# Experimental investigation of the accretion and shedding process on a heatable NACA0012 airfoil in ice crystal icing conditions

Yasir A. Malik, Norbert Karpen, Elmar Bonaccurso, Ilia Roisman, Jeanette Hussong, Philippe Villedieu

<figure><img src="image_1.png" /></figure>

## To cite this version:

Yasir A. Malik, Norbert Karpen, Elmar Bonaccurso, Ilia Roisman, Jeanette Hussong, et al. Experimental investigation of the accretion and shedding process on a heatable NACA0012 airfoil in ice crystal icing conditions. Cold Regions Science and Technology, 2023, 217, pp.104030. 10.1016/j.coldregions.2023.104030. hal-04607487

HAL Id: hal-04607487

https://hal.science/hal-04607487

Submitted on 10 Jun 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>
# Experimental investigation of the accretion and shedding process on a heatable NACA0012 airfoil in ice crystal icing conditions

Yasir A. Malik, Norbert Karpen, Elmar Bonaccurso, Ilia Roisman, Jeanette Hussong, Philippe Villedieu

<figure><img src="image_1.png" /></figure>

## To cite this version:

Yasir A. Malik, Norbert Karpen, Elmar Bonaccurso, Ilia Roisman, Jeanette Hussong, et al. Experimental investigation of the accretion and shedding process on a heatable NACA0012 airfoil in ice crystal icing conditions. Cold Regions Science and Technology, 2023, 217, pp.104030. 10.1016/j.coldregions.2023.104030. hal-04607487

HAL Id: hal-04607487

https://hal.science/hal-04607487v1

Submitted on 10 Jun 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>
<figure><img src="image_3.png" /></figure>

# Experimental investigation of the accretion and shedding process on a heatable NACA0012 airfoil in ice crystal icing conditions

Yasir A. Malik<sup>a, *, 1</sup>, Norbert Karpen<sup>b, c, d, 1, **</sup>, Elmar Bonaccurso<sup>b</sup>, Ilia Roisman<sup>d</sup>,
Jeanette Hussong<sup>d</sup>, Philippe Villedieu<sup>e</sup>

## ARTICLE INFO

**PACS:**

42.68.Ge

96.25.hf

44.90. + c

92.60.Nv

**Keywords:**

Ice crystal icing

Accretion

Shedding

Glaciated

Mixed-phase

Heatflux

## ABSTRACT

Ice crystal icing can lead to damage and flame-outs in the combustion chamber of an aircraft engine due to accretion and shedding of ice blocks. The present work aims at a better understanding of accretion and shedding phenomena by quantitatively analysing experimental investigations conducted at the icing wind tunnels of Airbus CRT and TU Braunschweig. Particular focus is laid on ice accretion and shedding resulting from ice crystal icing on heated substrates. Heatable NACA0012 airfoils were designed and tested in a broad range of parametric conditions. Generally, large ice accretions and large shed areas were observed on non-heated surfaces at positive wet bulb temperatures. On surfaces heated with a low heat flux the accreted area was larger, while with large heat fluxes mostly run-back of liquid water was observed. For the examined experimental conditions an ice accretion threshold existed beyond which there was continuous accretion or complete shedding. The experimental findings of this study not only consolidated previous studies in similar conditions, but also help identify new findings for heated surfaces at negative wet bulb temperatures and unheated surfaces with mixed-phase conditions at positive wet bulb temperatures. They form a large collection of new data on ice accretion and shedding and provide a comprehensive experimental database quantitatively analyzed for validating future physics based and numerical models.

## 1. Introduction

While aircraft icing due to supercooled droplet icing (SDI) is well-known and mitigations are in place (Gent et al., 2000; Cao et al., 2018), aircraft icing due to ice crystals is a phenomenon that started to be investigated only recently. Icing on external surfaces in sub-freezing temperatures is primarily linked to SDI wherein ice crystals simply bounce-off from the surface. However, internal engine components exposed to warm airflow facilitate ice crystal icing conditions leading to hazards concerning safety and operability of aircraft which makes it one of the most critical topics of research.

Severe detrimental effects on the performance of aircraft were connected to ice crystal icing in investigations carried out by Mason et al. in

2006 (Mason et al., 2006). At high flight altitudes near deep convective clouds and predominantly in tropical regions ice crystals blocked air data probes (Ayra et al., 2020) and are ingested by the engines. Ice accreted inside the low pressure compressor stages and large ice blocks shed off and impacted on structural components. Heavy damages, surge, even flame out events of the engine were observed. The operability of the aircraft was negatively affected by erroneous probe readings. Apart from the dangers of ice crystal icing to the aircraft structure and flight stability, also the detrimental effects resulted in reduction in aerodynamic performance efficiency of the engines. Since then, more and more detailed studies have been performed to investigate the effects of ice crystal icing (Mason et al., 2011; Currie et al., 2012a; Oliver, 2014; Fuleki et al., 2019; Bansmer et al., 2018). Large international projects

<footnote><sup>a</sup> Technische Universität Braunschweig, Institute of Fluid Mechanics, Hermann Blenk Strasse 37, Braunschweig 38108, Germany</footnote>

<footnote><sup>b</sup> Airbus Central Research and Technology, Willy-Messerschmitt-Str. 1, Taufkirchen 82024, Germany</footnote>

<footnote><sup>c</sup> SurfLabX GmbH, Willy-Messerschmitt-Str. 1, Taufkirchen 82024, Germany</footnote>

<footnote><sup>d</sup> Technical University of Darmstadt, Institute for Fluid Mechanics and Aerodynamics, Peter-Griinberg-Straße 10, Darmstadt 64287, Germany</footnote>

<footnote><sup>e</sup> ONERA / DMPE, Université de Toulouse, 2 Av. Edouard Belin, Toulouse 31000, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>** Corresponding author at: SurfLabX GmbH, Willy-Messerschmitt-Str. 1, Taufkirchen 82024, Germany.
E-mail addresses: y.malik@tu-braunschweig.de (Y.A. Malik), norbert.karpen@surflabx.com (N. Karpen).</footnote>

<footnote n="1">¹ Contributed equally as co-first authors.</footnote>
<figure><img src="image_3.png" /></figure>

# Experimental investigation of the accretion and shedding process on a heatable NACA0012 airfoil in ice crystal icing conditions

Yasir A. Malik<sup>a, *, 1</sup>, Norbert Karpen<sup>b, c, d, 1, **</sup>, Elmar Bonaccurso<sup>b</sup>, Ilia Roisman<sup>d</sup>,
Jeanette Hussong<sup>d</sup>, Philippe Villedieu<sup>e</sup>

## ARTICLE INFO

**PACS:**

42.68.Ge

96.25.hf

44.90. + c

92.60.Nv

**Keywords:**

Ice crystal icing

Accretion

Shedding

Glaciated

Mixed-phase

Heatflux

## ABSTRACT

Ice crystal icing can lead to damage and flame-outs in the combustion chamber of an aircraft engine due to accretion and shedding of ice blocks. The present work aims at a better understanding of accretion and shedding phenomena by quantitatively analysing experimental investigations conducted at the icing wind tunnels of Airbus CRT and TU Braunschweig. Particular focus is laid on ice accretion and shedding resulting from ice crystal icing on heated substrates. Heatable NACA0012 airfoils were designed and tested in a broad range of parametric conditions. Generally, large ice accretions and large shed areas were observed on non-heated surfaces at positive wet bulb temperatures. On surfaces heated with a low heat flux the accreted area was larger, while with large heat fluxes mostly run-back of liquid water was observed. For the examined experimental conditions an ice accretion threshold existed beyond which there was continuous accretion or complete shedding. The experimental findings of this study not only consolidated previous studies in similar conditions, but also help identify new findings for heated surfaces at negative wet bulb temperatures and unheated surfaces with mixed-phase conditions at positive wet bulb temperatures. They form a large collection of new data on ice accretion and shedding and provide a comprehensive experimental database quantitatively analyzed for validating future physics based and numerical models.

## 1. Introduction

While aircraft icing due to supercooled droplet icing (SDI) is well-known and mitigations are in place (Gent et al., 2000; Cao et al., 2018), aircraft icing due to ice crystals is a phenomenon that started to be investigated only recently. Icing on external surfaces in sub-freezing temperatures is primarily linked to SDI wherein ice crystals simply bounce-off from the surface. However, internal engine components exposed to warm airflow facilitate ice crystal icing conditions leading to hazards concerning safety and operability of aircraft which makes it one of the most critical topics of research.

Severe detrimental effects on the performance of aircraft were connected to ice crystal icing in investigations carried out by Mason et al. in

2006 (Mason et al., 2006). At high flight altitudes near deep convective clouds and predominantly in tropical regions ice crystals blocked air data probes (Ayra et al., 2020) and are ingested by the engines. Ice accreted inside the low pressure compressor stages and large ice blocks shed off and impacted on structural components. Heavy damages, surge, even flame out events of the engine were observed. The operability of the aircraft was negatively affected by erroneous probe readings. Apart from the dangers of ice crystal icing to the aircraft structure and flight stability, also the detrimental effects resulted in reduction in aerodynamic performance efficiency of the engines. Since then, more and more detailed studies have been performed to investigate the effects of ice crystal icing (Mason et al., 2011; Currie et al., 2012a; Oliver, 2014; Fuleki et al., 2019; Bansmer et al., 2018). Large international projects

<footnote><sup>a</sup> Technische Universität Braunschweig, Institute of Fluid Mechanics, Hermann Blenk Strasse 37, Braunschweig 38108, Germany</footnote>

<footnote><sup>b</sup> Airbus Central Research and Technology, Willy-Messerschmitt-Str. 1, Taufkirchen 82024, Germany</footnote>

<footnote><sup>c</sup> SurfLabX GmbH, Willy-Messerschmitt-Str. 1, Taufkirchen 82024, Germany</footnote>

<footnote><sup>d</sup> Technical University of Darmstadt, Institute for Fluid Mechanics and Aerodynamics, Peter-Griinberg-Straße 10, Darmstadt 64287, Germany</footnote>

<footnote><sup>e</sup> ONERA / DMPE, Université de Toulouse, 2 Av. Edouard Belin, Toulouse 31000, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>** Corresponding author at: SurfLabX GmbH, Willy-Messerschmitt-Str. 1, Taufkirchen 82024, Germany.
E-mail addresses: y.malik@tu-braunschweig.de (Y.A. Malik), norbert.karpen@surflabx.com (N. Karpen).</footnote>

<footnote n="1">¹ Contributed equally as co-first authors.</footnote>
were set up, such as between NASA and NRC (Addy and Veres, 2011), the European funded project HAIC (Eu Commission Page, 2023), and the successor project MUSIC-haic (Villedieu et al., 2020) to further the understanding of ice crystal icing physics. Several studies focused on the microphysical properties of ice particles in clouds and on the description of cloud properties (van Diedenhoven et al., 2014; Fontaine et al., 2017; Leroy et al., 2017; Fontaine et al., 2020; Haggerty et al., 2019). Oliver and Flegel et al. studied ice crystal icing with full-scale engine tests at the NASA Propulsion Systems Laboratory (Oliver, 2015; Flegel and Oliver, 2016). They retrieved first insights on the locations inside the engine prone to ice crystal icing risk and on the corresponding environmental conditions.

