Method and apparatus for measuring parameters of a stratified flow

Abstract

Various methods are described for measuring parameters of a stratified flow using at least one spatial array of sensors disposed at different axial locations along the pipe. Each of the sensors provides a signal indicative of unsteady pressure created by coherent structures convecting with the flow. In one aspect, a signal processor determines, from the signals, convection velocities of coherent structures having different length scales. The signal processor then compares the convection velocities to determine a level of stratification of the flow. The level of stratification may be used as part of a calibration procedure to determine the volumetric flow rate of the flow. In another aspect, the level of stratification of the flow is determined by comparing locally measured velocities at the top and bottom of the pipe. The ratio of the velocities near the top and bottom of the pipe correlates to the level of stratification of the flow. Additional sensor arrays may provide a velocity profile for the flow. In another aspect, each of the sensors in the array includes a pair of sensor half-portions disposed on opposing lateral surfaces of the pipe, and the signal processor determines a nominal velocity of the flow within the pipe using the signals.

1 . An apparatus for measuring a parameter of a flow passing through a pipe, the apparatus comprising: 
 a spatial array of sensors disposed at different axial locations along the pipe, each of the sensors providing a signal indicative of unsteady pressure created by coherent structures convecting with the flow; and    a signal processor configured to: 
 determine, from the signals, convection velocities of coherent structures having different length scales, and  
 compare the convection velocities to determine a level of stratification of the flow.  
   
   
   
       2 . The apparatus of  claim 1 , wherein, in comparing the convection velocities, the signal processor is configured to: 
 construct a plot of the convection velocities as a function of the length scales, and    determine a slope of a best-fit line through the plot, the slope of the line indicating the level of stratification of the flow.    
   
   
       3 . The apparatus of  claim 2 , wherein the plot is normalized by a nominal velocity of the flow and a diameter of the pipe.  
   
   
       4 . The apparatus of  claim 2 , wherein the slope is used to calibrate the signal processor to determine the volumetric flow rate of the flow.  
   
   
       5 . The apparatus of  claim 4 , wherein the signal processor is configured to: 
 construct from the signals at least a portion of a k-ω plot; and    determine a frequency range over which the signal processor analyzes a convective ridge in the k-ω plot for determining the volumetric flow rate.    
   
   
       6 . The apparatus of  claim 2 , wherein, in constructing the plot of convection velocity of the coherent structures as a function of frequency, the signal processor is configured to: 
 construct from the signals at least a portion of a k-ω plot;    identify a convective ridge in the k-ω plot over a first frequency range;    determine a first slope of the convective ridge, the first slope being indicative of a nominal velocity of the flow;    identify a plurality of portions of the convective ridge over a plurality of second frequency ranges, each second frequency range being smaller than the first frequency range and having a respective midpoint;    determine a second slope for each of the portions of the convective ridge, each second slope being indicative of a nominal convection velocity of coherent structures having a range of length scales corresponding to an associated second frequency range;    normalize the nominal convection velocities of coherent structures using the nominal velocity of the flow to provide normalized convection velocities; and    plot each normalized convection velocity as a function of the respective midpoint non-dimensionalized by the nominal velocity of the flow and the diameter of the pipe to provide the plot.    
   
   
       7 . The apparatus of  claim 6 , wherein the first frequency range is adjusted based on the slope.  
   
   
       8 . The apparatus of  claim 6 , wherein a non-dimensional length scale that is least sensitive to stratification is used to determine the mid-point of the first frequency range, the non-dimensional length scale that is least sensitive to stratification being determined by comparing a plurality of dispersion plots for different levels of stratification and identifying the pivot point of the dispersion plots from one dispersion plot to another.  
   
   
       9 . An apparatus for measuring a parameter of a flow passing through a pipe, the apparatus comprising: 
 a first spatial array of at least two sensors disposed at different axial locations along the pipe, each of the sensors in the first array providing a first signal indicative of unsteady pressure created by coherent structures convecting with a portion of the flow passing through an upper portion of the pipe;    a second spatial array of at least two sensors disposed at different axial locations along the pipe, each of the sensors in the second array providing a second signal indicative of unsteady pressure created by coherent structures convecting with a portion of the flow passing through a lower portion of the pipe; and    at least one signal processor configured to: 
 determine a first velocity of the flow passing through the upper portion of the pipe using the first signals,  
 determine a second velocity of the flow passing through the lower portion of the pipe using the second signals, and  
 compare the first and second velocities to determine the parameter of the flow.  
   
   
   
       10 . The apparatus of  claim 9 , wherein the parameter of the flow includes at least one of: level of stratification of the flow and volumetric flow rate of the flow.  
   
