Table of Contents

Although not often discussed, paddlewheel sensors can cost-effectively satisfy
a wide variety of your flow detection requirements. Give these easy-to-
install and reliable sensors a second look.

Jerry S.J. Chen,
Beverly Technologies Inc.
Figure 1. There are three candidate directions in which the rotor and shaft can be installed against the direction of flow. If the shart is aligned with the direction of flow, the sensor is defined as a turbine type (A). If the shaft is perpendicular to the direction of flow, the sensor is defined as a paddlewheel type (B and C).

If you need to detect the flow of liquid in a pipe, you can easily find details on an array of options--ultrasonic sensors, positive displacement sensors, magmeters, and turbine flow sensors. Often omitted from this list, however, are paddlewheel flow sensors. Take the time to investigate further, and you'll find that paddlewheel sensors have unique features that make them a versatile first choice.

Not Just Another Turbine

The paddlewheel sensor is sometimes described as a kind of turbine flow sensor. Both sensors have a rotor, a bearing, and a shaft, but there is a key difference that gives paddlewheels the advantage. A turbine sensor's shaft aligns with the flow direction (see Figure 1A), but a paddlewheel sensor's shaft is perpendicular to the flow direction (see Figures 1B and 1C. In comparison with a turbine sensor's shaft, the shaft of a paddlewheel sensor sustains less axial load (thrust) and, thus, less friction. A turbine sensor has more blades to receive the flow momentum, so a bigger impulse is needed to move the rotor and overcome the greater friction. Instead of making every part stronger and larger, paddlewheel sensor developers take advantage of light thrust to have good efficiency, low flow response, and lifetime consistency.

Types of Paddlewheel Sensors

Paddlewheel sensors come in two styles:

  • Insertion
  • Inline

Insertion sensors, as shown in Figure 2, typically consist of three subassemblies:

  • The rotor and shaft
  • The sensing mechanism
  • The main body
    Figure 2. An insertion-type paddlewheel sensor has a four-bladed rotor incorporating a magnet that activates the transducer in the main body. One blade opposing the main flow provides a spinning force; the other three resist spinning by means of skin friction.
    Figure 3. The friction force between rotor and shaft can be reduced by adding air pockets to the rotor. The density of the paddlewheel comes from the weight of the magnet, the air pocket, and the plastic selected for the rotor.
    Figure 4. An inline paddlewheel flow sensor has a housing that directs the flow path. The rotor is vertical and spins against the shaft. A lightweight rotor can reduce friction and wear on the shaft.

Figure 3 shows a popular design for the rotor and shaft. Notice that the bearing is built into the rotor, and the shaft slides through it as a center axis of spin. In an alternative setup, the shaft is attached to the rotor, and the bearing is built into the main body. In this plastic sensor, the rotor incorporates a magnet that activates the transducer embedded in the main body.

Figure 2 illustrates a common sensing mechanism. The transducer can be a Hall effect sensor, a giant magnetoresistive sensor, an induction coil, or a magnetostrictive sensor. The magnet can be alnico or samarium cobalt. If the rotor is a ferromagnetic material, the sensor can be the reluctance type or an induction coil.

An insertion sensor's main body is used for many purposes. The wet area blocks the flow and maximizes the push on the active blade. The upper portion of the main body controls the rotor, which must be inserted at the proper insertion depth and orientation in the pipe. The sensing transducer is located inside the main body. Generally, an O-ring is attached to the main body to allow easy retrieval of the sensor from the pipe for maintenance.

Inline paddlewheel sensors (see Figure 4) are normally used for small pipes. This type of sensor contains a rotor assembly and a main body. Because most of an inline sensor is plastic, the magnet is typically sealed in the rotor. The flow entry straightens the flow profile.

The simple geometry of the parts of either style of paddlewheel sensor allows them to be produced by either automated injection molding or CNC machining. The production cost is low, and the performance-to-cost ratio is high. Worn parts are easily replaceable. Large-pipe applications tend to entail more expensive inline sensors, but insertion devices can be inexpensively adapted for the job. The only necessary modification is to extend the length of an insertion sensor's main body.

