Patent Publication Number: US-7587948-B2

Title: Flow rate measurement for industrial sensing applications using unsteady pressures

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 11/124,753, filed May 9, 2005, now U.S. Pat. No. 7,261,002, which is a divisional patent application of U.S. patent application Ser. No. 10/007,736, filed Nov. 8, 2001, now U.S. Pat. No. 6,889,562, which is a continuation-in-part of U.S. patent application Ser. No. 09/346,607, filed Jul. 2, 1999, now abandoned, each of which are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     This invention relates to the measurement of flow rate of a fluid and more particularly to measuring flow rate using unsteady pressure measurements for use in industrial sensing applications. 
     BACKGROUND ART 
     An industrial process sensor is typically a transducer that responds to a measurand with a sensing element and converts a variable to a standardized transmission signal, e.g., an electrical or optical signal, that is a function of the measurand. Industrial process sensors utilize transducers that include flow measurements of an industrial process such as slurries, liquids, vapors and gasses in refinery, chemical, paper, pulp, petroleum, gas, pharmaceutical, food, mining, minerals and other fluid processing plants. Industrial process sensors are often placed in or near the process fluids, or in field applications. Often, these field applications are subject to harsh and varying environmental conditions that provide challenges for designers of such sensors. Flow measurement is one of the largest segments of the industrial sensing and instrumentation market. Industries in which flow measurement is prevalent includes petroleum, chemical, pulp, paper, food, and mining and minerals. 
     In many industries it is desirable to measure the flow rate of a multiphase fluid. In many industries such as refinery, chemical, paper, pulp, petroleum, gas, pharmaceutical, food, mining, minerals or comparable industries, for example, it is desirable to measure the flow rate of multiphase fluids, especially fluids having three phases, such as a constituent, water and gas. It is known also to measure the flow rate of certain fluids (one or more liquids and/or gases) in a pipe using cross-correlation flow meters. Such meters measure an element of the flow that moves or convects with (or is related to) the fluid flow (or a group of fluid particles). The meter measures this element at two locations separated by a known distance along the flow path and then calculates the time for such element to move between the two locations. The time delay is determined by a cross-correlation of the two measured signals. A velocity is then determined by the distance between the measurements divided by the time delay. The flow velocity is then related to the flow rate by calibration. 
     One such cross-correlation meter that measures flow rate in a multiphase flow is described in U.S. Pat. No. 5,591,922, entitled “Method and Apparatus for Measuring Multiphase Flow”, to Segeral et al, issued Jan. 7, 1997. In that case, a pair of venturis is located a predetermined distance apart which induce a change in flow speed through the venturi and a resulting pressure difference (or delta-P) across each venturi, which are measured. The delta-P pressure signals measured at each venturi are cross-correlated to determine the time delay which is indicative of the total volume flow rate. However, such a technique requires a change in the flow properties (e.g., flow velocity or density) at the two measurement points to make the measurement. Also, the delta-P is generated with an area contraction or constriction, and is not a naturally occurring observable characteristic of the fluid. 
     Other flowmeters of the prior art include turbine, vortex, electromagnetic and venturi and all have drawbacks and deficiencies solved by the flowmeter of the present invention. For instance all require a high level of maintenance and need to be removed from the process line wherein the operators need to shut down the manufacturing process. The flowmeters of the prior art require electrical wiring and power that requires enormous cost, safety issues and sometimes miles of wires. Many of the prior art meters use moving parts, such as turbines or diaphragms. Also, prior art flowmeters such as vortex, turbine and venturi types use obstructions in the flow path that disrupt the flow to varying degrees. In addition sediment, gumming, plugging, corrosion, and erosion of certain features of the sensing region of the meter can affect the accuracy of the flowmeter. 
     In particular, electromagnetic flowmeters are prone to problems caused by poor process grounding, and specialized sleeves that are prone to damage. Process noise is a problem and can be caused by slurries, high consistency pulp stock, or upstream chemical additions. Such process noise can lead to inaccurate flow measurement in these types of prior art flowmeters. In addition, process liquids must have a minimum conductivity that all but eliminates these meters from uses where the fluid is a hydrocarbon. The accuracy and sensitivity can be affected by the length of cabling for remote transmitters and can be adversely influenced by proximity to other electrical devices 
     Another flow meter of the prior art includes a friction flowmeter such as that set forth in U.S. Pat. No. 6,253,624, titled “Friction Flowmeter” wherein a transducer determines the pressure drop of a fluid flowing along a pipe. The device determines the flow rate of the fluid based on the pressure drop for a given friction factor of the inside surface of the pipe. Such a device requires external knowledge of various parameters of the fluid, such as density. In addition, with certain applications the surface of the pipe, and the friction factor thereby, would change over time and decrease the accuracy of the meter in predicting fluid flow rates. 
     Typical electronic, or other, transducers of the prior art often cannot be placed in industrial process environments due to sensitivity to electromagnetic interference, radiation, heat, corrosion, fire, explosion or other environmental factors. It is for these reasons that fiber optic based sensors are being incorporated into industrial process control environments in increasing number. 
     SUMMARY OF THE INVENTION 
     Objects of the present invention include provision of a system for measuring the flow rate (or velocity) of fluid flow in pipes in industrial fluid processes. 
     According to the present invention, an apparatus for use in an industrial process for measuring a velocity of a fluid moving in a pipe includes a probe portion disposed in said fluid flow. The probe portion includes a tube and an array of at least two sensors disposed at different axial locations along the tube. Each of the sensors measures inhomogeneous pressure disturbances at each of the respective axial locations. Each of the sensors further provides a pressure signal. The apparatus also includes a signal processor, responsive to the pressure signals, to provide a signal indicative of the velocity of the fluid in the pipe. 
     According further to the present invention, the sensors filter out wavelengths above a predetermined wavelength. Still further according to the present invention, at least one of the pressure sensors comprises a strain gage disposed on a surface of the pipe. Further according to the present invention, the strain gage comprises a fiber optic strain gage. 
     Still further according to the present invention, the signal processor comprises logic which calculates a cross-correlation between first and second inhomogeneous pressure signals and provides a time delay signal indicative of the time it takes for the vortical pressure field to move from a first location to a second location. Further according to the present invention, the velocity signal is indicative of the velocity of the fluid moving in the pipe. 
     The present invention provides a significant improvement over the prior art by providing a measurement of the average flow rate of fluid flow in a pipe or other conduit (where a fluid is defined as one or more liquids and/or gases) without requiring a flow restriction in the pipe or any other change in the flow velocity of the fluid. 
     The present invention determines a convection velocity by measuring unsteady (or dynamic or ac) pressures and extracting the pressure signal indicative of a vortical pressure (or flow) field (or perturbation) which convects at or near the average velocity of the fluid. The vortical pressure field is then used to determine the convection velocity by cross-correlation techniques, such convection velocity being proportional (or approximately equal to) the flow rate of the fluid. If needed, the flow rate of the fluid may then be determined by calibrating the convection velocity to the flow rate. 
     The invention may also be used to measure the velocity of any inhomogeneous flow field, such as gas bubbles, gas slugs, particles, or chunks of material, and its associated pressure field that propagates in a flow provided the sensors have a separation within the acceptable coherence length of the flow field to be measured and the sensor spacing within each spatial filter is longer than a characteristic axial length of the flow field. Also, the invention may be used to detect different flow rates within the same mixture (e.g., the flow rate of a vortical pressure field as well as other inhomogeneous pressure fields). 
