Fluid Mean Velocity Calculation via Gaussian Spectrum Fitting
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Solution Overview
Problem
Existing methods for determining the mean velocity of a fluid in open channels or partially filled ducts are cumbersome, requiring complex calibrations and simulations, which are time-consuming and often impractical, especially when hydraulic conditions vary.
Innovation Solution
A method that involves local velocity measurements at the surface, conversion of data using Fourier transforms to fit a Gaussian curve, and calculation of mean velocity based on the curve's parameters and the ratio of illuminated to total surface area, eliminating the need for simulation models and tedious calibrations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If calibration techniques are used to convert local velocity measurements into mean velocity, then measurement precision is improved, but measurement time and device complexity increase significantly
Solution Approach 1:
The patent extracts only the essential characteristics needed for calibration by using a single local velocity measurement combined with a single image of the free surface, rather than requiring comprehensive multi-point velocity readings under multiple hydraulic conditions. This extraction approach reduces calibration time while maintaining sufficient precision for mean velocity determination.
Solution Approach 2:
The patent performs preliminary action by capturing an image of the free surface and performing image processing to determine surface width before conducting the velocity measurement. This preliminary preparation allows the system to have all necessary geometric information ready, enabling immediate conversion of the single velocity measurement to mean velocity without requiring time-consuming calibration procedures during actual operation.
2Measurement precision
If comprehensive calibration under multiple hydraulic conditions is performed, then measurement precision is improved, but device complexity and operational difficulty increase
Solution Approach 1:
The patent extracts only the critical geometric parameter (free surface width from images) needed for calibration, rather than requiring comprehensive characterization of hydraulic conditions. This extraction simplifies the calibration system while maintaining the ability to accurately convert local velocity to mean velocity across varying conditions.
Solution Approach 2:
The system performs self-service calibration by automatically capturing images of the free surface, processing these images to determine surface width, and using this information to calibrate the velocity measurement conversion. This automated self-calibration eliminates the need for complex external calibration equipment and procedures, reducing device complexity while maintaining precision.
3Measurement precision
If multiple velocity measurement points are read to characterize hydraulic conditions, then measurement precision is improved, but productivity decreases due to time consumption
Solution Approach 1:
The patent extracts hydraulic condition information from a single image of the free surface rather than requiring multiple velocity measurements at different points. This extraction method provides sufficient characterization of hydraulic conditions to enable accurate mean velocity calculation, dramatically increasing measurement throughput while maintaining necessary precision.
Solution Approach 2:
The patent replaces the mechanical approach of physically moving measurement devices to multiple points with an optical/image-based system that captures the entire free surface geometry in a single shot. This substitution eliminates time-consuming mechanical operations while providing comprehensive hydraulic condition information, thereby improving productivity without sacrificing precision.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for precise and efficient determination of mean fluid velocity without extensive calibration, optimizing data analysis for slow-flow conditions and adapting to varying hydraulic conditions, thereby reducing measurement time and improving precision.
Implementation Method 1
surface velocity measurements in open channels by radar microwave, acoustic waves, optics and lasers
Implementation Method 2
conversion of the spectrum of discrete data expressed in the temporal domain into a spectrum of data expressed in a frequency domain via a Fourier transform
Data Source
AI summary
A method calculates mean speed of a fluid flowing in an open channel or a partially filled duct. Fluid having a free surface of width L1 extending between walls of the channel or duct includes local speed measurements at the surface of the fluid over a zone of width L2, the set of local measurements generating a spectrum of discrete data expressed in a temporal domain. The spectrum of discrete data is converted into a spectrum of data expressed in a frequency domain via a Fourier transform. A Gaussian curve is fitted to the spectrum and the mean μ and the standard deviation σ of the Gaussian curve are calculated. L2 and σ enable calculating the distribution of speeds over L2. The ratio L2/L1 is calculated and the mean speed of the fluid within the channel or duct is determined based on the Gaussian curve and the ratio L2/L1.