[American Institute of Aeronautics and Astronautics 43rd AIAA Aerospace Sciences Meeting and Exhibit - Reno, Nevada ()] 43rd AIAA Aerospace Sciences Meeting and Exhibit - A Grid Refinement

American Institute of Aeronautics and Astronautics Paper 2005-1247

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A Grid Refinement Strategy for Impingement Limits Computation for an

Eulerian Collection Approach

Luis C. de Castro Santos, Luiz Tobaldini Neto, Ramon Papa, Daniel B. V. F. Da Silva

EMBRAER, São José dos Campos, SP, BRAZIL, 12227-901

Sutikno Wirogo

FLUENT Inc., Lebanon, NH, USA, 03766-1442

Abstract

Based on previous experience of the use of different mesh topologies (hexahedral, tetrahedral and

hybrid), the present work provides a study on refinement strategies for impingement limits computation.

Although hexahedral meshes are more accurate in the representation of surface gradients they require a higher

level of user expertise in mesh generation for complex configurations. The grid refinement strategy is based

on gradients of volume fraction (α) relying on the ability of the CFD solver (FLUENT) to maintain mesh

quality. Results indicate that the impingement region limits are rather insensitive to mesh choice, but the

maximum and averaged collection can vary significantly. Some general levels of equivalency are proposed

based on the experiments performed for the DLR-F4 configuration.

Introduction

The design of ice protection systems

relies on the accurate prediction of: i) the thermal

load, directly related to the collection efficiency of

the aerodynamic surface, which is the amount of

energy necessary to prevent the supercooled

droplets from freezing; and ii) the impingement

limits, which define the extension of the protected

region, and consequently the geometrical sizing of

the system. As has been reported by several

authors in literature [1,2,3,4], the use of Eulerian

methods has several advantages for practical

applications. Discrete particle methods, although

extensively used in several industry codes, are not

cost effective when dealing with complex three-

dimensional shapes. The number of particles

seeded has to be very high in order to provide a

precise and smooth computation of β. Eulerian

methods, on the other hand, eliminate the particle

seeding issue since the droplets are represented as

a continuous phase. But, as any scalar transport

equation, it is subject to numerical issues such as

artificial dissipation, which can mask the actual

physical results. A common requirement of both

methods is a fine representation of the surface,

and therefore a significant fraction of the analysis

time is spent on rigorous grid generation followed

by an intensive number-crunching period. Since

this is the bottleneck of the analysis, any effort in

order to reduce analysis time can have a

significant impact on the overall cost of the risk

assessment. In the preliminary design phase, when

the configuration changes rapidly, it is important

to be able to provide a compatible estimate of the

ice protection system requirements in the same

rate of update as the other disciplines, in order to

remove any bottleneck of the multidisciplinary

design process. These requirements support the

use of tetrahedral meshes, which are considerably

easier to generate and automatize.

Previous results [8] for a non-lifting

configuration, a sphere, indicate clearly that levels

of collection are substantially lower for tetrahedral

meshes when compared with hexa and hybrid

meshes. The results indicated that for the sphere

the impingement limits are less sensitive than the

overall water catch (the surface integral of the

collection coefficient). A major issue is the

number of elements required to reach a similar

solution quality. From the pure hexa to hybrid

grid the increase of cell volumes is four fold,

consequently the computational cost rises four

times.

In order to validate the findings for the

sphere, a typical configuration, the DLR-F4 wing-

body geometry, was used. For an initial

comparison two meshes were used: An extra

coarse hexa mesh, obtained by de-refining the

coarse mesh generated by ICEM for Drag

Prediction Workshop, with 692558 volume cells

and 12710 surface quads; and a tetra mesh with a

prism layer generated also by ICEM, with

1964682 volume cells and 79124 surface tri.

