quantitative analysis of a two-dimensional ice accretion ... · lewice, trajice, and onera, which...

Journal of Mechanical Science and Technology 26 (4) (2012) 1059~1071

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0223-z

Quantitative analysis of a two-dimensional ice accretion on airfoils†

Chankyu Son, Sejong Oh and Kwanjung Yee* Department of Aerospace Engineering, Pusan National University, Pusan, 609-735, Korea

(Manuscript Received August 18, 2011; Revised January 22, 2012; Accepted February 1, 2012)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract This paper presents the development of a code that can determine the shape of accreted ice on a 2D airfoil, verification of the code via

quantitative parameters, and the variation in ice accretion according to ambient conditions. First, the 2D panel method is used as the aerodynamic solver, and Messinger’s model is used as the thermodynamic model. Second, the code is quantitatively verified through comparison with existing ice accretion analysis codes under rime, mixture, and glaze ice conditions. The parameters for comparison are the cross-sectional area of the ice, maximum ice thickness, ice heading, and distribution of the ice thickness measured on the airfoil sur-face. The verification shows that the developed code yields results of similar accuracy to existing analysis codes. Finally, ice shapes, depending on variations in the ambient conditions, are determined and investigated based on these parameters for comparison. The se-lected ambient condition parameters are freestream velocity, LWC, and temperature. The investigation is carried out for rime and glaze conditions. Increasing the freestream velocity produces an ice horn that increases the area over which the ice encounters liquid water in the air. The ambient temperature is the factor that alters ice accretion behavior; increasing the ambient temperature turns rime ice into glaze ice. Ice accretion area is increased at higher LWC. The LWC and the ice cross-sectional area show a linear relationship.

Keywords: Aircraft icing; Ice accretion shapes; Ice accretion area; Maximum thickness; Ice heading; Ice distribution ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

Aircraft icing is the phenomenon in which supercooled wa-ter droplets in the air hits an airplane surface and freezes on it. The ice accreted on the surface prevents the airplane from performing at its full capacity and threatens its operational safety [1]. To cope with ice accretion, many airplanes are equipped with anti/de-icing devices. However, because of installation and maintenance costs as well as weight issues, the operation of these devices is limited to small portions of the surface for as little time as possible. Therefore, the device should be designed for efficiency. Implementing an efficient anti/de-icing device requires estimation of the ice coverage and the heat capacity of the surface to eliminate the ice. These characteristics related to icing are available through researches into the icing behavior [2].

The investigation into icing behavior and its aerodynamic effects can be conducted by an experimental method or by numerical analysis. Experimental studies may take the form of flight tests or icing wind tunnel tests. In a flight test, the air-plane has to actually fly through the area in which the icing occurs. Therefore, the difficulties of running flight tests lie in

forecasting the conditions under which icing occurs; capturing, recording, and controlling the icing behavior; safety; and cost [3]. The icing wind tunnel test is limited by the cost of acquisi-tion and maintenance of the facility [3], in addition to scaling problems if a subscale model is used [4]. Therefore, in order to understand the ice accretion behavior under various icing conditions and estimate the reduction in aerodynamic per-formance of the wing, many researchers have relied on simu-lation codes rather than experiments. For example, the NASA Lewis Research Center developed LEWICE [5-7], and the Office National d’Etudes et de Researches Aérospatiales (ONERA) developed an ice accretion estimation code for 2-D and 3-D airfoils [8]. The Italian Aerospace Research Center (CIRA) developed both a code for 2-D multi-element airfoils [9] and IMPIN3D [10], a 3-D icing analysis code, and the DRA (now QinetiQ) of the U.K. developed a 2-D icing esti-mation code [11]. More recently, Numerical Technology In-ternational developed FENSAP-ICE, a Navier-Stokes (N-S) based 3-D icing simulation code [12].

On the domestic side, FENSAP-ICE, commercial program, has been used to predict the ice accretion shapes in various icing conditions [13]. While, the in house code were devel-oped by Back et al. [14], and Jung, et al. [15] to predict the ice accretion shapes. Two researches have difference in an aero-dynamic solver. The former adopts the governing equation as potential equation, while the latter adopts Navier-Stokes equa-

*Corresponding author. Tel.: + 82 51 51 2481 E-mail address: [email protected]

† Recommended by Associate Editor Gihun Son © KSME & Springer 2012

1060 C. Son et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1059~1071

tion. Both have limitation because those do not handle the thermodynamic effects occur in glaze ice conditions. For the development of aircraft, and certificate of airworthiness, it is essential to prediction of ice accretion shapes in various icing conditions.

Although there are many different numerical analysis tools, every icing behavior estimation code requires the following four models: 1) a model that calculates the velocity vector around the wing, 2) a model that estimates the trajectory of water droplets, 3) a thermodynamics model, and 4) a model that determines the thickness of ice and generates new sur-faces. Each analysis code introduced above has different mod-els applied to it. For example, the solvers of flow field around the wing range from the panel method to N-S-based CFD tools, and the trajectories of the particles are most commonly determined by Lagrangian or Eulerian approaches [1]. The four models are clearly distinguished in Lagrangian approach, while they are not distinguishable in Eulerian approach. How-ever, Eulerian analysis codes have the same capability. The codes mentioned above employ Messinger’s model as the thermodynamics model [16].

