Multi-directional, three component velocity measurement pressure probe

The development of a nearly-omni-directional pressure probe for three-velocity-component and pressure measurements is described, with particular focus on the techniques and technology employed in probe construction, calibration, electronic interfacing and frequency-response study. The device eliminates the velocity directionality limitations of current multi-hole probes and makes a valuable, rugged tool for use in complex 3-D flow mapping and aerodynamic design and evaluation, in basic research as well as industrial development settings. The probe performance is demonstrated in a flowfield with flow reversal downstream of a backward-facing step. The probe provides low-frequency response capabilities. The probe's main element is a multi-pressure port spherical head, which may include eighteen ports. Fiber optic interferometry techniques may be incorporated to significantly increase frequency response.

TECHNICAL FIELD OF THE INVENTION 
This invention generally relates to pressure probes and, more particularly, 
to a multi-directional velocity measurement pressure probe. 
BACKGROUND 
The design, evaluation and optimization of complex aerodynamic geometries 
involves extensive wind-tunnel testing and/or computationally-intensive 
numerical simulations. Even in the latter case, high-quality experimental 
wind-tunnel work with minimal, quantifiable errors is still necessary for 
code-validation purposes. Moreover, in aerodynamic testing facilities 
where large volumes of data need to be acquired in tight schedules, "down" 
time due to instrumentation lack of performance is highly undesirable. 
Such facilities include, among others, industrial testing wind tunnels, as 
well as high-productivity CFD code validation facilities. 
In such environments, flow measurement techniques such as Laser-Doppler 
Velocimetry (LDV) and Particle Image Velocimetry (PIV), although powerful, 
usually require painstaking efforts for their successful usage. Costly 
components, complex setups, troublesome flow "seeding" requirements, lack 
of flexibility, ruggedness and mobility and ease of misalignment often 
render such techniques impractical. Moreover, in testing of complex 
three-dimensional geometries, accessibility of the entire flow-field 
around the model is an essential issue. When employing optical techniques, 
large sections of the flow-field are physically obstructed by the presence 
of the model. To access such regions, repositioning of the instrumentation 
setup may be necessary. This is a time-consuming process having associated 
potential pitfalls. 
Multi-hole pressure probes have in many cases provided the easiest-to-use 
and most cost-effective method for three-component flow velocity 
measurements in research and industry environments. However, even though 
the measurement capabilities of such instruments have been expanded, the 
current pressure probe configurations and techniques have only a limited 
range of velocity inclinations that they can measure. Conventional probes 
are limited to five- or seven-hole configurations with conical probe 
heads. Current probes and techniques also have severe frequency-response 
limitations. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, disadvantages and problems 
associated with pressure probes have been identified and addressed. 
In one embodiment of the present invention, a pressure probe head is 
provided. The head includes a body having a plurality of pressure ports. 
The plurality of pressure ports includes eight or more pressure ports. 
In another embodiment of the present invention, a spherical probe head is 
provided. The head may have one or more ports spaced about the surface of 
the head. 
According to various aspects, the pressure ports are symmetrically spaced 
about a surface of the spherical head. The ports may be evenly distributed 
about the surface. 
According to another aspect, eighteen pressure ports may be provided. The 
pressure ports may be provided in one or more five-port arrangements. Four 
of the ports of any given arrangement may be peripheral ports, which may 
be evenly spaced about a circle defined by a surface of the spherical 
body. The fifth port may be a central port, which may be located at the 
intersection of the sphere and a central axis of the circle. Each 
peripheral port may be shared by an adjacent five-hole configuration. 
The head may be connected to a sting. The ports may be connected, via 
tubing, to pressure transducers incorporated in an integrated pressure 
scanner. 
The ports may be distributed based on a spherical coordinate system. The 
spherical coordinate system may be aligned along a longitudinal axis of 
the sting. 
