## 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 What is claimed is:
1. A flow meter comprising: a measurement tube installed in a fuel
supply conduit, wherein the fuel supply conduit supplies fuel to
at least one fuel injector in a fuel injection system; a laser-Doppler
anemometer generating a pair of laser beams intersecting in a control
measurement volume in a center line of fuel flow through the measurement
tube; a velocity calculating mechanism connected to the laser-Doppler
anemometer for calculating a series of instantaneous center line
velocities of fuel flow through the measurement tube; and a flow
rate calculating mechanism connected to the velocity calculating
mechanism for calculating a series of instantaneous volumetric flow
rates in the measurement tube and for calculating a mass flow rate
by integrating the series of instantaneous volumetric flow rates.
2. The flow meter of claim 1 wherein the flow meter is an on-board
flow meter which is installed in a vehicle.
3. The flow meter of claim 2 wherein the vehicle includes an electronic
engine control mechanism and at least one of: (a) the volumetric
flow rates; and (b) the mass flow rate are supplied to the electronic
engine control mechanism.
4. The flow meter of claim 3 wherein the electronic engine control
mechanism uses at least one of: (a) the volumetric flow rates; and
(b) the mass flow rate to adjust at least one fuel injection parameter
associated with the fuel injection system.
5. The flow meter of claim 2 wherein the vehicle includes a fuel
tank and the fuel supply conduit in which the measurement tube is
installed carries fuel from the fuel tank.
6. The flow meter of claim 2 wherein the vehicle includes a fuel
pump and the fuel supply conduit in which the measurement tube is
installed carries fuel from the fuel pump.
7. The flow meter of claim 1 wherein the measurement tube is constructed
at least in part from quartz glass.
8. The flow meter of claim 7 wherein the quartz glass is substantially
transparent.
9. The flow meter of claim 8 wherein the quartz glass is in the
form of an elongated tube.
10. The flow meter of claim 9 further comprising a protective
sheathe around at least a portion of the quartz glass.
11. The flow meter of claim 10 wherein the protective sheathe
is formed from steel.
12. The flow meter of claim 1 wherein the laser-Doppler anemometer
comprises a laser light source and a photodetector.
13. The flow meter of claim 12 wherein the laser light source
comprises a laser diode and the photodetector comprises a PIN diode.
14. The flow meter of claim 1 wherein the laser-Doppler anemometer
comprises: (a) a laser diode; (b) a beam splitting mechanism for
splitting a laser beam emitted by the laser diode into two laser
beams focused to intersect in the control measurement volume in
the center line of the measurement tube; and (c) a PIN diode for
receiving light scattered by fuel flowing in the control measurement
volume of the measurement tube.
15. The flow meter of claim 14 wherein each of the two laser beams
is directed into the measurement tube at an angle which is substantially
normal to the flow of fuel through the measurement tube.
16. The flow meter of claim 15 wherein: (a) the cross-section
of the measurement tube is substantially circular; (b) the two laser
beams are directed into the measurement tube at a first location
on the cross-section; and (c) the PIN diode is disposed to receive
light scattered by fuel flowing in the control measurement volume
from a second location on the cross-section.
17. The flow meter of claim 16 wherein the second location on
the cross-section is substantially 180 degrees from the first location
on the cross-section in both a clockwise and counter-clockwise direction.
18. The flow meter of claim 16 wherein the second location on
the cross-section is greater than 180 degrees from the first location
on the cross-section in one of a clockwise and a counter-clockwise
direction and the second location on the cross-section is less than
180 degrees from the first location on the cross-section in one
of a clockwise and counterclockwise direction.
19. The flow meter of claim 14 further comprising a focusing mechanism
for focusing scattered light from the control measurement volume
on the PIN diode.
20. The flow meter of claim 1 wherein the flow rate calculating
mechanism includes means for: (a) performing an inverse Fourier
transform to calculate a series of harmonic coefficients c.sub.0
. . . , c.sub.n from the series of instantaneous center line velocities;
(b) computing 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 ##EQU31## (c) computing a series of instantaneous
volumetric flow rates from the pressure coefficients P.sub.0 .
. . , P.sub.n, by solving the equation ##EQU32## (d) computing a
mass flow rate by integrating the volumetric flow rates using the
fluid density and cross sectional area of the measurement tube.
