Abstrict Various embodiments of the present invention provide a flow meter
device having a laser Doppler anemometer (LDA) which measures the
instantaneous center line velocity of fluid flow in a pipe. The
flow meter may process the instantaneous velocity so obtained to
compute the volumetric flow rate, mass rate, and/or other flow characteristics
(e.g., as instantaneous quantities and/or integrated over a time
interval) The flow meter may use an electronic processing method.
The electronic processing method may provide essentially an exact
solution to the Navier-Stokes equations for any periodically oscillating
flow.
Claims What is claimed is:
1. A flow meter for bench testing fuel flow characteristics in
a fuel injection system, which fuel injection system includes at
least one fuel injector, comprising: a measurement tube via which
fuel flowing through the fuel injector passes; 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 measurement tube is constructed
at least in part from quartz glass.
3. The flow meter of claim 2 wherein the quartz glass is substantially
transparent.
4. The flow meter of claim 1 further comprising an optical bench,
wherein at least one of the measurement tube and the laser-Doppler
anemometer is mounted to the optical bench.
5. The flow meter of claim 1 wherein the laser-Doppler anemometer
comprises a laser light source and a photodetector.
6. The flow meter of claim 5 wherein the laser light source comprises
a helium-neon laser and the photodetector comprises a photomultiplier
tube.
7. The flow meter of claim 5 wherein the laser light source comprises
a laser diode and the photodetector comprises a PIN diode.
8. 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
F the equations ##EQU55## (c) computing a series of instantaneous
volumetric flow rates from the pressure coefficients P.sub.0 .
. . ,P.sub.n, by solving the equation ##EQU56## (d) computing a
mass flow rate by integrating the volumetric flow rates using the
fluid density and cross sectional area of the measurement tube.
9. 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
##EQU57## (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 ##EQU58## (d)
computing a mass flow rate by integrating the volumetric flow rates
using the fluid density and cross sectional area of the measurement
tube.
10. 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
##EQU59## (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 ##EQU60##
11. The flow meter of claim 1 further comprising a fuel tank and
a fuel injection pump.
12. The flow meter of claim 11 further comprising a controller
connected to the fuel pump for controlling the duration and frequency
of a plurality of fuel injection pulses.
13. The flow meter of claim 12 wherein the controller is capable
of nanosecond pulse duration.
14. The flow meter of claim 1 wherein at least one of the velocity
calculating mechanism and the flow rate calculating mechanism includes
software.
15. A flow meter for bench testing fuel flow characteristics in
a fuel injection system, which fuel injection system includes at
least one fuel injector, comprising: at least one of an input pipe
for supplying fuel to the fuel injector and an output pipe for receiving
fuel from the fuel injector; a measurement tube installed in one
of the input pipe and the output pipe; 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.
16. The flow meter of claim 15 wherein the measurement tube is
constructed at least in part from quartz glass.
17. The flow meter of claim 16 wherein the quartz glass is substantially
transparent.
18. The flow meter of claim 15 further comprising an optical bench,
wherein at least one of the measurement tube, the input pipe, the
output pipe and the laser-Doppler anemometer is mounted to the optical
bench.
19. The flow meter of claim 15 wherein the laser-Doppler anemometer
comprises a laser light source and a photodetector.
20. The flow meter of claim 19 wherein the laser light source
comprises a helium-neon laser and the photodetector comprises a
photomultiplier tube.
21. The flow meter of claim 19 wherein the laser light source
comprises a laser diode and the photodetector comprises a PIN diode.
22. The flow meter of claim 15 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.o, . . . ,p.sub.n
from the harmonic coefficients c.sub.0 . . . , c.sub.n by solving
the equations ##EQU61## (c) computing a series of instantaneous
volumetric flow rates from the pressure coefficients p.sub.0 .
. . ,p.sub.n, by solving the equation ##EQU62## (d) computing a
mass flow rate by integrating the volumetric flow rates using the
fluid density and cross sectional area of the measurement tube.
23. The flow meter of claim 15 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
##EQU63## (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 ##EQU64## (d)
computing a mass flow rate by integrating the volumetric flow rates
using the fluid density and cross sectional area of the measurement
tube.
24. The flow meter of claim 15 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
##EQU65## (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 ##EQU66##
25. The flow meter of claim 15 further comprising a fuel tank
and a fuel injection pump.
26. The flow meter of claim 25 further comprising a controller
connected to the fuel pump for controlling the duration and frequency
of a plurality of fuel injection pulses.
27. The flow meter of claim 26 wherein the controller is capable
of nanosecond pulse duration.
28. The flow meter of claim 15 wherein: (a) a cross-section of
the input pipe is selected from the group of circular, oval, square
and rectangular; (b) a cross-section of the output pipe is selected
from the group of circular, oval, square and rectangular; and (c)
a cross-section of the measurement tube is selected from the group
of circular, oval, square and rectangular.
