Periodismo radial

Fig. 1 At WOT and n = 3000 min^–1; intake-manifold pressure ps= 0.96 bar;

mean air-flow rate QLMm= 157.3 kg/h

0 5 10 15 20

Time t

ms 300

kg/h

200

Air-mass flow QLM100 Q_LM

1 Crankshaft rotation

Pulsating air-flow mass QLMin the intake tract of an IC engine

1

æ

UAE0802E

On a 4-cylinder engine, the pulsations are generated at twice the crankshaft speed. This means that they can easily be in the range 50...100 Hz. With an air-mass meter featur-ing a linear characteristic curve and a nar-rower frequency bandwidth than above, it would suffice for it to follow the mean value of these rapidly fluctuating air flows. The mean value is in any case positive, so that the meter need not necessarily detect the correct sign.

Practically all of the air-mass meters actu-ally in use feature a characteristic curve which is far from linear, so that the measure-ment signal must be linearized electronically before it can be evaluated. If averaging takes place before linearisation, this can lead to considerable errors ("mean-value errors").

Being as the pulsations mostly have a pro-nounced non-sinusoidal characteristic, they therefore also have a considerable harmonic content. This fact means that such air-mass meters must be able to follow the pulsations rapidly enough. This necessitates a band-width of about 1000 Hz. Apart from this considerable bandwidth, the air-mass meters must also have a high switch-on time con-stant in order for them to be able to measure correctly during the engine start phase.

Similar to all flow meters, the versions used in the automobile are calibrated for

"tubular" flow with a symmetrical flow pro-file, in other words for a flow whose velocity

vector υ at practically every point in the flow cross-section of area A is only a function of the radius to the center line. The flow profile (laminar or turbulent, Fig. 2) is directly related to the Reynolds number Re. Re= υ · D/η

Where

D= Typical cross-section, and

η= kinematic viscosity of the medium.

Flow is laminar or turbulent when the Reynolds number R is below or above ap-prox. 1200. If the transition is in the center of the measuring range, marked irregularity of the characteristic curve can be expected at this point. As far as automotive applications are concerned, a purely turbulent flow (rec-tangular profile: υ = constr) can be reckoned with. This turbulence is sometimes pro-voked on purpose by means of a special grid element which also serves to protect the measuring system against damage. Assum-ing a homogeneous density
, the flow is simple to calculate as follows:

QV= υ · A Volume flow rate

QM=
· υ · A Mass flow rate Whereas in measurement techniques, long, straight, advance and overshoot sections of constant cross-section are stipulated in or-der to guarantee a symmetrical profile, such

Flow meters Measured quantities 97

Fig. 2

1 Laminar flow profile 2 Turbulent flow profile A Cross-section area

of the tube Q Flow R Tube radius r Distance from the

tube center υ(r) Flow profile (r)

r R

Q Q

A

A 1 2

υ Flow profiles

2

æ

UAE0803Y

conditions cannot be complied with in a vehicle’s cramped under-hood installation space. If pronounced asymmetries occur, the flow meter must be calibrated as a function of the actual installation conditions.

Impact pressure gauges, whose function will be dealt in more detail below, react to the pressure drop (∆p) at a special restriction (metering orifice) in the flow cross-section and measure a flow which corresponds neither to the volume flow rate nor the mass flow rate. Instead this flow value is the geo-metrical mean of the two:

QSt= const ·

· υ = const. ·
QV· QM

Whereby, the pressure loss at the flow meter (above all at WOT) is not to exceed

20...30 mbar.

Measuring principles

Up to now, of the practically unlimited var-iety of flow meters on the market, only those which operate according to the impact-pres-sure principle have come to the forefront for air-quantity measurement in the vehicle.

This principle still depends upon mechani-cally moving parts, and in principle correc-tion measures are still needed to compensate for density fluctuations.

Today, air-mass meters are increasingly be-ing used which use a thermal method with-out moving parts. Their wire" or "hot-film" principle enables them to follow sud-den flow changes with a minimum of delay.

Variable orifice plates (sensor plates) The calculation of the pressure drop across fixed orifice plates is based on two physical laws:

Continuity equation:

1· υ1· A1=
2· υ2· A2= const Bernoulli’s equation:

1 1

p1+ ·
1· υ12= p2+ ·
2· υ22= const

2 2

These laws are to be applied for two different measuring cross-sections A1and A2(Fig. 3).

