Abstrict The flow meter is a device having a laser Doppler anemometer (LDA)
which measures the instantaneous center line velocity of fluid flow
in a pipe and processes the instantaneous velocity so obtained to
compute the volumetric flow rate, mass rate, and other flow characteristics
as instantaneous quantities and/or integrated over a time interval
using an electronic processing method which provides an exact solution
to the Navier-Stokes equations for any periodically oscillating
flow. The flow meter is particularly adapted for measuring the flow
characteristics of high pressure automotive fuel injection systems.
Three embodiments of the flow meter are described, including a stationary
stand for off-line bench testing flow rate in a fuel injection system,
a portable flow meter for inline testing in a vehicle's fuel line,
and an on-board flow meter sensor connected to an engine control
module.
Claims I claim:
1. A on-board flow meter for installation in a fuel pipeline of
a fuel injection engine, comprising: (a) a measurement tube adapted
for installation in a fuel pipeline of a fuel injection engine;
(b) a laser-Doppler anemometer generating a pair of laser beams
intersecting in a control measurement volume in a center line of
fuel flow through said measurement tube; (c) an interface card connected
to said laser-Doppler anemometer for calculating a series of instantaneous
center line velocities of fuel flow through said measurement tube;
and (d) a processor connected to said interface card, the processor
having means for computing instantaneous and integral volumetric
and mass flow rates in said measurement tube, the processor being
connected to an engine electronic control unit; whereby the electronic
control unit uses the volumetric and mass flow rates to adjust fuel
injection parameters in order to optimize fuel flow in the engine.
2. The on-board flow meter according to claim 1 wherein said measurement
tube comprises: (a) an elongated, transparent, quartz glass tube;
and (b) a steel jacket, said quartz tube being sheathed within said
steel jacket.
3. The on-board flow meter according to claim 1 wherein said laser-Doppler
anemometer comprises: (a) a laser diode attached to said measurement
tube and disposed to emit a laser beam normal to a longitudinal
axis of said measurement tube; (b) beam splitting means for splitting
the laser beam emitted by said laser diode into two laser beams
focused to intersect in the control measurement volume in the center
line of said measurement tube; (c) a PIN diode for receiving light
scattered by fuel flowing in the control measurement zone of said
measurement tube, the PIN diode being disposed on a side of the
measurement tube opposite said laser diode to receive forward scatter;
and (d) focusing means for focusing scattered light from the control
measurement zone on said PIN diode.
4. The on-board flow meter according to claim 3 wherein said beam
splitting means comprises: (a) an X-Y traverse frame disposed between
said laser diode and said measurement tube; (b) an optic fiber disposed
on said traverse frame parallel to a crystal emitting stripe of
said laser diode; (c) a three-wire guitar having a highly reflecting
back surface disposed on said traverse frame, the three wires being
disposed to block zero order and second order harmonics of the split
laser beam, first order harmonics of the laser beam being focused
to intersect in the control measurement volume on the center line
of said measurement tube.
5. The on-board flow meter according to claim 3 wherein said focusing
means comprises: (a) an X-Y traverse frame disposed between said
PIN diode and said measurement tube; (b) an optic fiber mounted
on said traverse frame; and (c) a plate having a pinhole defined
therein mounted between said optic fiber and said PIN diode.
6. The on-board flow meter according to claim 1 wherein said means
for computing instantaneous and integral volumetric and mass flow
rates comprises: (a) a first set of instructions which cause said
processor to read basic parameters, including fuel viscosity, fluid
density, injection duration, injection period, and radius of the
measurement tube; (b) a second set of instructions which cause said
processor to compute constant parameters, including frequency and
angular frequency; (c) a third set of instructions which cause said
processor to input the series of instantaneous center line velocities
from said interface card; (d) a fourth set of instructions which
cause said processor to perform an inverse Fourier transform to
calculate a series of harmonic coefficients c.sub.0 . . . , c.sub.n
from the series of center line velocities; (e) a fifth set of instructions
which cause said processor to compute a series of pressure coefficients
p.sub.0 . . . , p.sub.n from the harmonic coefficients c.sub.0
. . . , c.sub.n by solving the equations 31 p 0 = 2 c 0 v R 2 and
p n = c n n 1 - 1 J 0 ( 3 / 2 Ta n ) ; (f) a sixth set of instructions
which cause said processor to compute a series of instantaneous
volumetric flow rates from the pressure coefficients p.sub.0 .
. . , p.sub.n by solving the equation 32 V ( t ) = R 2 2 ( R 2 p
0 4 v + n = 1 .infin. { p n n n t [ 4 1 / 2 J 1 ( 3 / 2 Ta n ) Ta
n J 0 ( 3 / 2 Ta n ) - 2 ] + C . C . } ) ; and(g) a seventh set
of instructions which cause said processor to compute a mass flow
rate by integrating the volumetric flow rates using the fluid density
and cross sectional area of the measurement tube.
7. The on-board flow meter according to claim 1 wherein said means
for computing instantaneous and integral volumetric and mass flow
rates comprises: (a) a first set of instructions which cause said
processor to read basic parameters, including fuel viscosity, fluid
density, injection duration, injection period, and radius of the
measurement tube; (b) a second set of instructions which cause said
processor to compute constant parameters, including frequency and
angular frequency; (c) a third set of instructions which cause said
processor to input the series of instantaneous center line velocities
from said interface card; (d) a fourth set of instructions which
cause said processor to perform an inverse Fourier transform to
calculate a first series of harmonic coefficients c.sub.0 . . .
, c.sub.n and a second series of harmonic coefficients c.sub.0',
. . . , c.sub.n' from the series of center line velocities, where
the summation in the first series is incremented when the Stokes
layer thickness is greater than ten times the optic interference
fringe from the intersection of the two laser beams and the summation
in the second series is incremented when the Stokes layer thickness
is not greater than ten times the optic interference fringe from
the intersection of the two laser beams; (e) a fifth set of instructions
which cause said processor to compute a series of pressure coefficients
p.sub.0 . . . , p.sub.n and p.sub.0', . . . , p.sub.n' from the
harmonic coefficients c.sub.0 . . . , c.sub.n and c.sub.0', . .
. , c.sub.n' by solving the equations 33 p o z = 2 c o v R 2 p nz
= c n n [ 1 - 1 J 0 ( 3 / 2 Ta n ) ] , n [ 1 N ] p nz ' + p nz
' p nr ' = 2 c n ' n [ 1 - 1 J 0 ( 3 / 2 Ta n ) ] , n [ N + 1
N meas ] ;(f) a sixth set of instructions which cause said processor
to compute a series of instantaneous volumetric flow rates from
the pressure coefficients p.sub.0 . . . , p.sub.n and p.sub.0
. . . , p.sub.n' by solving the equation 34 V . ( t ) = 2 0 R (
u ~ + u ' v ' _ ) r r = R 2 2 [ p 0 R 2 4 v + n = 1 .infin. ( p
nz - p nz ' 2 + p nz ' p nr ' 2 n n t { 4 1 / 2 J 1 ( 3 / 2 Ta n
) Ta n J 0 ( 3 / 2 Ta n ) - 2 } ) + C . C . ] ; and(g) a seventh
set of instructions which cause said processor to compute a mass
flow rate by integrating the volumetric flow rates using the fluid
density and cross sectional area of the measurement tube.
8. A flow meter for measuring fuel flow characteristics in a fuel
injection system, comprising: (a) a measurement tube adapted for
installation in a fuel pipeline of a fuel injection system; (b)
a laser-Doppler anemometer generating a pair of laser beams intersecting
in a control measurement volume in a center line of fuel flow through
said measurement tube; (c) an interface card connected to said laser-Doppler
anemometer for calculating a series of instantaneous center line
velocities of fuel flow through said measurement tube; and (d) a
processor connected to said interface card, the processor having
means for computing instantaneous and integral volumetric and mass
flow rates in said measurement tube.
9. The flow meter according to claim 8 further comprising: (a)
a fuel tank; (b) a fuel injection pump; (c) a fuel injector; (d)
a fuel pipeline connecting said fuel tank, said fuel pump, and said
fuel injector, said measurement tube being disposed in said fuel
pipeline between said fuel pump and said fuel injector; and (e)
wherein said laser-Doppler anemometer comprises: (i) an optical
bench, said measurement tube being disposed on the optical bench;
(ii) a laser light source attached to the optical bench disposed
to emit a laser beam normal to said measurement tube; (iii) a prism
disposed between said laser light source and said measurement tube
for splitting the laser beam into two collimated beams; (iv) a pair
of Braggs cells mounted on the optical bench, the Braggs cells modulating
the two laser beams with a fixed frequency difference; (v) a focusing
lens mounted on the optical bench to focus the two laser beams on
a control measurement volume on the centerline of said measurement
tube; and (vi) a photodetector mounted opposite said measurement
tube for detecting forward scatter of the two laser beams.
