Baseline measurements for testing of improved triple-sensor hot-wireanemometer probe in a momentum conserving turbulent round jet

F. Gökhan Ergin
Dantec Dynamics A/S, Skovlunde, DK
gokhan.ergin@dantecdynamics.com
Clara Marika Velte
Department of Mechanical Engineering
Technical University of Denmark
Kgs. Lyngby, DK
cmve@dtu.dk
expected to correspond to a free jet up until x/D = 70 fromthe jet exit, which is sufficient for the purpose of themeasurements performed herein. However, the probe ispositioned using a computer controlled traversing
mechanism (Fig. 1, on the left), which occupies
substantial amount of space in the enclosure. This maylead to the fact that the momentum conservation may failin particular in the outer edges of the measured profiles of
the round jet (Hussein et al. 1994).

ABSTRACT
Three-component velocity measurements have been
performed in a momentum conserving turbulent round jet
using a constant-temperature anemometer (CTA) system
and a new triple-sensor probe featuring straight prongs.
The objective is to test the reliability of the new probe in aclassical canonical flow that lends itself well to testing
physical quantities such as momentum flux conservation
as well as comparing directly to baseline data. The probe
is positioned in excess of 2500 positions in eachmeasurement plane using a computer controlled traversing
mechanism. A conventional two-step calibration is
performed where the directional calibration is conductedfollowing a velocity calibration. The calculated pitch andyaw factors are compared to expected values for similarprobes reported in the literature. An error analysis isperformed using the pitch / yaw - roll mechanism in order
to identify the acceptance angle for the probe for the data
reduction scheme. The measurements capture the main
well-known characteristics of the round jet such as the jetcenterline, jet half width, and virtual origin. Power spectra
were measured at 30 jet exit diameters downstream of thejet exit on the jet centerline, quarter-width, half-width,
three-quarters width and at full jet width, demonstrating
the variations in the dynamic statistical moments.

Figure 1 Jet facility, hot-wire probe and 3-axis traversing
mechanism. For practical reasons, flow blockage due tothe traversing system is difficult to avoid. This has beencountered by placing the probe on a lengthy, but stable,
extension arm to increase the distance between traversing
system and probe.

EXPERIMENTAL SETUP
The experimental setup is shown in Fig. 1. The jet isthe light blue cubic box of dimensions 58 x 58.5 x 59 cm3
fitted with an axisymmetric white plexiglass nozzle,
tooled into a fifth-order polynomial contraction from aninterior diameter of 6 cm to an exit diameter of D = 1 cm.
The interior of the box was stacked with foam baffles inorder to damp out disturbances from the fan that supplied
the generator with pressurized air. The air intake was
located inside the jet enclosure. For further details on thegenerator box, see Jung et al. (2004) and Gamard et al.
(2004). The exit velocity is monitored via a pressure tap in
the nozzle positioned upstream of the contraction andconnected to a digital manometer by a silicon tube. The
enclosure was a large tent of dimension 2.5 x 3 x 10 m3.
The jet was the same as that used by Ewing et al. (2007)
and the enclosure was similar as well. Under theseconditions, the jet flow generated in the facility should be

The measurement system is a constant-temperature
anemometer (CTA) system manufactured by Dantec
Dynamics (DD, Skovlunde Denmark). The system
consists of a StreamLine Pro Frame and Controller withthree CTA velocity channels, StreamLine Pro Automatic
Calibrator with Nozzle I, a Pitch/Yaw – Roll (PYR)
manipulator to perform directional calibrations andStreamWare Pro software. The system controller is a Dell
Precision T1600 PC with an Intel Xeon E31245 3.3Ghz
CPU and 8GB Ram, running on a 64-bit Windows 7Ultimate operating system. The measured voltages weretransferred to the computer via a National Instruments
connector box and an 8-channel simultaneous sampling
differential PCI A/D converter. The new 55P95 triple-wireprobe is positioned at multiple grid points using a1

computer-controlled 3-axis traversing system. The probe
is compatible with the 55H27 triple sensor probe support,
and was mounted on the traversing mechanism using this
support and a mechanical adapter.
The probe (Fig. 2) was placed in the (vertical)
calibration jet during the velocity calibration. Nozzle Iwas used to cover a velocity range of 1-60 m/s. For
accurate three-component measurements, an accurate
directional calibration was also performed using apitch/yaw-roll manipulator. During the directional
calibration, the probe is yawed and rolled around twoaxes, while it is exposed to a constant calibration velocity,which is half of the maximum velocity during velocity
calibration. Measuring the probe response with the actual
velocity on each sensor, the pitch and yaw factors arecalculated. Individual velocity and directional calibrations
improve the accuracy of the measurement compared toexperiments using standard pitch & yaw factors.

