Abstract:
System and method for remotely sensing the cross-flow orientation of a fluid (including a gaseous fluid) over an extended range. A Fourier transform of beam wander of a single beam can be used to determine the orientation of the flow field. Many applications depend upon accurate flow orientation data to provide correct information such as, for example, citing of turbines on wind farms and atmospheric/ocean weather prediction.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This Application is a non-provisional application claiming priority to provisional application 61/869,296 filed on Aug. 23, 2013, entitled SINGLE BEAM/DETECTOR OPTICAL REMOTE CROSS-FLOW SENSOR under 35 USC 119(e). The entire disclosure of the provisional application is incorporated herein by reference. 
     
    
     BACKGROUND 
       [0002]    Methods and systems disclosed herein relate generally to measuring fluid or gas flow, and more particularly to sensing cross-flow orientation and speed of a fluid over an extended range. 
         [0003]    The wind direction of the atmosphere is routinely monitored by remote sensing techniques such as Light Detection and Ranging (LIDAR) and Sonic Detection and Ranging (SODAR). The measurement principles usually employed are the Doppler shift in applications where the flow is in the direction of the detecting beam (Benedetti-Michelangeli et al.,  Measurements of aerosol motion and wind velocity in the lower troposphere by doppler optical radar, J Atmos Sci  29, 906-910 (1972)) and cross-correlation of the scintillation pattern in a crosswind geometry (T. Wang, G. R. Ochs, and R. S. Lawrence,  Wind measurements by the temporal cross - correlation of the optical scintillations, Appl Optics  20, 4073-4081 (1981)). 
         [0004]    Scintillometers are used for cross wind measurements over extended ranges. Most applications for this kind of measurement are found in meteorology, climate, and environmental sciences. Monitoring the flow (wind in case of the atmosphere) is important to understand the transport of heat, gases, nutrients, and other substances which affect the environment. Also the wind speed over airport runways is sometimes monitored remotely by dual large-aperture scintillometers (DLAS) or single large-aperture scintillometers (SLAS). Similar instruments are being used to survey the wind conditions at potential sites for wind farms. Cross-correlation of the scintillation between two beams is utilized to determine the flow direction (e.g. DLAS). SLAS on the other hand only provide information on the speed of the flow, but lack the ability to determine the flow direction. 
         [0005]    What is needed is a method that relies on the beam wander (also referred to herein interchangeably as wander, beam deflection, or deflection) of a single laser beam, measured in two orthogonal directions, to infer the cross-flow direction of an optically active turbulent medium. What is further needed is a system for remotely sensing the cross-flow orientation of a fluid (including a gaseous fluid) over an extended range. 
       SUMMARY 
       [0006]    The system and method of the present embodiment can remotely sense the cross-flow orientation of a fluid over an extended range. The cross-flow orientation of an optically active turbulent field can be determined by Fourier transforming the wander of a laser beam propagating in the turbulent field. The turbulent field can include any fluid. 
         [0007]    In the present embodiment, the beam wander of a single beam is used to find the flow orientation by Fourier transforming the beam wander. A single position sensitive detector, for example, but not limited to, quadrant detector or tetra-lateral PSD can be used to record the beam wander. Here beam wander refers to the position of the beam centroid independent of the precise shape of the beam. This simplifies the measurement setup compared to dual laser scintillometer implementations which also need two detectors. Position sensitive detectors (PSD) can use, for example, photodiode surface resistance to provide position data (X or Y coordinate data). 
         [0008]    The computer method of one embodiment for determining flow orientation in a turbulent fluid can include, but is not limited to including, projecting a light source through the turbulent fluid onto a position sensitive detector (PSD), monitoring, by a first special purpose computer, beam wander on the PSD over a pre-selected time period, calculating, by a second special purpose computer, Fourier transforms of the beam wander along different directions of the PSD, the Fourier transforms being related to Fourier amplitudes and Fourier frequencies, and determining, by a third special purpose computer, the flow orientation by selecting the directions for which the Fourier amplitudes reach a maximum at the highest of the Fourier frequencies. The turbulent fluid can optionally be, but is not limited to being an ocean and a planetary atmosphere. The light source can optionally be continuous or pulsing, and can optionally be, but is not limited to being, a laser, a point source, a natural source, for example the Sun or the moon, or a plain wave. 
