensing particle can move with the flow and record data generated by its own IMU sensor, enabling streamline plotting and flow velocity output at points along the streamline.

[0148] For IMU sensors, options include JY901B and ICM42688; for MCU microcontrollers, options include STM32, ESP32, and RV1101. Storage modules can include W25Q128 or TF cards. The battery uses 3.3V, with the positive terminal connected to the MCU motherboard's VCC and the negative terminal connected to the motherboard's GND. Waterproofing of the particles can be customized according to project requirements, such as using a plastic casing or potting compound for sealing.

[0149] The composition of the particles can be configured as follows:

[0150] (1) IMU module

[0151] The JY901B or ICM42688 models can be selected, and their specifications are shown in Tables 1 and 2.

[0152] Table 1. Specifications of JY901B Model IMU Module

[0153]

[0154] Table 2 Specifications of ICM42688 Model IMU Module

[0155]

[0156] (2) MCU module

[0157] Selected model: STM32F103C8T6, parameters and specifications are shown in Table 3:

[0158] Table 3 Specifications of ICM42688 Model IMU Module

[0159]

[0160] (3) FLASH module

[0161] Selected model: W25Q128

[0162] Table 4 Specifications of W25Q128 Model FLASH Module

[0163]

[0164] (4) Storage wiring (Tables 5-7)

[0165] Table 5 Storage Wiring Table

[0166]

[0167] Table 6 JY901B Wiring Table

[0168]

[0169] Table 7 ICM42688 Wiring Diagram

[0170]

[0171] In summary, this invention achieves improvements and innovations in the following aspects:

[0172] 1. Methodological Innovation: Utilizing a particle measurement system with a built-in IMU module to measure flow rate and flow regime.

[0173] The core principle of particle velocity measurement and trajectory recording with IMU module is as follows: the IMU module is used to sense the inertial parameters of the particle moving with the fluid, and the instantaneous velocity and spatial trajectory of the particle are obtained through kinematic calculation. Since there is no relative motion between the particle and the fluid, its motion data can be directly equivalent to the velocity and streamline data of the fluid.

[0174] (1) Core premise: "Undisturbed following" of particles and fluids

[0175] The particles are specially encapsulated, and their density and fluid matching error is ≤ ±5%. They can move completely synchronously with the fluid, so measuring the particle motion can indirectly obtain fluid motion information.

[0176] (2) The sensing core of the IMU module: collecting inertial motion parameters

[0177] The IMU integrates a three-axis accelerometer and a three-axis gyroscope, with its core function being the real-time acquisition of raw inertial data of particle motion. The three-axis accelerometer measures the linear acceleration of the particle in three-dimensional space, reflecting changes in fluid velocity, and corrects for the influence of gravitational acceleration through attitude data. The three-axis gyroscope measures the angular velocity of the particle around the three-dimensional coordinate axes, reflecting changes in the particle's direction of motion. The particle's built-in MCU uses a unique ID to achieve time synchronization of multi-particle data, ensuring that the motion data of different particles can be correlated and analyzed in the same time dimension.

[0178] (3) Flow velocity calculation principle: based on acceleration integral and attitude correction

[0179] Fluid velocity can be calculated by combining acceleration data collected by IMU with attitude correction. The core logic is "acceleration integral → velocity".

[0180] (4) Principle of trajectory recording: based on velocity integral and spatial positioning

[0181] The particle's trajectory is achieved through the quadratic integration of velocity data and initial position calibration. The core logic is "velocity integration → displacement → trajectory":

[0182] Initial position calibration: At the moment of particle release, its initial spatial coordinates in the pump inlet pipe are recorded. The calculated instantaneous velocity is integrated over time to obtain the particle's relative displacement at any given moment. Combined with the attitude angle data output from the gyroscope, the displacement direction is corrected, and the displacements at different moments are superimposed onto the global coordinate system to obtain the complete spatial trajectory of the particle from the pump inlet to the outlet. Trajectory data of different particles are distinguished by their unique particle IDs, forming a "spatially distributed" trajectory set, providing fundamental data for subsequent global flow field reconstruction.

[0183] 2. Structural Innovation: IMU Sensing Particles

[0184] Addressing the challenges of installing traditional fixed flow measurement equipment on-site and the inapplicability of PIV particles in prototypes, this invention proposes a design that encapsulates an IMU module, MCU module, FLASH module, and power supply unit within a small sphere. The core components of the IMU-sensing particle require high integration, ensuring the overall particle diameter does not exceed 2 cm. The sphere shell is constructed from pressure-resistant material and an outermost rubber layer, guaranteeing absolute waterproofing under water pressure. Simultaneously, the particle's interior provides space for a counterweight, allowing for adjustments to density to achieve measurements within different devices. This IMU-sensing particle can move with the flow and record data generated by its own IMU sensor, enabling streamline plotting and flow velocity output at points along the streamline.

