Mach-number measurements using a nonintrusive optical technique, laser-induced thermal acoustics (LITA), are compared to pressure probes in humid supersonic airflow. The two techniques agree well in dry flow (-35 C dew point), but LITA measurements show about five times larger fractional change in Mach number than that of the pressure-probe when water is purposefully introduced into the flow. Possible reasons for this discrepancy are discussed

Herring, G. C.

NASA Technical Reports Server

 1
Mach-Number Measurement with Laser and Pressure Probes in 
Humid Supersonic Flow 
 
G. C. Herring 
 
NASA Langley Research Center, M/S 493 
Hampton, VA  23681-2199 
 
Abstract 
 
Mach-number measurements using a nonintrusive optical technique, laser-induced 
thermal acoustics (LITA), are compared to pressure probes in humid supersonic airflow.  
The two techniques agree well in dry flow (-35 °C dew point), but LITA measurements 
show about five times larger fractional change in Mach number than that of the pressure-
probe when water is purposefully introduced into the flow.  Possible reasons for this 
discrepancy are discussed. 
 
 
Key words: Laser-induced thermal acoustics (LITA), Pressure probe, Mach number 
                        measurement in humid supersonic air      
 
 
 
 
 
 
 
 
https://ntrs.nasa.gov/search.jsp?R=20080037568 2019-08-30T05:17:56+00:00Z
 2
 
Laser-based vapor screen [1] is commonly used for flow visualization in some 
high-speed wind tunnels, including NASA Langley Research Center’s (LaRC) Unitary 
Plan Wind Tunnel (UPWT) [2].  Vapor screen visualization is accomplished by adding 
water to the wind tunnel circuit; the cooled supersonic flow condenses the H2O vapor into 
small H2O droplets or ice crystals.  Flow visualization is possible by illumination of the 
H2O particles with a laser light sheet.  However, adding H2O to a supersonic wind tunnel 
alters the flow conditions in the test section compared to otherwise identical, but dry 
conditions.  Hence, typical aeronautical testing with pressure probes is done under dry 
tunnel conditions.  Some flow facilities have measured and specified the effect of flow 
humidity on tunnel Mach number (e.g., see pp. 87 of Ref. 2), so that flow visualization 
users will know the effect of high humidity. 
Another optical technique, laser-induced thermal acoustics (LITA), has been 
recently demonstrated for Mach number measurement in a supersonic flow.  No seeding 
is required with this approach.  LITA-based, nonintrusive, time-averaged and 
simultaneous measurements of Mach number, static temperature, and static pressure at a 
localized point in the free-stream flow of UPWT are demonstrated and described in Ref. 
3.  The present note describes a novel comparative study of pressure probe and LITA-
based Mach number measurements versus humidity in the UPWT. 
A more-detailed description of LITA velocimetry at LaRC can be found for 
supersonic [3], transonic [4], and subsonic [5] flows, while the work of other groups is 
summarized in a recent review [6].  LITA is a laser diagnostic that typically measures 
sound speed and one directional component of Mach number simultaneously in a flow 
 3
volume defined by crossed laser beams.  If the flow composition is known, then 
translational temperature can be derived from the sound speed, and gas pressure is 
measurable under certain restricted circumstances [3, 7]. 
In LITA, two focused and crossed 1.06-μm laser beams from a Q-switched 
Nd:YAG (150 mJ / pulse / beam) induce two counter-propagating sound-wave packets in 
the sample volume defined by the crossing region.  These sound waves constitute gas-
density gratings in the fluid.  The ~ 100 dB (re 20 μPa) sound pressure level corresponds 
to a fractional density change of ~ 10-4.  Thus the technique can be characterized as 
nonintrusive.  Flow velocity and sound speed are determined from distinct Doppler shifts 
of Bragg-scattered light from a third laser beam (probe at 532-nm) that intercepts the 
sound wave packets.  The sound packets reflect a tiny fraction of the incident probe 
intensity to a detector positioned at the Bragg-scattering angle.  All LITA measurements 
presented here are time averaged over 17 sec (500 laser pulses at rate 30 Hz). 
Free-stream results comparing measurements of Mach number M by a pressure 
probe and LITA are given in Ref. 3 for dry airflow (dew point = -35 °C) at Reynolds 
number R = 6 x 104/m.  Fig. 1 summarizes some of those results and shows exceedingly 
good agreement (typical differences of Mach 0.003) between time-averaged 
measurements from both techniques, for the Mach range 1.6-2.2.  Open circles are from 
one day of testing, the solid triangle is from a second day, and the solid line represents 
