Flow meter

• US 6,510,842 B2
• Filed: 05/15/2001
• Issued: 01/28/2003
• Est. Priority Date: 07/03/2000
• Status: Expired due to Fees

• Current Assignee: Combustion Dynamics Corporation
• Original Assignee: Murad M. Ismailov
• Inventors: Ismailov, Murad M.
• Primary Examiner(s): ARGENBRIGHT, TONY MICHAEL
• Application Number:
  US09/854,561
• Publication Number:
  US 20020014224A1
• Time in Patent Office: 623 Days
• Field of Search: 123/478, 123/480, 123/494, 738/61, 356/28, 356/28.5
• US Class Current: 123/494
• CPC Class Codes: F02B 2075/125 Direct injection in the combustion chamber for spark ignition engines, i.e. not in pre-combustion chamber
• CPC Class Codes: F02D 2041/288 for performing a transformation into the frequency domain, e.g. Fourier transformation
• CPC Class Codes: F02D 2041/389 for injecting directly into the cylinder
• CPC Class Codes: F02D 2200/0614 Actual fuel mass or fuel injection amount
• CPC Class Codes: F02D 41/40 with means for controlling injection timing or duration
• CPC Class Codes: F02M 2200/24 Fuel-injection apparatus with sensors
• CPC Class Codes: F02M 51/0678 all portions having fuel passages, e.g. flats, grooves, diameter reductions
• CPC Class Codes: F02M 55/02 Conduits between injection pumps and injectors , e.g. conduits between pump and common-rail or conduits between common-rail and injectors
• CPC Class Codes: F02M 61/163 Means being injection-valves with helically or spirally shaped grooves
• CPC Class Codes: F02M 61/18 Injection nozzles, e.g. having valve seats; Details of valve member seated ends, not otherwise provided for
• CPC Class Codes: F02M 63/00 Other fuel-injection apparatus having pertinent characteristics not provided for in groups F02M39/00 - F02M57/00 or F02M67/00; Details, component parts, or accessories of fuel-injection apparatus, not provided for in, or of interest apart from, the apparatus of groups F02M39/00 - F02M61/00 or F02M67/00; Combination of fuel pump with other devices, e.g. lubricating oil pump
• CPC Class Codes: F02M 65/00 Testing fuel-injection apparatus, e.g. testing injection timing testing of ignition F02P17/00; measuring fuel consumption G01F9/00; Cleaning of fuel-injection apparatus
• CPC Class Codes: G01F 1/661 using light
• CPC Class Codes: G01F 1/86 Indirect mass flowmeters, e.g. measuring volume flow and density, temperature or pressure
• CPC Class Codes: Y02T 10/12 Improving ICE efficiencies
• CPC Class Codes: Y02T 10/40 Engine management systems

Abstract

The flow meter is a device having a laser Doppler anemometer (LDA) which measures the instantaneous center line velocity of fluid flow in a pipe and processes the instantaneous velocity so obtained to compute the volumetric flow rate, mass rate, and other flow characteristics as instantaneous quantities and/or integrated over a time interval using an electronic processing method which provides an exact solution to the Navier-Stokes equations for any periodically oscillating flow. The flow meter is particularly adapted for measuring the flow characteristics of high pressure automotive fuel injection systems. Three embodiments of the flow meter are described, including a stationary stand for off-line bench testing flow rate in a fuel injection system, a portable flow meter for inline testing in a vehicle'"'"'s fuel line, and an on-board flow meter sensor connected to an engine control module.

Claims

1. A on-board flow meter for installation in a fuel pipeline of a fuel injection engine, comprising:

(a) a measurement tube adapted for installation in a fuel pipeline of a fuel injection engine;

(b) a laser-Doppler anemometer generating a pair of laser beams intersecting in a control measurement volume in a center line of fuel flow through said measurement tube;

(c) an interface card connected to said laser-Doppler anemometer for calculating a series of instantaneous center line velocities of fuel flow through said measurement tube;

(d) a processor connected to said interface card, the processor having means for computing instantaneous and integral volumetric and mass flow rates in said measurement tube, the processor being connected to an engine electronic control unit;

whereby the electronic control unit uses the volumetric and mass flow rates to adjust fuel injection parameters in order to optimize fuel flow in the engine.