10. The flow meter according to claim 9 wherein: (a) said laser
light source comprises a helium-neon laser; and (b) said photodetector
comprises a photomultiplier tube.
11. The flow meter according to claim 9 wherein: (a) said laser
light source comprises a laser diode; and (b) said photodetector
comprises a PIN diode.
12. The flow meter according to claim 9 further comprising an
external controller connected to said fuel pump for controlling
the duration and frequency of fuel injection pulses.
13. The flow meter according to claim 9 further comprising an
electronic control unit connected to said fuel pump for controlling
the duration and frequency of fuel injection pulses, the electronic
control unit having a time base capable of nanosecond pulse duration.
14. The flow meter according to claim 8 wherein said measurement
tube comprises: (a) a cylindrical quartz glass tube having an inlet
end and an outlet end; (b) a rectangular glass tube having an inlet
end and an outlet end, the rectangular glass tube being disposed
about said quartz glass tube; (c) an inlet plug and an outlet plug,
each plug having a rectangular plate sealing the inlet and outlet
ends of the rectangular glass tube, respectively, and having a nipple
extending from the rectangular plate; (d) a cylindrical fitting
disposed in each said nipple, the inlet end of said quartz glass
tube extending into the nipple of the inlet plug and abutting the
cylindrical fitting, and the outlet end of the quartz glass tube
extending into the nipple of the outlet plug and abutting the cylindrical
fitting; (e) a cylindrical inlet unit attached to the inlet plug,
the cylindrical inlet unit being adapted for attachment to the fuel
pipeline; and (f) a cylindrical outlet unit attached to the outlet
plug, the outlet unit being adapted for attachment to a fuel injector.
15. The flow meter according to claim 8 wherein said laser-Doppler
anemometer comprises: (a) a laser diode emitting a laser beam; (b)
a prism redirecting the laser beam normal to said measurement tube;
(c) a first lens disposed between said laser diode and said prism
for collimating the laser beam; (d) a holographic splitter disposed
between said prism and said measurement tube for splitting the laser
beam into two beams and for focusing the two beams to intersect
in a control measurement volume in the center line of said measurement
tube; (e) a PIN diode disposed on a side of said measurement tube
opposite said laser diode to detect forward scatter from the intersecting
laser beams; (f) a pinhole mask disposed between said PIN diode
and said measurement tube; and (g) a second lens disposed between
said measurement tube and said pinhole mask for focusing the forward
scatter on said PIN diode.
16. The flow meter according to claim 15 further comprising a
box, said measurement tube and said laser-Doppler anemometer being
disposed in said box, said measurement tube being adapted for insertion
in a fuel pipeline of a fuel injection engine.
17. The flow meter according to claim 8 wherein: (a) said measurement
tube comprises: (i) an elongated, transparent, quartz glass tube
adapted for insertion in a fuel pipeline of a fuel injection engine;
(ii) a steel jacket, said quartz tube being sheathed within said
steel jacket; and (b) said laser-Doppler anemometer comprises: (i)
a laser diode attached to said measurement tube and disposed to
emit a laser beam normal to a longitudinal axis of said measurement
tube; (ii) beam splitting means for splitting the laser beam emitted
by said laser diode into two laser beams focused to intersect in
the control measurement volume in the center line of said measurement
tube; (iii) a PIN diode for receiving light scattered by fuel flowing
in the control measurement zone of said measurement tube, the PIN
diode being disposed on a side of the measurement tube opposite
said laser diode to receive forward scatter; and (iv) focusing means
for focusing scattered light from the control measurement zone on
said PIN diode.
18. The flow meter according to claim 8 wherein said means for
computing instantaneous and integral volumetric and mass flow rates
comprises: (a) a first set of instructions which cause said processor
to read basic parameters, including fuel viscosity, fluid density,
injection duration, injection period, and radius of the measurement
tube; (b) a second set of instructions which cause said processor
to compute constant parameters, including frequency and angular
frequency; (c) a third set of instructions which cause said processor
to input the series of instantaneous center line velocities from
said interface card; (d) a fourth set of instructions which cause
said processor to perform an inverse Fourier transform to calculate
a first series of harmonic coefficients c.sub.0 . . . , c.sub.n
and a second series of harmonic coefficients c.sub.0', . . . , c.sub.n'
from the series of center line velocities, where the summation in
the first series is incremented when the Stokes layer thickness
is greater than ten times the optic interference fringe from the
intersection of the two laser beams and the summation in the second
series is incremented when the Stokes layer thickness is not greater
than ten times the optic interference fringe from the intersection
of the two laser beams; (e) a fifth set of instructions which cause
said processor to compute a series of pressure coefficients p.sub.0
. . . , p.sub.n and p.sub.0', . . . , p.sub.n' from the harmonic
coefficients c.sub.0 . . . , c.sub.n and c.sub.0', . . . , c.sub.n'
by solving the equations 35 p o z = 2 c o v R 2 p nz = c n n [ 1
- 1 J 0 ( 3 / 2 Ta n ) ] , n [ 1 N ] p nz ' + p nz ' p nr ' =
2 c n ' n [ 1 - 1 J 0 ( 3 / 2 Ta n ) ] , n [ N + 1 N meas ] ;(f)
a sixth set of instructions which cause said processor to compute
a series of instantaneous volumetric flow rates from the pressure
coefficients p.sub.0 . . . , p.sub.n and p.sub.0', . . . , p.sub.n'
by solving the equation 36 V . ( t ) = 2 0 R ( u ~ + u ' v ' _ )
r r = R 2 2 [ p 0 R 2 4 v + n = 1 .infin. ( p nz - p nz ' 2 + p
nz ' p nr ' 2 n n t { 4 1 / 2 J 1 ( 3 / 2 Ta n ) Ta n J 0 ( 3 /
2 Ta n ) - 2 } ) + C . C . ] ; and(g) a seventh set of instructions
which cause said processor to compute a mass flow rate by integrating
the volumetric flow rates using the fluid density and cross sectional
area of the measurement tube.
19. The flow meter according to claim 8 wherein said means for
computing instantaneous and integral volumetric and mass flow rates
comprises: (a) a first set of instructions which cause said processor
to read basic parameters, including fuel viscosity, fluid density,
injection duration, injection period, and radius of the measurement
tube; (b) a second set of instructions which cause said processor
to compute constant parameters, including frequency and angular
frequency; (c) a third set of instructions which cause said processor
to input the series of instantaneous center line velocities from
said interface card; (d) a fourth set of instructions which cause
said processor to perform an inverse Fourier transform to calculate
a series of harmonic coefficients c.sub.0 . . . , c.sub.n from
the series of center line velocities; (e) a fifth set of instructions
which cause said processor to compute a series of pressure coefficients
p.sub.0 . . . , p.sub.n from the harmonic coefficients c.sub.0
. . . , c.sub.n by solving the equations 37 p 0 = 2 c 0 v R 2 and
p n = c n n 1 - 1 J 0 ( 3 / 2 Ta n ) ; (f) a sixth set of instructions
which cause said processor to compute a series of instantaneous
volumetric flow rates from the pressure coefficients p.sub.0 .
. . , p.sub.n by solving the equation 38 V ( t ) = R 2 2 ( R 2 p
0 4 v + n = 1 .infin. { p n n n t [ 4 1 / 2 J 1 ( 3 / 2 Ta n ) Ta
n J 0 ( 3 / 2 Ta n ) - 2 ] + C . C . } ) ; and(g) a seventh set
of instructions which cause said processor to compute a mass flow
rate by integrating the volumetric flow rates using the fluid density
and cross sectional area of the measurement tube.
