ADVERSE ENVIRONMENT ADVERSE ENVIRONMENT ADVERSE ENVIRONMENT ADVERSE ENVIRONMENT ROTOR TEST STAND CALROTOR TEST STAND CALROTOR TEST STAND CALROTOR TEST STAND CALIBRATIONIBRATIONIBRATIONIBRATION PROCEDURES PROCEDURES PROCEDURES PROCEDURES
AND ICE SHAPE CORRE AND ICE SHAPE CORRE AND ICE SHAPE CORRE AND ICE SHAPE CORRELATIONLATIONLATIONLATION
Jose L. Palacios
Research Associate
Edward W. Brouwers
Research Assistant
Yiqiang Han
Research Assistant
Edward C. Smith
Professor
The Vertical Lift Research Center of Excellence Department of Aerospace Engineering
The Pennsylvania State University, University Park, PA 16802
ABSTRACTABSTRACTABSTRACTABSTRACT
An Adverse Environment Rotor Test Stand (AERTS) has been designed, and constructed. The facility
is able to reproduce natural icing conditions on a hovering rotor. The motor/hub configuration is
designed to spin instrumented rotors of up to 9 ft. diameter and has the capability of providing tip
speeds of up to 470 ft/sec. A Liquid Water Content (LWC) calculation methodology was developed and
sensitivity studies to determine experimental LWC are presented in this paper. Correlation between
experimental ice accretion shapes obtained in the AERTS facility and experimental results obtained by
the NASA Icing Research Tunnel and the Air Force Arnold Engineering Development Center are
presented. These experimental correlations are conducted to demonstrate the capability of producing
an accurate realistic icing cloud of the new facility. All tests reported in this paper have been
conducted on 1 in. diameter circular cross section rotors. The majority of the experimental ice shapes
compared agree with results presented in literature with thickness errors as low as 2% and impingement limits discrepancies no greater than 15%.
NomenclatureNomenclatureNomenclatureNomenclature
Ac Accumulation parameter, dimensionless
b Relative heat factor, dimensionless
cp,ws Specific heat of water at the surface temperature, cal/g Khc
Convective heat-transfer coefficient, cal/s m2 K
hG Gas-phase mass-transfer coefficient, g/s m2
K Inertia parameter, dimensionless
K0 Modified inertia parameter, dimensionless
ka Thermal conductivity of air, cal/s m K
LWC Cloud liquid-water content, g/m3
Ma Mach Number, dimensionless
MVD Water droplet median volume diameter, μm
Nu Nusselt number, dimensionless
m& Mass Flux, Kg/m2 sec
Pr Prandtl Number
Pst Static pressure, psi
pw Vapor pressure of water in atmosphere, psi
pww Vapor pressure of water at the icing surface, psi
r Recovery factor, dimensionless
Re Reynolds number of model, dimensionless
Reδ Reynolds number of water droplet, dimensionless
τ Accretion time, min
t Temperature, °C
tf Freezing temperature of water, °C
ts Surface temperature, °C
V Free-stream velocity of air, m/s
β0 Collection efficiency at stagnation line, dimensionless
calculations is to find the collection efficiency, which
can be interpreted into how much water droplets are
going to hit on the model (i.e. the mass flux used in the
following equations). This is the basis of both analytical
and experimental expression of freezing fraction.
This analysis aims to find an expression for super-
cooled water drop distribution. The stagnation line
collection efficiency, βo, illustrates the impinging water
drop trajectory by considering the projection of a
stream tube from the far-field inflow at stagnation line.
The problem is simplified at the stagnation line, as it is
assumed that at this line there is no incoming
interference from other controlled volumes. The
analysis following are all based on this assumption[7,8].
The expression of collection efficiency at the stagnation
line is given by Equation 1:
( )( )
−+
−=
84.
0
84.
0
0
8/1*40.11
8/1*40.1
K
Kβ (1)
where, K0 is the Langmuir and Blodgett’s[9] expression for modified inertia parameter (Equation 2). This
equation was initially published for cylinders, but was
then validated for airfoils in the reference 9.