   
       11 . The apparatus of  claim 9 , wherein the microprocessor normalizes the first and second velocities before comparing the first and second velocities.  
   
   
       12 . The apparatus of  claim 9 , wherein the first spatial array is aligned axially along a top of the pipe and the second spatial array is aligned axially along a bottom of the pipe.  
   
   
       13 . The apparatus of  claim 9 , further comprising: 
 at least one additional spatial array of at least two sensors disposed at different axial locations along the pipe, each of the sensors in the at least one additional array providing a third signal indicative of unsteady pressure created by coherent structures convecting with a portion of the flow proximate the sensor, the at least one additional spatial array being aligned axially along the pipe and being positioned between the first and second spatial arrays; and    wherein, for each additional spatial array, the at least one signal processor is further configured to:    determine a third velocity of the flow near the additional spatial array using the third signals, and    compare the first, second, and third velocities to determine the parameter of the flow.    
   
   
       14 . The apparatus of  claim 13 , wherein the comparison of the first, second, and third velocities provides a velocity profile of the flow passing through the pipe.  
   
   
       15 . The apparatus of  claim 13 , wherein the parameter of the flow includes at least one of: level of stratification of the flow and volumetric flow rate of the flow.  
   
   
       16 . The apparatus of  claim 13 , wherein the microprocessor normalizes the first, second, and third velocities before comparing the first, second, and third velocities.  
   
   
       17 . The apparatus of  claim 9 , wherein the parameter of the flow includes a level of stratification of the flow and wherein, in response to the level of stratification of the flow, the microprocessor selects a number of sensors for use in determining a mean velocity of the flow.  
   
   
       18 . An apparatus for measuring a parameter of a flow passing through a pipe, the apparatus comprising: 
 a spatial array of sensors disposed at different axial locations along the pipe, each of the sensors comprising a pair of sensor half-portions disposed on opposing lateral surfaces of the pipe, wherein each pair of sensor half-portions provides a pressure signal indicative of unsteady pressure created by coherent structures convecting with the flow within the pipe at a corresponding axial location of the pipe; and    a signal processor configured to determine a nominal velocity of the flow within the pipe using the signals.    
   
   
       19 . A method for measuring a parameter of a flow passing through a pipe using a spatial array of sensors disposed at different axial locations along the pipe, each of the sensors providing a signal indicative of unsteady pressure created by coherent structures convecting with the flow, the method comprising: 
 determining, from the signals, convection velocities of coherent structures having different length scales, and    comparing the convection velocities to determine a level of stratification of the flow.    
   
   
       20 . The method of  claim 19 , wherein comparing the convection velocities includes: 
 constructing a plot of the convection velocities as a function of the length scales, and    determining a slope of a best-fit line through the plot, the slope of the line indicating the level of stratification of the flow.    
   
   
       21 . The method of  claim 20 , wherein the plot is normalized by a nominal velocity of the flow and a diameter of the pipe.  
   
   
       22 . The method of  claim 20 , further comprising: 
 constructing from the signals at least a portion of a k-ω plot; and    using the slope, determining a frequency range over which the signal processor analyzes a convective ridge in the k-ω plot for determining the volumetric flow rate.    
   
   
       23 . The method of  claim 20 , wherein constructing the plot of convection velocity of the coherent structures as a function of frequency comprises: 
 constructing from the signals at least a portion of a k-ω plot;    identifying a convective ridge in the k-ω plot over a first frequency range;    determining a first slope of the convective ridge, the first slope being indicative of a nominal velocity of the flow;    identifying a plurality of portions of the convective ridge over a plurality of second frequency ranges, each second frequency range being smaller than the first frequency range and having a respective midpoint;    determining a second slope for each of the portions of the convective ridge, each second slope being indicative of a nominal convection velocity of coherent structures having a range of length scales corresponding to an associated second frequency range;    normalizing the nominal convection velocities of coherent structures using the nominal velocity of the flow to provide normalized convection velocities; and    plotting each normalized convection velocity as a function of the respective midpoint non-dimensionalized by the nominal velocity of the flow and the diameter of the pipe to provide the plot.    
   
   
       24 . The method of  claim 23 , wherein the first frequency range is adjusted based on the slope.  
   
   
       25 . The method of  claim 24 , wherein a non-dimensional length scale that is least sensitive to stratification is used to determine the mid-point of the first frequency range, the non-dimensional length scale that is least sensitive to stratification being determined by comparing a plurality of dispersion plots for different levels of stratification and identifying the pivot point of the dispersion plots from one dispersion plot to another.