2. The on-board flow meter according to claim 1, wherein said measurement tube comprises:

(a) an elongated, transparent, quartz glass tube; and

(b) a steel jacket, said quartz tube being sheathed within said steel jacket.

3. The on-board flow meter according to claim 1, wherein said laser-Doppler anemometer comprises:

(a) a laser diode attached to said measurement tube and disposed to emit a laser beam normal to a longitudinal axis of said measurement tube;

(b) beam splitting means for splitting the laser beam emitted by said laser diode into two laser beams focused to intersect in the control measurement volume in the center line of said measurement tube;

(c) a PIN diode for receiving light scattered by fuel flowing in the control measurement zone of said measurement tube, the PIN diode being disposed on a side of the measurement tube opposite said laser diode to receive forward scatter; and

(d) focusing means for focusing scattered light from the control measurement zone on said PIN diode.

4. The on-board flow meter according to claim 3, wherein said beam splitting means comprises:

(a) an X-Y traverse frame disposed between said laser diode and said measurement tube;

(b) an optic fiber disposed on said traverse frame parallel to a crystal emitting stripe of said laser diode;

(c) a three-wire guitar having a highly reflecting back surface disposed on said traverse frame, the three wires being disposed to block zero order and second order harmonics of the split laser beam, first order harmonics of the laser beam being focused to intersect in the control measurement volume on the center line of said measurement tube.

5. The on-board flow meter according to claim 3, wherein said focusing means comprises:

(a) an X-Y traverse frame disposed between said PIN diode and said measurement tube;

(b) an optic fiber mounted on said traverse frame; and

(c) a plate having a pinhole defined therein mounted between said optic fiber and said PIN diode.

6. The on-board flow meter according to claim 1, wherein said means for computing instantaneous and integral volumetric and mass flow rates comprises:

(a) a first set of instructions which cause said processor to read basic parameters, including fuel viscosity, fluid density, injection duration, injection period, and radius of the measurement tube;

(b) a second set of instructions which cause said processor to compute constant parameters, including frequency and angular frequency;

(c) a third set of instructions which cause said processor to input the series of instantaneous center line velocities from said interface card;

(d) a fourth set of instructions which cause said processor to perform an inverse Fourier transform to calculate a series of harmonic coefficients c₀, . . . , c_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 p₀, . . . , p_n from the harmonic coefficients c₀, . . . , c_n by solving the equations $p_0=\frac{2<br><br>c_0<br><br>v}{R^2}$

 

and $p_n=\frac{c_n<br><br>\mathrm{<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}}{1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}};<br><br>$

(f) a sixth set of instructions which cause said processor to compute a series of instantaneous volumetric flow rates from the pressure coefficients p₀, . . . , p_n by solving the equation $V<br><br>\left(t\right)=\frac{\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R^2}{2}<br><br>\left(\frac{R^2<br><br>p_o}{4<br><br>v}+\underset{n=1}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left\{\frac{p_n}{n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}}<br><br>{\mathrm{<br><br><br><br>}}^{\mathrm{<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}<br><br>\left[\frac{4<br><br>{\mathrm{<br><br>}}^{1/2}<br><br>J_1<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}{{\mathrm{Ta}}_n<br><br>J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}-2\right]+C.C.\right\}\right);<br><br>$

 

and

(g) a seventh set of instructions which cause said processor to compute a mass flow rate by integrating the volumetric flow rates using the fluid density and cross sectional area of the measurement tube.

