Dual function flow measurement apparatus having an array of sensors

[0001] This application is a continuation patent application of U.S. patent application Ser. No. 10/875,857, filed on Jun. 24, 2004, now U.S. Pat. No. 7,127,360, which claimed the benefit of U.S. Provisional Patent Application No. 60/487,765 filed on Jul. 15, 2003, and U.S. Provisional Patent Application No. 60/487,678, filed on Jul. 15, 2003, all of which are incorporated by reference herein in their entirety.

[0002] This invention relates to an apparatus for measuring a parameter of a process flow passing within a pipe, and more particularly to a flow measurement apparatus having an array of sensors for processing data signals therefrom to provide an output indicative of the speed of sound propagating through the process flow and/or a flow parameter of the process flow passing through a pipe.

[0003] A fluid flow process (flow process) includes any process that involves the flow of fluid through pipes, ducts, or other conduits, as well as through fluid control devices such as pumps, valves, orifices, heat exchangers, and the like. Flow processes are found in many different industries such as the oil and gas industry, refining, food and beverage industry, chemical and petrochemical industry, pulp and paper industry, power generation, pharmaceutical industry, and water and wastewater treatment industry. The fluid within the flow process may be a single phase fluid (e.g., gas, liquid or liquid/liquid mixture) and/or a multi-phase mixture (e.g. paper and pulp slurries or other solid/liquid mixtures). The multi-phase mixture may be a two-phase liquid/gas mixture, a solid/gas mixture or a solid/liquid mixture, gas entrained liquid or a three-phase mixture.

[0004] Various sensing technologies exist for measuring various physical parameters of single and/or multiphase fluids in an industrial flow process. Such physical parameters include, for example, volumetric flow rate, composition, consistency, density, and mass flow rate.

[0005] The various different types of parameters that are measured throughout an industrial processing plant requires separate meters or flow measuring devices for each parameter. As one can appreciate, the need to monitor numerous steps in a process becomes very costly in the operation of the plant. It would be advantageous in the operation of industrial processes to deploy a flow measuring device that is capable of measuring a number of different parameters of a system.

[0006] Objects of the present invention include providing a flow measuring apparatus having a dual function of measuring the speed of sound propagating through a process flow moving within a pipe and measuring the velocity of the process flow.

[0007] In one aspect of the present invention, an apparatus for measuring at least two parameters of a process flow flowing within a pipe is provided. The apparatus includes at least two pressure sensors disposed at different axial locations along the pipe. Each of the pressure sensors provides a respective pressure signal indicative of a pressure disturbance within the pipe at a corresponding axial position. A signal processor, responsive to said pressure signals, provides a first signal indicative of a velocity of a pressure field moving with the process flow and provides a second signal indicative of a speed of sound propagating through the process flow.

[0008] In another aspect of the present invention, a method of measuring at least two parameters of a process flow flowing within a pipe is provided. The method includes providing respective pressure signal indicative of a pressure disturbance within the pipe at different axial locations along the pipe. The method then processes said respective pressure signals to determine a first signal indicative of a velocity of a pressure field moving with the process flow and to determine a second signal indicative of a speed of sound propagating through the process flow.

[0009] The foregoing and other objects, features and advantages of the present invention will become more apparent in light of the following detailed description of exemplary embodiments thereof.

[0021] FIG. 1 illustrates a schematic diagram of a flow measurement apparatus 10 that includes a sensing device (sensor head) 16 mounted to a pipe 14 and a processing unit (transmitter) 24. The apparatus 10 measures a characteristic or parameter of a single phase fluid (e.g., gas and liquid) and/or multiphase fluids 12 (e.g., gas/liquid mixtures, liquid/solid mixtures, gas/solid mixtures, steam, pulp and paper slurries, and aerated liquids and mixtures) flowing through the pipe 14. Specifically, the flow characteristics and flow parameters determined include the volumetric flow of the fluid, the consistency or composition of the fluid, the density of the fluid, the Mach number of the fluid, the size of particle flowing through the fluid, the air/mass ratio of the fluid, velocity of the flow, volumetric flow rate, gas volume fraction of the flow, the speed of sound propagating through the flow, and/or the percentage of entrained air within a liquid or slurry.

[0022] For instance, the apparatus 10, in accordance with the present invention, can determine the speed at which sound propagates through the fluid flow 12 within a pipe 14 to measure particular characteristics of the single or multi-phase fluids. The apparatus may also determine the speed at which pressure disturbances propagate through the pipe 14 to determine the velocity of the fluid flow 12. The pressure disturbances may be in the form of vortical disturbances (e.g., turbulent eddies FIG. 10) or other pressure disturbances that convect (or propagate) with the flow. To simplify the explanation of the present invention, the flow propagating through the pipe will be referred to as a process flow with the understanding that the fluid or process flow 12 may be a single phase or multi-phase flow, as described hereinbefore.