(%) with the acceptance angle at a constant jet speed of 25
m/s is given in Figure 3. The absolute measurement error
is <5% for yaw angles < 20 deg and < 10% for yaw angles< 30 deg. This means that this probe's full acceptancecone angle is 60 deg with the data reduction scheme
described herein.

Figure 3 Error variation with incidence angle.
RESULTS
Measurements have been performed throughout crossplanes with 51 x 51 measurement points each at 9downstream positions. The measurement plane side length
was expanded according to the downstream jet growthrate. The equidistantly spaced planes covered adownstream span of 10D – 50D, where D is the jet exit
diameter. Up to 30D, the jet is classically considered only
partially developed in the sense that the mean velocities
are self-similar while the second order statistical moments
only become fully developed from about 30D and beyond.
The jet can, to within reasonable approximation, beconsidered free and momentum conserving within thedownstream range covered. At 50D the ratio between thelocal jet momentum to the momentum at the nozzle M/M0
 0.997 (based on eqn. B10 in Hussein et al. 1994).
Fig. 4 displays the downstream evolution of themeasured streamwise velocity profiles. Further, lines
roughly indicating the jet centerline and the linearlygrowing jet half-width (where the mean streamwise
velocity has dropped to half the centerline value) are
included for guidance of the reader.

Figure 2 Novel triple-sensor probe with straight prongs.
CALIBRATION OF THE NEW PROBE 55P95
The calibration of the new 55P95 probe is a two-stepprocedure. First, a velocity calibration is performed from1 m/s to 50 m/s using Nozzle I at 10 points distributed
equally in the velocity range. Then, a directional
calibration is performed with constant jet speed of 25 m/swith a 30 deg yaw angle and in steps of 15 deg roll angle.
The measured pitch and yaw factors are summarised inTable 1, and are consistent with the expected values
reported previously for 55P91.
Table 1 Measured and expected pitch/yaw coefficients for
new 55P95 sensors
22
Measured
Wire 1Wire 2
Wire 3
Expectedkh

0,01120,03950,0226
0,025

1,0092
1,01801,0327
1,04
Figure 4 Jet profile development in the downstream
direction x. The nozzle is located at x,y=0.

Following calibration, the measurement accuracy ofthe new probe is verified using the calibration jet and thepitch/yaw manipulator. When the probe is placed
vertically in the laminar calibration jet, the probe isexpected to detect exclusively the streamwise velocity
component, as the other two velocity components shouldbe negligible in comparison. Similarly, when the probe isyawed in x-y plane and in x-z plane, the probe is expected
to detect negligible velocities in w- and v-components,respectively. The absolute measurement error variation

It is apparent from Fig. 4 that the jet centerline and thedownstream traversing direction are slightly misaligned.
The (developed) jet half-width follows 1/2/(x-xo)~0.09.
The virtual jet origin is determined from extrapolation tox0/D=4.
Correcting for the traversing system misalignment to
the jet development, the measurements are transferred into2

a polar coordinate system and analysed, see Figure 5(a).
Since the mean velocity becomes self-similar before
x=30D, all radial velocity profiles are expected to collapse
if scaled correctly, which is also observed in themeasurements, see Figure 5(b). Since each jet may
develop differently because of the turbulence dependency
upon initial conditions (George 2012), the provided
comparison to fittings from alternative data should not be
considered too seriously. Comparison should rather bemade to reliable data acquired for the very same jet flow(such as PIV or LDA measurement data).
The centreline velocity development is plotted inFigure 5(c). Again, the virtual origin of the jet is found to
be x0/D = 4 while the decay rate Bu = 7.1 for thisparticular jet flow (Hussein et al. 1994) where:Uc 

The streamwise velocity profiles at each downstream
position were plotted in regular and similarity scaling
variables, displaying clear similarity collapse of the mean
velocity even as far upstream as x/D=10. Due to theturbulence dependency upon initial conditions, the profile
could not be quantitatively validated against other jetmeasurements, although it was seen that themeasurements in general displayed the expected trends.
The jet expansion and centreline velocity developments
were determined from the data and a multiple check of themomentum flux conservation was performed. The results
indicated a general agreement, even though some spurious
points existed that were hypothesized to stem from thedifferences in measurement plane extent. The fullmomentum flux can naturally not be captured unless thefull region of non-zero momentum flux is covered in themeasurements.
The measured power spectra capture the expectedcharacteristics even at large distances from the jet
centreline where the turbulence intensity is exceptionallyhigh. These spectra will in the future be compared to highprecision laser Doppler anemometer (LDA) power spectra
for validation of the novel hot-wire probe design. The
LDA does not suffer from directional ambiguity and canprovide a valuable and unbiased baseline as long as
correct signal processing is implemented for extracting
static and dynamic statistical moments (Velte et al. 2014).
Further, static moments such as mean velocity, rms
values etc. measured with the novel hot-wire probe will becompared to corresponding LDA measurements in thesame jet facility. In particular, the comparison will focus
on the challenging case of high turbulence intensity in theouter parts of the jet where hot-wire probes haveclassically had significant difficulties in producing reliableresults. Future work also includes the comparison ofdifferent directional calibration schemes for reduced error
over a larger acceptance angle.