98 Flow meters Measuring principles

Fig. 3 a Ring orifice b Sensor plate 1 Orifice plate AS Plate diameter A_{1, 2}Measuring

cross-section p1, 2Measurement

pressure

∆_p Pressure drop QLMAir-mass flow

a ∆p

Q_LM Q_LM

Q_LM 1

b

1 A₂ p₂ p₁

p₂ p₁

A_S

A_S A₂ Q_LM A₁

A₁

∆p

Impact-pressure flowmeter with ring orifice (a) and sensor plate (b)

3

æ

UAE0804Y

Assuming constant density
=
1=
2, this results in the pressure drop:

1 1

∆p = QV2

·
· ( ––– – ––– )A22 A12

This pressure drop can be measured either directly with a differential-pressure flow meter, or by means of the force acting against a so-called sensor plate (Fig. 3).

Due to their r.m.s. relationship to the flow, fixed orifice plates permit only a 1:10 varia-tion of the measured-variable. When larger ranges are to be covered, several orifice plates must be used, or such versions which automatically adapt themselves to the mea-suring range by opening up a larger flow cross-section A2in line with the increasing impact pressure.

With such variable, moving sensor plates it is an easy matter to increase the variation to 1:100. Here, the increasing air flow causes the sensor plate to be deflected (usually against a constant counterforce) into an area whose cross section is specifically shaped so that the resulting deflection/angle relationship com-plies with the desired characteristic. In other words, linear for K-Jetronic and non-linear for L-Jetronic. The sensor plate’s (Fig. 4) set-ting is then a measure for the air flow which

is in relationship to the impact pressure defined above. The limit frequency for such air-mass meters is approx. 10 Hz.

Such sensor plates though are unable to fol-low the high pulsation frequencies which often occur. From the point of view of the pulsation, they can be regarded as fixed orifice plates with a square-law curve. Under certain load conditions this leads to considerable mean-value errors which can only be compensated for roughly by the use of suitable software.

Here, when the density
of the drawn-in air changes due to temperature fluctuations or changes in altitude, the measured signal changes by merely

. An air-temperature sensor and a barometric pressure sensor are needed in order to register the density fluc-tuation in full.

Hot-wire/Hot-film anemometers When current IHflows through a thin wire with electrical resistance R, its temperature increases. If at the same time a medium with density
, flows across it at velocity υ, a bal-ance is set up between the electrical power input Peland the power PVdrawn off by the air flow, whereby

Pel= IH2· R = PV= c1· λ · ∆

Here, the power drawn off by the air flow is proportional to the temperature difference

∆ and the coefficient of thermal conduc-tivity λ. The following applies in close ap-proximation:

λ =

· υ + c2=
QLM+ c2

Although λ is primarily a function of the mass flow QLM, with the medium at standstill (υ = 0) a certain heat loss takes place (convec-tion) represented by the additive constant c2

This results in the familiar interrelationship

∆ IH= c1·



^(
QLM



^{+ c2)}



^–––_R

between the heating current IHand the mass flow QLM.

Flow meters Measuring principles 99

Fig. 4

1 Sensor plate 2 Damping device 3 Soft return spring QLMAir-mass flow x = x(QLM)

sensor-plate setting depen-dent on flow Q_LM

x_max x

Q_LM 1 2

3

Impact-pressure flow meter with variable, moving sensor plate

4

æ

UAE0805Y

With the application of constant heating power (IH2R), which presents no problems, a reciprocal temperature increase ∆ would occur which decreases at a rate correspond-ing to the square root of the air-mass flow QLM. If on the other hand, the heating cur-rent IHis controlled such that a constant temperature increase (for instance, ∆ = 100 K) is maintained even when the flow rate increases, this will lead to a heating cur-rent which increases at the fourth root of the mass flow, and at the same time serves as a measure for the mass flow.

The essential advantage of such a control circuit lies in the fact that the electrical heater resistor always remains at the same temperature so that its calorific content need not be changed by means of time-wasting heat transfer. In fact, with a 70 µm platinum wire for instance, it is possible to achieve time constants in the 1 ms range for changes in air-flow rate. In cases where closed-loop control is not used the time constants would be 40...100 times higher (Fig. 5).