7. The on-board flow meter according to claim 1, wherein said means for computing instantaneous and integral volumetric and mass flow rates comprises:

(a) a first set of instructions which cause said processor to read basic parameters, including fuel viscosity, fluid density, injection duration, injection period, and radius of the measurement tube;

(b) a second set of instructions which cause said processor to compute constant parameters, including frequency and angular frequency;

(c) a third set of instructions which cause said processor to input the series of instantaneous center line velocities from said interface card;

(d) a fourth set of instructions which cause said processor to perform an inverse Fourier transform to calculate a first series of harmonic coefficients c₀, . . . , c_n and a second series of harmonic coefficients c₀′

, . . . , c_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 p₀, . . . , p_n and p₀′

, . . . , p_n′

from the harmonic coefficients c₀, . . . , c_n and c₀′

, . . . , c_n′

by solving the equations $p_{o<br><br>\text{\hspace{1em}<br><br>}<br><br>z}=2<br><br>\frac{c_o<br><br>v}{R^2}$$p_{\mathrm{nz}}=\frac{c_n<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br><br><br>}}{\left[1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}\right]},n\in <br><br>\left[1,N_{\mathrm{\delta <br><br>}}\right]$$p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}+\sqrt{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}<br><br>p_{\mathrm{nr}}^{\mathrm{\prime <br><br>}}}=\frac{2<br><br>c_n^{\mathrm{\prime <br><br>}}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br><br><br>}}{\left[1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}\right]},n\in <br><br>\left[N_{\mathrm{\delta <br><br>}}+1,N_{\mathrm{meas}}\right];<br><br>$

(f) a sixth set of instructions which cause said processor to compute a series of instantaneous volumetric flow rates from the pressure coefficients p₀, . . . , p_n and p₀, . . . , p_n′

by solving the equation $\stackrel{.}{V}<br><br>\left(t\right)=2<br><br>\mathrm{\pi <br><br>}<br><br>{\int <br><br>}_0^R<br><br>\left(\tilde{u}+\sqrt{\stackrel{\_}{u^{\mathrm{\prime <br><br>}}<br><br>v^{\mathrm{\prime <br><br>}}}}\right)<br><br>r<br><br>\text{\hspace{1em}<br><br>}<br><br><br><br>r=\frac{\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R^2}{2}<br><br>\left[\frac{p_0<br><br>R^2}{4<br><br>v}+\underset{n=1}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(\frac{p_{\mathrm{nz}}<br><br>〈<br><br>\frac{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}}{2}+\frac{\sqrt{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}<br><br>p_{\mathrm{nr}}^{\mathrm{\prime <br><br>}}}}{2}〉<br><br>}{n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}}<br><br>{\mathrm{<br><br><br><br>}}^{\mathrm{<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}<br><br>\left\{\frac{4<br><br>{\mathrm{<br><br>}}^{1/2}<br><br>J_1<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}{{\mathrm{Ta}}_n<br><br>J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}-2\right\}\right)+C.C.\right];<br><br>\mathrm{and}$

(g) a seventh set of instructions which cause said processor to compute a mass flow rate by integrating the volumetric flow rates using the fluid density and cross sectional area of the measurement tube.

8. A flow meter for measuring fuel flow characteristics in a fuel injection system, comprising:

(a) a measurement tube adapted for installation in a fuel pipeline of a fuel injection system;

(b) a laser-Doppler anemometer generating a pair of laser beams intersecting in a control measurement volume in a center line of fuel flow through said measurement tube;

(c) an interface card connected to said laser-Doppler anemometer for calculating a series of instantaneous center line velocities of fuel flow through said measurement tube; and

(d) a processor connected to said interface card, the processor having means for computing instantaneous and integral volumetric and mass flow rates in said measurement tube.

9. The flow meter according to claim 8, further comprising:

(a) a fuel tank;

(b) a fuel injection pump;

(c) a fuel injector;

(d) a fuel pipeline connecting said fuel tank, said fuel pump, and said fuel injector, said measurement tube being disposed in said fuel pipeline between said fuel pump and said fuel injector; and

(e) wherein said laser-Doppler anemometer comprises;

(i) an optical bench, said measurement tube being disposed on the optical bench;

(ii) a laser light source attached to the optical bench disposed to emit a laser beam normal to said measurement tube;

(iii) a prism disposed between said laser light source and said measurement tube for splitting the laser beam into two collimated beams;

(iv) a pair of Braggs cells mounted on the optical bench, the Braggs cells modulating the two laser beams with a fixed frequency difference;

(v) a focusing lens mounted on the optical bench to focus the two laser beams on a control measurement volume on the centerline of said measurement tube; and

(vi) a photodetector mounted opposite said measurement tube for detecting forward scatter of the two laser beams.

