Company Profile

Vortex Flow Meter Working Principle: Piezoelectric Crystal Vibration Frequency Math

Quick Answer: A vortex flow meter uses a bluff body to create alternating vortices in the flow. The shedding frequency is linear with flow velocity: f = St * v / d. A piezoelectric crystal detects pressure pulses from these vortices and converts them into an electrical frequency signal for flow rate calculation.

How a Vortex Flow Meter Works

In a vortex flow meter, a non-streamlined bluff body sits in the process line. Flow hits the bluff body and separates. Vortices form alternately on each side. This is the Karman vortex street. Each vortex creates a small local pressure drop. The pressure pulse repeats at a steady frequency when the Reynolds number stays within the linear range.

The shedding frequency depends on flow velocity, bluff body width, and the Strouhal number. For most industrial meters, the Strouhal number stays nearly constant between Reynolds number 5000 and 50000. In this range, f equals St times v divided by d. Here f is vortex frequency in Hz, St is the Strouhal number, v is average velocity at the bluff body in m/s, and d is the bluff body width in meters.

Piezoelectric Crystal Vibration Frequency Math

Many vortex flow meters use a piezoelectric crystal sealed inside the bluff body or behind it. The alternating vortices produce small mechanical stress. The piezoelectric element converts this stress into an electric charge. The output is a sine-like voltage pulse train. Each pulse corresponds to one vortex or one pair of vortices depending on sensor design.

The piezoelectric crystal has its own natural frequency. In a well-built sensor, this natural frequency sits far above the vortex frequency range. A crystal assembly may resonate at 8 kHz while the vortex signal stays between 1 Hz and 400 Hz. This gap prevents amplitude distortion and gives a clean signal for the transmitter.

Engineers sometimes ask for the math of the crystal frequency. A simple model for a piezoelectric element is f_n = 1 / (2 * pi * sqrt(Lm * Cm)). Lm is motional inductance and Cm is motional capacitance. This is the electrical equivalent circuit from the crystal resonance. In field use, the vortex meter does not need this math. The transmitter filters the charge signal and outputs the vortex frequency directly.

Flow Rate Formula and K Factor

The volume flow rate Q comes from the pipe cross-sectional area A and the average velocity v_avg. For a given pipe size, Q = A * v_avg. Because f = St * v / d, the flow rate Q is proportional to f. Manufacturers write this as Q = f / K. The K factor is the number of pulses per unit volume. It is determined by water calibration for each meter.

For a DN50 vortex meter, a typical K factor may be 7.2 pulses per litre. At a flow rate of 2 L/s, the frequency is about 14.4 Hz. At 5 L/s, the frequency is about 36 Hz. The linear relationship holds over a wide range. The transmitter converts frequency to a 4-20 mA HART signal, pulse output, or RS485 Modbus.

Temperature and Pressure Compensation for Steam and Gas

Vortex flow meters measure actual volumetric flow at operating conditions. For steam and gas service, mass flow requires pressure and temperature compensation. Silver Instruments offers vortex meters with built-in PT100 temperature sensors and external pressure transmitters. The flow computer uses the ideal gas equation or steam tables to calculate mass flow in kg/h.

Example from a Southeast Asian food plant. A customer in Vietnam measured saturated steam at 7 bar g and 170 °C in a DN80 pipe. The vortex frequency ranged from 38 Hz to 210 Hz. A pressure transmitter and a PT100 sent live signals to the display. The totalizer showed steam mass flow in kg/h. The meter has operated for 18 months without drift.

Installation and Straight Run Requirements

Vortex meters need proper upstrea