20. An electronic data processing method for measuring volumetric
flow rates and mass flow rates of a periodically oscillating fluid
flow in a pipeline, comprising the steps of: (a) inserting a measurement
tube in a pipeline; (b) measuring a series of instantaneous velocities,
u(t) on a center line of the pipeline by laser-Doppler anemometer;
(c) performing an inverse Fourier transform on the measured series
of instantaneous velocities to obtain a first series of harmonic
coefficients c.sub.0 . . . , c.sub.n and a second series of harmonic
coefficients c.sub.0', . . . , c.sub.n', where the summation in
the first series is incremented when the Reynolds number is .ltoreq.3000
and the summation in the second series is incremented when the Reynolds
number is >3000; (d) computing a series of pressure coefficients
p.sub.0 . . . , p.sub.n and p.sub.0', . . . , p.sub.n' from the
harmonic coefficients c.sub.0 . . . , c.sub.n and c.sub.0', . .
. , c.sub.n' by solving the equations 39 p o z = 2 c o v R 2 p nz
= c n n [ 1 - 1 J 0 ( 3 / 2 Ta n ) ] , n [ 1 N ] p nz ' + p nz
' p nr ' = 2 c n ' n [ 1 - 1 J 0 ( 3 / 2 Ta n ) ] , n [ N + 1
N meas ] ; and(e) computing a series of instantaneous volumetric
flow rates from the pressure coefficients p.sub.0 . . . , p.sub.n
and p.sub.0', . . . , p.sub.n' by solving the equation 40 V . (
t ) = 2 0 R ( u ~ + u ' v ' _ ) r r = R 2 2 [ p 0 R 2 4 v + n =
1 .infin. ( p nz - p nz ' 2 + p nz ' p nr ' 2 n n t { 4 1 / 2 J
1 ( 3 / 2 Ta n ) Ta n J 0 ( 3 / 2 Ta n ) - 2 } ) + C . C . ] .
Description CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This is a divisional application of U.S. Ser. No. 09/854561
filed May 15 2001 which is a continuation-in-part of Ser. No.
09/614381 filed Jul. 3 2000.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates to flow meters for measuring
the flow of fluid through a conduit. The flow meters described are
particularly adapted for measuring the volumetric flow rate for
a high pressure direct injection automotive fuel injection system.
Also described is a software method of determining the volumetric
flow rate for a periodic oscillating flow in a pipe from measurement
of the instantaneous center line velocity.
[0004] 2. Description of the Related Art
[0005] In automotive fuel injection systems, the power delivered
by the engine is related to the shape of the spray, as well as the
quantity and timing of fuel delivered to the combustion chamber.
The design of fuel injectors and control of the operation of fuel
injectors after installation would be greatly aided by a flow meter
capable of providing data on the instantaneous volumetric flow rate
in a fuel injection system, as well as a volumetric flow rate integrated
over a specified time period, or a combination of the two. The present
invention provides a flow meter which uses laser Doppler anemometry
to measure the instantaneous center line velocity of fuel in a fuel
pipe upstream from a fuel injector, and processes the data by Fourier
transform using a novel exact solution to Navier-Stokes equations
for any periodically oscillating flow to obtain the instantaneous
volumetric flow rate of fuel in the system, as well as other desired
flow characteristics.
[0006] Various devices for measuring fluid flow characteristics
have been described previously. U.S. Pat. No. 3548655 issued
Dec. 22 1970 to M. J. Rudd, describes a laser Doppler velocimeter
for measuring the velocity of fluid flow which measures the sinusoidal
variation in light intensity as a particle in the fluid passes through
interference fringes produced by laser beam which passes through
a two slit mask. No means for measuring instantaneous velocity is
described, nor is velocity necessarily measured on a center line.
Further, no processing means for computing volumetric flow rate
is described, and no means for indicating the direction of the velocity
is described.
[0007] U.S. Pat. No. 3825346 issued Jul. 23 1974 to J. Rizzo,
reaches an interferometer for measuring fluid flow which uses two
beams, a reference beam and a test beam, which travel equal path
lengths and recombine to form an interference pattern. U.S. Pat.
No. 3937087 issued Feb. 10 1976 to W. S. Heggie, teaches a transducer
for measuring pressure changes during fuel injection. The transducer
is a resistive element in the form of a coil wrapped around the
fuel line which varies in resistance as the fuel line expands and
contracts, the difference in current through the coil being measured
through a bridge.
[0008] U.S. Pat. No. 4073186 issued Feb. 14 1978 to C. L. Erwin,
Jr., describes a flow meter having a magnet mechanically attached
to a valve, the magnet generating current in a magnetic pickup as
the valve opens and closes for counting the flow pulses, the device
releasing metered amounts of fuel with each pulse. The device appears
to be for measuring fuel consumption, and not for regulating fuel
flow into an injector. U.S. Pat. No. 4192179 issued Mar. 11
1980 to E. Yelke, discloses a collar which fits around a fuel line
to a fuel injector and has piezoelectric material affixed to the
inside surface of the collar to develop an electrical signal as
the fuel line expands and contracts.
[0009] U.S. Pat. No. 5031460 issued Jul. 16 1991 to Kanenobu
et al., teaches a device for detecting pressure changes in pipes.
The device is a transducer with a bimorph piezoelectric transducer
strapped around the pipe to sense expansion of the pipe as fluid
is pulsed through the pipe. European Patent No. 489 474 published
Jun. 10 1992 describes a laser apparatus for measuring the velocity
of a fluid which uses an interferometer type device with a laser
beam split into a reference beam and a measurement beam which is
reflected back through the fluid so that the back scatter is compared
to the reference beam to measure velocity. No method for processing
the velocity to compute volumetric flow rate is described.
[0010] Japanese Patent No. 8-121288 published May 14 1996 shows
a device for measuring injection rate with a pressure sensor for
measuring the force of injection and a laser Doppler anemometer
for measuring velocity, and which uses a mathematical formula which
relates force and velocity to flow rate. Japanese Patent No. 8-121289
published May 14 1996 describes a device which uses two laser
Doppler anemometers, one in the main supply line, the other in a
bias flow generating unit fed by a divider pipe, to measure the
flow rate by a differential flow rate method.
[0011] Applicant has co-authored several publications which disclose
flow measuring devices. An article titled "Measurement of instantaneous
flow rates in periodically operating injection systems" by
F. Durst, M. Ismailov, and D. Trimis, published in Experiments in
Fluids, Vol. 20 pp. 178-188 in 1996 describes a technique for
measuring instantaneous flow rates using laser Doppler anemometry
to measure center line velocity in a capillary pipe and an improved
solution of the Navier-Stokes equations for any periodically oscillating
flow to calculate instantaneous volumetric flow rate. The device
measured the flow of water released by a magnetically operated valve
through a 2 mm diameter tube.
[0012] A paper presented at the Flomeko '98 9th International Conference
on Flow Measurement in June, 1998 titled "Accurate LDA Measurements
of Instantaneous and Integrated Flow Rates in High Pressure Gasoline
Injection System" by Ismailov et al., describes a device for
measuring flow rate in a gasoline injection system at 7 MPa with
a Unisia Jecs swirl injector. The device uses a 16 mW He--Ne laser
directed through a beam splitter and frequency shifted by Bragg
cells, focused by a lens to form a measurement control volume 485
.mu.m in length and 46 .mu.m in diameter on the center line of a
quartz pipe 300 mm long having an inner diameter of 3.5 mm. The
light is scattered by heptane and detected through a pinhole by
a photomultiplier tube elevated at a 30.degree., the output being
processed by a DOSTEK interface board. The center line velocities
are processed according to the method set forth in Durst, supra.
[0013] A paper presented at the 3rd ASME/JSME Joint Fluids Engineering
Conference Jul. 18-23 1999 titled "Instantaneous Flow Rates
in Gasoline Direct Injection System By Means of LDA and Bosch Meters"
by Ismailov et al., and an article titled "LDA/PDA measurements
of instantaneous characteristics in high pressure fuel injection
and swirl spray" by Ismailov et al. in Experiments in Fluids,
Vol. 27 pp. 1-11 (1999) present similar studies and describe similar
measuring devices to those presented in the Flomeko article, supra.
[0014] None of the above inventions, patents, and publications,
taken either singularly or in combination, is seen to describe the
instant invention as claimed. Thus a flow meter solving the aforementioned
problems is desired.
SUMMARY OF THE INVENTION
[0015] The flow meter is a device having a laser Doppler anemometer
(LDA) which measures the instantaneous center line velocity of fluid
flow in a pipe and processes the instantaneous velocity so obtained
to compute the volumetric flow rate, mass rate, and other flow characteristics
as instantaneous quantities and/or integrated over a time interval
using an electronic processing method which provides an exact solution
to the Navier-Stokes equations for any periodically oscillating
flow. The flow meter is particularly adapted for measuring the flow
characteristics of high pressure automotive fuel injection systems.