[0023] The sensing device 16 comprises an array of strain-based senors or pressure sensors 18-21 for measuring the unsteady pressures produced by vortical disturbances within the pipe and/or speed of sound propagating through the flow, which are indicative of parameters and/or characteristics of the process flow 12. The pressure signals P₁(t)-P_N(t) are provided to the processing unit 24, which digitizes the pressure signals and computes the appropriate flow parameter(s). A cable 13 electronically connects the sensing device 16 to the processing unit 24. The analog pressure sensor signals P₁(t)-P_N(t) are typically 4-20 mA current loop signals.

[0024] The array of pressure sensors 18-21 comprises an array of at least two pressure sensors 18,19 spaced axially along the outer surface 22 of the pipe 14, having a process flow 12 propagating therein. The pressure sensors 18-21 may be clamped onto or generally removably mounted to the pipe by any releasable fastener, such as bolts, screws and clamps. Alternatively, the sensors may be permanently attached to or integral (e.g., embedded) with the pipe 14. The array of sensors of the sensing device 16 may include any number of pressure sensors 18-21 greater than two sensors, such as three, four, eight, sixteen or N number of sensors between two and twenty-four sensors. Generally, the accuracy of the measurement improves as the number of sensors in the array increases. The degree of accuracy provided by the greater number of sensors is offset by the increase in complexity and time for computing the desired output parameter of the flow. Therefore, the number of sensors used is dependent at least on the degree of accuracy desired and the desire update rate of the output parameter provided by the apparatus 10. The pressure sensors 18-19 measure the unsteady pressures produced by acoustic waves propagating through the flow and/or pressure disturbances (e.g., vortical eddies) that convect with the flow within the pipe 14, which are indicative of the SOS propagating through the fluid flow 12 in the pipe and the velocity of disturbances propagating through the flow 12 of the mixture 12, respectively. The output signals (P₁(t)-P_N(t)) of the pressure sensors 18-21 are provided to a pre-amplifier unit 39 that amplifies the signals generated by the pressure sensors 18-21. The processing unit 24 processes the pressure measurement data P₁(t)-P_N(t) and determines the desired parameters and characteristics of the flow 12, as described hereinbefore.

[0025] The apparatus 10 also contemplates providing one or more acoustic sources 27 to enable the measurement of the speed of sound propagating through the flow for instances of acoustically quiet flow. The acoustic source may be a device the taps or vibrates on the wall of the pipe, for example. The acoustic sources may be disposed at the input end of output end of the array of sensors 18-21, or at both ends as shown. One should appreciate that in most instances the acoustics sources are not necessary and the apparatus passively detects the acoustic ridge provided in the flow 12, as will be described in greater detail hereinafter. The passive noise includes noise generated by pumps, valves, motors, and the turbulent mixture itself.

[0026] As suggested and further described in greater detail hereinafter, the apparatus 10 has the ability to measure the speed of sound (SOS) and flow rate (or velocity) using one or both of the following techniques described herein below:

[0027] 1) Determining the speed of sound of acoustical disturbances or sound waves propagating through the flow 12 using the array of pressure sensors 18-21, and/or

[0028] 2) Determining the velocity of pressure disturbances (e.g., vortical eddies) propagating through the flow 12 using the array of pressure sensors 18-21.

[0029] Generally, the first technique measures unsteady pressures created by acoustical disturbances propagating through the flow 12 to determine the speed of sound (SOS) propagating through the flow. Knowing the pressure and/or temperature of the flow and the speed of sound of the acoustic disturbances or waves, the processing unit 24 can determine determined include the volumetric flow of the fluid, the consistency or composition of the fluid, the density of the fluid, the Mach number of the fluid, the average size of particles flowing through the fluid, the air/mass ratio of the fluid, and/or the percentage of entrained air within a liquid or slurry, such as that described in U.S. patent application Ser. No. 10/349,716 (CiDRA Docket No. CC-0579), filed Jan. 23, 2003, U.S. patent application Ser. No. 10/376,427 (CiDRA Docket No. CC-0596), filed Feb. 26, 2003, U.S. patent application Ser. No. 10/762,410 (CiDRA Docket No. CC-0703), filed Jan. 21, 2004, which are all incorporated by reference.

[0030] The second technique measures the velocities associated with unsteady flow fields and/or pressure disturbances, such as that created by vortical disturbances or “eddies” 88 (see FIG. 6), that convect with the process flow 12 to determine the velocity of the process flow. The pressure sensors 18-21 measure the unsteady pressures P₁-P_N created by the vortical disturbances 88, for example, as these disturbances convect with the flow 12 through the pipe 14 in a known manner, as shown in FIG. 6. Therefore, the velocity of these vortical disturbances is related to the velocity of the flow 12 and hence the volumetric flow rate may be determined, as will be described in greater detail hereinafter.