29. The flow meter of claim 15 wherein: (a) the input pipe is
included; and (b) the measurement tube is installed in the input
pipe.
30. The flow meter of claim 29 wherein the output pipe is not
included.
31. The flow meter of claim 15 wherein: (a) the output pipe is
included; and (b) the measurement tube is installed in the output
pipe.
32. The flow meter of claim 31 wherein the input pipe is not included.
33. The flow meter of claim 31 further comprising a check valve
installed in the output pipe to control backpressure in the output
pipe.
34. The flow meter of claim 31 further comprising an orifice plate
installed in the output pipe to control pressure in the output pipe.
35. The flow meter of claim 31 further comprising: (a) a check
valve installed in the output pipe to control backpressure in the
output pipe; and (b) an orifice plate installed in the output pipe
to control pressure in the output pipe; wherein: (i) the output
pipe has a first end and a second end, which first end is connected
to the fuel injector; (ii) the check valve is installed at the second
end of the output pipe; and (iii) the orifice plate is installed
at a position in the output pipe between the check valve and the
measurement tube.
36. The flow meter of claim 35 further comprising a fuel injector
tip holder for connecting an output tip of the fuel injector to
the output pipe.
37. The flow meter of claim 36 further comprising a pressure transducer
disposed within the fuel injector tip holder.
38. The flow meter of claim 15 wherein at least one of the velocity
calculating mechanism and the flow rate calculating mechanism includes
software.
Description FIELD OF THE INVENTION
Various embodiments of the present invention relate to flow meters
(e.g., for measuring the flow of fluid through a conduit). In one
example (which example is intended to be illustrative and not restrictive)
the flow meters described may be adapted for measuring the volumetric
flow rate for a high pressure direct injection automotive fuel injection
system. Also described are software methods of determining the volumetric
flow rate for a periodic oscillating flow in a pipe from measurement
of the instantaneous center line velocity.
BACKGROUND OF THE INVENTION
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.
Various devices for measuring fluid flow characteristics, at various
points in the flow, have been described previously. For example:
U.S. Pat. No. 3338093 issued Aug. 29 1967 to J. D. Usry et
al. relates to an injectant stream analyzer for measuring the momentum
and solidity of fluid free streams from injection valves or the
like by causing a wire to transect the stream.
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 earns,
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. 4165635 issued Aug. 28 1979 to Komaroff et al.
relates to a method of testing fuel-injector spray nozzles in which
a laser beam is directed onto a light detector along a path passing
close to the spray orifice(s) of a fuel injector spray nozzle.
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. 4541272 issued Sep. 17 1985 to Bause relates
to an electronically controlled fuel injector system including an
electrically controllable injection valve disposed at a suction
pipe to supply fuel and an electro-optical spectrometer which analyses
the air-fuel mixture sucked in by the engine.
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; trapped
around the pipe to sense expansion of the pipe as fluid is pulsed
through the pipe.
U.S. Pat. No. 6049382 issued April 11 2000 to Lazaro Gomez
relates to an apparatus and procedure for characterization of sprays
composed by spherical particles, by means of a laser source generating
a collimated laser beam that is passed through the spray to be characterized.
German Patent No. DE3817096 published Dec. 8 1988 relates to
a method for testing injection valves and an apparatus for carrying
out the method. More particularly, a laser beam penetrating the
exit stream of an injection valve underneath its exit opening is
captured by a receiver to make a statement about the production
quality of the injection valve.
European Patent No. 489474 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.
French Patent No. FR2719871 published Nov. 17 1995 relates to
test equipment for fuel injectors of internal combustion engines.
More particularly, the characteristics of a jet of fuel are detected
by e.g., a CCD video camera with image processor, a laser granulometer
and a display.
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 violumetric 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 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) 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 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 July 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.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A and 1B are diagrammatic views of a stationary stand flow
meter according to two embodiments of 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 an embodiment of
the present invention;
FIG. 3 is a plan view of a capillary measurement pipe for insertion
into a pipeline according to an embodiment of the present invention;
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 an embodiment of the present invention;
FIGS. 6A, 6B, and 6C are charts showing typical output (in graphic
form) from a flow meter according to an embodiment of the present
invention;
FIG. 7 is a diagrammatic section view of the optical system for
a portable flow meter according to an embodiment of the present
invention;
FIG. 8 is a detail view of a holographic beam splitter used in
a flow meter according to an embodiment of the present invention;
FIG. 9 is a diagrammatic view of an on-board flow meter sensor
according to an embodiment of 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 according to an embodiment
of the present invention;
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 (e.g., for
use with a flow meter sensor associated with a diesel fuel injection
system ("FIS")) according to an embodiment of the present
invention;
FIGS. 16A and 16B show 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 an embodiment
of the present invention;
FIGS. 17A and 17B show a flow chart of a second electronic data
processing method for transforming center line velocity data into
volumetric and mass flow rates in a flow meter according to an embodiment
of the present invention;
FIGS. 18A and 18B are charts showing a comparison of test results
generated by the first electronic data processing method associated
with FIGS. 16A and 16B and the second electronic data processing
method associated with FIGS. 17A and 17B;
FIGS. 19A and 19B show parts for a flow meter according to an embodiment
of the present invention;
FIGS. 20A-20D are charts showing test results generated by a flow
meter according to an embodiment of the present invention; and
FIGS. 21A and 21B shown additional data relating to the test results
of FIGS. 20A-20D.
