**Preliminary Test Method 007 for the Determination of Cyclonic Flow
Velocity Components Using a Calculation Approach to Method 2F**

# **Scope, Application and Main Difference with/Improvement over the Current Method 2F**

This method is applicable for the determination of yaw angle, pitch
angle, axial velocity and the volumetric flow rate of a gas stream in a
stack or duct using a three-dimensional (3--D) probe. This method may be
used only when the average stack or duct gas velocity is greater than or
equal to 20 ft/sec. In this document we use the same nomenclature,
definitions and coordinate systems as in the description of the current
Method 2F, unless otherwise noted.

*[The main difference of the method proposed herein with Method 2F,
currently in effect, is that in the proposed method, during use of the
probe in actual field tests, no yaw nulling is required, i.e. the probe
does not have to be rotated in order to find the flow yaw angle by
equating pressures P2 and P3 (Figure 1). Instead, at every measurement
point along the stack diameter, the 5 pressures are acquired and proper
data-reduction algorithms are used to generate, from these 5 pressures,
both flow angles, pitch and yaw, as well as the velocity magnitude. It
is anticipated that the proposed method will yield significant time
savings in field stack measurements as well as better measurement
accuracies since less human-operator involvement is required thus
reducing the probability of human error. We anticipate that the new
method will result in time savings on the order of 70%..]{.underline}*

In what follows, we only discuss the procedures (for probe calibration
and probe field use) that are different from those discussed in Method
2F.

***Probe Calibration (Section 10.0 of current Method 2F)***

***Wind Tunnel Qualification Checks (Section 10.1 of current Method
2F)***

As in Section 10.1 of current Method 2F

***Probe Inspection (Section 10.2 of current Method 2F)***

As in Section 10.2 of current Method 2F

#### Pre-Calibration Procedures (Section 10.3 of current Method 2F)

## *Horizontal straightness Check*

As in Section 10.3.1 of current Method 2F

### Leak check

As in Section 10.3.2 of current Method 2F

### Calibration of all differential pressure-measuring devices

As in Section 10.3.3 of current Method 2F

*Calibration of Digital Inclinometers*

As in Section 10.3.4 of current Method 2F

***Placement of Reference Scribe Line (Section 10.4 of current Method
2F)***

In the new proposed method a scribe line is not needed. Instead a
Reference Block is attached to the shaft of the probe as shown in
Figures 2 and 3. The four faces of the block are perpendicular to each
other. The reference block, along with the axis of the probe, uniquely
define the coordinate system as shown in Figure 3. The yaw and pitch
angles are defined such that positive angles result in positive (along
the positive X, Y, Z axes) velocity components. The reference block can
be installed on the probe by following the procedure described below:

![](media/image1.png){width="5.451388888888889in"
height="7.570833333333334in"}

**Figure 1. Illustration of a five-hole prism-shaped (DAT) probe.**

The block is initially attached to the probe via set screws, such that
Reference Surface YZ is approximately parallel to the line defined by
pressure ports 2 and 3 (see Figure 1 for port numbering). This alignment
is initially performed visually. Then Reference Surface XY is
approximately parallel (within the accuracy of the visual alignment) to
the plane defined by pressure port 1 and the probe axis. Then the probe
is mounted on the calibration rig in the calibration wind tunnel, as
shown in Figure 4, such that Reference Surface XY is approximately
parallel to the free-stream velocity (the tunnel free-stream velocity is
accurately known in direction from the tunnel calibration procedure).
The calibration rig will be discussed later in more detail. Then the
probe is rolled until pressures P2 and P3 are equal (within the accuracy
specified in the current Method 2F). With the probe held in that
position, the reference block set screws are loosened and the block is
repositioned such that Reference Surface XY is parallel to the
free-stream tunnel velocity and the set screws are tightened. For
example, if the calibration is performed in a tunnel with the
free-stream in the horizontal directions, then through the use of a
digital inclinometer placed on Reference Surface XY, the block is
rotated until the inclinometer reads zero degrees. Then the set screws
are screwed in to affix the block to the probe.