[0031] As shown in FIGS. 2-5, the present invention contemplates a flow measurement apparatus 10 that combines the functionality of an apparatus for measuring the velocity of the process flow and an apparatus for measuring the speed of sound propagating through the flow within a pipe. The pressure signals P₁(t)-P_N(t) provided by the array of sensors 18-21 of the sensing device 16 may be processed using a number of different methods as illustrated in FIGS. 2-5.

[0032] In FIG. 2, the data or pressure signals P₁(t)-P_N(t) may be processed serially. In other words, the data is collected or accumulated and processed first by a convective processing unit 52 to provide output signals indicative of the velocity, Mach number and volumetric flow of the process flow. Additional data is then accumulated and processed by an acoustic processing unit 53 to provide output signals indicative of the consistency or composition of the flow, the density of the flow, the average size of particles within the flow, the air/mass ratio of the flow, gas volume fraction of the flow, and/or the speed of sound propagating through the flow.

[0033] As shown in FIG. 2, an apparatus 10 embodying the present invention has an array of at least two strain-based or pressure sensors 18,19, located at two locations x₁,x₂ axially along the pipe 14 for sensing respective stochastic signals propagating between the sensors 18,19 within the pipe at their respective locations. Each sensor 18,19 provides a signal indicating an unsteady pressure at the location of each sensor, at each instant in a series of sampling instants. One will appreciate that the sensor array may include more than two pressure sensors as depicted by pressure sensor 20,21 at location x₃,x_N. The pressure generated by the convective pressure disturbances (e.g., eddies 88) and acoustic waves 90 (see FIG. 9) may be measured through strained-based sensors and/or pressure sensors 18-21. The pressure sensors 18-21 provide analog pressure time-varying signals P₁(t),P₂(t),P₃(t),P_N(t) to the signal processing unit 24. The processing unit 24 serially processes the pressure signals to first provide output signals 51,55 indicative of the pressure disturbances that convect with the flow 12, and subsequently, provide output signals 57,59 in response to pressure disturbances generated by acoustic waves propagating through the flow 12, as discussed hereinbefore. While the apparatus 10 shows the convective pressure disturbance signals are initially processed first, the invention contemplates that the acoustic pressure signals may be initially processed first.

[0034] The convective processing function or unit 52 of the processing unit 24 in FIG. 2 receives the pressure signals from the array of sensors 18-21. A data acquisition unit 40 (e.g., A/D converter) converts the analog signals to respective digital signals. The digitized signals are provided to Fast Fourier Transform (FFT) logic 42. The FFT logic calculates the Fourier transform of the digitized time-based input signals P₁(t)-P_N(t) and provide complex frequency domain (or frequency based) signals P₁(ω),P₂(ω),P₃(ω),P_N(ω) indicative of the frequency content of the input signals. Instead of FFT's, any other technique for obtaining the frequency domain characteristics of the signals P₁(t)-P_N(t), may be used. For example, the cross-spectral density and the power spectral density may be used to form a frequency domain transfer functions (or frequency response or ratios) discussed hereinafter.

[0035] One technique of determining the convection velocity of the turbulent eddies 88 within the process flow 12 is by characterizing a convective ridge of the resulting unsteady pressures using an array of sensors or other beam forming techniques, similar to that described in U.S. patent application Ser. No. 10/007,736 (Cidra's Docket No. CC-0122A) and U.S. patent application Ser. No. 09/729,994 (Cidra's Docket No. CC-0297), filed Dec. 4, 200, now U.S. Pat. No. 6,609,069, which are incorporated herein by reference.

[0036] A data accumulator 44 accumulates the frequency signals P₁(ω)-P_N(ω) over a sampling interval, and provides the data to an array processor 46, which performs a spatial-temporal (two-dimensional) transform of the sensor data, from the xt domain to the k-ω domain, and then calculates the power in the k-ω plane, as represented by a k-ω plot.

[0037] The array processor 46 uses standard so-called beam forming, array processing, or adaptive array-processing algorithms, i.e. algorithms for processing the sensor signals using various delays and weighting to create suitable phase relationships between the signals provided by the different sensors, thereby creating phased antenna array functionality. In other words, the beam forming or array processing algorithms transform the time domain signals from the sensor array into their spatial and temporal frequency components, i.e. into a set of wave numbers given by k=2π/λ where λ is the wavelength of a spectral component, and corresponding angular frequencies given by ω=2πν.