Among those benefits and improvements that have been disclosed,
other objects and advantages of this invention will become apparent
from the following description taken in conjunction with the accompanying
figures. The figures constitute a part of this specification and
include illustrative embodiments of the present invention and illustrate
various objects and features thereof (of note, similar reference
characters denote corresponding features consistently throughout
the attached drawings).
DETAILED DESCRIPTION OF THE INVENTION
Detailed embodiments of the present invention are disclosed herein;
however, it is to be understood that the disclosed embodiments are
merely illustrative of the invention that may be embodied in various
forms. In addition, each of the examples given in connection with
the various embodiments of the invention are intended to be illustrative,
and not restrictive. Further, the figures are not necessarily to
scale, some features may be exaggerated to show details of particular
components. Therefore, specific structural and functional details
disclosed herein are not to be interpreted as limiting, but merely
as a representative basis for teaching one skilled in the art to
variously employ the present invention.
In one embodiment an on-board flow meter for installation in a
fuel pipeline of a fuel injection engine is provided, 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 low rates to adjust fuel injection parameters in order
to optimize fuel flow in the engine.
In one example, said measurement tube may comprise: (a) an elongated,
transparent, quartz glass tube; and (b) a steel jacket, said quartz
tube being sheathed within said steel jacket.
In another example, said laser-Doppler anemometer may comprise:
(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.
In another example, said beam splitting means may comprise: (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; and (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.
In another example, said focusing means may comprise: (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.
In another example, said means for computing instantaneous and
integral volumetric and mass flow rates may comprise:
(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, 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.o, . . . , p.sub.n from the harmonic coefficients p.sub.o,
. . . , p.sub.n by solving the equations ##EQU1##
(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.o, . . . ,p.sub.n, by solving the equation ##EQU2##
(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.
In another example, said means for computing instantaneous and
integral volumetric and mass flow rates may comprise:
(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.o, . . . ,p.sub.n and p.sub.o
', . . . ,p.sub.n ' from the harmonic coefficients c.sub.o, . .
. , c.sub.n and c.sub.o ', . . . ,c.sub.n ' by solving the equations
##EQU3##
(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.o, . . . ,p.sub.n and p.sub.o ', . . . ,p.sub.n
', by solving the equation ##EQU4##
(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.
In another embodiment a flow meter for measuring fuel flow characteristics
in a fuel injection system is provided, 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.
In one example, the flow meter may further comprise: (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 may comprise: (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.
In another example: said laser light source may comprise a helium-neon
laser and said photodetector may comprise a photomultiplier tube.
In another example: said laser light source may comprise a laser
diode; and said photodetector may comprise a PIN diode.
In another example, the flow meter may further comprise an external
controller connected to said fuel pump for controlling the duration
and frequency of fuel injection pulses.
In another example, the flow meter may further comprise 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.
In another example, said measurement tube may comprise: (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.
In another example, said laser Doppler anemometer may comprise:
(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.
In another example, the flow meter may further comprise 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.
In another example: (a) said measurement tube may comprise: (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 may comprise: (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.
In another example, said means for computing instantaneous and
integral volumetric and mass flow rates may comprise:
(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
c.sub.0 ', . . . , c.sub.n ' from the harmonic coefficients c.sub.0
. . . , c.sub.n and c.sub.o ', . . . , c.sub.n ' by solving the
equations ##EQU5##
(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 ##EQU6##
(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.
In another example, said means for computing instantaneous and
integral volumetric and mass flow rates may comprise:
(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;
(a) 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
##EQU7##
(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 ##EQU8##
(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.
In another embodiment an electronic data processing method for
measuring volumetric flow rates and mass flow rates of a periodically
oscillating fluid flow in a pipeline is provided, 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 ##EQU9##
(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 ##EQU10##
In another embodiment a flow meter for bench testing fuel flow
characteristics in a fuel injection system, which fuel injection
system includes at least one fuel injector is provided, comprising:
a measurement tube via which fuel flowing through the fuel injector
passes; 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.
In one example, the measurement tube may be constructed at least
in part from quartz glass.
In another example, the quartz glass may be substantially transparent.
In another example, the flow meter may further comprise an optical
bench, wherein at least one of the measurement tube and the laser-Doppler
anemometer is mounted to the optical bench.