However, a significantly simpler procedure is also proposed herein as an
alternative. The fact that the probe, as discussed later, is calibrated
in detail in the wind tunnel, facilitates the use of this simpler
procedure. According to it, the block is attached to the probe via set
screws, such that Reference Surface YZ is approximately parallel to the
line defined by pressure ports 2 and 3. This alignment is performed
visually. Assuming that this alignment is within +/- 15 deg. from the
yaw-nulling position, no further refinement of the block alignment is
necessary. The block reference surface XY serves as the probe alignment
surface in actual field measurements and has to be aligned parallel to
the stack axis. The fact that this position will not necessarily
correspond to the yaw-nulling orientation is automatically taken into
account by the probe calibration procedures and data-reduction
algorithm.

![](media/image2.wmf){width="6.472916666666666in"
height="4.760416666666667in"}

**Figure 2. Schematic illustrating the definition of yaw and pitch
planes and positioning of the reference block on probe shaft.**

![](media/image3.wmf){width="6.479861111111111in"
height="5.165277777777778in"}

**Figure 3. Schematic illustrating the definition of yaw and pitch
angles and coordinate system with respect to probe and reference
block.**

# **Yaw Angle, Pitch Angle and Velocity Pressure Calibration (Sections 10.4 and 10.5 of current Method 2F)**

This is one of the procedures that are different from the current Method
2F. The main difference is that the probe is calibrated not only over a
range of pitch angles but also over a range of yaw angles. Although the
procedure can be carried out manually, we strongly recommend probe
calibration via an automated positioning system as that shown in Figure
4. As shown in the figure, The probe is mounted on a frame, which,
through the use of two stepper motors, one for pitch positioning and one
for yaw positioning, can place the probe at a range of (pitch angle, yaw
angle) combinations, with respect to the tunnel free-stream. An example
of such a system is shown in Figure 5. This system is used with a
different type of 3-D probes but its principles of operation are
identical to those of Figure 4.

The probe, in Figure 4, enters the wind tunnel test section through a
slot along one of the test section side walls. This slot allows the
probe to be moved over a range of pitch angles (of at least +/- 15
deg.). This slot is sealed (so that there is no air exchange between the
interior and the exterior of the test section) through "brushes", which
have thickly distributed bristles to achieve sealing, but yet
sufficiently flexible bristles in order to allow the probe to move
through them. We have successfully used this way of sealing repeatedly
before.

![](media/image4.wmf){width="6.584027777777778in"
height="4.446527777777778in"}

![](media/image5.wmf){width="5.186805555555556in"
height="3.5520833333333335in"}

**Figure 4. Automated wind-tunnel calibration of probe. Upper: complete
assembly. Lower: test section removed to illustrate intersection of
pitch and yaw rotational axes.**

![](media/image6.png){width="3.111111111111111in" height="3.925in"}

**(a)**

![](media/image7.jpeg){width="4.652777777777778in"
height="3.079861111111111in"}

**(b)**

Figure 5. Example of automated calibration system. Schematic and picture
of probe positioning/indexing system (a and b).

The stepper motors are equipped with optical encoders so that the
position of the probe is accurately known. Also, the stepper motors can
be equipped with gear boxes, if finer stepping and increased torque are
desired. A typical stepper motor has a minimum step size of 0.9 deg. A
20-to-1 gear box can refine the step to 0.045 deg. and multiply the
available torque by a factor of 20. The penalty is that the positioning
process will be slower, which however is not an important issue, since
the entire process is automated and modern stepper motor controllers can
achieve speeds as high as 1000 steps per second. As an example, we are
using the above calibration system and procedures with our regular 3-D
probes and are repeatedly achieving calibration accuracies as high as
0.25 deg. in the pitch and yaw angles and 0.5% in the velocity
magnitude, in the range +/-20 deg. in pitch and yaw.