[0038] The prior art teaches many algorithms of use in spatially and temporally decomposing a signal from a phased array of sensors, and the present invention is not restricted to any particular algorithm. One particular adaptive array processing algorithm is the Capon method/algorithm. While the Capon method is described as one method, the present invention contemplates the use of other adaptive array processing algorithms, such as MUSIC algorithm. The present invention recognizes that such techniques can be used to determine flow rate, i.e. that the signals caused by a stochastic parameter convecting with a flow are time stationary and have a coherence length long enough that it is practical to locate sensor units apart from each other and yet still be within the coherence length.

[0039] Convective characteristics or parameters have a dispersion relationship that can be approximated by the straight-line equation,
k=ω/u,

[0040] where u is the convection velocity (flow velocity). A plot of k-ω pairs obtained from a spectral a analysis of sensor samples associated with convective parameters portrayed so that the energy of the disturbance spectrally corresponding to pairings that might be described as a substantially straight ridge, a ridge that in turbulent boundary layer theory is called a convective ridge. What is being sensed are not discrete events of turbulent eddies, but rather a continuum of possibly overlapping events forming a temporally stationary, essentially white process over the frequency range of interest. In other words, the convective eddies 88 is distributed over a range of length scales and hence temporal frequencies.

[0041] To calculate the power in the k-ω plane, as represented by a k-ω plot (see FIG. 7) of either the signals, the array processor 46 determines the wavelength and so the (spatial) wavenumber k, and also the (temporal) frequency and so the angular frequency ω, of various of the spectral components of the stochastic parameter. There are numerous algorithms available in the public domain to perform the spatial/temporal decomposition of arrays of sensor units 18-21.

[0042] The present invention may use temporal and spatial filtering to precondition the signals to effectively filter out the common mode characteristics P_{common mode} and other long wavelength (compared to the sensor spacing) characteristics in the pipe 14 by differencing adjacent sensors and retain a substantial portion of the stochastic parameter associated with the flow field and any other short wavelength (compared to the sensor spacing) low frequency stochastic parameters.

[0043] In the case of suitable turbulent eddies 88 (see FIG. 6) being present, the power in the k-ω plane shown in a k-ω plot of FIG. 7 shows a convective ridge 100. The convective ridge represents the concentration of a stochastic parameter that convects with the flow and is a mathematical manifestation of the relationship between the spatial variations and temporal variations described above. Such a plot will indicate a tendency for k-ω pairs to appear more or less along a line 100 with some slope, the slope indicating the flow velocity.

[0044] Once the power in the k-ω plane is determined, a convective ridge identifier 48 uses one or another feature extraction method to determine the location and orientation (slope) of any convective ridge 100 present in the k-ω plane. In one embodiment, a so-called slant stacking method is used, a method in which the accumulated frequency of k-ω pairs in the k-ω plot along different rays emanating from the origin are compared, each different ray being associated with a different trial convection velocity (in that the slope of a ray is assumed to be the flow velocity or correlated to the flow velocity in a known way). The convective ridge identifier 48 provides information about the different trial convection velocities, information referred to generally as convective ridge information.

[0045] The analyzer 50 examines the convective ridge information including the convective ridge orientation (slope). Assuming the straight-line dispersion relation given by k=ω/u, the analyzer 50 determines the flow velocity, Mach number and/or volumetric flow. The volumetric flow is determined by multiplying the cross-sectional area of the inside of the pipe with the velocity of the process flow.

[0046] After the output signals associated with the convective pressure signals are determined, the processing unit 24 then determines the output signals 57,59 associated with the speed of sound propagating through the flow 12, as indicated by connecting arrow 51. A second data acquisition unit 54 digitizes additional pressure signals P₁(t)-P_N(t) associated with the acoustic waves 14 propagating through the pipe 14. Similarly to the FFT logic 42, an FFT logic 56 calculates the Fourier transform of the digitized time-based input signals P₁(t)-P_N(t) and provide complex frequency domain (or frequency based) signals P₁(ω),P₂(ω),P₃(ω),P_N(ω) indicative of the frequency content of the input signals.

[0047] A second data accumulator 58 accumulates the additional signals P₁(t)-P_N(t) from the sensors, and provides the data accumulated over a sampling interval to an array processor 60, which performs a spatial-temporal (two-dimensional) transform of the sensor data, from the xt domain to the k-ω domain, and then calculates the power in the k-ω plane, as represented by a k-ω plot, similar to that provided by the convective array processor 46.

[0048] To calculate the power in the k-ω plane, as represented by a k-ω plot (see FIG. 8) of either the signals or the differenced signals, the array processor 60 determines the wavelength and so the (spatial) wavenumber k, and also the (temporal) frequency and so the angular frequency ω, of various of the spectral components of the stochastic parameter. There are numerous algorithms available in the public domain to perform the spatial/temporal decomposition of arrays of sensor units 18-21.