10. The flow meter according to claim 9, wherein:

(a) said laser light source comprises a helium-neon laser; and

(b) said photodetector comprises a photomultiplier tube.

11. The flow meter according to claim 9, wherein:

(a) said laser light source comprises a laser diode; and

(b) said photodetector comprises a PIN diode.

12. The flow meter according to claim 9, further comprising an external controller connected to said fuel pump for controlling the duration and frequency of fuel injection pulses.

13. The flow meter according to claim 9, further comprising an electronic control unit connected to said fuel pump for controlling the duration and frequency of fuel injection pulses, the electronic control unit having a time base capable of nanosecond pulse duration.

14. The flow meter according to claim 8, wherein said measurement tube comprises:

(a) a cylindrical quartz glass tube having an inlet end and an outlet end;

(b) a rectangular glass tube having an inlet end and an outlet end, the rectangular glass tube being disposed about said quartz glass tube;

(c) an inlet plug and an outlet plug, each plug having a rectangular plate sealing the inlet and outlet ends of the rectangular glass tube, respectively, and having a nipple extending from the rectangular plate;

(d) a cylindrical fitting disposed in each said nipple, the inlet end of said quartz glass tube extending into the nipple of the inlet plug and abutting the cylindrical fitting, and the outlet end of the quartz glass tube extending into the nipple of the outlet plug and abutting the cylindrical fitting;

(e) a cylindrical inlet unit attached to the inlet plug, the cylindrical inlet unit being adapted for attachment to the fuel pipeline; and

(f) a cylindrical outlet unit attached to the outlet plug, the outlet unit being adapted for attachment to a fuel injector.

15. The flow meter according to claim 8, wherein said laser-Doppler anemometer comprises:

(a) a laser diode emitting a laser beam;

(b) a prism redirecting the laser beam normal to said measurement tube;

(c) a first lens disposed between said laser diode and said prism for collimating the laser beam;

(d) a holographic splitter disposed between said prism and said measurement tube for splitting the laser beam into two beams and for focusing the two beams to intersect in a control measurement volume in the center line of said measurement tube;

(e) a PIN diode disposed on a side of said measurement tube opposite said laser diode to detect forward scatter from the intersecting laser beams;

(f) a pinhole mask disposed between said PIN diode and said measurement tube; and

(g) a second lens disposed between said measurement tube and said pinhole mask for focusing the forward scatter on said PIN diode.

16. The flow meter according to claim 15, further comprising a box, said measurement tube and said laser-Doppler anemometer being disposed in said box, said measurement tube being adapted for insertion in a fuel pipeline of a fuel injection engine.

17. The flow meter according to claim 8, wherein:

(a) said measurement tube comprises;

(i) an elongated, transparent, quartz glass tube adapted for insertion in a fuel pipeline of a fuel injection engine;

(ii) a steel jacket, said quartz tube being sheathed within said steel jacket; and

(b) said laser-Doppler anemometer comprises;

(i) a laser diode attached to said measurement tube and disposed to emit a laser beam normal to a longitudinal axis of said measurement tube;

(ii) beam splitting means for splitting the laser beam emitted by said laser diode into two laser beams focused to intersect in the control measurement volume in the center line of said measurement tube;

(iii) a PIN diode for receiving light scattered by fuel flowing in the control measurement zone of said measurement tube, the PIN diode being disposed on a side of the measurement tube opposite said laser diode to receive forward scatter; and

(iv) focusing means for focusing scattered light from the control measurement zone on said PIN diode.