Because there is no standard method defined for the verifi-cation of icing analysis codes, existing codes have shown their results in a Cartesian coordinate system, and judgments of their accuracy have relied on subjective opinion of the icing shape. However, such a verification method fails to provide a quantitative basis for analysis. In this study, to verify the de-veloped code and to understand the characteristics of the ice accretion, some parameters that quantitatively define icing behavior are selected, and quantitative analysis is conducted on these parameters as described in Wright [17]. Wright quan-titatively verified the icing shape based on the length of the ice horn, the angle of the ice horn, ice area, and ice coverage. However, his method does not use the actual cross-sectional area of the ice, and the measurement changes depending on the airfoil shape. This study resolves these problems by using the actual cross-sectional area of the ice and setting a datum point at the 25% chord to determine the heading and maxi-mum thickness of the ice. In addition, this study verifies the accuracy of the code by comparing it with other codes, such as LEWICE, TRAJICE, and ONERA, which employ similar numerical analysis techniques.

It is known that the behavior of ice accretion is influenced by various parameters [9]. This study selects the freestream velocity, liquid water content (LWC), and ambient tempera-ture as the principal parameters. The impact of the selected parameters on icing behavior is investigated in terms of the quantitative measures defined in Section 3.

In summary, this study 1) develops a numerical analysis code that employs the panel method and Messinger’s model, emphasizing calculation time at various icing conditions, 2) establishes the measures that describe icing behavior and con-ducts quantitative verification of the code, and 3) investigates the influence of the selected ambient parameters – freestream velocity, LWC, and temperature – on icing behavior in both

quantitative and qualitative ways.

2. Numerical analysis

This study follows four basic steps, similar to those intro-duced in the preceding section, to obtain the accreted ice shape. 1) The aerodynamics solver calculates the velocity vector around the airfoil. 2) The trajectory of an ice particle, the location where the particle impacts the surface, the collec-tion efficiency of the ice, and the inflow of the liquid water into the surface are determined based on the velocity vector. 3) Messinger’s model determines the amount of ice accreted on the surfaces and the amount of runback water. 4) The thickness of the accreted ice is determined, and a new surface grid is generated by moving the old grid by a distance equiva-lent to the ice thickness. Steps 1–4 are repeated until the preset accretion time is reached, at which point the final ice shape is achieved.

2.1 Aerodynamic solver

The most time-consuming step of the four repetitive steps mentioned above is the velocity field calculation. Even with recent advances in computer resources, Navier-Stokes-based CFD is not viable in terms of calculation time. Considering the advantage of calculation time, this study employs a 2-D steady source and doublet panel method [18] and boundary layer theory to calculate the velocity vector around the airfoil. When the panel method is used to calculate the droplet im-pingement, near the panel, the magnitude of velocity is dra-matically increased by the singularity. To avoid the singularity problem, the velocity is assumed as fourth-order polynomial known as Pohlhausen approximation [19].

The code is supplemented with boundary layer theory to ac-count for the viscosity effect, which cannot be captured by the panel method. As shown in Ref. [7], the laminar, turbulent, and transition models are established in the boundary layer to calculate the heat convection coefficient that the thermody-namics model requires.

Navier-Stokes based CFD approaches currently receive wide acceptance in fluid flow field analysis. Many researches into the icing behavior also employ CFD methods, such as FESANP-ICE, as an aerodynamic solver. However, the most time-consuming model of the four models required to estimate the icing behavior is the aerodynamic solver. Even with recent advances in computing techniques, CFD still requires tremen-dous computing resources. Especially for an estimation of the icing behavior, an analysis code employs a method that as-sumes the flow as a quasi-steady state and updates the itera-tion with the solution obtained during a time step Δt. Because this approach requires iteration, significant amount of comput-ing resources and time should be assigned. Furthermore, a complex geometry, such as ice horns, can hamper the conver-gence of solution, and generating a quality grid system for such geometry requires an extra effort.

C. Son et al. / Journal of Mechanical Science and Technology 26 (4) (2012) 1059~1071 1061

On the other hand, the present study employs a panel me-thod, which NASA and DRA use to establish the aerodynamic solver. The code is supplemented with boundary layer theory in Ref. [6] to account for the viscosity effect. The laminar, transition, and turbulent models are established in the bound-ary layer to calculate the heat convection coefficient that the thermodynamics model requires. The aerodynamic solver gives reasonable results in less time and resources than those a CFD method requires.