[0049] In the case of suitable acoustic waves 90 being present in both axial directions, the power in the k-ω plane shown in a k-ω plot of FIG. 8 so determined will exhibit a structure that is called an acoustic ridge 110,112 in both the left and right planes of the plot, wherein one of the acoustic ridges 110 is indicative of the speed of sound traveling in one axial direction and the other acoustic ridge 112 being indicative of the speed of sound traveling in the other axial direction.

[0050] The acoustic ridges represent the concentration of a stochastic parameter that propagates through the flow and is a mathematical manifestation of the relationship between the spatial variations and temporal variations described above. Such a plot will indicate a tendency for k-ω pairs to appear more or less along a line 110,112 with some slope, the slope indicating the speed of sound. The power in the k-ω plane so determined is then provided to an acoustic ridge identifier 62, which uses one or another feature extraction method to determine the location and orientation (slope) of any acoustic ridge present in the left and right k-ω plane. The velocity may be determined by using the slope of one of the two acoustic ridges 110,112 or averaging the slopes of the acoustic ridges 110,112.

[0051] Finally, information including the acoustic ridge orientation (slope) is used by an analyzer 64 to determine the flow parameters 57, 59 relating to measured speed of sound, such as the consistency or composition of the flow, the density of the flow, the average size of particles in the flow, the air/mass ratio of the flow, gas volume fraction of the flow, the speed of sound propagating through the flow, and/or the percentage of entrained air within the flow.

[0052] Similar to the array processor 46, the array processor 60 uses standard so-called beam forming, array processing, or adaptive array-processing algorithms, i.e. algorithms for processing the sensor signals using various delays and weighting to create suitable phase relationships between the signals provided by the different sensors, thereby creating phased antenna array functionality. In other words, the beam forming or array processing algorithms transform the time domain signals from the sensor array into their spatial and temporal frequency components, i.e. into a set of wave numbers given by k=2π/λ where λ is the wavelength of a spectral component, and corresponding angular frequencies given by ω=2πν.

[0053] One such technique of determining the speed of sound propagating through the flow 12 is using array processing techniques to define an acoustic ridge in the k-ω plane as shown in FIG. 8. The slope of the acoustic ridge is indicative of the speed of sound propagating through the flow 12. The speed of sound (SOS) is determined by applying sonar arraying processing techniques to determine the speed at which the one dimensional acoustic waves propagate past the axial array of unsteady pressure measurements distributed along the pipe 14.

[0054] The apparatus 10 of the present invention measures the speed of sound (SOS) of one-dimensional sound waves propagating through the mixture to determine the gas volume fraction of the mixture. It is known that sound propagates through various mediums at various speeds in such fields as SONAR and RADAR fields. The speed of sound propagating through the pipe and flow 12 may be determined using a number of known techniques, such as those set forth in U.S. patent application Ser. No. 09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147; U.S. patent application Ser. No. 10/795,111, filed Mar. 4, 2004; U.S. patent application Ser. No. 09/997,221, filed Nov. 28, 2001, now U.S. Pat. No. 6,587,798; U.S. patent application Ser. No. 10/007,749, filed Nov. 7, 2001, and U.S. patent application Ser. No. 10/762,410, filed Jan. 21, 2004, each of which are incorporated herein by reference.

[0055] While the sonar-based flow meter using an array of sensors to measure the speed of sound of an acoustic wave propagating through the mixture is shown and described, one will appreciate that any means for measuring the speed of sound of the acoustic wave may used to determine the entrained gas volume fraction of the mixture/fluid or other characteristics of the flow described hereinbefore.

[0056] The analyzer 64 of the acoustic processing unit 53 provides output signals indicative of characteristics of the process flow 12 that are related to the measured speed of sound (SOS) propagating through the flow 12. For example, to determine the gas volume fraction (or phase fraction), the analyzer 64 assumes a nearly isothermal condition for the flow 12. As such the gas volume fraction or the void fraction is related to the speed of sound by the following quadratic equation:
Ax²+Bx+C=0

[0057] wherein x is the speed of sound, A=1+rg/rl*(K_eff/P−1)−K_eff/P, B=K_eff/P−2+rg/rl; C=1−K_eff/rl*a_meas^2); Rg=gas density, rl=liquid density, K_eff=effective K (modulus of the liquid and pipewall), P=pressure, and a_meas=measured speed of sound.

[0058] Effectively,
Gas Voulume Fraction (GVF)=(−B+sqrt(B^2−4*A*C))/(2*A)

[0059] Alternatively, the sound speed of a mixture can be related to volumetric phase fraction (φ_i) of the components and the sound speed (a) and densities (ρ) of the component through the Wood equation.