     Also, the invention may be used with any combination of liquids and/or gases and may include particles. The invention will also work in any other environment or applications or any other fluids (one or more liquids and/or gases) or mixtures. The invention will work with any pipe or tube or with any conduit that carries fluid. Also, the invention has no inherent flow range limitations and, as such, can measure very low flow rates and has no maximum flow rate limit. The invention will also work if the fluid is flowing in either direction in the pipe. Further, the invention may be used directly on a pipe or on a tube inserted into a flowing fluid. 
     Also, the invention may be combined with a controller and other devices and used in an industrial process control system. 
     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. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic block diagram of a velocity measurement system, in accordance with the present invention. 
         FIG. 2  is a side view of a pipe having two sensors that measure a parameter that convects with the flow in the pipe. 
         FIG. 3  is a graph of two curves, one from each of the two sensors of  FIG. 2 . 
         FIG. 4  is a graph of a cross-correlation between the two curves of  FIG. 3 . 
         FIG. 5  is a graph of power spectral density plotted against frequency for an unsteady acoustic pressure signal P acoustic  and unsteady vortical pressure signal P vortical , in accordance with the present invention. 
         FIG. 6  is a graph of wavelength versus frequency for unsteady acoustic pressures P acoustic  nd unsteady vortical pressures P vortical , in accordance with the present invention. 
         FIG. 7  is a graph of power spectrum of two unsteady pressures and the difference between the two pressures, in accordance with the present invention. 
         FIG. 8  is a graph of a cross-correlation between two of the curves of  FIG. 7 , in accordance with the present invention. 
         FIG. 9  is a graph of measured velocity against reference velocity, in accordance with the present invention. 
         FIG. 10  is a side view of a pipe having three pairs of unsteady pressure sensors spaced axially along the pipe, in accordance with the present invention. 
         FIG. 11  is a graph of a cross correlation coefficient versus time delay for the three pairs of sensors, in accordance with the present invention. 
         FIG. 12  is a graph of measured flow rate against reference flow rate for various different mixtures, in accordance with the present invention. 
         FIG. 13  is an end view of a pipe showing pressure inside and outside the pipe, in accordance with the present invention. 
         FIG. 14  is a side view of a pipe having optical fiber wrapped around the pipe at each unsteady pressure measurement location and a pair of Bragg gratings around each optical wrap, in accordance with the present invention. 
         FIG. 15  is a side view of a pipe having optical fiber wrapped around the pipe at each unsteady pressure measurement location with a single Bragg grating between each pair of optical wraps, in accordance with the present invention. 
         FIG. 16  is a side view of a pipe having optical fiber wrapped around the pipe at each unsteady pressure measurement location without Bragg gratings around each of the wraps, in accordance with the present invention. 
         FIG. 17  is an alternative geometry of an optical wrap of  FIGS. 14 ,  15  and  16 , of a radiator tube geometry, in accordance with the present invention. 
         FIG. 18  is an alternative geometry of an optical wrap of  FIGS. 14 ,  15  and  16 , of a race track geometry, in accordance with the present invention. 
         FIG. 19  is a side view of a pipe having a pair of gratings at each axial sensing location, in accordance with the present invention. 
         FIG. 20  is a side view of a pipe having a single grating at each axial sensing location, in accordance with the present invention. 
         FIG. 21  is a side view of a pipe having two pairs of pressure sensors where the sensors in each pair are located across the pipe from each other, in accordance with the present invention. 
         FIG. 22  is an end view of a pipe showing a pair of pressure sensors located at various circumferential spacings from each other, in accordance with the present invention. 
         FIG. 23  is a side view of a pipe having two pairs of pressure sensors where the sensors in each pair are located transversely across the pipe and spaced axially along the pipe from each other, in accordance with the present invention. 
         FIG. 24  is a side view of a pipe having a set of three pressure sensors that form a spatial filter, in accordance with the present invention. 
         FIG. 25  is a side view of a pipe having an inner tube with axially distributed optical fiber wraps for unsteady pressure sensors, in accordance with the present invention. 
         FIG. 26  is a side view of a pipe having an inner tube with axially distributed unsteady pressure sensors located along the tube, in accordance with the present invention. 
         FIG. 27  is a side view of a pipe having an inner tube with four axially distributed optical fiber wrapped hydrophones located within the tube, in accordance with the present invention. 
         FIG. 28  is an end view of a pipe showing a pair of pressure sensors spaced apart from each other within the pipe, in accordance with the present invention. 
         FIG. 29  is a side view of a pipe having a pair of unsteady pressure sensors spaced axially within the pipe, in accordance with the present invention. 
         FIG. 30  is a side view of a pipe having a pair of unsteady pressure sensors spaced transversely within the pipe, in accordance with the present invention. 
         FIG. 31  is a side view of a pipe having a pair of unsteady pressure sensors axially and radially spaced within the pipe, in accordance with the present invention. 
         FIG. 32  is a side view of a pipe having a set of three pressure sensors that make up two spatial filters, in accordance with the present invention. 
         FIG. 33  is a schematic drawing of a flow meter in an industrial process control system, in accordance with the present invention. 
         FIG. 34  is a plan view of alternate geometries for electronic strain gages in accordance with the present invention. 
         FIG. 35  is a side view of a pipe having a spatial filter disposed thereon comprised of electronic strain gages in accordance with the present invention. 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     Referring to  FIG. 1 , a velocity and flow measurement system includes a sensing section  10  along a pipe  12  and a velocity logic section  40 . The pipe (or conduit)  12  has two measurement regions  14 ,  16  located a distance ΔX apart along the pipe  12 . At the first measurement region  14  are two unsteady (or dynamic or ac) pressure sensors  18 ,  20 , located a distance X 1  apart, capable of measuring the unsteady pressure in the pipe  12 , and at the second measurement region  16 , are two other unsteady pressure sensors  22 ,  24 , located a distance X 2  apart, capable of measuring the unsteady pressure in the pipe  12 . Each pair of pressure sensors  18 ,  20  and  22 ,  24  act as spatial filters to remove certain acoustic signals from the unsteady pressure signals, and the distances X 1 , X 2  are determined by the desired filtering characteristic for each spatial filter, as discussed hereinafter. 
     The flow measurement system  10  of the present invention measures velocities associated with unsteady flow fields and/or pressure disturbances represented by  15  associated therewith relating to turbulent eddies (or vortical flow fields), inhomogeneities in the flow (such as bubbles, slugs, and the like), or any other properties of the flow, fluid, or pressure, having time varying or stochastic properties that are manifested at least in part in the form of unsteady pressures. The vortical flow fields are generated within the fluid of the pipe  12  by a variety of non-discrete sources such as remote machinery, pumps, valves, elbows, as well as the fluid flow itself. It is this last source, the fluid flowing within the pipe  12 , that is a generic source of vertical flow fields primarily caused by the shear forces between the fluid and the wall of the pipe that assures a minimum level of disturbances for any fluid piping systems for which the present invention takes unique advantage. The flow generated vortical flow fields generally increase with mean flow velocity and do not occur at any predeterminable frequency. As such, no external discrete vortex generating source is required within the present invention and thus may operate using passive detection. It is within the scope of the present that the pressure sensor spacing may be known or arbitrary and that as few as two sensors are required if certain information is known about the acoustic properties of the system as will be more fully described herein below. 