## 1.1. State of the Art

Icing is a highly multidisciplinary field and aircraft engine icing is a complex combination of various sub processes, which must be individually investigated and understood. Trajectories of ice particles in an air flow were studied by Widhalm (Widhalm, n.d.), Norde et al. (Norde et al., 2018), and Soubrié et al. (Soubrié et al., 2022). The influence of particle rotation including melting of ice particles in an airflow with positive ambient temperatures was studied by Kintea et al. and Hauk et al. (Kintea et al., 2015; Hauk et al., 2016). The impact and fragmentation behavior of individual ice particles on rigid surfaces was the topic of many experimental studies (Guégan et al., 2011; Vargas et al., 2014; Vargas et al., 2015; Hauk et al., 2015; Hong and Moon, 2017; Han et al., 2018; Reitter et al., 2021; Karpen et al., 2021). The collected experimental data supported the development and validation of empirical and physical models (Trontin et al., 2016; Tippmann et al., 2013; Roisman and Tropea, 2015; Kintea et al., 2016a; Roisman, 2022; Senoner et al., 2022).

Numerous experimental and numerical studies of the ice accretion and shedding process components of aircraft engines or on NACA airfoils, hemispheres, and wedges were performed on non-heated substrates. Ice accretion and shedding processes were analyzed with respect to the ice shapes, ice masses, surface temperatures, water-ice layer compositions, and accretion and shedding cycles. Mazzawy developed the first ice accretion model taking into account mixed-phase conditions, i.e., supercooled droplets mixed with ice crystals (Mazzawy, 2007). At NASA and NRC significant experimental and numerical research was carried out, key findings were reported, and models were gradually refined (Currie et al., 2012a; Currie et al., 2015; Nilamdeen et al., 2021). Their work focused on ice particle melting, icing simulation and fundamental study of mixed phase icing with application to ice crystal accretion in aircraft jet engines. On the basis of the experimental results from Currie et al. (Currie et al., 2012a) on non-heated substrates in mixed phase flow, numerical models for the heat transfer process in ice crystal layers were developed by Kintea et al. (Kintea et al., 2014; Kintea et al., 2016b).

Bucknell et al. carried out experimental and numerical ice accretion and erosion investigations at NRC (Bucknell et al., 2017; Bucknell et al., 2018; Bucknell et al., 2021). Their research work focused on ice crystal accretion and erosion modeling at engine-realistic conditions. Baumert et al. investigated ice crystal ice accretion experimentally and numerically (Baumert et al., 2018; Baumert, 2019). The research focused on aircraft icing in mixed phase conditions wherein a strong influence of the ambient temperature on the icing process was observed and correlations between accretion shape and growth rate were identified. Trontin et al. presented a comprehensive numerical model for simulating ice accretion in ice crystal icing conditions (Trontin and Villedieu, 2018). The modeling approach properly accounted for the influence of ice crystal melting ratio on the accretion shapes. Moreover, the model was able to correctly predict typical conical accretion shapes which are exclusive to ice crystal icing.

Previously experimental investigations have been carried out on a NACA0012 airfoil in ice crystal icing conditions at NASA and CNRC

(Struk et al., 2018). However, the heating capability of the test article was a missing feature which serves as a novelty and is covered as part of the presented experimental investigation.

In the aforementioned research works a strong dependence of the ice accretion severity on the wet bulb temperature ($T_{wb}$) was found experimentally. At $T_{wb}$ close to zero the ice accretion severity is largest, while at $T_{wb}$ far below freezing no ice accretion was observed (Currie et al., 2012a; Struk et al., 2011). Ice accretion was later differentiated between melt-dominated icing at $T_{wb}$ above freezing and freeze-dominated icing at $T_{wb}$ below freezing (Tsao et al., 2014). The transition between the two icing processes at around 0°C was found to depend on the airspeed. For larger airspeeds the transition was slightly shifting to lower $T_{wb}$ due to increased kinetic heat fluxes. Furthermore, a strong dependence of icing severity on the melting ratio, i.e. the ratio between (supercooled) liquid water and solid ice was found. Currie et al. reported a maximum of the icing severity for melting ratios between 0.1 and 0.2, while no icing occurred below and above these limits (Currie et al., 2014a; Knezevici et al., 2013a). These limits were later reported to depend on the airspeed and on the $T_{wb}$ (Baumert et al., 2018; Baumert, 2019; Bartkus et al., 2019).

The erosion effect of solid particles impacting on ice layers was experimentally investigated by Kott et al. (Kott et al., 2020; Currie et al., 2014b). The erosion phenomena was modelled and numerically studied by Charton et al. (Charton et al., 2020). Its severity is influenced by the size, airspeed, and the impact angle of the ice crystal. The inception of ice accretion by ice crystal impact was investigated by Löwe et al. (Löwe et al., 2016a) and Karpen et al. (Karpen et al., 2022). It was found that on a heated substrate the inception of ice crystal accretion is determined by the instant when the surface temperature reaches the freezing temperature. Substrate heating resulted in melting the impacting ice crystals and accreted ice layer and the formed liquid water imbibed in the ice layer results in ice accretion growth. The extent and kinetics of the imbibition process were investigated for artificially generated ice layers in a laboratory environment by Köbschall et al. (Köbschall et al., 2021).

## 1.2. Objectives

The current models of ice crystal accretion and shedding aim at relating the influences of $T_{wb}$, ambient pressure, airspeed, particle size distributions, melting ratio, and angles of attack to the accretion growth rate and to the shedding mean frequency but they do not take into account the influence of a heat flux from the wall. Systematic experimental studies on the influence of an externally applied heat flux to ice crystal ice accretion and shedding were only recently investigated by Karpen et al. and Malik et al. (Karpen et al., 2022; Malik et al., 2022) on a limited dataset. A constant heat flux from the substrate to the ice layer adds more complexity to the heat and mass balance and therefore has a great influence on accretion and shedding phenomena. Contrary to unheated surfaces, heated substrates can lead to significant icing in fully glaciated ice crystal conditions even at negative $T_{wb}$ conditions.

Ice accretion due to the sticking of ice crystals to a surface is affected by the presence (or the absence) of a liquid water film on the outermost ice layer surface which is able to retain the ice crystals by capillary force. In mixed-phase conditions, ice accretion at low negative $T_{wb}$ is limited due to the complete icing of the liquid water, after which no capillary force causes additional ice crystals to stick by capillary imbibition. An external heat flux can keep the outermost surface of the ice layer wet, thus maintaining the “sticky” water film in place for a long time.

In this work we performed new experimental studies focused on characterizing the ice accretion and shedding processes.

In particular, the objectives of this study were to.

* build on previous research by generating a comprehensive database of purely glaciated ice crystal cloud ice accretion and shedding test cases and including the influences of parameters investigated in the
were set up, such as between NASA and NRC (Addy and Veres, 2011), the European funded project HAIC (Eu Commission Page, 2023), and the successor project MUSIC-haic (Villedieu et al., 2020) to further the understanding of ice crystal icing physics. Several studies focused on the microphysical properties of ice particles in clouds and on the description of cloud properties (van Diedenhoven et al., 2014; Fontaine et al., 2017; Leroy et al., 2017; Fontaine et al., 2020; Haggerty et al., 2019). Oliver and Flegel et al. studied ice crystal icing with full-scale engine tests at the NASA Propulsion Systems Laboratory (Oliver, 2015; Flegel and Oliver, 2016). They retrieved first insights on the locations inside the engine prone to ice crystal icing risk and on the corresponding environmental conditions.

## 1.1. State of the Art

Icing is a highly multidisciplinary field and aircraft engine icing is a complex combination of various sub processes, which must be individually investigated and understood. Trajectories of ice particles in an air flow were studied by Widhalm (Widhalm, n.d.), Norde et al. (Norde et al., 2018), and Soubrié et al. (Soubrié et al., 2022). The influence of particle rotation including melting of ice particles in an airflow with positive ambient temperatures was studied by Kintea et al. and Hauk et al. (Kintea et al., 2015; Hauk et al., 2016). The impact and fragmentation behavior of individual ice particles on rigid surfaces was the topic of many experimental studies (Guégan et al., 2011; Vargas et al., 2014; Vargas et al., 2015; Hauk et al., 2015; Hong and Moon, 2017; Han et al., 2018; Reitter et al., 2021; Karpen et al., 2021). The collected experimental data supported the development and validation of empirical and physical models (Trontin et al., 2016; Tippmann et al., 2013; Roisman and Tropea, 2015; Kintea et al., 2016a; Roisman, 2022; Senoner et al., 2022).

Numerous experimental and numerical studies of the ice accretion and shedding process components of aircraft engines or on NACA airfoils, hemispheres, and wedges were performed on non-heated substrates. Ice accretion and shedding processes were analyzed with respect to the ice shapes, ice masses, surface temperatures, water-ice layer compositions, and accretion and shedding cycles. Mazzawy developed the first ice accretion model taking into account mixed-phase conditions, i.e., supercooled droplets mixed with ice crystals (Mazzawy, 2007). At NASA and NRC significant experimental and numerical research was carried out, key findings were reported, and models were gradually refined (Currie et al., 2012a; Currie et al., 2015; Nilamdeen et al., 2021). Their work focused on ice particle melting, icing simulation and fundamental study of mixed phase icing with application to ice crystal accretion in aircraft jet engines. On the basis of the experimental results from Currie et al. (Currie et al., 2012a) on non-heated substrates in mixed phase flow, numerical models for the heat transfer process in ice crystal layers were developed by Kintea et al. (Kintea et al., 2014; Kintea et al., 2016b).

Bucknell et al. carried out experimental and numerical ice accretion and erosion investigations at NRC (Bucknell et al., 2017; Bucknell et al., 2018; Bucknell et al., 2021). Their research work focused on ice crystal accretion and erosion modeling at engine-realistic conditions. Baumert et al. investigated ice crystal ice accretion experimentally and numerically (Baumert et al., 2018; Baumert, 2019). The research focused on aircraft icing in mixed phase conditions wherein a strong influence of the ambient temperature on the icing process was observed and correlations between accretion shape and growth rate were identified. Trontin et al. presented a comprehensive numerical model for simulating ice accretion in ice crystal icing conditions (Trontin and Villedieu, 2018). The modeling approach properly accounted for the influence of ice crystal melting ratio on the accretion shapes. Moreover, the model was able to correctly predict typical conical accretion shapes which are exclusive to ice crystal icing.

Previously experimental investigations have been carried out on a NACA0012 airfoil in ice crystal icing conditions at NASA and CNRC

(Struk et al., 2018). However, the heating capability of the test article was a missing feature which serves as a novelty and is covered as part of the presented experimental investigation.