The sting may include a number of parallel first pressure tubes 
corresponding to the number of pressure ports. Each of the pressure ports 
may be connected to a corresponding first pressure tube by a second 
pressure tube. Each of the second pressure tubes may extend normal to a 
surface of the head. The first tubes may be arranged according to a 
hexagonal arrangement within the sting.

DETAILED DESCRIPTION OF THE INVENTION 
FIG. 3 depicts a probe assembly 10 in accordance with an embodiment of the 
present invention. Probe assembly 10 includes a probe head 12, a sting 14 
and an integrated pressure scanner 16. Probe assembly 10 is configured to 
provide a near-omni-directional probe, which can measure almost any 
velocity vector regardless of its orientation and which operates in a wide 
range of Reynolds numbers in the incompressible regime of flows. 
The present invention may be discussed in terms of certain directional 
conventions. A velocity inclination and a conventional seven-hole probe 
are shown in FIG. 1. The velocity inclination is indicated as angle 
.theta.. .theta..sub.max is the maximum velocity inclination that can be 
reliably measured by a probe. For example, a probe with a .theta..sub.max 
of 40.degree. can accurately measure any velocity vector that is contained 
within a cone with its apex included angle of 80.degree.. This included 
cone angle will be referred to as the cone angle. A cone angle for a 
conventional probe is depicted in FIG. 2. 
Known devices are limited to a maximum measurable cone angle of 
150.degree., which may be achieved with a seven-hole probe. By way of 
contrast, an embodiment of the present invention provides a probe head 
having a cone angle approximating 360.degree.. A probe incorporating the 
head has a cone angle on the order of about 340.degree.. Thus, the probe 
can measure virtually any velocity vector regardless of its orientation. 
Conventional multi-hole probes may consist of several small diameter tubes 
axisymmetrically arranged inside a larger tube with one end machined into 
a cone. The apex of the cone coincides with the central hole which is 
surrounded by four or six equally-spaced holes. As can be seen from FIG. 
1, a normal axis of each of the holes forms an acute angle with the 
longitudinal axis of the sting. These simple probes are limited to a small 
range of flow angularity. 
Probe 10 preferably has a head with more than seven ports. In one 
embodiment, probe 10 has eighteen holes. Probe 10 may be utilized to 
overcome previous limitations with respect to the small range of flow 
angularity. To achieve a larger number of holes relative to conventional 
probes, the present invention incorporates a probe design which deviates 
from traditional five- and seven-hole probe designs. With conventional 
probe designs, additional holes are undesirable because they would 
complicate the design without improving the performance of the probe. 
According to an embodiment of the present invention, a sphere is used as 
the basis for arranging the ports on probe head 12. The symmetry of the 
sphere allows for the realization of omni-directionality. No single hole 
is considered the "central" hole and the spherical shape changes the 
"straight through" tubing configuration found in conventional five- and 
seven-hole probes. According to an aspect of this embodiment, a particular 
arrangement of eighteen holes on a sphere facilitates a feasible design. 
The basic structural features of the spherical probe head are illustrated 
in FIGS. 4-7. For clarity the port arrangement on the spherical probe head 
12 is presented in two different coordinate systems. A coordinate system 
that emphasizes the grouping of the eighteen ports in six five-hole 
configurations is shown in FIG. 4. In FIG. 4, the sting 14 is omitted for 
clarity. In the coordinate system of FIG. 4, pressure ports 18 are 
represented by black dots and are distributed as follows (in terms of 
their spherical coordinates): 
8 ports at .theta.=90.degree. and .phi.=0.degree., 45.degree., 90.degree., 
135.degree., 180.degree., 225.degree., 270.degree. and 315.degree.; 
4 ports at .phi.=0.degree. and .theta.=0.degree., 45.degree., 135.degree., 
180.degree.; 
2 ports at .phi.=180.degree. and .theta.=45.degree., 135.degree.; 
2 ports at .phi.=90.degree. and .theta.=45.degree., 135.degree.; and 
2 ports at .phi.=270.degree. and .theta.=45.degree., 135.degree. 
