Unsteady Liquid Flow Measurement via Pressure Sensor Error Correction
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Solution Overview
Problem
Calculating the absolute value of unsteady liquid flowrate in high-pressure applications is challenging due to the difficulty in determining the initial flowrate and the impact of zero errors from pressure sensors, especially when measuring small oscillations in pressure and flowrate.
Innovation Solution
A method using a system of partial differential equations to calculate the average flowrate, incorporating wall friction terms and Fourier expansions to account for pressure differences and sensor errors, allowing for the elimination of zero errors and enabling the measurement of unsteady flowrate with two pressure sensors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Difficulty of detecting and measuring
If two pressure sensors are used to calculate absolute unsteady flowrate, then flowrate measurement capability is improved, but measurement precision deteriorates due to zero errors affecting small oscillations
Solution Approach 1:
The patent extracts and eliminates the zero error component from the pressure sensor measurements by using a reference pressure sensor to determine zero errors, which are then subtracted from the raw pressure signals to obtain error-corrected measurements for accurate flowrate calculation
Solution Approach 2:
The patent introduces a reference pressure sensor as an intermediary element that measures ambient pressure variations and zero drift, serving as a mediator to correct the zero errors in the upstream and downstream pressure sensors without requiring absolute pressure accuracy from each sensor
2Ease of manufacture
If initial flowrate is assumed null at t=0, then calculation simplicity is improved, but measurement precision deteriorates when initial flowrate cannot be considered null
Solution Approach 1:
The patent performs preliminary action by measuring and storing the initial flowrate value at t=0 using the same pressure sensor system before the unsteady flow conditions begin, allowing this initial value to be used in the integration constant calculation rather than assuming it is zero
Solution Approach 2:
The patent uses feedback by continuously monitoring the pressure signals and using the determined initial flowrate condition to adjust and correct the integration constant in the flowrate calculation, ensuring accuracy even when initial flowrate is non-zero
Data Source
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AI summary
A method for the measurement of an unsteady flowrate of a homogeneous liquid comprising the steps of: - measuring the pressure variation (Δp(t)) along a supply pipe (7) of the liquid; - calculating an absolute unsteady flowrate (Formula (I)) and/or a fluctuation of the flowrate (Formula II) of the liquid on the basis of a solution of the approximation of a system of partial differential equations comprising the equation of conservation of mass and the momentum balance equation, in which the wall friction (τw) is modelled so as to comprise at least one first term (Formula III) proportional to the square of the average flowrate over time (Formula IV) by means of a proportionality constant which is a function at least of the Reynolds number referring to the liquid and to the pipe (7), of the density of the fluid and the section of the pipe.