     The vortical flow fields  15  are, in general, comprised of pressure disturbances having a wide variation in length scales and which have a variety of coherence length scales such as that described in the reference “Sound and Sources of Sound”, A. P. Dowling et al, Halsted Press, 1983. Certain of these vortical flow fields convect at or near/or related to the mean velocity of at least one of the fluids within a mixture flowing in a pipe. More specifically, the vortices convect in a predictable manner with reference to the fluids. The vortical pressure disturbances  15  that contain information regarding convection velocity have temporal and spatial length scales as well as coherence length scales that differ from other disturbances in the flow. The present invention utilizes these properties to preferentially select disturbances of a desired axial length scale and coherence length scale as will be more fully described hereinafter. For illustrative purposes, the terms vortical flow field and vertical pressure field will be used to describe the above-described group of unsteady pressure fields having temporal and spatial length and coherence scales described herein. 
     The pressures P 1 , P 2 , P 3 , P 4  may be measured through holes in the pipe  12  ported to external pressure sensors or by other techniques discussed hereinafter. The pressure sensors  18 ,  20 ,  22 ,  24  provide time-based pressure signals P 1 (t), P 2 (t), P 3 (t), P 4 (t) on lines  30 ,  32 ,  34 ,  36 , respectively, to Velocity Logic  40  which provides a convection velocity signal U c (t) on a line  42  which is related to an average flow rate U f (t) of the fluid flowing in the pipe  12  (where fluid may comprise one or more liquids and/or gases; where the gas(es) may be dissolved in the liquid or in free gas form, such as bubbles, slugs, sand, particulates, slurry, etc.), and wherein the fluid may include non-liquid elements therein as will be discussed more hereinafter. 
     Also, some or all of the functions within the Velocity Logic  40  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. 
     In particular, in the Velocity Logic  40 , the pressure signal P 1 (t) on the line  30  is provided to a positive input of a summer  44  and the pressure signal P 2 (t) on the line  32  is provided to a negative input of the summer  44 . The output of the summer  44  is provided on a line  45  indicative of the difference between the two pressure signals P 1 , P 2  (e.g., P 1 −P 2 =P as1 ). 
     The pressure sensors  18 ,  20  together with the summer  44  create a spatial filter  33 . The line  45  is fed to bandpass filter  46 , which passes a predetermined passband of frequencies and attenuates frequencies outside the passband. In accordance with the present invention, the passband of the filter  46  is set to filter out (or attenuate) the do portion and the high frequency portion of the input signals and to pass the frequencies therebetween. For example, in a particular embodiment passband filter  6  is set to pass frequencies from about 1 Hz to about 100 Hz, for a 3 inch ID pipe flowing water at 10 ft/sec. Other passbands may be used in other embodiments, if desired. Passband filter  46  provides a filtered signal P asf   1  on a line  48  to Cross-Correlation Logic  50 , described hereinafter. 
     The pressure signal P 3 (t) on the line  34  is provided to a positive input of a summer  54  and the pressure signal P 4 (t) on the line  36  is provided to a negative input of the summer  54 . The pressure sensors  22 ,  24  together with the summer  54  create a spatial filter  35 . The output of the summer  54  is provided on a line  55  indicative of the difference between the two pressure signals P 3 , P 4  (e.g., P 3 −P 4 =P as2 ). The line  55  is fed to a bandpass filter  56 , similar to the bandpass filter  46  discussed hereinbefore, which passes frequencies within the passband and attenuates frequencies outside the passband. The filter  56  provides a filtered signal P asf   2  on a line  58  to the Cross-Correlation Logic  50 . The signs on the summers  44 ,  54  may be swapped if desired, provided the signs of both summers  44 ,  54  are swapped together. In addition, the pressure signals P 1 , P 2 , P 3 , P 4  may be scaled prior to presentation to the summers  44 ,  54 . 
     The Cross-Correlation Logic  50  calculates a known time domain cross-correlation between the signals P asf   1  and P asf   2  on the lines  48 ,  58 , respectively, and provides an output signal on a line  60  indicative of the time delay τ it takes for an vortical flow field  15  (or vortex, stochastic, or vortical structure, field, disturbance or perturbation within the flow) to propagate from one sensing region  14  to the other sensing region  16 . Such vortical flow disturbances, as is known, are coherent dynamic conditions that can occur in the flow which substantially decay (by a predetermined amount) over a predetermined distance (or coherence length) and convect (or flow) at or near the average velocity of the fluid flow. As described above, the vortical flow field  15  also has a stochastic or vortical pressure disturbance associated with it. In general, the vortical flow disturbances  15  are distributed throughout the flow, particularly in high shear regions, such as boundary layers (e.g., along the inner wall of the pipe  12 ) and are shown herein as discrete vortical flow fields  15 . Because the vortical flow fields  15  (and the associated pressure disturbance) convect at or near the mean flow velocity, the propagation time delay r is related to the velocity of the flow by the distance ΔX between the measurement regions  14 ,  16 , as discussed hereinafter. 
     Although pressure disturbances associated with vortical flow fields  15  occur naturally in most flow conditions, an optional circumferential groove  70  may be used in the inner diameter of the pipe  12  to help generate unsteady flow fields in the form of vertices into the flow. However, the groove  70  is not required for the present invention to operate, due to vortex generation which naturally occurs along the pipe inner wall, as discussed hereinbefore. Instead of a single circumferential groove  70  a plurality of axially spaced circumferential grooves may be used. The dimensions and geometry of the groove(s)  70  may be set based on the expected flow conditions and other factors. The axial cross-sectional shape of the groove  70  may be rectangular, square, triangular, circular, oval, star, or other shapes. Other techniques may be used as vortex generators if desired including those that may protrude within the inner diameter of pipe  12 . 
     A spacing signal ΔX on a line  62  indicative of the distance ΔX between the sensing regions  14 ,  16  is divided by the time delay signal T on the line  60  by a divider  64  which provides an output signal on the line  42  indicative of the convection velocity U c (t) of the fluid flowing in the pipe  12 , which is related to (or proportional to or approximately equal to) the average (or mean) flow velocity U f (t) of the fluid, as defined below:
 
 U   c ( t )=Δ X/τ∝U   f ( t )  Eq. 1
 
     The convection velocity U c (t) may then be calibrated to more precisely determine the mean velocity U f (t) if desired. The result of such calibration may require multiplying the value of the convection velocity U c (t) by a calibration constant (gain) and/or adding a calibration offset to obtain the mean flow velocity U f (t) with the desired accuracy. Other calibration may be used if desired. For some applications, such calibration may not be required to meet the desired accuracy. The velocities U f (t), U c (t) may be converted to volumetric flow rate by multiplying the velocity by the cross-sectional area of the pipe. 
     Referring to  FIGS. 2 ,  3  and  4 , as is known, cross-correlation may be used to determine the time delay τ between two signals y 1 (t), y 2 (t) separated by a known distance ΔX, that are indicative of quantities  80  that convect with the flow (e.g., density perturbations, concentration perturbations, temperature perturbations, vortical pressure disturbances, and other quantities). In  FIG. 3 , the signal y 2 (t) lags behind the signal y 1 (t) by 0.15 seconds. If a time domain cross-correlation is taken between the two signals y 1 (t), y 2 (t), the result is shown in  FIG. 4  as a curve  84 . The highest peak  86  of the curve  84  shows the best fit for the time lag τ between the two signals y 1 (t), y 2 (t) is at 0.15 seconds which matches the reference time delay shown in  FIG. 3 . 