Rugged as the Rest

In the past, the lighter weight of paddlewheel flow sensors gave them the (now undeserved) reputation of being less accurate and rugged. When these sensors were first introduced, losing the rotor was a major problem. The usual progression was:

1. The friction that wears the bearing surface and the shaft created a bigger gap than normal.

2. When the bearing hole got bigger, the rotor bounced (rather than spinning smoothly) around the shaft. The accuracy of the sensor was gradually lost.

3. As the gap continued to become larger, the dynamic impact of the rotor on the shaft got bigger. This is explained mathematically as:

impact force ~ M • • (2 • 3.14 • f)2
(1)

where:

M = mass of rotor

= average displacement of rotor, same as average of gap

f = frequency of rotor bouncing around shaft

4. The bearing surface or shaft broke, and the rotor was blown out of the sensor.

The steps toward a solution were:

  • Minimize the mass of rotor M without proportionally reducing the size of the bearing surface.
  • Keep the gap small and consistent through the sensor's lifetime.
  • Design a simple and easy installation method, making the sensor rugged and easy to replace when necessary.
  • Use compatible materials to avoid chemical corrosion.

In this practice, designers developed a lightweight rotor by using a low-density rotor. The air pocket is sealed in the rotor assembly. If the average density of the rotor is the same as that of the fluid, by Archimedes' law the sensor should be able to detect any flow in the pipe. Because the rotor is lifted by fluid buoyancy, the load on the shaft is light. This disconnects the relation of the size to weight. Thus, the physical dimension of rotor and shaft can be big relative to its weight, ensuring its strength-to-wear resistance.

The Mathematics of Paddlewheels

The physics behind paddlewheel sensors is straightforward. Consider a standard four-blade rotor immersed in a pipe as shown in Figure 2. The upper three blades are shielded from the direct impact of flow, while the lower blade is pushed and rotates toward downstream. The force exercised on the lower blade is the main force spinning the rotor. The frictional force on the other three blades creates a resistance to spin. Based on the Moody formula, the motion of the paddlewheel rotor is :

Fd = Cd • A • (1/2) • d • (ULOCAL2 – Ut2)
(2)

and

Fr = Cd • A • (1/2) • d • (Ut2)
(3)

where:
Figure 5. Equation (7) predicts the performance of a paddlewheel flow sensor; experimental results support the theory.

Cd = drag coefficient

UMEAN = mean velocity of fluid in the pipe

ULOCAL = velocity of fluid at tip of paddlewheel; if rotor is inserted at right location, ULOCAL = UMEAN

Fd = force pushing blade toward downstream

Fr = resistance force that pushes the blades toward upstream (backward)

A = projected area of rotor that is subject to flow impulse

d = density of fluid

Ut = velocity of blade
Tip-to-Speed Ratio Related to K Factor
K factor = P / Q = [Ut / (2 * 3.14 * R) N] / (UMEAN * 3.14 / 4 * D2)
where:
D = pipe insertion depth
Q = flow rate
In a rotor and sensing mechanism design, N is fixed and the sensor's K factor is related to the efficiency as:
K factor = (Ut / UMEAN) * (2 * N) / (D2 * R)

The friction force, or the rubbing of the rotor against the shaft, can be expressed as:

Fw = • W
(4)

where:

Fw = frictional force

m = friction coefficient

W = weight of rotor less the weight of fluid of the same volume

The balance of the torque in steady state is expressed as:

Fd • R = 3 • Fr • R + Fw • r
(5)

where:

R = mean radius of rotor blade

r = radius of shaft

3 = constant from three blades in resistance

Substituting Equations (2), (3), and (4) into Equation (5) yields:

Ut / ULOCAL = 1/2 • {1 – •W • r / [Cd • A • R • (ULOCAL2)] / 2}0.5
(6)

When turbulence velocity is fully developed in the pipe, the rotor stays 12% of the diameter away from the boundary, and the local velocity (ULOCAL) equals the mean velocity (UMEAN). Thus, for a properly installed paddlewheel sensor, Equation (6) becomes:

Ut / UMEAN = 1/2 • {1 – • W • r / [Cd • A • R • (UMEAN2)] / 2}0.5
(7)

The value of Ut/UMEAN (tip-to-speed ratio) is directly related to the K factor (see text box). In turbulent flow, Cd is essentially a constant. Therefore, Equation (7) describes the physics of the paddlewheel sensor. A couple of performance points are important to keep in mind:

  • At low flow, where UMEAN is small, the tip-to-speed-ratio is dominant by frictional force Fw.
  • At high flow or in a very low friction design, tip-to-speed ratio is asymptotic to a constant. Thus, a paddlewheel sensor can be a linear flow sensor.
  • Under more general conditions, the frictional force is close to a constant, C.

Equation (7) can be simplified to:

Tip-to-speed ratio ~ (1 – C / UMEAN2)0.5
(8)

Figure 5 plots a typical tip-to-speed ratio produced by a metal flow sensor (Signet 2540) in a 3 in. flow loop. The insertion depth of the sensor was 10% of the pipe insertion depth. This sensor used an induction coil technique to detect the spinning of the rotor, which generated four pulses per revolution. Pulses were collected at each flow rate. Figure 4's vertical axis, Ut (tip-to-speed ratio), is based on the pulse measured from the test sensor and calculated by Equation (9):

Ut = 2 • 3.14 • R • P/N
(9)

where:

P = number of pulses output per second

R = mean radius of rotor

N = number of pulses output per revolution of rotor

The horizontal axis in Figure 4, UMEAN, shows the mean flow rate at each step of the test.

For further discussion of Equation (9), consult Chen 1997, 1998, and forthcoming in "For Further Reading."
TABLE 1
Sensor Component Materials of Construction
Parts Material option Consideration
Plastic rotor and shaft PVdF, PPS, Tefzel,polypropylene, PEEK Lightweight, chemicalresistance, seal capability cleanliness, durability
Metal rotor Stainless steel Fluid temperature, pressure,resistance to wear
Metal shaft Titanium, stainless steel Resistance to wear, corrosion resistance
Plastic housing PVC, PVdF, polypropylene,PPS Cost, molding dimensional stability,chemical resistance,durability
Metal body Stainless steel, brass Material suitability to the fluid temperature and pressure

Material Selection

Another way to maximize a paddlewheel sensor's performance in a given application is to use the proper materials. Keep in mind the following considerations:

  • Chemical resistance, if the fluid contains certain chemicals
  • Resistance to water impurities, such as silk sands
  • Temperature sustainability to the fluid
  • The leach effect from the sensor, if the fluid is clean

Typical plastics and metals used in paddlewheel sensor components are detailed in Table 1.

Summary

Paddlewheel sensors were once considered unreliable and inaccurate. This is no longer true. If properly designed and manufactured, a paddlewheel sensor can be very reliable and consistent, thanks to recent technical enhancements. The parameters addressed include bearing/ shaft construction, weight control of the rotor, linearity design, and materials. Paddlewheel sensors offer the advantages of an attractive performance-to-cost ratio and user-friendly installation and maintenance, from small to large pipes, and low to high flow rates.

For Further Reading

Chen, S.J. Oct. 1998. "Calculating
Calibration Constant K for Mechanical
Flow Sensors," Sensors, Vol. 15, No. 10.

------. July 1997. "Instrumentation for
Industrial Water and Wastewater Flow
Control, A smart and compatible
choice," Proc ICSD Conf, Los Angeles,
CA.

------. "On the Design of Wide Range
Mini-Flow Paddlewheel Flow Sensors,"
publication forthcoming.

Schlichting, H. 1974. Boundary Layer
Theory, Ch. 20, McGraw-Hill.

Stodola, A. and Louis C. Loewenstein.
Steam and Gas Turbine. McGraw-Hill.


Jerry S.J. Chen, Ph.D., is Director of Beverly Technologies Inc., 1830 W. Beverly Dr., Orange, CA 92868; 714-246-4037, fax 714-978-1516, chens1027@aol.com


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