−+=
8
1
8
10
KKStokes
λ
λ, for
8
1>K (2)
The inertia parameter, K, in Equation 2 can be expressed as:
a
w
d
VK
µ
δρ
18
2
= (3)
And Stokes
λλ / is defined as the dimensionless droplet
range parameter,
δδλ
λ
Re1847.0Re001483.08388.0
1
++=
Stokes
(4)
where
a
aV
µ
δρδ =Re (5)
4.1.2. Energy Balance Analysis during Impingement
As mentioned, one of the most important variables
during icing testing is the freezing fraction, which
denotes the fraction of water droplets that freezes at the
surface of a body, thus indicating the heat balance at
the ice surface.
Analytical freezing fraction can be found by the
following Equation:
+
Λ=
b
Cn
f
wsp
a
θφ
,
,0 (6)
where, ф and θ , are defined as droplet energy transfer and air energy transfer coefficients respectively:
wsp
stfc
Vtt
,
2
2−−=φ (7)
v
st
www
c
G
ap
stsp
pp
h
h
c
Vtt Λ
−+
−−=
,
2
2θ (8)
The relative heat factor, b, is introduced by Tribus[9] as:
c
wsp
h
cmb
,&
= (9)
The convective heat-transfer coefficient, hc, can be calculated from Equation 11.
a
c
k
dhNu = (10)
The numerical expression of Nu in this code is chosen according to different Re numbers: for Re > 105, as per reference 9:
472.0Re10.1=Nu (11)
and for Re < 105, as per reference 9: 5.040
Re141.
rP.Nu = (12)
Based on the trajectory analysis at stagnation line in the
last section and assuming βo and ρi remain the same while the ice shape changes during the test, the mass
flux can be expressed as:
0β⋅⋅= VLWCm& (13)
Here, it can be seen that LWC can be determined from
the analytical freezing fraction. by introducing a
correlation between freezing fraction and ice thickness
in next section, the LWC can be finally determined.
4.1.3 Ice Accretion Analysis
Based on the previous analysis, a time-span analysis
during ice accretion can be performed. Total ice
thickness at stagnation line, ∆, can be expressed as:
0n
m
i
⋅=∆ρ
τ& (14)
By Substituting Equation 10 into Equation 14 and
introducing an accumulation parameter Ac, Equation 15 is found.
d
VLWCA
i
cρ
τ⋅⋅= (15)
The non-dimensional total ice thickness is defined in
Equation 16.
0,0β
ceAn
d=
∆ (16)
The experimental freezing fraction, η0,e, can be related to the analytical freezing fraction, η0,a, by using a linear curve fitting as it is suggested by Anderson and Tsao[7]:
aenn
,0,0107.10184.0 += (18)
The relationship between total thickness and LWC can
be shown to be monotonic. Thus, an exhaust algorithm
can be implemented to find experimental LWC from
total ice thickness per time. The scheme of the code is
summarized in Figure 6.
4.1.4. Evaluation of LWC Calculation Code
The calculated LWCs based on the total ice thickness
per time are compared with the analytic LWCs
presented in literature for both cylinders [10] and airfoils [7]. The correlation between calculated LWC and results
presented in literature are shown in Figure 7 and Figure
8. It can be concluded that this code calculates
acceptable LWC from total ice thickness per time
(within ±15% error) for nearly 90% of all the cases
presented in literature. Taking into account the
uncertainties related to experimental test data, these
results can be assumed to be useful and reliable to
support the LWC calibration of the facility.
4.1.6. Uncertainty Analysis
From Figure 7, and Figure 8, it is shown that
experiment-derived LWCs generally result in a good
agreement with literature data, presenting correlation
discrepancies of less than 15% for the majority of the
cases compared. Several cases deviate between
calculations and experimental results presented by the
referenced documents. The two main contributions of
this kind of error come from uncertainty of
measurement; and error transmitted between
calculation equations.
Firstly, for most experiments performed at NASA IRT
to which this paper is comparing, the uncertainty
related to LWC calibration at IRT is claimed to be
about ±12%[7] . Also there is ±12% uncertainty in MVD. ]In addition, in most icing tests, hand-tracing
measurement methods are prevalently used, and for
this reason, the thickness record has its own inherent
uncertainty. For similar shapes, it can be shown that
the experimental ice thicknesses can differ by up to
18.8% [7] between the centerline of a test section and
some small distance above centerline. Given the limited
data set, these uncertainties cannot be effectively
resolved.