In the aforementioned research works a strong dependence of the ice accretion severity on the wet bulb temperature ($T_{wb}$) was found experimentally. At $T_{wb}$ close to zero the ice accretion severity is largest, while at $T_{wb}$ far below freezing no ice accretion was observed (Currie et al., 2012a; Struk et al., 2011). Ice accretion was later differentiated between melt-dominated icing at $T_{wb}$ above freezing and freeze-dominated icing at $T_{wb}$ below freezing (Tsao et al., 2014). The transition between the two icing processes at around 0°C was found to depend on the airspeed. For larger airspeeds the transition was slightly shifting to lower $T_{wb}$ due to increased kinetic heat fluxes. Furthermore, a strong dependence of icing severity on the melting ratio, i.e. the ratio between (supercooled) liquid water and solid ice was found. Currie et al. reported a maximum of the icing severity for melting ratios between 0.1 and 0.2, while no icing occurred below and above these limits (Currie et al., 2014a; Knezevici et al., 2013a). These limits were later reported to depend on the airspeed and on the $T_{wb}$ (Baumert et al., 2018; Baumert, 2019; Bartkus et al., 2019).

The erosion effect of solid particles impacting on ice layers was experimentally investigated by Kott et al. (Kott et al., 2020; Currie et al., 2014b). The erosion phenomena was modelled and numerically studied by Charton et al. (Charton et al., 2020). Its severity is influenced by the size, airspeed, and the impact angle of the ice crystal. The inception of ice accretion by ice crystal impact was investigated by Löwe et al. (Löwe et al., 2016a) and Karpen et al. (Karpen et al., 2022). It was found that on a heated substrate the inception of ice crystal accretion is determined by the instant when the surface temperature reaches the freezing temperature. Substrate heating resulted in melting the impacting ice crystals and accreted ice layer and the formed liquid water imbibed in the ice layer results in ice accretion growth. The extent and kinetics of the imbibition process were investigated for artificially generated ice layers in a laboratory environment by Köbschall et al. (Köbschall et al., 2021).

## 1.2. Objectives

The current models of ice crystal accretion and shedding aim at relating the influences of $T_{wb}$, ambient pressure, airspeed, particle size distributions, melting ratio, and angles of attack to the accretion growth rate and to the shedding mean frequency but they do not take into account the influence of a heat flux from the wall. Systematic experimental studies on the influence of an externally applied heat flux to ice crystal ice accretion and shedding were only recently investigated by Karpen et al. and Malik et al. (Karpen et al., 2022; Malik et al., 2022) on a limited dataset. A constant heat flux from the substrate to the ice layer adds more complexity to the heat and mass balance and therefore has a great influence on accretion and shedding phenomena. Contrary to unheated surfaces, heated substrates can lead to significant icing in fully glaciated ice crystal conditions even at negative $T_{wb}$ conditions.

Ice accretion due to the sticking of ice crystals to a surface is affected by the presence (or the absence) of a liquid water film on the outermost ice layer surface which is able to retain the ice crystals by capillary force. In mixed-phase conditions, ice accretion at low negative $T_{wb}$ is limited due to the complete icing of the liquid water, after which no capillary force causes additional ice crystals to stick by capillary imbibition. An external heat flux can keep the outermost surface of the ice layer wet, thus maintaining the “sticky” water film in place for a long time.

In this work we performed new experimental studies focused on characterizing the ice accretion and shedding processes.

In particular, the objectives of this study were to.

* build on previous research by generating a comprehensive database of purely glaciated ice crystal cloud ice accretion and shedding test cases and including the influences of parameters investigated in the
prior studies, such as the airspeed, IWC, and $T_{wb}$ (from below to slightly above freezing)

* examine the additional effects of a regulated substrate heat flux on accretion and shedding,

* quantify all the parameters which govern accretion and shedding and compare the parameter influences between $T_{wb}$ above and below freezing, which represent majorly different icing behaviors,

* further our understanding of the icing physics, and to support the future development and validation of a more complete ice crystal accretion and shedding model.

## 2. Materials and methods

The experimental investigations and the analysis of the results were performed at the Airbus Central Research and Technology (ACRT) icing wind tunnel and at the Technical University of Braunschweig (TUBS) icing wind tunnel facility. Both research facilities feature icing wind tunnels (IWT) capable of studying ice crystal icing at partially overlapping and partially different test conditions. Both facilities complement each other and allow to extend the range of investigated icing conditions.

Two separate NACA 0012 airfoils with different chord lengths were installed in the respective IWTs. For cross comparison the TUBS model was used at both the TUBS IWT and the ACRT IWT.

### 2.1. ACRT iCORE ice crystal icing experimental test setup

Ice crystal accretion and shedding tests were carried out in the iCORE icing wind tunnel (Airbus, Taufkirchen, Germany). The iCORE is a closed-loop wind tunnel with a maximum airspeed (TAS: True Air Speed) of 155 $ms^{-1}$ and a minimum air temperature (SAT: Static Air Temperature) of -30°C. The icing wind tunnel operates at the ambient pressures present in the iCORE laboratory, which is positioned at an altitude of 560 m with ambient pressures between 930 and 980 mbar. The test section has a rectangular cross section with a height of 150 mm and a width of 100 mm. The length of the test section is 450 mm. Different sample shapes and sizes can be tested. For this study, NACA0012 airfoils with a chord length of 178 mm and width of 100 mm were used. More details about the wind tunnel can be found in Hauk et al. (Hauk et al., 2013) and in previous studies performed at ACRT (Karpen et al., 2021; Karpen et al., 2022).

The ice crystal production is split into two process steps. In the first step, water is evaporated by using two ultrasonic water vapour gener-

ators (1500 mL $h^{-1}$) in a large closed water compartment with excess air. The two water vapour generators are turned on alternately for half an hour each and a total time of 12 h (during the night). A pushing fan installed on top of the compartment transports the evaporated water through a pipe from the closed compartment to a chest freezer, where it nucleates at the walls. The temperature measured at the bottom of the chest freezer is raised by the incoming wet air stream at ambient temperature and levels off at approx. -25°C. In the second step the generated ice is collected by a scraper and sieved with a mechanical metal sieve with a mesh size of 800µm inside the chest freezer.

To feed the desired mass of ice crystals into the wind tunnel a rotating feeder was designed and manufactured. The rotating feeder is placed in a cooling box. The cooling box is cooled down to -21°C by placing one eutectic plate (Kängabox Cold pack GN 1/2) on each inner wall of the cooling box. The density of the ice crystals is determined by measuring their weight (scale) and their volume (measuring cup) before feeding them onto a rotating conveyor disk through a funnel. To guarantee a homogeneous ice crystal flow, the funnel is vibrated by a mechanical shaker. An air ejector collects the ice crystals from the rotating conveyor disk and disperses them into the airflow in the settling chamber. Fig. 1 shows a schematic drawing of the test setup.

Two machine vision video cameras were installed to record ice crystal impact, accretion and shedding on the leading edge of the NACA-0012 airfoil from a top view and from a side view. To obtain well contrasted videos, LED lights (Vision Devices VD7000) and milky glasses for light diffusion were used. For the optical characterisation of the icing cloud particle size distribution a high speed camera was used to record shadowgraphy images of the ice particles in the air flow prior to their impact on the NACA profile. A python script was developed for analysing the high speed videos. An average MVD of 110 µm with a standard deviation of 20 µm, a D10 of 50 µm with a standard deviation of 10 µm and a D90 of 225 µm with a standard deviation of 25 µm was assessed. For larger airspeeds the size distribution shifts to larger particle sizes with an MVD of 95 µm at 40 $ms^{-1}$ to an MVD of 130 µm at 80 $ms^{-1}$. This optical setup was also used for a characterisation of the particle speeds in relation to the airspeed. For each airspeed in the test matrix (40 $ms^{-1}$ to 80 $ms^{-1}$) a single video was recorded at a frame rate of 180,000 fps. From these videos it was determined that the ice crystals have a velocity with high conformity to the airspeed, i.e., approx. 90% for larger particles and > 95% for smaller particles.

The test article used to study accretion and shedding phenomena was a heatable NACA0012 airfoil. A glass fibre composite with embedded

<figure><img src="image_4.png" /><figcaption>Fig. 1. Schematic drawing of the iCORE ice crystal accretion and shedding test setup.</figcaption></figure>
prior studies, such as the airspeed, IWC, and $T_{wb}$ (from below to slightly above freezing)

* examine the additional effects of a regulated substrate heat flux on accretion and shedding,

* quantify all the parameters which govern accretion and shedding and compare the parameter influences between $T_{wb}$ above and below freezing, which represent majorly different icing behaviors,

* further our understanding of the icing physics, and to support the future development and validation of a more complete ice crystal accretion and shedding model.

## 2. Materials and methods

The experimental investigations and the analysis of the results were performed at the Airbus Central Research and Technology (ACRT) icing wind tunnel and at the Technical University of Braunschweig (TUBS) icing wind tunnel facility. Both research facilities feature icing wind tunnels (IWT) capable of studying ice crystal icing at partially overlapping and partially different test conditions. Both facilities complement each other and allow to extend the range of investigated icing conditions.

Two separate NACA 0012 airfoils with different chord lengths were installed in the respective IWTs. For cross comparison the TUBS model was used at both the TUBS IWT and the ACRT IWT.

### 2.1. ACRT iCORE ice crystal icing experimental test setup

Ice crystal accretion and shedding tests were carried out in the iCORE icing wind tunnel (Airbus, Taufkirchen, Germany). The iCORE is a closed-loop wind tunnel with a maximum airspeed (TAS: True Air Speed) of 155 $ms^{-1}$ and a minimum air temperature (SAT: Static Air Temperature) of -30°C. The icing wind tunnel operates at the ambient pressures present in the iCORE laboratory, which is positioned at an altitude of 560 m with ambient pressures between 930 and 980 mbar. The test section has a rectangular cross section with a height of 150 mm and a width of 100 mm. The length of the test section is 450 mm. Different sample shapes and sizes can be tested. For this study, NACA0012 airfoils with a chord length of 178 mm and width of 100 mm were used. More details about the wind tunnel can be found in Hauk et al. (Hauk et al., 2013) and in previous studies performed at ACRT (Karpen et al., 2021; Karpen et al., 2022).

The ice crystal production is split into two process steps. In the first step, water is evaporated by using two ultrasonic water vapour gener-

ators (1500 mL $h^{-1}$) in a large closed water compartment with excess air. The two water vapour generators are turned on alternately for half an hour each and a total time of 12 h (during the night). A pushing fan installed on top of the compartment transports the evaporated water through a pipe from the closed compartment to a chest freezer, where it nucleates at the walls. The temperature measured at the bottom of the chest freezer is raised by the incoming wet air stream at ambient temperature and levels off at approx. -25°C. In the second step the generated ice is collected by a scraper and sieved with a mechanical metal sieve with a mesh size of 800μm inside the chest freezer.

To feed the desired mass of ice crystals into the wind tunnel a rotating feeder was designed and manufactured. The rotating feeder is placed in a cooling box. The cooling box is cooled down to -21°C by placing one eutectic plate (Kängabox Cold pack GN 1/2) on each inner wall of the cooling box. The density of the ice crystals is determined by measuring their weight (scale) and their volume (measuring cup) before feeding them onto a rotating conveyor disk through a funnel. To guarantee a homogeneous ice crystal flow, the funnel is vibrated by a mechanical shaker. An air ejector collects the ice crystals from the rotating conveyor disk and disperses them into the airflow in the settling chamber. Fig. 1 shows a schematic drawing of the test setup.