[0060] $\frac{1}{{\rho }_{\mathrm{mix}}{a}_{{\mathrm{mix}}_{\infty }}^2}=\sum _{i=1}^N\frac{{\varphi }_i}{{\rho }_i{a}_i^2}$ $\mathrm{where}$ ${\rho }_{\mathrm{mix}}=\sum _{i=1}^N{\rho }_i{\varphi }_i$

[0061] One dimensional compression waves propagating within a mixture 12 contained within a pipe 14 exert an unsteady internal pressure loading on the pipe. The degree to which the pipe displaces as a result of the unsteady pressure loading influences the speed of propagation of the compression wave. The relationship among the infinite domain speed of sound and density of a mixture; the elastic modulus (E), thickness (t), and radius (R) of a vacuum-backed cylindrical conduit; and the effective propagation velocity (a_eff) for one dimensional compression is given by the following expression:

[0062] $\begin{array}{cc}{a}_{\mathrm{eff}}=\frac{1}{\sqrt{1/a_{{\mathrm{mix}}_{\infty }}^2+{\rho }_{\mathrm{mix}}\frac{2R}{\mathrm{Et}}}}& \left(\mathrm{eq}1\right)\end{array}$

[0063] The mixing rule essentially states that the compressibility of a mixture (1/(ρ a²)) is the volumetrically-weighted average of the compressibilities of the components. For gas/liquid mixtures 12 at pressure and temperatures typical of paper and pulp industry, the compressibility of gas phase is orders of magnitudes greater than that of the liquid. Thus, the compressibility of the gas phase and the density of the liquid phase primarily determine mixture sound speed, and as such, it is necessary to have a good estimate of process pressure to interpret mixture sound speed in terms of volumetric fraction of entrained gas. The effect of process pressure on the relationship between sound speed and entrained air volume fraction is shown in FIG. 9.

[0064] As described hereinbefore, the apparatus 10 of the present invention includes the ability to accurately determine the average particle size of a particle/air or droplet/air mixture within the pipe 14 and the air to particle ratio. Provided there is no appreciable slip between the air and the solid coal particle, the propagation of one dimensional sound wave through multiphase mixtures is influenced by the effective mass and the effective compressibility of the mixture. For an air transport system, the degree to which the no-slip assumption applies is a strong function of particle size and frequency. In the limit of small particles and low frequency, the no-slip assumption is valid. As the size of the particles increases and the frequency of the sound waves increase, the non-slip assumption becomes increasing less valid. For a given average particle size, the increase in slip with frequency causes dispersion, or, in other words, the sound speed of the mixture to change with frequency. With appropriate calibration the dispersive characteristic of a mixture 12 will provide a measurement of the average particle size, as well as, the air to particle ratio (particle/fluid ratio) of the mixture.

[0065] In accordance with the present invention the dispersive nature of the system utilizes a first principles model of the interaction between the air and particles. This model is viewed as being representative of a class of models that seek to account for dispersive effects. Other models could be used to account for dispersive effects without altering the intent of this disclosure (for example, see the paper titled “Viscous Attenuation of Acoustic Waves in Suspensions” by R. L. Gibson, Jr. and M. N. Toksöz), which is incorporated herein by reference. The model allows for slip between the local velocity of the continuous fluid phase and that of the particles.

[0066] The following relation can be derived for the dispersive behavior of an idealized fluid particle mixture.

[0067] $a_{\mathrm{mix}}\left(\omega \right)=a_f\sqrt{\frac{1}{1+\frac{{\phi }_p{\rho }_p}{{\rho }_f\left(1+{\omega }^2\frac{{\rho }_p^2{v}_p^2}{K^2}\right)}}}$
In the above relation, the fluid SOS, density (ρ) and viscosity (φ) are those of the pure phase fluid, v_p is the volume of individual particles and φ_p is the volumetric phase fraction of the particles in the mixture.

[0068] Two parameters of particular interest in steam processes and air-conveyed particles processes are particle size and air-to-fuel mass ratio or steam quality. To this end, it is of interest to examine the dispersive characteristics of the mixture as a function of these two variables. FIGS. 10 and 11 show the dispersive behavior in relations to the speed of sound for coal/air mixtures with parameters typical of those used in pulverized coal deliver systems.

[0069] In particular FIG. 10 shows the predicted behavior for nominally 50 μm size coal in air for a range of air-to-fuel ratios. As shown, the effect of air-to-fuel ratio is well defined in the low frequency limit. However, the effect of the air-to-fuel ratio becomes indistinguishable at higher frequencies, approaching the sound speed of the pure air at high frequencies (above ˜100 Hz).

[0070] Similarly, FIG. 11 shows the predicted behavior for a coal/air mixture with an air-to-fuel ratio of 1.8 with varying particle size. This figure illustrates that particle size has no influence on either the low frequency limit (quasi-steady ) sound speed, or on the high frequency limit of the sound speed. However, particle size does have a pronounced effect in the transition region.