In another example, the laser-Doppler anemometer may comprise a
laser light source and a photodetector.
In another example, the laser light source may comprise a helium-neon
laser and the photodetector may comprise a photomultiplier tube.
In another example the laser light source may comprise a laser
diode and the photodetector may comprise a PIN diode.
In another example, the flow rate calculating mechanism may include
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.o, . . .
,p.sub.n from the harmonic coefficients c.sub.0 . . . , c.sub.n
by solving
the equations ##EQU11##
(c) computing a series of instantaneous volumetric flow rates from
the pressure coefficients p.sub.0 . . . ,p.sub.n, by solving the
equation ##EQU12##
(d) computing a mass flow rate by integrating the volumetric flow
rates using the fluid density and cross sectional area of the measurement
tube.
In another example, the flow rate calculating mechanism may include
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 ##EQU13##
(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 ##EQU14##
(d) computing a mass flow rate by integrating the volumetric flow
rates using the fluid density and cross sectional area of the measurement
tube.
In another example, the flow rate calculating mechanism may include
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 ##EQU15##
(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 ##EQU16##
In another example, the flow meter may further comprise a fuel
tank and a fuel injection pump.
In another example, the flow meter may further comprise a controller
connected to the fuel pump for controlling the duration and frequency
of a plurality of fuel injection pulses.
In another example, the controller may be capable of nanosecond
pulse duration.
In another example, at least one of the velocity calculating mechanism
and the flow rate calculating mechanism may include software.
In another embodiment a flow meter for bench testing fuel flow
characteristics in a fuel injection system, which fuel injection
system includes at least one fuel injector is provided, comprising:
at least one of an input pipe for supplying fuel to the fuel injector
and an output pipe for receiving fuel from the fuel injector; a
measurement tube installed in one of the input pipe and the output
pipe; 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.
In one example, the measurement tube may be constructed at least
in part from quartz glass.
In another example, the quartz glass may be substantially transparent.
In another example the flow meter may further comprise an optical
bench, wherein at least one of the measurement tube, the input pipe,
the output pipe and the laser-Doppler anemometer is mounted to the
optical bench.
In another example, the laser-Doppler anemometer may comprise a
laser light source and a photodetector.
In another example, the laser light source may comprise a helium-neon
laser and the photodetector may comprise a photomultiplier tube.
In another example, the laser light source may comprise a laser
diode and the photodetector may comprise a PIN diode.
In another example, the flow rate calculating mechanism may include
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 ##EQU17##
(c) computing a series of instantaneous volumetric flow rates from
the pressure coefficients p.sub.0 . . . ,p.sub.n, by solving the
equation ##EQU18##
(d) computing a mass flow rate by integrating the volumetric flow
rates using the fluid density and cross sectional area of the measurement
tube.
In another example, the flow rate calculating mechanism may include
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 ##EQU19##
(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 ##EQU20##
(d) computing a mass flow rate by integrating the volumetric flow
rates using the fluid density and cross sectional area of the measurement
tube.
In another example, the flow rate calculating mechanism may include
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 ##EQU21##
(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 ##EQU22##
In another example, the flow meter may further comprise a fuel
tank and a fuel injection pump.
In another example, the flow meter may further comprise a controller
connected to the fuel pump for controlling the duration and frequency
of a plurality of fuel injection pulses.
In another example, the controller may be capable of nanosecond
pulse duration.
In another example: (a) a cross-section of the input pipe may be
selected from the group of circular, oval, square and rectangular;
(b) a cross-section of the output pipe may be selected from the
group of circular, oval, square and rectangular; and (c) a cross-section
of the measurement tube may be selected from the group of circular,
oval, square and rectangular.
In another example: (a) the input pipe may be included; and (b)
the measurement tube may be installed in the input pipe.
In another example, the output pipe may be not included.
In another example: (a) the output pipe may be included; and (b)
the measurement tube may be installed in the output pipe.
In another example, the input pipe may be not included.
In another example, the flow meter may comprise a check valve installed
in the output pipe to control backpressure in the output pipe.
In another example, the flow meter may comprise an orifice plate
installed in the output pipe to control pressure in the output pipe.
In another example, the flow meter may further comprise: (a) a
check valve installed in the output pipe to control backpressure
in the output pipe; and (b) an orifice plate installed in the output
pipe to control pressure in the output pipe; wherein: (i) the output
pipe has a first end and a second end, which first end is connected
to the fuel injector; (ii) the check valve is installed at the second
end of the output pipe; and (iii) the orifice plate is installed
at a position in the output pipe between the check valve and the
measurement tube.
In another example, the flow meter may further comprise a fuel
injector tip holder for connecting an output tip of the fuel injector
to the output pipe.
In another example, the flow meter may further comprise a pressure
transducer disposed within the fuel injector tip holder.
In another example, at least one of the velocity calculating mechanism
and the flow rate calculating mechanism may include software.