21. The flow meter of claim 1 wherein the flow rate calculating
mechanism includes means for: (a) performing 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 instantaneous 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; (b) 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
##EQU33## (c) 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 ##EQU34## (d)
computing a mass flow rate by integrating the volumetric flow rates
using the fluid density and cross sectional area of the measurement
tube.
22. The flow meter of claim 1 wherein the flow rate calculating
mechanism includes means for: (a) performing an inverse Fourier
transform on the series of instantaneous center line 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; (b) 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 ##EQU35## (c) 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
##EQU36##
23. The flow meter of claim 1 wherein at least one of the velocity
calculating mechanism and the flow rate calculating mechanism includes
software.
## Description BACKGROUND OF THE INVENTION
1. Field of the Invention
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.
2. Description of the Related Art
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
FIG. 1 is a diagrammatic view of a stationary stand flow meter
according to the present invention.
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.
FIG. 3 is a plan view of a capillary measurement pipe according
to the present invention for insertion into a pipeline.
FIG. 4 is a section view along the lines 4--4 of FIG. 3.
FIG. 5 is an end view of the capillary measurement pipe according
to the present invention.
FIGS. 6A, 6B, and 6C are charts showing typical output from a flow
meter according to the present invention in graphic form.
FIG. 7 is a diagrammatic section view of the optical system for
a portable flow meter according to the present invention.
FIG. 8 is a detail view of a holographic beam splitter used in
a flow meter according to the present invention.
FIG. 9 is a diagrammatic view of an on-board flow meter sensor
according to the present invention.
FIG. 10 is a detail view of the on-board flow meter sensor of FIG.
9.
FIG. 11 is a section view along lines 11--11 of FIG. 10.
FIG. 12 is a diagrammatic perspective view of the elliptical cone
shaped laser beam emitted by the laser diode.
FIG. 13 is a view of a divergence mask used for the transmitting
laser diode of FIG. 9.
FIG. 14 is a view of a mask used for the PIN diode detector of
FIG. 9.
FIG. 15 is a block diagram of a custom interface board for use
of the flow meter sensors with diesel FIS.
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.
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.
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.
Similar reference characters denote corresponding features consistently
throughout the attached drawings.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
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.
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.
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.
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 2.41 .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.
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.
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.
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.
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, ##EQU1##
versus the phase angle. FIG. 6C shows the pressure gradient dp/dt
versus the phase angle.
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.
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: ##EQU2##
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.
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.
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.
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.
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 180.degree. 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.
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.
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.
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.
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.
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.
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.
According to this method, the instantaneous volumetric flow rate
V(t) is expressed as: ##EQU3##
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=v-1 Ta.sub.n
is the nth Taylor number ##EQU4##
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: ##EQU5##
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:
##EQU6##
The harmonic coefficients p.sub.0 and p.sub.n can be determined
from equations (3) and (4) as follows: ##EQU7##
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.
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.
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.,
##EQU8##
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:
##EQU9##
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.
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: ##EQU10##
which is the time series P_Z(ln) where ##EQU11##
At step 320 the program outputs the computed values, either to
a display device, or to the ECU 214.
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.=v2.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.
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: ##EQU12##
respectively, where the tilde overscore denotes the sum of mean
and fluctuation parts of the Reynolds decomposition, so that p=P+p',
u=U+u', and 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: ##EQU13##
respectively.
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:
With respect to the pressure, three parts (stationary, oscillating,
and fluctuating) are also superposed, so that: ##EQU14##
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: ##EQU15##
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: ##EQU16##
and the r-momentum is expressed by: ##EQU17##
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 ##EQU18##
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 ##EQU19##
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 .LAMBDA.. 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: ##EQU20##
and the r-momentum expressed as: ##EQU21##
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 u velocity component and turbulent velocity correlation
v{square root over(u'v')} projected on the same pipe axis as follows:
##EQU22##
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.nz p.sub.nr
: ##EQU23##
When this velocity is measured on the centerline, r=0 equation
24 reduces to: ##EQU24##
The experimentally measured center line velocity time series may
be expressed as the Fourier expansion: ##EQU25##
where switching in the Fourier expansion is dependent on the following
criteria: ##EQU26##
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): ##EQU27##
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.
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.
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: ##EQU28##
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 ##EQU29##
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.
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.
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.
As shown in FIG. 18B, the laminar model LDA 1 has an accuracy,
calculated by ##EQU30##
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.
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. |