Velocity vector field mapping using electrical capacitance sensors

1. A system for generating a velocity profile of a vessel interior or other object, the system comprising:

a capacitance sensor device comprising a plurality of electrodes arranged in a plurality of planes for placement around the vessel or the object, wherein the capacitance sensor device is adapted to provide electric field distribution and sensor sensitivity in three geometric dimensions;

data acquisition electronics in communication with the capacitance sensor device for receiving input data from the capacitance sensor device, the data acquisition electronics is comprised of a measurement circuit adapted to receive current from a plurality of capacitance pairs formed by pairs of the plurality of electrodes of the capacitance sensor device and to convert the received current to an output voltage;

a processing system in communication with the data acquisition electronics, the processing system programmed with instructions for executing on the processing system to: 1) receive two successive capacitance measurements for a first and second frame taken from the capacitance sensor device; 2) determine the time interval between the capacitance measurements by the inverse of frame rate; 3) reconstruct an image from the capacitance measurements of the first frame; 4) obtain an initial volumetric permittivity distribution inside the vessel; 5) calculate a sensitivity gradient numerically from sensor sensitivity distribution and voxel dimensions; and 6) determine a three dimensional velocity profile from a time rate change of capacitance, the initial volumetric permittivity distribution and the sensitivity gradient.

2. The system according to claim 1 , wherein the capacitance sensor device is comprised of at least two planes of electrodes to provide sensor sensitivity in the axial and radial directions.

3. The system according to claim 1 , wherein the processing system is programmed with an image reconstruction algorithm.

4. The system according to claim 3 , wherein the image reconstruction algorithm is adapted to provide real-time imaging of multiphase flow within the vessel.

5. The system according to claim 1 , wherein the processing system is programmed to calculate capacitance data from the input data received by the data acquisition electronics.

6. The system according to claim 1 , wherein the processing system is programmed with instructions to: 1) convert a three-dimensional image into an image vector, wherein elements of the image vector are voxels of the three-dimensional image; 2) define a three-dimensional sensitivity matrix related to the image vector and based on geometry of the geometrically three-dimensional capacitance sensor device and a matrix of measured capacitance; 3) compute a volume image vector using a reconstruction algorithm selected based on the three-dimensional sensitivity matrix and matrix of the measured capacitance; and 4) convert the volume image vector to the three-dimensional volume-image.

7. The system according to claim 1 , wherein the processing system is programmed with instructions to determine the three dimensional velocity profile based on Linear Back Projection or Landweber Iteration methods.

8. The system according to claim 1 , wherein the processing system is programmed with instructions to determine the three dimensional velocity profile in real-time.

9. The system according to claim 1 , wherein the capacitance sensor device is an adaptive ECVT sensor.

10. The system according to claim 1 , wherein the processing system is programmed with instructions to: 1) determine second derivatives of the capacitance measurements; 2) determine a second order gradient of a sensitivity matrix of the sensor; and 3) determine acceleration vector fields from the second derivatives of the capacitance measurements and the second order gradient of the sensitivity matrix.