The ports 18, when properly combined in six groups of five, as indicated in 
FIG. 4, form a network of five-hole probe configurations. An example of 
one of the six five-hole probe groups is the group of four peripheral 
ports coinciding with circle 20 plus the central port coinciding with the 
intersection between the sphere and the positive z-axis. Each one of these 
configurations is operable as a five-hole probe. The central ports of 
these five-hole configurations are the ports located at the intersections 
of the x-, y- and z- coordinate axes with the surface of the sphere. As 
can be seen, each of the four peripheral ports of a given five-hole 
configuration is also a peripheral port for an adjacent five-hole 
configuration. Therefore, even though there are six five-hole 
configurations, there are only a total of eighteen ports. 
In terms of construction and calibration, the port arrangement is best 
visualized in the spherical coordinate system of FIG. 5, which is aligned 
with the sting. One may consider a cube, with a port placed at the center 
of each one of its six sides and a port placed at the midpoint of each one 
of its twelve edges. This allows for six five-hole configurations, one on 
each face of the cube. If a sphere is now inscribed within the cube, the 
eighteen-hole probe head takes shape. 
Probe sting 14 obviously interferes with the global symmetry of the 
spherical probe. Preferably, however, its effect is minimized by having 
the sting enter along a major diagonal of the cube, thus intersecting the 
sphere at the geometrical center of three adjacent five-hole port 
configurations. In this coordinate system, the pressure ports are located 
as follows (.theta. referenced from the sting axis, as shown in FIG. 5): 
ports 1-3 at .theta.=35.27.degree. and .phi.=60.degree., 180.degree., 
300.degree.; 
ports 4-6 at .theta.=54.73.degree. and .phi.=0.degree., 120.degree., 
240.degree.; 
ports 7-12 at .theta.=90.00.degree. and .phi.=30.degree., 90.degree., 
150.degree., 210.degree., 270.degree., 330.degree.; 
ports 13-15 at .theta.=125.27.degree. and .phi.=60.degree., 180.degree., 
300.degree.; and 
ports 16-18 at .theta.=144.73.degree. and .phi.=0.degree., 120.degree., 
240.degree. 
Another advantage of this configuration is that the holes align themselves 
with the sting in such a way as to facilitate hexagonal spacing of the 
tubes inside the sting, which in turn minimizes the thickness or diameter 
of the sting. 
The internal tubing of the sphere is significantly more complex than that 
of five- or seven-hole probe designs. Preferably, precision machining of a 
brass sphere is used to drill holes at each of the individual ports normal 
to the spherical surface of probe head 12. These holes are then 
intersected with 18 parallel holes drilled from the back of sting 14. FIG. 
6 shows the internal tubing structure as viewed along the longitudinal 
axis of the sting 14. FIG. 7 is a partial perspective schematic of the 
fabricated probe assembly 10, showing the drilled holes on the spherical 
surface of probe head 12 and on the base of sting 14. 
Preferably, each of these holes is on the order of about 0.010" in 
diameter. This dimension imposes, by geometry, a low limit to the sting 
diameter and, implicitly low limit to the sphere diameter. The result is a 
spherical probe head of about 0.242" in diameter with a sting of about 
0.090" in diameter. The present invention is not limited to components of 
these sizes and larger or 
smaller measurements may be incorporated depending, for example, on the 
application. 
In general, the size of probe 10 is preferably kept small for minimum 
possible intrusiveness and maximum possible spatial resolution, but yet 
large enough to allow for limited temporal resolution capabilities. The 
pressure measurement hardware is designed to be integrated close to the 
probe head to avoid long pressure tubing that would significantly increase 
data-acquisition times. A probe head with the above-described dimensions, 
combined with the preferred tubing configuration yields transient times in 
the pressure tubing as low as 0.2 sec. 