Three embodiments of the flow meter are described, including a stationary
stand for off-line bench testing flow rate in a fuel injection system,
a portable flow meter for inline testing in a vehicle's fuel line,
and an on-board flow meter sensor connected to an engine control
module.
[0016] All three embodiments have an LDA which includes a laser
light source which is split into two beams which are focused to
intersect in a control measurement zone on the center line of a
capillary pipe through which the fluid flows, and a photodetector
to detect forward scatter. An interface board converts the Doppler
frequency shift to instantaneous velocity measurements at a programmable
sampling rate with nanosecond resolution. The velocity measurements
provide data for a processor programmed to perform a discrete Fourier
transform, to determine the coefficients of a Fourier expansion
of the time resolved LDA measurements, and to use those coefficients
to compute instantaneous pressure gradients, which are then used
to compute instantaneous volumetric flow rates, mass flow rates,
and other transient injection characteristics.
[0017] The stationary stand uses an He--Ne laser focused through
a beam splitter to produce two coherent beams which are focused
to intersect in the capillary pipe, which is mounted on an optical
bench. The forward scatter is detected by a photomultiplier tube,
which outputs the detected current to an interface board which may
be mounted in a personal computer. Fluid flow is provided by a fuel
system having a high pressure pump which is triggered to provide
injection pulses to a swirl fuel injector at a predetermined or
controllable frequency. The instantaneous and integral mass rates
permit the testing, calibration, and setup of optimal characteristics
of a fuel injection system and fuel injectors.
[0018] The portable flow meter uses a laser diode focused to reflect
the beam through a prism and a holographic splitter which provides
two beams focused to intersect in the control measurement zone of
the capillary pipe. The capillary pipe is mounted in-line in a motor
vehicle's fuel line. Forward scatter is focused on a PIN diode.
The interface and electronic data processing system may be the same
as that used in the stationary stand embodiment. The use of semiconductor
components renders the portable flow meter compact and lightweight
for transport, and adaptation of the capillary pipe for insertion
into the vehicle's fuel line provides dynamic, in situ diagnostic
test, calibration, and setup data for optimal adjustment of the
vehicle's fuel injection system.
[0019] The on-board sensor has essentially the same optical components
as the portable flow meter, except that the beam from the laser
diode is not reflected through a prism, but focused directly through
an optic wire normal to the capillary pipe. The capillary pipe is
encased in a steel sheathe, so that the sensor may be permanently
installed in the vehicle's fuel pipeline. The PIN diode detector
is connected through an interface to the vehicle's engine control
module, and the module's processor executes the data processing
software, integrating the flow meter sensor's input with other sensor
data to control and adjust injection system characteristics to provide
fuel economy, power increase, and reduced exhaust emissions.
[0020] Accordingly, it is a principal object of the invention to
provide a stationary stand flow meter for testing, calibration and
setup of optimal fuel injection system characteristics for a high
pressure fuel injection system, the flow meter indicating transient
injection characteristics through instantaneous and integral mass
rates.
[0021] It is another object of the invention to provide a portable,
compact, lightweight flow meter capable of connection into a vehicle's
fuel line which provides data on transient high pressure fuel injection
system characteristics for testing, calibration and setup of optimal
fuel injection system parameters.
[0022] It is a further object of the invention to provide an on-board
fuel meter sensor connected to a gasoline or diesel engine control
module for providing measurement, calculation, and control of transient
fuel injection characteristics in order to improve fuel economy,
increase engine power, and reduce harmful or noxious exhaust emissions.
[0023] Still another object of the invention is to provide an electronic
data processing apparatus and method for computing instantaneous
and integral volumetric and mass flow rates in a periodically oscillating
fluid flow pipe from instantaneous center line velocity measurements.
[0024] It is an object of the invention to provide improved elements
and arrangements thereof for the purposes described which is inexpensive,
dependable and fully effective in accomplishing its intended purposes.
[0025] These and other objects of the present invention will become
readily apparent upon further review of the following specification
and drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026] FIG. 1 is a diagrammatic view of a stationary stand flow
meter according to the present invention.
[0027] FIG. 2 is a diagram showing a center line velocity to be
measured by an LDA component of a flow meter according to the present
invention.
[0028] FIG. 3 is a plan view of a capillary measurement pipe according
to the present invention for insertion into a pipeline.
[0029] FIG. 4 is a section view along the lines 4-4 of FIG. 3.
[0030] FIG. 5 is an end view of the capillary measurement pipe
according to the present invention.
[0031] FIGS. 6A, 6B, and 6C are charts showing typical output from
a flow meter according to the present invention in graphic form.
[0032] FIG. 7 is a diagrammatic section view of the optical system
for a portable flow meter according to the present invention.
[0033] FIG. 8 is a detail view of a holographic beam splitter used
in a flow meter according to the present invention.
[0034] FIG. 9 is a diagrammatic view of an on-board flow meter
sensor according to the present invention.
[0035] FIG. 10 is a detail view of the on-board flow meter sensor
of FIG. 9.
[0036] FIG. 11 is a section view along lines 11-11 of FIG. 10.
[0037] FIG. 12 is a diagrammatic perspective view of the elliptical
cone shaped laser beam emitted by the laser diode.
[0038] FIG. 13 is a view of a divergence mask used for the transmitting
laser diode of FIG. 9.
[0039] FIG. 14 is a view of a mask used for the PIN diode detector
of FIG. 9.
[0040] FIG. 15 is a block diagram of a custom interface board for
use of the flow meter sensors with diesel FIS.
[0041] FIGS. 16A and 16B is a flow chart of a first electronic
data processing method for transforming center line velocity data
into volumetric and mass flow rates in a flow meter according to
the present invention.
[0042] FIGS. 17A and 17B is a flow chart of a first electronic
data processing method for transforming center line velocity data
into volumetric and mass flow rates in a flow meter according to
the present invention.
[0043] FIGS. 18A and 18B are charts showing a comparison of tests
results generated by the first and second electronic data processing
methods according to the present invention.
[0044] Similar reference characters denote corresponding features
consistently throughout the attached drawings.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0045] The present invention is a flow meter for measuring the
instantaneous center line velocity in a pipe which uses an electronic
data processing method to compute instantaneous and/or integral
volumetric and mass flow rates, as well as other transient flow
characteristics, from the velocity data by an exact solution of
the Navier-Stokes equations for any periodically oscillating fluid
flow in a pipe. The embodiments of the flow meter described herein
are particularly adapted for measuring flow rates in a high pressure
fuel injection system, although it will be obvious to those skilled
in the art that the devices and principles described herein are
easily modified for applications in industry, pharmacology and medicine.
[0046] Each embodiment of the flow meter includes a laser-Doppler
anemometer (LDA) for measuring the center line instantaneous velocity
of fluid flow through a capillary measurement pipe, and data processing
software for computing flow rates from the measured velocity data.
[0047] FIG. 1 shows a stationary stand flow meter 110 for bench
testing, calibration, and setup of the optimal characteristics of
a diesel or gasoline electronic fuel injection system. For testing
purposes, the fuel injection system includes a water-cooled fuel
tank 111 with a capacity of ten to twenty liters, a low-pressure
pump 112 with fuel filters, and a high pressure pump 114 for delivering
the fuel at a maximum pressure of about 7 MPa for testing gasoline
direct injection systems, or at a maximum of about 80.0 MPa for
testing diesel engines. A fuel injector 116 is installed into the
frame of a two-dimensional traversal stand and is directly connected
to the high-pressure pump fuel line 118. A motor-synchronized time
controller 120 provides a means for setting an injection frequency
of 0.5 to 60 Hz and an injection duration of 0.25 to a few milliseconds
with an encoding signal of 360 bin/cycle, which may be doubled or
tripled at the user's option to increase the resolution.
[0048] The LDA optical units include a laser source 122 mounted
on an optical bench 124 which transmits a beam through a beam splitter
126 which divides the beam into two beams. A pair of Bragg cells
128 or acoustical-optical modulators, introduce a fixed frequency
difference between the two beams so that the direction of the velocity
may be determined. The two beams are focused by lens 130 so that
they intersect in the plane of the velocity center line 132 (shown
in FIG. 2) of the fluid flow through measurement pipe 134 defining
a control measurement volume or zone which typically measures about
485 .mu.m in length and 46 .mu.m in diameter with a fringe space
of 2.4 .mu.m. The fuel does not need to be seeded. The high pressure
(greater than 5 MPa for gasoline FIS and greater than 80 MPa for
diesel FIS) causes cavitation to occur in the flow so that micrometer
and submicrometer gaseous bubbles appear and Mi-scattering of the
laser light occurs at the boundaries of the micro-bubbles. The scattered
light is collected through a pinhole by an elevated photodetector
136 situated to receive forward scatter. The scattered light contains
a Doppler shift, the Doppler frequency, which is proportional to
the velocity component of the fluid perpendicular to the bisector
of the two beams. The varying intensity of the light causes a varying
current which is fed to an interface board 138 which converts the
current to the velocity at the sampling rate selected by the user.