If the heater temperature were to be main-tained constant simply by keeping its (tem-perature-dependent) resistance constant, with constant mass flow and higher medium temperature, this would result in a current drop and therefore a false measurement. In

practice, this error is avoided by using a bridge circuit containing a second high-ohm

"compensation resistor" RKof the same type (e.g. platinum). Here, the heater resistor is kept at a constant overtemperature ∆ com-pared to the medium (Fig. 6). In case of a sudden jump in the medium temperature, the sensor reacts with a long time constant since in this case the calorific content of the heater wire must be changed.

The heater resistors in the first air-mass meters (anemometers) used for automotive applications were of very fine platinum wire.

This wire was mounted in trapezoidal form across the flow cross-section so that it was able take the mean of irregularities in the flow profile. Service lives which were accept-able from the technical viewpoint only be-came possible when the platinum wire was stabilised by alloy additives so that its resis-tance no longer changed due to deposits and cracks on its surface. This meant though that the deposits on the heater wire had to be burned-off following every operating phase (approx. 1000 °C).

Notwithstanding a number of functional advantages, this sensor concept was far too costly. Although a thick-film version (HFM2) was able to combine all the resistors con-cerned with the measurement on a single ceramic substrate, this failed to bring the

100 Flow meters Measuring principles

Fig. 5

1 Theoretical charac-teristic

2 Experimental charac-teristic

Fig. 6

QLMAir-mass flow UM Measurement

voltage RH Hot-wire resistor RK Compensation

resistor

R_M Measuring resistor R1, 2Trimming resistor

0

0 20 40

Air-mass flow Q_LM

60 kg/h 4

5 6 7 V 8

Signal voltage U

1 2 Hot-wire air-mass meter

5

æ

UAE0806E

R_K R_H I_H t_L

R_M R₁

R₂ U_M

Q_M

Hot-wire air-mass meter (electronic closed-loop control)

6

æ

UMK0311-1Y

hoped-for advantages with regard to the costs. Due to the substrate’s considerable thermal capacity, it was difficult not to ex-ceed the maximum permissible switching constants. Furthermore, a complicated saw cut had to be made to reduce the undesir-able heat coupling between heating and compensation resistors. On the other hand though, this version permitted the burn-off process to be dispensed with since the spe-cial flow conditions no longer led to un-wanted deposits.

In contrast to both its predecessor types, a further silicon-based micromechanical ver-sion (HFM5) fulfilled practically all expec-tations. In particular, this version is able to measure in both directions with the correct sign (Fig. 7). This means that the brief re-turn flows that occur as a result of pulsation no longer lead to measuring errors (Fig. 8).

To this end, in addition to the heater con-trol circuit used in the previous versions, a temperature sensor is located on each side of the heater resistor, in other words upstream and downstream. This principle is similar to the "Thomas process" often encountered in literature. When there is no flow (QML= 0), each of these sensors indicates the same temperature. When flow starts though, since the upstream sensor is cooled by the

medium and the other is heated by it, the

higher the flow the higher the temperature difference between the two sensors. The out-put signal derived from the temperature dif-ference has a similar characteristic to the anemometers used up to now, whereby its sign is a clear indication of the flow direc-tion.

Due to its small size, the micromechanical flow meter is only a partial-flow meter. In other words, it is no longer in any way able to average-out any non-homogeneity in the flow velocity as a function of the flow cross-sectional area. Rather, this flow meter must ensure that the partial flow it measures rep-resents the same fraction of the total flow throughout the whole measuring range. This is not always an easy matter.

Examples of application

Sensor-plate air-mass meter LMM,

Hot-wire air-mass meter HLM,

Hot-film air-mass meter HFM2 und

Hot-film air-mass meter HFM5.

Flow meters Measuring principles 101

Fig. 7 QR Return flow

Fig. 8

At WOT and speed n = 900 min^–1 1 Hot-wire air-mass

meter

2 Hot-film air-mass meter

0

-100 0 100 200

Air-mass flow Q_LM Q_R

300 kg/h 3

2 1 5 4 V

Signal voltage U

Micromechanical hot-film mass meter with air-quantity measurement in both directions

7

æ

UAE0807E -50

0

0 10 20 30 40

Time t

50 ms 100

50 kg/h

Air-mass flow QLM

1

2

Pulsating air-mass flow of a 4-cylinder engine

8

æ

UAE0808E

Sensor-flap (impact-pressure)

In document Facultad de Ciencias de la Comunicación. Ciencias de la Comunicación. Programa Especial de Titulación (página 43-62)