     Referring to  FIG. 1 , as discussed hereinbefore, since pressure disturbances associated within the vortical flow field  15  convect (or flow) at or near the average velocity of the fluid flowing in the pipe  12 , the vortical pressure disturbances observed at the downstream location  16  are substantially a time lagged version of the vortical pressure disturbances observed at the upstream location  14 . However, the total vortical pressure perturbations or disturbances in a pipe may be expressed as being comprised of vortical pressure disturbances (P vortical ), acoustic pressure disturbances (P acoustic ) and other types of pressure disturbances (P other ) as shown below expressed in terms of axial position along the pipe at any point in time:
 
 P ( x,t )= P   vortical ( x,t )+ P   acoustic ( x,t )+ P   other ( x,t )  Eq. 2
 
     As a result, the unsteady pressure disturbances P vortical  can be masked by the acoustic pressure disturbances P acoustic  and the other types of pressure disturbances P other . In particular, the presence of the acoustic pressure disturbances that propagate both upstream and downstream at the speed of sound in the fluid (sonic velocity) can prohibit the direct measurement of velocity from cross-correlation of direct vortical pressure measurements. 
     The present invention uses temporal and spatial filtering to precondition the pressure signals to effectively filter out the acoustic pressure disturbances P acoustic  and other long wavelength (compared to the sensor spacing) pressure disturbances in the pipe  12  at the two sensing regions  14 ,  16  and retain a substantial portion of the vortical pressure disturbances P vortical  associated with the vortical flow field  15  and any other short wavelength (compared to the sensor spacing) low frequency pressure disturbances P other . In accordance with the present invention, if the low frequency pressure disturbances P other  are small, they will not substantially impair the measurement accuracy of P vortical . 
     The P vortical  dominated signals from the two regions  14 ,  16  are then cross-correlated to determine the time delay τ between the two sensing locations  14 ,  16 . More specifically, at the sensing region  14 , the difference between the two pressure sensors  18 ,  20  creates a spatial filter  33  that effectively filters out (or attenuates) acoustic disturbances for which the wavelength λ of the acoustic waves propagating along the fluid is long (e.g., ten-to-one) compared to the spacing X 1  between the sensors. Other wavelength to sensor spacing ratios may be used to characterize the filtering, provided the wavelength to sensor spacing ratio is sufficient to satisfy the two-to-one spatial aliasing Nyquist criteria. 
     Thus, if the pressure sensors P 1 , P 2  have an axial spacing X 1 , and assuming that the spatial filter  33  will attenuate acoustic wavelengths longer than about 10 times the sensor spacing X 1 , the smallest acoustic wavelength λ min  that is attenuated would be:
 
λ min =10 ( X   1 )  Eq. 3
 
     One dimensional acoustic disturbances are also governed by the following known inverse wavelength-frequency relation:
 
λ= a/f  or  f=a/λ   Eq. 4
 
where a is the speed of sound of the fluid, f is the frequency of the acoustic disturbance, and λ is the wavelength of the acoustic disturbance.
 
     Using Eq. 4, such a spatial filter would filter out frequencies below about:
 
 f   max   =a/λ   min   Eq. 5
 
     For example, using water (a=5,000 ft/sec) with a sensor spacing X 1 =3 inches, the above described spatial acoustic filtering would filter out acoustic frequencies up to a maximum frequency of about 2000 Hz (or 5,000*12/30). Thus, the acoustic frequency content of the output signal P as1  of the spatial filter  33  (i.e., differenced vortical pressure signal) will be effectively removed for frequencies below about 2000 Hz and wavelengths above 30 inches (using Eq. 3). 
     The above discussion on the spatial filter  33  also applies to the second spatial filter  35  comprising the other pair of pressure signals P 3 , P 4 , axially spaced a distance X 2  apart, which provides the differenced vortical pressure signal P as2 . 
     Referring to  FIG. 5 , relevant features of the power spectral density (PSD) of typical vortical pressure disturbances P vortical  is shown by a curve  90  that has a flat region (or bandwidth) up to a frequency F v  and then decreases with increasing frequency f. The value of F v  is approximately equal to U/r, where U is the flow rate and r is the radius of the pipe. For example, for a flow rate U of about 10 ft/sec and a pipe radius r of about 0.125 ft (or about 1.5 inches), the bandwidth F v  of the vertical pressure disturbances P vortical  would be about 80 Hz (10/0.125). The PSD of the acoustic pressure disturbances P acoustic  has a profile that is determined by the environment and other factors and is indicated in the figure by an arbitrary curve  91 , and typically has both low and high frequency components. 
     Referring to  FIG. 6 , in general, the acoustic pressure disturbances P acoustic  have an inverse wavelength-frequency relationship as shown in Eq. 4, which has long wavelengths at low frequencies and short wavelengths at high frequencies as indicated by the regions  96 ,  98 , respectively. Conversely, the vortical pressure disturbances P vortical  have both long and short wavelengths as indicated by the regions  96 ,  97 , respectively; however, they exist primarily at low frequencies (as discussed hereinbefore with reference to  FIG. 5 ). Thus, both P acoustic  and P vortical  exist in the long wavelength, low frequency region  96 , and only P vortical  exists in the short wavelength low frequency region  97 . 
     The acoustic spatial filters  33 ,  35  ( FIG. 1 ) discussed hereinbefore block or attenuate wavelengths longer than λ as  and frequencies below f as , as indicated by the region  96 . Also, the bandpass filters (BPF)  46 ,  56  ( FIG. 1 ) block or attenuate high frequencies above f pb  having short and long wavelengths as indicated by a region  102  and pass frequencies below f as  where the P vortical  signals exist. Thus, after the spatial filters  33 ,  35  and the BPF&#39;s  46 ,  56 , the resultant filtered signals P asf   1 , P asf   2  on the lines  48 ,  58  ( FIG. 1 ) will be dominated by the short wavelength unsteady pressure disturbances P vortical  as indicated by the region  97  ( FIG. 6 ) at frequencies below f pb  and as indicated by a portion  94  of the curve  90  in the BPF passband  95  ( FIG. 5 ). 
     Accordingly, referring to  FIG. 5 , the spatial filters  33 ,  35  ( FIG. 1 ) block the long wavelengths, which, for the acoustic pressure disturbances P acoustic , occur at low frequencies as indicated to the left of a dashed line  92  at frequencies below the frequency f as . A dashed line  93  indicates the attenuation of the acoustic pressure P acoustic  signal  91  below the frequency f as  at the output of the spatial filters. The vortical pressure disturbances P vortical  are substantially not attenuated (or only slightly attenuated) because P vortical  has short wavelengths at low frequencies that are substantially passed by the spatial filter. The BPF&#39;s  46 ,  56  ( FIG. 1 ) block or attenuate frequencies outside the passband indicated by a range of frequencies  95 , and passes the unsteady pressure disturbances associated with stochastic flow fields  15  ( FIG. 1 ) within the passband  95 . 
     Alternatively, instead of the filters  46 ,  56  being bandpass filters, provided the de content is acceptably small, in one embodiment the filters  46 ,  56  may comprise low pass filters, having a bandwidth similar to the upper band of the high pass filters discussed hereinbefore. If a low pass filter is used as the filters  46 ,  56 , the passband is shown as a range of frequencies  89 . It should be understood that the filters  46 ,  56  are not required for the present invention if the PSD of the acoustic pressure disturbances P acoustic  has substantially no or low PSD energy content in frequencies above the stopband of the spatial filter that does not adversely affect the measurement accuracy. 
