Source: https://patents.google.com/patent/US20050171710
Timestamp: 2018-07-23 02:24:32
Document Index: 296583353

Matched Legal Cases: ['Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60', 'Application No. 60']

US20050171710A1 - Apparatus and method for measuring parameters of a mixture having solid particles suspended in a fluid flowing in a pipe - Google Patents
US20050171710A1
US20050171710A1 US10512401 US51240104A US2005171710A1 US 20050171710 A1 US20050171710 A1 US 20050171710A1 US 10512401 US10512401 US 10512401 US 51240104 A US51240104 A US 51240104A US 2005171710 A1 US2005171710 A1 US 2005171710A1
US10512401
US7275421B2 (en )
An apparatus 10 and method is provided that includes a spatial array of unsteady pressure sensors 15-18 placed at predetermined axial locations x1-xN disposed axially along a pipe 14 for measuring at least one parameter of a solid particle/fluid mixture 12 flowing in the pipe 14. The pressure sensors 15-18 provide acoustic pressure signals P1(t)-PN(t) to a signal processing unit 30 which determines the speed of sound amix(ω) of the particle/fluid mixture 12 in the pipe 14 using acoustic spatial array signal processing techniques. The primary parameters to be measured include fluid/particle concentration, fluid/particle mixture volumetric flow, and particle size. Frequency based sound speed is determined utilizing a dispersion model to determine the parameters of interest. the calculating the at least one parameter uses an acoustic pressure to calculate
This application is a continuation in part of U.S. patent application Ser. No. 10/349,716 (Cidra Docket No. CC-0579) filed on Jan. 23, 2003, which claimed the benefit of U.S. Provisional Application No. 60/351,232 (Cidra Docket No. CC-0410), filed Jan. 23, 2002; U.S. Provisional Application No. 60/359,785 (Cidra Docket No. CC-0403), filed Feb. 26, 2002; U.S. Provisional Application No. 60/375,847 (Cidra Docket No. CC-0468), filed Apr. 24, 2002; U.S. Provisional Application No. 60/425,436 (Cidra Docket No. CC-0538), filed Nov. 12, 2002; and U.S. Provisional Application No. 60/426,724 (Cidra Docket No. CC-0554), filed Nov. 15, 2002; and is a continuation in part of U.S. patent application Ser. No. 10/376,427 (Cidra Docket No. CC-0596) filed on Feb. 26, 2003, which claimed the benefit of U.S. Provisional Application No. 60/359,785 (Cidra Docket No. CC-0403), filed Feb. 26, 2002; and is a continuation-in-part of U.S. patent application Ser. No. 10/349,716 (Cidra Docket No. CC-0579), filed Jan. 23, 2003, which claims the benefit of U.S. Provisional Application No. 60/351,232 (Cidra Docket No. CC-0410), filed Jan. 23, 2002; U.S. Provisional Application No. 60/359,785 (Cidra Docket No. CC-0403), filed Feb. 26, 2002; U.S. Provisional Application No. 60/375,847 (Cidra Docket No. CC-0468), filed Apr. 24, 2002; U.S. Provisional Application No. 60/425,436 (Cidra Docket No. CC-0538), filed Nov. 12, 2002; and U.S. Provisional Application No. 60/426,724 (Cidra Docket No. CC-0554), filed Nov. 15, 2002, all of which are incorporated herein by reference in their entirety.
This invention relates to an apparatus for measuring the flow passing within a pipe, and more particularly to an apparatus and method for measuring the speed of sound propagating in the flow, having particles suspended within a continuous fluid, to determine parameters, such as particle/fluid ratio, particle size and volumetric flow rate of the flow in pipes using acoustic dynamic pressures.
Objects of the present invention include providing a system for measuring the speed of sound propagating through a particle/fluid mixture in pipes in industrial boiler systems and related processes, such as coal fired boiler systems, to determine particular parameters of the mixture.
According to the present invention, an apparatus for measuring at least one parameter of a particle/fluid mixture in a pipe includes a spatial array of at least two pressure sensors, disposed at different axial locations along the pipe. Each of the pressure sensors measures an unsteady pressure within the pipe at a corresponding axial location. Each of said sensors provides a pressure signal indicative of the unsteady pressure within the pipe at said axial location of a corresponding one of said sensors. A signal processors responsive to said pressure signals, provides a signal indicative of the at least one parameter of the mixture in the pipe.