As shown in Figure 4lower, it should be noted that the pitch axis and
the yaw axis are perpendicular to each other and intersect at the probe
tip (the part of the probe performing the measurements). This forces the
probe tip to stay at the same physical location in the test section,
regardless of the pitch and yaw angles it is rotated to. This eliminates
calibration errors that could be introduced if there are spatial
velocity gradients (non-uniform velocity distribution) in the test
section.

A typical calibration procedure would be as follows. The probe is rolled
to a yaw angle of --18 deg. Then, keeping the yaw angle fixed, the probe
is pitched from --18 deg. to 18 deg. in steps of 3.6 deg. (which is 4
times the minimum stepper motor step, if gear motors are not used). For
each probe location, the 5 port pressures, P1, P2, P3, P4, P5 plus the
reading from the pitot tube are sampled and stored. All pressures are
measured by differential pressure transducers, with the reference
pressure of all transducers being the static pressure of the pitot tube.
Once all pitch positions (for the fixed yaw angle of --18 deg.) are
spanned (a total of 11 pitch positions: -18 deg., -14.4 deg., -10.8
deg., -7.2 deg., -3.6 deg., 0.0 deg., 3.6 deg., 7.2 deg., 10.8 deg.,
14.4 deg., 18 deg.), then the probe is rolled to the next yaw position,
-14.4 deg. and all the pitch angles are spanned again, and for every
position the 5 pressures and the pitot reading are sampled and stored.
The next yaw position will be --10.8 deg., and so on, with the final yaw
position being 18 deg. In the above both yaw and pitch angles are
advanced in steps of 3.6 deg. Our experience with probe calibration
shows that this stepping interval is good enough to yield calibration
quality and thus probe measurement accuracies quite a bit better than
the minimum accuracies stipulated in the current Method 2F.

The above procedure is then repeated one more time as per the
requirements of the current Method 2F. Also, before and after each
calibration the temperature and barometric pressure should be recorded.
Then repeat the calibration procedures at the second selected nominal
wind tunnel velocity.

Then for every point of each one of the calibrations, the following
coefficients are calculated:

$B_{\alpha} = \frac{(P_{4} - P_{5})}{q}$ (1)

$B_{\beta} = \frac{(P_{3} - P_{2})}{q}$ (2)

$A_{t} = \frac{(P_{1} - P_{t})}{q}$ (3)

where, the pseudo dynamic pressure, q, is defined as:

$q = P_{1} - \frac{(P_{2} + P_{3})}{2}$ (4)

and P~t~ is the pitot tube dynamic pressure reading (already corrected
by taking into account the Pitot tube calibration). It should be noted
that P~t~ is also the total pressure measured with respect to the
reference pressure used to reference the differential pressure
transducers, which in the calibration case is equal to the free-stream
static pressure.

Then for the two calibrations corresponding to each of the two nominal
tunnel velocities, perform a comparison procedure similar to that
described in section 10.6.13 of the current Method 2F. However, now the
comparisons will have to be performed, not just for F2 (current Method
2F) but for both
$\text{ B}_{\alpha}\ \text{and}\ B_{\beta}\text{.}$Velocity drift checks
(10.6.14) will not have to be performed since for every calibration
point, paired readings (5 probe pressures and pitot tube pressure) have
been acquired. Finally, comparison and average procedures similar to
that of section 10.6.16 of the current Method 2F will have to be
performed.

Finally, the collected calibration data is used to generate second-order
polynomials for the two flow angles, α, β, and the dynamic pressure
coefficient A~t~, as functions of the two pressure
coefficients$\text{ B}_{\alpha}\ \text{and}\ B_{\beta}$, using
least-squares techniques:

$\alpha(B_{\alpha}\text{,B}_{\beta}) = a_{0} + a_{1} \cdot B_{\alpha} + a_{2} \cdot B_{\beta} + a_{3} \cdot B_{\alpha^{2}} + a_{4} \cdot B_{\beta^{2}} + a_{5}\ B_{\alpha}B_{\beta}$
(5)

$\beta(B_{\alpha}\text{,B}_{\beta}) = b_{0} + b_{1} \cdot B_{\alpha} + b_{2} \cdot B_{\beta} + b_{3} \cdot B_{\alpha^{2}} + b_{4} \cdot B_{\beta^{2}} + b_{5}\ B_{\alpha}B_{\beta}$
(6)