Bu  M 10 2
( x  x0 )M0 = (d/2)2  U0 = 0.0866 kg m/s2 is the momentum flux
at the jet exit and U0 = 30 m/s is the jet exit velocity. The
momentum flux for a free jet is conserved withdownstream distance so long as the enclosure is not too
small or other disturbances too large to create significant
back-flow and other secondary effects (Hussein et al.
1994):1M ( x ) M 0  2  U 2  u 2  v 2  w2  r dr2
0
Since the jet half-width 1/2=0.09(x-x0) the product Uc
1/2 = Bu M01/2 0.09 = Bu M1/2(x) 0.09 = constant. This has
been tested in Figure 5(d), where good agreement has
been achieved except for x/D = 45 and 55 where it isbelieved that the spatial extent of the measuring plane may
have been too narrow to capture all the energy in the flow.
Reducing the momentum flux expression to first order(removing the second order moments) displays negligible
impact on the result.
The measured velocity power spectra for u, v, and w
at x=30D on the jet centerline, at quarter jet width, at half
jet width, ¾ jet width, and at full jet width are shown inFig. 6. The results show a distinctly non-isotropic
behaviour at lower frequencies (<100Hz) with the axial
turbulent kinetic energy being an order of magnitude
higher than the secondary components. The higher
frequencies collapse with increased radial distance fromthe jet centreline as is expected for temporal spectra inhigh intensity jet flows (Lumley 1965).

ACKNOWLEDGMENTS
The authors are grateful to Mr. Carsten Pedersen forsoftware implementation.
REFERENCES
Ewing D, Frohnapfel B, George WK, Pedersen JM,Westerweel J (2007) Two-point similarity in the round jet.
Journal of Fluid Mechanics, 557:309330.
Gamard S, Jung D, George WK (2004) Downstream
evolution of the most energetic modes in a turbulent
axisymmetric jet at high Reynolds number. Part 2: The
far-field region. Journal of Fluid Mechanics, 514, 205230.
H.J. Hussein, S.P. Capp, and W.K. George. Velocity
measurements in a high-Reynolds-number, momentumconserving, axisymmetric, turbulent jet. J. Fluid Mech.
258: 31–75, 1994.
Jung D, Gamard S, George WK (2004) Downstream
evolution of the most energetic modes in a turbulent
axisymmetric jet at high Reynolds number. Part 1: The
near-field region. Journal of Fluid Mechanics, 514, 173204.

CONCLUSIONSThe new probe design produces accurate directional
calibrations by eliminating the prong effects observed forprevious designs. As a direct result of this, thereconstructed 3D velocity vector is more accurate within
the acceptance cone of the probe – approximately 60 deg
for the current prong configuration and data reduction
scheme.

3George, W. K. (2012). Asymptotic effect of initial andupstream conditions on turbulence. Journal of Fluids
Engineering, 134. 061203-1
Lumley, J. L. (1965). Interpretation of time spectra
measured in high intensity shear flows. Physics of Fluids,
8, 1056. Doi: 10.1063/1.1761355
Velte, C. M. et al. (2014). Estimation of burst-mode
LDA power spectra. Experiments in Fluids, 55:1674. DOI
10.1007/s00348-014-1674-z

(a)

(b)

(c)

(d)

Figure 5 Streamwise velocity (u) profiles at all measured downstream positions x/D = 10, 15,20, 25, 30, 35, 40, 45 & 50. Darker green corresponds to larger downstream distance. (a)Unscaled velocity profiles. (b) Similarity scaled velocity profiles. (c) Centerline velocity
downstream development. (d) Check of consistency for momentum flux conservation.

4

(a)

(d)

(e)

(b)

(f)
(c)

Figure 6 Power spectra for u, v, and w at 30D on (a) the jet centerline, (b) quarter jet width, (c)half jet width, (d) ¾ jet width, (e) jet width, (f) positions of PSD computations at x = 30D.

5