Note: Descriptions are shown in the official language in which they were submitted.
Apparatus and Method for Measuring Velocity Perturbations in a Fluid
Related Application
This application claims the benefit of the filing date of U.S. Application No.
62/841,569,
filed on May 1, 2019, the contents of which are incorporated herein by
reference.
Field
This invention relates to apparatus and methods for measuring velocity
perturbations in a
fluid medium. Applications may include deployment for tracking and prediction
of the spread of
toxic chemicals, radiation, and other particulate and flow field measurement
for wind-farm siting
or meteorological analysis.
Background
The dispersal of various species or particulate matter in a fluid such as air
or water is
governed by mixing through eddies ¨ often turbulent in nature - in the air or
water. Naturally
occurring phenomena, industrial accidents, and warfare may result in the
release of species and
particulate matter such as chemical, biological, radiological, and nuclear
agents into the
atmosphere and/or large bodies of water, which may present a serious threat to
the environment
and local communities. Real-time and instantaneous flow data collected over a
large spatial
domain is necessary to predict the exact dispersal of such threats. Current
data acquisition
techniques that rely on sensors deployed on weather balloons, wind masts, and
ocean drifters
only provide slow responses due to their large inertia, and consequently flow
predictions suffer
from large bias errors that accumulate in time. As a result, measured
velocities are akin to a time-
averaged signal, only useful when mean fluid properties rather than velocity
perturbations are
desired.
Large-scale particle tracking velocimetry (LSPTV) and large-scale particle
image
velocimetry (LSPIV) have been used to experimentally characterize the
atmospheric boundary
layer using unconventional tracers including soap bubbles and natural
snowfall. While these
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results prove that heavier-than-air tracers can be used for optical velocity
measurements,
obtaining accurate data in unsteady or turbulent scales remains a challenge.
The inertia of large
tracer particles results in a significant time-lag in velocity response,
rendering such tracers of
limited use for measurement of transient phenomena, such as turbulent scales.
Summary
One aspect of the invention relates to apparatus for measuring position,
acceleration, and
rotation of an object moving in a fluid. Another aspect of the invention
relates to apparatus for
calculating the local and instantaneous velocity of the fluid in which the
apparatus is immersed.
Embodiments include features that allow for velocity measurements in complex
unsteady fluid
environments, and thus overcome obstacles which have prevented data collection
for the
development of a robust velocity measurement system for such conditions.
Embodiments include an in-air velocity sensor that is configured for passive
or active
flight involving a passive measurement phase where the object is allowed to
move freely with
the surrounding fluid. Such embodiments allow velocity measurement to be
directly tied to the
mechanics of the fluid eddies responsible for mixing processes. Embodiments
for chemical
dispersal provide data that allows for the reconstruction of the flow field in
the affected zone,
and provide information that can predict the spread of the chemical in real-
time. Embodiments
have the capability to provide users with data that reflects the live
conditions of the theatre of
operations and provide higher quality intelligence, such that relief and
containment efforts are
cost effective and prioritize those at highest risk.
Embodiments may be configured for other applications where a flow field in
other liquids or in
gaseous media such as air is required. For example, embodiments may measure
velocities in any
location of interest, which may be coupled with existing fluid simulation
techniques to provide
more meaningful predictions, allowing the user to perform more detailed
analysis and produce
more accurate simulations of real-world fluid phenomena including weather,
pollutant
dispersion, ocean currents, etc.
In one embodiment, an apparatus for measuring velocity perturbation in a fluid
comprises
one or more sensor vehicle adapted to be deployed in the fluid; a device that
obtains data
comprising at least one of position and acceleration of the one or more sensor
vehicle; and a
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processor that applies a physical model of the one or more sensor vehicle
behaviour to transform
the obtained data into a velocity field of the fluid, and outputs a map of the
velocity field in the
fluid.
In one embodiment, each of the one or more sensor vehicles is an active sensor
vehicle
comprising an inertial measurement unit (IMU) and a global positioning system
(GPS) unit; the
device that obtains data includes a receiver that receives IMU data and GPS
data from each of
the one or more sensor vehicles; and the processor applies the physical model
of the one or more
sensor vehicle to transform the received IMU and GPS data into the velocity
field of the fluid.
