Thermopile Flow Sensors and Differential Pressure Flow Meters

Xiang Zheng Tu

 

Air conditioning can refer to any form of technology that modifies the condition of air including heating, cooling, (de-)humidification, cleaning, and ventilation. In order to do so air movement needs to be created and air flow needs to be measured. This is hwy differential pressure flow meters are popular for a long time. But in recent years things have changed. Differential pressure flow meters have been gradually and irreversibility replaced by thermopile flow sensors.

It is not surprising in view on the working mechanism of the differential pressure meters and related limitations to the flow measurements. The working mechanism is based on Bermoulli’s Equation. Bernoulli’s equation states that the pressure drop across the constriction is proportional to the square of the flow rate, as shown in the following figure.

 

It can be seen from the above figure that using this relationship, 10 percent of full scale flow produces only 1 percent of the full scale differential pressure. At 10 percent of full scale flow, the differential pressure flow meter accuracy is dependent upon the meters being accurate over a 100:1 range of differential pressure. The meters accuracy is typically degraded at low differential pressures in its range, so flow meter accuracy can be similarly degraded. Therefore, this non-linear relationship can have a detrimental effect on the accuracy and turndown of differential pressure flow meters. Remember that our interest is the accuracy of the flow measurements instead of the differential pressure measurements.

In addition, the flow rate measured by the differential pressure flow meters is not mass flow rate that is required by many applications. According to ideal gas law, gas pressure changes with its temperature and volume. To obtain a mass flow rate, it is necessary to measure additional parameters: differential pressure; absolute pressure; and absolute temperature. These measurements with the differential pressure measurement then sent to a computer for calculating the mass flow rate.

All these limitations with the differential pressure flow meters can be eliminated by the thermopile mass flow sensors. The thermopile flow sensors use the thermal properties of the fluid to measure the flow rate. A measured amount of heat is applied to the heater of the sensor. Some of this heat is lost to the flowing fluid. As flow rate increases, more heat is lost. The amount of heat lost is measured using the thermopile(s) in the sensor. The output of the thermopile(s) represents the fluid flow velocity or flow rate.

The thermopile flow sensors are fabricated using micromachining techniques in a CMOS production line. They offer many advantages over the differential pressure meters, including but not limited to:

• Large dynamic range
• High accuracy
• Excellent low flow sensitivity
• Direct mass flow sensing
• Low pressure drop
• Very low power consumption
• Miniaturization and small device footprint
• Manufactured in CMOS production line and low cost

The thermopile flow sensors are not only used for air flow measurement in air conditioning, but also for monitoring flow in clean room, in fan/filter units, controlling flow in production facilities in the pharmaceutical, food processing and semiconductor industries; and monitoring flow in glove boxes, insulators, medical equipment such as anaesthetic machines and respirators in order to maximize energy efficiency, and also increase the accuracy of gas flow control.

Low Detectable Range Thermopile Flow Sensors

Xiang Zheng Tu

Thermal flow sensors are inevitably influenced by natural convection. An operating thermal flow sensor is a hot source surrounding by air. The air receives heat from the sensor, becomes less dense and rises. The cooler air then moves to replace it. This cooler air is then heated and the process continues, forming the convection current around the sensor. The temperature of the sensor will changes due to a part heat of the sensor is carried away by the convection current. Therefore the temperature change will add to the signal of sensor as a part of offset of the sensor.

But for thermopile flow sensors the natural convection can be reduced as low as being ignore. The installation of the thermopile flow sensors in a tube is commonly required to have their hot surface facing down to the Earth’s surface. In this case the heat transferred from the sensor chip by natural convection is the lowest. This is not surprising, since the hot air is “trapped” under the sensor chip and can not move away from the sensor chip easily. As a result, the cooler air in the vicinity of the sensor chip will have difficulty reaching the sensor chip, which results in a reduced rate of heat transfer.