[0185] 3. Innovative Application Scenarios: Direct Measurement of Closed Complex Flow Channels

[0186] Breaking away from the reliance of PIV flow measurement on transparent channels, this method is adapted to the closed environment of the prototype where there are no transparent pipes. Particles are naturally injected through the water pump inlet, eliminating the need for openings in the water pump housing, setting up observation windows, or modifying the flow channel structure.

[0187] 4. Data Output Innovation: Integration and Visualization of Flow and Streamlines

[0188] Breaking through the limitations of traditional flow measurement techniques that only output single flow rate data, this innovative approach achieves integrated visualization output of "flow rate data + streamline plotting." It upgrades "single data output" to "concrete flow field presentation," addressing the pain point of traditional flow measurement techniques that "can only provide abstract data and cannot intuitively reflect the flow field morphology," thus providing a more intuitive and comprehensive quantitative and visual basis for flow field analysis.

[0189] 5. Innovative method for calculating flow integral: Flow rate is calculated using a combination of measured streamlines and 3D model dimensions.

[0190] This invention breaks through the limitations of traditional flow calculation methods that rely on empirical cross-section selection. It uses IMU particle-captured streamline data to select cross-sections with uniform streamline distribution and relies on a three-dimensional model of the pump's internal flow channel to extract precise geometric parameters. The two work together to achieve high-precision integral calculation of flow rate under complex flow channels.

[0191] The above are some specific embodiments. Finally, it should be noted that these embodiments are only used to illustrate the technical solutions of the present invention, and not to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. These modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for measuring the flow field of a water pump based on inertial guidance, characterized in that, The steps are as follows: S1, Assemble and calibrate a set of velocity-measuring particles with a built-in inertial detection unit (IMU), including: IMU sensor, microcontroller, data storage module, battery and waterproof housing, wherein the particle density is adjusted to match the fluid to ensure that the particles have no relative motion with the fluid; S2, obtain the geometric parameters of the target flow section of the water pump, establish a three-dimensional model of the water pump flow channel by measuring or reading the design drawings, and extract at least one flow section area and normal vector; S3, under normal pump operation, rapidly release velocity-measuring particles at the pump inlet and record their initial spatial coordinates in the pump inlet pipe. S4, recovers velocity-measuring particles at the outlet of the water pump; S5 reads the raw data from the inertial sensor from the recovered velocimeters and performs the following calculations using a computer: S51, Zero bias calibration: Before the experiment, the particle is placed at rest for 5 to 10 seconds, and the average value of the data during this rest period is taken as the zero bias calibration estimate of acceleration and angular velocity. S52, Attitude calculation: The attitude quaternion is updated based on gyroscope data, and complementary filtering correction is performed using accelerometer data to obtain the particle's rotation matrix from the body coordinate system to the navigation coordinate system. ; S53, the acceleration of the body coordinate system Switch to the navigation frame and subtract the gravity vector of the navigation frame. The actual acceleration of the particle in the navigation coordinate system is obtained. Then solve for the velocity and displacement; for Speed ​​is obtained by integrating over time. Integrating again yields the displacement trajectory. , S54, zero-velocity correction, uses data from the stationary phase after particle recovery to linearly correct integral drift: S55, Full-field flow reconstruction: Using trajectory data of multiple particles, the velocity field inside the water pump is reconstructed through radial basis function (RBF) interpolation. S56, Flow integral: The total volumetric flow rate passing through the inlet or outlet cross-section of a water pump per unit time is equal to the surface integral of the velocity along the normal direction of the cross-section, thus yielding the volumetric flow rate. ,unit : In the formula, This refers to the inlet / outlet cross-sectional area of ​​the water pump, in units of... , Let (x, y) be the velocity vector of a point (x, y) on the cross section, in units. , It is the unit normal vector of the cross section (pointing in the positive direction of flow). For the first Line 1 The velocity vector of the column grid is obtained by RBF interpolation. For the first Line 1 Area of ​​grid elements, unit ; S57, Streamline and Velocity Cloud Map Generation: Based on the reconstructed velocity field, the fourth-order Runge-Kutta method is used to trace the streamlines. Starting from the seed point, the integral is performed along the velocity direction to map the velocity magnitude into a pseudo-color image.

