Mass Flowmeters

One of the early designs of self-contained mass flowmeters operated using angular momentum (Figure 5-1B). It had a motor-driven impeller that imparted angular momentum (rotary motion) by accelerating the fluid to a constant angular velocity. The higher the density, the more angular momentum was required to obtain this angular velocity. Downstream of the driven impeller, a spring-held stationary turbine was exposed to this angular momentum. The resulting torque (spring torsion) was an indication of mass flow.


Figure 5-1: Click on figure to enlarge.

These electronic flowmeters all had moving parts and complex mechanical flow meter designs. First developed for the measurement of aircraft fuel, some are still in use. However, because of their complex nature and high maintenance costs, they are gradually being replaced by more robust and less maintenance-demanding designs.

Mass flow also can be measured by batch weighing or by combining an accurate level sensor with a densitometer. Another method is to mount two d/p transmitters on the lower part of an atmospheric tank at different elevations. In this case, the output of the top d/p cell will vary with the level in the tank, while the lower one will measure the hydrostatic head over a fixed elevational distance. This pressure differential yields the density of the material in the tank. Such systems have been used to measure the total mass flow of slurries.

Heated-Tube Design

Heated-tube flowmeters were developed to protect the heater and sensor elements from corrosion and any coating effects of the process. By mounting the sensors externally to the piping (Figure 5-8B), the sensing elements respond more slowly and the relationship between mass flow and temperature difference becomes nonlinear. This nonlinearity results from the fact that the heat introduced is distributed over some portion of the pipe's surface and transferred to the process fluid at different rates along the length of the pipe.

The pipe wall temperature is highest near the heater (detected as T_w in Figure 5-8B), while, some distance away, there is no difference between wall and fluid temperature. Therefore, the temperature of the unheated fluid (T_f) can be detected by measuring the wall temperature at this location further away from the heater. This heat transfer process is non-linear, and the corresponding equation differs from the one above as follows:

m^0.8 = Kq/(C_p(T_w - T_f))

This flowmeter has two operating modes: one measures the mass flow by keeping the electric power input constant and detecting the temperature rise. The other mode holds the temperature difference constant and measures the amount of electricity


Figure 5-12: Click on figure to enlarge.

needed to maintain it. This second mode of operation provides for a much higher meter rangeability.

Heated-tube designs are generally used for the measurement of clean (e.g., bottled gases) and homogeneous (no mixtures) flows at moderate temperature ranges. They are not recommended for applications where either the fluid composition or its moisture content is variable, because the specific heat (C_p) would change. They are not affected by changes in pressure or temperature. Advantages include wide rangeability (the ability to measure very low flows) and ease of maintenance. The temperature difference (or heater power), flowmeter geometry, thermal capacity, specific heat, and viscosity of the process fluid must stay constant when using this design.

Bypass-Type Design

The bypass version of the thermal mass flowmeter was developed to measure larger flow rates. It consists of a thin-walled capillary tube (approximately 0.125 in diameter) and two externally wound self-heating resistance temperature detectors (RTDs) that both heat the tube and measure the resulting temperature rise (Figure 5-9A). The meter is placed in a bypass around a restriction in the main pipe and is sized to operate in the laminar flow region over its full operating range.

When there is no flow, the heaters raise the bypass-tube temperature to approximately 160°F above ambient temperature. Under this condition, a symmetrical temperature distribution exists along the length of the tube (Figure 5-9B). When flow is taking place, the gas molecules carry the heat downstream and the temperature profile is shifted in the direction of the flow. A Wheatstone bridge connected to the sensor terminals converts the electrical signal into a mass flow rate proportional to the change in temperature.

The small size of the bypass tube makes it possible to minimize electric power consumption and to increase the speed of response of the measurement. On the other hand, because of the small size, filters are necessary to prevent plugging. One serious limitation is the high pressure drop (up to 45 psi) needed to develop laminar flow. This is typically acceptable only for high pressure gas applications where the pressure needs to be reduced in any case.

This is a low accuracy (2% full scale), low maintenance, and low cost flowmeter. Electronic packages within the units allow for data acquisition, chart recording, and computer interfacing. These devices are popular in the semiconductor processing industry. Modern day units are also available as complete control loops, including a controller and automatic control valve.