Time difference method –ultrasonic flow meter working principle
Time-of-flight ultrasonic gas flow measurement technology, which is a key part of the ultrasonic flow meter working principle, calculates the axial average velocity Vz along the plane formed by the sound channel and the axis by measuring the difference in the time required for ultrasonic waves to propagate in the downstream and upstream directions of a gas medium.
The time taken for ultrasonic waves to travel in the downstream and upstream directions is different. The downstream time and the reversal time is:
Without considering the influence of the internal pipe environment on sound velocity, the area-averaged flow velocity equation is:
Vs = L / (2cosφ) · (tU - tD) / (tD · tU) (2.4)
By measuring the downstream ultrasonic wave transit time tD and upstream ultrasonic wave transit time tU, the time difference between upstream and downstream ultrasonic wave transit times can be calculated:
Δt = tU - tD (2.5)
Using the transit-time method, the area-averaged flow velocity along one acoustic path can be measured. Based on the velocity distribution of different acoustic paths, corresponding algorithms can be used to calculate the average flow velocity across the entire cross-section. This flow velocity is also called the bulk-averaged flow velocity V.
By measuring the time difference between upstream and downstream ultrasonic wave transit times and calculating the average flow velocity (bulk velocity) V of the fluid inside the pipe, this flow measurement method is called the transit-time ultrasonic flow measurement method. Flow meters that use the transit-time ultrasonic flow measurement method to measure the volumetric flow rate of fluid inside pipes are called transit-time ultrasonic flow meters.
The relationship between the path-averaged flow velocity measured by the transit-time ultrasonic flow meter and the bulk-averaged flow velocity inside the pipe is:
K = V / Vs (2.6)
Where K is called the velocity correction factor. The velocity correction factor is derived from a velocity distribution profile mathematical model through the flow meter's measurement section.
Based on the gas flow conditions inside the pipe, the velocity correction factor can be derived. From equations (2.4) and (2.6), the bulk-averaged gas flow velocity inside the pipe can be obtained:
V = KVs (2.7)
Converting to volumetric flow rate through equation (2.7):
qv = AV (2.8)
Where A is the cross-sectional area of the pipe.
After pressure and temperature compensation for volumetric flow rate, the mass flow rate can be obtained:
qm = ρ0 · (P / P0) · (T0 / T) · (1 / Z) · qv (2.9)
Where Z is the gas compressibility factor; P0 and P are the pressure parameters under standard conditions and actual conditions respectively; T0 and T are the temperature values under standard conditions and actual conditions respectively; ρ0 is the density of the gas medium under standard conditions.
After obtaining the flow velocity, the flow rate through a pipe of a certain diameter within a given time period can be calculated. The flow rate F through the pipe within 1 hour is:
F = (3.6 × 10³ × π × V × D²) / 4 = 3.6 × 10³ × π × D³ × (1/tD - 1/tU) × 1/sin(2φ) (2.10)