The flow field corresponds to an average

holding pattern at 15,000 ft, ISA, at 200 knots,

43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-1247

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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AOA 2°, with MVD=40 µm droplets. Both flow

and droplet Eulerian phase where obtained using

FLUENT, just as the previous sphere cases. For

the hexa mesh the shadowing effects on the wing

due to the presence of the fuselage and the sharp

impingement limit boundary, especially in the

lower surface of the wing where clearly

estabilished. On the tetra + prism mesh although

the maximum level of collection is reached, when

compared to the hexa mesh, there is a

considerable spread in the impinged area.

Therefore an issue related to the influence of the

section lift on the impingement limits was raised,

since for the sphere both hexa and hybrid meshes

display similar impingement limits.

Based on this experience a study on grid

refinement is performed in an attempt to remedy

this problem. The purpose of the present work is

to investigate the effect on both pressure

distribution and levels of volume fraction (α) of

the adaptation of a baseline coarse tetrahedral

mesh to evaluate this process in the support of

preliminary design studies. The DLR-F4

configuration is again used as baseline to

represent a typical aircraft configuration.

Numerical Method

For ice accretion analysis it is assumed that

the volume fraction of the water droplets is small

and the aerodynamic effects on the continuous gas

flow field are negligible. This permits the

computation of the droplet motion to be

decoupled from the gas flow calculations. The

flow field of the gas phase around the body is

calculated using the FLUENT general-purpose

solver, which is applicable to inviscid/viscous and

incompressible/compressible flow fields. A

description of the solver can be found in the

Fluent User’s Guide [9].

The droplet motion can be solved either in the

Lagrangian or the Eulerian frame. The governing

equations for the particle motion in the

Lagrangian frame is:

Fuuu

a+−= )(K

dt

d (1)

where u is the droplet velocity vector and ua is the

gas phase velocity vector. F is the force per unit

mass on the droplet due to external sources other

than the drag. Such external forces can be the

pressure gradients in the fluid, the added mass

effect or the force due to gravity.

The corresponding droplet conservation

equations in the Eulerian frame are given below:

( ) 0=⋅∇+∂

∂uαρ

αρ

t (2)

( ) Fuuu uu

aαραραρ

αρ+−=⊗∇+

∂

∂)( K

t

(3)

where⊗ is the dyadic product, α ,is the droplet

volume fraction and K is the momentum exchange

coefficient related to drag.

The droplet x, y and z velocities along with its

volume fraction are defined as User-Defined-

Scalars in FLUENT. These are solved according

to equations (2) and (3) in finite volume

formulation using the User-Defined-Scalar-

Transport framework in FLUENT. The boundary

conditions and the relation to compute the

collection coefficient (β) can be found on

references [1,2,3].

Reference [4] presents several validation

cases, with respect to other tools as LEWICE [5]

and FENSAP-ICE [3], and also to experimental

data, including full three-dimensional geometries

such as the Boeing 737-300 engine nacelle wind

tunnel model [7]. All these results support the

confidence on the use of the computational model

provided by FLUENT as a reliable tool for ice

colletion analysis.

Mesh Generation and Adaptation

As previously mentioned, the generation of

pure tetra meshes, even for complex

configurations, has become extremely simple and

fast in modern day grid generation tools, such as

GAMBIT and ICEM-CFD. Therefore during the

preliminary design phase, due to the continuous

update of the configuration, it is desirable to use

such mesh topology. But a compromise in

solution quality must be met. In order to illustrate

this issue with regard to ice collection and ice

protection system design, a coarse baseline tetra

mesh for the DLR-F4 is generated. This mesh has

230479 volume cells and 36448 surface tri. As

before, the flow field corresponds to average a

holding pattern at 15,000 ft, ISA, at 200 knots,

AOA 2°, with MVD=40 µm droplets. The

solution for the volume fraction for is show in

Figure 4. Based on this solution a sequence of

adapted meshes is generated using FLUENT. The

gradient of the volume fraction computed, with

maximum magnitude reaching 0.22. This mesh is


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adapted for refinement only (coarsening is

disabled) and only conformal elements are

allowed (preventing hanging nodes). Only a

maximum of two levels of refinement are allowed.