2.2 Impingement model

The impingement model determines the amount of liquid water that inflows onto the surface. As the inflow mass of liquid water is impossible to calculate directly from the air, it is indirectly calculated using the collection efficiency. As shown in Fig. 1, this is the ratio of the distance between parti-cles Δy0 and the distance Δs on the surface where the particles may stick. The collection efficiency depends on the trajectory of each particle. This study determines the trajectory using the Lagrangian approach. Assuming that the water droplet is a sphere smaller than 500 μm [20], the forces acting on a non-rotating particle are buoyancy, drag, and gravity. The equation of motion of the particle under these forces is

( ) ( )1- - - .2 dd d a d d a p D f d f dm a V g A C V V V Vρ ρ ρ= +

(1)

The drag coefficient is determined by the Reynolds number

based on the particle size, as follows [21]:

24 (Re 10)RedD d

dC = < (2)

12 (Re 10).RedD d

d

C = > (3)

As Eq. (1) indicates, the drag depends on the relative veloc-ity between the liquid water and the air flow. The air velocity is given by the aerodynamic solver in the previous step. The numerical integration of the acceleration given in Eq. (1) yields the location of the particle and the impact point on the surface.

Assuming that the particles are uniformly distributed in the air, the mass inflow of the liquid water to the surface is deter-mined as follows:

.comm LWC V sβ= ⋅ ⋅ Δ∞ (4)

Previous research [14] deals with aerodynamic solver and

impingement model of validations and more details.

2.3 Thermodynamic model

Messinger’s model is used to determine the heat transfer be-tween the liquid water and the surface. A control volume is established on the surface, as shown in Fig. 2, and the mass and energy are conserved within the control volume, as shown by Eqs. (5) and (6).

com in ice out evam m m m m+ = + + (5)

com in ice out eva convE E E E E E+ = + + + (6) The calculation is conducted rearward from the stagnation

point. The mass flow rate of incoming water becomes 0 at the stagnation point because there is no previous panel that trans-fers water mass. The water mass on the surface is calculated from the impingement model of the previous section. The remaining unknowns are evaporated water mass, ice mass, and runback water mass, all of which are required to uphold mass conservation. Water evaporation is a function of surface temperature, as shown in Eq. (7), and the ice mass and the runback water mass are determined as per Eqs. (9) and (10). This is done in terms of the freezing fraction defined in Eq. (8), which gives a ratio of freezing ice mass to total water mass.

Stagnation pointy0

V∝

V∝

B

VrelD

W

Δy0 Δs

Fig. 1. Flow chart for the correction of the roll forming process design.

BoundaryLayer

Water Filmice

ApproachingWater Droplets

Airfoil

outout em && ,

inin em && ,

comcom em && ,

iceice em && ,

evaeva em && ,conve&

Fig. 2. Conservation of mass and energy in a control volume.


( ) ( )( ) ( )

13 , , , ,

, , ,

/ / / /Pr(1/ 0.622) / /v sur v sur h e e v s v sc

evap a e e v sur v sur

P T r P T P Thm sc Sc P T P T

−⎛ ⎞= Δ⎜ ⎟ −⎝ ⎠

(7)

ice

com in

mfm m

=+

(8)

( )ice com inm f m m= +

(9)

( )1 ( )out com in evam f m m m= − + −

(10) From the energy conservation of Eq. (6), the energies com-

ing from the air and from the adjacent panel are calculated as per Eqs. (11) and (12), respectively.

( )2

, 2com com p w sur iVE m c T T ∞⎡ ⎤

= − +⎢ ⎥⎣ ⎦

(11)

( ), ( 1)in in p w sur I iE m c T T−⎡ ⎤= −⎣ ⎦

(12) The rest of the terms in Eq. (6) are given as Eqs. (13)-(16).

All mass and energy conservation terms become functions of freezing fraction and surface temperature.

( ),eva eva p w sur i vE m c T T L⎡ ⎤= − +⎣ ⎦

(13)

2

,2c

conv c sur ep a

r VE h T T sc∞

⎡ ⎤⎛ ⎞= − + Δ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(14)

( ),ice ice p i sur e fE m c T T L⎡ ⎤= − −⎣ ⎦

(15)

( ),out out p w sur iE m c T T⎡ ⎤= −⎣ ⎦

(16) Assuming that the surface temperature is the freezing point

of 273.15K, Eq. (6) yields the freezing fraction, which is be-tween 0 and 1. Any freezing fraction between 0 and 1 indi-cates that the initial guess of the surface temperature is feasi-ble, and the terms in Eq. (6) taken together satisfy energy con-servation and mass conservation. If the freezing fraction is calculated to be less than 0, the initial guess of the surface temperature is higher than the actual temperature, so the sur-face temperature in Eq. (6) is recalculated with a higher initial guess. On the other hand, if the freezing fraction is greater than 1, it must be set to 1, and the surface temperature must be decreased before being applied to Eq. (6).

The freezing fraction and the surface temperature are de-termined by the thermodynamics model. Because each term of the conservation equations is a function of freezing fraction and surface temperature, solving the conservation equations yields the amount of ice that accumulates on the surface.

2.4 Ice growth model

Based on the ice mass determined by the thermodynamics model, the thickness of the ice is calculated as follows:

.ice

ice

mh tsρ

= ΔΔ

(17)

The ice growth model generates a new grid of the surface, reflecting the thickness of the ice. Fig. 3 illustrates how the new grid is generated. First, new nodes are placed at the calcu-lated thickness in a direction perpendicular to the old surface. Next, the new surface grids are generated by connecting the average points between the nodes.