         [0009]    In another embodiment, the computer method for surveying wind for a wind farm plan can include, but is not limited to including, computing, by a first special purpose computer, flow orientation. Computing flow orientation can include, but is not limited to including, projecting a continuous wave light source through the wind onto a position sensitive detector (PSD), monitoring beam wander on the PSD over a pre-selected time period, calculating Fourier transforms of the beam wander along different directions of the PSD, the Fourier transforms being related to Fourier amplitudes and Fourier frequencies, and determining the flow orientation by selecting the directions for which the Fourier amplitudes reach a maximum at the highest of the Fourier frequencies. The method for surveying wind can further include incorporating the flow orientation into a wind farm siting model, and executing, by a second special purpose computer, the model to create the wind farm plan. The light source in this embodiment can also optionally be continuous or pulsed, and can be, but is not limited to being, a laser, a point source, a natural source, or a plain wave. 
         [0010]    In yet another embodiment, the computer system for determining flow orientation in a turbulent fluid can include, but is not limited to including, a position sensitive detector (PSD), a light source projecting a light beam through the turbulent fluid onto the PSD, a monitor processor executing on a first special purpose computer monitoring beam wander on the PSD over a pre-selected time period, and a flow orientation processor executing on a second special purpose computer calculating Fourier transforms of the beam wander along different directions of the PSD, the Fourier transforms being related to Fourier amplitudes and Fourier frequencies, the flow orientation processor determining the flow orientation by selecting the directions for which the Fourier amplitudes reach a maximum at the highest of the Fourier frequencies. The turbulent fluids can be, for example, but not limited to, an ocean or a planetary atmosphere. As in other embodiments, the light source can be continuous or pulsing, and can be a laser, a point source, a natural source, or a plain wave, for example. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    This patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
           [0012]      FIG. 1  is graphical display of the system of the present embodiment; 
           [0013]      FIG. 2  is a flowchart of the method of the present embodiment; 
           [0014]      FIG. 3  is a pictorial representation of information about beam wander in the present embodiment; 
           [0015]      FIG. 4A  is a pictorial representation of beam wander through a turbulent fluid; 
           [0016]      FIG. 4B  is a graphical representation of the coordinate system in which beam wander is measured; 
           [0017]      FIG. 5  is a pictorial representation of possible light sources; 
           [0018]      FIG. 6  is a pictorial representation contrasting beam wander with beam distortion; and 
           [0019]      FIG. 7  is a graphical representation of the method of the present embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0020]    The problems set forth above as well as further and other problems are solved by the present teachings. These solutions and other advantages are achieved by the various embodiments of the teachings described herein below. The system and method of the present embodiment automatically compute flow orientation from a single light source, for example, continuous or pulsing. 
         [0021]    Referring now to  FIG. 1 , method  150  for determining flow orientation in a turbulent fluid can include, but is not limited to including, projecting  151  a light source through the turbulent fluid onto a position sensitive detector (PSD), monitoring  153  beam wander on the PSD over a pre-selected time period, calculating  155  Fourier transforms of the beam wander along different directions of the PSD, the Fourier transforms being related to Fourier amplitudes and Fourier frequencies; and determining  157  the flow orientation by selecting the directions for which the Fourier amplitudes reach a maximum at the highest of the Fourier frequencies. 
         [0022]    Referring now to  FIG. 2 , system  100  for determining flow orientation in a turbulent fluid can include, but is not limited to including, position sensitive detector (PSD)  111 , light source  113  projecting a light through the turbulent fluid onto the PSD, monitor processor  115  monitoring beam wander on the PSD over a pre-selected time period; and flow orientation processor  117  calculating Fourier transforms of the beam wander along different directions of the PSD, the Fourier transforms being related to Fourier amplitudes and Fourier frequencies, the flow orientation processor determining the flow orientation by selecting the directions for which the Fourier amplitudes reach a maximum at the highest of the Fourier frequencies. 
         [0023]    Referring now to  FIG. 3 , diagram  20 A illustrates beam deflection perpendicular to the flow caused by single turbulent cell  13  with cell index of refraction (n c ) smaller than the surrounding index of refraction (n s ) in which cell  13  is offset slightly to the right of beam  11  (flow orientation  17  into diagram  20 A). Diagram  20 B illustrates beam deflection parallel to flow orientation  17  for cell  13  entering beam  11  from the right and flowing to the left with flow orientation  17 . Diagram  10 A illustrates beam deflection  15  over time and amplitude  15 A of the Fourier transform of beam wander represented by beam  11  in diagram  20 A. Likewise, diagram  10 B illustrates beam deflection  15  over time and amplitude  15 A of the Fourier transform of beam wander of beam  11  in diagram  20 B. 
