DROPLET IMPINGEMENT AND FILM LAYER MODELING …essay.utwente.nl/69293/1/report-EJBeld-14-8-2013.pdf · DROPLET IMPINGEMENT AND FILM LAYER MODELING AS A BASIS FOR AIRCRAFT ICING SIMULATIONS

DROPLET IMPINGEMENT AND FILM

LAYER MODELING AS A BASIS FOR

AIRCRAFT ICING SIMULATIONS IN

OPENFOAM

August 13, 2013

Internship Report:

Erik Jan Belds0162566

[email protected]

April 1st - July 5th 2013CIRA Italian Aerospace Research Center

Capua, ItalyMentor: Emiliano Iuliano

Universiteit TwenteEngineering Fluid Dynamics

prof.dr.ir. H.W.M. Hoeijmakers

Abstract

In this report, the open source CFD software package OpenFOAM is evaluatedfor the simulation of impinging water droplets on an airfoil surface, creating aliquid film layer as a basis for future glaze ice accretion simulations.After a short introduction about icing phenomena, the OpenFOAM softwarepackage is described, discussing its general features, as well as focusing on par-ticular utilities used for this evaluation.Two aerodynamic OpenFOAM solvers are evaluated with use of a test case withthe NACA 0012 airfoil, and validated using XFoil and the in-house CFD pack-age ZEN, showing reasonable results.The liquid film layer is simulated with use of OpenFOAM ’s reactingParcelFilm-Foam solver, creating a cloud of water droplets impinging on a NACA 0012airfoil, showing promising results.A short analysis has been made concerning the future work to make the re-actingParcelFilmFoam solver suitable for the simulation of glaze ice accretion,based on Messinger’s model and the Shallow Water Icing Model.

Contents

1 Introduction 1

2 The in-flight icing problem 2

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 Types of icing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.3 Numerical approach . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 The OpenFOAM software package 5

3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3.1 Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3.2 Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3.3 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . 9

3.4 RANS equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.5 The k − ω − sst turbulence model . . . . . . . . . . . . . . . . . 11

3.6 The SIMPLE algorithm . . . . . . . . . . . . . . . . . . . . . . . 12

4 Aerodynamic analysis with OpenFOAM solvers 13

4.1 Aerodynamic flow solution around a Naca 0012 airfoil . . . . . . 13

4.1.1 Mesh generation . . . . . . . . . . . . . . . . . . . . . . . 14

4.1.2 Incompressible flow using simpleFoam . . . . . . . . . . . 15

4.1.3 Compressible flow using rhoSimpleFoam . . . . . . . . . . 18

4.1.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2 Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5 Water film analysis 25

5.1 Droplet impingement and film layer in OpenFOAM . . . . . . . . 25

5.1.1 Droplet injection . . . . . . . . . . . . . . . . . . . . . . . 25

5.1.2 Film layers using OpenFOAM . . . . . . . . . . . . . . . . 26

5.1.3 Tuning parameters . . . . . . . . . . . . . . . . . . . . . . 27

5.2 Film layer results . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.2.1 Simulation time comparison . . . . . . . . . . . . . . . . . 28

5.2.2 Size distribution . . . . . . . . . . . . . . . . . . . . . . . 28

5.2.3 Droplet size comparison . . . . . . . . . . . . . . . . . . . 30

5.2.4 LWC comparison . . . . . . . . . . . . . . . . . . . . . . . 32

iv

Contents

6 Future ice accretion simulations based on the Messinger model 356.1 Comparison with Messinger model . . . . . . . . . . . . . . . . . 356.2 Shallow Water Icing Model . . . . . . . . . . . . . . . . . . . . . 37

7 Summary and Outlook 38

8 Acknowledgements 40

Appendices 42

A ReactingCloud1Propterties 43

v

Chapter 1

Introduction

A main problem in aviation is the formation of ice on aircrafts which can ulti-mately lead to aircraft failure. There are several de-icing and anti-icing systemsto protect the aircraft against ice accretion, but in practice these systems’ per-formances are limited. In order to facilitate the development of anti-icing andde-icing methods, it is important to be able to simulate ice accretion using CFDanalysis. Existing icing predictions using CFD software were mainly focused onthe prediction of accretion of rime ice, for which there’s no need for the creationof an intermediate liquid film layer. This report evaluates the suitability of theOpenFOAM software package for modeling of a surface film layer, as a basis forglaze ice accretion simulations.

1

Chapter 2

The in-flight icing problem

2.1 Overview

Ice accretion on aircraft bodies is caused by the presence of supercooled waterdroplets inside clouds. These supercooled waterdroplets arise when the ambienttemperature is between −40 ◦C and 0 ◦C. Unless the fact that the temperatureof these droplets is below the freezing temperature of water, the droplets stay ina liquid phase due to the absence of a solid object to catalyze the solidification.This solidification will take place as soon as a supercooled droplet hits theaircraft causing an accretion of ice on the aircraft body. Due to this ice accretion,the aircraft will gain weight, and more importantly, the aerodynamic shape ofthe aircraft changes, which can have serious influence on the performance ofthe aircraft, and can ultimately lead to insufficient lift to keep the aircraftairborne. [1]

The rate of ice accretion depends on a number of cloud conditions. Thefirst parameter is the so called liquid water content (LWC), which gives aninsight in the amount of supercooled water present inside a cloud. Since thisLWC only gives global information, without saying anything about the droplets,a second important cloud parameter is the droplets’ mean volume diameter(MVD), to give an indication about the droplets’ size. Droplet diameters foundin clouds can vary from 10µm up to 200µm, which for meteorologists is a typicaldemarcation between cloud droplets and rain droplets. [1]

2.2 Types of icing

Ice accretion on aircraft bodies can roughly be divided into two categories,accretion of rime ice and accretion of glaze ice. The difference between thosetwo icing phenomena lies in the freezing fraction, which is the fraction of asupercooled water droplet which solidifies into ice as soon as it hits the aircraftbody.

Glaze ice occurs in case of low freezing fractions i.e. when only part of thewater droplet which hits the aircraft turns into ice on impact, while the rest ofthe water runs back onto the surface and freezes downstream. This is caused by

2

Chapter 2. The in-flight icing problem

the fact that the part of the droplet that freezes on impact, loses latent heat dueto the phase change. This thermal energy heats up the rest of the water dropletwhich prevents this part from freezing at impact. Instead a liquid water film iscreated which will run, and in the end freeze, in downstream direction. Glaze iceoccurs at relatively high temperatures, just below 0 ◦C, since the temperatureincrease due to the latent heat must be sufficient to warm up part of the waterdroplet to above freezing temperature. In case of glaze icing, the accreted icehas shapes that can have a major influence on the aerodynamic shape of theaircraft, which may be very hazardous for the aircraft performance. An exampleof a glaze ice profile is illustrated in Figure 2.1-b.

Accretion of rime ice appears for ambient temperature far below freezingtemperature, and is characterized by the fact that (almost) all the supercooledwater that hits the aircraft turns into ice on impact, i.e. a high freezing fraction.The penalties on the aerodynamic performance of the aircraft in case of Rime iceare minor compared to glaze ice, since the rime ice profile more or less replicatesthe shape of the aircraft body, as can be seen in Figure 2.1-a.

Figure 2.1: Illustration of accretion of rime ice (a) and glaze ice (b) on an airfoil

2.3 Numerical approach

In the previous section, several differences have been mentioned between rimeice and glaze ice. However, concerning the numerical simulation of the two ic-ing types there is another big difference. Since rime ice occurs for large freezingfractions there’s no need to simulate a liquid film layer. However glaze icingoccurs for low freezing fractions, which means that there will be a liquid filmlayer present on the aircraft body. This liquid film layer enables the growthof characteristic glaze ice shapes, and thus needs to be simulated in order toacquire a representative glaze ice profile.