As the calculation interval increases, the shape may become distorted because the new grid is too long compared to the old one. In order to prevent distortion, a new node is added in the middle of the grid if the new grid is twice or more than twice the length of the original. Because the direction and rate of ice growth are not uniform, the grid for glaze ice accretion may be twisted as it grows. If a twist occurs, the intersection is identi-fied, and a new node is assigned at the intersection. The nodes that do not fall on the twisted grid are then renumbered. Re-peating the grid generation throughout the time that the airfoil is exposed to icing conditions yields the final shape of the accreted ice.

This study follows four basic steps, similar to those intro-duced in the preceding section, to obtain the accreted ice shape. 1) The aerodynamics solver calculates the velocity vector around the airfoil. 2) The trajectory of an ice particle, the location where the particle impacts the surface, the collec-tion efficiency of the ice, and the inflow of the liquid water into the surface are determined based on the velocity vector. 3) Messinger’s model determines the amount of ice accreted on the surfaces and the amount of runback water. 4) The thickness of the accreted ice is determined, and a new surface grid is generated by moving the old grid by a distance equiva-lent to the ice thickness. Steps 1–4 are repeated until the preset accretion time is reached, at which point the final ice shape is achieved.

3. Quantitative measurement

Previous studies on icing, which emphasized duplicating the shape of the accreted ice, compared the estimated ice

Mid-pointat the end of panels

New surface grid

1

2

3

45

6

7

8

9

10 11

1

2

3

4 5

6

7

Panel direction

h

8

Fig. 3. The method of new surface grid generation and rearrangement of the twisted surface.


shapes directly to the results from tests or other analysis codes in Cartesian coordinate systems. However, such evaluations run into difficulties with the quantitative analysis of the ice shape and accuracy of the code. In an effort to quantitatively investigate icing behavior, Wright and Potatpczuk quantified the ice shape in terms of height, width, and direction of the ice horn [22]. However, their work is limited to the ice horn and lacking in elements for quantitative investigation into the overall behavior of ice on the wing. Furthermore, the measur-ing standards for each parameter are not clear, so the result varies depending on how the measurement is taken. Wright [17] quantified the icing behavior according to length and angle of the ice horn, ice area, and ice coverage, all of which can be clearly measured. However, Wright’s ice area is not the actual cross-sectional area of the ice. Furthermore, the dimen-sions of the ice horn are dependent on the airfoil shape be-cause they are measured at the center of the leading edge, which varies.

This paper proposes the cross-sectional area of ice, the max-imum thickness, the ice heading, and the thickness distribution of the ice on the airfoil surface as the characteristic parameters that quantify the icing behavior of both the ice horn and the overall shape. They are measured as follows:

The cross-sectional area of the ice is calculated using Green’s theorem, shown in Eq. (18), which expresses the rela-tionship between a closed curve and the area. The closed curve consists of the ice and the airfoil, as shown in Fig. 4. The line integral of the closed curve yields the cross-sectional area. The cross-sectional area reflects the actual area of icing, i.e. the actual amount of ice, and it can be one of the indicators of ice accretion behavior.

1 ( )2area ydx xdyσ = − +∫

(18)

The cross-sectional area, i.e. the amount of accreted ice, is associated with the amount of liquid water coming into the control volume and the sublimation or evaporation out of the control volume, as shown in Eq. (5). However, because the mass of incoming liquid water is much greater than the subli-mated or evaporated liquid water, the incoming liquid water dominates the cross-sectional area. Therefore, determining the accurate amount of incoming liquid water precedes accurate estimation of the cross-sectional area of the ice.

The maximum thickness and heading of the accreted ice are the indicators that describe the shape of the ice horn that occurs under glaze icing conditions. They also show the direction of the ice growth under rime icing conditions. They are defined at the 25% chord in a polar coordinate system, which allows an intuitive comparison of the different icing behaviors. The ori-gin of the polar coordinates can be set anywhere, such as on the leading edge, the trailing edge, or the leading edge center. Plac-ing the origin on the leading edge makes the angle measure-ment too large, and placing it on the trailing edge makes the measurement too small. Furthermore, when the angle is meas-ured at the leading edge or the trailing edge, it is not aligned with the direction in which the ice actually grows. If the origin is at the center of the leading edge circle, it is easier to measure the heading and maximum thickness of the ice. However, there are limitations associated with every location of the origin, depending on the airfoil. Therefore, the origin cannot be placed in a standard position that is universally applicable. Instead, this study sets the origin at the 25% chord, which is the aero-dynamic center of most airfoils. This position resolves the problems associated with the leading edge and the trailing edge and gives consistent results regardless of airfoil selection.

The maximum thickness, as shown in Fig. 5, is defined as the distance between the airfoil surface and the point on the ice farthest from the origin. Fig. 5 also shows the definition of the heading of the ice horn, which is the bearing angle of the maximum thickness point.

Fig. 4. Closed loop to which Green’s theorem is applied.

θ

δ

-90-60

-30

0

30

6090

0

0.10.15

0.20.25

RectangularCoordinate

(0.25,0)

+θhorn

δmax

Radial direction

δmax

+θhorn

Fig. 5. Definition of the maximum thickness and ice heading in a polar coordinate system.


