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Proceedings ArticleDOI

Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

24 Jun 2013-

AbstractRobust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

Topics: Glaze ice (58%), Accretion (meteorology) (55%), Mesh generation (55%), Volume mesh (51%)

Summary (4 min read)

NASA Glenn Research Center, Cleveland, OH, 44315, USA

  • Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem.
  • There are several technical challenges associated with mesh generation for simulating ice accretion on a three-dimensional configuration.
  • Any mesh generation strategy will necessarily require the ability to handle such complex geometries if it is to represent a viable, long-term solution.
  • ¶Assistant Research Professor, Center for Advanced Vehicular Systems, PO Box 5405, Member.
  • The authors are developing a solver-neutral interface propagation tool that computes the position of a discrete surface as it evolves under an accretion rate map specified by LEWICE3D.

II. Background: Surface Evolution

  • One of the challenges associated with evolving a faceted, discrete surface is that the normal at a node is not unique.
  • One approach that has shown promise for evolving a surface mesh while conserving volume is the method developed by Jiao.2,3 Jiao employs a singular value decomposition (SVD) to solve a least square problem and then applies an eigenvalue/eigenvector analysis at each node to resolve its normal motion, which generates the surface geometry, and its tangential motion, which maintains mesh quality.
  • (1) Here, each row of the system corresponds to one of the m faces that are incident on the node and elements of a are the offset distances for each incident face.
  • The solution to Equation 2 represents an advective motion in which the resulting surface is the intersection of the propagated face planes.
  • A simple solution is to assume the direction of the displacement will not change and adjust the displacement to satisfy the required offset.

III. Approach

  • Generating an ice shape for a specified accretion time tice is accomplished by performing a series of quasi-static, loosely-coupled, ice accretion/flow simulation steps.
  • The authors term each of these quasi-static steps an “ice accretion step” with an associated time interval ∆t.
  • As noted below, each time interval ∆t may be further subdivided into subintervals ∆ts.
  • For each ice accretion step: (1) a CFD simulation is performed to compute the flow field about the current ice shape, (2) a LEWICE3D computation is performed to determine the new ice shape, or alternatively, the accretion rate map, and (3) the surface and volume meshes are evolved based on the ice accretion rate using iceSurf and gridMover, respectively.
  • Deform the volume mesh by projecting the surface deformations into the volume mesh using gridMover 3 of 20 American Institute of Aeronautics and Astronautics Each of these processes is described in the sections that follow.

III.A. Generate Accretion Rate Map using Lofting

  • Currently, LEWICE3D does not provide an accretion rate map.
  • Two different strategies were employed to circumvent this shortcoming.
  • The icing rate for each surface element is calculated assuming that no evaporation or runback occurred and is given by dvice dt =.
  • A two-dimensional coordinate system (S,T ) is employed for the loftings for which S is the axial coordinate and T is either the spanwise coordinate for wing-type lofts or the circumferential angle for body of revolution-type lofts .
  • The local coordinates systems generated for the surface point and icing cut points are used to transform the local surface points into the local ice cut point coordinate system for the interpolation of the ice thickness .

III.B. Surface Mesh Evolution

  • The authors have developed a computational tool (iceSurf ) that employs elements of Jiao’s algorithm2,3 to evolve a discrete surface mesh in response to the ice accretion rate.
  • Like Jiao’s algorithm, the algorithm used in iceSurf emphasizes conservation of the accreted volume.
  • IceSurf uses the offset direction in the primary space defined by Jiao’s method as the initial nodal displacement direction and then employs global and local smoothing algorithms to maintain mesh quality.
  • B.1. Identify Geometrical Features iceSurf provides special treatment for the nodes associated with these features.
  • If the angle between the two faces that share a given edge is greater than a threshold, then this edge is considered to be a geometrical edge.

III.B.2. Define Nodal Offset Direction

  • The next step in the process is to generate an initial nodal offset direction.
  • This temporarily circumvents the need for knowledge of the face displacement.
  • An additional change is that the weight matrix W in Jiao’s algorithm (see Equation 3) is based on the face areas of the triangles incident on the node under consideration while their weight matrix is based on the included angles of the faces incident to the node.
  • Once the primary direction is defined, it is held fixed throughout the remainder of the process.