In one embodiment, each of the one or more sensor vehicles is a passive sensor
vehicle;
the device that obtains data includes a camera that obtains image data of the
one or more sensor
vehicles; and the processor determines position, velocity, and acceleration of
the one or more
sensor vehicles from the image data and applies the physical model of the one
or more sensor
vehicle to transform the image data into a velocity field of the fluid.
In one embodiment, an apparatus for measuring velocity perturbations in a
fluid
.. comprises one or more sensor vehicle adapted to be deployed in the fluid; a
device that obtains
data comprising position and acceleration of each sensor vehicle; and a
processor that applies a
physical model of the one or more sensor vehicle behaviour to transform the
obtained data into a
velocity field of the surrounding fluid, and outputs a fluid velocity field.
In one embodiment, each of the one or more sensor vehicles includes an IMU and
a GPS;
the device that obtains data includes a receiver that receives IMU data and
GPS data from each
of the one or more sensor vehicles; and the processor applies the physical
model of the one or
more sensor vehicle to transform the received IMU and GPS data into a velocity
field of the
fluid.
In one embodiment, the one or more sensor vehicles are optically tracked,
using one or
more cameras and a processor to obtain position and velocity information of
each sensor vehicle.
The processor applies the physical model of the one or more sensor vehicles to
transform the
obtained data into a velocity field of the surrounding fluid, and outputs a
fluid velocity field.
In one embodiment, the one or more sensor vehicles are adapted to move
passively with
the fluid (i.e., to be transported by the surrounding fluid itself).
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In one embodiment, the velocity field provides an indication of movement of
species
and/or particulate matter of interest in the fluid in real time. The
species/particulate matter may
comprise a chemical compound.
Another aspect of the invention relates to a method for measuring velocity
perturbations
in a fluid, comprising: deploying one or more sensor vehicle in the fluid;
obtaining data
comprising position and acceleration of each sensor vehicle; and using a
processor to apply a
physical model of the one or more sensor vehicle behaviour to transform the
obtained data into a
velocity field of the fluid; and outputting a fluid velocity field.
In one embodiment, the method may include obtaining IMU data and GPS data from
each of the one or more sensor vehicles; and transforming the received IMU and
GPS data into a
fluid velocity field.
In one embodiment the method comprises deploying one or more sensor vehicle in
the
fluid; obtaining data comprising at least one of position and acceleration of
the one or more
sensor vehicle; using a processor to apply a physical model of the one or more
sensor vehicle
behaviour to transform the obtained data into a velocity field of the fluid;
and outputting a
velocity field map of the fluid.
In one embodiment the method comprises deploying one or more active sensor
vehicle
comprising inertial measurement unit (IMU) and a global positioning system
(GPS) unit;
obtaining IMU data and GPS data from each of the one or more sensor vehicles;
wherein the
processor applies the physical model of the one or more sensor vehicle to
transform the IMU and
GPS data into a velocity field of the fluid.
In one embodiment the method comprises deploying one or more passive sensor
vehicle;
using a camera to obtain image data of the one or more sensor vehicles;
wherein the processor
determines position, velocity, and acceleration of the one or more sensor
vehicles from the image
data and applies the physical model of the one or more sensor vehicle to
transform the image
data into a velocity field of the fluid.
The method may include generating the velocity field to provide an indication
of
movement of species and/or particulate matter of interest in the fluid in real
time, wherein the
species/particulate matter may comprise a chemical compound.
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Brief Description of the Drawings
For a greater understanding of the invention, and to show more clearly how it
may be
carried into effect, embodiments will be described, by way of example, with
reference to the
accompanying drawings, wherein:
Figs. lA and 1B are diagrams showing systems having one sensor vehicle,
according to
embodiments.
Fig. 2 is a diagram showing a system with multiple sensor vehicles, and an
output
comprising a corrected flow map produced by applying a wind-correction
algorithm to the sensor
vehicle data, according to one embodiment.
Fig. 3A is a flowchart overview of a flow-sensing process, from start to
completion of a
measurement, according to a generalized embodiment based on an active sensor
vehicle.
Fig. 3B is a flowchart overview of a flow-sensing process, from start to
completion of a
measurement, according to a generalized embodiment based on a passive sensor.
Fig. 4A is a flowchart overview of a wind-correction algorithm, according to a
generalized embodiment.