The velocity data is fed to a processor 140 which computes instantaneous
and/or integral volumetric flow rates, mass flow rates, pressure
gradients, and other data for calibrating the performance of the
fuel injector 116.
[0049] The measurement pipe 134 is described in more detail in
FIGS. 3 4 and 5. In FIGS. 3 and 4 fuel enters the measurement
pipe 134 on the right and flows through the pipe 134 to the left.
Referring to the right side of FIG. 4 the inlet unit 142 is made
from stainless steel and is a cylindrical body which receives a
cut end of the high pressure fuel pipeline 118 through which fuel
is transported to the injector 116. Disposed within the inlet unit
142 is a stainless steel cylindrical fitting 144 which is axially
aligned with a cylindrical nipple 146 integral with and extending
from a rectangular, stainless steel plug 148. Plug 148 forms a seal
at one end of a rectangular tube housing 150 made of Duron.TM. glass.
A cylindrical quartz tube 152 is disposed within housing 150 and
extends into the nipple 146 of plug 148. O-ring 154 forms a hermetic
seal between quartz tube 152 and fitting 144 and nipple 146 while
a second O-ring 156 forms a hermetic seal between nipple 146 and
inlet unit 142 preventing fuel leakage. A plurality of screws extend
through bores 158 in inlet unit 142 and are secured in threaded
bores 160 in rectangular plug 148. Referring to the left side of
FIG. 4 the outlet side of measurement pipe 134 is symmetrical and
identical in construction to the right side, except that outlet
unit 162 has a different internal geometry adapted for connection
to injector 116.
[0050] Fuel flows from the fuel pipeline 118 through inlet fitting
144 quartz tube 152 outlet fitting 144 and into injector 116.
Rectangular tube housing 150 is transparent, so that the beams from
laser source 122 pass through the wall of housing 150 to intersect
in the center line of quartz tube 152 the housing 150 serving to
protect the operator in case of sudden breakage of quartz tube 152.
Quartz tube 152 is cylindrical and preferably has a length between
200 and 350 mm, depending on injection pressure, and is between
3.0 and 3.5 mm in diameter. Scattered light passes out of quartz
tube 152 and through the planar opposite wall of housing 150 to
photodetector 136.
[0051] For a gasoline fuel injection system, operating at injection
pressures between about 5.0 and 7.0 MPa, the laser source 122 may
be a 16 mW He--Ne laser and the detector 136 may be a photomultiplier
tube. The interface board 138 may be a Dostek model 1400A Laser
Velocimeter Interface, made by Dostek, Inc. of Canada, or other
conventional LDA interface board. The processor 140 may be a an
IBM PC-compatible computer. For a gasoline FIS, the processor 140
may be programmed to resolve instantaneous and/or integral volumetric
and mass flow rates for one-dimensional pipe flow, as described
below with reference to FIGS. 16A and 16B.
[0052] Typical output from the software is shown in graphical form
in FIGS. 6A, 6B, and 6C. FIG. 6A shows the instantaneous center
line velocity, U.sub.0 versus the phase angle. In FIG. 6A, the
letter A marks opening of the fuel injector valve and the letter
D marks closure of the injector valve, with points B, C, and E marking
transitions at various phase angles. FIG. 6B shows the calculated
instantaneous volumetric flow rate, dV/dt, and integrated mass,
1 m ( t ) = 0 t V t t ,
[0053] versus the phase angle. FIG. 6C shows the pressure gradient
dp/dt versus the phase angle.
[0054] For a diesel fuel injection system, operating at injection
pressures between about 80.0 and 100.0 MPa, the components of the
stationary stand 110 need to be modified because of the very high
injection pressure and higher fuel flow velocity in the fuel transport
common rail (up to 32 m/s, instead of the 6 m/s in gasoline FIS),
and the very fast transitions in the flow. First, the laser source
122 must have more power than the He--Ne laser due to the extremely
decreased time of the scattering particles passing the LDA control
measurement volume at the intersection of the beams. Therefore,
for diesel FIS the laser source is preferably a diode pumped solid
state laser with-the emitting second harmonic wavelength of 532
nm (pumping by 808 nm) and power of 50 mW beam pre-collimated optics.
Although the detector 136 may be a photomultiplier tube, an avalanche
photodiode (at an elevation angle of 28.degree. instead of 30.degree.)
is used as the detector 136 as it is more sensible in the range
of 532 nm laser wave length, and it is more compact and flexible
to install.
[0055] Furthermore, in a diesel FIS, the temporal resolution is
very important for instantaneous flow rate measurements. In order
to measure turbulent fluctuations, it is necessary to have the measurement
time span .DELTA.t=T/N.sub.meas, where N.sub.meas=10000 bins per
injection stroke controlled by an electronic time generator or clock
pulse. The main criterion to select clock watch resolution is: 2
n 2 v n = v t ( 1 )
[0056] where .LAMBDA., an optic fringe span in the laser beam intersection
point, is dependent on laser wavelength .lambda. and a half intersection
angle .theta. determined from .LAMBDA.=.lambda./(2 sin .theta.).
In order to determine micron and submicron scattering particles,
.LAMBDA. fringe was fixed to be 1.3 .mu.m. For diesel injection
flow, .DELTA.t must be on the order of 1 .mu.s, i.e., the time generator
must provide a frequency higher than 1 MHz. Stable pulse generation
is also required, with frequency fluctuation not lower than 0.1%
from the base frequency. Therefore, for diesel FIS, the time controller
120 is not an external controller. Rather, the stationary stand
110 uses the quartz clock generator of the 32.768 series with a
base frequency of 9.2333 MHz, installed in the Electronic Control
Unit of existing diesel engines (this clock generator is used in
the Detroit Diesel ECU). The second harmonic at 4.617 MHz is used.
The measurement Fast Fourier Transform index is 10000 (10000 spans
or output bins per injection stroke) because the typical injection
period is varied from a few tens of milliseconds down to a few milliseconds.
[0057] Again, in a diesel FIS, the Dostek interface, as well as
other conventional LDA interface boards, provides unacceptable performance
as an interface board 138 since the Dostek 1400A uses a time/crank
angle reference only with a fixed injection period. For diesel systems,
it is necessary to have an interface board which provides flexibility
in changing the measurement time span at widely varied injection
periods or engine speeds. Therefore, a customized interface card
138 described below with respect to FIG. 15 is used for diesel FIS.
Finally, the software for resolution of instantaneous and/or integral
volumetric and mass flow rates for one-dimensional pipe flow, as
described below with reference to FIGS. 16A and 16B, proves to be
inadequate for accurately resolving instantaneous rates at the higher
pressures and velocities in a diesel system. Therefore, the processor
140 is programmed with improved software for resolution of instantaneous
and/or integral volumetric and mass flow rates for three-dimensional
turbulent pipe flow, as described with reference to FIGS. 17A and
17B.
[0058] FIG. 7 shows the optical components of a portable flow meter
170 which are integrated into a single compact box 172 measuring
about 110.times.80.times.20 mm. A quartz measurement tube 174 having
an internal diameter between about 3.0 to 3.5 mm is encased in a
protective sheathe and passes axially through the center of the
box 172. In use, the measurement tube 174 in inserted into the vehicle
fuel pipeline between the fuel tank, or fuel pump, and the injector
116. Mounted within the box 172 is a laser diode 176 which emits
a laser beam 178 through a collimating lens 180 to a prism 182
which redirects the beam 178 in a direction normal to the axis of
the tube 174. The beam 178 passes through a holographic splitter
184 shown in FIG. 8 which splits the beam into two beams focused
to intersect in a control measurement volume 192 in the center line
of the tube 172. Light is scattered by micro-bubbles in the fuel,
and focused by lens 186 through a pinhole mask on PIN diode 188
which is mounted on pre-amplifier board 190. The output from the
pre-amplifier board 190 may then be routed to an interface board
138 and processor 140 as described above. Triggering of clock pulses
may be accomplished through an external controller 120 for gasoline
FIS, or through a custom controller for diesel FIS for the reasons
described above.