The thickness of the ice is defined as the perpendicular dis-tance from the airfoil surface to the ice contour, as illustrated in Fig. 6. The thickness is measured from the geometrical leading edge along the airfoil surface. The positive distance indicates the upper surface, and the negative distance indicates the lower surface.

4. Code validation

The developed code is validated with ice accretion on the NACA0012 airfoil under the three conditions shown in Table 1. The estimated icing behavior is cross-checked with the analysis results from NASA, ONERA, and DRA in terms of the quantitative measures previously discussed. Calculation times of each case take under 30 mins on 3.0 GHz single core Intel CPU. It shows that the developed code takes far shorter calculation time than that of N-S based CFD icing code.

Fig. 7 shows the ice shape obtained at a temperature of -22.8°C. At this temperature, the liquid water does not run back. Instead, it turns into ice as soon as it impacts the surface. Therefore, the accretion shape is relatively simple. There is no significant qualitative difference in the resultant ice shape

from this study and the shape predicted by LEWICE or the test results. From a quantitative perspective, as shown in Fig. 8, the present code estimates the icing heading within a 1.6° difference and the maximum thickness within a 2% difference from the test results. In addition, the present code estimates the icing area, presented in the bar chart of Fig. 9, within a reasonable range of error. The distribution of the icing thick-ness shown in Fig. 10 indicates that the peak and the location of the peak are correctly captured in this study. However, at the lower surface (S/C<-0.05), the code underestimates the ice accumulation so that the icing area is 13% lower than the test result. In general, the results of the code correlate well with the results of the test and LEWICE under rime icing condi-tions.

Table 1. Ambient conditions used to validate the developed code.

Case 1 [6] Case 2 [6] Case 3 [22]

Chord (m) 0.533 0.533 0.533

Α (°) 4 4 4

V∞ (m/s) 102.8 102.8 93.89

T∞ (°C) -22.8 -11.1 -12.2

LWC (g/m3) 0.55 0.6 1.05

MVD (µm) 20 15 20

Time (s) 400 384 372

θhorn

δmax

-5

00.0280.0290.030.0310.032

ExperimentPresent MethodLEWICE

Fig. 8. Maximum thickness and ice heading.

σ are

a

0

0.0005

0.001

0.0015

0.002

0.0025

-13%

-5%

LEW

ICE

Expe

rimen

t

Pres

entM

etho

d

Fig. 9. Ice accretion area.

Fig. 6. Ice thickness along the airfoil surface (ice distribution).

X/C

Y/C

-0.04 -0.02 0 0.02 0.04-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

ExperimentPresent MehodLEWICEClean Airfoil

Fig. 7. Ice accretion shape.


Fig. 11 compares the Case 2 icing shape from the present code with the results from LEWICE, ONERA, TRAJICE2, and CIRA. However, such a simple comparison in Cartesian coordinates does not give much information about the accu-racy of the code or how to explain the differences. This raises a demand for quantitative investigation of the icing shape. Comparison of the icing area between methods in Fig. 12 shows that the present code gives the estimate closest to the test result. Because the icing area is mainly associated with the total inflow of liquid water, Fig. 12 indicates that the present code accurately estimates the amount of liquid water inflow. Furthermore, Fig. 13 demonstrates that the code correctly estimates the location of the peak, peak height, and icing lim-its. However, it overestimates the ice thickness around the stagnation point (-0.20<S/C<0) as a result of the aerodynamic solver overestimating the heat transfer rate. Because the heat transfer rate appears greater than the latent heat, the freezing fraction becomes almost 1 [26]. Therefore, there is very little runback water along the surface around the stagnation point, and the ice is thin. Fig. 14 shows the maximum thickness and the heading from various analysis codes, making it obvious

that the present code successfully estimates the heading. The maximum thickness is underestimated for the same reason that the ice is thin around the stagnation point, but the estimation error is within the same bounds as in the other codes.

Under the ambient conditions specified in Case 3, all of the LWC, freestream speed, and temperature are high, and the ice horn – an indication of glaze ice – grows. Because the frees-tream speed is high, the kinetic energy of the air at the stagna-tion point is also high. Thus, the ice becomes thin and runback

S/C

t

-0.15 -0.1 -0.05 00

0.005

0.01

0.015

0.02

0.025

0.03

0.035

ExperimentPresent MethodLEWICE

Fig. 10. Ice thickness along the airfoil surface (ice distributions).

X/C

Y/C

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

Clean AirfoilExperimentPresent MethodLEWICEONERATRAJICE2CIRA

Fig. 11. Ice accretion shapes.

σ are

a

0

0.0004

0.0008

0.0012

0.0016

0.002

Pres

entM

etho

d

Expe

rimen

t

ON

ERA

TRA

JIC

E2

CIR

A

LEW

ICE

-7.3%

7.8%

38.2%

18.7%


S/C

t

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

ExperimentPresent MethodLEWICEONERATRAJICE2CIRA

Stagnationregion


θhorn

δmax

-10

0

10

0.0150.02

0.0250.03

0.0350.04

0.045

ExperimentPresent MethodLEWICEONERATRAJICE2CIRA

ONERA

CIRA

LEWICE

TRAJICE2

Experiment

Present Method

Fig. 14. Maximum thickness and ice heading.


increases. The runback that occurs at the stagnation point flows along the surface and freezes in the region where the heat transfer rate is high. The ice in this region becomes thick, and the air passing over it accelerates. The accelerated air further increases the heat transfer rate, resulting in even thicker ice. As a result, the ice accumulates in a particular region, forming a horn. When an ice horn occurs the surface area that liquid water may contact increases. This in turn in-creases the icing area, as shown in Fig. 16.