Two machine vision video cameras were installed to record ice crystal impact, accretion and shedding on the leading edge of the NACA-0012 airfoil from a top view and from a side view. To obtain well contrasted videos, LED lights (Vision Devices VD7000) and milky glasses for light diffusion were used. For the optical characterisation of the icing cloud particle size distribution a high speed camera was used to record shadowgraphy images of the ice particles in the air flow prior to their impact on the NACA profile. A python script was developed for analysing the high speed videos. An average MVD of 110 µm with a standard deviation of 20 µm, a D10 of 50 µm with a standard deviation of 10 µm and a D90 of 225 µm with a standard deviation of 25 µm was assessed. For larger airspeeds the size distribution shifts to larger particle sizes with an MVD of 95 µm at 40 $ms^{-1}$ to an MVD of 130 µm at 80 $ms^{-1}$. This optical setup was also used for a characterisation of the particle speeds in relation to the airspeed. For each airspeed in the test matrix (40 $ms^{-1}$ to 80 $ms^{-1}$) a single video was recorded at a frame rate of 180,000 fps. From these videos it was determined that the ice crystals have a velocity with high conformity to the airspeed, i.e., approx. 90% for larger particles and > 95% for smaller particles.

The test article used to study accretion and shedding phenomena was a heatable NACA0012 airfoil. A glass fibre composite with embedded

<figure><img src="image_4.png" /><figcaption>Fig. 1. Schematic drawing of the iCORE ice crystal accretion and shedding test setup.</figcaption></figure>
graphene heater layer was glued from the inside to a NACA0012 shaped
aluminum skin. Three type T thermocouples (Omega 5TC-TT-TI-36-1 M)
were sandwiched in between the aluminum skin and the heater to
monitor the temperatures close to the surface. The positions of the
thermocouples are shown in Fig. 1.

## 2.2. TU Braunschweig Icing Wind Tunnel

A comprehensive dataset on accretion and shedding was generated by carrying out experiments in TU Braunschweig IWT. Fig. 2 provides pictorial illustration of the IWT facility highlighted in dark blue color. The tunnel is closed loop with airflow velocities reaching up to 40 ms⁻¹ in a test section with cross-sectional area of 500 × 500 mm⁻². Static temperature inside the tunnel can be maintained in the range of -20°C to 30°C by means of a dedicated cooling system with components highlighted in the top right corner of Fig. 2. The icing wind tunnel operates at the ambient pressures present in the laboratory, which is positioned at an altitude of 75 m with ambient pressure in the proximity of 990 mbar.

Ice crystals were generated inside a cooling chamber where the generation, dosing, sieving and transport of the ice crystals to the wind tunnel test section take place. The cooling chamber has a dedicated cooling unit with the capability of ensuring glaciated ice crystals into the wind tunnel by means of an after-cooler. The temperature inside the chamber was kept at – 15°C. The ice water content inside the test sec-

tion was in the range from 3 g⁻³ to 20 g⁻³. By means of an isokinetic
probe, high speed imaging, and a particle collection tube system the
icing cloud was characterized inside the test section (Bansmer et al.,
2018; Esposito et al., 2019). The median mass diameter (MMD = D50)
was 79 µm, where D10 and D90 represented the 10% and 90% of the
cumulative mass as 20 µm and 220 µm respectively (Bansmer et al.,
2018; Baumert et al., 2016). A more elaborate overview of the testing
facility with details concerning design, construction and commissioning
of the braunschweig icing wind tunnel was previously documented by
Bansmer et al. (Bansmer et al., 2018).

### 2.2.1. Test article

A NACA0012 airfoil with a chord length of 416 mm and a span of 93 mm was used as an aerodynamic test article. The surface temperature was measured by temperature sensors placed in stagnation region and downstream of the test article. Heaters were installed at the back of the model and allowed for a uniform heating in different test conditions. To allow heat transfer predominantly in the direction of the crystal impingement, a high quality multi-therm insulation (MultiTHERM 550) was used (Fig. 3).

PT1000-type resistance temperature detectors (RTD) with accuracy class A were embedded in the aluminum body of the leading edge of the NACA0012 profile. In total, 21 RTDs were housed in the leading edge on the outer surface. For recording the temperature with a high spatial resolution in the region of highest temperature gradients, 15 of the 21

<figure><img src="image_5.png" /><figcaption>Fig. 2. Schematics of TU Braunschweig Ice Wind Tunnel - Crystal Generation and Conveyance Mechanism (Bansmer et al., 2018).</figcaption></figure>
graphene heater layer was glued from the inside to a NACA0012 shaped aluminum skin. Three type T thermocouples (Omega 5TC-TT-TI-36-1 M) were sandwiched in between the aluminum skin and the heater to monitor the temperatures close to the surface. The positions of the thermocouples are shown in Fig. 1.

## 2.2. TU Braunschweig Icing Wind Tunnel

A comprehensive dataset on accretion and shedding was generated by carrying out experiments in TU Braunschweig IWT. Fig. 2 provides pictorial illustration of the IWT facility highlighted in dark blue color. The tunnel is closed loop with airflow velocities reaching up to 40 ms⁻¹ in a test section with cross-sectional area of 500 × 500 mm⁻². Static temperature inside the tunnel can be maintained in the range of -20°C to 30°C by means of a dedicated cooling system with components highlighted in the top right corner of Fig. 2. The icing wind tunnel operates at the ambient pressures present in the laboratory, which is positioned at an altitude of 75 m with ambient pressure in the proximity of 990 mbar.

Ice crystals were generated inside a cooling chamber where the generation, dosing, sieving and transport of the ice crystals to the wind tunnel test section take place. The cooling chamber has a dedicated cooling unit with the capability of ensuring glaciated ice crystals into the wind tunnel by means of an after-cooler. The temperature inside the chamber was kept at -15°C. The ice water content inside the test section

was in the range from 3 g⁻³ to 20 g⁻³. By means of an isokinetic probe, high speed imaging, and a particle collection tube system the icing cloud was characterized inside the test section (Bansmer et al., 2018; Esposito et al., 2019). The median mass diameter (MMD = D50) was 79 µm, where D10 and D90 represented the 10% and 90% of the cumulative mass as 20 µm and 220 µm respectively (Bansmer et al., 2018; Baumert et al., 2016). A more elaborate overview of the testing facility with details concerning design, construction and commissioning of the braunschweig icing wind tunnel was previously documented by Bansmer et al. (Bansmer et al., 2018).

### 2.2.1. Test article

A NACA0012 airfoil with a chord length of 416 mm and a span of 93 mm was used as an aerodynamic test article. The surface temperature was measured by temperature sensors placed in stagnation region and downstream of the test article. Heaters were installed at the back of the model and allowed for a uniform heating in different test conditions. To allow heat transfer predominantly in the direction of the crystal impingement, a high quality multi-therm insulation (MultiTHERM 550) was used (Fig. 3).

PT1000-type resistance temperature detectors (RTD) with accuracy class A were embedded in the aluminum body of the leading edge of the NACA0012 profile. In total, 21 RTDs were housed in the leading edge on the outer surface. For recording the temperature with a high spatial resolution in the region of highest temperature gradients, 15 of the 21

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Schematics of TU Braunschweig Ice Wind Tunnel - Crystal Generation and Conveyance Mechanism (Bansmer et al., 2018).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Cross section schematic of the leading edge of the TUBS NACA-0012 test article (left) and exploded view of the model (right).</figcaption></figure>

temperature sensors were placed in the close vicinity of the stagnation line. The sensors measured 1.3 mm × 2.0 mm × 2.5 mm and the leading edge had a wall thickness of 4 mm. To route the cables of the temperature sensors 1 mm deep grooves were milled into leading edge to enable smooth form and shape of the test article. The sensors were molded into the pockets with a highly thermally conductive two-component adhesive (Duralco 132). To create a smooth finish of the target surface where ice crystals impinge, an aluminum sheet with a thickness of 0.2 mm was wrapped around the airfoil. The leading edge was heated from the inside by means of thin flexible heaters in such a way that they would allow different heat fluxes between the stagnation line and the area downstream, which would not have been possible with a single large heater (Fig. 4). The composition as well as the characterisation of the different layers of the test article have been summarized in tabular form in Table A 3 presented in 6.

### 2.2.2. Experimental setup

The experimental setup enabled the quantitative measurement of ice accretion by means of shadowgraphy technique utilizing two cameras with the centers of lenses aligned to the leading edge from the top and side perspective. In total four DSLR-cameras were placed around the test section (Fig. 5) to allow for qualitative and quantitative observation of ice accretion and shedding. For tracking the maximum ice thickness

along the leading edge of the airfoil, camera (1) was positioned vertically above the model, pointing straight down the leading edge.

A beamer flicker free LED light source (3) (7000 lm) was placed on the opposite side of the test section and pointing straight into camera (1). Camera (2) was positioned upstream above the test sample pointing at the leading edge for tracking the runback of melt water and ice. From the wall side of the test section, camera (5) points at the stagnation line. Opposite to camera (5) another LED light source (4) was placed. With the side camera (5), the contour of the ice accretion wrapping the airfoil was recorded via shadowgraphy. A high qualitative overall image of the accretion process was acquired with camera (6) positioned upstream and pointing from an oblique view to the leading edge.

Variable electrical power sources were connected to the heaters. A temperature control unit monitored the temperatures of all 21 RTDs, whose signals were acquired and digitally converted via a Lab View (National Instruments, NI-9205, USA) program with temporal resolution of 10 Hz.

## 2.3. Experiment overview

Three experimental campaigns were conducted at the ACRT and TUBS IWT facilities with combinations of NACA0012 airfoil chord lengths (see Fig. 6).

<figure><img src="image_7.png" /><figcaption>Fig. 4. Model building tree of the TUBS NACA-0012 model.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Cross section schematic of the leading edge of the TUBS NACA-0012 test article (left) and exploded view of the model (right).</figcaption></figure>

temperature sensors were placed in the close vicinity of the stagnation line. The sensors measured 1.3 mm × 2.0 mm × 2.5 mm and the leading edge had a wall thickness of 4 mm. To route the cables of the temperature sensors 1 mm deep grooves were milled into leading edge to enable smooth form and shape of the test article. The sensors were molded into the pockets with a highly thermally conductive two-component adhesive (Duralco 132). To create a smooth finish of the target surface where ice crystals impinge, an aluminum sheet with a thickness of 0.2 mm was wrapped around the airfoil. The leading edge was heated from the inside by means of thin flexible heaters in such a way that they would allow different heat fluxes between the stagnation line and the area downstream, which would not have been possible with a single large heater (Fig. 4). The composition as well as the characterisation of the different layers of the test article have been summarized in tabular form in Table A 3 presented in 6.

### 2.2.2. Experimental setup

The experimental setup enabled the quantitative measurement of ice accretion by means of shadowgraphy technique utilizing two cameras with the centers of lenses aligned to the leading edge from the top and side perspective. In total four DSLR-cameras were placed around the test section (Fig. 5) to allow for qualitative and quantitative observation of ice accretion and shedding. For tracking the maximum ice thickness

along the leading edge of the airfoil, camera (1) was positioned vertically above the model, pointing straight down the leading edge.