         [0024]    Continuing to refer to  FIG. 3 , beam deflection  15  perpendicular to flow  17  has the form of Gaussian-shaped hump  12  towards the left or the right, depending on the position of cell  13  relative to beam  11 . Deflection  15  along flow orientation  17 , however, traces the first derivative of a single Gaussian, i.e., hump  12 A in the direction opposite to flow  17  followed immediately by hump  12  in flow orientation  17 . For cells  13  of higher refractive index compared to its surrounding (n c &gt;n s ), deflections  15  occur in opposite directions. The magnitude of the Fourier transform, in accordance with the shift theorem (Eq. 1) (J. W. Goodman,  Introduction to Fourier optics, Roberts &amp; Co, ( 2005)), is invariant of translation in the time domain, and therefore is independent of the time cell  13  passes through beam  11 : 
         [0000]      | F ( g ( t−a ))|=| F ( g ( t )) e   −iωa   |=|F ( g ( t ))|  (1)
 
         [0000]    For example, Fourier transforming the Gaussian-like signal for deflection perpendicular to the flow caused by a single turbulent cell will result in a Gaussian-like magnitude centered at zero frequency regardless of the time the cell transitions. 
         [0025]    Furthermore, the Fourier transform of the derivative of any function is proportional to the Fourier transform of the function, multiplied by the frequency (Eq. 2). In the case of the derivative of a Gaussian, a Gaussian centered at the origin results are multiplied by its frequency variable: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
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         [0026]    Since the Fourier transform is a linear operator, the signals from a series of deflections will sum to either a Gaussian or a Gaussian multiplied by the frequency, independent of the time of the deflection. However, the randomly arriving pulses in the time domain will accumulate with random phases in the frequency domain. Therefore the signals from individual pulses interfere, which produces the fast varying, noise-like signal seen in the Fourier transform data. 
         [0027]    Referring now to  FIG. 4A , in order to illustrate the method of the present embodiment, the refractive index variations in an optically active turbulent field can be considered to come in the form of spherical cells  13  (D. A. Dewolf,  A random - motion model of fluctuations in a nearly transparent medium, Radio Sci  18, 138-142 (1983)), that are considered to be static in shape on the relevant time scales (Taylor&#39;s frozen turbulence hypothesis (G. I. Taylor,  The spectrum of turbulence, Proc R Soc Lon Ser - A  164, 0476-0490 (1938)). If a single such turbulent cell  13  transitions beam  11  whose diameter is small in comparison to cell  13 , beam  11  will be deflected as a whole (beam wander) and will not undergo significant distortion (L. C. Andrews, R. L. Phillips, R. J. Sasiela, and R. R. Parenti,  Strehl ratio and scintillation theory for uplink Gaussian - beam waves: beam wander effects, Opt Eng  45 (2006), L. C. Andrews and R. L. Phillips,  Laser beam propagation through random media, SPIE Press  (2005)). Beam deflection  15 , caused by single cell  13  with an index of refraction smaller than its surrounding, moving in a plane perpendicular to beam  11  is considered. Deflection  15  along the axis parallel to flow orientation  17  will initially be in the direction of flow orientation  17  as cell  13  enters beam  11 , and against flow orientation  17  as it exits beam  11 . When cell  13  is exactly midway, there will be no deflection parallel to flow  17 . 
         [0028]    Referring to  FIG. 4B , deflection  15  caused by cell  13  in the direction perpendicular to flow  17  will be to the right if cell  13  is displaced slightly to the left of beam  11 , or to the left if cell  13  is displaced to the right of beam  11 . No deflection perpendicular to flow  17  will be observed if cell  13  is centered on beam  11 . In the example shown, if flow  17  is in the positive y-direction and beam  11  propagates along the positive z-direction, right and left refer to the directions along the positive and negative x-axis direction respectively, assuming a right handed coordinate system. 
         [0029]    Referring now to  FIG. 5 , light sources that could be part of system  100  ( FIG. 2 ) are shown. Single beam source  113  can be received directly from PSD  111 , whereas both point source  53  and plain wave  55  require lens  57  to concentrate beam  11  onto PSD  111 . 