In summary, under one embodiment of the present invention a flow
meter having a laser Doppler anemometer (LDA) is provided. Such
a flow meter may be used to measure 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/or other flow characteristics as instantaneous quantities and/or
integrated over a time interval using an processing method (e.g.,
electronic) which provides an exact solution to the Navier-Stokes
equations for any periodically oscillating flow. The flow meter
may be adapted, for example, for measuring the flow characteristics
of high pressure automotive fuel injection systems. A number of
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.
The flow meter may include an LDA, which itself may include: (a)
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 (b) a photodetector
to detect forward scatter. An interface board may convert the Doppler
frequency shift to instantaneous velocity measurements at a programmable
sampling rate (e.g., with nanosecond resolution). The velocity measurements
may 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/or other transient injection characteristics).
FIG. 1 shows one embodiment of a stationary stand flow meter. More
particularly, stationary stand flow meter 10 may be used for bench
testing, calibration, and/or 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 (e.g., with a capacity of ten to twenty liters), a low-pressure
pump 112 (e.g., with fuel filters), and a high pressure pump 114
(e.g., 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 rotor-synchronized time controller 120 provides a means for setting
an injection frequency (e.g., of 0.5 to 60 Hz) and an injection
duration (e.g., of 0.25 to a few milliseconds) with an encoding
signal of, for example 360 bin/cycle (which may which may changed
(e.g., 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, for example, 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 (e.g., 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
of 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/or other data for
calibrating the performance of the fuel injector 116.
The measurement pipe 134 is described in more detail in connection
with 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 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 may have a length, for example, of between
200 and 350 mm, depending on injection pressure, and may be between
about 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 (e.g., 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, ##EQU23##
versus the phase angle. FIG. 6C shows the pressure gradient dp/dt
versus the phase angle.
For a diesel fuel injection system (e.g., operating at injection
pressures between about 80.0 and 100.0 MPa), the components of the
stationary stand 110 may need to be modified because of the very
high injection pressure and higher fuel now velocity in the fuel
transport common rail (e.g., 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 may need 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 may be, for example,
a diode pumped solid state laser with the emitting second harmonic
wavelength of 532 nm, (pumping by 808 run) 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., for example) may be 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 may be 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: ##EQU24##
where A, 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./(2 sin .theta.)
in order to determine micron and submicron scattering particles,
^-fringe was fixed to be 1.3 .mu.m. For diesel injection
flow, .DELTA.t may need to 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, for example. Therefore,
for diesel FIS, the time controller 120 may not necessarily be an
external controller. Rather, the stationary stand 110 may use the
quartz clock generator of the 32.768 series with a base frequency
of 9.2333 MHz, installed in the Electronic Control Unit of typical
existing diesel engines (it is believed that this clock generator
is used, for example, in the Detroit Diesel ECU). The second harmonic
at 4.617 MHz may be used. The measurement Fast Fourier Transform
index may be 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, may provide unacceptable performance
as an interface board 138 since the Dostek 1400A uses time/crank
angle reference only with a fixed injection period. For diesel systems,
it may be 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 may be 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, may
prove to be inadequate in accurately resolving instantaneous rates
at the higher pressures and velocities in a diesel system. Therefore,
the processor 140 may programmed with the 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, for
example, about 110.times.80.times.20 mm. A quartz measurement tube
174 having an internal diameter between about 3.0 to 3.5 mm, for
example, 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
low meter 200 includes a cylindrical quartz measurement tube 202
of about (for example) 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, for example, a laser diode 206 (832 rim, 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 (e.g.,
load as determined by engine rpm, emissions data, etc.) to determine,
for example, 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 about 150 and 180 .mu.m (for example)
in order to restrict emission of the laser beam(s) 220 to a narrow
plane or laser sheet about 150 .mu.m thick (for example). 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. (for example)
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 5 .mu.m
(for example) that emits a highly divergent beam in an elliptical
cone which may be considered in an XYZ coordinate system, with the
X direction indicating 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 32 having
a diameter of about 10 .mu.m (for example) 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 (for example)
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 (for example)
is mounted is 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 (for example). 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
(for example) 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, with the stationary stand,
and/or with the portable flow meter (e.g., when 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 (e.g., injection fluid temperature
T(t) and pressure P(t), angular velocity (w) and injection duration
t(t)) and calls the software program encoded on a custom integrated
circuit processor 274 which calculates instantaneous volumetric
flow rates, mass rates, and/or 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.
Referring now to FIG. 1B, another embodiment of the present invention
is shown. As seen in this FIG. 1B, the flow meter (i.e., stationary
stand 110') may be part of an injection test and/or calibration
machine. The stationary stand 110' may comprise two subsystems:
a high-pressure hydraulics (HPH) subsystem directly related to the
specified FIS and a laser Doppler anemometry (LDA) subsystem. These
subsystems may be incorporated and operated as a single test unit
that performs very accurate volumetric and/or flow rate measurements.