A beamer flicker free LED light source (3) (7000 lm) was placed on the opposite side of the test section and pointing straight into camera (1). Camera (2) was positioned upstream above the test sample pointing at the leading edge for tracking the runback of melt water and ice. From the wall side of the test section, camera (5) points at the stagnation line. Opposite to camera (5) another LED light source (4) was placed. With the side camera (5), the contour of the ice accretion wrapping the airfoil was recorded via shadowgraphy. A high qualitative overall image of the accretion process was acquired with camera (6) positioned upstream and pointing from an oblique view to the leading edge.

Variable electrical power sources were connected to the heaters. A temperature control unit monitored the temperatures of all 21 RTDs, whose signals were acquired and digitally converted via a Lab View (National Instruments, NI-9205, USA) program with temporal resolution of 10 Hz.

## 2.3. Experiment overview

Three experimental campaigns were conducted at the ACRT and TUBS IWT facilities with combinations of NACA0012 airfoil chord lengths (see Fig. 6).

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Model building tree of the TUBS NACA-0012 model.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 5. TUBS experimental setup – Vertical (left) and horizontal cross section (right).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Illustration of the combinations of airfoils and IWT used for the three test campaigns reported in this study. The combinations are color coded as in the result plots.</figcaption></figure>

One campaign was carried out in the TUBS IWT with the TUBS airfoil with a chord length of 430 mm. Two campaigns were carried out at the ACRT IWT, one with the ACRT airfoil with a chord length of 180 mm and the second with the TUBS airfoil. It should be pointed out here that in the last case (i.e. TUBS 430 mm used at ACRT) the blockage effects are not negligible since the profile thickness is not negligible compared to the test section dimensions. Table 1 shows the experimental test conditions of three test campaigns.

This study focuses on one Angle of Attack of 0° only and on solely glaciated ice particles fed to the wind tunnel. Depending on the $T_{wb}$, though, the ice particles might partially melt on the way to the test section. The $T_{wb}$ is described in the literature as the lowest temperature to which air can be cooled by the evaporation of water into the air at a constant pressure (Razak, 2007). For icing conditions this translates into ice particle melting at $T_{wb} > 0$, whereas $T_{wb} < 0$ affects film freezing (Baumert, 2019). The $T_{wb}$ can be calculated from the air temperature and the relative humidity using the Stull formula (Stull, 2011).

## 2.4. Data analysis

The video analysis of the top and side views was done similarly at ACRT and TUBS. Before the test campaigns, the video images were calibrated with objects of known size, from which the pixel scale was determined. The frames are filtered with a binary threshold filter to

<table><caption>**Table 1**
Boundary condition ranges for parametric variation to study shedding process at ACRT and TUBS.</caption><thead><tr><th>Parameter</th><th>Air Temp.</th><th>Airspeed</th><th>Heat Power Density</th><th>IWC</th></tr></thead><tbody><tr><td>Symbol</td><td>$T_{WB}$</td><td>$U_{\infty}$</td><td>$\dot{q}$</td><td>IWC</td></tr><tr><td>Unit</td><td>°C</td><td>ms<sup>-1</sup></td><td>Wcm<sup>-2</sup></td><td>gm<sup>-3</sup></td></tr><tr><td>Campaign 1</td><td>-20 to +5</td><td>20 to 40</td><td>0 to 1.15</td><td>3 to 12</td></tr><tr><td>Campaign 2</td><td>-10 to +5</td><td>40 to 80</td><td>0 to 1.3</td><td>4 to 14</td></tr><tr><td>Campaign 3</td><td>-10 to -5</td><td>20 to 80</td><td>0.3 to 0.7</td><td>4 to 10</td></tr></tbody></table>

yield black and white images of the recorded scene with the airfoil and ice being depicted in black pixels, and the background illumination in white pixels. With the still frames of a clean NACA airfoil a mask is generated, which is deducted from the later video frames with ice accretion on the NACA airfoil leading edge. Fig. 7 illustrates the post-processing method for a test case with side and top view frames.

More details on the TUBS in-house code used for obtaining quantitative ice accretion data can be found in Malik et al. (Malik et al., 2022).

## 3. Results and discussion

Accretion and shedding are strongly coupled and the latter only takes place if previously an ice layer has accreted on the substrate. However, shedding dynamics differ in different test conditions. Therefore, an in depth characterisation of the shed ice area is presented with a differentiation of the types of area losses and a direct correlation to the accretion process.

The influences of airspeed, wet bulb temperature ($T_{wb}$), and ice water content (IWC) are compared to findings in mixed-phase ice crystal icing conditions in this study and in recent research publications. From here on-wards, the wet bulb temperature ($T_{wb}$) refers to Centigrade scale with the freezing threshold being at 0°C. The influence of the airfoil size is also discussed based on the two different airfoils used in the test campaigns. The main novelty of this work is substrate heating and assessing how this additional test parameter influences ice crystal accretion and shedding.

From the experimental results and observations it becomes apparent that overall there are two main driving mechanisms that limit accretion and promote shedding:

* the continuous shedding mechanism, which corresponds to the cases where ice is continuously removed by erosion, splashing, melting, and aerodynamic shear forces at the surface. In this case, the accretion area cannot exceed a certain limit in terms of thickness and maximum area;

* the cyclic shedding mechanism, which prevails when the physical phenomena involved in the continuous shedding mechanism are not effective enough to prevent accretion from growing until the ice layer has reached a sufficient surface area and thickness for the aerodynamic pressure forces to cause its sudden detachment;

* for a few cases cyclic and continuous shedding co-exist wherein the aerothermal and icing conditions promote continuous shedding in the earlier stages of accretion where small ice pockets melt, erode and detach running downstream until a coherent ice layer develops on the surface which sheds in a cyclic manner.

When $T_{wb}$ is <0°C, cyclic shedding may or may not occur depending
<figure><img src="image_8.png" /><figcaption>Fig. 5. TUBS experimental setup – Vertical (left) and horizontal cross section (right).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Illustration of the combinations of airfoils and IWT used for the three test campaigns reported in this study. The combinations are color coded as in the result plots.</figcaption></figure>

One campaign was carried out in the TUBS IWT with the TUBS airfoil with a chord length of 430 mm. Two campaigns were carried out at the ACRT IWT, one with the ACRT airfoil with a chord length of 180 mm and the second with the TUBS airfoil. It should be pointed out here that in the last case (i.e. TUBS 430 mm used at ACRT) the blockage effects are not negligible since the profile thickness is not negligible compared to the test section dimensions. Table 1 shows the experimental test conditions of three test campaigns.

This study focuses on one Angle of Attack of 0° only and on solely glaciated ice particles fed to the wind tunnel. Depending on the $T_{wb}$, though, the ice particles might partially melt on the way to the test section. The $T_{wb}$ is described in the literature as the lowest temperature to which air can be cooled by the evaporation of water into the air at a constant pressure (Razak, 2007). For icing conditions this translates into ice particle melting at $T_{wb} > 0$, whereas $T_{wb} < 0$ affects film freezing (Baumert, 2019). The $T_{wb}$ can be calculated from the air temperature and the relative humidity using the Stull formula (Stull, 2011).

## 2.4. Data analysis

The video analysis of the top and side views was done similarly at ACRT and TUBS. Before the test campaigns, the video images were calibrated with objects of known size, from which the pixel scale was determined. The frames are filtered with a binary threshold filter to

<table><caption>**Table 1**
Boundary condition ranges for parametric variation to study shedding process at ACRT and TUBS.</caption><thead><tr><th>Parameter</th><th>Air Temp.</th><th>Airspeed</th><th>Heat Power Density</th><th>IWC</th></tr></thead><tbody><tr><td>Symbol</td><td>$T_{WB}$</td><td>$U_{\infty}$</td><td>$\dot{q}$</td><td>IWC</td></tr><tr><td>Unit</td><td>°C</td><td>ms<sup>-1</sup></td><td>Wcm<sup>-2</sup></td><td>gm<sup>-3</sup></td></tr><tr><td>Campaign 1</td><td>-20 to +5</td><td>20 to 40</td><td>0 to 1.15</td><td>3 to 12</td></tr><tr><td>Campaign 2</td><td>-10 to +5</td><td>40 to 80</td><td>0 to 1.3</td><td>4 to 14</td></tr><tr><td>Campaign 3</td><td>-10 to -5</td><td>20 to 80</td><td>0.3 to 0.7</td><td>4 to 10</td></tr></tbody></table>

yield black and white images of the recorded scene with the airfoil and ice being depicted in black pixels, and the background illumination in white pixels. With the still frames of a clean NACA airfoil a mask is generated, which is deducted from the later video frames with ice accretion on the NACA airfoil leading edge. Fig. 7 illustrates the post-processing method for a test case with side and top view frames.

More details on the TUBS in-house code used for obtaining quantitative ice accretion data can be found in Malik et al. (Malik et al., 2022).

## 3. Results and discussion

Accretion and shedding are strongly coupled and the latter only takes place if previously an ice layer has accreted on the substrate. However, shedding dynamics differ in different test conditions. Therefore, an in depth characterisation of the shed ice area is presented with a differentiation of the types of area losses and a direct correlation to the accretion process.

The influences of airspeed, wet bulb temperature ($T_{wb}$), and ice water content (IWC) are compared to findings in mixed-phase ice crystal icing conditions in this study and in recent research publications. From here on-wards, the wet bulb temperature ($T_{wb}$) refers to Centigrade scale with the freezing threshold being at 0°C. The influence of the airfoil size is also discussed based on the two different airfoils used in the test campaigns. The main novelty of this work is substrate heating and assessing how this additional test parameter influences ice crystal accretion and shedding.

From the experimental results and observations it becomes apparent that overall there are two main driving mechanisms that limit accretion and promote shedding:

* the continuous shedding mechanism, which corresponds to the cases where ice is continuously removed by erosion, splashing, melting, and aerodynamic shear forces at the surface. In this case, the accretion area cannot exceed a certain limit in terms of thickness and maximum area;

* the cyclic shedding mechanism, which prevails when the physical phenomena involved in the continuous shedding mechanism are not effective enough to prevent accretion from growing until the ice layer has reached a sufficient surface area and thickness for the aerodynamic pressure forces to cause its sudden detachment;

* for a few cases cyclic and continuous shedding co-exist wherein the aerothermal and icing conditions promote continuous shedding in the earlier stages of accretion where small ice pockets melt, erode and detach running downstream until a coherent ice layer develops on the surface which sheds in a cyclic manner.

When $T_{wb}$ is <0°C, cyclic shedding may or may not occur depending
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Masking and ice detection process from top view (left). Ice accretion growth over time (highlighted in red) from side and top perspective (right). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

on the test conditions because the ice layer may be too strongly adhered to the wall. In the case where $T_{wb}$ is >0°C, shedding always seems to occur at some point.

## 3.1. Characteristics of the accretion and shedding process

### 3.1.1. Differentiation between types of mass losses

The time evolution of the top view ice accretions is further processed to extract accretion and shedding events as well as other area loss events. Fig. 8 shows an exemplary top view accretion plot with three types of ice accretion slopes. Increasing slopes represent ice accretion and are marked in blue; rapidly decreasing slopes represent ice shedding and are marked in red; slowly decreasing slopes represent other mass loss events such as sliding, erosion, or melting of ice layer marked in yellow. From these graphs we extract quantitative descriptors (Table 2) used for analysing and rationalizing the accretion and shedding results.