$\text{ A}_{t}(B_{\alpha}\text{,B}_{\beta}) = c_{0} + c_{1} \cdot B_{\alpha} + c_{2} \cdot B_{\beta} + c_{3} \cdot B_{\alpha^{2}} + c_{4} \cdot B_{\beta^{2}} + c_{5}\ B_{\alpha}B_{\beta}$
(7)

For each of the above functions, the least-squares technique yields the
values of the coefficients: a~i~ , b~i~ , c~i~, where i takes values
from 0 to 5. These values are stored and will be used in the data
reduction process.

***Using the Probe in Actual Field Tests ("Sample Collection and
Analysis", Section 8.0 of current Method 2F)***

All of the procedures described in Section 8.0 of the current Method 2F
still hold except for the following:

-   *[Yaw Alignment of Probe]{.underline}*: When the probe is inserted
    into the test port, the only yaw alignment that is needed at every
    measurement point, before a measurement is taken, is to orient the
    reference surface YZ perpendicular to the stack axis, or reference
    surface XY parallel to the stack axis.

-   *[No Yaw Nulling Necessary]{.underline}*: At every measurement
    location, no yaw nulling procedure is necessary. The probe is simply
    traversed to the new measurement location, its reference
    block/surface is properly aligned and the five pressures from the
    five ports are sampled and stored. Any rotational offset is
    automatically accounted for by the probe calibration and data
    reduction processs.

-   *[Data Reduction (Data Analysis):]{.underline}* The data reduction,
    i.e. the conversion of the sampled data to velocity and flow angles
    (pitch and yaw) can be performed on-line, as the data acquisition is
    performed, as long as the following quantities are also
    measured/known:

> the absolute stack or duct pressure, P~s~
>
> the absolute stack or duct temperature, T~s~
>
> the molecular weight of the stack or duct gas, wet basis, M~s~.
>
> Or, the sampled data can be stored for later, off-line data
> reduction/analysis. Regarding data analysis see also the section that
> follows.

***Data Analysis and Calculations (Section 12.0 of current Method 2F)***

This procedure is also referred to as "data reduction" and uses the five
measured probe pressures to derive, at the measurement location of a
field test, the yaw and pitch angles and all three velocity components,
thus the flue axial gas velocity.

The five measured pressures are first plugged into Equations 1, 2 and 4
to calculate: q, $\text{ B}_{\alpha}\ \text{and}\ B_{\beta}$. Then the
calculated $\text{ B}_{\alpha}\ \text{and}\ B_{\beta}$are plugged into
Equations 5 through 7 to calculate α, β and A~t~. Then, the actual total
pressure (measured with respect to the reference pressure used to
reference the differential pressure transducers during the actual field
test) is calculated from the non-dimensional pressure coefficient A~t~ ,
as follows:

$P_{t} = P_{1} - A_{t} \cdot q$ (8)

If during the actual field test the differential pressure transducers
are referenced to the local barometric pressure P~bar~ , then the
velocity magnitude at the measurement point is calculated from the
following formula:

$V = K_{P}\sqrt{\frac{(P_{t} + P_{\text{bar}} - P_{s})T_{s}}{P_{s}M_{s}}}$
(9)

where:

P~s~ is the absolute stack or duct pressure in mm Hg

T~s~ is the absolute stack or duct temperature in degrees Kelvin

K~P~ is a conversion factor equal to 34.97 and

M~s~ is the molecular weight of the stack or duct gas, wet basis, in
g/g-mole

In Equation 9, all pressures are in mm Hg and the calculated velocity
magnitude is in m/sec.

Then the axial flue gas velocity at the measurement location is
calculated by:

$v_{\text{axial}} = V\text{cos}(\alpha)\text{cos}(\beta)$ (10)

Finally the flue flow rate is calculated according to the procedures
described in sections 12.3 through 12.5 of the current Method 2F.