III.B.4. Smooth the Height Field

  • In general, the heights for two triangular faces that share an edge will not be equal.
  • A height field smoothing that conserves volume is then employed to redistribute the volume.
  • Assume that the authors have two triangles, T1 and T2, that share an edge, with heights h1 and h2, respectively, and h1 > h2.
  • The resulting accreted volume is then compared to the value obtained by multiplying the accretion rate by the time increment ∆ts.
  • The resulting volume residue is converted to a rate and then added or subtracted during the next subinterval step as appropriate.

III.B.5. Compute Nodal Positions

  • The next step is to determine the nodal positions using the smoothed height field.
  • In contrast, for wavefront motion, the node should reside on a smooth nonlinear patch.
  • Of course, there are multiple faces associated with this node.
  • The final nodal displacement is given by a weighted average of the displacement from the faces incident on the node.
  • The weighting is based on the included angles of the faces at that node.

III.B.6. Smooth the Evolved Surface Mesh

  • The nodal positions are then smoothed using the null space smoothing described by Jiao.
  • Null space smoothing moves nodes in the tangent plane or in the direction of minimum curvature of the surface and therefore, tends to preserve the volume better than other forms of smoothing, such as Laplacian.
  • Their approach takes boundary displacements as input and returns a deformed volume mesh.
  • The local rotation for a given node is computed by using a least squares fitting to determine the rotation about the node that best matches the displacements of all edges and normals from surface facets that reference the given node.
  • This accelerated IDW approach has been shown to be competitive with the considerably more expensive radial basis function (RBF) proposed by deBoer et al.7.

IV. Results

  • The authors now present results that demonstrate the efficacy of the mesh evolution and deformation algorithms.
  • The authors then employ the algorithms in a loosely coupled approach utlizing Loci/Chem and LEWICE3D for a rime icing condition and a more challenging glaze icing condition.

IV.A. Test Cases: Sphere with Prescribed Accretion Map

  • A face volume accretion rate was then computed by multiplying the face area by the accretion velocity.
  • This was performed by iceSurf using six substeps to produce the surface shown in figure 8.
  • The resulting accretion closely matched the expected analytical results.
  • The surface evolution algorithm employed in iceSurf produced a valid surface mesh even for a discontinuous rate map and no smoothing.

IV.B. Rectangular Planform Wing with GLC305 Cross Section

  • Loosely-coupled Loci/CHEM-LEWICE3D simulations of ice accretion on a rectangular planform wing with a constant GLC305 airfoil section were performed and the results compared with available LEWICE2D and LEWICE3D simulation results and experimental data.
  • A far field boundary condition was also applied at the top, bottom, and outboard 9 of 20 American Institute of Aeronautics and Astronautics side boundaries of the computational domain, all of which were located approximately five chords from the wing.
  • A droplet tracking window was specified near the airfoil covering the whole span.
  • The effects of employing substeps and height smoothing in iceSurf will now be discussed.
  • In the comparisons that follow, the authors note that only single-step ice accretions can be generated by 10 of 20 American Institute of Aeronautics and Astronautics LEWICE3D.

IV.B.1. Results for Rime Ice Conditions

  • The icing conditions considered for this case were a liquid water content (LWC) of 0.405 gm/m3, an ambient temperature and pressure of 257.88 K and 1 atm, respectively, and a relative humidity of 100 percent.
  • At this temperature, the water droplets freeze on impact without runback, so the simplified method for estimating the icing rate based on collection efficiency described in Section III.
  • In both cases, a single accretion step was used with no smoothing.
  • These figures also show a comparison of ice shapes generated by iceSurf and LEWICE3D for two different icing times.
  • The authors are currently investigating this discrepancy.

IV.B.2. Results for Glaze Icing Conditions

  • The icing conditions for this case corresponded to Case 072604 in the LEWICE2D validation report.9.
  • A comparison of ice shapes generated by iceSurf, LEWICE3D, and LEWICE2D and experimental data is illustrated in figure 13.
  • The authors now discuss the ripples that appear in the surface as shown in figure 14.
  • Starting from the single-step, 6-min ice accretion, the authors intended to advance the ice shape for a total icing time of 22.5 min using multiple 2-min intervals, which would correspond to Case 072605 in the LEWICE2D validation report.
  • These images show that, as the surface mesh evolved, the volume mesh was deformed in a manner that maintains mesh quality up to the point that the calculation failed due to the self-intersection of the surface mesh.