Besides the quantified accreted area measured from the top perspective (Camera ①), as displayed in Fig. 5, the side oblique view (Camera ⑥) and top oblique view (Camera ②) aid in manual identification of continuous and cyclic shedding events.

### 3.1.2. Shedding dependency on accretion

Fig. 9 shows the ratio of the largest shed area and the largest accreted area plotted over the largest accreted area. The dotted lines are visual guidelines representing observed trends in the data plot and have no

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Exemplary plot of top view ice accretion vs. time. Slopes marked with red color represent shedding events and slopes marked with yellow color represent other mass loss events. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

further physical meaning.

At negative $T_{wb}$, the guidelines asymptotically go to unity or zero, i.e. complete shedding or no shedding, respectively. The two lines seem to suggest that their intersection point defines a threshold below which it is possible to determine whether ice further accretes, sheds completely or partially, while above it ice either completely sheds off in a cyclic manner or accretes indefinitely. This threshold is of the order of a few hundred squared millimeters for all tests that were performed. Considering the 100 mm span of the airfoil section on average an ice layer must grow to a few millimeters in thickness, after which it has gained enough cohesion to stay intact and continue growing. It can also shed off in its entirety if the heat flux gets large enough to generate a water layer at the interface between ice and surface and the aerodynamic drag is large enough to remove the ice layer. At positive $T_{wb}$, the trend is that larger ice accretions are more prone to entirely shed off the airfoil. At positive $T_{wb}$ the ice layer contains more liquid water and is more slushy - and thus easier to be moved around or shed off by aerodynamic friction forces resulting in continuous shedding. The data points again suggest that above a few hundred micrometers accreted ice layers tend to shed off completely, while below this threshold they can partially shed off or continue growing.

At both negative and positive $T_{wb}$, smaller ice accretions seem prone to cyclic loops of partial shedding and accretion, indicating that during the previous accretion phase an ice layer with a low internal cohesion or a low adhesion to the surface was formed. We observed, however, that in some test conditions small ice accretions were able to slowly grow and did not shed. Here, the conditions were such that strong melting and sliding (large heat flux) or high erosion loads (large airspeed) kept the accretion from growing considerably beyond the threshold, maintaining a stable size for an extended time without shedding.

Fig. 10 shows the frequency of shedding events plotted over the largest accreted area for negative and positive $T_{wb}$. For both $T_{wb}$s the shedding frequency decreases with increasing largest accreted area. For a given limited accretion rate this is to be expected because of the direct dependency of the shedding frequency to the cycle duration of the ice accretion. Larger ice accretions accrete for a longer period of time and lead to a reduced number of shedding events (or no shedding events) and to a reduced (or zero) shedding frequency. For small ice accretion areas a wide range from small to large shedding frequencies was observed. Especially for ice accretions smaller than a few hundred micrometers the shedding frequencies are larger because no full ice layer builds up and the small ice accretions shed off cyclically.

Fig. 11 shows the ratio of the shed area and the total lost area plotted over the airspeed. No distinction between melting, sliding and erosion is possible here from the top view area analysis. The total lost area depicted in the plots is thus a combination of shedding plus the other three sources of losses.

At negative $T_{wb}$ glaciated ice layers accrete and mass loss is a
<figure><img src="image_10.png" /><figcaption>Fig. 7. Masking and ice detection process from top view (left). Ice accretion growth over time (highlighted in red) from side and top perspective (right). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

on the test conditions because the ice layer may be too strongly adhered to the wall. In the case where $T_{wb}$ is >0°C, shedding always seems to occur at some point.

## 3.1. Characteristics of the accretion and shedding process

### 3.1.1. Differentiation between types of mass losses

The time evolution of the top view ice accretions is further processed to extract accretion and shedding events as well as other area loss events. Fig. 8 shows an exemplary top view accretion plot with three types of ice accretion slopes. Increasing slopes represent ice accretion and are marked in blue; rapidly decreasing slopes represent ice shedding and are marked in red; slowly decreasing slopes represent other mass loss events such as sliding, erosion, or melting of ice layer marked in yellow. From these graphs we extract quantitative descriptors (Table 2) used for analysing and rationalizing the accretion and shedding results.

Besides the quantified accreted area measured from the top perspective (Camera ①), as displayed in Fig. 5, the side oblique view (Camera ⑥) and top oblique view (Camera ②) aid in manual identification of continuous and cyclic shedding events.

### 3.1.2. Shedding dependency on accretion

Fig. 9 shows the ratio of the largest shed area and the largest accreted area plotted over the largest accreted area. The dotted lines are visual guidelines representing observed trends in the data plot and have no

<figure><img src="image_11.png" /><figcaption>Fig. 8. Exemplary plot of top view ice accretion vs. time. Slopes marked with red color represent shedding events and slopes marked with yellow color represent other mass loss events. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

further physical meaning.

At negative $T_{wb}$, the guidelines asymptotically go to unity or zero, i.e. complete shedding or no shedding, respectively. The two lines seem to suggest that their intersection point defines a threshold below which it is possible to determine whether ice further accretes, sheds completely or partially, while above it ice either completely sheds off in a cyclic manner or accretes indefinitely. This threshold is of the order of a few hundred squared millimeters for all tests that were performed. Considering the 100 mm span of the airfoil section on average an ice layer must grow to a few millimeters in thickness, after which it has gained enough cohesion to stay intact and continue growing. It can also shed off in its entirety if the heat flux gets large enough to generate a water layer at the interface between ice and surface and the aerodynamic drag is large enough to remove the ice layer. At positive $T_{wb}$, the trend is that larger ice accretions are more prone to entirely shed off the airfoil. At positive $T_{wb}$ the ice layer contains more liquid water and is more slushy - and thus easier to be moved around or shed off by aerodynamic friction forces resulting in continuous shedding. The data points again suggest that above a few hundred micrometers accreted ice layers tend to shed off completely, while below this threshold they can partially shed off or continue growing.

At both negative and positive $T_{wb}$, smaller ice accretions seem prone to cyclic loops of partial shedding and accretion, indicating that during the previous accretion phase an ice layer with a low internal cohesion or a low adhesion to the surface was formed. We observed, however, that in some test conditions small ice accretions were able to slowly grow and did not shed. Here, the conditions were such that strong melting and sliding (large heat flux) or high erosion loads (large airspeed) kept the accretion from growing considerably beyond the threshold, maintaining a stable size for an extended time without shedding.

Fig. 10 shows the frequency of shedding events plotted over the largest accreted area for negative and positive $T_{wb}$. For both $T_{wb}$ the shedding frequency decreases with increasing largest accreted area. For a given limited accretion rate this is to be expected because of the direct dependency of the shedding frequency to the cycle duration of the ice accretion. Larger ice accretions accrete for a longer period of time and lead to a reduced number of shedding events (or no shedding events) and to a reduced (or zero) shedding frequency. For small ice accretion areas a wide range from small to large shedding frequencies was observed. Especially for ice accretions smaller than a few hundred micrometers the shedding frequencies are larger because no full ice layer builds up and the small ice accretions shed off cyclically.

Fig. 11 shows the ratio of the shed area and the total lost area plotted over the airspeed. No distinction between melting, sliding and erosion is possible here from the top view area analysis. The total lost area depicted in the plots is thus a combination of shedding plus the other three sources of losses.

At negative $T_{wb}$ glaciated ice layers accrete and mass loss is a
<table><caption>**Table 2**
Overview of the extracted shedding parameters.</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Unit</th><th>Info</th></tr></thead><tbody><tr><td>Max. ever accreted area</td><td>A<sub>accr,max</sub></td><td>mm<sup>2</sup></td><td>The maximum ice accretion area over the entire test run. The largest ever accreted area is an indicator for the stability of the ice layer.</td></tr><tr><td>Total accreted area</td><td>A<sub>accr,un</sub></td><td>mm<sup>2</sup></td><td>The area sum of all accretions.</td></tr><tr><td>Max. ever shed area</td><td>A<sub>shed,max</sub></td><td>mm<sup>2</sup></td><td>The maximum shed area of all recognized shedding events. It is an indicator of the severity of the shedding and the mechanical rigidity of the ice layer.</td></tr><tr><td>Total shed area</td><td>A<sub>shed,un</sub></td><td>mm<sup>2</sup></td><td>The area sum of all recognized shedding events.</td></tr><tr><td>Ratio max shed area / max accreted area</td><td>R<sub>shed,accr,max</sub></td><td>–</td><td>The ratio of the maximum ever shed area and the maximum ever accreted area is an indicator for the shedding probability of an ice layer. It is dimensionless and ranges from 0 (None of the maximum accreted ice area shed) to unity (All of the maximum accreted ice area shed).</td></tr><tr><td>Shedding frequency</td><td>f<sub>shed</sub></td><td>s<sup>-1</sup></td><td>The shedding frequency is the number of the recognized shedding events divided by the total test time. The shedding frequency is an indicator for the instability of the ice layer with respect to shedding only.</td></tr><tr><td>Total lost area</td><td>A<sub>lost,un</sub></td><td>mm<sup>2</sup></td><td>The sum of areas lost in all mass loss events including shedding and other mass losses, such as erosion, sliding, melting, etc. It is an indicator of the overall instability of the ice layer with respect to shedding and other mass losses due to mechanically weak ice accretions.</td></tr><tr><td>Ratio total shed area / total lost area</td><td>R<sub>shed,lost,un</sub></td><td>–</td><td>The ratio of the total shed area and the total lost area is an indicator for the mechanical rigidity of the ice layer. It is dimensionless and ranges from 0 (Only mass losses due to low mechanical ice rigidity and thus larger erosion, sliding, or melting) to unity (Only rapid shedding of large ice blocks). It is also an indicator for the severity of the mass loss events with large shed ice blocks being very harmful to the engine, and erosion, melting, sliding posing no threat to the engine safety.</td></tr><tr><td>Ratio total lost area / total accreted area</td><td>R<sub>lost,accr,un</sub></td><td>–</td><td>The ratio of the total lost area and the total accreted area is an indicator for the mechanical rigidity of the ice layer. It is dimensionless and ranges from 0 (None of the accreted ice area lost) to unity (All accreted ice area lost). The total lost ice area entails all mass events, i.e., erosion, melting, sliding, and shedding.</td></tr></tbody></table>

consequence of interfacial melting. It is experimentally observed that at low airspeeds shedding and other mass losses (melting/sliding/erosion) contribute to the detachment of ice from the surface. Furthermore, there is no strong trend observed at low airspeeds, whilst melting, sliding, and erosion become stronger at airspeeds above $50 \text{ ms}^{-1}$, which is inline with previous studies (Norde et al., 2018; Currie et al., 2014b; Currie et al., 2012b; Currie et al., 2013).