FIG. 7 is a plot of sound speed as a function of frequency for air/coal mixtures with fixed particle size (50 mun) and varying air-to-fuel mass Ratio in accordance with the present invention.
FIG. 13 is a kω plot of data processed from an array of pressure sensors use to measure the speed of sound of a coal/air mixture flowing in a pipe, in accordance with the present invention.
FIG. 14 is a side elevational view of a plurality of pressure sensors, having PVDF, clamped to the outer surface of the pipe, in accordance with the present invention.
FIG. 15 is a partial perspective view of one of the pressure sensors of FIG. 14.
Referring to FIG. 1, a flow meter 10 embodying the present invention is provided that measures a number of parameters/characteristics of a mixture 12 of solid particles suspended within a continuous fluid flowing within a pipe or conduit 14, wherein a fluid is defined as a liquid and/or a gas. The flow meter may be configured and programmed to measure the speed of sound propagating through the mixture. The flow meter can measure at least one of the following parameters of the mixture flow 12: the fluid/particle concentration (volumetric phase fraction), the volumetric flow rate, the size of the solid particles, the mass flow of the mixture and the velocity of the mixture. To determine any one of these parameters, the flow meter 10 measures the unsteady pressures created by the speed of sound (SOS) propagating through the mixture flowing in the pipe 14, which will be described in greater detail hereinafter.
The solid particles of the mixture 12 may be of any size, shape and material. For example, the particles may be small in size as in the form of a powder, in a granular form, or greater in size. The flow meter 10 can be used in any application that carries solid particles suspended in a fluid through a pipe, such as in chemical, pharmaceutical, petroleum and power generation applications. For example, the present invention is well suited to measure the parameters (e.g. air/coal ratio, particle size) for power generation systems that use pulverized coal to fire the furnace a steam boiler system.
As is known, non-uniformities in the PF delivery system 1 can result in variation of the fuel to air ratios, causing hot spots, regions of high NOx generation, and unburned fuel. The connection between performance of a PF fuel delivery system 1 and boiler system 2 is well recognized. The flow meter 10 embodying the present invention is capable of measuring the fuel to air ratio and particle size of the pulverized coal provided to the furnace to thereby provide feedback to the operator to provide more efficient combustion of the coal.
As described hereinbefore, the flow meter 10, of the present invention may be configured and programmed to measure and process the detected unsteady pressures P1(t)-PN(t) created by acoustic waves propagating through the mixture to determine parameters of the mixture flow 12. One such flow meter 10 is shown in FIG. 1 that measures the speed of sound (SOS) of one-dimensional sound waves propagating through the fluid/particle mixture to determine the composition the mixture, namely the liquid/particle ratio of the mixture. The flow meter is also capable of determining the average size of the particles, velocity of the mixture, and the volumetric flow rate 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 of a mixture within a pipe 14 may be determined using a number of known techniques, such as those set forth in U.S. Pat. No. 6,354,147, entitled “Fluid Parameter Measurement in Pipes Using Acoustic Pressures”, issued Mar. 12, 2002, and U.S. patent application Ser. No. 10/007,749, entitled “Fluid Parameter Measurement in Pipes Using Acoustic Pressures”, filed Nov. 7, 2001, each of which are incorporated herein by reference. The present invention utilizes at least one flow meter 10 to determine various parameters of the liquid/particle mixture, wherein one of the parameters is the speed at which sound travels within the mixture pipe system as will be more fully described herein below.
In accordance with the present invention, the speed of sound propagating through the mixture 12 is measured by passively listening to the flow with an array of unsteady pressure sensors to determine the speed at which one-dimensional compression waves propagate through the liquid/particle mixture contained within the pipe 14.