Fig. 17 shows the length and heading of the upper horn. It is apparent that the estimations of the present code and LEWICE both correlate well with the experimental results. The ice dis-tribution in Fig. 18 also shows that the present code ade-quately estimates the icing limit, peak height, and location of the peak of the upper horn. However, it fails to capture the behavior of the lower part of the ice horn; LEWICE, ONERA, and the present code all underestimate the icing area of the lower horn. These codes calculate the heat transfer rate in the boundary layer model. On the other hand, TRAJICE2 esti-mates the heat transfer rate to reflect a correlation with the values of cylindrical shapes; thus, its estimation of the lower horn is more accurate [23]. The present code needs improve-

ment in order to achieve more precise estimation of the heat transfer rate on the lower surface.

In summary, when estimating the quantitative measures of both rime icing and glaze icing, the present code performs better than or at least within the same error bounds as other analysis codes.

5. The effects of various icing conditions

Investigation into the impact of ambient air conditions on the behavior and strength of icing can provide fundamental data for the design of anti/de-icing devices. Furthermore, the icing area, maximum thickness, heading, and icing limits prove crucial to determining the range of device operation and the heat capacity of the surface.

This study estimates ice accretion according to the ambient conditions and quantitatively investigates ice shapes to under-stand the relationship between ambient conditions and the behavior of ice accretion. The ambient temperature, LWC, and freestream speed are selected as the dominant parameters that influence icing behavior, and icing shapes are estimated

X/C

Y/C

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Clean AirfoilExperimentPresent MethodLEWICEONERATRAJICE2

Fig. 15. Ice accretion shapes.

σ are

a

0

0.001

0.002

0.003

0.004

0.005

Expe

rimen

t

Pres

entM

etho

d

LEW

ICE

TRA

JIC

E2

ON

ERA

+22.7%

-14% -7% -6.5%


θhorn

δmax-10

0

10

20

0.050.06

0.070.08

0.090.1

0.11

ExperimentPresent MethodLEWICEONERATRAJICE2

ONERA

PresentMethod

LEWICE

TRAJICE2

Experiment

Fig. 17. The maximum thickness and ice heading.

S/C

t

-0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.040

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

ExperimentPresent MethodLEWICEONERATRAJICE2

Ice horn at thepressure side



according to variations in each parameter, under both rime ice and glaze ice conditions, as is shown in Table 2.

MVD is the one of the parameters which can change the ice accretion shape. The dropt diameter affects the drag coeffi-cient, as shown in Eqs. (2), and (3), consequently, it changes the droplet trajectories, collection efficiency, and the icing limits. FAR Part25, the airworthiness requirements set, de-fines the ranges of MVD. It varies from 15 to 50 μm. In the defined range, the change of drag coefficient and droplet tra-jectories are smaller than that of SLD conditions in which the MVD is over 40 μm [24]. Indeed, the previous research [25] shows that ice accretion shape does not depend on the MVD. By considering the result, ambient temperature, LWC, and freestream velocity are selected as the dominant parameters.

The estimated ice shapes are investigated by the quantita-tive measures described in Section 3, and the relationship be-tween the behavior of ice accretion and the ambient conditions is drawn in both qualitative and quantitative ways.

5.1 LWC (Liquid Water Content)

The LWC affects the inflow of the liquid water mass, as Eq. (4) describes. An increase in the LWC increases the liquid water inflow onto the surface, resulting in a greater total area of ice for both rime ice (Fig. 19(a)) and glaze ice (Fig. 20(a)) conditions. Because the LWC does not seriously influence the heat convection coefficient, the ice forms to some extent even under glaze ice conditions in which runback occurs. The flu-ent accretion of ice does not significantly increase the contact area; thus, there is no sharp change in the total ice area, and the ice area and the LWC are linearly proportional. Under rime ice conditions, as the LWC increases, the maximum thickness also grows while maintaining the same heading, as shown in Fig. 19(b). The peak remains in the same location, as the ice distributions of Fig. 19(c) and Fig. 20(c) exhibit. Under warm glaze ice conditions, runback occurs as the inflow water increases due to the high LWC. The runback water flows rearward from the stagnation point, spreading the ice coverage. The changes in LWC affect the ice area and the icing limits rather than altering the ice shape. Therefore, to reflect the variation in LWC, it is more important to determine the ap-propriate coverage for an anti/de-icing device than it is to in-crease its heat capacity.

Table 2. Ambient conditions with various icing conditions.