Fig. 4B is a flowchart of a model-based wind correction algorithm, according
to one
embodiment.
Fig. 5 is a photograph of a prototype spherical active sensor vehicle, shown
opened to
reveal internal hardware.
Fig. 6 is a diagram of a wind tunnel used to a test a prototype sensor
vehicle.
Figs. 7A and 7B are plots of position/distance, velocity, and acceleration
data obtained by
processing data from large and small sensor vehicles, respectively, together
with data obtained
from high-speed camera images for comparison, in prototype testing and data
processing based
on a first physical model of the sensor vehicles.
Figs. 8A and 8B are plots of flow velocity as measured by large and small
sensor
vehicles, respectively, and calculated (predicted) velocity for the two
sensors in the wind tunnel
of Fig. 6, in prototype testing and data processing based on a first physical
model of the sensor
vehicles.
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Fig. 9 shows plots of position/distance, velocity, and acceleration data
obtained by
processing data from the large sensor vehicle, using a second physical model,
together with data
obtained from high-speed camera images, for comparison.
Fig. 10 is a plot of flow velocity as measured by the large spherical
prototype sensor
.. vehicle of Fig. 5 and calculated (predicted) velocity for the sensor in the
wind tunnel of Fig. 6, in
prototype testing and data processing based on a second physical model of the
sensor vehicle.
Fig. 11 is a representative drawing of a typical milkweed seed, used as an
optically-
tracked passive sensor vehicle.
Fig. 12 is a plot of flow velocity measured using an optically tracked passive
sensor
vehicle in the wind tunnel of Fig. 5, and calculated (predicted) velocity for
the sensor, in
prototype testing.
Detailed Description of Embodiments
Force generated by a body immersed in a fluid exposed to a perturbation such
as a rapid
flow acceleration, or gust, is generally characterized by a sharp increase in
fluid forces before
relaxing back to a steady state. Such acceleratory motions are ubiquitous in
wind, where the
flow is characterized by turbulent fluctuations and gusts. Measuring turbulent
events is difficult
outside of a laboratory setting, due to the limitations of conventional
sensors which, as described
above, only provide unresponsive point-data due to their relatively heavy and
large
embodiments.
According to one aspect of the invention, physical modelling techniques are
provided that
accurately capture small-scale acceleratory events in a fluid. Embodiments
described herein may
be used to overcome the difficulty encountered with prior techniques
associated with in-situ
turbulence measurements. Embodiments based upon a combination of measurements
and
.. physical modelling offer significantly lower computational costs, and allow
for real-time
measurements and sensor feedback. Embodiments may employ Lagrangian (i.e.,
flow-
following) methods for turbulence measurements over large domains.
According to another aspect of the invention, apparatus is provided including
sensor
platforms that respond to real turbulent scales, and thereby are able to
follow a path taken by a
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particle in a turbulent flow, or the path of the turbulent flow. Sensor
platform embodiments may
include one or more active or passive sensor vehicles, and include sensor data
acquisition
components adapted to acquire data from active or passive sensor vehicles.
Some embodiments
include a plurality of sensor vehicles that may be deployed as a "swarm" in a
region of interest
(e.g., an atmospheric or aquatic/oceanic environment). By exploiting sensor
vehicle behaviour in
which sensor vehicles respond to real turbulent scales, the sensor vehicles
thus provide data
corresponding to actual fluid mixing, flow, and dispersal phenomena. By
employing sensors that
operate in a Lagrangian frame, embodiments provide superior spatial
resolution, and improved
efficiency in data acquisition over prior approaches based on large
measurement domains. To
accurately determine flow conditions from inertial measurements, embodiments
may be based on
a system that employs low-order force modelling to determine flow velocity.
As used herein, the term "turbulence" or "turbulent flow" refers to fluid
motion
characterized by perturbations in pressure and flow velocity, resulting in,
for example, enhanced
fluid mixing. Turbulence or turbulent flow may also be described by the
presence of coherent
structures within the flow, that are responsible for transport of momentum,
energy, and/or other
scalar quantities.