As shown in FIG. 1, the flow meter 10 has an array of at least three acoustic pressure sensors 15,16,17, located at three locations x1, x2, x3 axially along the pipe 14. One will appreciate that the sensor array may include more than three pressure sensors as depicted by pressure sensor 18 at location xN. The pressure generated by the acoustic waves may be measured through holes in the pipe 14 reported external pressure sensors 15-18 or by other techniques discussed hereinafter. The pressure sensors 15-18 provide pressure time-varying signals P1(t), P2(t), P3(t), PN(t) on lines 20,21,22,23 to a signal processing unit 30 to known Fast Fourier Transform (FFT) logics 26,27,28, 29, respectively. The FFT logics 26-29 calculate the Fourier transform of the time-based input signals P1(t)-PN(t) and provide complex frequency domain (or frequency based) signals P1(ω), P2(ω), P3(ω), PN(ω) on lines 32,33,34,35 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)-PN(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.
The frequency signals P1(ω)-PN(ω) are fed to amix-Mx Calculation Logic 38 which provides a signal to line 40 indicative of the speed of sound propagating through the mixture amix(ω), which is a function frequency (discussed more hereinafter). The amix(ω) signal is provided to map (or equation) logic 42, which converts amix(ω) to a percent composition of the PF/air mixture and provides a % Comp signal to line 44 indicative thereof (as discussed hereinafter). Also, if the Mach number Mx(ω) is not negligible and is desired, the calculation logic 40 may also provide a signal Mx(ω) to line 46 indicative of the Mach number Mx(ω) which is a function of frequency.
For circular ducts or pipes 12 as shown in FIG. 1, only plane waves propagate for frequencies below the cut-on frequency (ref Acoustics of Ducts and Mufflers, M. J. Munjal, John Wiley & Sons, New York, 1987): f < 1.84 π ⁢ ⁢ D ⁢ a
For a mixture with a sound speed of 500 m/sec in an 18 inch pipe, the cut-off frequency is approximately 600 Hz. Thus, for this example, only one-dimensional acoustic waves propagate below 600 Hz. It is important to note that one-dimensional waves can still propagate above this frequency, but higher order modes may or may not be present.
where A,B are the frequency-based complex amplitudes of the right and left traveling waves, respectively, x is the pressure measurement location along a pipe, ω is frequency (in rad/sec, where ω=2πf), and kr,kl are wave numbers for the right and left travelling waves, respectively, which are defined as: k r ≡ ( ω a mix ⁡ ( ω ) ) ⁢ 1 1 + M x ⁡ ( ω ) ⁢ ⁢ and ⁢ k l ≡ ( ω a mix ⁡ ( ω ) ) ⁢ 1 1 - M x ⁡ ( ω ) ⁢ Eq . ⁢ 2
where amix(ω) is the speed of sound of the mixture in the pipe, ω is frequency (in rad/sec), and Mx(ω) is the axial Mach number of the flow of the mixture within the pipe, where: M x ⁡ ( ω ) ≡ V mix a mix ⁡ ( ω ) Eq . ⁢ 3
Referring to FIG. 1, we have found that using Eq. 4 for P(x,ω) at three axially distributed pressure measurement locations x1, x2, x3 along the pipe 12 leads to an equation for amix as a function of the ratio of frequency based pressure measurements, which allows the coefficients A,B to be eliminated. For optimal results, A and B are substantially constant over the measurement time and substantially no sound (or acoustic energy) is created or destroyed in the measurement section. The acoustic excitation enters the test section only through the ends of the test section 51 and, thus, the speed of sound within the test section 51 can be measured independent of the acoustic environment outside of the test section. In particular, the frequency domain pressure measurements P1(ω), P2(ω), P3(ω) at the three locations x1, x2, x3, respectively, along the pipe 12 using Eq. 1 for right and left traveling waves are as follows:
P 2(ω)=P(x=x 2,ω)=Ae ik r x 2 +Be +ik l x 2 Eq. 6