Three meshes are generated for gradient threshold

of 0.20, 0.15 and 0.05; that is any cell which

gradient is above such level is refined. This

procedure resulted in meshes with 690408,

734605 and 1003030 cells respectively, which

represents a growth ratio with respect to the

original tetra mesh of 3.00, 3.19 and 4.35. The

number of triangular faces is respectively 38930,

39456 and 42714, representing growth ratios of

1.07, 1.08 and 1.17. The relation between surface

refinement, which is very important for accurate

impingement limit computation, and number of

cells which controls the overall solution quality,

as presented above, stress how is the steep rate of

growth of computational cost. Figure 4 shows the

mesh overview along a cut plane at y=0.8, which

is a section close to the wing root of the DLR-F4

model.

Collection Efficiency Results

Both the flow field and scalar transport are

computed for each of the meshes obtained by

adaptation. Figure 4 show a cut plane located at y

= 0.8, close to the wing root. On Figure 4a the

baseline tetra mesh is shown. On Figure 4b,

Figure 4c and Figure 4d respectively one can see

the meshes for the gradient threshold of 0.2, 0.15

and 0.05. It is clearly noticeable that adaptation

process concentrated points near the leading edge

where the gradient between the impinged and the

shadow is higher. The computed collection

coefficient (β) for each mesh is shown on Figure

5. The sequence of refinement is better observed

on the fuselage surface. In general there isn’t

much change on the surface distribution β on the

wing surface, except for the most refined mesh

(gradient threshold 0.05), in which there is a

considerable loss of quality. This effect is rather

odd, but as one analyzed the plots of β for every

wing section, on Figure 6, this anomaly seems to

be confined to first section. It is believed that

since this is the mostly adapted mesh, starting

from the original baseline coarse tetra, the

smoothing and edge swapping algorithm of

FLUENT was unable to improve the mesh quality,

even being applied several successive times,

mainly due to the proximity of the fuselage on

that region of the wing. An analysis of the results

for the collection coefficient (β) for each section

is summarized on Table I. In average there is an

under prediction of the maximum β of 75%. With

respect to impingement limits for the upper

surface the error is much lower than on the lower

surface, being more critical closer to the fuselage.

Comparing figures 4a-4d one can conclude that

surface mesh quality is a more critical issue than

surface number of elements when we consider

collection efficiency distribution.

Surface Pressure Distribution

The results for collection efficiency raised an

issue regarding the accurate representation of the

flowfield itself. Therefore, on Figure 7, the plots

for negative Cp are displayed in sequence from

the inboard to the outboard of the wing. It is

clearly visible that the adaptation procedure was

effective in better representing both the suction

peak on the upper surface as the stagnation point.

Conclusions

The analysis of the previous results leads to

the conclusion that the effectiveness of the

adaptation for ice collection based on tetrahedral

meshes is questionable. To reach the level

accuracy of a hexahedral mesh seems to be

impractical due to level of refinement required.

Adaptation, which allows the addition of points

where needed, seems also to require a lot from the

mesh correcting algorithms, and therefore for

higher level of quality may also be unfeasible.

The use of quickly generated tetra meshes may

still be justified since, at least qualitatively, the

thermal load, which proportional to the integral of

the collection profile is very similar.

Additional studies on those issues will be

performed in a near future.

References

[1] - Y. Bourgault, Z. Boutanios and W.G.

Habashi.: An Eulerian Approach to 3-D Droplet

Impingement Simulation Using FENSAP-ICE.

Part I: Model, Algorithm and Validation, Journal

of Aircraft, 37:95-103, 2000.

[2] - Y. Bourgault and W.G. Habashi: A new

PDE-based Icing Model in FENSAP-ICE.

Canadian Aeronautics and Space Institute, 7th

CASI Aerodynamics Symposium, Montreal,

Quebec, Canada, May 2-5, 1999.

[3] - Y. Bourgault and W.G. Habashi: A new

PDE-based Icing Model in FENSAP-ICE.

Canadian Aeronautics and Space Institute, 7th


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CASI Aerodynamics Symposium, Montreal,

Quebec, Canada, May 2-5, 1999.