Embodiments which may be used for applications such as measurement of
atmospheric
or aquatic/ocean currents include a plurality of sensor vehicles that are
dispersed over a
measurement domain in the atmosphere or in water. Some embodiments use active
sensor
vehicles wherein each sensor vehicle includes at least one active (e.g.,
powered or energized) on-
board instrument that senses one or more parameter of the sensor vehicle
behaviour in the
measurement domain, and/or of the local fluid motion in which it is immersed
or dispersed. For
example, an on-board instrument may be an inertial measurement unit (IMU), a
global
positioning system (GPS) unit, etc. The sensed parameters are used to compute
fluid velocity
and acceleration along sensor path lines, which are tracked via a suitable
technology such as the
GPS. In one example, the acquired sensor data may be used to generate an
accurate flow map
based on each location of the plurality of sensor vehicles. This may be fed
into existing large-
scale models (e.g., models obtained using conventional methods) for improved
accuracy.
Other embodiments use one or more passive sensor vehicles, wherein each
passive sensor
vehicle does not include any active on-board instrument. A plurality of
passive sensor vehicles
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may be deployed in a region of interest and tracked using one or more cameras
or other suitable
device to obtain sensor data. Embodiments may use optical tracking at visible
or non-visible
(e.g., infra-red (IR)) wavelengths. Use of wavelengths such as IR may
advantageously allow for
data to be obtained from passive sensor vehicles at night or in low-light or
low-visibility
-- conditions. In one embodiment sensor data is acquired as camera images
which can then be
processed to obtain position, velocity, and acceleration data of each sensor
vehicle. Further
processing of the data using a physical model may be performed to obtain a
corrected flow map.
Optionally, sensor vehicles may be equipped with other instruments such as
sensors for
detecting substances, such as, for example, gases, pollutants, salinity, etc.,
and the data used to
-- correlate substance concentration with the flow regime and behaviour. Thus,
the dispersal,
concentration, etc., of such substances may be tracked and/or predicted in an
atmospheric or
aquatic/oceanic environment.
According to one embodiment, a plurality of active sensor vehicles equipped
with
suitable sensors may be deployed in a hazardous region for measuring and
tracking harmful
-- substance dispersal. The sensor vehicle swarm is dispersed into the
measurement domain prior
to measurement. Whereas any number of sensor vehicles may be deployed, and
greater numbers
may enhance tracking flow and predicting dispersal, the number of sensor
vehicles deployed may
depend on one or more of the specific application, the cost, and the data
acquisition and
processing capabilities of the system.
For atmospheric applications, the dispersal of sensor vehicles may be achieved
any of a
number of ways. For example, a ground-based launcher may send the sensor
vehicles up to the
desired altitude, or the sensor vehicles may have active flight capabilities
to reach the
measurement domain from a base station, or the sensor vehicles may be released
from an aircraft
or drone. For water-borne applications, the dispersal may be achieved, e.g.,
from a boat, an
-- aircraft, or drone. Once within the measurement domain, the sensor vehicles
move passively
throughout the flow and the on-board sensors track their motion in time. The
data collected can
then be processed to determine an output such as a fluid velocity field,
velocity map, etc. The
velocity map produced by the sensors, potentially coupled with in-situ
measurements of harmful
substance concentration, can be used to track and predict species and
particulate dispersal. Thus,
-- such Lagrangian measurements allow for acquisition of data at a scale
relevant to fluid mixing,
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allowing for accurate predictions of species and particulate dispersal. Such
an embodiment may
optionally use real-time sensor data transmission for near instantaneous
feedback, as may be
desired in emergency situations such as an industrial disaster where immediate
action must be
taken.
According to another embodiment, a plurality of passive sensor vehicles may be
dispersed into a measurement domain prior to measurement. For atmospheric
applications, the
dispersal may be achieved any of a number of ways. For example, a ground-based
launcher may
send the sensor vehicles up to the desired altitude, or the sensor vehicles
may be released from an
aircraft or drone. For water-borne applications, the dispersal may be
achieved, e.g., from a boat,
an aircraft, or drone. Once within the measurement domain, the sensor vehicles
move passively
throughout the flow, and their movement is detected and tracked using optical
tracking. For
example, the plurality of sensor vehicles may be tracked using one or more
cameras. The sensor
data (i.e., camera images) collected may then be processed to obtain position
and velocity data of
each sensor vehicle. Further processing of the data using a physical model may
be performed to
.. determine and output a fluid velocity field, a velocity map, etc. Such
outputs may be used to
track and predict species and particulate dispersal in the fluid environment,
to track and predict
weather, etc. Use of such Lagrangian measurements allows for acquisition of
data at a scale
relevant to fluid mixing, enabling accurate predictions of, e.g., species and
particulate dispersal.