P 3(ω)=P(x=x 3,ω)=Ae −ik r x 3 +Be +ik 1 x 3 Eq. 7
where, for a given frequency, A and B are arbitrary constants describing the acoustic field between the sensors 14,16,18. Forming the ratio of P1(ω)/P2(ω) from Eqns. 6, 7, and solving for B/A, gives the following expression: R ≡ B A = ⅇ - ⅈ ⁢ ⁢ k r ⁢ x 1 - [ P 1 ⁡ ( ω ) P 2 ⁡ ( ω ) ] ⁢ ⅇ - ⅈ ⁢ ⁢ k r ⁢ x 2 [ P 1 ⁡ ( ω ) P 2 ⁡ ( ω ) ] ⁢ ⅇ - ⅈ ⁢ ⁢ k l ⁢ x 2 - ⅇ - ⅈ ⁢ ⁢ k l ⁢ x 1 Eq . ⁢ 8
Forming the ratio of P1(ω)/P3(ω) from Eqs. 5 and 7 and solving for zero gives: ⅇ - ⅈ ⁢ ⁢ k r ⁢ x 1 + Re ⅈ ⁢ ⁢ k l ⁢ x 1 ⅇ - ⅈ ⁢ ⁢ k r ⁢ x 3 + Re ⅈ ⁢ ⁢ k l ⁢ x 3 - [ P 1 ⁡ ( ω ) P 2 ⁡ ( ω ) ] = 0 Eq . ⁢ 9
where R=B/A is defined by Eq. 8 and kr and kl are related to amix as defined by Eq. 2. Eq. 9 may be solved numerically, for example, by defining an “error” or residual term as the magnitude of the left side of Eq. 9, and iterating to minimize the error term. mag ⁡ [ ⅇ - ⅈ ⁢ ⁢ k r ⁢ x 1 + Re ⅈ ⁢ ⁢ k l ⁢ x 1 ⅇ - ⅈ ⁢ ⁢ k r ⁢ x 3 + Re ⅈ ⁢ ⁢ k l ⁢ x 3 - [ P 1 ⁡ ( ω ) P 2 ⁡ ( ω ) ] ] ≡ Error Eq . ⁢ 10
The data from the array of sensors may be processed in any domain, including the frequency/spatial domain, the temporal/spatial domain, the temporal/wave-number domain or the wave-number/frequency (k−ω) domain. As such, any known array processing technique in any of these or other related domains may be used if desired.
In addition, the present invention incorporates the compliance of the pipe 14 to determine the effective speed of sound of the pipe/PF/air mixture system. The acoustic pressure signals P1(t)−PN(t) are generated within the PF/air mixture of the pipe 14 by a variety of non-discrete sources such as remote machinery, mills, fans 4 (FIG. 2), valves, elbows, as well as the PF/air mixture flow itself. It is this last source, the PF/air mixture 12 flowing within the pipe 14, which is a generic source of acoustic noise that assures a minimum level of acoustics for any PF/air mixture piping systems for which the present invention takes unique advantage. The flow generated acoustics increase with mean flow velocity and the overall noise levels (acoustic pressure levels) are a function of the generating mechanism and the damping mechanism. As such, no external discrete noise source is required within the present invention and thus may operate using passive listening. While the flow meter 10 passively listens to the mixture flow 12, the present invention contemplates adding an acoustic source to inject a desire acoustic wave into the flow to be measured, such as by compressing, vibrating and/or tapping the pipe, to name a few examples.
The length of the array (aperture) ΔX of the pressure sensors (15-18) is at least a significant fraction of the measured wavelength of the acoustic waves being measured. As will be described in greater detail, the acoustic wavelength to be measured is a function of at least the dispersion characteristics of the mixture 12, wherein the dispersion characteristic is a function of at least the size and mass of the particles, and the viscosity of the fluid. The greater the dispersion of the mixture (e.g. the greater the size and mass, and/or the less viscous the fluid), the longer the length of the array is needed. Conversely, the lesser the dispersion of the mixture (e.g. the lesser the size and mass, and/or the more viscous the fluid), the shorter the length of the array is needed.
Further, it is within the scope of the present that the spacing of the pressure sensors may be known or arbitrary, provided the location of the sensors is known. The sensors 15-18 may also be equi-spaced (as shown in FIG. 1) or any non-even or non equi-spaced location, as will be described in greater detail hereinafter. One will appreciate that as few as two sensors are required if certain information is known about the acoustic properties of the PF/air mixture piping system.
