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9.2 Thermal Flow Sensors                                                      225

                  heat source and heat detection [Figure 9.5(c)]. The time of flight mode is the least
                  sensitive to changes in ambient temperature as the time of arrival of the heat pulse
                  maxima are measured. A minimum of two wires is needed. A third wire renders the
                  sensor bidirectional. The time of flight mode works best in a regime of large flow
                  velocities. In this case, the shape of the heat pulse is not seriously deformed by diffu-
                  sion, which leads to sharp signals [12]. The measurement range can be set by the dis-
                  tance between the heat source and the heat detection. For lower flow rates, the
                  distance needs to be short, and for large flow rates the distance should be large.
                  However, the fluid flow will broaden the signal and if the detector is too far away
                  from the source, the signal pulse is broadened so much that a peak cannot be
                  distinguished.
                      This category of thermal flow sensors has not been used as often as anemome-
                  ters or calorimeters. A silicon micromachined time of flight flow sensor in combina-
                  tion with an anemometer was presented by Ashauer et al. [41] and was described
                  above. Figure 9.13 shows a typical measurement curve for a time of flight flow sen-
                  sor, giving the signal of the sensor downstream of the heater. It can be seen that for
                  fast-flowing fluids the pulse arrives quickly at the temperature sensor, and for
                  smaller flow rates, the heat pulse broadens, is less intense, and arrives later at the
                  sensor. Analytical and numerical investigations have been done by Durst et al. [72].
                  Sensors using a nonthermal time of flight measurement principle are described in
                  Section 9.5.


                  9.2.2  Commercial Devices
                  As with accelerometers and gyroscopes, the incentive for developing MEMS flow
                  sensors to the commercialization stage came from the car industry. In previous
                  automotive air mass flow sensors, hot wire anemometers were used, which were
                  dynamically fast due to the small thermal mass, but they could not detect reverse
                  flow rates and were prone to damage. Other sensors were made of thin-film plati-
                  num resistors on a glass or ceramic film, which were unable to follow fast changing
                  flow (high thermal mass and hence longer heating/cooling times). Depending on the
                  number of revolutions per minute of the engine and the geometry of the suction
                  pipe, the air flow can change from simple pulsation to an oscillating flow with large
                  amplitudes [50]. Considering these aspects, micromachined sensors are of major
                  advantage. They have the dynamic speed of a hot wire, the robustness of a




                                                                Fast flow
                                       [V]                      Medium flow
                                       signal                   Slow flow

                                       Output




                                        0
                                                  Time [ms]
                  Figure 9.13  Typical measurement curve of a thermal time of flight flow sensor. A heat pulse from
                  the heater is given at t =0.
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