V. Conclusion

  • The authors describe a meshing strategy designed for simulating the accretion of ice on aerodynamic surfaces.
  • Additionally, the authors employ a fast algebraic approach to project the surface deformation into the volume mesh.
  • Results obtained for the rime ice case, for which the accretion rate map is based on collection efficiency, show similar trends to results predicted using LEWICE3D ; however, discrepancies exist that can be attributed to the manner in which the accretion rate is computed.
  • Results for the glaze ice case demonstrate that their approach can handle more complex shapes.
  • The authors are concurrently developing tools that employ local quality improvement operations, such as edge swaps, etc., and local mesh regeneration to maintain geometric mesh quality as the accreted surface and volume mesh evolve.

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Discrete Surface Evolution and Mesh Deformation for
Aircraft Icing Applications
David Thompson
, Xiaoling Tong
, Qiuhan Arnoldus
, Eric Collins
§
,
David McLaurin
, and Edward Luke
k
Mississippi State University, Mississippi State, MS, 39762, USA
Colin Bidwell
∗∗
NASA Glenn Research Center, Cleveland, OH, 44315, USA
Robust, automated mesh generation for problems with deforming geometries, such as
ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a
technique to deform a discrete surface as it evolves due to the accretion of ice. The surface
evolution algorithm is based on a smoothed, face-offseting approach. We also describe a fast
algebraic technique to propagate the computed surface deformations into the surrounding
volume mesh while maintaining geometric mesh quality. Preliminary results presented here
demonstrate the efficacy of the approach for a sphere with a prescribed accretion rate, a
rime ice accretion, and a more complex glaze ice accretion.
I. Introduction
There are several technical challenges associated with mesh generation for simulating ice accretion on a
three-dimensional configuration. First, ice accretion is an evolutionary process; therefore, the mesh must
evolve in response to the growth of the ice shape. Assuming a loosely coupled ice accretion strategy, such
as that used in LEWICE3D,
1
a sequence of quasi-static accretion steps is performed to generate the final
ice shape. Since the ice shape changes, each accretion step requires a new mesh. However, a full mesh
regeneration may be expensive for complex configurations. An alternative strategy is to deform the mesh
in response to the ice growth. The second challenge is that accreted ice shapes can become quite complex.
While the current state of the art in ice accretion prediction does not produce shapes with exceedingly
complicated geometries, the predicted ice shapes can nevertheless present significant challenges for meshing
software. Additionally, as the fidelity of ice accretion prediction increases, the complexity of the numerically-
generated ice shapes will increase. Any mesh generation strategy will necessarily require the ability to handle
such complex geometries if it is to represent a viable, long-term solution.
Currently, there is no automated mesh generation process designed to work with LEWICE3D. The re-
sulting capability gap precludes routine grid-based, multi-time-step simulations of ice accretion on complex
configurations. As part of the NASA Atmospheric Environment Safety Technology Project, an ongoing
effort at Mississippi State University seeks to facilitate routine simulation of ice accretion on realistic, three-
dimensional configurations by developing a suite of meshing tools that will produce unstructured, mixed
element (hybrid) meshes for evolving ice shapes in an automatic, efficient, and robust manner. Such auto-
mated mesh generation is a necessary step in the enhancement of existing ice accretion prediction tools as
well as in the development of the next generation of these tools.
Associate Professor, Department of Aerospace Engineering, PO Box A, Associate Fellow.
Assistant Research Professor, Center for Advanced Vehicular Systems, PO Box 5405, Associate Member.
Research Associate II, Center for Advanced Vehicular Systems, PO Box 5405, Nonmember.
§
Postdoctoral Associate, Center for Advanced Vehicular Systems, PO Box 5405, Member.
Assistant Research Professor, Center for Advanced Vehicular Systems, PO Box 5405, Member.
k
Associate Professor, Department of Computer Science and Engineering, PO Box 9637, Senior Member.
∗∗
Aerospace Engineer, Icing Branch, 21000 Brookpark Road, Member.
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American Institute of Aeronautics and Astronautics