         [0030]    Referring now to  FIG. 6 , beam deflection result  60  is compared to beam distortion result  70 . The system and method of the present embodiment rely on beam wander to compute flow orientation. If there is beam distortion, the centroid of the beam can be tracked. For example 2-D tetra-lateral PSD measurement accuracy and resolution are independent of the spot shape and size. 
         [0031]    Referring now primarily to  FIG. 7 , field measurements  40  are shown. Red lines  21  represent beam deflection perpendicular to flow orientation  17  ( FIG. 4B ) and black lines  23  represent beam deflection parallel to the flow orientation  17  ( FIG. 4B ) of single beam  11  ( FIG. 4B ). Fourier amplitude  25  of beam  11  ( FIG. 4B ) parallel to the flow orientation  17  ( FIG. 4B ) and Fourier amplitude  27  of beams  11  ( FIG. 4B ) perpendicular to flow orientation  17  ( FIG. 4B ) are shown. Amplitude  29  of the Fourier calculated for angles from 0° to 360° with respect to PSD orientation is also shown. To compute flow orientation  17  ( FIG. 4B ), the Fourier transform giving the power spectral density can be computed for several, for example, but not limited to, forty to fifty, different directions and plotted as amplitude  29 . Flow orientation  17  ( FIG. 4B ) can be derived from amplitude  29  by determining maximum  31  of the combined power spectral densities. There is a 180° ambiguity in the determination of flow orientation  17  ( FIG. 4B ) that comes from the plurality of maximum shift of the maxima of the Fourier amplitude  29  over 360°. Flow orientation  17  ( FIG. 4B ) is measured with respect to the x and y directions on PSD  111  ( FIG. 4A ). Beam  11  ( FIG. 4B ) is perpendicular to x and y of the PSD and therefore no information is extracted in the direction of beam  11  ( FIG. 4B ). The regions of high amplitude will form a sinusoidal shaped color band along the horizontal axis. 
         [0032]    Embodiments of the present teachings are directed to computer systems such as system  100  ( FIG. 2 ) for accomplishing the methods such as method  150  ( FIG. 1 ) discussed in the description herein, and to computer readable media containing programs for accomplishing these methods. The raw data and results can be stored for future retrieval and processing, printed, displayed, transferred to another computer, and/or transferred elsewhere. Communications links such as electronic communications  124  ( FIG. 2 ) can be wired or wireless, for example, using cellular communication systems, military communications systems, and satellite communications systems. In an exemplary embodiment, the software for the system is written in FORTRAN and C. The system can operate on a computer having a variable number of CPUs. Other alternative computer platforms can be used. The operating system can be, for example, but is not limited to, the LINUX® operating system. 
         [0033]    The present teachings are also directed to software for accomplishing the methods discussed herein, and computer readable media storing software for accomplishing these methods. The various modules described herein can be accomplished on the same CPU, or can be accomplished on different computers. In compliance with the statute, the present embodiment has been described in language more or less specific as to structural and methodical features. It is to be understood, however, that the present embodiment is not limited to the specific features shown and described, since the means herein disclosed comprise forms of putting the present teachings into effect. 
         [0034]    Methods such as method  150  ( FIG. 1 ) of the present teachings can be, in whole or in part, implemented electronically. Signals representing actions taken by elements of the system and other disclosed embodiments can travel over at least one live communications network  124  ( FIG. 2 ). Control and data information can be electronically executed and stored on at least one computer-readable medium. System  100  ( FIG. 2 ) can be implemented to execute on at least one computer node in at least one live communications network  124  ( FIG. 2 ). Common forms of at least one computer-readable medium can include, for example, but not be limited to, a floppy disk, a flexible disk, a hard disk, magnetic tape, or any other magnetic medium, a compact disk read only memory or any other optical medium, punched cards, paper tape, or any other physical medium with patterns of holes, a random access memory, a programmable read only memory, and erasable programmable read only memory (EPROM), a Flash EPROM, or any other memory chip or cartridge, or any other medium from which a computer can read. Further, the at least one computer readable medium can contain graphs in any form including, but not limited to, Graphic Interchange Format (GIF), Joint Photographic Experts Group (JPEG), Portable Network Graphics (PNG), Scalable Vector Graphics (SVG), and Tagged Image File Format (TIFF). 
         [0035]    Although the present teachings have been described with respect to various embodiments, it should be realized these teachings are also capable of a wide variety of further and other embodiments.