Further, by capturing sensor data in real time, a velocity map may be
generated substantially
instantaneously, as may be desired in emergency situations (e.g., an
industrial disaster where a
dangerous substance is released) where immediate action must be taken.
Thus, a system as described herein, which may include one or more sensor
vehicle, may
be used in diverse applications in gaseous or liquid environments, for
obtaining data relating to
dispersal of particulate matter, chemical compounds, etc., in such
environments, and for
predicting dispersal of such particulate matter in such environments. Further
applications, such
as monitoring and predicting weather, are also contemplated.
According to some embodiments, an active sensor vehicle may include sensors
for
measuring acceleration and orientation of the sensor vehicle. In one
embodiment, the sensors are
implemented with a 3-axis accelerometer, a 3-axis gyroscope, and a 3-axis
magnetometer. These
sensors may be located substantially at the vehicle's centre of gravity, for
accurate determination
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of the sensor vehicle's orientation. A sensor vehicle may also include a radio
transmitter for
transmitting the sensor data to a base station. The accelerometer, gyroscope,
and magnetometer
may be implemented with an inertial measurement unit (IMU). The sensor vehicle
may also
include a GPS device, coupled with the IMU data, for accurate dead-reckoning
(i.e., determining
the sensor vehicle geographic position).
Fig. 1A shows a basic system according to embodiments described herein. As
shown in
Fig. 1, the system includes one or more active sensor vehicle 100a equipped
with a radio
transmitter and a base station 120a including a radio receiver 122a and a
processor 124a. The
sensor vehicle is small and light-weight, and has sensors that measure
acceleration from a wind
gust 110a acting upon it. The sensor vehicle transmits sensor data to the base-
station 120a for
processing. The system may include a sensor vehicle calibration for the flow
in which it is
deployed. For example, a calibration for neutrally buoyant vehicles for water-
borne applications
or lightweight and high drag vehicles for atmospheric applications.
Fig. 1B shows a basic system according to other embodiments described herein.
As
shown in Fig. 1B, the system includes one or more passive sensor vehicle 100b,
at least one
camera 105, and a base station 120b including an optional receiver 122b and a
processor 124b.
Relative to the embodiment of Fig. 1A, the passive sensor vehicle 100b may be
smaller and is
very light-weight, such that it may be adapted to move passively through the
fluid and/or to be
transported by the fluid, e.g., carried by a wind gust 110b acting upon it. At
least one camera
105 captures images of the sensor vehicle(s) 100b and relays or transmits the
images, i.e., sensor
data, to the base-station 120b for processing. The system may include a sensor
vehicle
calibration for the flow in which it is deployed. For example, a calibration
for neutrally buoyant
sensor vehicles for water-borne applications or for lightweight and high drag
vehicles for
atmospheric applications.
In one embodiment, the base station comprises a radio receiver that receives
sensor data
signals from one or more active sensor vehicles. The radio receiver is
connected to a processor,
such as a laptop computer, with a suitable connection such as a universal
serial bus (USB).
Alternatively, the base station may be configured with a radio receiver and
dedicated processor,
central processing unit (CPU), storage device, etc., so that a separate
computing device is not
required. In another embodiment, the base station receives image data for one
or more passive
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sensor vehicles from one or more cameras. The base station, together with the
processor,
receives real-time sensor vehicle data and stores the data for post-
processing, or performs
substantially live processing so that information about the flow field is
instantly available. The
data recorded and processed may include one or more of x-axis, y-axis, and z-
axis accelerations,
angular accelerations, magnetic field strength, etc.