Ice accretion and shedding experiments with the 180 mm chord length NACA-0012 airfoil at ACRT (Orange squares) showed a strong influence of airspeed on the ice accretion and shedding process. For airspeeds above $60 \text{ ms}^{-1}$ no combination of heat flux, IWC, and $T_{wb}$ led to significant ice accretion, since highly frequent accretion and sliding cycles of sub-millimeter thickness ice accretions occurred. Also ice crystals rebounding from the surface showed rebound trajectories by-

passing the airfoil. It is in line with earlier studies. At CNRC (Knezevici et al., 2012; Knezevici et al., 2013b; Currie and Fuleki, 2016) it was shown that with large ice crystals (in particular large DV90) erosion and splashing become important phenomena at high speed and accretion is not observed anymore. Specifically, with MVD = 57 µm the limit Mach number for possible accretion was $Ma = 0.4$ and at MVD = 28 µm the limit was $Ma = 0.65$.

Bucknell et al. (Bucknell et al., 2020) shared similar findings detailing the influence of particle mass and airspeed on erosive effects on accreted ice layers, thereby leading to stagnation of the ice accretion growth. It was found that at Mach numbers of $Ma = 0.4$ MVDs larger than 50 µm led to a sticking efficiency curve flattened to zero.

In this study at TUBS a particle cloud with MVD = 130 µm and an airspeed of $Ma = 0.12$ led to the start of erosion. At ACRT with MVDs of around 100 µm and $Ma = 0.175$ no accretion could be observed. The combination of the lower speeds and larger ice particles in both test facilities seem to arrive at similar findings for the limits of possible accretion. In fact when superposing the data of the referenced studies and this study, the critical Mach numbers vs. the MVD above which no accretion is possible seems to follow a distinct trend (Fig. 12).

Experiments with the 430 mm chord length NACA-0012 airfoil from TUBS in the ACRT test facility (dark blue points) showed potential for larger ice accretions towards higher airspeeds in comparison to the airfoil with shorter chord length. We assume that ice accretion also depends on airfoil thickness, especially in a test section of limited height as in the iCORE where we must consider wall effects. The thicker airfoil experiences a higher probability of rebounding or eroded ice crystals reimpacting the surface. These reimpacting particles have a lower impact velocity and thus a higher surface sticking efficiency. In the range of airspeeds examined at positive $T_{wb}$, no airspeed influence could be observed.

## 3.2. Influence of parametric variation on accretion and shedding

### 3.2.1. Influence of heat flux

In the past, substrate heating with controlled heat flux for quantitative analysis of ice crystal icing was not investigated in detail which we address in this section. Whilst Malik et al. (Malik et al., 2023) investigated the ice accretion inception on a heatable flat plate model, only a qualitative description of ice accretion was provided which served as a limitation for development of icing physics models. This gap is filled in the present work and a detailed quantitative analysis of ice crystal accretion and shedding mechanism on a heated geometry is presented for a wide range of parametric conditions.

Fig. 13 shows an exemplary temperature vs. time plot for an ice crystal cloud impacting on a heated substrate. In dry air configuration and before turning on the icing cloud, the NACA0012 airfoil reached thermal equilibrium with the surrounding airstream and settled at a steady surface temperature of approx. 45°C. Shortly before turning on the icing cloud, a protection shield was introduced in front of the airfoil, leading to an effective increase of approx. 5°C of the measured surface temperature. Once the icing cloud stabilized in the test section which takes around 30 s, the protection shield was removed and the ice crystals started impacting on the heated surface. This is the inception point of ice accretion: the transient phase starts with a pure liquid water layer from the ice crystals melted by the heating from the substrate, continues with a mixed water-ice layer, and ends up in an equilibrium phase with an ice layer as soon as the surface temperature reaches the melting phase change temperature of water (i.e., 0°C) (Karpen et al., 2022; Löwe et al., 2016b).

Vertical dashed lines mark the inception of ice accretion, the inception of the equilibrium temperature, and mass loss events, respectively. Horizontal blue dashed lines indicate the initial and the equilibrium temperatures.

Fig. 13 illustrates the dependency of the leading edge surface temperature on the ice accretion development for mixed-phase conditions at
<table><caption>**Table 2**
Overview of the extracted shedding parameters.</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Unit</th><th>Info</th></tr></thead><tbody><tr><td>Max. ever accreted area</td><td>A<sub>accr,max</sub></td><td>mm<sup>2</sup></td><td>The maximum ice accretion area over the entire test run. The largest ever accreted area is an indicator for the stability of the ice layer.</td></tr><tr><td>Total accreted area</td><td>A<sub>accr,un</sub></td><td>mm<sup>2</sup></td><td>The area sum of all accretions.</td></tr><tr><td>Max. ever shed area</td><td>A<sub>shed,max</sub></td><td>mm<sup>2</sup></td><td>The maximum shed area of all recognized shedding events. It is an indicator of the severity of the shedding and the mechanical rigidity of the ice layer.</td></tr><tr><td>Total shed area</td><td>A<sub>shed,un</sub></td><td>mm<sup>2</sup></td><td>The area sum of all recognized shedding events.</td></tr><tr><td>Ratio max shed area / max accreted area</td><td>R<sub>shed,accr,max</sub></td><td>–</td><td>The ratio of the maximum ever shed area and the maximum ever accreted area is an indicator for the shedding probability of an ice layer. It is dimensionless and ranges from 0 (None of the maximum accreted ice area shed) to unity (All of the maximum accreted ice area shed).</td></tr><tr><td>Shedding frequency</td><td>f<sub>shed</sub></td><td>s<sup>-1</sup></td><td>The shedding frequency is the number of the recognized shedding events divided by the total test time. The shedding frequency is an indicator for the instability of the ice layer with respect to shedding only.</td></tr><tr><td>Total lost area</td><td>A<sub>lost,un</sub></td><td>mm<sup>2</sup></td><td>The sum of areas lost in all mass loss events including shedding and other mass losses, such as erosion, sliding, melting, etc. It is an indicator of the overall instability of the ice layer with respect to shedding and other mass losses due to mechanically weak ice accretions.</td></tr><tr><td>Ratio total shed area / total lost area</td><td>R<sub>shed,lost,un</sub></td><td>–</td><td>The ratio of the total shed area and the total lost area is an indicator for the mechanical rigidity of the ice layer. It is dimensionless and ranges from 0 (Only mass losses due to low mechanical ice rigidity and thus larger erosion, sliding, or melting) to unity (Only rapid shedding of large ice blocks). It is also an indicator for the severity of the mass loss events with large shed ice blocks being very harmful to the engine, and erosion, melting, sliding posing no threat to the engine safety.</td></tr><tr><td>Ratio total lost area / total accreted area</td><td>R<sub>lost,accr,un</sub></td><td>–</td><td>The ratio of the total lost area and the total accreted area is an indicator for the mechanical rigidity of the ice layer. It is dimensionless and ranges from 0 (None of the accreted ice area lost) to unity (All accreted ice area lost). The total lost ice area entails all mass events, i.e., erosion, melting, sliding, and shedding.</td></tr></tbody></table>

consequence of interfacial melting. It is experimentally observed that at low airspeeds shedding and other mass losses (melting/sliding/erosion) contribute to the detachment of ice from the surface. Furthermore, there is no strong trend observed at low airspeeds, whilst melting, sliding, and erosion become stronger at airspeeds above $50 \text{ ms}^{-1}$, which is inline with previous studies (Norde et al., 2018; Currie et al., 2014b; Currie et al., 2012b; Currie et al., 2013).

Ice accretion and shedding experiments with the 180 mm chord length NACA-0012 airfoil at ACRT (Orange squares) showed a strong influence of airspeed on the ice accretion and shedding process. For airspeeds above $60 \text{ ms}^{-1}$ no combination of heat flux, IWC, and $T_{wb}$ led to significant ice accretion, since highly frequent accretion and sliding cycles of sub-millimeter thickness ice accretions occurred. Also ice crystals rebounding from the surface showed rebound trajectories by-

passing the airfoil. It is in line with earlier studies. At CNRC (Knezevici et al., 2012; Knezevici et al., 2013b; Currie and Fuleki, 2016) it was shown that with large ice crystals (in particular large DV90) erosion and splashing become important phenomena at high speed and accretion is not observed anymore. Specifically, with MVD = 57 µm the limit Mach number for possible accretion was $Ma = 0.4$ and at MVD = 28 µm the limit was $Ma = 0.65$.

Bucknell et al. (Bucknell et al., 2020) shared similar findings detailing the influence of particle mass and airspeed on erosive effects on accreted ice layers, thereby leading to stagnation of the ice accretion growth. It was found that at Mach numbers of $Ma = 0.4$ MVDs larger than 50 µm led to a sticking efficiency curve flattened to zero.

In this study at TUBS a particle cloud with MVD = 130 µm and an airspeed of $Ma = 0.12$ led to the start of erosion. At ACRT with MVDs of around 100 µm and $Ma = 0.175$ no accretion could be observed. The combination of the lower speeds and larger ice particles in both test facilities seem to arrive at similar findings for the limits of possible accretion. In fact when superposing the data of the referenced studies and this study, the critical Mach numbers vs. the MVD above which no accretion is possible seems to follow a distinct trend (Fig. 12).

Experiments with the 430 mm chord length NACA-0012 airfoil from TUBS in the ACRT test facility (dark blue points) showed potential for larger ice accretions towards higher airspeeds in comparison to the airfoil with shorter chord length. We assume that ice accretion also depends on airfoil thickness, especially in a test section of limited height as in the iCORE where we must consider wall effects. The thicker airfoil experiences a higher probability of rebounding or eroded ice crystals reimpacting the surface. These reimpacting particles have a lower impact velocity and thus a higher surface sticking efficiency. In the range of airspeeds examined at positive $T_{wb}$, no airspeed influence could be observed.

## 3.2. Influence of parametric variation on accretion and shedding

### 3.2.1. Influence of heat flux

In the past, substrate heating with controlled heat flux for quantitative analysis of ice crystal icing was not investigated in detail which we address in this section. Whilst Malik et al. (Malik et al., 2023) investigated the ice accretion inception on a heatable flat plate model, only a qualitative description of ice accretion was provided which served as a limitation for development of icing physics models. This gap is filled in the present work and a detailed quantitative analysis of ice crystal accretion and shedding mechanism on a heated geometry is presented for a wide range of parametric conditions.

Fig. 13 shows an exemplary temperature vs. time plot for an ice crystal cloud impacting on a heated substrate. In dry air configuration and before turning on the icing cloud, the NACA0012 airfoil reached thermal equilibrium with the surrounding airstream and settled at a steady surface temperature of approx. 45°C. Shortly before turning on the icing cloud, a protection shield was introduced in front of the airfoil, leading to an effective increase of approx. 5°C of the measured surface temperature. Once the icing cloud stabilized in the test section which takes around 30 s, the protection shield was removed and the ice crystals started impacting on the heated surface. This is the inception point of ice accretion: the transient phase starts with a pure liquid water layer from the ice crystals melted by the heating from the substrate, continues with a mixed water-ice layer, and ends up in an equilibrium phase with an ice layer as soon as the surface temperature reaches the melting phase change temperature of water (i.e., 0°C) (Karpen et al., 2022; Löwe et al., 2016b).