18. The flow meter according to claim 8, wherein said means for computing instantaneous and integral volumetric and mass flow rates comprises:

(a) a first set of instructions which cause said processor to read basic parameters, including fuel viscosity, fluid density, injection duration, injection period, and radius of the measurement tube;

(b) a second set of instructions which cause said processor to compute constant parameters, including frequency and angular frequency;

(c) a third set of instructions which cause said processor to input the series of instantaneous center line velocities from said interface card;

(d) a fourth set of instructions which cause said processor to perform an inverse Fourier transform to calculate a first series of harmonic coefficients c₀, . . . , c_n and a second series of harmonic coefficients c₀′

, . . . , c_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 p₀, . . . , p_n and p₀′

, . . . , p_n′

from the harmonic coefficients c₀, . . . , c_n and c₀′

, . . . , c_n′

by solving the equations $p_{o<br><br>\text{\hspace{1em}<br><br>}<br><br>z}=2<br><br>\frac{c_o<br><br>v}{R^2}$$p_{\mathrm{nz}}=\frac{c_n<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br><br><br>}}{\left[1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}\right]},n\in <br><br>\left[1,N_{\mathrm{\delta <br><br>}}\right]$$p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}+\sqrt{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}<br><br>p_{\mathrm{nr}}^{\mathrm{\prime <br><br>}}}=\frac{2<br><br>c_n^{\mathrm{\prime <br><br>}}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br><br><br>}}{\left[1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}\right]},n\in <br><br>\left[N_{\mathrm{\delta <br><br>}}+1,N_{\mathrm{meas}}\right];<br><br>$

(f) a sixth set of instructions which cause said processor to compute a series of instantaneous volumetric f low rates from the pressure coefficients p₀, . . . , p_n and p₀′

, . . . , p_n′

by solving the equation $\stackrel{.}{V}<br><br>\left(t\right)=2<br><br>\mathrm{\pi <br><br>}<br><br>{\int <br><br>}_0^R<br><br>\left(\tilde{u}+\sqrt{\stackrel{\_}{u^{\mathrm{\prime <br><br>}}<br><br>v^{\mathrm{\prime <br><br>}}}}\right)<br><br>r<br><br>\text{\hspace{1em}<br><br>}<br><br><br><br>r=\frac{\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R^2}{2}<br><br>\left[\frac{p_0<br><br>R^2}{4<br><br>v}+\underset{n=1}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(\frac{p_{\mathrm{nz}}<br><br>〈<br><br>\frac{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}}{2}+\frac{\sqrt{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}<br><br>p_{\mathrm{nr}}^{\mathrm{\prime <br><br>}}}}{2}〉<br><br>}{n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}}<br><br>{\mathrm{<br><br><br><br>}}^{\mathrm{<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}<br><br>\left\{\frac{4<br><br>{\mathrm{<br><br>}}^{1/2}<br><br>J_1<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}{{\mathrm{Ta}}_n<br><br>J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}-2\right\}\right)+C.C.\right];<br><br>\mathrm{and}$

(g) a seventh set of instructions which cause said processor to compute a mass flow rate by integrating the volumetric flow rates using the fluid density and cross sectional area of the measurement tube.

19. The flow meter according to claim 8, wherein said means for computing instantaneous and integral volumetric and mass flow rates comprises:

(a) a first set of instructions which cause said processor to read basic parameters, including fuel viscosity, fluid density, injection duration, injection period, and radius of the measurement tube;

(b) a second set of instructions which cause said processor to compute constant parameters, including frequency and angular frequency;

(c) a third set of instructions which cause said processor to input the series of instantaneous center line velocities from said interface card;

(d) a fourth set of instructions which cause said processor to perform an inverse Fourier transform to calculate a series of harmonic coefficients c₀, . . . , c_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 p₀, . . . , p_n from the harmonic coefficients c₀, . . . , c_n by solving the equations $p_0=\frac{2<br><br>c_0<br><br>v}{R^2}$

 

and $p_n=\frac{c_n<br><br>\mathrm{<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}}{1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}}$