The sting 14 obviously affects the flowfield sensed by the adjacent 
five-hole configurations. This effect may be at least partly accounted for 
in the calibration process. Preferably, the probe assembly 10 is 
calibrated for a Reynolds number range in which laminar flow separation 
occurs over the spherical probe head 12. Noting that, typically, 
transition to turbulent separation occurs on spheres at a diameter-based 
Reynolds number of 3.times.10.sup.5, it can be calculated that a 
0.242"-diameter probe head experiences laminar separation for the entire 
range of incompressible conditions. 
Preferably, each one of the probe surface pressure ports 18 is connected 
through tubing to a pressure transducer. Therefore, a total of eighteen 
pressure transducers are used. Mechanical Scanivalve.TM. systems that 
utilize only one pressure transducer and mechanical scanning are not good 
candidates due to their slow pressure data acquisition rates. According to 
an aspect of the invention, the probe assembly may incorporate a miniature 
integrated electronic pressure scanner, which includes the eighteen 
pressure transducers. Preferably, the scanner is located close to the 
spherical probe head. This allows for much shorter length of tubing, 
thereby increasing the frequency response of the entire system. 
Preferably, each one of the five-hole configurations is calibrated to 
provide accurate measurement of any velocity vector within a cone angle of 
120.degree. or, equivalently, any velocity vector with .theta..sub.i 
&lt;=60.degree., where .theta..sub.i measures from the axis of the i.sup.th 
five-hole configuration (i=1 to 6). Thus, if, all six five-hole 
configurations and their measurement ranges are combined together, any 
possible velocity vector can be accurately measured. 
With respect to calibration, the spherical probe head may be first 
calibrated with the apparatus described in this section and then assembled 
with its dedicated electronics to form the probe shown in FIG. 3. A probe 
calibration assembly 22 is shown in FIG. 8. Calibration assembly 22 
includes a base 24 and a first arm 26 which rotates about a first axis 
passing through the center of and normal to the surface of base 24. First 
arm 26 is offset 90.degree. from the first axis. A second arm 28 is 
coupled to an end of first arm 26 and is offset 90.degree. from first arm 
26. Second arm 28 is parallel to the first axis. A probe mount 30 is 
provided at the end of second arm 28. Probe mount 30 is preferably capable 
of rotating probe assembly 10 about a second axis perpendicular to the 
first axis. Thus, probe assembly 10 is rotatable about two perpendicular 
axes. 
Probe assembly 10 may be mounted to calibration assembly 22, such that 
probe assembly 10 is disposed, for example, in a wind tunnel. The wind 
tunnel may be, for example, either a 3'.times.4' or a 2'.times.3' wind 
tunnel. Calibration assembly 22 includes a dual-axis stepper-motor to 
provide rotation about the first and second axes. Calibration assembly 22 
is preferably computer-controlled and capable of varying the cone and roll 
angles (.theta., .phi.) at least within the ranges 0.degree. to 
180.degree. and -180.degree. to 180.degree., respectively. Thus, a 4.pi. 
solid angle of the calibration domain may be covered. 
In a test of the above-described apparatus, the cone angle was varied 
between 0.degree. and 160.degree.. While the cone angle could be rotated 
to the full 180.degree., the sting interferes with the accuracy of 
calibration in the 160.degree.-180.degree. range. The test resulted in a 
calibration range corresponding to a solid angle of 3.72.pi. or 93.3% of 
the total possible velocity orientation range corresponding to a solid 
angle of 4.pi.. The positioning resolution for calibration assembly 22 was 
0.32.degree. in cone and 0.9.degree. in roll, allowing for a maximum of 
375,000 calibration data points over the 3.72.pi. solid angle. Preferably, 
approximately 10,000 calibration points are used to calibrate the probe. 
Preferably, the calibration assembly 22 positions the probe according to a 
user-defined array of probe orientations (.theta..sub.i, .phi..sub.i), 
i=1, . . . ,m. The integrated scanner 16 is preferably connected to a 
computer 32, which may include a data acquisition system. The data 
acquisition system collects nineteen pressures referenced to the wind 
tunnel static pressure. Eighteen pressure measurements correspond to the 
eighteen pressure ports of the probe. One pressure measurement corresponds 
to the stagnation port of a pitot tube, which is preferably located 
upstream and away from the probe assembly. 