     Referring to  FIGS. 7 and 1 , for the four ac pressure sensors  18 ,  20 ,  22 ,  24  evenly axially spaced at 1 inch apart (X 1 , X 2 ) along the pipe  12 , and providing ac pressure signals P 1 , P 2 , P 3 , P 4 , respectively, the frequency power spectrum for P 1  and P 2  are shown by curves  100 ,  102 , respectively, for water flowing in an horizontal flow loop at a velocity of 11.2 ft/sec in a 2 inch diameter schedule  80  pipe using conventional piezoelectric ac pressure transducers. The power spectra of the curves  100 ,  102  are nearly identical. The power spectrum of the difference P as1  between the two signals P 1 , P 2 , shown by a curve  104  is reduced in certain frequency bands (e.g., 100-150 Hz) and increased in other frequency bands (e.g., 200-250 Hz) as compared to the individual signals  100 ,  102 . 
     Referring to  FIGS. 8 and 1 , the cross correlation between the signals P as1  (or P 1 -P 2 ) and P as2  (P 3 -P 4 ) is shown as a curve  110 . The highest peak  112  indicates the best fit for the time lag between the two signals P as1 , P as2  as 0.015 seconds. Because the four sensors P 1  to P 4  were evenly axially spaced 1 inch apart, the effective distance ΔX between the sensor pairs is 2 inches. Thus, the velocity measured from Eq. 1 is 11.1 ft/sec (2/12/0.015) using the present invention and the actual velocity was 11.2 ft/sec. 
     Referring to  FIG. 9 , for the configuration described with  FIGS. 1 ,  7  and  8  above, the velocity was measured at various flow rates and plotted against a reference velocity value. A solid line  120  shows the reference velocity, the triangles  122  are the measured data, and a line  124  is a curve fit of the data  122 . This illustrates that the present invention predicts the flow velocity within a pipe (or conduit). 
     The pressure sensors  18 ,  20 ,  22 ,  24  described herein may be any type of pressure sensor capable of measuring the unsteady (or ac or dynamic) pressures within a pipe such as, for example, piezoelectric, optical, capacitive, piezo-resistive (e.g., Wheatstone bridge), accelerometers, velocity measuring devices, displacement measuring devices, etc. If optical pressure sensors are used, the sensors  18 ,  20 ,  22 ,  24  may be Bragg grating based pressure sensors, such as that described in copending 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. Alternatively, the sensors  18 - 24  may be electrical or optical strain gages attached to or embedded in the outer or inner wall of the pipe which measure pipe wall strain, including microphones, hydrophones, or any other sensor capable of measuring the unsteady pressures within the pipe  12 . In an embodiment of the present invention that utilizes fiber optics as the pressure sensors  18 ,  20 ,  22 ,  24 , the sensors  18 ,  20 ,  22 ,  24  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 (discussed more hereinafter). 
     Harsh environments are typically found in the industrial process area and include sensor exposure to acids, caustics, nuclear energy, electromagnetic interference and exposure to explosive vapors among other hazards. Because the sensor is glass based it is chemically impervious to most industrial process related chemicals. Further, because the sensor of the present invention uses light for signal transmission it does not require any electrical power and as such is not influenced by electromagnetic fields and cannot create arcing or explosions when used in the presence of flammable vapors. In addition the sensor of the present invention has no moving parts such as a bellows, which makes the device more reliable and less susceptible to system hysteresis found in other mechanical pressure sensors that utilize diaphragms bellows or other displacement type devices. 
     Referring to  FIG. 13 , if a strain gage is used as one or more of the pressure sensors  18 ,  20 ,  22 ,  24  ( FIGS. 14-20 ), it may measure the unsteady (or dynamic or ac) pressure variations P in  inside the pipe  12  by measuring the elastic expansion and contraction, as represented by arrows  350 , of the diameter (and thus the circumference as represented by arrows  351 ) of the pipe  12 . In general, the strain gages would measure the pipe wall deflection in any direction in response to unsteady pressure signals inside the pipe  12 . The elastic expansion and contraction of pipe  12  is measured at the location of the strain gage as the internal pressure P in  changes, and thus measures the local strain (axial strain, hoop strain or off axis strain), caused by deflections in the directions indicated by arrows  351 , on the pipe  12 . The amount of change in the circumference is variously determined by the hoop strength of the pipe  12 , the internal pressure P in , the external pressure P out  outside the pipe  12 , the thickness T w  of the pipe wall  352 , and the rigidity or modulus of the pipe material. Thus, the thickness of the pipe wall  352  and the pipe material in the sensor sections  14 ,  16  ( FIG. 1 ) may be set based on the desired sensitivity of filter  33  and other factors and may be different from the wall thickness or material of the pipe  12  outside the sensing regions  14 ,  16 . 
     Still with reference to  FIG. 13  and  FIG. 1 , if an accelerometer is used as one or more of the pressure sensors  18 ,  20 ,  22 ,  24  ( FIGS. 14-20 ), it may measure the unsteady (or dynamic or ac) pressure variations P in  inside the pipe  12  by measuring the acceleration of the surface of pipe  12  in a radial direction, as represented by arrows  350 . The acceleration of the surface of pipe  12  is measured at the location of the accelerometer as the internal pressure P in  changes and thus measures the local elastic dynamic radial response of the wall  352  of the pipe. The magnitude of the acceleration is variously determined by the hoop strength of the pipe  12 , the internal pressure P in , the external pressure P out  outside the pipe  12 , the thickness T w  of the pipe wall  352 , and the rigidity or modulus of the pipe material. Thus, the thickness of the pipe wall  352  and the pipe material in the sensor sections  14 ,  16  ( FIG. 1 ) may be set based on the desired sensitivity of filter  33  and other factors and may be different from the wall thickness or material of the pipe  12  outside the sensing region  14 . Alternatively, the pressure sensors  18 ,  20 ,  22 ,  24  may comprise a radial velocity or displacement measurement device capable of measuring the radial displacement characteristics of wall  352  of pipe  12  in response to pressure changes caused by unsteady pressure signals in the pipe  12 . 
     Referring to  FIGS. 14 ,  15 ,  16 , if an optical strain gage is used, the ac pressure sensors  18 ,  20 ,  22 ,  24  may be configured using an optical fiber  300  that is coiled or wrapped around and attached to the pipe  12  at each of the pressure sensor locations as indicated by the coils or wraps  302 ,  304 ,  306 ,  308  for the pressures P 1 , P 2 , P 3 , P 4 , respectively. The fiber wraps  302 ,  304 ,  306 ,  308  are wrapped around the pipe  12  such that the length of each of the fiber wraps  302 ,  304 ,  306 ,  308  changes with changes in the pipe hoop strain in response to unsteady pressure variations within the pipe  12  and thus internal pipe pressure is measured at the respective axial location. Such fiber length changes are measured using known optical measurement techniques as discussed hereinafter. Each of the wraps measures substantially the circumferentially averaged pressure within the pipe  12  at a corresponding axial location on the pipe  12 . Also, the wraps provide axially averaged pressure over the axial length of a given wrap. While the structure of the pipe  12  provides some spatial filtering of short wavelength disturbances, we have found that the basic principle of operation of the invention remains substantially the same as that for the point sensors described hereinbefore. 
     Referring to  FIG. 14 , for embodiments of the present invention where the wraps  302 ,  304 ,  306 ,  308  are connected in series, pairs of Bragg gratings ( 310 ,  312 ), ( 314 ,  316 ), ( 318 ,  320 ), ( 322 ,  324 ) may be located along the fiber  300  at opposite ends of each of the wraps  302 ,  304 ,  306 ,  308 , respectively. The grating pairs are used to multiplex the pressure signals P 1 , P 2 , P 3 , P 4  to identify the individual wraps from optical return signals. The first pair of gratings  310 ,  312  around the wrap  302  may have a common reflection wavelength λ 1 , and the second pair of gratings  314 ,  316  around the wrap  304  may have a common reflection wavelength λ 2 , but different from that of the first pair of gratings  310 ,  312 . Similarly, the third pair of gratings  318 ,  320  around the wrap  306  have a common reflection wavelength λ 3 , which is different from λ 1 , λ 2 , and the fourth pair of gratings  322 ,  324  around the wrap  308  have a common reflection wavelength λ 4 , which is different from λ 1 , λ 2 , λ 3 . 