3

Chapter 2. The in-flight icing problem

generate meshstart (t = 0)

airfoil shape

aerodynamicsolution

flight conditions

parcel im-pingement andfilm layer (∆t)

cloud conditions

thermodynamicsolution

update aero-dynamic shape

desiredtime spanreached?

ice accretionsolution

ambient conditions

no

yes

Figure 2.2: illustration of numerical approach for ice accretion simulations

The numerical simulation of accretion of glaze ice, is done in a discreteapproach, that can be described by several consecutive sub-processes, illustratedin Figure 2.2:

The process starts by generating a mesh around the airfoil shape of interest,which in this report will be the NACA 0012 airfoil.

Second, a steady aerodynamic flow is simulated until convergence.In the third step a cloud of supercooled water droplets is simulated using the

injection of parcels. The necessary parcel injection parameters can be derivedfrom the cloud conditions containing the liquid water content (LWC) and thedroplets’ mean volume diameter (MVD). Parcels impinging on the airfoil surfaceform a liquid film layer, yet without any thermodynamic effects such as icingor evaporation. This parcel impingement is performed for a certain amount oftime ∆t. The value of ∆t should on one side be kept sufficiently small to allowa discrete approach for a, in reality, continuous icing process, and it should belarge enough to create a representative liquid film layer.

After the film layer is created, the thermodynamic solution is derived, tocalculate the ice accretion.

The last step is to include the ’new’ ice accretion into the aerodynamic shape.If the simulated time span is not yet sufficient, this aerodynamic shape can beused for the next iteration step, starting with the meshing step.

4

Chapter 3

The OpenFOAM softwarepackage

3.1 Motivation

Simulations presented in this report are performed with use of the OpenFOAMsoftware package. OpenFOAM is short for ”Open source Field Operation AndManipulation” and it is an open source software package. Although OpenFOAMis mainly focused on CFD applications, it is also suitable to serve for a widerange of other application such as chemical reactions, heat transfer or soliddynamics. OpenFOAM is written in the C++ programming language and is aactually a collection of tools and applications. These applications can be dividedin roughly three categories; first are the Pre-processing tools, such as meshingtools, to set up the desired case, second the solvers which can be standard solversor user made solvers, and third the Post-processing applications to verify andextract the results. This is also illustrated in Figure 3.1. In section 3.3 theseutilities are described in more detail.

OpenFOAM

Pre-processing

UtilitiesMeshingTools

Solving

User Ap-plications

StandardApplications

Post-processing

ParaView Others

Figure 3.1: An illustration of the OpenFOAM application structure

5

Chapter 3. The OpenFOAM software package

3.2 Structure

OpenFOAM uses a fixed folder structure for any kind of simulation. Beforesimulation usually three folders are present in the case directory, which are thesystem folder, the constant folder and the 0 folder.

The system folder contains roughly two different types of files. First it con-tains all information regarding solving, such as numerical schemes, relaxationfactors, simulation time, time steps etc. Second, the system folder contains spe-cial dictionary files needed to use a particular utility, such as the extrudeMesh-Dict needed to run extrudeMesh.

Content stored in the constant folder can be very diverse. The constantfolder contains information about turbulence, material properties and most im-portantly all mesh information is stored in the constant/polymesh folder.

Apart from the system and constant directory, there are the time directories.Before solving, only the 0 directory is present. In the 0 directory the boundary,and initial conditions of all relevant parameters are stored.

Casedirectory

System ConstantTime di-rectories

controlDict

fvSchemes

fvSolution

polyMesh

triSurface

RASProperties

thermophysicalProp.

U

p

k

omega

3.3 Features

3.3.1 Meshing

OpenFOAM has a large number of meshing utilities, the three main applications,blockMesh, snappyHexMesh and surfacefeatureextract which will be discussed inthis paragraph.

blockMesh blockMesh is an application that generates structured meshes.Before blockMesh can be used a dictionary file has to be set up which is called

6


blockMeshDict and should be stored in the /constant/polyMesh subdirectory. Inthis dictionary file, first the coordinates of block vertices are created. Blocks canbe defined by first labeling the vertices creating the block and second defining thedesired number of mesh cells and the mesh grading for every spatial direction.Optionally, edges can be defined, for example if some of the block edges need tobe curved. Finally, boundary patches have to be defined by setting the patchtype, e.g. ’wall’, the patch name and the vertices containing this boundary.blockMesh is only able to generate 3D meshes, so in case of a 2D problem, emptyboundary conditions have to be applied at the boundaries normal to the 3rddimension, for which no solution is required. The blockMesh application is oftenused to generate background meshes for the snappyHexMesh application [2]

snappyHexMesh snappyHexMesh is a meshing utility that generates, in con-trary to blockMesh, unstructered meshes, and compared to blockMesh, it is morecapable of generating meshes around complex shaped bodies. The shape of thesecomplex bodies has to be a shape which is entirely closed by a bounding sur-face can be implemented using an STL-file. Similar to the blockMesh utility,snappyHexMesh uses a dictionary file called snappyHexMeshDict, which shouldis stored in the system subdirectory. Since the snappyHexMeshDict dictionaryfile, can be rather complex, a useful and easy-to-use tool for the generation ofa good snappyHexMesh dictionary file is called HELYXos. Although it doesnot support all features provided by the snappyHexMesh utility, it enables youto create a base dictionary file from which unsupported features can easily bemodified.The snappyHexMesh meshing proces is an iterative proces that can be dividedinto 6 steps.- The first step is the generation of a background mesh (see Figure 3.2), this isdone with the blockMesh application discussed above.- Second, shape of the body described by the STL-file is projected onto thebackground mesh, and mesh refinements specified in the snappyHexMeshDictdictionary file are applied. One refinement level is applied by splitting a meshcell in half, in all spatial directions.

Figure 3.2: foto1 [2] Figure 3.3: foto3 [2]

- Since the implemented body shape is enclosed entirely, the mesh can eitherbe generated inside or outside the body. In order to distinguish the domainthat should be meshed, the locationInMesh parameter should be set in thesnappyHexMeshDict file. Cells from which 50% or more of their volume isoutside of the meshing domain, are removed, as can be seen in Figure 3.4.

7


- Optionally mesh refinement can be applied in domains around the body shape(Figure 3.5). These domains should also be specified in the snappyHexMeshDictdictionary file.


- The next step is the process from which the algorithm received its name,because to fix the notches at the body surface, cell vertices close to the bodysurface are ’snapped’ onto the body surface (Figure 3.6) and then smoothenedwith use of some relaxation sweeps.- A final, optional, step is addition of surface layers. In order to improve themesh quality close to the surface body, surface layers can be added, by ’pushing’the existing mesh outwards. The surface layer addition may strongly reduce faceskewness and non-orthogonality close to the surface. The layer addition processis illustrated in Figure 3.7.


surfaceFeatureExtract Another handy tool for meshing in OpenFOAM issurfaceFeatureExtract, it is a tool that improves mesh quality onto angularshapes. In the paragraph about snappyHexMesh there was an example of amesh generated around a car shaped object. Originaly this object had someclear and sharp angles, but in the final mesh these angles had been smoothenedout. In some cases this behaviour can be very undesirable, for example in caseof an airfoil with a sharp trailing edge. SurfaceFeatureExtract works by readingthe given body surface, the STL-file, and extracting points on the body at whichthe there is an angle sharper than a given reference angle. Subsequently onecan apply an extra mesh refinement near this points. Due to this extra meshrefinement, sharp angles are less vulnerable for the surface relaxation after the

8


snapping process in snappyHexMesh. Although surfaceFeatureExtract does notreally generate meshes, it can be a very handy tool to improve the mesh qualitynear sharp angles.

