Brooks Instrument SLA5800 Series - Manual (Page 33)

3-1
Brooks ® Digital MFC's & MFM's
Section 3 Operation Installation and Operation Manual
X-TMF-SLA5800-MFC-eng
Part Number: 541B027AAG
April, 2013
3-1 Overview
This section contains the following information:
• Theory of Operation
• Features
3-2 Theory of Operation for Flow Measurement
The thermal mass flow measurement system consists of two components:
the restrictor and the flow sensor. Figure 3-1 contains a diagram of the flow
stream through the MFC/MFM with an enlarged view of the flow sensor.
Gas flow entering the MFC/MFM is separated into two paths; one straight
through the restrictor and the other through the flow sensor. This is
represented in Figure 3-1 where the total flow A+B enters the MFC/MFM
and is separated into streams A and B. The streams are joined again at the
far side of the restrictor.
The separation of the flow streams is caused by the restrictor. During flow
conditions there will be a pressure differential across the restrictor which
forces gas to flow in the sensor.
The pressure difference caused by the restrictor varies linearly with total
flow rate. The sensor has the same linear pressure difference versus flow
relationship. The ratio of sensor flow to the flow through the restrictor
remains constant over the range of the MFC/MFM (A/B = constant). The
full scale flow rate of the MFC/MFM is established by selecting a restrictor
with the correct pressure differential for the desired flow.
The flow sensor is a very narrow, thin-walled stainless steel tube. Onto this
tube are built upstream and downstream temperature sensing elements on
either side of a heating element. Constant power is applied to the heater
element, which is located at the midpoint of the sensor tube. During no-
flow conditions, the amount of heat reaching each temperature sensor is
equal, so temperatures T1 and T2 (Fig. 3-1) are equal. Gas flowing
through the tube carries heat away from the upstream temperature sensor
and toward the downstream sensor. The temperature difference, T2 - T1,
is directly proportional to the gas mass flow. The equation is:
DT = A x P x Cp x m
Where,
DT = Temperature difference T2 - T1 (°K)
A = Constant of proportionality (s
2 -°K 2 /kJ 2 )
P = Heater Power (kJ/s)
Cp = specific heat of the gas at constant pressure (kJ/kg - °K)
m = Mass Flow (kg/s)
A bridge circuit and a differential amplifier interpret the temperature difference
and generate an electrical signal directly proportional to the gas mass flow
rate.