     Referring to  FIG. 15 , instead of having a different pair of reflection wavelengths associated with each wrap, a series of Bragg gratings  360 ,  362 ,  364 ,  366 ,  368  with only one grating between each of the wraps  302 ,  304 ,  306 ,  308  may be used each having a common reflection wavelength λ 1 . 
     Referring to  FIGS. 14 and 15  the wraps  302 ,  304 ,  306 ,  308  with the gratings  310 ,  312 ,  314 ,  316 ,  318 ,  320 ,  322 ,  324  ( FIG. 14 ) or with the gratings  360 ,  362 ,  364 ,  366 ,  368  ( FIG. 15 ) may be configured in numerous known ways to precisely measure the fiber length or change in fiber length, such as an interferometric, Fabry Perot, time-of-flight, or other known arrangements. One example of time-of-flight (or Time-Division-Multiplexing; TDM) would be where an optical pulse having a wavelength is launched down the fiber  300  and a series of optical pulses are reflected back along the fiber  300 . The length of each wrap can then be determined by the time delay between each return pulse. 
     While the gratings  310 ,  312 ,  314 ,  316 ,  318 ,  320 ,  322 ,  324  are shown oriented axially with respect to pipe  12 , in  FIGS. 14 ,  15 , they may be oriented along the pipe  12  axially, circumferentially, or in any other orientations. Depending on the orientation, the grating may measure deformations in the pipe wall  352  with varying levels of sensitivity. If the grating reflection wavelength varies with internal pressure changes, such variation may be desired for certain configurations (e.g., fiber lasers) or may be compensated for in the optical instrumentation for other configurations, e.g., by allowing for a predetermined range in reflection wavelength shift for each pair of gratings. Alternatively, instead of each of the wraps being connected in series, they may be connected in parallel, e.g., by using optical couplers (not shown) prior to each of the wraps, each coupled to the common fiber  300 . 
     Referring to  FIG. 16 , alternatively, the sensors  18 ,  20 ,  22 ,  24  may also be formed as individual non-multiplexed interferometric sensor by wrapping the pipe  12  with the wraps  302 ,  304 ,  306 ,  308  without using Bragg gratings where separate fibers  330 ,  332 ,  334 ,  336  may be fed to the separate wraps  302 ,  304 ,  306 ,  308 , respectively. In this particular embodiment, known interferometric techniques may be used to determine the length or change in length of the fiber  10  around the pipe  12  due to pressure changes, such as Mach Zehnder or Michaelson Interferometric techniques such as those set forth in U.S. patent application Ser. No. 09/726,059, titled “Method and Apparatus for Interrogating Fiber Optic Sensors,” filed Nov. 29, 2000, now U.S. Pat. No. 6,785,004 issued Aug. 31, 2004. 
     The interferometric wraps may be multiplexed such as is described in Dandridge, et al, “Fiber Optic Sensors for Navy Applications”, IEEE, February 1991, or Dandridge, et al, “Multiplexed Interferometric Fiber Sensor Arrays”, SPIE, Vol. 1586, 1991, pp 176-183. Other techniques to determine the change in fiber length may be used. Also, reference optical coils (not shown) may be used for certain interferometric approaches and may also be located on or around the pipe  12  but may be designed to be insensitive to pressure variations. 
     Referring to  FIGS. 17 and 18 , instead of the wraps  302 ,  304 ,  306 ,  308  being optical fiber coils wrapped completely around the pipe  12 , the wraps  302 ,  304 ,  306 ,  308  may have alternative geometries, such as a “radiator coil” geometry ( FIG. 17 ) or a “race-track” geometry ( FIG. 18 ), which are shown in a side view as if the pipe  12  is cut axially and laid flat. In this particular embodiment, the wraps  302 ,  304 ,  306 ,  308  are not necessarily wrapped 360 degrees around the pipe, but may be disposed over a predetermined portion of the circumference of the pipe  12 , and have a length long enough to optically detect the changes to the pipe circumference. Other geometries for the wraps may be used if desired. Also, for any geometry of the wraps described herein, more than one layer of fiber may be used depending on the overall fiber length desired. The desired axial length of any particular wrap is set depending on the characteristics of the ac pressure desired to be measured, for example the axial length of the pressure disturbance caused by a vortex to be measured. 
     Referring to  FIGS. 19 and 20 , embodiments of the present invention include configurations wherein instead of using the wraps  302 ,  304 ,  306 ,  308 , the fiber  300  may have shorter sections that are disposed around at least a portion of the circumference of the pipe  12  that can optically detect changes to the pipe circumference. It is further within the scope of the present invention that sensors may comprise an optical fiber  300  disposed in a helical pattern (not shown) about pipe  12 . As discussed herein above, the orientation of the strain sensing element will vary the sensitivity to deflections in pipe wall  352  caused by unsteady pressure transients in the pipe  12 . 
     Referring to  FIG. 19 , in particular, the pairs of Bragg gratings ( 310 ,  312 ), ( 314 ,  316 ), ( 318 ,  320 ), ( 322 ,  324 ) are located along the fiber  300  with sections  380 ,  382 ,  384 ,  386  of the fiber  300  between each of the grating pairs, respectively. In that case, known Fabry Perot (resonator, cavity, interferometer or other known Fabry Perot arrangement), interferometric, time-of-flight or fiber laser sensing techniques may be used to measure the strain in the pipe. 
     Referring to  FIG. 20 , alternatively, individual gratings  370 ,  372 ,  374 ,  376  may be disposed on the pipe and used to sense the unsteady variations in strain in the pipe  12  (and thus the unsteady pressure within the pipe) at the sensing locations. When a single grating is used per sensor, the grating reflection wavelength shift will be indicative of changes in pipe diameter and thus pressure. 
     Any other technique or configuration for an optical strain gage may be used. The type of optical strain gage technique and optical signal analysis approach is not critical to the present invention, and the scope of the invention is not intended to be limited to any particular technique or approach. 
     For any of the embodiments described herein, the pressure sensors, including electrical strain gages, optical fibers and/or gratings among others as described herein, may be attached to the pipe by adhesive, glue, epoxy, tape or other suitable attachment means to ensure suitable contact between the sensor and the pipe  12 . The sensors may alternatively be removable or permanently attached via known mechanical techniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. Alternatively, the strain gages, including optical fibers and/or gratings, may be embedded in a composite pipe. If desired, for certain applications, the gratings may be detached from (or strain or acoustically isolated from) the pipe  12  if desired. 
     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 piezoresistive, electronic or electric, strain gages attached to or embedded in the pipe  12 . Referring to  FIG. 29  different known configurations of highly sensitive piezoresistive strain gages are shown and may comprise foil type gages. Referring to  FIG. 30  an embodiment of the present invention is shown wherein pressure sensors  18 ,  20 , comprise strain gages  203 . In this particular embodiment strain gages  203  are disposed about a predetermined portion of the circumference of pipe  12 . The axial placement of and separation distance X 1  between pressure sensors  18 ,  20  are determined as described hereinabove. In particular, the placement is dependent upon the characteristics of the ac pressure desired to be measured, for example the spatial (axial or transverse) length and coherence length of the pressure disturbance caused by the vortex, or unsteady pressure disturbance, to be measured. 