[0059] FIGS. 9 through 14 show an on-board fuel flow meter sensor
200 which may be installed as original equipment or as an after-market
modification in a-motor vehicle. Referring to FIG. 9 the on-board
flow meter 200 includes a cylindrical quartz measurement tube 202
about 300 to 350 mm in length and between 3.0 and 3.5 mm in diameter
which is encased in a steel sheathe 204 and inserted in the fuel
pipeline between the fuel tank, or fuel pump, and the fuel injector.
The laser-Doppler anemometer (LDA) optical components include a
laser diode 206 (832 nm, 18 mW) to emit the laser beam and a PIN
diode detector 208 which are mounted in protective casings 210 in
openings defined in the steel sheathe 204 on opposite sides of the
measurement tube 202. The laser diode 206 and PIN diode 208 are
electrically connected to interface board 212. The interface board
212 may be a separate component electrically connected to the Electronic
Control Unit (ECO) 214 or may be made integral with the ECU 214.
The ECU 214 includes a processor either integral with the ECU 214
or connected to the ECU 214 which is programmed to compute volumetric
and/or mass flow rates and other data which the ECU 214 uses in
connection with other sensor data input (load as determined by engine
rpm, emissions data, etc.) to determine the optimal injection timing
and pulse duration.
[0060] As shown in FIGS. 10 and 11 disposed in the opening defined
in the steel sheathe 204 are two thin cylindrical rings 216 and
218 respectively, which encircle the quartz measurement tube 202
and are separated by a gap of between 150 and 180 .mu.m in order
to restrict emission of the laser beam(s) 220 to a narrow plane
or laser sheet about 150 .mu.m thick. The laser diode 206 is positioned
to direct the beam(s) 220 normal to the longitudinal axis of the
measurement tube 202 and across a diameter of the tube 202. The
PIN diode 208 detector is not positioned exactly 1800 opposite the
laser diode 206 but is radially offset from the diameter by an
angle .theta. of about 18.degree. to detect scatter from the intersection
of the split beam 220 in the control measurement zone 222 in the
center line 224 of the measurement tube 202.
[0061] As shown diagrammatically in FIG. 12 the laser diode 206
has an emitting semiconductor layer in a generally rectangular Fabry-Perot
cavity which presents a crystal emitting stripe 226 of about 1.5
.mu.m that emits a highly divergent beam in an elliptical cone which
may be considered in an XYZ coordinate system, with the X direction
indication lateral deflection, the Y direction indicating vertical
deflection, and the Z direction indicating translational distance
from the diode 206.
[0062] In order to collimate and split the beam 220 a divergence
mask 228 shown in FIG. 13 is used. The mask includes a rectangular
X-Y traverse frame 230 on which an optic fiber or wire 232 having
a diameter of about 10 .mu.m is mounted. The frame 230 is mounted
so that the optic fiber 232 is positioned about 1.6 to 1.7 times
the diameter of the fiber from the diode and extends parallel to
the crystal emitting stripe 226 normal to the beam 220. This geometry
results in an excellent splitting of the beam in a number of "prism-like
or pin-gap like" orders, symmetrically discharged in the Y
plane, indicated by the Y arrows in FIG. 13 from which the minus
and plus first order beams are selected for the LDA measurement.
The geometry also results in beams 220 which are well collimated
in the X plane, indicated by the X arrows in FIG. 13 which is important
to conserve laser light energy. In order to make precise adjustments,
the X-Y frame 230 is mounted on the emitting substrate 206 in such
manner as to permit the optic fiber 232 to move linearly and rotate
slightly in the X-Y plane. Also mounted on the frame 230 is a three-wire
guitar 234a, 234b, and 234c with a highly back-reflecting surface
to block direct propagation of the zero order and plus/minus second
orders of the split beam 220. The divergence mask 228 focuses the
split beam 220 to intersect in the control measurement zone 222
on the center line 224 of the measurement tube 202. Only light propagated
in the Z plane reaches the detector 208 optics.
[0063] A similar mask 236 shown in FIG. 14 is used in front of
the PIN diode detector 208. The mask 236 also has an X-Y traverse
frame 240 on which an optic fiber 238 of 18 .mu.m diameter is mounted
as described above. The frame 240 is mounted on the PIN diode substrate
208 so that the optic fiber 238 is positioned at a distance of about
2.1 times the diameter of the optic fiber 238 from the PIN diode
208 surface. Also mounted on the frame 240 between the PIN diode
208 and the optic fiber 238 is an aluminum plate 242 with a pinhole
244 about 50 .mu.m in diameter defined therein to focus the scattered
laser beam 220 on the PIN diode 208.
[0064] FIG. 15 shows a block diagram of an interface board 212
for use with the on-board flow meter sensor 200 and with the stationary
stand 110 or portable flow meter 170 when the stationary stand 110
or portable flow meter 170 are used to test diesel FIS. The interface
board 212 includes a power supply bus 250 which receives power from
the ECU 214 for supplying power to the various circuits and components
on the interface board 212 as well as power for the laser diode
206 and pin diode 208 in the on-board sensor 200. The interface
board 212 includes various temperature controller circuitry 252
for receiving temperature sensor data from the laser diode 206 and
PIN diode 208 and for controlling the temperature of the laser
diode 206 and PIN diode 208 by controlling the current. The raw
analog LDA sensor input is applied from the PIN diode 208 in succession
to a pre-amplifier circuit 254 a bandpass filter 256 for screening
out noise frequencies, an amplifier with adjustable gain 258 an
analog to digital (A/D) converter 260 and a 24-bit parallel digital
input circuit 262 to format the input for a 24-bit timer/angle counter
264 which receives clock and reset pulses from the ECU 214. The
counter's 264 output is transferred to a first-in first-out (FIFO)
buffer 266 and then to a processor data ready trigger 268 which
serves as a register for transferring the velocity data U(t) to
a processor 270 via the ECU 214. The individual circuits and components
comprising the interface board 212 are conventional, and will not
be described further.
[0065] The processor 270 may be a separate board, or it may be
made integral with the ECU 214. The processor 270 includes a host
instantaneous flow rate meter processor 272 which receives the velocity
data U(t) as well as other input parameters (injection fluid temperature
T(t) and pressure P(t), angular velocity (.omega.) and injection
duration .tau.(t)) and calls the software program encoded on a custom
integrated circuit processor 274 which calculates instantaneous
volumetric flow rates, mass rates, and other sensor data which are
input to the ECU 214 via the host processor 272 as data for calculating
the optimal fuel injection timing and pulse duration.
[0066] Whether the instantaneous center line velocity, U(t) data,
is measured with the stationary stand 110 the portable flow meter
170 or the on-board sensor 200 the velocity data is input to the
processor 140 or 274 for processing by software which implements
solutions to the Navier-Stokes equations to compute instantaneous
volumetric flow rates, mass rates, etc. For a gasoline fuel injection
system, the software may implement a solution for one dimensional
laminar flow for any periodically oscillating flow.
[0067] According to this method, the instantaneous volumetric flow
rate V(t) is expressed as: 3 V ( t ) = R 2 2 ( R 2 p 0 4 v + n =
1 .infin. { p n n n t [ 4 1 / 2 J 1 ( 3 / 2 Ta n ) Ta n J 0 ( 3
/ 2 Ta n ) - 2 ] + C . C . } ) ( 2 )
[0068] where R is the radius of the measurement tube, .nu. is the
kinematic viscosity of the fluid, p.sub.0 and p.sub.n are harmonic
coefficients, .omega. is the angular frequency, t is the time, i={square
root}{square root over (-1)}, Ta.sub.n is the nth Taylor number
4 Ta n = R n v ,
[0069] and C.C. is the complex conjugate. J.sub.0 and J.sub.1 are,
of course, zero order and first order Bessel functions. The theoretical
center line velocity is expressed as: 5 U ( r 0 t ) = R 2 p 0
4 v + n = 1 .infin. { p n n n t [ 1 J 0 ( 3 / 2 Ta n ) - 1 ] + C
. C . } ( 3 )
[0070] On the other hand, the measured time series of center line
velocities from the LDA measurements in N.sub.exp output bins within
the period of an injection cycle can be transformed into the Fourier
expansion: 6 U ( r 0 t ) = c 0 2 + n = 1 N exp ( c n n t + C .
