Humidity Compensated MEMS Air Mass Flow Meters

Xiang Zheng Tu

Mass flow rate of air entering a fuel-injected internal combustion engine is necessary for the engine control unit (ECU) to balance and deliver the correct fuel mass to the engine. Air mass flow rate varies with the ambient absolute humidity, which means that a mass flow sensor should be in injunction with a humidity sensor for determining the quantity of intake air in each cylinder. That is hwy POSIFA Microsystems Company provides humidity compensated MEMS air mass flow meters.

The humidity compensated MEMS air mass flow meter is located ahead of a throttle body. After an air filter, the meter utilizes a MEMS thermal conductivity sensor measures the absolute humidity of air entering the throttle body. Then the entered air passes through a MEMS thermal mass flow sensor, which is incorporated in the same body and is used to measures the air mass flow rate. A microcontroller of the meter processes the data collected by the two sensors and provides a humidity compensated air (or dry air flow rate) to ECU.  

The combustion of gasoline or octane in pure oxygen follows this reaction:

2 C₈H₁₈ + 25 O₂ → 16 CO₂ + 18 H₂O                                                 (1)

This is so-called “on ratio” or “stoiechiometric” combustion. Molecular weights of the above reagents are C₈H₁₈ = 114, O₂ = 32, CO₂ = 44, H₂O = 18. The ratio of mass of oxygen to mass of octane is 25 x 32 / mol / 2 x 114 /mol = 3.51, which means that 1 kg of octane reacts with 3.51 kg of oxygen to produce 3.09 kg of carbon dioxide and 1.42 kg of water.

By volume, dry air contains 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.04% carbon dioxide, and small amounts of other gases. Air also contains a variable amount of water vapor, on average around 1% at sea level, and 0.4% over the entire atmosphere.

So in dry air the reaction is expressed as:

2 C₈H₁₈ + 25 (O₂ + 3.7 N₂) → 16 CO₂ + 18 H₂O                                (2)

The ratio of mass of air to mass of octane is 12.99. Therefore for octane, the dry air–octane mixture is 12.99 i.e. for every one gram of octane 12.99 grams of air is required.

Combustion process never runs stoichiometric. It always incorporates a modest amount of excess air - 10 to 20% more than needed to burn the gasoline completely.

If insufficient amount of air is supplied to engine, unburned fuel, soot, smoke, and carbon monoxide are exhausted from the engine. The results are heat transfer surface fouling, pollution, lower combustion efficiency, flame instability and a potential for explosion.

Like all thermal mass flow meters, humidity affects their output. Sine water vapor is added to the dry air, the total mass is increased and both the overall thermal conductivity and overall viscosity change. To correct the mass flow readings of the meters what percentage of the water vapor should be know.

The thermal flow sensor of the humidity Compensated MEMS air mass flow meter consists of a thermal insulating base, a resistive heater and two thermopiles. The heater is structured as a long stripe extending from one side of the base to the opposite side and the hot junctions of the two thermopiles are arranged along the two opposite sides of the heater respectively. The cold junctions of the two thermopiles are arranged along the two opposite edges of the base. As air flows by the sensor, molecules of the flowing air transport heat away from the sensor, the sensor cools, and energy is lost, which is governed by the equation as

Qt = ΔT [ k + 2 (k V_v ρ π d V_avg)^1/2 ]                                                  (3)

Where:

qt = rate of heat loss per unit time

ΔT = mean temperature elevation of the thermal insulating base

d = width of the resistive heater

k = thermal conductivity of the air passing through the sensor

C_v = specific heat of the air passing through the sensoe

Ρ = density of the air passing through the sensor

V_avg = average velocity of the air passing through the sensor

In this equation, ρ, V_avg, qt, and ΔT are the unknowns, because they change with time while the other variables are known. However, q_t and ΔT can be obtained through measuring devices, leaving in the product of ρ and V_avg and cross section area of the pipe.

The thermal conductivity sensor the humidity Compensated MEMS air mass flow meter is the same as the thermal flow sensor except that the thermal insulating base is replaced by a plate suspending over a cavity. The cavity is filled with a measured humidity air and by conduction the humidity air transports heat away from the sensor.

According to the Wassiljewa Equation the thermal conductivity of a humidity air can be expressed as:

k_h = x_d k_d / (x_d A_d + x_w A_w) + x_w k_w / (x_d A_d + x_w A_w)                          (4)

Where:

x_d  = mole concentration of dry air

x_w = mole concentration of water vapor

k_h = thermal conductivity of humidity air

k_d = thermal conductivity of dry air

k_w = thermal conductivity of water vapor

A_d, A_w = constants to be specified

It could be convenient to use linear least squares method for anglicizing the measurement data of the thermal conductivity sensor. The regression model can be expressed as:

V_out = β x_d + β_w x_w                                                                                (5)

x_d + x_w = 1                                                                                             (6)

Where V_out is the output of the thermal conductivity sensor, β and β_w are constants to be specified by experiments. 

Assuming:

m_h = mass flow rate of humidity air which is measured by the thermal flow sensor

m_w = mass flow rate of water vapor which is calculated using absolute humidity measured by the thermal conductivity sensor

The following expression can be established:

m_d = m_h – m_w                                                                                                         (7)

Where m_d = mass flow rate of dry air which is required by all combustion engines.

In conclusion, POSIFA Microsystems Company provides humidity compensated MEMS air mass flow meters which combine air flow rate and absolute air humidity measurements and directly output dry air flow rate without adding temperature and pressure measurements.