LWC V∞

Rime ice Glaze ice Rime ice Glaze ice T∞

NACA0012, 0.5334 m, α = 4˚

T∞ (˚C) -20, -5 -25, -10 -3,-6,-9,-12,-15,-18,-21

V∞ (m/s) 50 33,48,64,81,101,129 120

LWC (g/m3) 0.25,0.5,0.75,1.0,1.25,1.5 0.6 0.6

MVD (µm) 20 15 15

Time (s) 300 384 384

σ are

a

00.0

003

0.00

060.0

009

0.001

20.0

015

1.50

g/m

3

0.25

g/m

3

0.50

g/m

3

0.75

g/m

3

1.00

g/m

3

1.25

g/m

3

Area

LinearLine

Fig. 19(a). Ice accretion shapes and ice accretion area with various LWC under rime ice conditions.

θhorn δmax

-20

-10

0

10

20

00.005

0.010.015

0.020.025

(f)1.5(a)0.25(b)0.5(c)0.75 (d)1.0(e)1.25

Increase δmax

Fig. 19(b). Ice heading and maximum thickness.

S/C

t

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.0200.0

040.0

080.0

120.0

160.0

20.0

24

0.25g/m3

0.50g/m3

0.75g/m3

1.0g/m3

1.25g/m3

1.5g/m3

Fig. 19(c). Ice distributions.


5.2 Ambient temperature

Because the ambient temperature does not directly influ-ence the liquid water inflow, there is no clear relationship between the ambient temperature and the ice area (Fig. 21(a)). However, changes in ice shape, which may be caused by tem-perature variation, alter the liquid water inflow. As a result, the ice area begins to change between the temperatures of -3°C and -9°C, at which point the shape change occurs. For a higher

temperature, runback increases, and hence the ice covers more airfoil surface while becoming thinner. However, under rime ice conditions below -12°C, at which changes in ice shape do not occur, no significant variation in the ice area is observed. The variation in heading and maximum thickness is also small, as shown in Fig. 21(b). Although the ambient temperature influences the behavior of the icing, this influence does not appear below the temperature at which rime ice occurs.

σ are

a

00.0

003

0.000

60.0

009

0.001

20.0

015

1.50

g/m

3

0.25

g/m

3

0.50

g/m

3

0.75

g/m

3 1.00

g/m

3

1.25

g/m

3

Area

Linear Line

Fig. 20(a). Ice accretion shapes and ice accretion area with variousLWC under glaze ice conditions.

θhorn δmax

-20

-10

0

10

20

00.003

0.0060.009

0.0120.015

0.018

(f)1.5(a)0.25(b)0.5(c)0.75

(d)1.0(e)1.25

Increase δmax


S/C

t

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.0200.0

040.0

080.0

120.0

16

0.25g/m3

0.50g/m3

0.75g/m3

1.0g/m3

1.25g/m3

1.5g/m3


σ are

a

00.0

010.0

020.

003

-15°

C

-3°C -6°C

-9°C

-12°

C

-21°

C

-18°

C

Fig. 21(a). Ice accretion shapes and ice accretion area with various ambient temperatures.


S/C

t

-0.16 -0.12 -0.08 -0.04 0 0.0400.0

060.0

120.0

180.0

240.0

30.0

36

-3°C-6°C-9°C-12°C-15°C-18°C-21°C



5.3 Freestream velocity

Eq. (1) indicates that the freestream velocity directly affects the inflow of liquid water onto the airfoil surface. The frees-tream velocity also influences the kinetic energy of the frees-tream, convection, and evaporation, as Eqs. (11), (13), and (14) show. Variations in freestream velocity under rime ice conditions form a fluent and gradual change in ice area, as shown in Fig. 22(a). This resembles the response to LWC variation under low temperatures. Another similarity between

freestream and LWC variations is found in ice growth: the heading remains the same, while the maximum thickness var-ies. However, icing behavior differs greatly under high tem-peratures. Specifically, the increase in inflow and kinetic en-ergy due to a higher freestream velocity cause runback. Such runback freezes where the heat transfer rate is high, resulting in the ice horns illustrated by Fig. 23(a). An ice horn makes

σ are

a

00.0

006

0.001

20.0

018

0.002

433

m/s

48m

/s

64m

/s 81m

/s 101m

/s

129m

/s

Fig. 22(a). Ice accretion shapes and ice accretion area with variousfreestream velocities under rime ice conditions.


S/C

t

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.0200.0

070.0

140.0

210.0

280.0

35

33m/s48m/s64m/s81m/s101m/s129m/s


σ are

a

00.0

010.0

020.0

03

129m

/s

33m

/s

48m

/s

64m

/s 81m

/s

101m

/s 110m

/s

Ice horn shape

Fig. 23(a). Ice accretion shapes and ice accretion area with various freestream velocities under glaze ice conditions.


S/C

t

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.0200.0

080.0

160.0

240.0

320.0

4

33m/s48m/s64m/s81m/s101m/s110m/s129m/s



the frontal area larger; hence, more liquid water contacts the surface and ultimately the inflow increases. Fig. 23(a) con-firms this, showing that the icing area drastically increases after an ice horn forms at the freestream velocity of 110m/s. Because of the ice horn, the heading and thickness increase, as shown in Fig. 23(b). Furthermore, as shown in Fig. 23(c), the peak that was at the lower surface (S/C < 0) moves upward.