Even the hot surface of the sensor intersects the Earth’s surface at a specific angle, the formed natural convection current is small and the influence still can be ignore. The reason can be explained as follows. Natural convection is characterized by Grashof number G_r which expresses the ratio between buoyancy forces due to spatial variation in air density to viscous forces acting on air. It is given as:

Gr = gβ(T_sensor - T_air )L³ /  ע² ,                   (1)

where g is the acceleration due to gravity; β is the volumetric thermal expansion coefficient; T_s and T_air are temperature of the heater of the sensor and the surrounding air, respectively; L is the characteristic length and the ע is the kinematic viscosity of the surrounding air. With g = 9.8 m/s², β = 3.25x10^-3 /k,   ע = 1.65 x 10^-5, T_s - T_air = 21.9 ^oC, and assuming the characteristic dimension L = 1x10^-3 m, we have

Gr = gβ(T_s - T_air )L³ /  ע² = 2.56    (2)

As well know, the ratio Gr/Re₂ defines the importance of natural convection in respect to a forced convection. The R_e is Rayleigh Number which represents forced convection and can be expressed as R_e = vL/ ע. The thermopile flow sensors provided by POSIFA Microsystems have been widely used for air mass flow meters. The characteristic length of the house tube of the air mass flow meter is 6mm. If assuming the velocity of air flow is 0.1mm/s, the Re is calculated to be 3.64 and the ratio Gr/Re₂ to be 0.19. This is lower than the lower bound of Gr/Re2 =0.3, which means that compare with the forced convection the contribution of the natural convection to the heat transfer can be negligible. (E. M. Sparrow, R. Eichhorn, and J. L. Gregg, “Combined forced and free convection in a boundary layer flow,” Phys. Fluids, vol. 2, no. 3, pp. 319–328, 1959.)

In addition to natural convection, the noises of the thermopile flow sensors are also limiting the detectable flow velocity. The noises of the thermopile flow sensors are basically the temperature noise and the thermal noise. The temperature noise is caused by temperature fluctuations in the surrounding atmosphere. This noise can be cancelled because the thermopile flow sensors are responsive to the temperature difference between a hot place and a cold place instead of a temperature. The thermal noise or the Johnson noise is an electrical noise source caused by random motion of electrical charges in the material. It is determined by the following equation:

V_noise = (4k_bT_eR∆f)^1/2               (3)

where k_B is the Boltzmann’s constant; T_e is the absolute temperature in kelvin ; R is the electrical serial resistance and ∆f is the frequency bandwidth.

Thermal noise calculation can be carried out online. The following results are given by http://www.sengpielaudio.com/calculator-noise.htm.

In the calculation T = 45.9 ⁰c representing the operating temperature of the thermopile flow sensor, R = 150 kΩ representing the serial resistance of a thermopile of the sensor. The bandwidth is calculated using equation ∆f = f_cutoff – 20 Hz, where f_cutoff is determined by measuring the response time of the sensor, as shown in the following figure.

 

It can be obtained from Fig.1 that the response time of the sensor is 0.74ms corresponding cutoff frequency 1351 Hz. With these parameters the thermal noise of the sensor is 1.88µV.

In conclusion, the thermopile flow sensors provided by POSIFA Microsystems can detect as low as 0.1mm/s velocity for air mass flow meter applications. This is resulted by the inherence low Grashof number of the sensors, which is down to 2.56. The temperature noise of the sensor can be canceled since the sensor is responsive to the temperature difference instead of temperature. The thermal noise or the Johnson noise is calculated to be 1.88µV, which is very low and is suitable for medical applications.  Furthermore the cutoff frequency of the sensors is up to 1331Hz, which is required by several medical instruments such as spirometers.

Low Detectable Range Thermopile Flow Sensors

 Xiang Zheng Tu

Thermal flow sensors are inevitably influenced by natural convection. An operating thermal flow sensor is a hot source surrounding by air. The air receives heat from the sensor, becomes less dense and rises. The cooler air then moves to replace it. This cooler air is then heated and the process continues, forming the convection current around the sensor. The temperature of the sensor will changes due to a part heat of the sensor is carried away by the convection current. Therefore the temperature change will add to the signal of sensor as a part of offset of the sensor.