As discussed, the flow meter 10 measures the speed of sound of one-dimensional sound waves propagating through the fluid/particle mixture to determine the composition of the mixture. Specifically, the speed of sound propagating through dilute solid/air mixtures can be directly related to the mass fraction particles of the flow. A typical PF fuel delivery system 1 may operate with an air to coal mass ratio of 1.5 to 2.5 with coal density of 1200 to 1400 kg/m3 compared to 1.2 kg/m3 for air at standard atmospheric conditions. Thus, meeting the desired mass ratio results in a very dilute mixture of coal on a volumetric basis, on the order of one part in 1000 by volume.
Assuming that the particles of coal are small enough and the acoustic frequencies and the frequencies of perturbations associated with the acoustics are low enough for the solid particles to exhibit negligible slip (both steady and unsteady), the sound speed can be assumed to be non-dispersive (that is constant with frequency) and the volumetric phase fraction of the mixture could be determined through the Wood equation: ρ mix = ∑ i = 1 N ⁢ ⁢ ϕ i ⁢ ρ i 1 ρ mix ⁢ a mix 2 = ∑ i = 1 N ⁢ ⁢ ϕ i ρ i ⁢ a i 2 ∑ i = 1 N ⁢ ⁢ ϕ i = 1
Including the effect of the compliance introduced by the conduit 12 (in this case a circular pipe of modulus E, radius R and wall thickness t) 1 ρ mix ⁢ a measured 2 = 1 ρ mix ⁢ a mix 2 + σ ⁢ ⁢ where ⁢ ⁢ σ ≡ 2 ⁢ R Et
However, it has been discovered that the physical properties of pulverized coal/air mixtures are generally such that there will be velocity slip at all but very low frequencies (on the order of <1-2 Hz for nominally 50 μm coal particles in air), as shown in FIGS. 7 and 8 which will described in greater detail hereinafter.
Further shown in FIG. 5, the sound speed increases with increasing frequency and asymptotes toward a constant value. The sound speed asymptote at higher frequencies is essentially the sound speed propagating through air only with no influence of the suspended particles. Also, it is apparent that the sound speed of the coal/air mixture has not reached the quasi-steady limit at the lowest frequency for which sound speed was measured. The sound speed is continuing to decrease at the lower frequency limit. An important discovery of the present invention is that the speed at which sound propagates through dilute particles suspended in a continuous fluid is said to be dispersive. As defined herein, the speed at which acoustic waves propagate through dispersive mixtures varies with frequency.
Measuring the sound speed of a mixture 12 at progressively lower and lower frequencies becomes inherently less accurate as the total length of the array of pressure sensors 15-18 (Δxaperature) which define the aperature of the array, becomes small compared to the wavelength of the acoustics. In general, the aperture should be at least a significant fraction of a wavelength of the sound speed of interest. In a particular embodiment sound speed data was recorded with an array of four sensors, spaced at 12 inches, for a total aperture of three feet. At 50 Hz, a 1000 ft/sec sound wave has a wavelength of 20 ft. Thus, the aperture of this particular array (approx. 36 inches) spanned only 3/20ths of a wavelength, and the array's ability to accurately resolve sound speeds below this was clearly impaired. It is an important aspect of the present invention that the ability to resolve sound speed at low frequencies is directly related to aperture of the array. Consequently longer arrays are used to resolve sound speeds at lower frequencies. As shown in FIG. 6, the standard deviation associated with determining the speed of sound in air is shown as a function of frequency for three arrays of varying aperture, namely 1.5 ft, 3 ft and 10 ft.
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. The drag force on the particles by the continuous fluid is modeled by a force proportional to the difference between the local fluid velocity and that of the fluid particles and is balanced by inertial force: F drag = K ⁡ ( U f - U p ) = ρ p ⁢ v p ⁢ ∂ U p ∂ t
The effect of the force on the continuous fluid phase by the fluid particles is modeled as a force term in the axial momentum equation. The axial momentum equation for a control volume of area A and length Δx is given by: P x - P x + Δ ⁢ ⁢ x - K ⁡ ( U f - U p ) ⁢ { ϕ p ⁢ Δ ⁢ ⁢ x v p } = ∂ ∂ t ⁢ ( ρ f ⁢ U f ⁢ Δ ⁢ ⁢ x )
The particle drag force is given by: F drag = K ⁡ ( U f - U p ) = C d ⁢ A p ⁢ 1 2 ⁢ ρ f ⁡ ( U f - U p ) 2
Using Stokes law for drag on a sphere at low Reynold's number gives the drag coefficient as: C d = 24 Re = 24 ⁢ ⁢ μ ρ f ⁡ ( U f - U p ) ⁢ D p
Using the above relations and 1-dimensional acoustic modeling techniques, the following relation can be derived for the dispersive behavior of an idealized fluid particle mixture. a mix ⁡ ( ω ) = a f ⁢ 1 1 + φ p ⁢ ρ p ρ f ⁡ ( 1 + ω 2 ⁢ ρ p 2 ⁢ v p 2 K 2 )
FIGS. 7 and 8 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. As best shown in FIG. 8, the speed of sound propagating through the mixture is substantially the same regardless of the particle size in the low frequency range. In the low frequency range the mixture exhibits a quasi-steady model or a no slip (non-dispersive) characteristic. As shown in the intermediate frequency range, the speed of sound propagating through the mixture is dependent on the size of the particle, and thus exhibits dispersive characteristics. For the high frequency range, the speed of sound propagating through the mixture is unaffected by the particles. In other words, the speed of sound in the higher frequency range propagating through the mixture is substantially equally to the speed of sound propagating through the just the fluid with the particles having for effect, which will be described in greater detail hereinafter.
Knowing the effect of dispersion on the speed of sound through a mixture as described herein before, one will appreciate that to determine the concentration of the mixture (e.g., air/fuel ratio), the frequency of the measured acoustic wave is within the low frequency range that exhibits little or no slip (non-dispersive/quasi-steady state), as best shown in FIG. 7. Further, one will appreciate that to determine the particle size within the mixture 12, the frequency of the measured acoustic wave is within the intermediate frequency range that exhibits dispersive characteristics, as shown in FIG. 8.
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.
The quasi-steady (no-slip condition) sound speed is given by the low frequency limit of the above relation, where AFR is air/fuel ratio: a mix ⁡ ( ω → 0 ) = a f * 1 1 + φ p ⁢ ρ p ρ f ≅ a f * 1 1 + 1 AFR
Using the model described above, which yields the equation shown below, and experimentally determined sound speed as function of frequency, the present invention includes an optimization procedure to simultaneously determine particles size and AFR in coal/air mixtures a mix ⁡ ( ω ) = a f ⁢ 1 1 + φ p ⁢ ρ p ρ f ⁡ ( 1 + ω 2 ⁢ ρ p 2 ⁢ v p 2 K 2 )
Referring to FIG. 10 there is shown an optimization procedure in accordance with the present invention in which the free parameters of an analytical model are optimized to minimize an error function. For illustration purposes, the error function utilized is the sum of the differences of the sound speeds between an analytical model and the experimentally determined sound speed as a function of frequency: err = ∑ f = f low f = f high ⁢ ( a ⁡ ( f ) model - a ⁡ ( f ) measured ) 2
As suggested herein before, the length of the array of pressure sensors should be at least a significant fraction of a wavelength of the sound speed of interest. The significant fraction of the wavelength may be at least 30 percent of the wavelength, however, this fraction may be less than 30 percent depending on the desired accuracy of the measurement, the measured wavelength and/or the strength of the acoustic wave (e.g., low signal/noise ratio). Therefore, the length of the array is dependent on the frequency of the sound speed of interest (frequency being inversely proportional to wavelength), wherein the frequency of the sound speed of interest is dependent on the measurement to be determined (e.g., air/particle ratio and particle size) and the dispersion characteristics of the mixture. For example, the low frequency range of the plot of the speed of sound (quasi-steady state) for measuring the concentration of the mixture (e.g., air/particle ratio), shown in FIG. 7, is lower as dispersion of the mixture increases. As described herein before, the dispersion characteristics of the mixture is dependent on the size of the particles among other factors. As the particle size increases, the dispersion becomes greater, and as the particle size decreases, the dispersion becomes lower. Consequently, the length of the array is a function of the size of the particle within the mixture, and therefore, as best shown in FIG. 8, the transition point (low frequency cut-off) between the low frequency range and the intermediate frequency decreases in frequency as the particle size increases.