(f) a sixth set of instructions which cause said processor to compute a series of instantaneous volumetric flow rates from the pressure coefficients p₀, . . . , p_n by solving the equation $V<br><br>\left(t\right)=\frac{\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R^2}{2}<br><br>\left(\frac{R^2<br><br>p_0}{4<br><br>v}+\underset{n=1}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left\{\frac{p_n}{n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}}<br><br>{\mathrm{<br><br><br><br>}}^{\mathrm{<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}<br><br>\left[\frac{4<br><br>{\mathrm{<br><br>}}^{1/2}<br><br>J_1<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}{{\mathrm{Ta}}_n<br><br>J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}-2\right]+C.C.\right\}\right);<br><br>$

 

and

(g) a seventh set of instructions which cause said processor to compute a mass flow rate by integrating the volumetric flow rates using the fluid density and cross sectional area of the measurement tube.

20. An electronic data processing method for measuring volumetric flow rates and mass flow rates of a periodically oscillating fluid flow in a pipeline, comprising the steps of:

(a) inserting a measurement tube in a pipeline;

(b) measuring a series of instantaneous velocities, u(t), on a center line of the pipeline by laser-Doppler anemometer;

(c) performing an inverse Fourier transform on the measured series of instantaneous velocities to obtain a first series of harmonic coefficients c₀′

, . . . , c_n and a second series of harmonic coefficients c₀′

, . . . , c_n′

, where the summation in the first series is incremented when the Reynolds number is 3000 and the summation in the second series is incremented when the Reynolds number is >

3000;

(d) computing a series of pressure coefficients p₀, . . . , p_n and p₀′

, . . . , p_n′

from the harmonic coefficients c₀, . . . , c_n and c₀′

, . . . , c_n′

by solving the equations $p_{o<br><br>\text{\hspace{1em}<br><br>}<br><br>z}=2<br><br>\frac{c_o<br><br>v}{R^2}$$p_{\mathrm{nz}}=\frac{c_n<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br><br><br>}}{\left[1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}\right]},n\in <br><br>\left[1,N_{\mathrm{\delta <br><br>}}\right]$$p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}+\sqrt{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}<br><br>p_{\mathrm{nr}}^{\mathrm{\prime <br><br>}}}=\frac{2<br><br>c_n^{\mathrm{\prime <br><br>}}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br><br><br>}}{\left[1-\frac{1}{J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}\right]},n\in <br><br>\left[N_{\mathrm{\delta <br><br>}}+1,N_{\mathrm{meas}}\right];<br><br>$

 

and

(e) computing a series of instantaneous volumetric flow rates from the pressure coefficients p₀, . . . , p_n and p₀′

, . . . , p_n′

by solving the equation $\stackrel{.}{V}<br><br>\left(t\right)=2<br><br>\mathrm{\pi <br><br>}<br><br>{\int <br><br>}_0^R<br><br>\left(\tilde{u}+\sqrt{\stackrel{\_}{u^{\mathrm{\prime <br><br>}}<br><br>v^{\mathrm{\prime <br><br>}}}}\right)<br><br>r<br><br>\text{\hspace{1em}<br><br>}<br><br><br><br>r=\frac{\mathrm{\pi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>R^2}{2}<br><br>\left[\frac{p_0<br><br>R^2}{4<br><br>v}+\underset{n=1}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(\frac{p_{\mathrm{nz}}<br><br>〈<br><br>\frac{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}}{2}+\frac{\sqrt{p_{\mathrm{nz}}^{\mathrm{\prime <br><br>}}<br><br>p_{\mathrm{nr}}^{\mathrm{\prime <br><br>}}}}{2}〉<br><br>}{n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}}<br><br>{\mathrm{<br><br><br><br>}}^{\mathrm{<br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>n<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\omega <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>t}<br><br>\left\{\frac{4<br><br>{\mathrm{<br><br>}}^{1/2}<br><br>J_1<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}{{\mathrm{Ta}}_n<br><br>J_0<br><br>\left({\mathrm{<br><br>}}^{3/2}<br><br>{\mathrm{Ta}}_n\right)}-2\right\}\right)+C.C.\right].$