3.3.2 Solving

There are a large amount of solvers available in OpenFOAM, that cover a widerange of scientific problems. There are several aerodynamic solvers such aspotentialFoam for potential flow, or icoFoam for transient incompressible flows.On the other hand OpenFOAM is also able to handle several non-CFD problems,such as magnetic fields with use of magneticFoam. This report is focused mainlyon three types of OpenFOAM solvers:

• simpleFoam, a steady-state SIMPLE solver (see section 3.6: ”The SIMPLEalgorithm”) for incompressible RANS (Reynolds Averaged Navier-Stokes)flow

• rhoSimpleFoam, a steady-state SIMPLE solver for compressible RANSflow

• reactingParcelFilmFoam, a transient PISO solver for compressible flow,with reacting Lagrangian parcels, and surface modelling (see section 5.1).

In OpenFOAM there are basically three input files that contain informationabout the solving process. The first one is fvSchemes in which you can setthe numerical schemes that should be used. The assigned numerical schemesare separate for different types of mathematical operations, such as gradient,divergence or time derivatives, and for different field variables. Another inputfile is fvSolution, in which parameters for smoothing, relaxation factors andconvergence criteria can be set. The last file is the so called controlDict in whichparameters such as calculation time, time step, and also output parameters, suchas write interval and write format.

3.3.3 Post-processing

In order to extract useful data, OpenFOAM offers several kinds of post-processingutilities. The main post-processing application is paraFoam, which makes use ofthe open source visualization software paraView. ParaView is an easy to use vi-sualization program, mainly suitable for quick post-processing operations. How-ever for more complex operations, the paraView features are too limited. Alter-native post-processing solutions are the utilities that convert OpenFOAM datainto data, readable for more comprehensive (commercial) post-processing soft-ware. For this report, the foamToTecplot360 utility is used for post-processingusing Tecplot.

3.4 RANS equations

The governing equations used to solve the aerodynamic cases in this reportare the so-called Reynolds-Averaged-Navier-Stokes or RANS equations. TheRANS equations are a time averaged form of the standard Navier Stokes equa-tions, which can derived using Reynolds decomposition, by decomposing the

9


time dependent quantities in into their time-averaged and fluctuating terms, forexample for the velocity vector this would become:

U = u + u’

in which u is the time averaged term, and u’ is the fluctuating term of thevelocity vector. By definition, time averaging the fluctuating term is equal tozero and time averaging the time averaged term has no effect:

u’ = 0 (3.1) u = u (3.2)

The derivation of the RANS equation [3] starts with the standard Navier-Stokes equations:

∇ ·U = 0 (3.3)

Ut + U · ∇U = −∇P + ν∆U (3.4)

First, applying Reynolds decomposition on the continuity equation resultsin:

∇ · (u + u’) = ∇ · u +∇ · u’ = 0

This equation can easily be time-averaged, since the nabla vector is inde-pendent of time:

∇ · u +∇ · u’ = ∇ · u +∇ · u’ = ∇ · u +∇ · u’ = 0

With use of equation 3.1 and 3.2, this leads to the time averaged continuityequation:

∇ · u = 0 (3.5)

If we use this in the decomposed non-time-averaged continuity equation wealso obtain:

∇ · u’ = 0 (3.6)

Next, to time average the momentum equation, again Reynolds decomposi-tion is applied.

(u + u’)t + (u + u’) · ∇(u + u’) = −∇(p+ p′) + ν∆(u + u’)

The time averaged part of the time derivative is by definition equal to zero,and thus can be eliminated. The dot product on the left hand side can beexpanded, resulting in:

u’t + u · ∇u + u · ∇u’ + u’ · ∇u + u’ · ∇u’ = −∇(p+ p′) + ν∆(u + u’)

Next the equation is time averaged, resulting in:

u’t + u · ∇u + u · ∇u’ + u’ · ∇u + u’ · ∇u’ = −∇(p+ p′) + ν∆(u + u’)

10


With use of equation 3.1, the first term on the left hand side can be elimi-nated, also furthermore since u, p and ∇ are time independent and using equa-tion 3.1 and 3.2:

u · ∇u’ = u · ∇u’ = 0

u’ · ∇u = u’ · ∇u = 0

−∇(p+ p′) = −∇p

ν∆(u + u’) = ν∆u

The resulting, simplified RANS momentum equations are:

u · ∇u + u’ · ∇u’ = −∇p+ ν∆u

The first term on the left hand side of the equation can be written differently,with use of the product rule for ∇ · (uu):

u · ∇u = ∇ · (uu)− u (∇ · u)︸︷︷︸=0

The part between the brackets in the second term on the right hand side isequal to the time averaged continuity equation, and thus zero. This can also bedone with the second term of the RANS equations in a similar fashion resultingin the final form of the RANS equations:

∇ · (uu) +∇ · (u’u’) = −∇p+ ν∆u (3.7)

By rearranging and using Einstein notation, we end up with:

ρ∂

∂xjuiuj =

∂

∂xj

[−pδij + µ

(∂ui∂xj

+∂uj∂xi

)− ρu′iu′j

](3.8)

The last term in the RANS equations is the so-called Reynolds stress, con-taining the velocity field fluctuations. In order to solve the RANS equations, aturbulence model should be used for this Reynolds stress term.

3.5 The k − ω − sst turbulence model

Like already mentioned in the previous section, in order to solve the RANSequations, a turbulence model is needed to model the Reynolds stress term inthe RANS equations. There are many different turbulent models available tosolve this Reynolds stress term. For linear eddy viscosity models, the Reynoldsstress is modeled using a linear constitutive relation in which µt is the eddyviscosity, and k is the mean turbulent kinetic energy:

−ρu′iu′j = µt

(∂Ui∂xj

+∂Uj∂xi

)− 2

3

(ρk +

∂Uk∂xk

)δij (3.9)

For calculations in this report the two equation k − ω − sst turbulence modelis used, in which an equation for k, the mean turbulent kinetic energy, and an

11


equation for ω, the specific dissipation, is solved. The k − ω − sst model com-bines the best of the standard k−ω model and the k− ε model. The advantageof a k − ω model is that it is usable all the way to the wall. The k − ω − sstmodel behaves like a k − ε model in freestream regions, where standard k − ωmodels are too sensitive for inlet turbulence parameters. In the k − ω − sstturbulence model, the eddy viscosity is calculated using equation 3.10, where Sis an invariant measure of the strain rate, and F2 is a blending function. [4] [5]

µt =ρa1k

max(a1ω, SF2)(3.10)

3.6 The SIMPLE algorithm

The aerodynamic OpenFOAM solvers used for this report are based on theSIMPLE algorithm which is short for Semi-Implicit Method for Pressure-LinkedEquations. The SIMPLE algorithm is a pressure based algorithm that usesboth the momentum equation and a pressure correction equation (derived froma combination of momentum equation and continuity equation to enforce massconservation) in an iterative process. The iterative process can be described asfollows [6]:

1. Set the boundary conditions.

2. Solve the discretized momentum equation to compute the intermediatevelocity field.

3. Compute the mass fluxes at the cells faces.

4. Solve the pressure correction equation and correct pressure field.

5. Correct the velocities on the basis of the new pressure field.

6. Update the boundary conditions.

7. Repeat till convergence.

The steps 4 and 5 can be repeated for a prescribed number of time to correctfor non-orthogonality. [6]

12

Chapter 4

Aerodynamic analysis withOpenFOAM solvers

4.1 Aerodynamic flow solution around a Naca0012 airfoil

In order to choose a suitable OpenFOAM aerodynamic solver and to vali-date that this OpenFOAM solver produces reliable flow field solutions, a casehas been set up in which a comparison is made between several aerodynamicsolvers. Firstly two OpenFOAM solvers will be examined, namely the sim-pleFoam solver, which is a steady-state incompressible flow solver based on thesimple algorithm discussed in section 3.6 and rhoSimpleFoam, which is a steady-state compressible flow solver also based on the simple algorithm. These twoOpenFOAM solver are compared and validated with two other solvers, firstlyXfoil, which is a solver made for the design of subsonic airfoils, and is based onthe panel method. Secondly the in house CFD solver ZEN is used.In the performed case, the aerodynamic flow solution around a NACA 0012 air-foil has been examined. The NACA 0012 airfoil is chosen because of its simplegeometry and because of the large amount of experimental data available for thisairfoil shape. The flow field parameters used for this test case can be found inTable 4.1. Since both a compressible and an incompressible OpenFOAM solveris examined with the same case the free-stream Mach number is set to slightlyabove 0.3, which is a rule of thumb for the limit until it is allowed to treatan aerodynamic flow as incompressible. Although Mach 0.3 is below the cruisespeed of modern aircrafts, ice accretion mainly appears in the period after takeoff and before landing, when the aircraft flies at altitudes at which clouds arepresent, and Mach 0.3 is in the range of aircraft speeds after take off and beforelanding.

13

Chapter 4. Aerodynamic analysis with OpenFOAM solvers

Table 4.1: Test case flow field parameters

M∞ freestream Mach number 0.328 [-]Re Reynolds number 4.49e06 [-]α angle of attack 4 [deg]c chord 0.533 [m]U∞ freestream velocity 102.8 [m/s]p∞ freestream static pressure 9e5 [Pa]T∞ ambient temperature 244 [K]µ dynamic viscosity 1.568e-05 [Pa s]

4.1.1 Mesh generation

The mesh type used for this aerodynamic case is an unstructured mesh generatedwith use of three OpenFOAM meshing utilities: blockMesh, snappyHexMesh andextrudeMesh.The mesh generation procedure starts with generation of a control volume withblockMesh. The control volume size is chosen such that all boundaries (that isdownstream, upstream, upper and lower boundary) will be at around 18 chordlengths away from the airfoil surface (see Figure 4.1). This should be sufficientto prevent boundary disturbances in the flow field.

Figure 4.1: global view of mesh

With use of snappyHexMesh the airfoil shape is implemented into the meshand the prescribed mesh refinements are applied, as already described in moredetail in section 3.3.1. On the airfoil surface a mesh refinement level of 9 isapplied. A total of 5 surface layers are used in order to ensure a good meshquality at the body surface.Finally, the extrudeMesh utility is used, in order to create a fully 2D mesh,without the needless mesh refinement in spanwise direction, like discussed insection 3.3.1.

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Figure 4.2: a close view of the mesh at the leading edge

At the trailing edge there is a problem concerning the mesh quality. This iscaused by the fact that the surface layers on the body become highly skewed andget high aspect ratios at the trailing edge due to the fact that the trailing edgeangle is too sharp for the formation of layers. This problem is partly solved withuse of the surfaceFeatureExtract tool, discussed in section 3.3.1, which allowseach surface layer to pass through a separate mesh point near the trailing edge,illustrated in Figure 4.3.

Figure 4.3: a view of the bad trailing edge mesh

4.1.2 Incompressible flow using simpleFoam

The incompressible flow simulation is performed with the OpenFOAM simple-Foam solver. The boundary conditions used for this simulation can be foundin table 4.2. The case considered in this chapter is a 2D problem. Therefore,no solution is needed for flow parameters in the third spatial dimension. Thisis done by applying ’empty’ boundary conditions on the so-called ’symmetryplanes’. For the velocity an inlet/outlet boundary condition is applied at thecontrol volume boundaries, which means that a Dirichlet boundary condition(U = constant) is applied in case the direction of the flow is inside the control

volume, and a Neumann boundary condition (∂~U∂~n = constant) is applied when

the direction of the flow is outside the control volume. At the airfoil surface,

15


the no-slip condition is imposed by specifying Dirichlet boundary condition ofzero velocity. The zero gradient boundary condition used for the pressure andthe turbulence parameters is a Neumann boundary condition with a normalgradient equal to zero. For turbulence parameters k, ω and νt a special wall-Function boundary condition is used on the airfoil surface. The temperaturefield is not calculated in simpleFoam, because due to the already known density,the temperature can easily be calculated using the equation of state.

Table 4.2: Boundary conditions for incompressible flow simulation

control volume airfoil surface symmetry planes

U inlet/outlet fixed value ( 0 0 0 ) emptyp zero gradient zero gradient emptyk zero gradient kqrWallFunction emptyω zero gradient omegaWallFunction emptyνt zero gradient nutUSpaldingWallFunction empty

The simulation is run for 5000 iterations. The residual plot of the simulationcan be found in Figure 4.4a, showing a convergence of at least 7 orders of mag-nitude for all parameter residuals, this convergence can be considered sufficient.Figure 4.4b shows the continuity error during the simulation, demonstrating amass discontinuity of the order 10−15 which can be considered zero.

(a) Convergence plot of simpleFoam simulation (b) Continuity during simpleFoam simulation

Figure 4.4

The paraview post-processing software is used to visualize the the pressureand the velocity fields. The figure of pressure field (Figure 4.5a) shows a highpressure area around the stagnation point at the leading edge, and a low pressurearea above the airfoil, which is in accordance with the expected pressure fieldaround an airfoil.The velocity field figure (Figure 4.5b) shows a classical velocity field profile,with a relatively high velocity above the airfoil, and a relatively low velocitybelow the airfoil, including a stagnation point just below the leading edge anda wake downstream. The minimum velocity, at the stagnation point, is unequal

16


to zero (≈ 5.4m/s), which may be due to the fact that the actual stagnationpoint may be in between two mesh points.

(a) Pressure field around the airfoil (b) Velocity field around the airfoil

Figure 4.5

The turbulent kinetic energy is plotted in Figure 4.6a. Far from the airfoilsurface the turbulent kinetic energy is close to zero and thus the flow can beconsidered laminar, while close to the airfoil surface, at the boundary layer re-gion, the turbulent kinetic energy is large. With use of the plot of the turbulentkinematic viscosity in Figure 4.6b one can see that the turbulence area increasesgradually from the leading edge to the trailing edge, with a high turbulent areajust after the trailing edge, indicating the turbulence originated from the de-tachment from the airfoil surface. Further downstream the turbulent kinematicviscous area seems to increase rapidly however this is caused by the coarseningof the mesh downstream.

(a) Turbulent kinetic energy (b) Turbulent kinematic viscosity

Figure 4.6

The coefficients of the forces acting on the airfoil are calculated after eachiteration step. In case of convergence, the forces acting on the body, should

17


settle at a constant value after a certain number of iterations. Figure 4.7 showsa graph of the body forces in which one can see that the body forces are alreadywell converged after 100 iterations. A graph of only the first 100 iterations isshown in order to have a clear look at the convergence.

Figure 4.7: force coefficients of the airfoil during computations

4.1.3 Compressible flow using rhoSimpleFoam

rhoSimpleFoam is used to calculate a compressible flow field around the NACA0012 airfoil. The boundary conditions used for this compressible case differfrom the incompressible case. For the velocity the pressure and the tempera-ture, freestream boundary conditions are used on the control volume boundaries.These freestream boundary conditions make use of the Riemann invariants.Since in this case subsonic flow is obtained, flow information is propagated bothdownstream and upstream, while for supersonic flow, information would onlybe propagated in upstream direction. Due to this subsonic flow, the freestreamboundary condition, gathers boundary information from both the internal flowfield as well as from the defined freestream flow conditions. For the turbulenceparameters k and ω the Inlet/Outlet boundary conditions is used which meansthat a Dirichlet boundary condition is applied in case the direction of the flow isinside the control volume, and a Neumann boundary condition is applied whenthe direction of the flow is outside the control volume.

18


Table 4.3: Boundary conditions for compressible flow simulation

control volume airfoil surface symmetry planes

U Freestream fixed value (0 0 0) emptyp Freestream zero gradient emptyT Freestream zero gradient emptyk Inlet/Outlet compr. kqrWallFunction emptyω Inlet/Outlet compr. omegaWallFunction emptyµt calculated mutkWallfunction emptyαt calculated alphatWallFunction empty

Similar to the incompressible case, the compressible case is run for 5000iterations. Figure 4.8a shows a convergence of at least 6 orders of magnitudefor all parameter residuals, which is sufficient for a simple aerodynamic flowproblem. Furthermore, the mass discontinuities during the simulation are shownin Figure 4.8b and have, like in the incompressible case, magnitudes of 10−15

which is small enough to be considered zero.

(a) residual plot during the rhoSimpleFoam calculations (b) continuity during the rhoSimpleFoam calculations

Figure 4.8

The pressure field of the compressible flow solution is shown in Figure 4.9a.The pressure field is very similar to the pressure field of the incompressible case,except for the fact that the pressure variations are larger e.g. the compressiblecase has a larger stagnation pressure.

The velocity field shown in Figure 4.9b is also similar to the velocity field inthe incompressible case, with a stagnation point near the leading edge, a highvelocity region on top of the airfoil, and a wake downstream. The compressiblesolution results in larger variations compared to the incompressible solution.

19


(a) the pressure field around the airfoil (b) the velocity field around the airfoil

Figure 4.9

The turbulent kinetic energy plotted in Figure 4.10a shows similar featuresas in the incompressible case, with high turbulent kinetic energy only close tothe airfoil body, indicating the boundary layer region. In the compressible casethe turbulent dynamic viscosity (µt = ρνt) is used instead of the turbulentkinematic viscosity in incompressible case. Despite of this slightly different tur-bulent parameter, similar features can be found compared to the incompressible.Firstly a gradually increasing turbulent area from the leading edge to the trail-ing edge due to the increase in boundary layer thickness and secondly a highturbulence area just after the trailing edge due to the flow detachment from theairfoil surface.

(a) turbulent kinetic energy (b) turbulent dynamic viscosity

Figure 4.10

The coefficients of the forces acting on the airfoil body, Figure 4.11, indicatea reasonable convergence after just 100 iterations.

20


Figure 4.11: force coefficients during the computation

4.1.4 Validation

The validation of the OpenFOAM solvers is done by a comparison with Xfoiland ZEN discussed earlier. First a comparison has been made of the pressurecoefficient on the airfoil body, as can be seen in Figure 4.12a. At first sight, allsolvers seem to have produced very similar results. At the stagnation point thepressure coefficient should be equal to 1, which is the case for all four solvers.At the low pressure region just after the leading edge on top of the airfoil,there is a somewhat larger difference between the different solvers, illustratedin Figure 4.12b.

First of all, there is quite a significant difference between the two OpenFOAMsolvers. This can be explained with use of the Prandtl-Glauert compressibilitycorrection (equation 4.1), which gives an approximation of the pressure coeffi-cient of a compressible fluid (Cp), with use of the pressure coefficient calculatedwith a solver for incompressible fluids (Cp0), and the freestream Mach num-ber (M∞). Although the Prandtl-Glauert rule is based on inviscid flow, it stillgives a decent relation between the pressure coefficients of compressible andincompressible flow in this viscous case.

Cp ≈Cp0√

1−M2∞

(4.1)

For example, the minimum value for the pressure coefficient is approximately−1.445 for simpleFoam and approximately −1.53 for rhoSimpleFoam, so usingthe Prandtl-Glauert correction results in:

Cp ≈−1.445√

1− 0.3282= −1.529

Apart from the differing results of the two OpenFOAM solvers there are alsosome deviations between both OpenFOAM solvers and Xfoil and ZEN. Althoughit is difficult, and beyond the scope of this report, to perform a precise analysis

21


(a) Pressure coefficient comparison (b) Magnification of the low-Cp region

Figure 4.12

about the origin of these deviations, there are some factors that most probablycaused them. First of all there is a big difference between the solving algorithmof the OpenFOAM solvers and the Xfoil and ZEN solvers, for example thetwo OpenFOAM solvers have used an unstructured grid while ZEN has used astructured gird and Xfoil used a panel method, which may be one of the originsof these slight deviations.

Another parameter to validate the OpenFOAM solvers on is the skin fric-tion coefficient. This is mainly important because it gives an indication aboutthe calculated velocity field near the airfoil surface. This velocity field will beof great importance for the velocity of the film layer discussed in Chapter 5.Equation 4.2 gives the definition of the skin friction coefficient, in which τw isthe local wall shear stress calculated according to equation 4.3 where y is thedistance to the wall.

Cf =τw

12ρU

2∞

(4.2) τw = µ

(∂u

∂y

)y=0

(4.3)

The skin friction coefficient along the airfoil surface for all for all four solversis plotted in Figure 4.13. The skin friction coefficients of the two OpenFOAMsolvers are very similar and are a little bit lower on the entire airfoil surfacecompared two Xfoil and ZEN. For the rear part of the airfoil this difference isnegligible, but especially near the leading edge the deviation of the OpenFOAMsolvers seems to be too large. A reason for this could be that the in the meshused in OpenFOAM the mesh size near the leading edge is too coarse due tothe use of a fixed mesh size on the entire airfoil surface, instead of using a gridexpansion rate along the airfoil surface resulting in a much finer mesh at theleading edge.

22


Figure 4.13: Friction coefficient comparison

4.2 Issues

During the aerodynamic analysis discussed in the previous section, the Open-FOAM software package revealed some silly ’defects’. The main ’defects’ will bediscussed in this section in order to inform the reader and prevent these defectsto slow down eventual future work.

The first main defect occurred when using snappyHexMesh. OpenFOAMmeshing utilities are only able to generate 3D meshes. When a 2D problemis obtained, this problem can be solved by only using 1 mesh cell, with ancertain size in the ’3rd’ spatial dimension of the initial background mesh. Snap-pyHexMesh is a meshing utility for unstructured grids, that are generated inan iterative manner. During the mesh generation, some mesh quality checksare performed, including a check on the aspect ratio. This aspect ratio checkis performed for all three spatial dimensions, which means that the used sizeof the single mesh cell in the 3rd spatial dimension does affect the success orfailure of this mesh quality check, even though this size does not have any affecton the aerodynamic solution.

Another issue occurred when applying mesh refinements . Mesh refinementsin snappyHexMesh are applied in all three dimensions. When using snappy-HexMesh in a semi-2D mesh i.e. a 3D mesh with only one mesh cell in the ’3rd’spatial dimension this means that mesh refinements are also applied in the ’3rd’spatial dimension resulting in an unnecessary high amount of mesh cells, andthus an unnecessary amount of calculation effort when solving. This problemcan be solved by using extrudeMesh utility after finishing snappyHexMesh.

23


In the dictionary file of snappyHexMesh a maximum number of mesh cellsshould be set. When this maximum number of mesh cells is set too low, themeshing process obviously will fail, but more importantly, the process will notnotice in a clear way, that it failed due to exceeding the maximum number ofcells.

When using the aerodynamic solvers, some problems concerning the conver-gence of the residual of the pressure occurred. While residuals of other pa-rameters converged drastically, the pressure residual in some cases stagnatedconvergence at about one order of magnitude. Unlike the high residual, thecalculated pressure field seemed to be converged well. After a software updatethe problem was practically solved.

24

Chapter 5

Water film analysis

5.1 Droplet impingement and film layer in Open-FOAM

The simulation of the impingement of super-cooled droplets with aircraft bod-ies and the creation of a surface film layer is done with use of OpenFOAM ’sreactingParcelFilmFoam solver, which uses Lagrangian particle tracking (LPT)to define the particles’ paths. A steady flow field, calculated with use of one ofthe aerodynamic solvers discussed in the previous chapter, is used as a startingpoint. Particles are injected upstream with a predefined starting velocity. Dragand gravitational forces acting on each particle define the taken path (LPT),according to equation 5.1, in which U is the local velocity of the flow, and UPis the velocity of the particle, ρp is the density of the particles’ fluid, and d isthe diameter of the particle.

mpdUP

dt= − 1

2ρp|UP −U|(UP −U)

πd2

4CD︸︷︷︸

drag

+ mpg︸︷︷︸gravity

(5.1)

A one-sided interaction is assumed between the flow field and the particles, i.e.the flow field does influence the particles’ path, but the particles’ presence doesnot have any effect on the flow field.

5.1.1 Droplet injection

Droplet injection in OpenFOAM can be done with several different injectiontypes. For example, one of the simplest injection types is manualInjection inwhich you can manually specify fixed injection points and velocities in Cartesiancoordinates. Another, more sophisticated injection type is called patchInjection,whereat you have to specify a mesh patch from which parcels have to be injected.The injection points will be the centers of all cell faces this patch contains.In order to simulate a realistic uniform cloud, using a limited amount of injectionpoints, droplet dispersion is very important. An injection model that can handledispersion is coneInjection which is similar to manualInjection except for thefact that particles are not injected with the single predefined starting velocity.Instead, the starting velocity of the injected particles is equal to the predefined

25

Chapter 5. Water film analysis

starting velocity plus a certain deviation angle. This deviation angle is setwith use of a distribution, in which the maximum deviation angle is specified(thetaOuter), together with a mean deviation angle (thetaInner).

Figure 5.1: cone injection inside an aerodynamic flow

Parameters for droplet injection have to be set in the reactingCloud1Propertiesfile in the constant directory. Appendix A contains an example of the injectionparameters that can be set in the reactingCloud1Properties file. One of thethings that have to be kept in mind is that the injection model system in Open-FOAM is over defined. For example, OpenFOAM needs the user to set theduration of the injection, the number of injectors, the number of parcels persecond and the number of parcels per injector. Clearly this is an over definedsituation however, OpenFOAM only uses the most strictly set parameters todefine the injection case. An advantage of this is that in this way there is morefreedom to choose which parameters are used, by setting the desired injectionparameters, and use a very loose value for the rest of the parameters.

5.1.2 Film layers using OpenFOAM

In order to model film layers in OpenFOAM a special external mesh region needsto be extruded from the aerodynamic region. In this extruded mesh region allwall film parameters are modeled. This mesh region can be created with useof two OpenFOAM utilities. First the topoSet utility is used to extract all cellfaces of the airfoil patch from the existing aerodynamic mesh. This is doneusing a topoSetDict stored in the system sub-directory. The extracted cell facesare stored in a seperate sets folder in the constant/polyMesh directory. Secondthe extracted set of cell faces is used to extrude a new mesh region from, us-ing the extrudeToRegionMesh utility. Also for this utility a dictionary calledextrudeToRegionMeshDict is needed. In this dictionary file parameters such asthe to be used cell face set, the number of layers and the extrusion thicknessare set. The extruded mesh region used in this report contains just one layerand has a thickness of 0.1 mm.For modeling of the film layer, a so-called thin film approximation is used, whichmeans that the velocity normal to the mesh wall is assumed to be zero. Since inthis report a two-dimensional flow case is considered, this means that the wallfilm velocity can be considered one-dimensional. Furthermore, wall-tangential

26


diffusion is considered negligible compared to wall-normal diffusion. [7] The wallfilm flow is solved with use of the continuity equation (equation 5.2) and themomentum equations(equation 5.3) in which δ is the film layer thickness. Thecontinuity equation contains four source terms, representing the mass added tothe film layer due to impinging particles, and mass leaving the film layer dueto splashing particles, evaporation, and due to potential separation of the filmlayer.

∂ρδ

∂t+∇ · (ρδU) = Simp + Ssplash + Sevap + Ssep (5.2)

∂ρδU

∂t+∇ · (ρδUU) = −δ∇p+ SρδU (5.3)

5.1.3 Tuning parameters

Cloud conditions are mainly defined with use of the liquid water content (LWC)and the mean volume diameter (MVD). Since it is not possible to specify theseparameters in the parcel injection dictionary file they should be translated intosome OpenFOAM injection parameters. The LWC is defined as equation 5.4,where mw is the total mass of liquid water droplets, present in volume V .

LWC =mw

V

[kg m−3

](5.4)

The total mass of liquid water droplets can be written in terms of injectionparameters, as can be seen in the numerator of equation 5.5, where Ns is thenumber of injected parcels per second, and ρw is the density of water. Theobtained volume is described in the denominator, with use of the x componentof the freestream velocity, the height of the created cloud h, and the span ofthe used airfoil s. Since a 2D case will be considered using a 3D mesh, theused span, is not relevant for the final film layer/ice accretion results, but it willaffect the amount of injected parcels needed and thus the amount of calculationwork. Therefore it can be beneficial to reduce the span of the used airfoil inorder to reduce the calculation work, as long as there will be sufficient parcelsto create an uniform cloud of parcels.

LWC =43π(MVD

2

)3ρwNs

Ux∞ s h

[kg m−3

](5.5)

Equation 5.5 can be rewritten to extract the required number of injectedparcels per second:

Ns =LWC U∞ s h43π(MVD

2

)3ρw

[s−1]

5.2 Film layer results

As described in previous sections, parcel impingement and film layer creationhas been done using reactingParelFilmFoam. In order to get a better idea of thefilm layer thicknesses, film layers will be plotted with a magnification of 1000.A standard case has been set up with the following parameters:

27


Table 5.1: standard impingement case parameters

LWC 0.5 g/m3

MVD 50 µmdroplet size distribution Rosin-Rammlersimulation time 1 s

In this chapter, the standard case is used as a starting point for a sensitivityanalysis of the parcel impingement and film layer process.

5.2.1 Simulation time comparison

Firstly the standard case has been run. Resulting film layer thicknesses areplotted after three different time steps, 0.1, 0.5 and 1.0 seconds(Figure 5.2).Comparing the first two time steps, it is clear that after 0.1 seconds, the filmlayer is still a very smooth layer which is increasing in thickness. The last twotime steps however show a stagnating film layer growth near the stagnationpoint.

Figure 5.2: Film layer thickness after three different time-steps

5.2.2 Size distribution

For the so-called standard case, a Rosin-Rammler size distribution has beenused, which is an often used model to describe particle size distributions. Equa-tion 5.6 is the probability density function of the Rosin-Rammler distribution,in which D is the mean diameter, and k is the shape factor.

28


f(d,D, k) =

{kD ( dD )k−1exp(−(d/D)k) for d ≥ 00 for d < 0

(5.6)

In the standard case, a mean diameter of 50µm is used together with a shapefactor of 2.5. The resulting probability density function is plotted in Figure 5.3.

Figure 5.3: Probability density function of the Rosin Rammler size distribution

A test case has been set up comparing the film layer creation process firstusing the Rosin-Rammler particle size distribution discussed above, and seconda mono-dispersed case in which all particles have a fixed size equal to the MVD.Figure 5.4 shows the impingement of the cloud of particles on the airfoil surface,for both cases. Although the difference in droplet size dispersion is visible, itis difficult to point out a clear difference in impingement behavior. The smalldroplets around, and in the wake of the airfoil, are caused by splashing.

29


(a) Impingement with distributed sized droplets (b) Impingement of mono-dispersed droplets

Figure 5.4

The film layer thickness for both the Rosin-Rammler distributed as themono-dispersed case is showed in Figure 5.5 with, as mentioned before, a mag-nification factor of 1000. Discarding some minor differences, both cases producevery similar film layers, which may question the use of a droplet size distribution.

(a) 0.5 second (b) 1.0 second

Figure 5.5: Comparison of film layer thickness between distributed and mono-dispersed droplets size

5.2.3 Droplet size comparison

The mean volume diameter is an important parameter when describing cloudconditions however, increasing the used MVD can be highly beneficial in terms

30


of calculation effort, since the number of particles needed to reach the desiredLWC, is inversely proportional to the MVD cubed. For this reason a comparisonhas been made between the standard MVD of 50µm and two alternative MVD’sof 100µm and 200µm. For all thre cases a rosin-rammler size distribution hasbeen used with a shape factor of 2.5 (Figure 5.6).

Figure 5.6: Probability density function of the Rosin-Rammler size distribution

The impingement in all three cases is showed in Figure 5.7. The increase inMVD, creates really sparse clouds especially in the 200µm, for which the rate ofuniformity can be doubted. Although the MVD only affects cloud droplets, theMVD increase also clearly influences the splashing of particles from the airfoil,since the large decrease of splashed particles for the 100µm and the 200µmcases, which may have effect on the resulting film layer thickness.

(a) MVD = 50 micron (b) MVD = 100 micron (c) MVD = 200 micron

Figure 5.7: Impingement of droplets for different mean volume diameters (MVD)

The film layer thicknesses for the three cases are displayed in Figure 5.8.Despite the large difference in droplet density in the clouds, The resulting filmlayer thicknesses do not differ as much as the corresponding clouds discussedabove, especially near the stagnation point. More distant from the leading edge,

31


the film layers for large droplet diameters seem to be smoothed compared tothe standard case. This effect of the MVD increase on the resulting film layerprofile is too big to be neglected.


Figure 5.8: Comparison of film layer thickness for different MVD

5.2.4 LWC comparison

In order to get insight into the influence of LWC on the resulting film layerthickness, a comparison has been made between the film layer profile for threedifferent LWCs, plotted in Figure 5.9. At first sight, the observed influence ofthe LWC on the film layer profile seems plausible, a higher LWC leads to athicker film layer and vice versa.

32



Figure 5.9: Comparison of film layer thickness for different LWC

According to [8], the film layer on a stagnation point probe in a simulatedcloud can be best correlated using equation 5.7, where h is the obtained filmlayer thickness, d is the leading edge diameter of the used probe, and ρw is thedensity of water.

h/d ∝

(LWC

ρw

)1/2

Re−1/4 (5.7)

Since for this case a fixed Reynolds number and airfoil was used, and onlythe LWC was varied, the resulting film layer thicknesses at the stagnation point,should be proportional to the square root of the used LWC. The function fitof the film layer thickness after 1 second of simulation (Figure 5.10), shows areasonably good fit, although only 3 data points are used, which is rather spare.

33


Figure 5.10: Function fit of the film layer thickness as function of the LWC

34

Chapter 6

Future ice accretionsimulations based on theMessinger model

The Messinger model [9] is a popular and accepted approach for nowadaysice accretion predictions. This section describes main differences between theMessinger model and the model used in OpenFOAMs reactingParcelFilmFoamsolver. The goal is to get a clear view on future modifications that need to bedone to make reactingParcelFilmFoam able to run ice accretion simulations.

6.1 Comparison with Messinger model

The Messinger model describes a mass and a heat balance of a stationary con-tinuous water film inside a finite volume cell adjacent to the airfoil surface.Assumed is that sufficient water is present to form a continuous water filmwithout solving the amount of water present, and thus without solving thefilm layer height. The messinger model only uses a mass balance and a heatbalance to solve film layer parameters, so contrary to the model used in react-ingParcelFilmFoam, the Messinger model does not solve a momentum equation,and thus no film layer dynamics like film velocity are solved.

The mass balance equation is solved (equation 6.1), describing added massdue to impinging particles and mass transferred from upstream. Mass is sub-tracted due to solidification into ice, evaporation or sublimation into vapor andwater transferred downstream. As already mentioned, amount of residual wateris not solved.

mimp(β) +mrbin = mi(f, β) +mevs(Ts) +mrbout (6.1)

The partial differential equation for the conservation of mass used in re-actingParcelFilmFoam can be found in equation 6.2. When comparing thisequation to the mass balance equation of the Messinger model, we can see thatrunback water in and out of the cell from the Messinger model is handled withuse of the divergence term on the left hand side. Furthermore, there are terms

35

Chapter 6. Future ice accretion simulations based on the Messinger model

for impinging mass and mass evaporation, just like in the Messinger model. Ad-ditionally, equation 6.2 contains terms for splashing water, and for water filmseparation, which are not included in the Messinger model. On the other hand,the Messinger model contains a term representing water leaving the film layerdue to solidification into ice, mi, which is not included in reactingParcelFilm-Foam.

∂ρδ

∂t+∇ · (ρδU) = Simp + Ssplash + Sevap + Ssep (6.2)

The heat balance of the Messinger model is shown in equation 6.3. The firstterm represents heat added due to the kinetic energy of impinging particles. Thenext three terms are contributions of phase changes, from which Qf is latentheat added to the film layer due to freezing, and Qevap and Qsub are latent heatsleaving the film layer due to evaporation and sublimation. The fifth term Qsh isthe contribution of sensible heat, which is heat needed to cool (or warm) waterto the surface temperature, illustrated in figure 6.1.

Figure 6.1: Illustration of freezing process calculation

In order to describe the red path starting at ’I’ with super cooled waterand ending in ’F’, with ice at surface temperature, the water is first heated tothe freezing temperature, next the latent heat is released to form ice, then theice is cooled to the airfoil’s surface temperature. The first and the last stepare described in the sensible heat term, while the latent heat is described inthe second term of equation 6.3. Qadh and Qcv represent heat added due toadiabatic heating of surrounding air, and heat due to convection. Often theseterms are combined into one convective heat term. Since ice is considered to beadiabatic, the contribution of the conduction of heat from the airfoil body Qcdis considered zero. This term may be different in case an anti-icing system istested. Also heat transfer due to radiation (Qrad) is often neglected.

Qkin +Qf +Qevap +Qsub +Qsh +Qadh +Qcv +Qcd +Qrad = 0 (6.3)

36

Chapter 6. Future ice accretion simulations based on the Messinger model

Equation 6.4 is the partial differential equation for the conservation of en-ergy used in reactingParcelFilmFoam. The first term on the right hand siderepresents the kinetic energy of impinging particles, similar to the first term inthe heat balance of the Messinger model. Furthermore, the partial differentialequation accounts for convection and adiabatic heating (qc), conduction of heatthrough the airfoil surface (qw) and latent heat due to evaporation (SevapLev).The divergence term on the left hand side is the contribution of sensible heat,but only sensible heat for water already present and staying in the film layer,which means that sensible heat of grown ice and impinging water droplets andshould be added. Also latent heat due to solidification and sublimation is notincluded, although the latter could be omitted when assumed that all the iceis covered with a liquid film layer. Heat transfer due to radiation is also notincluded, however since radiation is often considered negligible, this may be ofless importance.

∂ρδh

∂t+∇ · (ρδUh) = Simp

U2imp

2+ qc − qw + SevapLev (6.4)

6.2 Shallow Water Icing Model

In order to make reactingParcelFilmFoam suitable for the simulation of ice ac-cretion, some adjustments should be done to the used film layer equations,illustrated in equations 6.5, 6.6 and 6.7, which are the original partial differen-tial equations used to solve the film layer parameters in reactingParcelFilmFoamsupplemented with some additional terms, which are marked red, resulting inthe so-called Shallow Water Icing Model (SWIM).The mass conservation equation of the Shallow Water Icing Model has one ad-ditional term compared to the one used in reactingParcelFilmFoam, which is thecontribution of mass leaving the film layer due to solidification into ice (Sice).

∂ρδ

∂t+∇ · (ρδU) = Simp + Ssplash + Sevap + Ssep + Sice (6.5)

The energy conservation equation of the SWIM model contains three addi-tional terms compared to the equation used in reactingParcelFilmFoam. Firstly,the sensible heats not covered by the divergence term on the left hand side of theequation, which are the sensible heat of impinging water, and the sensible heatof grown ice. The last additional term is the latent heat due to solidificationinto ice.

∂ρδh

∂t+∇ · (ρδUh) = Simp

U2imp

2+ qc − qw + SevapLev

+ Simpcw(Timp − T0) + Sicecice(T0 − Ts) + SiceLf (6.6)

The momentum equation of the SWIM model is identical to the one inreactingParcelFilmFoam.

∂ρδU

∂t+∇ · (ρδUU) = −δ∇p+ SρδU (6.7)

37

Chapter 7

Summary and Outlook

In this report the OpenFOAM software package is used for the simulation ofdroplet impingement and the modeling of a surface film layer on an airfoil sur-face.Firstly, the performance of two aerodynamic OpenFOAM solvers (simpleFOAMand rhoSimpleFoam) was examined with use of a validation case. The flow solu-tion around a NACA 0012 airfoil was compared with XFoil and an in-house flowsolver ZEN, showing good results concerning the pressure coefficient. The fric-tion coefficient calculated by the two OpenFOAM solvers however showed somedeviations around the leading edge with respect to XFoil and ZEN. Possibly thisis cause by a lack of extra mesh refinement near the leading edge, due to thefact that a uniform mesh size is used along the airfoil surface. Another reasonfor the deviation of the friction coefficient may be the fact that the thickness ofthe used mesh layers around the airfoil surface was not sufficient to cover thethe boundary layer of the flow.Another problem concerning the used mesh was the usage of a too coarse meshin the wake of the airfoil, causing distorted graphs in this region, especially forthe turbulent viscosities (Figure 4.6b & 4.10b).

The simulation of droplet impingement and the creation of a surface filmlayer was done with use of reactingParcelFilmFoam. A standard case was setup, from which individual parameters, such as simulation time, LWC, MVDand droplet size distribution, were adjusted to test sensitivity with respect tothe resulting surface film layer. Although the performed analysis is too short tobe able to make an accurate judgement about the solver’s performance, the setup case showed promising results. The influence of the LWC on the resultingfilm layer thickness was compared to a correlation (Equation 5.7) obtained fromexperimental data, showing a good correspondence.

For particle injection, the desired LWC is imposed by adjusting the numberof injected particles, discussed in section 5.1.3. There are however some uncer-tainties about the accuracy of the imposed LWC which arises from the fact thatthe height of the created cloud of particles is needed in order to convert thedesired LWC to the required number of injection particles. For simulations inthis report the cloud height is determined by the distance between the top andbottom injection point. Since the used droplet injection method uses dispersed

38

Chapter 7. Summary and Outlook

parcel initial velocity (Figure 5.1) to create a uniformly distributed cloud of par-ticles, the resulting cloud of particles will be slightly wider, resulting in a lowerLWC. A possible way to solve this uncertainty in future simulations is to checkthe real LWC in the generated cloud is by using OpenFOAM ’s particle collec-tor, which is a tool to measure the mass flow through a predefined plane in space.

As a recommendation for future investigation about ice accretion simula-tion with use of reactingParcelFilmFoam the current model used in reacting-ParcelFilmFoam was compared with the Messinger model, which is a well ac-cepted but slightly outdated model for icing predictions. Recommended adjust-ments to the current reactingParcelFilmFoam model are based on this compar-ison with the Messinger model, and result in the so-called Shallow Water IcingModel.

39

Chapter 8

Acknowledgements

I would like to thank the following people:

- Emiliano Iuliano, first for giving me great support during my internship asa mentor, and also outside of work for his great care and sociability

- Domenico Quagilarella, for his great care and service by bringing me towork and home every day without any hesitation

40

Bibliography

[1] F. S. I. Paraschivoiu, Aircraft Icing. John Wiley & Sons, 2006.

[2] OpenFOAM Version 2.1.1 User Guide (May 2012).

[3] J. McDonough, Introductory Lectures on Turbulence, 2004.

[4] M. K. F.R. Menter and R. Langtry, Ten Years of Industrial Experience withthe SST Turbulence model, Y. N. K. Hanjalic and M. Tummers, Eds. BegellHouse, 2003.

[5] “Sst k-omega model @ONLINE.” [Online]. Available: http://www.cfd-online.com/Wiki/SST k-omega model

[6] “The simple algorithm in openfoam @ONLINE.” [Online]. Available:http://openfoamwiki.net/index.php/The SIMPLE algorithm in OpenFOAM

[7] K. Meredith, “Thin liquid film modeling in openfoam,” 2010.

[8] D. N. Anderson and A. Feo, “Ice-accretion scaling using water-film thicknessparameters,” AIAA Journal, 2003.

[9] B. Messinger, “Equilibrium temperature of an unheated icing surface asfunction of airspeed,” Journal of the Aeronautical Sciences, vol. 20, pp. 29–42, 1953.

41

Appendices

42

Appendix A

ReactingCloud1Propterties

injectionModels

{

model1

{

type coneInjection;

SOI 0.000;

duration 2.000;

positionAxis

(

((-1.0 -0.5 -0.06) (102.55 0 7.17))

((-1.0 -0.5 -0.07) (102.55 0 7.17))

((-1.0 -0.5 -0.08) (102.55 0 7.17))

((-1.0 -0.5 -0.09) (102.55 0 7.17))

((-1.0 -0.5 -0.10) (102.55 0 7.17))

((-1.0 -0.5 -0.11) (102.55 0 7.17))

((-1.0 -0.5 -0.12) (102.55 0 7.17))

((-1.0 -0.5 -0.13) (102.55 0 7.17))

((-1.0 -0.5 -0.14) (102.55 0 7.17))

((-1.0 -0.5 -0.15) (102.55 0 7.17))

);

massTotal 2.5e-04;

parcelsPerInjector 156689.4795;

parcelsPerSecond 783447.3977;

parcelBasisType mass;

flowRateProfile constant 1.0e-04;

Umag constant 102.8;

thetaInner constant 5;

thetaOuter constant 5;

sizeDistribution

{

type RosinRammler;

RosinRammlerDistribution

{

minValue 5e-06;

maxValue 500e-06;

d 50e-06;

n 2.5;

}

}

}

}

43

Documents

DROPLET IMPINGEMENT AND FILM LAYER MODELING …essay.utwente.nl/69293/1/report-EJBeld-14-8-2013.pdf · DROPLET IMPINGEMENT AND FILM LAYER MODELING AS A BASIS FOR AIRCRAFT ICING SIMULATIONS