     Referring to  FIG. 10 , there is shown an embodiment of the present invention comprising three spatial filters  33 ,  35 ,  37  each comprising a pair of pressure sensors measuring at total of six unsteady pressures P 1 -P 6  (three pairs), each pressure sensor being a plurality (e.g., 10 meters) of fiber optic wraps and the sensors being evenly axially spaced at 1.8 inches apart, on a pipe having an inner diameter of 3.0 inches, a wall thickness of 0.22 inch and made of J55 steel production tubing, is shown. The three spatial filters,  33 ,  35 ,  37  provide spatially filtered ac pressure signals P as1 , P as2 , P as3 , respectively. 
     These ac pressure signals P sa1 , P as2 , P as3  may be used as input to a variety of devices and used as desired. It is within the scope of the present invention that any number of spatial filters and spatial time filters may be used and that the particular embodiment will dictate the quantity and the spacing (not shown in  FIG. 10 ) between each spatial filter. It is noted that although pressure sensors P 1 -P 6  are shown as point sensors it is within the scope of the present invention that the sensors comprise any configuration capable of accurately detecting pressure changes in pipe  12  including fiber optic wraps as described herein. 
     Referring to  FIG. 11 , for the configuration of  FIG. 10 , and for a liquid flow mixture of 100% oil at 111.2 gal/minute (or about 5.05 ft/sec for a 3 inch pipe), the invention provides cross-correlation curves  130 ,  132 ,  134 . The curves  130 ,  132 ,  134  correspond to velocities of 5.538 ft/sec, 5.541 ft/sec, 5.5822 ft/sec, for the cross-correlation between P sa1  and P as2  (vel-a), P as2  and P as3  (vel-b), and P as1  and P as3  (vel-c), for the groups of sensors a, b, c, respectively, shown in  FIG. 10 . 
     Referring to  FIG. 12 , it is shown that the present invention will work over a wide range of oil/water mixtures. In particular, the first two pairs of sensors (P 1 , P 2 , and P 3 , P 4 ) of  FIG. 10  measured the velocity at various flow rates against a reference velocity value. Data points  151 - 162  are groupings of measured velocity data points derived from the sensors (P 1 , P 2 , P 3 , P 4 ) and are plotted against a reference velocity line  150 . The data points  151 - 162  also show the invention will work for fluid flowing in either direction in the pipe  12 . The negative flow data points  151 - 158  were taken with a fluid of 100% oil and the positive flow data points  159 - 162  were taken over a range of various oil/water mixtures. Specifically, data points  159  represent 100 individual data points taken at velocities from about 5.2 ft/sec to about 5.7 ft/sec and in oil/water mixtures from 0% to 100% water. Data point  160  represents a single individual data point taken at a velocity of about 9.9 ft/sec in an oil/water mixture of 0% water. Data point  161  represents a single individual data point taken at velocity of about 13.7 ft/sec in an oil/water mixture of 0% water. Similarly, data points  162  represent 21 individual data points taken at velocities from about 18.0 ft/sec to about 19.0 ft/sec and in oil/water mixtures from 0% to 100% water. The departure of the raw data  151 - 162  from the reference velocity line  150  is caused, in part, by the fact that the points were not calibrated and that the reference velocity at each point was taken manually by a technician. Had the data points been calibrated and electronically matched to the sensed points the departure from the reference line  150  would not have been as large as depicted in the figure. 
     The present invention will also work over a wide range of multiphase fluid mixtures. Also, the invention will work for very low flow velocities, e.g., at or below 1 ft/sec (or about 20.03 gal/min, in a 3 inch diameter ID pipe) and has no maximum flow rate limit. Further, the invention will work with the pipe  12  being oriented vertical, horizontal, or any other orientation. Also the invention will work equally well independent of the direction of the flow along the pipe  12 . 
     Referring to  FIG. 21 , instead of the unsteady pressure sensors  18 ,  20  and the corresponding unsteady pressure signals P 1 , P 2  being spaced axially along the pipe  12 , the sensors  18 ,  20  may be spaced circumferentially apart at substantially the same axial location. In that case, the spatial filter  33  ( FIG. 1 ) (i.e., the difference between the two signals P 1 , P 2 , P 3 , P 4 ) filters out substantially all one dimensional acoustic waves propagating through the sensing region  14 . 
     Alternatively, referring to  FIG. 22 , instead of the pressure sensors  18 ,  20  being located directly across from each other, the signal P 2  may be measured at a distance circumferentially closer to the sensor  18 , as indicated by a sensor  200 . The circumferential distance  53  between the two sensors  18 ,  200  should be large enough to independently measure a propagating vortical pressure field  15  such that the spatial filter  33  output is not zero for the measured vortex  15 , i.e., that the circumferential distance  53  is greater than the transverse spatial length of vortex  15 . In addition, the distance X 1  ( FIG. 1 ) should be less than or equal to the axial coherence length of the vortex  15  such that the spatial filter output is indicative of a measured vortex  15 . 
     The thickness and rigidity of the outer wall of the pipe  12  is related to the acceptable spacing X 1  ( FIG. 1 ) between the sensors  18 ,  20  of the spatial filter  33 . More specifically, the thinner or less rigid the pipe  12  wall, the closer the sensors  18 ,  20  can be to each other. 
     Also, for optimal performance, the distance X 1  between the two sensors  18 ,  20  should be larger than the spatial length of the vortical pressure field  15  such that each of the sensors  18 ,  20  can independently measure the propagating vortical pressure field  15  between the sensors  18 ,  20  at different times (such that the spatial filter  33  output is not zero for the measured vortex  15 ). Also, the distance X 1  should be within the coherence length of the vortex  15  such that the spatial filter output is indicative of a measured vortex  15 . Also, for optimal performance, the overall length L 1  between the first sensor  18  and the last sensor  24  of the velocity sensing section should be within the coherence length of the vortices  15  desired to be measured. The coherence length of the vortical flow field  15  is the length over which the vortical flow field remains substantially coherent, which is related to and scales with the diameter of the pipe  12 . 
     Vortices that are sensed by only one of the spatial filters, because either a vortex is generated between the spatial filters or generated outside the spatial filters and decay between them, will be substantially random events (in time and location) that will not be correlated to the vortices that are sensed by and continuously occurring past both spatial filters and, as such, will not significantly affect the accuracy of the measurement. 
     Referring to  FIG. 24 , a particular embodiment of the present invention is shown therein where more than two sensors may be used for one or both of the spatial filters  33 ,  35 . In particular, the summer  44  may have three inputs P 1 , P 2 , P 3 , from three pressure sensors  220 ,  222 ,  224  where the output signal P sa1 =P 1 −2P 2 +P 3 . For optimal performance, the overall axial length L of the filter  33  should be within the coherence length of the vortices  15  being measured and the individual spacing between the sensors  220 ,  222 ,  224  should have the same criteria discussed hereinbefore for the spacing between two sensors  18 ,  20 . 
     Referring to  FIG. 32 , instead of using four pressure sensors to make the spatial filters  33 ,  35  three pressure sensors  600 ,  602 ,  604  may be used where the middle sensor  602  is used for both the spatial filters  33 ,  35 . 
     Referring to  FIGS. 28-31 , instead of measuring the unsteady pressures P 1 -P 4  on the exterior of the pipe  12 , the invention will also work when the unsteady pressures are measured inside the pipe  12 . In particular, the pressure sensors  18 ,  20  that measure the pressures P 1 , P 2 , may be located anywhere within the pipe  12 , having the same constraints discussed hereinbefore for the exterior measurements. Any technique may be used to measure the unsteady pressures inside the pipe  12 . 