But for thermopile flow sensors the natural convection can be reduced as low as being ignore. The installation of the thermopile flow sensors in a tube is commonly required to have their hot surface facing down to the Earth’s surface. In this case the heat transferred from the sensor chip by natural convection is the lowest. This is not surprising, since the hot air is “trapped” under the sensor chip and can not move away from the sensor chip easily. As a result, the cooler air in the vicinity of the sensor chip will have difficulty reaching the sensor chip, which results in a reduced rate of heat transfer.

Even the hot surface of the sensor intersects the Earth’s surface at a specific angle, the formed natural convection current is small and the influence still can be ignore. The reason can be explained as follows. Natural convection is characterized by Grashof number G_r which expresses the ratio between buoyancy forces due to spatial variation in air density to viscous forces acting on air. It is given as:

Gr = gβ(T_sensor - T_air )L³ /  ע² ,     (1)

where g is the acceleration due to gravity; β is the volumetric thermal expansion coefficient; T_s and T_air are temperature of the heater of the sensor and the surrounding air, respectively; L is the characteristic length and the ע is the kinematic viscosity of the surrounding air. With g = 9.8 m/s², β = 3.25x10^-3 /k,   ע = 1.65 x 10^-5, T_s - T_air = 21.9 ^oC, and assuming the characteristic dimension L = 1x10^-3 m, we have

Gr = gβ(T_s - T_air )L³ /  ע² = 2.56     (2)

As well know, the ratio Gr/Re₂ defines the importance of natural convection in respect to a forced convection. The R_e is Rayleigh Number which represents forced convection and can be expressed as R_e = vL/ ע. The thermopile flow sensors provided by POSIFA Microsystems have been widely used for air mass flow meters. The characteristic length of the house tube of the air mass flow meter is 6mm. If assuming the velocity of air flow is 0.1mm/s, the Re is calculated to be 3.64 and the ratio Gr/Re₂ to be 0.19. This is lower than the lower bound of Gr/Re2 =0.3, which means that compare with the forced convection the contribution of the natural convection to the heat transfer can be negligible. (E. M. Sparrow, R. Eichhorn, and J. L. Gregg, “Combined forced and free convection in a boundary layer flow,” Phys. Fluids, vol. 2, no. 3, pp. 319–328, 1959.)

In addition to natural convection, the noises of the thermopile flow sensors are also limiting the detectable flow velocity. The noises of the thermopile flow sensors are basically the temperature noise and the thermal noise. The temperature noise is caused by temperature fluctuations in the surrounding atmosphere. This noise can be cancelled because the thermopile flow sensors are responsive to the temperature difference between a hot place and a cold place instead of a temperature. The thermal noise or the Johnson noise is an electrical noise source caused by random motion of electrical charges in the material. It is determined by the following equation:

V_noise = (4k_bT_eR∆f)^1/2       (3)

where k_B is the Boltzmann’s constant; T_e is the absolute temperature in kelvin ; R is the electrical serial resistance and ∆f is the frequency bandwidth.

Thermal noise calculation can be carried out online. The following results are given by http://www.sengpielaudio.com/calculator-noise.htm.

  

In the calculation T = 45.9 ⁰c representing the operating temperature of the thermopile flow sensor, R = 150 kΩ representing the serial resistance of a thermopile of the sensor. The bandwidth is calculated using equation ∆f = f_cutoff – 20 Hz, where f_cutoff is determined by measuring the response time of the sensor, as shown in the following figure.

It can be obtained from Fig.1 that the response time of the sensor is 0.74ms corresponding cutoff frequency 1351 Hz. With these parameters the thermal noise of the sensor is 1.88µV.

In conclusion, the thermopile flow sensors provided by POSIFA Microsystems can detect as low as 0.1mm/s velocity for air mass flow meter applications. This is resulted by the inherence low Grashof number of the sensors, which is down to 2.56. The temperature noise of the sensor can be canceled since the sensor is responsive to the temperature difference instead of temperature. The thermal noise or the Johnson noise is calculated to be 1.88µV, which is very low and is suitable for medical applications.  Furthermore the cutoff frequency of the sensors is up to 1331Hz, which is required by several medical instruments such as spirometers.