Fig. 2 shows a representation of an implementation of a system according to
embodiments described herein. As shown in Fig. 2, multiple sensor vehicles are
dispersed
throughout a measurement domain 210. In this example, there are four sensor
vehicles 212a,
212b, 212c, 212d. At each timestep t-1, t, t+1, t+2, parameters (i.e., data)
for each sensor
vehicle, such as position, velocity, acceleration, and/or other parameters of
interest are recorded
and transmitted to the base station 220 where processing occurs. The time
steps may be
synchronized or different for all or subsets of the sensor vehicles. A
corrected flow map 230 is
produced, which may comprise true wind-vectors, for example. This is shown in
Fig. 2 where it
can be seen that streamlines in the corrected flow map 230 are different from
path lines of the
sensor vehicles in 210, due to non-ideal sensor vehicle response. In some
embodiments the
sensor vehicle path lines are not directly transformed into the fluid
streamlines. The streamlines
depend upon the resulting vector field after a correction algorithm is
applied. Thus, applying a
correction algorithm to the data, as described herein, allows for a more
accurate flow
measurement.
Processing active sensor vehicle data may include the processor executing one
or more
algorithms, such as an orientation algorithm to determine sensor vehicle
orientation, optionally
wherein measurements are oriented to a ground-fixed coordinate system. Fig. 3A
is a flowchart
showing processing steps carried out by the processor, according to a
generalized embodiment.
Upon dispersing one or more sensor vehicles 302, sensor data relating to
inertial measurements
are obtained 304 from the accelerometer, gyroscope, and magnetometer. The
processor
computes a velocity vector 306 based on this data. In one embodiment, the
processor executes
the Madgwick IMU and attitude and heading reference system (AHRS) sensor
fusion algorithm
(https://x-io.co.uk/open-source-imu-and-ahrs-algorithms/), although other
algorithms may also
be used. A wind correction algorithm is then executed 308 to correct for the
effect of wind on
the sensor vehicle(s). Ground-fixed accelerations may be used as inputs for
the wind correction
algorithm. The measured flow is then output 310 for each sensor vehicle. The
processing steps
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of Fig. 3A may be executed repeatedly at a selected time interval (e.g., at a
rate of 1, 10, 100,
1000 Hz, etc.) to obtain flow measurements from each sensor vehicle over time
as the sensor
vehicles move through the flow field.
Processing passive sensor vehicle data may include the processor executing one
or more
algorithms, such as the embodiment shown in the flowchart of Fig. 3B. Upon
dispersing one or
more sensor vehicles 322, sensor vehicle image data are obtained 324 from one
or more cameras.
The processor analyzes the image data 326 and computes a velocity vector 330
based on the
data. For example, the processor may execute a computer vision algorithm 328
to obtain motion
tracking data (e.g., position, velocity, and acceleration) from the image data
324. A wind
correction algorithm is then executed 332 to correct for the effect of wind on
the sensor
vehicle(s). Ground-fixed accelerations may be used as inputs for the wind
correction algorithm.
The measured flow is then output 334 for each sensor vehicle. The processing
steps of Fig. 3B
may be executed repeatedly at a selected time interval (e.g., at a rate of 1,
10, 100, 1000 Hz, etc.)
to obtain flow measurements from each sensor vehicle over time as the sensor
vehicles move
through the flow field.
Fig. 4A shows an example of a generalized wind-correction algorithm. The
algorithm
can of course be adapted for use with other fluids. Upon receiving the
recorded or computed
velocity of an active or passive sensor vehicle 400, various aerodynamic
properties 404 of the
sensor vehicle are inputted to a physical model, i.e., a model based upon the
sensor vehicle
interaction with its surrounding flow, e.g., a drag force model 406, and the
model is evaluated
with respect to parameters such as quasi-steady-state drag and added mass 408.
An example of a drag force model for a spherical sensor vehicle is described
by the
following equation:
FD = 0.5pACD(u ¨ U)2n-R2 + -113pARR3K d(u-U)
dt (1)
where PA is the density of air, CD is the drag coefficient of a sphere, u is
the wind velocity, U is
the sensor velocity, R is the radius of the sensor body and K is the added-
mass coefficient for a
sphere. U, and its rate of change, are measured by the sensor vehicle,
allowing for u to be
calculated by solving the differential equation. For other sensor vehicles
(i.e., other shapes,
sizes, etc.) or other fluids, an appropriate model would be used instead at
406.