2. The method for measuring the flow field of a water pump based on inertial guidance according to claim 1, characterized in that, The formulas for calculating the estimated values ​​of S51 acceleration and angular velocity zero-bias calibration are as follows: In the formula, The zero-biased acceleration vector, in units. , The total number of samples in the static calibration section, N≥1000. For the static segment One acceleration sample, unit , Let be the initial static orientation rotation matrix. This is the zero bias vector of the gyroscope, in units. , For the static segment angular velocity samples, unit ; The initial attitude quaternion , This is the acceleration measurement value for the first frame of the stationary segment, in units of... , This is a function used to deduce the initial attitude from the gravity vector (the direction of acceleration should point to...). The navigation system is vertically downward.

3. The method for measuring the flow field of a water pump based on inertial guidance according to claim 1, characterized in that, S52, Attitude quaternion update uses the first-order Runge-Kutta method (RK1) to integrate the quaternion differential equation: in, ; For the current quaternion, For sampling interval, in units , Let x be the differential of a quaternion, the function on the right-hand side, and y be the rate of change of the quaternion. normalize(x) represents normalizing the quaternion so that... To prevent numerical divergence, It is the transpose symbol; The angular velocity error corrected by complementary filtering is: In the formula, This is the angular velocity error vector, in units. , These are the three imaginary components of a quaternion. It is the transpose of the rotation matrix. The gravity vector of the navigation system ,unit , The measured acceleration values ​​of the system after zero bias compensation are in units. ; The angular velocity input is the PI-corrected value, used for quaternion integration, unit , The result is the original angular velocity measurement after zero bias compensation; For proportional gain, Control the speed of error correction; Integral gain, eliminating steady-state error. This is the integral term of the angular velocity error, in units of... .

4. The method for measuring the flow field of a water pump based on inertial guidance according to claim 3, characterized in that, 。 5. The method for measuring the flow field of a water pump based on inertial guidance according to claim 1, characterized in that, S53 Real Motion Acceleration The calculation method is as follows: In the formula, , This is the volume acceleration vector after zero-bias compensation, in units. , This is a physical value for acceleration, including a gravitational component, in units of... , The zero-biased acceleration vector, in units. , Let gravitational vector be the force vector of the navigation system, in units. , This is the rotation matrix at the current moment.

6. The method for measuring the flow field of a water pump based on inertial guidance according to claim 1, characterized in that, The zero-speed correction described in S54 uses a linear error allocation method: In the formula, The corrected velocity vector at time i ( ),unit , The original integral velocity before correction, in units , , is the weighting coefficient for the static segment, which increases linearly from 0 to 1. The measured integral velocity at the end point k of the stationary segment, in units of... , The total duration of the static segment is expressed in seconds. Sampling interval time, in units , They are respectively End-of-shaft velocity drift, in units .

7. The method for measuring the flow field of a water pump based on inertial guidance according to claim 1, characterized in that, S55, the full-field flow reconstruction uses Gaussian radial basis functions: In the formula, For any point in the entire field after interpolation reconstruction velocity vector, unit , Let p be the RBF weight vector of the p-th particle, in units. , The total number of particles participating in the interpolation. For radial basis functions, ,unit , The three-dimensional coordinates of the trajectory point of the p-th particle, in units ; In the formula, For Gaussian radial basis functions, r is the Euclidean distance from the target point to the data point, in units. , For kernel bandwidth parameters, in units , , , where is the bandwidth scaling factor.

8. The method for measuring the flow field of a water pump based on inertial guidance according to claim 1, characterized in that, The tracing streamline described in S57 uses the fourth-order Runge-Kutta method: In the formula, For the coordinates of the next step on the streamline, Coordinates of the current streamline point Unit: m The arc length step for tracing along the streamline, in meters, Δs = 0.1~1m; These represent the first, second, third, and fourth slopes of RK4, respectively. ， ， ， 。 9. A velocity-measuring particle for use in the method of any one of claims 1 to 8, characterized in that, It can move with the flow and record data generated by its own IMU sensor, enabling streamline plotting and outputting the flow velocity at various points along the streamline, including: An inertial measurement unit (IMU) integrates a three-axis accelerometer and a three-axis gyroscope to collect three-axis linear acceleration and three-axis angular velocity. A microcontroller (MCU) is used to control data acquisition and storage; A Flash data storage module is used to store the raw IMU data; One power supply unit supplies power to all modules; A waterproof outer shell encapsulates the above components into a sphere; At least one replaceable counterweight is installed inside the housing to adjust the overall particle density to match the fluid being measured. The IMU sensor, MCU processor, flash memory, counterweight, and battery are encapsulated inside a waterproof housing, forming a spherical shape. The waterproof outer shell is covered with a rubber sleeve.

10. The velocity-measuring particle according to claim 8, characterized in that, The particle diameter is ≤2cm, and the density and fluid matching error is ≤±5% to ensure that the particles have no relative motion with the fluid.

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