In this embodiment, the LDA measurement is taken in connection
with the fuel expelled from the injector into a pipe 600. The flow
itself represents an oscillatory fuel with a dense flow of micro-size
(e.g., 1-5 .mu.m) bubbles as the result of a cavitation process
during discharge of the fuel throughout the injector nozzles. This
"bubbled" flow would be quickly dissipated along the pipe
600; therefore, it may be necessary to maintain pressure into the
pipe 600 in order to keep cavitation flow along the injector tip
a certain distance where the LDA measurement may be reliably made.
In any case, as seen in this FIG. 1B, the stationary stand 110'
may include a well-sealed injection tip holder 601 (with a pressure
transducer 602); an orifice plate 604 to maintain the average pressure
level (e.g., over 40 and up to 100 bar, i.e. a cavitation flow "freezing"
condition); a pipe extension 606 to damp remaining flow before the
fuel discharge (e.g., into free space for mass balance measurement);
and a check valve 608 (e.g., to control backpressure). Changes in
injection rate cause changes in pressure of the measurement pipe
inlet and in flow therethrough. The backpressure may be setup by
adjusting the check valve 608. The backpressure damping may be dependent
on the pipe length, inner diameter, and injection repetition rate--it
is widely varied upon multi-burst injection mode. One important
aspect is related to cycle-to-cycle variability of the fuel injection
equipment ("FIE") itself. The repeatability of injection
characteristics should be provided by the FIE original pressure
control and injection timing equipment.
In one example, the following should be known or determined:
1. Original FIE properties should be available based on independent
measurements of fuel discharge amount and injection/nozzle pressure
timing, for instance using a positive displacement flow measurements.
The injection maps should be obtained at all practical injection
repetition rates (RPM) and loads (partial and full).
2. The pressure spectra should be obtained incrementally along
the pipe length in order to evaluate cavitation flow length limit
L.sub.DFM.
3. Within L.sub.DFM a series of LDA setups should be tested to
have data rate over 10 kHz.
4. The time-arrival and cyclic series should be processed to estimate
accuracy limit.
5. Both HPH and LDA sub-systems should be well aligned to reach
targeted accuracy (e.g., 0.1-0.5%).
Still referring to FIG. 1B, the following example (which example
is intended to be illustrative and not restrictive) is provided:
The pipe 600 may wound as a rectangular (or oval) tin-plated steel
tubing to be installed into the given test machine space, approximately
of 5".times.10". The total length of pipe may be about
15 to 25 m with inner diameter of about 4 to 6 mm. One turn of these
wounds may be used for installation of the measurement section 600'
with a flexibly adjusted size, approximately of 2".times.5",
using high-pressure fitting in-/outlet connections. A strain gauge
(or any other type pressure sensor 602) may be installed into the
injector tip holder for measuring injection pressure trace (intensity
and/or phasing). A digital oscilloscope (for example, a Yokogama
DL 1520 type), may be used for the pressure data acquisition. The
pressure in the range of 0-100 bar may be precisely controlled by
the check valve 608. The check valve 608 may be mounted at the end
of the pipe extension 606. The backpressure may be monitored by
a liquid-filled Bourdon tube pressure gauge (or pressure sensor)
with a reasonable accuracy (e.g., .about.1-3%). The fuel ejected
from the check valve 608 may be accumulated into a mass-balance
glass-vessel (not shown) for reference calibration.
Referring now to the LDA subsystem of FIG. 1B, any desired LDA
system may be used. The LDA may be applied to measure centerline
velocity of the fuel flow passed through the quartz tube installed
into the measurement intersection 600'. The measurement and post-processing
procedures both for laminar and turbulent flows are described elsewhere
in this application.
In one example (which example is intended to be illustrative and
not restrictive), the flow meter must be properly configured for
measurement of centerline velocity in a capillary reversible flow
(diesel injection) into the range of -5 to +20 m/s (Bragg cell frequency
shift alignment) with already seeded (cavitation) particles of 1-5
.mu.m. The specific design parameters for this example are as follows:
1. Separated transmitting (half intersection angle<15 deg) and
receiving heads with minimum available sizes must be installed in
off-axis geometric plane.
2. Effective emitting laser power per each of two beams must be
more than 15 mW to have enough power of the scattering light on
diode-based compact photo-detector. If laser power output from the
transmitting lens is more than 60 mW, the backscattering optics
can be used for photo-detecting of scattered light.
3. Synchronization of the signal processor with en encoder signal
is setup to process data as a cyclic series.
4. Synchronized external pressure trace input through multi-channel
interface is fed to adjust any time phase constant delays between
the LDA signal output and the injection electronic setup.
