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 Vv
ρ π d Vavg)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
Cv =
specific heat of the air passing through the sensoe
Ρ = density of the air
passing through the sensor
Vavg =
average velocity of the air passing through the sensor
In this equation, ρ, Vavg,
qt, and ΔT are the unknowns,
because they change with time while the other variables are known.
However, qt and ΔT can be obtained through measuring
devices, leaving in the product of ρ and Vavg 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:
kh = xd kd / (xd
Ad + xw Aw) + xw kw / (xd
Ad + xw Aw) (4)
Where:
xd = mole
concentration of dry air
xw = mole concentration of water vapor
kh = thermal conductivity of humidity air
kd = thermal conductivity of dry air
kw = thermal conductivity of water vapor
Ad, Aw = 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:
Vout = β xd + βw xw
(5)
xd + xw = 1
(6)
Where Vout is
the output of the thermal conductivity sensor, β and βw are
constants to be specified by experiments.
Assuming:
mh = mass flow rate of humidity air which is
measured by the thermal flow sensor
mw = mass flow rate of water vapor which is
calculated using absolute humidity measured by the thermal conductivity sensor
The following expression can be established:
md = mh – mw (7)
Where md = 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.