     Referring to  FIGS. 25-27 , the invention may also measure the velocity of flow outside a pipe or tube  400 . In that case, the tube  400  may be placed within the pipe  12  and the pressures P 1 -P 4  measured at the outside of the tube  400 . Any technique may be used to measure the unsteady pressures P 1 -P 4  outside the tube  400 . 
     Referring to  FIG. 25 , for example, the tube  400  may have the optical wraps  302 ,  304 ,  306 ,  308  wrapped around the tube  400  at each sensing location. Alternatively, any of the strain measurement or displacement, velocity or accelerometer sensors or techniques described herein may be used on the tube  400 . Referring to  FIG. 26 , alternatively, the pressures P 1 -P 4  may be measured using direct pressure measurement sensors or techniques described herein. Any other type of unsteady pressure sensors  18 ,  20 ,  22 ,  24  may be used to measure the unsteady pressures within the pipe  12 . 
     Alternatively, referring to  FIG. 27 , hydrophones  402 ,  404 ,  406 ,  408  may be used to sense the unsteady pressures within the pipe  12 . In that case, the hydrophones  402 ,  404 ,  406 ,  408  may be located in the tube  400  for ease of deployment or for other reasons. The hydrophones  402 ,  404 ,  406 ,  408  may be fiber optic, electronic, piezoelectric or other types of hydrophones. If fiber optic hydrophones are used, the hydrophones  402 ,  404 ,  406 ,  408  may be connected in series or parallel along the common optical fiber  300 . 
     The tube  400  maybe made of any material that allows the unsteady pressure sensors to measure the pressures P 1 -P 4  and may be hollow, solid, or gas filled or fluid filled. One example of a dynamic pressure sensor is described in co-pending commonly-owned U.S. Pat. No. 6,233,374, entitled “Mandrel Wound Fiber Optic Pressure Sensor”. Also, the end  422  of the tube  400  may be closed or open. If the end  422  is closed, the flow path would be around the end  422  as indicated by lines  424 . If the end  422  is open, the flow path would be through the inside of the tube, as indicated by a line  426  and the pressure would be measured inside of the pipe  12 . For harsh environment industrial applications, the tube  400  may be coiled tubing having the pressure sensors for sensing P 1 -P 4  inside the tubing  400 . 
     Although the invention has been described with respect to the detection of certain types of unsteady flow fields and the pressure disturbances associated therewith, it should be understood that the invention will also detect any unsteady stochastic flow field and its associated pressure field that propagates within the flow, provided the spatial filters have a separation within the acceptable coherence length of the flow field to be measured and the sensor spacing within each spatial filter is longer than a characteristic spatial length of the disturbance. Some examples of such other stochastic flow fields are gas bubbles, gas slugs, particles, or chunks of material, which may travel in the flow at different rates than the mean flow velocity, thereby creating a traveling pressure disturbance, which exhibits a velocity slip between it and the other constituents in the mixture. 
     Accordingly, the invention may be used to detect such different flow rates within the same mixture (e.g., the flow rate of an unsteady pressure field within the mixture). Also, such unsteady flow fields, when traveling at different rates from other portions of the mixture, may also shed vortices in the flow that may propagate with the flow and be detected as an unsteady flow field by the present invention. 
     Referring to  FIG. 33 , there is shown an embodiment of the present invention in a typical industrial processing application, the sensing section  51  may be connected to or part of process tubing  502  (analogous to the pipe  12  in the test section  51 ) within an industrial process control system  500 . The isolation sleeve  410  may be located over the sensors  18 ,  20 ,  22 ,  24  as discussed hereinbefore and attached to the pipe  502  at the axial ends to protect the sensors  18 ,  20 ,  22 ,  24  (or fibers) from damage during deployment, use, or retrieval, and/or to help isolate the sensors from acoustic external pressure effects that may exist outside the pipe  502 , and/or to help isolate ac pressures in the pipe  502  from ac pressures outside the pipe  502 . The advantages and effect of the isolation sleeve  410 , as well as other isolation techniques, are described in commonly owned, copending U.S. patent application Ser. No. 09/344,070, entitled “Measurement of Propagating Acoustic Waves in Compliant Pipes” incorporated herein by reference in its entirety. The sensors  18 ,  20 ,  22 ,  24  are connected to a cable  506  which may comprise the optical fiber and is connected to a transceiver/converter  510  of the control system  500 . 
     When optical sensors are used, the transceiver/converter  510  may be used to receive and transmit optical signals to the sensors  18 ,  20 ,  22 ,  24  and provides output signals indicative of the pressure P 1 -P 4  at the sensors  18 ,  20 ,  22 ,  24  on the lines  30 ,  32 ,  34 ,  36 , respectively. Also, the transceiver/converter  510  may be part of the Velocity Logic  40 . The transceiver/converter  510  may be any device that performs the corresponding functions described herein. In particular, the transceiver/converter  510  together with the optical sensors described hereinbefore may use any type of optical grating-based measurement technique, e.g., scanning interferometric, scanning Fabry Perot, acousto-optic-tuned filter (AOTF), optical filter, time-of-flight, etc., having sufficient sensitivity to measure the ac pressures within the pipe. 
     A plurality of the sensors  10  of  FIG. 33  of the present invention may be connected to a common cable and multiplexed together using any known multiplexing technique by connecting end  511  to other sensors (not shown). For instance, it is contemplated that the various embodiments of the sensor  10  of the present invention include the capability being multiplexed as well as capable of communication with various protocols and systems currently in use in the industrial sensing area. For instance, and with reference to  FIG. 33  there is shown a portion of a process control system  500  incorporating a sensor  10  in accordance with the present invention. Fluid velocity logic  40  communicates signal Uc(t) along line  42  to control device  70 , a computer or micro-processor for example, where the information may be used to control the fluid velocity in pipe  502  through known controls means such as a pump, valve, throttle, etc. (not shown). In certain embodiments of control system  500  and with appropriate electro-optical conversion of the sensor return signal to a conventional 4-20 mA signal the signal can be combined with other control devices and sensors at control device  70  via separate electrical lines. In this particular embodiment the communication from the fiber optic sensor is performed with a 4-20 mA analog signal, and the open protocol HART® (Highway Addressable Remote Transducer) digital communications format. Similarly, communication from the fiber optic sensor  10  may also be performed with open and interoperable protocol FOUNDATION™ Fieldbus that provides a digital communication link among intelligent field level and control devices via electrical lines. The control device  70  can be configured for use with other process protocols, including Device Bus, Sensor Bus, Profibus, the ethernet, and others in use throughout the world. The use of feedthroughs  511 , as shown in  FIG. 33 , make the sensor  10  of the present invention uniquely qualified for industrial applications requiring multiple sensors. The use of sensors having feedthroughs in a large multi-point process enables connectivity to the multiple sensors through a single fiber optic cable. Electronic sensors of the prior art require dedicated wiring to the sensor and back to the instrumentation. For instance, a typical industrial process control system that utilizes electronic flowmeters of the prior art requires an electrical process loop to facilitate both a power signal to the transmitters and bi-directional communication, and can be constructed in accordance with a number of the aforementioned process communication protocols. 
     In operation, industrial process uses for the present invention include reverse osmosis, coking, general refining uses, in-line pressure sensors for emissions monitoring, sensors for monitoring hydrogen, combustion control, gas composition analysis, distributed sensors in tank gauging, multi-phase computational fluid dynamics, instrumentation of multiphase flows, among others. 
     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. 
     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.