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Another example of a drag force model for a sphere is described by equation
(2). This
model is based on an energized-mass approach (Galler, J.N., et al.,
Application of the Energized-
Mass Concept to Describe Gust-Body Interactions, AIAA Scitech 2020 Forum,
2020) which
offers a robust kinetic energy based framework for modelling forces resulting
from separated
flow around an object (i.e., a sensor vehicle), requiring only kinematics,
Reynolds number, and
geometry-based inputs.
dme du dU
FD= ¨dt (tt ¨ U) + M e(¨dt ¨ ¨dt) (2)
where me is energized mass, which is modelled by the following equation:
1 22p7tR2 4) (u ¨ U)Re-,idt while < - Cdpn-R2(u ¨ U)
dt 2
rne _ ¨ 1 t (3)
m_7 + -pn-R2Cd fT(u ¨ U)dt
2 otherwise t> T
where t is time, T is the time at which steady-state conditions are satisfied
and Re is Reynolds
number in the body-fixed frame of reference. Of course, other approaches may
be used to
develop a physical model for a sensor vehicle, depending on factors such as
Reynolds number,
Mach number, geometric shape of sensor vehicle, etc.
Returning to Fig. 4A, after the model is evaluated, the true wind velocity is
obtained 410,
.. at which point sensor tracks and vectors can be exported 412 for further
processing. These steps
may be repeated at the selected time interval of the processing of Fig. 3A or
3B until the
measurement is complete 414.
Fig. 4B shows an example of a physical model-based wind correction algorithm.
Prior to
a measurement, an equation of motion 450 specific to a selected sensor vehicle
is determined
based upon forces to be experienced by the sensor vehicle. An example of an
equation of motion
is shown at 452. During or post measurement, the data is processed 454 through
the equation of
motion to extract the unknown wind velocity 456, and, optionally, the wind
acceleration is
computed and outputted 458. In the case of an active sensor vehicle,
processing may include
using IMU data 460 received from the sensor vehicle. These steps may be
repeated at the
.. selected time interval of the processing of Fig. 3A or 3B until the
measurement is complete 462.
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The invention is further described by way of the following examples. It will
be
understood that the examples are provided for illustrative purposes, and are
not to be construed
as limiting the scope of the invention in any way.
Example 1
The following example describes a prototype that was built and tested to
demonstrate an
embodiment based on active sensor vehicles.
Prototype sensor vehicles were constructed from StyrofoamTM spheres. A "large"
sensor
vehicle was 9.5 cm in diameter and had a mass of 17 g, and a "small" sensor
vehicle was 6.0 cm
in diameter and had a mass of 10 g. The Styrofoam spheres were cut in half,
and cavities were
cut to accommodate hardware. Fig. 5 is a photograph showing one of the sensor
vehicles with
Styrofoam sphere halves 510a, 510b opened to reveal the internal hardware. The
hardware was a
printed circuit board 512, which included an IMU, data transmission circuitry
and antenna, and
power regulator, and a battery 514. A physical model was developed for the
spherical sensor
vehicles (see Equation (1)).
Fig. 6 is a diagram of the wind tunnel in which prototype testing was carried
out. The
wind tunnel was constructed in a vertical, open-jet configuration with an
unsteady capability to
both mimic natural updrafts, and to reduce complexity in tracking the sensor
vehicle's motion.
A 3 x 3 array of high-power computer fans 612 in the base 610 were used for
flow generation,
and were capable of producing wind speeds up to 72 km/h. A single honeycomb
layer (not
shown) was installed above the fan array for flow straightening, and two mesh
screens (not
shown) were installed to reduce the turbulence intensity of the flow itself
612. A contraction 614
was designed using a Bell-Mehta curve for smooth outflow conditions and
mounted above clear
PlexiglassTM walls. A pulse-width-modulation based controller was designed
using Lab View
and a National Instruments 6212-USB data acquisition (DAQ) system. A servo-
based sensor
vehicle release mechanism 616 was used to release the sensor vehicle into the
wind tunnel and
the sensor vehicle was allowed to respond freely to gusts of up to 54 km/h
provided by the fan
array. Sensor vehicle motion was recorded with a Photron FASTCAM 5A4 high
speed camera
618. The flow profile was determined using particle image velocimetry for
comparison to
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measured results. Theatre fog was used to seed the flow, and a 3W Nd:YAG
continuous laser
was used for illumination.