The freestream velocity is a factor that greatly influences ic-ing behavior, considerably altering the maximum thickness, peak location, icing coverage, and heading.

6. Conclusions

This paper presented the development of an analysis code for icing behavior under rime ice and glaze ice conditions. The code consisted of Messinger’s model and an aerodynamic solver that employed the panel method and boundary layer theory. Some quantitative parameters, e.g. icing area, maxi-mum thickness, heading, and ice distribution, were selected to verify the code and explain the icing behavior in a quantitative manner. Through quantitative investigation, the accuracy of the code was verified objectively, and the behavior of ice ac-cretion was characterized. In addition, the influence of ambi-ent conditions on icing behavior was investigated in terms of the selected parameters, and the following conclusions were drawn:

(1) The present code yielded results within the same error bounds as other codes that used similar methods. Although the present code left something to be desired in its estimation of irregular shapes and ice horns on the lower surface of the air-foil, it performed satisfactorily in other estimates – i.e. the icing area, maximum thickness, ice heading, and icing cover-age – under all rime, mixture, and glaze ice conditions.

(2) The LWC was a parameter that indicated the inflow of liquid water onto the surface. As the LWC did not alter any thermodynamic characteristics of the airfoil surface, such as heat transfer, it did not cause changes in ice shape. In other words, the LWC did not influence the formulation of an ice horn. As a result, the LWC did not influence the frontal area either. However, an increase in the LWC increased the inflow of liquid water, resulting in an icing area increase. A linear relationship was observed between the LWC and the icing area.

(3) The freestream velocity was a dominant factor in estab-lishing the characteristics of kinetic energy, convection, and evaporation. A high freestream velocity caused runback that froze in the region where the rate of heat convection was high, eventually forming an ice horn. Once the horn formed, as the liquid water contacted the larger frontal area, the iced area grew rapidly. The freestream velocity was the factor that had the greatest influence on the behavior of ice accretion at a given temperature.

(4) The increase in ambient temperature altered rime ice conditions to glaze ice conditions. As the temperature rose, less water froze on the surface and more runback occurred, increasing the heading and ice coverage and decreasing the

maximum thickness. Below the temperature at which rime ice forms, no remarkable changes in icing behavior were ob-served.

Acknowledgment

This work was supported by the National Research Founda-tion of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0024757).

Nomenclature------------------------------------------------------------------------

a : Acceleration Ap : Cross-sectional area of water droplet, m/s2 β : Collection efficiency, m2 c : Chord length, m cp : Pressure coefficient δmax : Maximum thickness, m E& : Energy flow rate, W∙ K f : Freezing fraction g : Acceleration due to gravity, 9.81m/2

h : Ice thickness, m hc : Convective heat transfer coefficient, W/m2/K L : Latent heat, J/kg LWC : Liquid water content, kg/m3

m : Mass, kg m& : Mass flow rate, kg/s P : Pressure, N/m2

Pr : Prandtl number Red : Reynolds number based on water droplet diameter rh : Recovery factor ρ : Density, kg/m3

S : Surface length (distance along the airfoil surface), m Sc : Schmidt number θhorn : Ice heading direction or horn angle, deg σarea : Ice accretion area, m2

T : Temperature, K Tice : Assumed ice temperature t : Icing time, sec Δt : Icing time increment, sec V : Freestream velocity, m/s Vd : Droplet volume, m3

Subscripts

a : Air d : Droplet com : Impinging water conv : Convection e : Edge of the boundary layer eva : Evaporation or sublimation i : Ice I : Control volume I-1 : Preceding control volume in : Runback into control volume


ice : Freezing ice f : Fusion, field out : Runback out of control volume sur : Surface condition s : Static condition v : Vapor, vaporization w : Liquid water ∞ : Freestream

References

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and drag of small water drops by means of a wind tunnel, J. of Atmospheric Science, 26 (5) (1969) 1066-1072.

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Chankyu Son received a B.S. degree in Aerospace Engineering from Pusan National University in 2010. He is cur-rently an M.S. candidate at the graduate school of Aerospace Engineering at Pusan National University in Pusan, Korea. His research interests are in the area of aerodynamics, and heat transfer.

Sejong Oh received a B.S. and M.S. degree in Aerospace Engineering from Seoul National University in 1979, and 1982 respectively. He finished his Ph.D. degree from Stanford University in 1988. Prof. Oh is currently a Professor at De-partment of Aerospace Engineering at Pusan National University in Pusan,

Korea. Prof. Oh’s research interests are in the area of vortex flow, and rotorcraft aerodynamics.

Kwanjung Yee received a B.S., M.S., and Ph.D. degree in Aerospace Engi-neering from Seoul National University in 1992, 1994, and 1998, respectively. Dr. Yee is currently an Associate Pro-fessor at Department of Aerospace En-gineering at Pusan National University in Pusan, Korea. His major research area

covers unsteady aerodynamics, rotorcraft flight dynamics, and multidisciplinary design optimization.

quantitative analysis of a two-dimensional ice accretion ... · lewice, trajice, and onera, which...

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