Thermopile Flow Sensors Operating at as low as 45.9⁰C

Tu Xiang Zheng

There are two types of popular micromachined thermal flow sensors: resistive flow sensors and thermopile flow sensors. Both the thermal flow sensors work by heat convection transfer away from a heated resistor. As the resistor cool, the corresponding change in voltage or current can be calculated to fluid flow. The major difference between the resistive flow sensors and the thermopile flow sensors is the heat sensing element. Their heat sensing elements are unheated resistors and thermopiles, respectively.

An infrared camera is used to take the temperature image of a thermopile flow sensor. To do this, a DC voltage is applied to the resistor of the sensor. A typical temperature image is shown in Fig.1.The brightest (warmest) parts of the image are customarily colored white, intermediate temperatures reds and yellows, and the dimmest (coolest) parts black.

As can be seen, the highest temperature is 45.9⁰c at the central region of the sensor chip and the lowest temperature is 24.4⁰c at the surrounding region of the sensor chip. It can be seen from this image that the thermopile flow sensor can be operated at 45.9⁰c. This operating temperature is much lower than the operating temperature of any resistive flow sensors, which is usually over 100⁰c.

The circuit module of the thermopile flow sensor is also shown in Fig.1. The module includes a thermopile flow sensor, a microcontroller, a regulator, and an amplifier. The regulator may input a buttery voltage and output a regulated voltage to the microcontroller. The microcontroller may create a pulse width modulation (PWM) voltage to the heated resistor of the thermopile flow sensor. The thermopile of the thermopile flow sensor may provide a static output voltage to the amplifier. The microcontroller may process the static output voltage for adjusting the PWM voltage so as to set an original offset of the amplifier to be as close to zero as possible.

In order to operate the thermopile flow sensor at 45.9⁰c, the following settings should be made. The buttery voltage is 5V and the regulated voltage is 3V. The resistance of the resistive heater is 240Ω. The PWM applied to the resistive heater is 2.54V. These settings result in a heating power of 26.9mW, an operating temperature of 45.9⁰c, and a 20mV static output of a thermopile. The 20mV static output is the original offset of the thermopile, which may drift over time. It is necessary to be able to maintain the original offset by adjusting the PWM output accordingly. For this reason, the PWM is set a duty cycle of 60% yielding 1.8V and 90% yielding 2.7V so that a duty cycle is 84.7% can yield 2.54V PWM output.

The low temperature operating thermopile flow sensors can provide several advantages over high temperature operating resistive flow sensors. An outstanding advantage is that oil droplets can be avoided to form around the sensor chips when they use for automobile air mass flow meters. The reason for this can be explained using Fig. 2 that is a graph showing the relationship between partial pressure and temperature of gasoline vapor in a gaseous mixture of air. 

Reference to Fig.2, P_ms represents the saturated vapor pressure curve and P_m represents the un-saturated vapor pressure curve. The yellow star with 24.4⁰c indicates the temperature and un-saturated vapor pressure of the gaseous mixture and the green star with 45.9⁰c represents the temperature and saturated vapor pressure of the gaseous mixture in the temperature boundary layer over the heated sensor chip. As can be seen, when the gaseous mixture in the temperature boundary layer over enters its surrounding space it still keeps un-saturated. But if the sensor chip is heated up to higher than 60⁰c as indicated by the red star, the gaseous mixture entered the surrounding space will become saturated and condense to be gasoline droplets.

It should be noted that a laminar flow is supposed to form over the heated sensor chip with a temperature boundary layer built up thereon. Since the gaseous mixture of air in the temperature boundary layer is heated, its volume increases and its partial vapor pressure decreases correspondingly. This will result in a partial vapor pressure difference between the temperature boundary layer and the surrounding space which drives vapors diffuse from the surrounding space to the temperature layer until reach the balance between these two spaces. This is why the vapor pressure in the temperature boundary layer on the heated sensor chip is indicated by the green star vapor pressure instead of the corresponding yellow star vapor pressure.