A base station including a radio receiver and data acquisition hardware was
connected to
a laptop computer. The base station communicated with the sensor vehicle to
receive data, and
passed the data to a processing algorithm based on Fig. 3A executed by the
laptop computer.
Inertial measurements provided by the sensor vehicles were received and
corrected using a wind-
correction algorithm based on Fig. 4A and the physical models developed for
the spherical
sensor vehicles, and the applied wind (gust) was calculated.
First, a physical model was developed based on the equation of motion given
above
(equation (1)) and used to process the data. Figs. 7A and 7B show plots of
position/distance,
velocity, and acceleration data obtained by processing data from the small and
large sensor
vehicles, respectively, using the developed model and algorithm, together with
data obtained
from the high-speed camera images, for comparison.
Figs. 8A and 8B show plots of flow velocity as measured by the small and large
sensor
vehicles, respectively, and calculated (predicted) velocity for the two
sensors in the wind tunnel.
Equation (1) was used to generate the calculated plots after processing the
direct outputs from
the sensor vehicles. By inputting the correctly oriented velocity vectors into
the variable U, the
wind was calculated by stepping through the equation in time. It can be seen
that both sensor
vehicles capture the gust trends, however, vehicle inertia causes a time lag.
Second, an alternative physical model (equation (2)) was developed and used to
analyze
data from the large sensor vehicle. Fig. 9 shows plots of position/distance,
velocity, and
acceleration data obtained by processing data from the large sensor vehicle,
using the alternative
developed model and algorithm, together with data obtained from the high-speed
camera images,
for comparison.
Fig. 10 shows plots of flow velocity as measured using the large sensor
vehicle, and
calculated (modelled) velocity for the sensor in the wind tunnel. The solid
line shows the true
wind velocity measured via particle image velocimetry, the dashed line shows
the velocity of the
sensor vehicle, and the dotted line with square markers shows the corrected
wind velocity
produced by processing the sensor vehicle motion. The model was used to
generate the
calculated plots after processing the direct outputs from the sensor vehicle.
By inputting the
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correctly oriented velocity vectors into the model, the wind was calculated by
stepping through
the equation in time. It can be seen that the sensor vehicle captures the gust
trends, however,
vehicle inertia causes a slight time lag.
Example 2
A milkweed seed was used as a passive sensor vehicle due to its naturally high
drag and
relatively low mass. Passive sensor vehicles may of course be manufactured
according to
required/selected specifications, which may be tailored to measurement
applications of interest.
Fig. 11 is a representative drawing of a typical milkweed seed. The milkweed
seed has many
hairs sprouting from a central seed in a near-spherical pattern, providing an
overall geometry that
is relative straight-forward to physically model. A physical model was
developed for the sensor
vehicle using equation (2), assuming negligible effects of porosity and
flexibility. The sensor
vehicle used in this example weighed 1.93 mg and is representative of sensors
that may be used
for optical measurements in volumes of tens of cubic metres.
The wind tunnel of Fig. 6 was used to perform the experiments, following the
same
procedure as Example 1, except the high speed camera (Photron FASTCAM SA4) was
used to
optically record the motion of the sensor vehicle in response to a wind gust.
The image data were
processed on a laptop computer running an open-source Python-based computer
vision algorithm
(https://www.pyimagesearch.com/2015/09/14/ball-tracking-with-opencv/) which
was modified
to obtain motion tracking data (position, velocity, and acceleration) from the
recorded sensor
vehicle data.
Fig. 12 shows plots of flow velocity, sensor vehicle response, and modelled
flow velocity
extracted from the images recorded of the sensor vehicle, using a processing
algorithm based on
Fig. 3B. The solid line shows the true wind velocity measured via particle
image velocimetry, the
dashed line shows the velocity of the sensor vehicle and the dotted line with
square markers
shows the corrected wind velocity produced by processing the sensor vehicle
motion. Applying a
wind-correction algorithm, in this case, based on Fig. 4A, allows for the true
wind velocity to be
extracted from the motion image data of the sensor vehicle.
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All cited publications are incorporated herein by reference in their entirety.
Equivalents
While the invention has been described with respect to illustrative
embodiments thereof,
it will be understood that various changes may be made to the embodiments
without departing
from the scope of the invention. Accordingly, the described embodiments are to
be considered
merely exemplary and the invention is not to be limited thereby.
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