Any approach that has the potential to make grid-based ice accretion simulations for realistic configura-
tions commonplace occurrences must have the following characteristics:
Automation: Simulating the evolving ice shape necessarily requires generating a new mesh for each
ice shape. For this approach to be routine, it is necessary that the mesh generation process be as
automated as possible. Once an initial mesh is generated, the user should be removed from the loop,
even in cases where the surface evolution initially produces an invalid mesh or a mesh of poor quality
due to the complexity of the ice shape.
Efficiency: Although a new mesh must be generated for each ice shape, the process must be efficient.
The simplest approach, completely regenerating the mesh, is potentially a time-consuming task for
complex aircraft configurations and not appropriate for ice accretion simulations.
Robustness: Any mesh generation tool that is to be employed in an automated analysis environment
must be robust. In the context of mesh generation for ice accretion simulations, robustness implies
that a valid mesh of reasonable quality must be generated for ice shapes of varying complexity. The
challenge here is to ensure that the mesh retains sufficient quality as the ice surface evolves.
In this paper, we briefly describe the algorithms we employ to evolve the discrete surface mesh that
represents the accreting ice and to project these deformations into the volume mesh. We are developing a
solver-neutral interface propagation tool that computes the position of a discrete surface as it evolves under
an accretion rate map specified by LEWICE3D. The surface evolution tool, iceSurf, is designed to produce
a new surface mesh given the current surface mesh, a face-centroid accretion rate map, and the icing time.
The output from iceSurf provides input, in the form of a surface displacement file, to the mesh deformation
tool gridMover to produce a new volume mesh. We include preliminary results for a sphere with a prescribed
accretion rate field, a relatively simple rime ice accretion, and a more complex glaze ice accretion.
II. Background: Surface Evolution
Figure 1. Face offsetting produces unambiguous nodal po-
sitions in two dimensions.
One of the challenges associated with evolving a
faceted, discrete surface is that the normal at a node
is not unique. This is caused by the discontinuous
nature of the discrete representation of the surface.
One possible solution is to define a displacement di-
rection at each node, based on the normals in the
adjacent faces, and displace the surface a prescribed
distance in this direction at each node. However,
there are numerous challenges associated with this
approach not the least of which is conservation of
volume. Alternatively, the surface evolution could be modeled by generating a plane that is parallel to a
given face by extruding a specified distance the product of the accretion rate and the time step from the
face centroid in the direction of the face normal as shown for a two-dimensional surface in figure 1. As seen in
the figure, there is no ambiguity in the location of the nodes in the new surface in two dimensions; however,
this is not the case in three dimensions in which any two of these offset planes (not parallel), intersect in a
line while three non-parallel planes intersect at a point. In general, the intersection of four or more planes
is not defined in three dimensions. Except in special cases, the number of faces that share a given node in
a typical triangular surface mesh is usually more than three and, consequently, the node determination is
overspecified. This results in an ambiguity in how the nodal positions are defined in the new surface.
One approach that has shown promise for evolving a surface mesh while conserving volume is the method
developed by Jiao.
2, 3
Jiao employs a singular value decomposition (SVD) to solve a least square problem and
then applies an eigenvalue/eigenvector analysis at each node to resolve its normal motion, which generates
the surface geometry, and its tangential motion, which maintains mesh quality.
The first step is to propagate each evolving face in its normal direction. Since the face velocity is given,
a simple, first-order Euler scheme is chosen to integrate along the face normal. This provides the offset
distance for each face.
The second step is to reconstruct the vertices. After computing the new face positions, a new position
for each node on the surface must be determined. For simplicity, assume that the node under consideration
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American Institute of Aeronautics and Astronautics