perfect agreement between the two techniques. 
Results comparing the two Mach number measurements versus steady-state water 
content are given in Fig. 2, at approximately Mach 2.  Pressure-probe results are from 
Fig. 27, pp. 87, of Ref. 2, and the LITA results were obtained during the work of Ref. 3.  
 4
Pressure-probe results were obtained at Mach 2.17, while LITA results were obtained at 
Mach 1.97.  This is the closest Mach-number match that is possible for the limited 
humidity studies from the two unrelated works of Refs. 2 and 3.  Results at other Mach 
numbers, illustrated on page 87 of Ref. 2, suggest that one expects only a small change in 
the effect of adding water between these two slightly different Mach numbers.  Thus it 
appears reasonable to compare these two data sets. 
 Pressure-probe results are plotted using the right-hand Mach-number scale, while 
LITA results use the left-hand Mach scale.  Offsetting the two scales by Mach 0.2 
provides a simple normalized comparison of the relative change in Mach number at the 
two slightly different Mach numbers.  Horizontal lines provide a convenient reference for 
the eye.  Open squares are probe results at R = 6 x 104/m, open diamonds are probe 
values at R = 12 x 104/m, and solid triangles are LITA results at R = 6 x 104/m.  The left-
most triangle is the same lone triangle plotted in Fig. 1.  The abscissa gives the dew point 
of the airflow.  A dew point of -12 °C corresponds to a water concentration of 0.5% at the 
stagnation conditions 70 kPa (0.7 atm) and 52 °C.  As water concentration in the flow is 
increased, the difference between the two methods increases for the change in Mach 
number, illustrating a potential error in one or both techniques.  LITA measures a factor 
of five larger change in Mach number due to the addition of water, as the humidity varies 
from the driest dew point of -35 °C (-30 °F)  to -12 °C (+11 °F).  Along with the decrease 
in Mach number, LITA also measures the free-stream static temperature T to increase 
(data omitted for brevity) from - 93 °C to - 86 °C as dew point varies from -35 °C to -12 
°C.  This temperature increase and Mach number decrease come from the heat release 
during water vapor condensation into particles. 
 5
Uncertainties in the LITA data [3] are typically < 0.2%, or ΔM = + 0.004.  
Uncertainties in the pressure-probe data are not quoted in Ref. 2, but the precision is 
estimated to be ΔM = + 0.005 from the point-to-point variation from an imaginary 
smooth curve through the probe data.  Thus the difference in ΔM (a factor of five) for the 
two measurement techniques, at -12 °C, exceeds the estimated combined uncertainty of 
ΔM ≈ + 0.009 of both measurements.  The good agreement of the two methods in Fig. 1 
is typical of many comparisons of LITA and traditional methods, performed at LaRC 
over one decade, so the disagreement of Fig. 2 is surprising. 
One potential reason for the discrepancy is an error in the LITA measurement due 
to a change in molecular mass μ from adding water vapor to air.  The highest humidity in 
Fig. 2 is equivalent to ≈ 2% water vapor before supersonic expansion.  Adding this H2O 
would reduce the average molecular mass by only 1% and increase the sound speed Vs by 
0.5% (Vs2 ∝ T / μ).  Furthermore, most water vapor is condensed into particles in the 
expansion to Mach 2 and is not in vapor phase in the test section.  The error in measured 
M is likely << 0.5% and negligible. 
In the dry airflow of Fig. 1, LITA generates only acoustic gratings from a purely 
electrostrictive effect.  Solid, liquid and vapor phases of water have weak absorptions at 
the pump-laser wavelength of 1064 nm.  Gas heating after an optical absorption leads to a 
second possible error in the humid LITA measurements of Fig. 2: a LITA-generated 
thermal-based grating in gas density.  In fact, in humid flow, we do observe that LITA 
generates a weak thermal grating (in addition to the acoustic grating).  The thermal 
grating increases in strength as the humidity increases.  At -12 °C, the thermal-grating 
signal was about equal to the acoustic-grating signal.   An absorption coefficient of ~ 10-4 
 6
cm-1 is inferred by an estimated (not measured) thermal grating reflectivity of ~ 10-9.  The 
absorbed energy is more than enough to heat the gas by 7 °C and reduce M from 1.96 to 
1.91, if it is assumed that all absorbed energy were to be transferred to the gas (e.g., by 
vaporization of the ice particles).  If the crystals do not vaporize and only a small fraction 
of the energy absorbed by the crystals is transferred to the gas in the LITA observation 
time of 1 μsec, the thermal grating is unlikely to account for the Mach number 
discrepancy.  The estimated laser peak intensity of 1011 W/cm2 and our observation of 
rare laser-induced breakdown (once every 1000 laser pulses) suggest that a majority of 
the water particles survive the laser pulse [8].  Although this potential error should not be 
ruled out yet, the best evidence for asserting that it is negligible is that the strength of the 
thermal grating is about the same as the strength of the acoustic grating, which is known 
[9] to exhibit fractional changes in gas density and temperature of ~ 10-4. 
A third explanation for the difference of Fig. 2 is an error in the pressure probe 
measurement, related to the particle laden free-stream.  As particles transit the shock 
from the pressure probe, they are heated.  Immediate (or delayed) evaporation of these 
H2O particles, directly behind the probe shock (or in the probe duct), would anomalously 
alter the flow conditions sampled by the probe.  In this scenario, the disagreement in 
humid flow is speculatively attributed to the probe because of the heating and 
evaporation of the water particles that are entrained in the cold free-stream flow.  Two 
different estimates of the probe error can be made.  First, the energy available to heat the 
gas (if all H2O in the flow condenses into crystals in the nozzle expansion and then all 
particles vaporize as they cross the probe shock) is given by the heats of fusion and 
vaporization.  This estimate gives ΔT ~ 8 °C for 0.5% fractional water vapor, more 
 7
consistent with the LITA measurement of ΔT ≈ 7 °C than the inferred probe measurement 
of ΔT ~ 1 °C.  This inferred ΔT from the probe was estimated using isentropic expansion 
tables to convert ΔM to ΔT.  Second, with the same assumptions, ideal 1-dimensional 
flow with heat addition [10] predicts ΔM ~ 0.09, more consistent with LITA’s 
measurement of ΔM ≈ 0.05 than the probe measurement of ΔM ≈ 0.01. 
In summary, pressure probe and noninvasive LITA-based Mach-number data 
were compared and found to disagree in humid supersonic airflow, although they agree 
well in dry flow.  Additional work would be useful to unambiguously determine whether 
the difference in the two methods is due to the LITA or probe method. 
 I gratefully thank M. T. Fletcher and R. C. Hart for their significant contributions 
to this work. 
References 
[1] G. E. Erickson and A. S. Inenaga, “Fiber-Optic-Based Laser Vapor Screen Flow 
Visualization System for Aerodynamic Research in Larger Scale Subsonic and 
Transonic Wind Tunnels,” NASA TM-4514, Jan. 1994. 
[2] C. M. Jackson, Jr., W. A. Corlett, and W. J. Monta, “Description and Calibration of 
the Langley Unitary Plan Wind Tunnel,” NASA TP-1905, Nov. 1981. 
[3] R. C. Hart, G. C. Herring, & R. J. Balla, “Pressure Measurement in Supersonic Air 
Flow by Differential Absorptive Laser-Induced Thermal Acoustics,” Optics Letters, 
Vol. 32, No. 12, 2007, pp. 1689-1691. 
[4] G. C. Herring, R. C. Hart, R. J. Balla, and B. S. Henderson, “Prospects for Nonlinear 
Laser Diagnostics in Jet Noise Laboratory,” NASA TM-214893, Aug. 2007. 
 8
[5] R. C. Hart, G. C. Herring, & R. J. Balla, “Common-Path Heterodyne Laser-Induced 
Thermal Acoustics for Seedless Laser Velocimetry,” Optics Letters, Vol. 27, No. 9, 
2002, pp. 710-712. 
 [6] M. S. Brown, Y. Li, W. L. Roberts, and J. R. Gord, "Analysis of Transient-Grating 
Signals for Reacting-Flow Applications," Applied Optics, Vol. 42, No. 3, 2003, pp. 
566-578. 
[7] R. Stevens and P. Ewart, "Single-Shot Measurement of Temperature & Pressure 
Using Laser-Induced Thermal Gratings With a Long Probe Laser," Applied Physics 
B, Vol. 78, No. 1, 2004, pp. 111-117. 
[8] P. Chylek, M. A. Jarzembski, V. Srivastava, and R. G. Pinnick, “Pressure 
Dependence of the Laser-Induced Breakdown Thresholds of Gases and Droplets,” 
Applied Optics, Vol. 29, 1990, pp. 2303-2306. 
[9] M. S. Brown, and W. L. Roberts, "Analysis of Transient-Grating Signals for 
Reacting-Flow Applications," Journal of Propulsion and Power, Vol. 15, No. 3, 
1999, pp. 119-127. 
[10] J. E. A. John, “Measurements in Compressible Flow,” Gas Dynamics, 1st ed., Allyn 
and Bacon, Inc., Boston, 1984, pp. 204-220. 
Figure Captions 
1. Probe and LITA-based Mach-number for dry air (dew point = -35 °C). 
2. Probe and LITA-based Mach-number versus water concentration. 
 
 9
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
1.5 1.6 1.7 1.8 1.9 2 2.1 2.2
Probe Mach Number
LI
TA
 M
ac
h 
N
um
be
r
 
Figure 1 
1.9
1.91
1.92
1.93
1.94
1.95
1.96
1.97
-40 -30 -20 -10 0 10
Dew Point (  C)
LI
TA
 M
ac
h 
N
um
be
r
2.1
2.11
2.12
2.13
2.14
2.15
2.16
2.17
Pr
ob
e 
M
ac
h 
N
um
be
r
LITA
Probe
° 
 
 
Figure 2 
 


Mach-Number Measurement with Laser and Pressure Probes in Humid Supersonic Flow

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server