For example when measuring the concentration of the mixture, as the size of the particles increase, the low frequency cut-off decreases and thus, the acoustic wavelength of interest increases to thereby necessitate the length of the array to be longer. Conversely, as the size of the particles decrease, the low frequency cut-off increase and thus, the acoustic wavelength of interest decreases to thereby necessitate the length of the array to be shorter. Simply stated, the larger the particle, the longer the array and vice versa. The same comparison is true when determining the size of the particles within the mixture. However, for optimal performance of the flow meter, the measurement of the concentration of the mixture may require a longer array than the measurement of the particle size because measurement of the concentration is at a lower frequency (longer wavelength) than the intermediate frequency (shorter wavelength) of the particle size.
The lowest practical measurable frequency range is approximately 10-25 Hz, therefore the measurement of large particle may not be possible to measure the quasi-steady model, which may in some instances be less than 10 Hz (i.e., cut-off frequency less than 10 Hz). Under these circumstances, the frequency of the speed of sound of interest is above the cut-off frequency. However, the measured speed of sound is curve fit to a dispersion model of the mixture by varying the size of the particle and the composition of the mixture to determine the particle size and/or concentration of the mixture, as shown in FIG. 10 that will be described in greater detail hereinafter.
While the length of the array is dependent on the particle size, the length may also be dependent on other parameters that define the amount of dispersion, such as mass of the particles and the viscosity of the fluid within the mixture.
Another factor that defines (or effects) the length of the array of pressure sensors 15-18 includes the signal strength of the acoustic wave received by the processor. As the signal strength improves or is greater, the shorter the length of the array must be. The signal strength is dependent on a number of factors, such as the strength of the acoustic wave itself, the signal/noise ratio of the sensors, the matching of the sensors and others.
The spacing may be equi-spaced as shown in FIG. 1, however the flow meter 10 of the present invention contemplates that the sensors may have non-equal or uneven spacing therebetween. The sensors may be spaced any desired distance, provided the location or position of the sensors are known. For ported pressure sensors, the minimum spacing is limited by mechanical limitations of the sensors. For strain-based sensors, such as PVDF bands described hereinafter, the compliance of the pipe limits the closeness of the spacings. For example, the more rigid the pipe, the greater the spacing of the sensors must be, and conversely, the more compliant the pipe, the closer the sensors may be spaced.
The spacing of the pressure sensors may also be defined by the number of sensors disposed within an array of a given length. The more sensors disposed within the array of a given length, the closer the spacing. The number of sensors disposed within an array is dependent on the required or desired accuracy of the flow meter 10. The greater the number of sensors in the array, a more precise measurement of the acoustic pressure field can be achieved. In other words, a greater number of samples or measurements of the acoustic pressure wave over a given length of the array (or wavelength) provided the sensors enable greater resolution in the measurement of the acoustic wave to be measured or characterized.
where aR=velocity of a right traveling acoustic wave relative to a stationary observer (i.e. the pipe 14), aL=velocity of a left traveling acoustic wave apparent to a stationary observer, amix=fluid speed of sound (if the fluid were not flowing) and u=the mean flow velocity (assumed to be flowing from left to right in this instance). Combining these two equations yields an equation for the mean velocity, u = a R - a L 2
ω=kα mix
The k-w plot shown in FIG. 13 illustrates the fundamental principle behind sonar based flow measure, namely that axial arrays of pressure sensors can be used in conjunction with sonar processing techniques to determine the speed at which naturally occurring turbulent eddies convect within a pipe. FIG. 13 shows a k-ω plot generated for acoustic sound field of a coal/air mixture flowing through a pipe. Two acoustic ridges are clearly evident. Each of the slopes of the two depicted acoustic ridges respectively defines the speed of sound traveling with and against the mean flow, respectively. A parametric optimization method was used to determine the “best” line representing the slope of the acoustic ridge.
Further, FIG. 13 illustrates the ability of the present invention to determine the velocity of a fluid moving in a pipe. FIG. 14 shows a wave number-frequency plot (k-w plot) of unsteady pressure. The contours represent the relative signal power at all combinations of frequency and wave number. The highest power “ridges” represent the acoustic wave with slope of the ridges equal to the propagation speed. The dashed lines show the best-fit two-variable maximization of the power with the two variables being sound speed and flow velocity. The right-side ridge represents the acoustic wave traveling in the same direction as the bulk flow and therefore its slope is steeper than the left-side ridge that represents the acoustic wave traveling in the opposite direction of the bulk flow. This indicates that the acoustic wave traveling in the same direction of the flow is traveling faster than the acoustic wave traveling in the opposite direction of the bulk flow relative to the stationary sensors located on the pipe.
While the present invention illustrates that the array of pressure sensors comprises a plurality of like sensors, the present invention contemplates that any combination of different or similar pressure sensors may be used within an array.
While the present invention is capable of measuring solid particles suspended in a fluid, one will appreciate that other multi-phase mixtures or flows may be measured using an array of sensors, such as steam flow. It is further recognize the that effects of dispersion on large solid particles in a fluid would be similar to large droplets of a liquid dispersed in a gas or air, and thus similar considerations when measuring the steam quality and droplet size should be addressed.
9. The apparatus of claim 1 wherein at least one of said pressure sensors measures a circumference-averaged pressure at said axial location of said sensor.
10. The apparatus of claim 9 wherein at least one of said pressure sensors includes a piezoelectric sheet material.
11. The apparatus of claim 1 wherein the piezoelectric sheet material is polarized fluoropolymer, polyvinylidene fluoride (PVDF).
12. The apparatus of claim 1 wherein at least one of said pressure sensors measures strain on the pipe.
13. The apparatus of claim 3 wherein the frequency based sound speed is determined utilizing a dispersion model to determine the at least one parameter of the mixture.
14. The apparatus of claim 3 wherein the array of acoustic sensors are spaced sufficiently such that the entire length of the array is at least a significant fraction of the measured wavelength of the acoustic waves being measured.
15. A method for measuring at least one parameter of a particle/fluid mixture in a pipe, said method comprising:
25. The method of claim 24 wherein the measured unsteady pressures are acoustic pressures to provide a signal indicative of an acoustic noise within the pipe.
26. The method of claim 25, wherein the calculating the at least one parameter uses an acoustic pressure to calculate a speed of sound propagating in the pipe.
27. The method of claim 26 wherein the calculating the at least one parameter uses an acoustic pressure to calculate a speed at which sound propagates along said spatial array.
28. The method of claim 26 wherein the calculating the at least one parameter uses an acoustic pressure to calculate a frequency based signal for each of said acoustic pressure signals.
29. The method of claim 27 wherein said acoustic pressure signals each comprise a frequency based signal and wherein said signal processor comprises logic which calculates a ratio of two of said frequency based signals.
30. The method of claim 24 wherein measuring the unsteady pressures is at at least three of said sensors.
31. The method of claim 26 wherein the calculating the at least one parameter uses an acoustic pressure to calculate a fluid composition of the mixture in the pipe.
32. The method of claim 24 wherein measuring unsteady pressure includes measuring a circumference-averaged pressure at at least an axial location of a sensor.
33. The method of claim 32 wherein measuring unsteady pressures uses at least one of said pressure sensors includes a piezoelectric sheet material.
34. The method of claim 24 wherein the piezoelectric sheet material is polarized fluoropolymer, polyvinylidene fluoride (PVDF).
34. The method of claim 24 wherein at least one of said pressure sensors measures strain on the pipe.
35. The method of claim 26 wherein the frequency based sound speed is determined utilizing a dispersion model to determine the at least one parameter of the mixture.
36. The method of claim 26 wherein the array of acoustic sensors are spaced sufficiently such that the entire length of the array is at least a significant fraction of the measured wavelength of the acoustic waves being measured.
US10512401 2002-01-23 2003-04-24 Apparatus and method for measuring parameters of a mixture having solid particles suspended in a fluid flowing in a pipe Active 2023-03-09 US7275421B2 (en)
US10/349716 2003-01-23
US10/376427 2003-02-26
US20050171710A1 true true US20050171710A1 (en) 2005-08-04
US7275421B2 US7275421B2 (en) 2007-10-02
ID=37447065
US10512401 Active 2023-03-09 US7275421B2 (en) 2002-01-23 2003-04-24 Apparatus and method for measuring parameters of a mixture having solid particles suspended in a fluid flowing in a pipe
US (1) US7275421B2 (en)
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