is located at the origin. Each plane passing through a point p with unit normal n can be expressed by a
linear equation n
T
x = δ, where δ = n
T
p. If there are m faces passing through a node, an m × 3 linear
system will be formed
Nx = a. (1)
Here, each row of the system corresponds to one of the m faces that are incident on the node and elements of
a are the offset distances for each incident face. The linear system given by Eq. 1 can be under-determined or
over-determined depending on the value of m. To address this difficulty, a least square solution is computed.
A point is chosen that minimizes the weighted sum of squared distances to the face planes, which is a solution
of the following 3 × 3 linear system:
Ax = b (2)
where A = N
T
WN, b = N
T
Wa, and W is an m × m diagonal matrix with W
ii
equal to the weight
associated with the i
th
face, which is based on the area of the face incident on node p.
Since the matrix A in Eq. 2 is symmetric and positive semi-definite, it has an eigenvalue decomposition
A = VΛV
T
, where Λ is the diagonal matrix consisting of the eigenvalues of A, which are real and non-
negative, and the corresponding eigenvectors are the columns of V. Since A = N
T
WN, the following
singular value decomposition can be derived
WN = U
ΛV
T
, (3)
where U is a m × 3 matrix.
The vector space spanned by the eigenvectors corresponding to the larger eigenvalues of A is called
the primary space and the complementary space is the null space. An eigenvalue analysis is performed to
identify the primary space. All of the eigenvectors corresponding to eigenvalues smaller than a threshold will
be filtered to avoid instability due to division by a very small number. The nodal displacement is restricted
to the primary space.
The solution to Equation 2 represents an advective motion in which the resulting surface is the intersection
of the propagated face planes. For wavefront motion, such as that produced by burning, erosion, and
deposition, the displacement in the primary space satisfies an entropy condition. Unfortunately, the exact
displacement for wavefront motion can be difficult to compute. A simple solution is to assume the direction
of the displacement will not change and adjust the displacement to satisfy the required offset.
After the displacement is computed, Jiao improves mesh quality by performing a null space smoothing by
computing a tangential motion t at each vertex v. t is a weighted average of the neighborhood of v projected
onto the null space. This smoothing scheme has been shown to preserve sharp features and to introduce
only very small volume errors. Jiao suggests repeating this step without displacement in the primary space
to incorporate a global smoothing into the algorithm that preserves the accreted volume.
III. Approach
Generating an ice shape for a specified accretion time t
ice
is accomplished by performing a series of
quasi-static, loosely-coupled, ice accretion/flow simulation steps. This approach is necessary because, as the
ice shape evolves, it changes the flow field, which, in turn impacts the local ice accretion rate. We term
each of these quasi-static steps an “ice accretion step” with an associated time interval t. As noted below,
each time interval t may be further subdivided into subintervals t
s
. For each ice accretion step: (1)
a CFD simulation is performed to compute the flow field about the current ice shape, (2) a LEWICE3D
computation is performed to determine the new ice shape, or alternatively, the accretion rate map, and (3)
the surface and volume meshes are evolved based on the ice accretion rate using iceSurf and gridMover,
respectively. Here, we focus on the the process employed to compute the deformation of the computational
mesh in response to the ice accretion, which can be divided into three distinct phases:
Generate a volume accretion rate map on the wetted surface
Evolve the surface mesh based on the accretion rate map using iceSurf
Deform the volume mesh by projecting the surface deformations into the volume mesh using gridMover
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American Institute of Aeronautics and Astronautics

Each of these processes is described in the sections that follow.
III.A. Generate Accretion Rate Map using Lofting
Currently, LEWICE3D does not provide an accretion rate map. LEWICE3D generates ice shapes using the
strip-based strategy employed in LEWICE2D,
4
which is based on the Messinger icing model.
5
In future
generations of LEWICE3D, a fully three-dimensional approach will be employed to generate an ice accretion
rate map that will be used by the surface mesh evolution algorithm. Two different strategies were employed
to circumvent this shortcoming.
The first approach, which is applicable only for cold, rime icing accretions, uses the collection efficiency
to estimate a surface icing rate. The underlying assumption employed in this approach is that the droplets
freeze on impact producing a pure deposition problem. The icing rate for each surface element is calculated
assuming that no evaporation or runback occurred and is given by
dv
ice
dt
=
V
× β × LW C × A
ρ
ice
(4)
where V
is the freestream airspeed, β is the local collection efficiency, LW C is the free stream liquid water
context, A is the area of the surface element under consideration, and ρ
ice
is the ice density.
The second approach, which is applicable for warmer, glaze icing conditions, uses a lofting method to
generate the icing rate map. The lofting algorithm assumes that the ice thickness varies linearly along
spanwise lines for wings and circumferentially for bodies of revolution (e.g. inlets, spinners and radomes).
Lofting information is used to generate transformations that facilitate interpolation of ice thickness from
the strip-based ice accretions to the surface. This method is flexible and robust and allows interpolation on
wings with taper, twist, and leading edge curvature and bodies-of-revolution.
The ice patch lofting scheme uses the ice thickness values for the surface nodes, which are interpolated
from the LEWICE3D ice shape values, along with the surface normal at the nodes to generate the new iced
surface. Volume elements are formed from the original surface element and the new displaced iced surface
element. The icing rate is then determined by calculating the volume of these iced volume elements and then
dividing this volume by the icing time. The use of ice thickness interpolated from the LEWICE3D ice shapes
allows a convenient, robust method for generating three-dimensional iced surfaces which have run-back and
evaporation effects.
Two types of lofts are available to describe various surfaces of interest. The first lofting type is a wing-
type lofting. This lofting requires the input of the leading edge and trailing edge of the wing. The second
lofting type is a body of revolution-type lofting. The body of revolution lofting requires the line of rotation
and the leading edge center of rotation. A two-dimensional coordinate system (S,T ) is employed for the
loftings for which S is the axial coordinate and T is either the spanwise coordinate for wing-type lofts or the
circumferential angle for body of revolution-type lofts (figure 2).
Figure 2. LEWICE3D planform types and their associated local coordinate systems wing(left) and body of revolution
(right).
The position (s,t), and the local coordinate system (u,v,w) at a position (x,y,z) on the lofting are
generated using an iterative process. The up-vector w is the planform normal vector at (S,T ). For wing-
type lofts, the planform normal is generated by taking the cross product of the leading edge direction vector
at T and a vector formed from a line at T between the leading edge and trailing edge lines. For the body of
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American Institute of Aeronautics and Astronautics