C . ) ( 4 )
[0071] The harmonic coefficients p.sub.0 and p.sub.n can be determined
from equations (3) and (4) as follows: 7 p 0 = 2 c 0 v R 2 and p
n = c n n 1 - 1 J 0 ( 3 / 2 Ta n ) ( 5 )
[0072] The derivation of equations (2) through (5) is explained
in Durst et al., supra, except that the equation for p.sub.n is
incorrect in Durst (p. 180 equation 12) due to an algebraic error.
[0073] FIGS. 16A and 16B show an exemplary flow chart for a software
program for implementing equations (2) through (5). When the processor
140 is a personal computer, the software may be written in any high
level language, although Fortran is preferred due to its built in
support for complex number arithmetic. When the processor is a custom
integrated circuit, the software instructions may be encoded in
ROM or an EPROM in assembly language, or in dedicated circuitry.
[0074] As shown in FIGS. 16A and 16B, certain basic parameters
are read 300 or input to the processor, or hard coded into ROM,
such as the injection period T0 kinematic viscosity .nu., fluid
density .rho., radius of the pipe R, injection duration .tau., etc.
In the next step 302 certain constant parameters can be computed,
such as frequency f=1/T0 and angular frequency .omega.=2.pi.f, etc.
In step 304 the LDA velocities are input to the processor 140 or
274 either directly or via the ECU 214. In step 306 the raw LDA
velocities u(n) are used to compute the harmonic coefficients c.sub.0
and c.sub.n by an inverse discrete Fourier transform (IDFT) of equation
(4), i.e., 8 c ( m ) = 2 N n = 0 N - 1 u ( n ) m2 n / N ( 6 )
[0075] where m=0 . . . , N/2 output bins and N is the number of
LDA measurements per injection cycle. Only the first M=N/2 output
bins are used due to symmetry and due to the fact that the input
values are real. In equation (6) the factor 2/N is a scaling factor
to correct the amplitude. In step 308 a forward discrete Fourier
transform DFT: 9 U ( n ) = c 0 2 + m - 1 M = N / 2 c ( m ) - m2
n / N ( 7 )
[0076] where n=0 . . . ,N is used to calculate the velocity series
according to equation 4. In step 310 the values of p.sub.0 and
p.sub.n are determined using equation (5) and the values of c.sub.0
. . . c.sub.n previously calculated in step 306. In step 312 the
instantaneous volumetric flow rate V(t) is calculated using equation
(2) and the values of p.sub.0 . . . , p.sub.n previously calculated
in step 310.
[0077] In step 314 the integrated volumetric flow rate is obtained
by summing the instantaneous volumetric flow rates and dividing
the sum by the number of samples N. In step 316 the integrated mass
flow rate is obtained by multiplying the integrated volumetric flow
rate by the density .rho., and the mean mass flow rate is obtained
by multiplying the first term of the Fourier volumetric flow rate
series V(t) by the density .rho.. Optionally, at step 318 the instantaneous-pressure
gradient series may be obtained by solving: 10 P z = - [ p 0 + n
= 1 .infin. ( p n n t + C . C . ] ( 8 )
[0078] which is the time series P_Z(ln) where 11 P_Z ( ln ) = -
[ p 0 + j = 1 N / 2 p ( j ) j 2 ln / N ] ( 9 )
[0079] At step 320 the program outputs the computed values, either
to a display device, or to the ECU 214.
[0080] The effectiveness of the solution for one-dimensional laminar
flow for any periodically oscillating flow is limited by the Reynolds
number Re.sub..delta..ltoreq.700 where the Stokes layer thickness
.delta.={square root}{square root over (2.nu./.omega.)} limits application
of the method. The effect of this limitation is that the software
solution described in FIGS. 16A and 16B is limited to gasoline direct
injection engines, which have a lower injection pressure than diesel
fuel injection systems.
[0081] In order to obtain accurate flow meter calculations of the
volumetric flow rate in diesel fuel injection systems, a more exact
solution of the Navier-Stokes equations for turbulent flow in a
circular pipeline is required. The z-momentum and r-momentum Navier-Stokes
equations are: 12 ( u ~ ) t + z ( u ~ u ~ ) + 1 r r ( r v ~ u ~
) = - p ~ z + z ( u ~ z ) + 1 r r ( r u ~ r ) ( 10 ) ( v ~ ) t +
z ( u ~ v ~ ) + 1 r r ( r v ~ v ~ ) = - p ~ z + z ( v ~ z ) + 1
r r ( r u ~ r ) - v ~ r 2 ( 11 )
[0082] respectively, where the tilde overscore denotes the sum
of mean and fluctuation parts of the Reynolds decomposition, so
that {tilde over (p)}=P+p', =U+u' and {tilde over (v)}=V+v'. In
high pressure fuel injection pipe flow, the radial partial derivatives
are two or three orders of magnitude less than the axial partial
derivatives. Therefore, equations (10) and (11) can be simplified
to: 13 ( u ~ ) t + z ( u ~ u ~ ) = - p ~ z + z ( u ~ z ) + 1 r r
( r u ~ r ) ( 12 ) ( v ~ ) t + z ( u ~ v ~ ) = - p ~ r ( 13 )
[0083] respectively.
[0084] The velocity components may be decomposed to the mean velocity
W=W.sub.st+W.sub.osc, where W.sub.st is a stationary portion of
velocity and W.sub.osc is an oscillating portion of velocity, and
the fluctuating velocity W', so that:
=U+u'=U.sub.st+U.sub.osc+u' and {tilde over (v)}=V.sub.st+V.sub.osc+v'
(14)
[0085] With respect to the pressure, three parts (stationary, oscillating,
and fluctuating) are also superposed, so that: 14 P z = - ( P )
( p o z + n = 1 .infin. ( p lz + p iz ' ) n t + C . C . pz ) ( 15
)
[0086] where p.sub.oz is the stationary portion of pressure, p.sub.lz
is the oscillating portion, and p' is the fluctuating portion. The
fluid density is a linear compressible term, iterated at each i-step
calculation: 15 ( P ) = ( P 0 ) + n = 1 i P P ( 16 )
[0087] Using equations (14) and (15), the z-momentum and r-momentum
equations (12) and (13) can be rewritten as a system of transport
equations, so that the z-momentum is expressed by: 16 ( U ) t =
( P ) ( p o z + n = 1 .infin. p lz n t + C . C . pz ) + 1 r r (
r U r ) ( 17 ) ( u ' ) t + z ( u 2 ) = ( P ) ( n = 1 .infin. p iz
' n t + C . C . pz ) + z ( u ' z ) + 1 r r ( r u ' r ) ( 18 )
[0088] and the r-momentum is expressed by: 17 ( V ) t = ( P ) (
p or + n = 1 .infin. p lr n t + C . C . pr ) ( 19 ) ( v ' ) t +
z ( u ' v ' ) = ( P ) ( n = 1 .infin. p ir ' n t + C . C . pr )
( 20 )
[0089] Equations (17) and (19) may then be integrated in conventional
fashion. With respect to equations (18) and (20), the Reynolds scale
in high-pressure injection oscillating capillary flow is the Stokes
layer thickness 18 = 2 v .