In another example (which example is intended to be illustrative
and not restrictive), the incorporation of the LDA may be made in
essentially two steps. The first step is design and fabrication
of the measurement intersection 600' (MI) itself. The design for
an MI operated under injection pressures up to about 100 (MI-100)
is described elsewhere in this application, The design of MI-2000
is shown in FIGS. 19A and 19B. Specifically, MI-2000 (identified
in FIG. 19A with reference numeral 700) was designed for very high
pressures up to about 2000 bar. Its main part is a quartz pipe 701
with an inner diameter of 1.90 mm and outer diameter of 6.06 mm
that was thermally pressed into a thick metal tube 703. So, the
quartz tube 701 was strengthened due to radial strength from the
outer steel tube 703. That enabled it to withstand diesel injection
pressures very well (of note, the size of MI-100 and MI-2000 housings
can be flexibly changed according to the installation space). The
second step is related to precise alignment of the portable LDA
optical head on the measurement intersection with respect to the
flow axis. That may require fabricating a 2D or 3D mechanism for
the flexible alignment and final adjustment of the head and the
intersection.
Referring now to FIGS. 20A-20D, some illustrative measurement results
associated with stationary stand 110' are shown. More particularly,
FIGS. 20A-20D relate to six-shot injection dynamics presented by
a cyclic-series, respectively to the Pilot, Pre-Main, Main 1 Main
2 After-M and Post injection events (shots). According to the flow
rate measurement, these phases are 124.sup.0 176.sup.0 180.sup.0
185.sup.0 268.sup.0 and 313.sup.0. All events having long dwell
intervals before the shot are characterized by almost exact time/angular
phase that was electronically set up; there is enough time to recover
the pressure drop in the injector accumulation chamber. Vice versa,
in the vicinity centered three-shots (Pre-M, Main 1 and Main 2)
are set up closely (dwells 300 and 400 .mu.s), the phases are shifted
relative to the initial SOI sets because the pressure needs a recovery
time with the delay constant determined by a specific injector design.
The sequential injection events can be clearly seen from the accumulated
mass series represented by a cascade; the number of cascaded stages
is equal to the number of injection shots.
In order to obtain the fuel masses injected per individual event
during multiple injections shown FIGS. 20A-20D, the injection cycle
was split into a number of intervals including 6 active injection
fractions as shown in the diagram of FIGS. 21A and 21B: Pilot, Pre-Main,
Main-1 Main-2 After-Main and Post shots. The results of fuel mass
integration (for each injection shot) are reflected in the table
of the FIG. 21B. In this particular case, for an injected mass resolution,
the smallest amount of fuel, 3.52 mg, was injected during the Pre-Main
shot, the largest, 10.58 mg, was during the Main-1 shot. The cyclic
resolution was set up at 360 bins per cycle. Increasing it to 3600
bins, the injection mass resolution can be about 1 .mu.g. However,
such a level of control requires a high LDA-data rate (e.g., over
10 kHz).
As seen in FIGS. 20A-20D and 21A-21B, a high data rate allowed
resolution of each injection event, i.e., its timing characteristics
and masses distributed within the injection cycle. Time arrival-
and cyclic- type data were obtained and sorted upon the angular
phase and processed to obtain the time/angular resolved series of:
(i) flow rate: (ii) pressure gradient; and (iii) integrated mass
relating to individual injections. This flow metering system is
applicable to any high-pressure FIE (e.g., diesel-based) for the
testing of a variety of FIE units including the injector itself.
The technique provides a wide dynamic range and high temporal and
fuel mass resolution for flow rate measurements. It may be applied
to the testing, calibration and/or evaluation of multiple injection
diesel equipment.
Whether the instantaneous center line velocity, U(t) data, is measured
with the stationary stand 110 the stationary stand 110' the portable
flow meter 170 or the on-board sensor 200 the velocity data is
input to the processor for processing (e.g., 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: ##EQU25##
where R is the radius ##EQU26##
measurement tube, v is the kinematic i=v-1 viscosity of the fluid,
p.sub.o and p.sub.n are harmonic coefficients, w is the angular
frequency, t is the time, Ta.sub.n is the nth Taylor number ##EQU27##
and C.C. is the complex conjugate. J.sub.o and J.sub.t are, of
course, zero order and first order Bessel functions. The theoretical
center line velocity is expressed as: ##EQU28##
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:
##EQU29##
The harmonic coefficients P.sub.o and P.sub.n can be determined
from equations (3) and (4) as follows: ##EQU30##
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 is
a personal computer, the software may be written in any language
(e.g., a high level language). In one example (which example is
intended to be illustrative and not restrictive), Fortran may be
used due to its built in support for complex number arithmetic.