rotation type geometries the planform normal is the radial vector at T . The spanwise vector, v is generated
by interpolation from the leading edge and trailing edge lines at (S,T ) for wing-type planforms. For body of
rotation type planforms the spanwise vector is the tangential vector at T . The axial vector, u is generated by
taking the cross product of the up-vector and the spanwise vector (figure 2). The local coordinates systems
generated for the surface point and icing cut points are used to transform the local surface points into the
local ice cut point coordinate system for the interpolation of the ice thickness (figure 3).
Figure 3. Local coordinate systems for surface point and ice shape.
Two lines are formed in the local ice cut point system (figure 4). One line segment connects neighboring
ice cut points (l1). The other line is formed using the local ice cut spanwise vector as the slope and the
transformed surface point as the intercept (l2). A set of tests is performed to determine if the minimum
distance between the l1 and l2 occurs within the endpoints of l1 and if this minimum distance is reasonably
small value. If both tests are positive the ice thickness is interpolated linearly from the two ice cut thickness
values at the ice cut endpoints. The local coordinates systems generated for the surface point and icing cut
points are used to transform the local surface points into the local ice cut point coordinate system for the
interpolation of ice thickness (figure 3).
Figure 4. Ice thickness interpolation scheme for surface point.
This procedure is repeated for all of the ice cuts associated with the local surface point. If more than
one intercept is found for the local surface point then a linear interpolation on T is performed from the two
surrounding intercepts (larger T and smaller T than the surface point T ). If the value of T of the surface
point is either greater than the T ’s of all of the ice cut intercepts or is less than the T ’s of all of the ice cut
intercepts the value of ice thickness is set to zero. If an intercept has been found and only one cut has been
associated with the local surface point then an extrapolation is assumed and the ice thickness at the local
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American Institute of Aeronautics and Astronautics

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6 citations


Journal ArticleDOI
Abstract: This paper presents a mesh generation strategy that facilitates the numerical simulation of ice accretion on realistic aircraft configurations by automating the deformation of surface and volume meshes in response to the evolving ice shape. The discrete surface evolution algorithm is based on a face-offsetting strategy that uses an eigenvalue decomposition to determine 1) the nodal offset direction and 2) a null space in which the quality of the surface mesh is improved via point redistribution. A fast algebraic technique is then used to propagate the computed surface deformations into the surrounding volume mesh. Due to inherent limitations in the icing model employed here, there is no intent to present a tool to predict three-dimensional ice accretions but, instead, to demonstrate a meshing strategy for surface evolution and mesh deformation that is appropriate for aircraft icing applications. In this context, sample results are presented for a complex glaze-ice accretion on a rectangular-planform wing ...