[0071] FIGS. 10 and 11 illustrate an important aspect of the present invention. Namely, that the dispersive properties of dilute mixtures of particles suspended in a continuous fluid can be broadly classified into three frequency regimes: low frequency range, high frequency range and a transitional frequency range. Although the effect of particle size and air-to-fuel ratio are inter-related, the predominant effect of air-to-fuel ratio is to determine the low frequency limit of the sound speed to be measured and the predominate effect of particle size is to determine the frequency range of the transitional regions. As particle size increases, the frequency at which the dispersive properties appear decreases. For typical pulverized coal applications, this transitional region begins at fairly low frequencies, ˜2 Hz for 50 μm size particles.

[0072] Given the difficulties measuring sufficiently low frequencies to apply the quasi-steady model and recognizing that the high frequency sound speed contains no direct information on either particle size or air-to-fuel ratio, it becomes apparent that the dispersive characteristics of the coal/air mixture should be utilized to determine particle size and air-to-fuel ratio based on speed of sound measurements.

[0073] Some or all of the functions within the processing unit 24 may be implemented in software (using a microprocessor or computer) and/or firmware, or may be implemented using analog and/or digital hardware, having sufficient memory, interfaces, and capacity to perform the functions described herein.

[0074] While data acquisition units 40,54, FFT logic 42,56, data accumulators 44,58, array processors 46,60 and ridge identifiers 48, 62 are shown as separate elements or separate software/processing routines, one will appreciate that each of these elements may be common and able to process the data associated with both the pressure signals associated with the speed of sound and the pressures that convect with the procees flow.

[0075] FIGS. 3-5 show an apparatus 120,130,140 embodying the present invention processes the pressure signals P1(t)-PN(t) from the sensing device 16 in parallel to provide both an output signal(s) 51,55 in response to pressure disturbances 88 that convective with the flow 12 and an output signal(s) 57,59 in response to pressure disturbances created by acoustic waves 90 propagating through the flow. In FIG. 3, the processing unit 24 of the apparatus 120 includes independent data acquisition and processing of the pressure signals to enable the processing unit 24 multitask. This method is similar to the full serial processing method described hereinbefore in FIG. 2, wherein the difference is the multitasking architecture of the processing unit 24 is used to process independent calculations simultaneously. This method of processing may be inefficient, however, produces fast updates rates of the output signals. One will appreciate that the elements of prior embodiments having the same reference number function substantially the same as that described in other embodiments of the present invention.

[0076] In FIG. 4, the apparatus 130 shows a processing unit 24 processing the data in parallel, wherein the processing unit includes common data acquisition unit 132, but independent calculations of the acquired pressure signals P₁(t)-P_N(t). This method utilizes the similarities between the two calculations to employ more efficient architectures. The first primary common component of the two calculations is the pressure signals P₁(t)-P_N(t) processed by each processing unit 52,53. By making some adjustments to the accumulated pressure signals, either method to extract the required information may be performed using a single data acquisition step. The calculations still remains independent by the elimination of a common step which reduces the update time. In this instance, more pressure signals are accumulated than required by the flow rate calculation in order to accommodate the speed of sound calculation.

[0077] FIG. 5 shows an apparatus 140 embodying the present invention wherein the processing unit 24 has common data acquisition 142, FFT logic 144, data accumulator 146 and array processor 148 with efficient common algorithm usage and multitasking independent operations. This architecture utilizes the fact that many algorithm components are shared between the two measurements. In this method, common data acquisition is used and as many upfront algorithms are used for both calculations. Examples of common algorithms include the normalization code, the FFT code of the FFT logic, and some of the specific capon algorithms of the array processors. Other portions of the code, such as the convective ridge identifier 48, acoustic ridge identifier 62 and respective analyzers 50,64 are left independent.

[0078] In one embodiment as shown in FIG. 1, each of the pressure sensors 18-21 may include a piezoelectric film 50 attached to a unitary multi-band strap 52 to measure the unsteady pressures of the flow 12 using either technique described hereinbefore. The piezoelectric film sensors 18-21 are mounted onto a unitary substrate or web which is mounted or clamped onto the outer surface 22 of the pipe 14, which will described in greater detail hereinafter.

[0079] The piezoelectric film sensors 18-21 include a piezoelectric material or film 50 to generate an electrical signal proportional to the degree that the material is mechanically deformed or stressed. The piezoelectric sensing element 50 is typically conformed to allow complete or nearly complete circumferential measurement of induced strain to provide a circumferential-averaged pressure signal. The sensors can be formed from PVDF films, co-polymer films, or flexible PZT sensors, similar to that described in “Piezo Film Sensors Technical Manual” provided by Measurement Specialties, Inc., which is incorporated herein by reference. A piezoelectric film sensor that may be used for the present invention is part number 1-1002405-0, LDT4-028K, manufactured by Measurement Specialties, Inc. While the piezoelectric film material 50 is provided substantially the length of the band 44, and therefore the circumference of the pipe 14, the present invention contemplates that the piezoelectric film material may be disposed along a portion of the band of any length less than the circumference of the pipe.