When the processor is a custom integrated circuit, the software
instructions may be encoded, for example, in ROM and/or an EPROM
in assembly language (for example), and/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,
for example, the injection period T0 kinematic viscosity v, fluid
density p, radius of the pipe R, injection duration T, etc. In the
next step 302 certain constant parameters can be computed, such
as frequency f=1/T0 and angular frequency w=2.pi.f etc. In step
304 the LDA velocities are input to the processor directly (or
via the ECU 214 for example). In step 306 the raw LDA velocities
u(n) are used o compute the harmonic coefficients c.sub.0 and c.sub.n
by an inverse discrete Fourier transform (IDFT) of equation (4),
i.e., ##EQU31##
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 ins 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: ##EQU32##
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 p 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 p. Optionally, at step 318 the instantaneous-pressure
gradient series may be obtained by solving: ##EQU33##
which is the time series P_Z (In) where ##EQU34##
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.=v2v/w limits application of the method. The effect of this
limitation is that the software solution described in FIGS. 16A
and 16B may be essentially 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 may be required. The z-momentum and r-momentum Navier-Stokes
equations are: ##EQU35##
respectively, where the tilde overscore denotes the sum of mean
and fluctuation parts of the Reynolds decomposition, so that p=P+p',
ū=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: ##EQU36##
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 W', velocity,
so that:
With respect to the pressure, three parts (stationary, oscillating,
and fluctuating) are also superposed, so that: ##EQU37##
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: ##EQU38##
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: ##EQU39## ##EQU40##
and the r-momentum is expressed by: ##EQU41##
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 ##EQU42##
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, thc critical
space ##EQU43##
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: ##EQU44##
and the r-momentum expressed as: ##EQU45##
In order to obtain the instantaneous volumetric flow rate over
m pipe cross section in the direction of the pipe axis, it is necessary
to integrate the ū velocity component and turbulent velocity
correlation vu'v' projected on the same pipe axis as follows: ##EQU46##
This flow rate reflects an effective axial velocity composing our
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.nz
: ##EQU47##
then this velocity is measured on the centerline, r.uparw.0 equation
24 reduces to: ##EQU48##
The experimentally measured center line velocity time series may
be expressed as the Fourier expansion: ##EQU49##
where switching in the Fourier expansion is dependent on the following
criteria: ##EQU50##
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): ##EQU51##
FIGS. 17A and 17B show an exemplary flow chart for a software program
for implementing equations (10) through (28). When the processor
is a personal computer, the software may be written in any language
(e.g., a high level language). In one example (which example is
intended to be illustrative and not restrictive), Fortran may be
used due to its built in support for complex number arithmetic.
When the processor is a custom integrated circuit, the software
instructions may be encoded, for example, in ROM and/or an EPROM
in assembly language (for example), and/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 RON, such as the
injection period T0 kinematic viscosity v tables where viscosity
is a function of temperature, fluid density p tables where density
is a function of pressure, radius of the pipe R, injection duration
r, etc. In the next step 402 certain constant parameters can be
computed, such as frequency f=1/T0 and angular frequency w=2.pi.f,
Stokes layer thickness .delta., etc. In step 404 the DA velocities
are input to the processor directly (or via the ECU 214). For diesel
or high pressure fuel injection systems, the number of velocities
measured per cycle, N.sub.meas, may be 10000 for example. 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.o, . . . c.sub.n, and c.sub.o ', . .
. , c.sub.n ' by an inverse discrete Fourier transform (IDFT) of
equation (26) analogous to that shown in equation (6), supra, essentially
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.o, p.sub.n, and
p.sub.n ', are determined using equation (28) and the values of
c.sub.o, . . . c.sub.n, and c.sub.o ' 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.o, . . .
,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: ##EQU52##
In step 418 the integrated mass flow rate is obtained by multiplying
the integrated volumetric flow rate by the density p, 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 p. 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: ##EQU53##
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 new 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 ##EQU54##
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
he velocity field does not reflect the turbulent fluctuation and
therefore gives a lower velocity field than is actually developed
n 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) may therefore be preferred
with the high injection pressures and velocities (e.g., as 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.
From the point of instantaneous flow rate measurements, the present
invention may be applied anywhere desired in the fuel flow stream.
For example, the test point may be before the fuel injector receives
the fuel, e.g., in the case of gasoline, direct injection gasoline
and common rail type injection systems where direct flow/pressure
is continuously applied from a high pressure source to an injector
tip along the whole fuel delivery line. Due to this flow continuity,
the pressure wave propagation permits measurement of velocity and/or
pressure and/or flow rates at any reasonable point along the line.
The instantaneous flow rate information is directly related to the
pressure gradient reflecting any pressure change along the line.
The opening and closing of the injector valve reflects the changes
in time series with essentially the only differences in time-phases
and intensities (there may be further flow differences between closed
line, typically presented in the gasoline systems, and closed loop
systems in the common rail, where the pressure control spill valves,
installed in common rail and injector, splits the flow into two
streams, i.e., one for injection and one or two for return--in such
cases, the mass balance measurements used for flow rate measurement
verification may be directly comparable with the LDA mean volume/mass
obtained through the integration of flow rate over the injection
cycle).
In another example, the test point may be after the fuel injector
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