[4] – S. Wirogo, S. Srirambhatla; An Eulerian

Method to Calculate the Collection Efficiency on

Two and Three Dimensional Bodies. 42th AIAA

Annual Meeting and Exhibit, Reno, Nevada,

2003.

[5] - Ruff, G.A., and Berkowitz, B.M., 1990.

“Users Manual for the NASA Lewis Ice Accretion

Prediction Code (LEWICE).” NASA CR185129.

[6] – Bidwell, C.S., and Mohler, S.R. Jr., 1995.

“Collection Efficiency and Ice Accretion

Calculations for a Sphere, a Swept MS(1)-317

Wing, a Swept NACA-0012 Wing Tip, an

Axisymmetric Inlet, and a Boeing 737-300 Inlet.”

NASA TM 106831.

[ 7] - Papadakis, M., Elongonan, R., Freund, G.A.

Jr., Breer, M., Zumwalt, G.W., and Whitmer, L.,

1989. “An Experimental Method for Measuring

Water Droplet Impingement Efficiency on Two-

and Three-Dimensional Bodies.” NASA CR 4257.

[8] – L. C. de C.Santos , L. Tobaldini Neto, R.

Papa, G.L. Oliveira, A.B. Jesus, S. Wirogo : Grid

Sensitivity Effects in Collection Efficiency

Computation. 43th AIAA Annual Meeting and

Exhibit, Reno, Nevada, 2004.

[9] - Fluent 6.0 User’s Guide, 2001, Fluent Inc.

Table I – Mesh Comparison

hexa prism base tetra tetra adpt 0.20 tetra adpt 0.15 tetra adpt 0.05

volume cells 692558 1964682 230479 690408 734605 1003030

surface faces 12710 79124 36448 38930 39456 42714

max beta y 0.8 0.45 0.45 0.37 0.37 0.37 0.20

imp lim low y 0.8 0.04 -0.07 -0.10 -0.10 -0.10 -0.10

imp lim hi y 0.8 0.14 0.15 0.15 0.15 0.15 0.15

max beta y 2.0 0.67 0.67 0.41 0.42 0.42 0.43

imp lim low y 2.0 0.15 0.08 0.08 0.08 0.08 0.08

imp lim hi y 2.0 0.2 0.22 0.22 0.22 0.22 0.22

max beta y 4.0 0.75 0.75 0.5 0.6 0.6 0.6

imp lim low y 4.0 0.34 0.295 0.295 0.295 0.295 0.295

imp lim hi y 4.0 0.375 0.38 0.38 0.38 0.38 0.38

max beta y 5.5 0.775 0.725 0.5 0.5 0.51 0.52

imp lim low y 5.5 0.48 0.455 0.455 0.455 0.455 0.455

imp lim hi y 5.5 0.5 0.515 0.515 0.515 0.515 0.515


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Fig. 3 Baseline Tetra Mesh - UDM 3 (volume fraction) - Contours for select cuts (y=0.8, 2.0, 4.0, 5.5)


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(a) tetra baseline (b) tetra adapted gradient threshold 0.20

(c) tetra adapted gradient threshold 0.15 (d) tetra adapted gradient threshold 0.05

Fig. 4 – Cut planes (y=0.8)

(a) tetra baseline


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(b) tetra adapted gradient threshold 0.20

(c) tetra adapted gradient threshold 0.15

(d) tetra adapted gradient threshold 0.05

Fig. 5 – Surface plot of Collection Efficiency (UDM4) and grid refinement for different meshes


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(a) y = 0.8

(b) y = 2.0


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(c) y = 4.0

(d) y = 5.5

Fig. 6 – Local Collection Coefficient (UDM4) Comparison along y-stations for different meshes


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(a) y = 0.8

(b) y = 2.0


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(c) y = 4.0

(d) y = 5.5

Fig. 7 – Pressure Distribution Comparison along y-stations for different meshes

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[American Institute of Aeronautics and Astronautics 43rd AIAA Aerospace Sciences Meeting and Exhibit - Reno, Nevada ()] 43rd AIAA Aerospace Sciences Meeting and Exhibit - A Grid Refinement