[0080] Piezoelectric film (“piezofilm”) 50, like piezoelectric material, is a dynamic material that develops an electrical charge proportional to a change in mechanical stress. Consequently, the piezoelectric material measures the strain induced within the pipe 14 due to unsteady or stochastic pressure variations (e.g., vortical and/or acoustical) within the process flow 12. Strain within the pipe is transduced to an output voltage or current by the attached piezoelectric sensor 18-21. The piezoelectrical material or film 50 may be formed of a polymer, such as polarized fluoropolymer, polyvinylidene fluoride (PVDF). The piezoelectric film sensors are similar to that described in U.S. patent application Ser. No. 10/712,818 (CiDRA Docket No. CC-0675), filed Nov. 12, 2003 and U.S. patent application Ser. No. 10/795,111 (CiDRA Docket No. CC-0731), filed Mar. 4, 2004, which are incorporated herein by reference. The advantages of this clamp-on technique using piezoelectric film include non-intrusive flow rate measurements, low cost, measurement technique requires no excitation source. One will appreciate that the sensor may be installed or mounted to the pipe 14 as individual sensors or all the sensors mounted as a single unit as shown in FIG. 1.

[0081] The pressure sensors 18-21 of FIG. 1 described herein may be any type of sensor, capable of measuring the unsteady (or ac or dynamic) pressures or parameter that convects with the flow within a pipe 14, such as piezoelectric, optical, capacitive, resistive (e.g., Wheatstone bridge), accelerometers (or geophones), velocity measuring devices, displacement measuring devices, ultra-sonic devices, etc. If optical pressure sensors are used, the sensors 18-21 may be Bragg grating based pressure sensors, such as that described in U.S. patent application Ser. No. 08/925,598, entitled “High Sensitivity Fiber Optic Pressure Sensor For Use In Harsh Environments”, filed Sep. 8, 1997, now U.S. Pat. No. 6,016,702, and in U.S. patent application Ser. No. 10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensor for Measuring Unsteady Pressures within a Pipe”, which are incorporated herein by reference. In an embodiment of the present invention that utilizes fiber optics as the pressure sensors 14 they may be connected individually or may be multiplexed along one or more optical fibers using wavelength division multiplexing (WDM), time division multiplexing (TDM), or any other optical multiplexing techniques.

[0082] In certain embodiments of the present invention, a piezo-electronic pressure transducer may be used as one or more of the pressure sensors 18-21 and it may measure the unsteady (or dynamic or ac) pressure variations inside the pipe 14 by measuring the pressure levels inside of the pipe. These sensors may be ported within the pipe to make direct contact with the process flow 12. In an embodiment of the present invention, the sensors comprise pressure sensors manufactured by PCB Piezotronics. In one pressure sensor there are integrated circuit piezoelectric voltage mode-type sensors that feature built-in microelectronic amplifiers, and convert the high-impedance charge into a low-impedance voltage output. Specifically, a Model 106B manufactured by PCB Piezotronics is used which is a high sensitivity, acceleration compensated integrated circuit piezoelectric quartz pressure sensor suitable for measuring low pressure acoustic phenomena in hydraulic and pneumatic systems.

[0083] It is also within the scope of the present invention that any strain sensing technique may be used to measure the variations in strain in the pipe, such as highly sensitive piezoelectric, electronic or electric, strain gages and piezo-resistive strain gages attached to the pipe 12. Other strain gages include resistive foil type gages having a race track configuration similar to that disclosed U.S. patent application Ser. No. 09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147, which is incorporated herein by reference. The invention also contemplates strain gages being disposed about a predetermined portion of the circumference of pipe 12. The axial placement of and separation distance ΔX₁, ΔX₂ between the strain sensors are determined as described herein above.

[0084] It is also within the scope of the present invention that any other strain sensing technique may be used to measure the variations in strain in the pipe, such as highly sensitive piezoelectric, electronic or electric, strain gages attached to or embedded in the pipe 14.

[0085] While the description has described the apparatus as two separate meters that measure the vortical disturbances and the speed of sound, respectively, as suggested by FIG. 1, the processing could function as two separate meters, a combination (simultaneous operation) of both function, or selectively chose between operations.

[0086] It should be understood that any of the features, characteristics, alternatives or modifications described regarding a particular embodiment herein may also be applied, used, or incorporated with any other embodiment described herein.

[0087] Although the invention has been described and illustrated with respect to exemplary embodiments thereof, the foregoing and various other additions and omissions may be made therein and thereto without departing from the spirit and scope of the present invention.