Figure 6: Scheme of Experimental LWC Calculation Code
Figure 7: Cylinder LWC Calculations from Total Thickness and Correlation with Results Presented in Reference 10
Figure 8: NACA 0012 LWC Calculations Compared to
Experimental Results Presented in Reference 7
Secondly, due to the small size of the ice thickness itself, a
slight error in tracing the ice thickness will then be
transmitted and amplified through equations and
computing loops of the presented code, resulting in a
relatively big error between analytic LWC and thickness-
based or experimental LWC.
It can be seen from presented equations, that the change
in thickness has large effects on the calculated LWC. As
stated before, there is a linear relationship between
thickness, freezing fraction and eventually the LWC.
Small changes in ice thickness (> 0.5 mm) will produce
deviations of LWC of up to 50%.
In the reference [7], although with a different analysis
method and ignoring the difference between analytical
and experimental LWC, Anderson and Tsao also did some
comparisons between analytical freezing fraction and
experimental freezing fraction based on the ice thickness.
In two test groups (test case number 8 – 14 and 32 – 35
with regard to Figure 8 in this article), large discrepancies
between ηa and ηa can be found in these two groups. The greatest one is found in case 3-12-02/1(test case number
32 in Figure 8, with regard to this article), where ηa = 0.275 and ηe = 0.190; i.e., the error can be as high as 45% (error with respect to ηe, from which the experimental LWC is determined), much bigger than ±12% as they
expected for most cases. These errors are also reflected in
the LWC calculation code in Figure 8. The same
phenomena are also found in Figure 7, test case number 9
and 10.
Anderson and Tsao believe this is because there can be
significant uncertainty in the ice thickness values found
from tracings at low freezing fractions. This is true as
already mentioned above. Also, the relatively large
discrepancies between the analytical LWCs and the ones
calculated from the measured thickness can also be
explained by the slope of the relationship between ice
thickness and LWC (Equation 19). The slope, S, of the equation could be very small (≈0.025), greatly affecting
the LWC value for errors introduced in the measurement
of the ice thickness.
rLWCS +⋅=∆ (19)
For example, in some cases, a change in thickness of 0.005
in. results in a change on the calculated LWC of 0.43 g/m3.
For this reason, careful measurement of the ice shapes
must be performed.
In addition, the empirical equations used in this code
(such as relationships between ηe and ηa, or the numerical expression of Nu.) will add error into the calculation as
icing conditions diverge from those used during the
definition of these empirical equations.
With these assumptions of uncertainty, each analytic
LWC is plotted in Figure 7 and Figure 8 with an error bar
of ±15%. Calculated LWC results correlate with values
presented in literature, validating the usage of the code to
When liquid droplets impact a crystal, the droplet is
immediately crystallized, which creates a chain reaction[5].
Larger numbers of particles in the chamber increase this
effect due to saturation and are generated when using
higher air pressure inputs to the nozzle. To maintain a
desired MVD at higher air pressures, water pressures need
to be increased to maintain the proper pressure
differential, as detailed in Figure 3 and explained in
Reference 1. Since the water flow rate is dependent on
this pressure differential, the mass of water added to the
chamber increases, creating a large number of droplets. If
the droplets crystallize, they erode ice shapes, providing
“spear” shaped ice accretion, as shown in Figure 14. The
maximum pressure differential to avoid crystallization
problems was experimentally determined to be 23 psi.
Similar ice shape erosion is documented by Tsao et al. in
reference 12. During tests conducted at the IRT, there was
evidence indicating that ice erosion occurred for rime ice
shapes obtained at 250 knots. Erosion was identified by
shapes lacking expected small-scale feathers and increased
stagnation ice thickness, as seen in Figure 15[12].
Figure 15: Example of Eroded Rime Ice Tracing at the IRT,
Reference 12
5. AERTS ICE SHAPE C5. AERTS ICE SHAPE C5. AERTS ICE SHAPE C5. AERTS ICE SHAPE CORRELATION TO NASA AORRELATION TO NASA AORRELATION TO NASA AORRELATION TO NASA AND ND ND ND