[0090] The measurement time span .DELTA.t is on the order of .about.10.sup.-6
s and diesel fuel has a viscosity of about 2 to 4.5.times.10.sup.-6
m.sup.2/s. With respect to such high temporal resolution, the critical
space 19 = v t
[0091] for detection of the flow fluctuation becomes an order of
magnitude of 10.sup.-6 m, which is comparable with the optic interference
fringe span .nu.. Within such a very short time interval, the fluctuation
of the velocity may be considered "frozen", as well as
the liquid density. With these simplifications and manipulation
with transfer functions, equations (18) and (20) may be further
simplified and combined with the integration of equations (17) and
(19) to produce the full solution for the velocity components, with
the z-momentum expressed as: 20 u ~ = R 2 p 0 z 4 v ( 1 - r 2 R
2 ) + n = 1 .infin. ( p nz - p nz ' 2 n n t ( J 0 ( 3 / 2 Ta n r
R ) J 0 ( 3 / 2 Ta n ) - 1 ) + C . C . U ) ( 21 )
[0092] and the r-momentum expressed as: 21 v ~ = R 2 p 0 r 4 v
( 1 - r 2 R 2 ) + n = 1 .infin. ( p nr - p nr ' 2 n n t ( J 0 (
3 / 2 Ta n r R ) J 0 ( 3 / 2 Ta n ) - 1 ) + C . C . U ) ( 22 )
[0093] In order to obtain the instantaneous volumetric flow rate
over a pipe cross section in the direction of the pipe axis, it
is necessary to integrate the velocity component and turbulent velocity
correlation {square root}{square root over (u'v')} projected on
the same pipe axis as follows: 22 V . ( t ) = 2 0 R u ~ + u ' v
' _ r r = R 2 2 [ p 0 R 2 4 v + n = 1 .infin. ( p nz - p nz ' 2
+ p nz ' p nr ' 2 n n t { 4 1 / 2 J 1 ( 3 / 2 Ta n Ta n J 0 ( 3
/ 2 Ta n ) - 2 } ) + C . C . ] ( 23 )
[0094] This flow rate reflects an effective axial velocity composing
four terms, i.e., a stationary part associated with p.sub.oz, an
oscillatory part associated with p.sub.nz, a u-pulsation part associated
with p'.sub.nz, and a uv-pulsation part associated with p.sub.nzp.sub.nr:
23 u ~ ef = [ R 2 p o z 4 v ( 1 - r 2 R 2 ) + n = 1 .infin. ( p
nz - p nz ' 2 + p nz ' p nr ' 2 n n t { J 0 ( 3 / 2 Ta n r R ) J
0 ( 3 / 2 Ta n ) ( 24 )
[0095] When this velocity is measured on the centerline, r=0 equation
24 reduces to: 24 u ~ ef = R 2 p o z 4 v + n = 1 .infin. ( p nz
- p nz ' 2 + p nz ' p nr ' 2 n n t { 1 J 0 ( 3 / 2 Ta n ) - 1 }
) ( 25 )
[0096] The experimentally measured center line velocity time series
may be expressed as the Fourier expansion: 25 U LDA ( t ) = U st
+ U osc ( t ) + U puls ( t ) = c 0 2 + n = 1 N c n ( n t ) + c n
' ( n t ) ( 26 )
[0097] where switching in the Fourier expansion is dependent on
the following criteria: 26 n [ 1 N ] if n 2 v n > 10 n [ N
+ 1 N meas ] if n 2 v n 10 ( 27 )
[0098] Comparing equations (23) and (24) gives final expression
for the pressure gradient series, which are needed to compute the
instantaneous volumetric flow rate as expressed by equation (23):
27 p o z = 2 c o v R 2 p nz = c n n [ 1 - 1 J 0 ( 3 / 2 Ta n ) ]
, n [ 1 N ] p nz ' + p nz ' p nr ' = 2 c n ' n [ 1 - 1 J 0 ( 3
/ 2 Ta n ) ] , n [ N + 1 N meas ] ( 28 )
[0099] FIGS. 17A and 17B show an exemplary flow chart for a software
program for implementing equations (10) through (28). When the processor
140 is a personal computer, the software may be written in any high
level language, although Fortran is preferred due to its built in
support for complex number arithmetic. When the processor is a custom
integrated circuit, the software instructions may be encoded in
ROM or an EPROM in assembly language, or in dedicated circuitry.
[0100] As shown in FIGS. 17A and 17B, certain basic parameters
are read 400 or input to the processor, or hard coded into ROM,
such as the injection period T0 kinematic viscosity .nu. tables
where viscosity is a function of temperature, fluid density .rho.
tables where density is a function of pressure, radius of the pipe
R, injection duration .tau., etc. In the next step 402 certain
constant parameters can be computed, such as frequency f=1/T0 and
angular frequency .omega.=2.pi.f, Stokes layer thickness .delta.,
etc. In step 404 the LDA velocities are input to the processor
140 or 274 either directly or via the ECU 214. For diesel or high
pressure fuel injection systems, the number of velocities measured
per cycle, N.sub.meas, is preferably 10000. In step 406 the fluid
density series is calculated using equation (16). In step 408 the
raw LDA velocities u(n) are used to compute the harmonic coefficients
c.sub.0 . . . , c.sub.n, and c.sub.0', . . . , c.sub.n' by an inverse
discrete Fourier transform (IDFT) of equation (26) analogous to
that shown in equation (6), supra, the only difference being that
each crank angle n is tested according to equations (27) to determine
whether c.sub.n or c.sub.n' is incremented. In step 410 a forward
discrete Fourier transform DFT, analogous to equation (7), is used
to calculate the velocity series according to equation (25). In
step 412 the values of p.sub.0 p.sub.n, and p.sub.n' are determined
using equation (28) and the values of c.sub.0 . . . c.sub.n and
c.sub.0', . . . , c.sub.n' calculated in step 408. In step 414
the instantaneous volumetric flow rate V(t) is calculated using
equation (23) and the values of P.sub.0 . . . , p.sub.n and p.sub.0',
. . . , p.sub.n' calculated in step 412.
[0101] In step 416 the integrated volumetric flow rate is obtained
by summing the instantaneous volumetric flow rates and dividing
the sum by the number of samples N. During calculation of the integrated
volumetric flow rate, the injected fuel mass in the present cycle,
m.sub.j, can be obtained from: 28 m j = 0 t V . ( t ) = T N meas
- 1 n = 1 n i n V . n n ( 29 )
[0102] In step 418 the integrated mass flow rate is obtained by
multiplying the integrated volumetric flow rate by the density .rho.,
and the mean mass flow rate is obtained by multiplying the first
term of the Fourier volumetric flow rate series V(t) by the density
.rho.. Optionally, at step 420 the optimal fuel injection rate
may be computed given other sensor input provided to the ECU 214
regarding the load, emissions, etc. At step 422 the optimal flow
rate is compared to the actual mass flow rate computed in step 416
for example, by 29 = m j + m j - 1 2 m op ( 30 )
[0103] In step 424 the ECU 214 may adjust such injection parameters
as injection pulse duration, period between injection pulses, injector
pressure, etc. in order to bring the actual flow rate into agreement
with the optimal flow rate.
[0104] Referring to FIGS. 18A and 18B, it will be seen that the
solution described for a periodically oscillating, turbulent flow
in a pipeline of circular cross section with regard to FIGS. 17A
and 17B provides more accurate results for high pressure diesel
fuel injection systems than the solution for one-dimensional laminar
flow described with respect to FIGS. 16A and 16B.
[0105] In order to test the relative merits of the two methods,
a test was run using n-heptane having a density of 684 kg/m.sup.3
and a kinematic viscosity of 6.1.times.10.sup.-7 m.sup.2/s. A high
pressure injection system was run at pressures ranging from 0.5
to 7.0 MPa. Mass balance measurements were obtained within 60 s
within a range of a few tenths of a gram to a few hundredths of
a gram. The relationship between injection pressure and mean flow
rate, measured by mass balance, is shown for injection periods of
0.5 ms, 1.0 ms, 2.0 ms, 4.0 ms, and open valve (steady flow) in
FIG. 18A Results of the measurements by mass balance, the software
method (LDA 1) of FIGS. 16A and 16B, and the software method (LDA
2) of FIGS. 17A and 17B are shown in FIG. 18B.
[0106] As shown in FIG. 18B, the laminar model LDA 1 has an accuracy,
calculated by 30 = V . LDA - m . mass balance m . mass balance (
31 )
[0107] within .+-.2% when Re<2300 and flow rate is lower than
2 g/s. At increased injection pressures (or velocities, so that
Re>3000)., the method is limited and has an accuracy decreased
by -24% because the velocity field does not reflect the turbulent
fluctuation and therefore gives a lower velocity field than is actually
developed in the flow. On the other hand, the turbulent model (LDA
2.) demonstrates excellent correlation with mass balance measurement
within a range of -1.4 to 2.0%. The turbulent model (LDA 2) is therefore
preferred with the high injection pressures and velocities encountered
in diesel fuel injection systems, and may be used with either diesel
or gasoline fuel injection systems. The laminar model (LDA 1) may,
however, be used with reasonably acceptable performance, particularly
with gasoline fuel injection systems, for reasons of economy.
[0108] It is to be understood that the present invention is not
limited to the embodiments described above, but encompasses any
and all embodiments within the scope of the following claims. It
will be noted, for example, that although the software methods are
described using discrete Fourier transforms to calculate instantaneous
flow rates, that a fast Fourier transform (FFT) technique may be
used, such as the radix-2 technique in which the number of samples
is an integral power of 2 and the samples are padded with zeroes,
in order to take advantage of the increased calculation speeds resulting
from symmetry, or other FFT techniques known in the digital signal
processing art may be used.
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