Modern Control Engineering

110 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems

Air supply

Orifice

Input

0

Nozzle

(a) (b)

Flapper

To control

valve

Ps

Pb

Ps

Pb

Pa

X

X

Figure 4–5

(a) Schematic

diagram of a

pneumatic nozzle–

flapper amplifier;

(b) characteristic

curve relating nozzle

back pressure and

nozzle–flapper

distance.

Pneumatic Nozzle–Flapper Amplifiers. A schematic diagram of a pneumatic

nozzle–flapper amplifier is shown in Figure 4–5(a). The power source for this amplifier

is a supply of air at constant pressure. The nozzle–flapper amplifier converts small

changes in the position of the flapper into large changes in the back pressure in the noz-

zle. Thus a large power output can be controlled by the very little power that is needed

to position the flapper.

In Figure 4–5(a), pressurized air is fed through the orifice, and the air is ejected from

the nozzle toward the flapper. Generally, the supply pressure for such a controller

is 20 psig (1.4 kgfcm^2 gage). The diameter of the orifice is on the order of 0.01 in.

(0.25 mm) and that of the nozzle is on the order of 0.016 in. (0.4 mm). To ensure prop-

er functioning of the amplifier, the nozzle diameter must be larger than the orifice

diameter.

In operating this system, the flapper is positioned against the nozzle opening. The

nozzle back pressure is controlled by the nozzle–flapper distance X. As the flapper

approaches the nozzle, the opposition to the flow of air through the nozzle increases, with

the result that the nozzle back pressure increases. If the nozzle is completely closed

by the flapper, the nozzle back pressure becomes equal to the supply pressure If

the flapper is moved away from the nozzle, so that the nozzle–flapper distance is wide

(on the order of 0.01 in.), then there is practically no restriction to flow, and the nozzle

back pressure takes on a minimum value that depends on the nozzle–flapper device.

(The lowest possible pressure will be the ambient pressure )

Note that, because the air jet puts a force against the flapper, it is necessary to make

the nozzle diameter as small as possible.

A typical curve relating the nozzle back pressure to the nozzle–flapper distance

Xis shown in Figure 4–5(b). The steep and almost linear part of the curve is utilized in

the actual operation of the nozzle–flapper amplifier. Because the range of flapper dis-

placements is restricted to a small value, the change in output pressure is also small,

unless the curve is very steep.

The nozzle–flapper amplifier converts displacement into a pressure signal. Since

industrial process control systems require large output power to operate large pneu-

matic actuating valves, the power amplification of the nozzle–flapper amplifier is usually

insufficient. Consequently, a pneumatic relay is often needed as a power amplifier in

connection with the nozzle–flapper amplifier.

Pb

Pa.

Pb

Pb Ps.

Pb

Pb

Ps

Openmirrors.com