During testing, pressure data acquisition was accomplished with an 
alternative to the above-described integrated pressure scanner. Pressure 
data-acquisition was performed with a 32-transducer Electronic Pressure 
Scanner (ESP).TM. from PSI, Inc. with a full scale pressure of .+-.20 in 
H.sub.2 O. The ESPTM pressure scanner was interfaced with a laboratory 
computer and was calibrated on-line. 
Calibration and data acquisition was performed in the 3'.times.4' Aerospace 
Engineering Wind Tunnel of Texas A&M University. This is a closed-circuit 
tunnel with a test section equipped with a breather so that the static 
freestream pressure is equal to the control room pressure. The clear 
Plexiglas.TM. test section was four feet wide, three feet tall and six 
feet long. The test section was accessible from the side either through a 
swinging door or through three round manholes on one of which the 
calibration assembly 22 was mounted. The contraction ratio was 9 to 1. The 
maximum speed achieved in the tunnel was about 200 ft/sec with a 
free-stream turbulence less than 0.16%. To avoid temperature variations 
over time there was an active cooling system to keep freestream 
temperature at about 60.degree. F. during testing. 
In order to describe the technique used to reduce the eighteen pressures 
acquired in a flow survey experiment to the three velocity components and 
the local static pressure, one may consider one of the six five-hole 
configurations. The flow over a five-hole probe can be divided into two 
flow regimes--a low-angle regime and a high-angle regime as shown, for 
example, in FIG. 9. The low-angle flow regime is defined as the .theta. 
range for which the pressure registered by the central port, is the 
highest among the five measured pressures. In FIG. 9, this regime is 
identified as domain 1. FIG. 9 represents the possible relative 
velocity/probe orientations, in terms of pitch and yaw angles (.alpha., 
.beta. in FIG. 1). It should be noted here that there is a one-to-one 
correspondence between the pairs (.alpha., .beta.) and (.theta., .phi.) 
defined by the following relations: 
sin(.theta.)sin(.phi.)=sin(.alpha.)cos(.beta.) 
sin(.theta.)cos(.phi.)=sin(.beta.) 
Each domain in FIG. 9 is identified by a number indicating the hole that 
senses the highest pressure for all the possible velocity orientations in 
that domain. For high-angle flows the highest pressure occurs in one of 
the peripheral domains 2 through 5, which correspond to the four outer 
ports of the five-hole configuration. The high-angle regime thus includes 
domains 2 through 5. 
At every measurement location in a flow mapping experiment, the local 
velocity vector can be fully characterized by four variables: pitch 
.alpha., yaw .beta., total pressure coefficient A.sub.t, static pressure 
coefficient A.sub.s (for the low-angle regime) or cone .theta., roll 
.phi., A.sub.t, A.sub.s (for the high-angle regime). Therefore, these 
variables need to be determined as functions of the five measured 
pressures or equivalently, the two nondimensional pressure coefficients 
B.sub.c, B.sub.r formed from these pressures. 
The definitions of all the above variables are: 
Low-angle regime (domain 1): 
EQU B.sub.c =(P.sub.5 -P.sub.4)/Q', B.sub.r =(P.sub.2 -P.sub.3)/Q' 
EQU A.sub.t =(P.sub.1 -P.sub.t)/Q', A.sub.s =(P.sub.1 -P.sub.s)/Q' 
(where Q'=P.sub.1 -(P.sub.2 +P.sub.3 +P.sub.4 +P.sub.5)/4 and P.sub.t is 
the local total pressure and P.sub.s is the local static pressure) 
High-angle regimes (domains 2 through 5): 
EQU B.sub.c =(P.sub.i -P.sub.1)/Q', B.sub.r =(P.sub.i.sup.+ -P.sub.1.sup.-)/Q' 
EQU A.sub.t =(P.sub.i -P.sub.t)/Q', A.sub.s =(P.sub.i -P.sub.s)/Q' 
(where Q'=P.sub.i -(P.sub.i.sup.+ +P.sub.i.sup.-)/2; P.sub.i is the 
highest detected pressure; and where P.sub.i.sup.+ and P.sub.i.sup.- are 
the pressures of the two peripheral holes adjacent to, and either side, of 
hole i) 
Referring to FIG. 9, P.sub.i.sup.+ is adjacent to P.sub.i in the clockwise 
direction and P.sub.i.sup.- in the counter-clockwise direction. The angles 
.alpha., .beta., .theta., .phi., have already been defined in FIG. 1. 