6 citations


References
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Journal ArticleDOI
Abstract: Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

12,746 citations


Journal ArticleDOI
TL;DR: A new mesh movement algorithm for unstructured grids is developed which is based on interpolating displacements of the boundary nodes to the whole mesh with radial basis functions (RBF's), which can handle large mesh deformations caused by translations, rotations and deformations.
Abstract: A new mesh movement algorithm for unstructured grids is developed which is based on interpolating displacements of the boundary nodes to the whole mesh with radial basis functions (RBF's). A small system of equations, only involving the boundary nodes, has to be solved and no grid-connectivity information is needed. The method can handle large mesh deformations caused by translations, rotations and deformations, both for 2D and 3D meshes. However, the performance depends on the used RBF. The best accuracy and robustness with the highest efficiency are obtained with a C^2 continuous RBF with compact support, closely followed by the thin plate spline. The deformed meshes are suitable for flow computations as is shown by performing calculations around a NACA-0012 airfoil.

546 citations


Journal ArticleDOI
Abstract: The thermal analysis of a heated surface in icing conditions has been extensively treated in the literature. Except for the work of Tribus, however, little has been done on the analysis of an unheated icing surface. This latter analysis is significant in the design of cyclic thermal deicing systems that are attractive for small high-speed aircraft for which thermal anti-icing requirements have become severe. In this paper, a complete analysis of the temperature of an unheated surface in icing conditions is presented for the several significant regimes (i.e., less than 32°F., at 32°F., and above 32°F.) as a function of air speed, altitude, ambient temperature, and liquid water content. The results are presented in graphical form and permit the rapid determination of surface temperature for a wide range of variables. Curves are presented to determine the speeds beyond which no ice accretion will occur. Curves are also presented to indicate the surface temperature and the rate of ice sublimation which takes place when an ice-covered surface emerges into clear air. One significant result of this study is the introduction of a new basic variable referred to as the "freezing-fraction," which denotes the proportion of the impinging liquid which freezes in the impingement region. The fact that some of the liquid does not freeze in the impingement region tends to explain the observed variation in ice formation shape with temperature, speed, and water catch. New test data obtained at Mt. Washington, N.H., for stagnation-point surface temperatures of an unheated plastic cylinder in natural and artificial icing conditions are included in the Appendix. These data substantiate the validity of the assumptions made in the theoretical analysis.

482 citations


Journal ArticleDOI
TL;DR: A novel mesh deformation algorithm for unstructured polyhedral meshes is developed utilizing a tree-code optimization of a simple direct interpolation method, shown to provide mesh quality that is competitive with radial basis function based methods, with markedly better performance in preserving boundary layer orthogonality in viscous meshes.
Abstract: A novel mesh deformation algorithm for unstructured polyhedral meshes is developed utilizing a tree-code optimization of a simple direct interpolation method. The algorithm is shown to provide mesh quality that is competitive with radial basis function based methods, with markedly better performance in preserving boundary layer orthogonality in viscous meshes. The parallelization of the algorithm is described, and the algorithm cost is demonstrated to be O(nlogn). The parallel implementation was used to deform meshes of 100 million nodes on nearly 200 processors demonstrating that the method scales to large mesh sizes. Results are provided for a simulation of a high Reynolds number fluid-structure interaction case using this technique.

161 citations


01 Sep 1999
Abstract: A research project is underway at NASA Glenn to produce a computer code which can accurately predict ice growth under a wide range of meteorological conditions for any aircraft surface. This report will present a description of the code inputs and outputs from version 2.2.2 of this code, which is called LEWICE. This version differs from release 2.0 due to the addition of advanced thermal analysis capabilities for de-icing and anti-icing applications using electrothermal heaters or bleed air applications. An extensive effort was also undertaken to compare the results against the database of electrothermal results which have been generated in the NASA Glenn Icing Research Tunnel (IRT) as was performed for the validation effort for version 2.0. This report will primarily describe the features of the software related to the use of the program. Appendix A of this report has been included to list some of the inner workings of the software or the physical models used. This information is also available in the form of several unpublished documents internal to NASA. This report is intended as a replacement for all previous user manuals of LEWICE. In addition to describing the changes and improvements made for this version, information from previous manuals may be duplicated so that the user will not need to consult previous manuals to use this code.

127 citations


Frequently Asked Questions (1)
Q1. What have the authors contributed in "Discrete surface evolution and mesh deformation for aircraft icing applications" ?

Here the authors describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The authors also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality.