Flow Measurement: Intro and Mass Flow Rate [16]

Introduction

We now move on to look at flow measurement in this section. Flow measurement is concerned with quantifying the rate of flow of materials. Such measurement is quite a common requirement in the process industries. The material measured may be in a solid, liquid, or gaseous state. When the material is in a solid state, flow can only be quantified as the mass flow rate, this being the mass of material that flows in one unit of time. When the material is in a liquid or gaseous state, flow can be quantified as either the mass flow rate or the volume flow rate, with the latter being the volume of material that flows in one unit of time. Of the two, a flow measurement in terms of mass flow rate is preferred if very accurate measurement is required. The greater accuracy of mass flow measurement arises from the fact that mass is invariant whereas volume is a variable quantity.

A particular complication in the measurement of flow rate of liquids and gases flowing in pipes is the need to consider whether the flow is laminar or turbulent. Laminar flow is characterized by a motion of the fluid being in a direction parallel to the sides of the pipe, and it occurs in straight lengths of pipe when the fluid is flowing at a low velocity. However, it should be noted that even laminar flow is not uniform across the cross section of the pipe, with the velocity being greatest at the center of the pipe and decreasing to zero immediately next to the wall of the pipe. In contrast, turbulent flow involves a complex pattern of flow that is not in a uniform direction. Turbulent flow occurs in no straight sections of pipe and also occurs in straight sections when the fluid velocity exceeds a critical value. Because of the difficulty in measuring turbulent flow, the usual practice is to restrict flow measurement to places where the flow is laminar, or at least approximately laminar. This can be achieved by measuring the flow in the center of a long, straight length of pipe if the flow velocity is below the critical velocity for turbulent flow. In the case of high mean fluid velocity, it’s often possible to find somewhere within the flow path where a larger diameter pipe exists and therefore the flow velocity is lower.

Mass Flow Rate

The method used to measure mass flow rate is determined by whether the measured quantity is in a solid, liquid, or gaseous state, as different techniques are appropriate for each. The main techniques available for measuring mass flow rate are summarized here.

Conveyor-Based Methods

Conveyor-based methods are appropriate for measuring the flow of solids in the form of powders or small granular particles. Such powders and particles are produced commonly by crushing or grinding procedures in process industries, and a conveyor is a very suitable means of transporting materials in this form. Transporting materials on a conveyor allows the mass flow rate to be calculated in terms of the mass of material on a given length of conveyor multiplied by the speed of the conveyor. --- a typical measurement system. A load cell measures the mass, M, of material distributed over a length, L, of the conveyor. If the conveyor velocity is v, the mass flow rate, Q, is given by

Q = Mv=L:

As an alternative to weighing flowing material, a nuclear mass-flow sensor can be used, in which a g-ray source is directed at the material being transported along the conveyor. The material absorbs some radiation, and the amount of radiation received by a detector on the other side of the material indicates the amount of material on the conveyor. This technique has obvious safety concerns and is therefore subject to licensing and strict regulation.

Coriolis Flowmeter

As well as sometimes being known by the alternative name of inertial flowmeter, the Coriolis flowmeter is often referred to simply as a mass flowmeter because of its dominance in the mass flowmeter market. However, this assumption that a mass flowmeter always refers to a Coriolis meter is wrong, as several other types of devices are available to measure mass flow, although it’s true to say that they are much less common than Coriolis meters.

Coriolis meters are used primarily to measure the mass flow rate of liquids, although they have also been used successfully in some gas-flow measurement applications. The flowmeter consists either of a pair of parallel vibrating tubes or as a single vibrating tube that is formed into a configuration that has two parallel sections. The two vibrating tubes (or the two parallel sections of a single tube) deflect according to the mass flow rate of the measured fluid that is flowing inside. Tubes are made of various materials, of which stainless steel is the most common. They are also manufactured in different shapes, such as B shaped, D shaped, U shaped, triangular shaped, helix shaped, and straight. These alternative shapes are sketched, and a U-shaped tube is shown in more detail. The tubes are anchored at two points. An electromechanical drive unit, positioned midway between the two anchors, excites vibrations in each tube at the tube resonant frequency. Vibrations in the two tubes, or the two parallel sections of a single tube, are 180 degrees out of phase.

The vibratory motion of each tube causes forces on the particles in the flowing fluid. These forces induce motion of the fluid particles in a direction that is orthogonal to the direction of flow, which produces a Coriolis force. This Coriolis force causes a deflection of the tubes that is superimposed on top of the vibratory motion. The net deflection of one tube relative to the other is given by d =kfR, where k is a constant, f is the frequency of the tube vibration, and R is the mass flow rate of the fluid inside the tube. This deflection is measured by a suitable sensor.

Coriolis meters give excellent accuracy, with measurement uncertainties of _0.2% being typical. They also have low maintenance requirements. However, apart from being expensive (typical cost is $9000), they suffer from a number of operational problems. Failure may occur after a period of use because of mechanical fatigue in the tubes. Tubes are also subject to both corrosion caused by chemical interaction with the measured fluid and abrasion caused by particles within the fluid. Diversion of the flowing fluid around the flowmeter causes it to suffer a significant pressure drop, although this is much less evident in straight tube designs.

Thermal Mass Flow Measurement

Thermal mass flowmeters are used primarily to measure the flow rate of gases. The principle of operation is to direct the flowing material past a heated element. The mass flow rate is inferred in one of two ways: (a) by measuring the temperature rise in the flowing material or (b) by measuring the heater power required to achieve a constant set temperature in the flowing material. In both cases, the specific heat and density of the flowing fluid must be known.

Typical measurement uncertainty is _2%. Standard instruments require the measured gas to be clean and noncorrosive. However, versions made from special alloys can cope with more aggressive gases. Tiny versions of thermal mass flowmeters have been developed that can measure very small flow rates in the range of nano-liters (10^-9 liters) or microliters (10^-6 liters) per minute.

Joint Measurement of Volume Flow Rate and Fluid Density

Before the advent of the Coriolis meter, the usual way of measuring the mass flow rate was to compute this from separate, simultaneous measurements of the volume flow rate and the fluid density. In many circumstances, this is still the least expensive option, although measurement accuracy is substantially inferior to that provided by a Coriolis meter.

NEXT: Volume Flow Rate

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