To resolve the u, v, w velocity components from the eighteen hole probe 
press data, a multiple-point interpolation algorithm may be employed. A 
large set of calibrated data containing known cone, roll, and pressure 
information is taken using the previously discussed calibration apparatus. 
The set of test data containing only known pressures is then reduced by 
the following procedure. Given a single test point, the port with maximum 
pressure is detected and the corresponding low- or high-angle calibration 
sector is determined. The calibration data is then searched, the 
calibration points associated with the particular sector are identified 
and the n.sup.th closest points to the test point (in terms of proximity 
in the {B.sub.c, B.sub.r } plane, as shown in FIG. 10) are retained. The 
number n is user-defined. FIG. 10 graphically depicts the interpolation 
that is performed for cone angle.theta.. Each of the n selected 
calibration points (represented by circles in FIG. 10) has an angle.theta. 
associated with it. The calibration algorithm calculated the 
surface.theta. versus {B.sub.c B.sub.r } that corresponds to the n 
selected calibration points. This surface is then interpolated to find the 
cone angle of the test point (represented by a square in FIG. 10). This 
interpolation procedure is repeated for the other three variables 
(A.sub.t, A.sub.s, .phi.). This technique may be used for .alpha., .beta., 
A.sub.t and A.sub.s in the low-angle regime. During testing, a 
backward-facing step was constructed in the test section of the 
3'.times.4' wind tunnel. The step height was H=6" and spanned the entire 
tunnel width. A flow survey downstream of the step was conducted with the 
eighteen-hole probe, along a plane parallel to the free stream and 
perpendicular to the tunnel floor. Data was taken on a 72 .times.13 point 
orthogonal grid with a 0.51" spacing in both directions. The freestream 
velocity was 75 ft/sec corresponding to a Reynolds number, based on the 
step height, of 0.22 .times.10.sup.6. 
FIG. 11 depicts a velocity vector plot downstream of the step. The velocity 
component perpendicular to the graph was consistently measured to be 
within +/-1.5 ft/sec. If the flow is assumed to be perfectly 
two-dimensional, this reading corresponds to an error of 2%. 
Although a particular embodiment has been described in which eighteen ports 
are spaced evenly about a spherical head, the present invention is not so 
limited. According to other aspects, the head may comprise other shapes, 
so long as the number of ports is increased to eight or more. For example, 
a partial sphere. Another alternative may include a multifaceted geometric 
shape approximating a sphere. Other possible head shapes exist. 
Also, a spherical head with greater or fewer than eighteen ports may be 
used. Further, a head may be used in which not all of the ports are 
symmetrically or evenly spaced. 
Also, the number and arrangement of pressure ports on the head may be 
varied. Preferably, the number and configuration are such that the cone 
angle is greater than the maximum 150.degree. cone angle of conventional 
probes. 
As discussed above, conventional probes are characterized by the fact that 
a normal axis extending from each port forms an acute angle with the axis 
of the sting. The present invention provides a probe in which at least one 
port has a normal axis forming at least a 90.degree. angle with the sting 
axis. Preferably, at least one such angle is obtuse. 
The present invention has been described in connection with the preferred 
embodiments which are intended as examples only. It will be understood by 
those having ordinary skill in the pertinent art that modifications to the 
preferred embodiments may be easily made without materially departing from 
the scope and spirit of the present invention as defined by the appended 
claims.