Vertical dashed lines mark the inception of ice accretion, the inception of the equilibrium temperature, and mass loss events, respectively. Horizontal blue dashed lines indicate the initial and the equilibrium temperatures.

Fig. 13 illustrates the dependency of the leading edge surface temperature on the ice accretion development for mixed-phase conditions at
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Ratio of the largest shed area and the largest accreted area vs. the largest overall accreted area for the three test campaigns for all heated and unheated test samples at negative (left) and positive (right) T<sub>wb</sub>. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Shedding frequency vs. largest overall accreted area for the three test campaigns for all heated and unheated cases at negative (left) and positive (right) T<sub>wb</sub>. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Ratio of total shed area and total lost area vs. airspeed for the three test campaigns for all heated and unheated surfaces at negative (left) and positive (right) T<sub>wb</sub>. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 9. Ratio of the largest shed area and the largest accreted area vs. the largest overall accreted area for the three test campaigns for all heated and unheated test samples at negative (left) and positive (right) T<sub>wb</sub>. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. Shedding frequency vs. largest overall accreted area for the three test campaigns for all heated and unheated cases at negative (left) and positive (right) T<sub>wb</sub>. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11. Ratio of total shed area and total lost area vs. airspeed for the three test campaigns for all heated and unheated surfaces at negative (left) and positive (right) T<sub>wb</sub>. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Critical Ma vs. MVD for possible accretion as seen in several studies. The points are fitted with an exponent fit as a visual guideline.</figcaption></figure>

positive $T_{wb}$ with an unheated airfoil (a) and glaciated conditions at negative $T_{wb}$ with a heated airfoil (b). Prior to the start of the test ($t < 0$ s) at $t = -50$s, the airfoil surface has acquired the temperature of the ambient air also referred to as the thermal equilibrium temperature. A shield is positioned for 40 s in front of the airfoil to ensure a homogeneous icing cloud distribution in the test section (Bansmer et al., 2018). However, the compromise of using such a shield is that it prevents the impact of cold airflow on the heated test article which results in rise in surface temperature as can be observed between $t = 0$ s) and $t = -50$s. Once the icing cloud is homogeneous, the shield is removed and the ice cloud impacts on the airfoil, which reduces the leading edge temperature rapidly. Glaciated conditions on a heated surface at negative $T_{wb}$ and mixed-phase conditions on a non-heated surface at positive $T_{wb}$ show similar trends of the leading edge temperature. Both decrease until the inception of ice accretion and subsequently reaching the final temperature.

Previous studies (Currie et al., 2015; Kintea et al., 2016b) showed experimentally and theoretically that in unheated cases, upon starting the icing cloud, the surface reaches the phase change temperature of water of 0°C. After the surface and the water-ice mixed cloud reach 0°C, additional heat transfer can take place without additional temperature change due to the potential phase change at the ice-substrate interface resulting from ambient airflow. The ice layer heat balance relies on the

<figure><img src="image_16.png" /><figcaption>**Fig. 13.** Exemplary temporal accretion and leading edge temperature developments in a) mixed-phase conditions at positive $T_{wb}$ with an unheated airfoil [Params.: $T_{wb} = 2.5$°C, $U = 20$ ms$^{-1}$, IWC = 4.1 g$^{-3}$, $q = 0$ W cm$^{-2}$] and b) glaciated conditions at negative $T_{wb}$ with a heated airfoil [Params.: $T_{wb} = -10$°C, $U = 20$ ms$^{-1}$, IWC = 5.4 g$^{-3}$, $q = 0.88$ W cm$^{-2}$].</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Critical Ma vs. MVD for possible accretion as seen in several studies. The points are fitted with an exponent fit as a visual guideline.</figcaption></figure>

positive $T_{wb}$ with an unheated airfoil (a) and glaciated conditions at negative $T_{wb}$ with a heated airfoil (b). Prior to the start of the test ($t < 0$ s) at $t = -50$s, the airfoil surface has acquired the temperature of the ambient air also referred to as the thermal equilibrium temperature. A shield is positioned for 40 s in front of the airfoil to ensure a homogeneous icing cloud distribution in the test section (Bansmer et al., 2018). However, the compromise of using such a shield is that it prevents the impact of cold airflow on the heated test article which results in rise in surface temperature as can be observed between $t = 0$ s) and $t = -50$s. Once the icing cloud is homogeneous, the shield is removed and the ice cloud impacts on the airfoil, which reduces the leading edge temperature rapidly. Glaciated conditions on a heated surface at negative $T_{wb}$ and mixed-phase conditions on a non-heated surface at positive $T_{wb}$ show similar trends of the leading edge temperature. Both decrease until the inception of ice accretion and subsequently reaching the final temperature.

Previous studies (Currie et al., 2015; Kintea et al., 2016b) showed experimentally and theoretically that in unheated cases, upon starting the icing cloud, the surface reaches the phase change temperature of water of 0°C. After the surface and the water-ice mixed cloud reach 0°C, additional heat transfer can take place without additional temperature change due to the potential phase change at the ice-substrate interface resulting from ambient airflow. The ice layer heat balance relies on the

<figure><img src="image_16.png" /><figcaption>**Fig. 13.** Exemplary temporal accretion and leading edge temperature developments in a) mixed-phase conditions at positive $T_{wb}$ with an unheated airfoil [Params.: $T_{wb} = 2.5$°C, $U = 20$ ms$^{-1}$, IWC = 4.1 g$^{-3}$, $q = 0$ W cm$^{-2}$] and b) glaciated conditions at negative $T_{wb}$ with a heated airfoil [Params.: $T_{wb} = -10$°C, $U = 20$ ms$^{-1}$, IWC = 5.4 g$^{-3}$, $q = 0.88$ W cm$^{-2}$].</figcaption></figure>
melting ratio of the icing cloud and on the ambient temperature of the air, which do not change. At positive $T_{wb}$, the water-ice layer becomes more glaciated after the substrate transferred all its heat (heat conduction) to the water-ice layer. Previous studies also showed that at negative $T_{wb}$, the water-ice layer becomes more wet as the mixed water-ice cloud transfers heat (enthalpy of freezing) to the surface until it reaches 0°C.

If the surface is heated, the water-ice layer will also reach the phase change temperature of 0°C, but contrary to the non-heated case, heat continues to be transferred to the water-ice layer. This additional heat generates a temperature gradient in the water-ice layer. When ice starts accreting, the ice layer insulates the surface from incoming ice particles and cold air, similar to the shield used before starting the cloud. Due to the constant heat flux from the substrate or in cases with positive wet bulb temperature in non-heated cases due to warm airflow, the majority of the ice in contact with the substrate melts and ultimately the substrate temperature rises to an equilibrium/steady-state temperature above 0°C as can be seen in Fig. 13 where the surface temperature hovers at around 1°C even though the ice layer has already accreted on the surface.

Therefore, heated test cases do not always show a perfectly flat temperature equilibrium curve, because the substrate temperature depends on a delicate thermodynamic equilibrium, on the airspeed, and on the accretion/shedding ice mass balance on the airfoil.

### 3.2.1.1. Variation of the surface temperature.
Fig. 14 (a) shows the equilibrium temperature at the leading edge plotted against the heat flux. The results are color and size mapped for a range of IWC. All test cases considered in this plot reached the equilibrium temperature at some time, from which point onward ice accretion could start.

Increasing the heat flux from 0 to 1.2 W cm⁻² creates a nearly linear increase of the surface temperature from approx. 0.5°C to approx. 2.5°C. On heated surfaces, the equilibrium temperature is always larger than on unheated surfaces, even accounting for the latent heat of crystallization released by supercooled melt water. The melt ratio close to the surface increases until only liquid water is available. This liquid layer is then heated to a temperature above the melting phase change temperature and even for small heat fluxes at equilibrium the temperature of the water layer at the surface is always >0°C and no ice is present immediately next to the surface. This is in line with the recent findings on ice crystal accretion inception on heated surface by Malik et al. (Malik et al., 2023).

The equilibrium temperature takes different values for the same heat flux (Fig. 14), since it depends on a set of experimental parameters. The IWC color mapping for heat fluxes between 0 and approx. 0.6 W cm⁻²

reveals that for the tests run at higher IWC the temperatures tend to lie on the lower end of the data cloud. We conclude that in this range of heat fluxes, larger IWC tend to cool the surface more strongly due to an increased mass of glaciated ice crystals. For a constant heat flux this leads to a thinner liquid layer and to a lower melt ratio in the water-ice layer. This trend seems to be lost for heat fluxes approx. >0.6 W cm⁻², where the supplied heat seems to be sufficient to melt all ice crystals, independently of the IWC used in our study. More test data points are needed, though, to confirm this observation.

Fig. 14 (b) shows the equilibrium temperature plotted vs. the heat flux, this time color-mapped is for the largest accreted area. A trend similar to that for IWC is observed here and the data points of the larger ice accretions roughly condense on the lower end of the data cloud. The above observations hold only in the range of heat fluxes used here, from low to moderate values. For larger heat fluxes, the melting rate of ice crystals is such that we observed always complete runback and no ice could accrete on the heated surfaces. It is important to point out here that the higher end of the plots with larger surface temperature corresponds to the cases with positive wet bulb temperature as the probability of melt water generation in those cases is higher due to the combined influence of melt water generated from the heat transfer between substrate and ice crystals as well as natural melting of ice layer due to warm airflow which makes the ice layers more prone to growth as well as shedding.

The melt water at the interface controls the probability of ice shedding events. Thick water layers favor a detachment of the ice layer from the heated surface. This threshold for the onset of shedding was modelled for non-heated surfaces by Kintea et al. (Kintea et al., 2016c).

### 3.2.1.2. Coupling effects of heat flux with influential parameters.
Fig. 15 (a) illustrates the maximum accreted area plotted vs. the heat flux for a range of airspeed at negative $T_{wb}$. The maximum ice accretion decreases for increasing airspeed. Within each airspeed field (differently colored dots) ice accretions tends to grow with increasing heat flux. This can be rationalized by the enhanced amount of heat transfer and potentially mass transport of melt water from the substrate interface to the outermost ice layer surface. This, in turn, increases the sticking efficiency of the incoming ice crystals and allows more ice to grow.

Fig. 15 (b) shows the results for positive $T_{wb}$. Contrary to negative $T_{wb}$, the maximum accreted area decreases with increasing heat flux which stems from a critical heat flux beyond which the tendency is inverted (i.e. plateau like behavior). This is due to the coupled influence of $T_{wb}$ and heat transfer from the surface. On non-heated surfaces, ice accretion depends only on the natural melting of the ice crystals before

<figure><img src="image_17.png" /><figcaption>**Fig. 14.** Surface temperature vs. heat flux for all heated and non-heated surfaces at negative and positive $T_{wb}$. a) Color- and size-mapped by IWC and b) Color- and size-mapped by largest accreted area. The angle of attack of all tests was 0° and the cloud consisted solely of glaciated ice crystals, which might have partially melted on the way to the surface.</figcaption></figure>
melting ratio of the icing cloud and on the ambient temperature of the air, which do not change. At positive $T_{wb}$, the water-ice layer becomes more glaciated after the substrate transferred all its heat (heat conduction) to the water-ice layer. Previous studies also showed that at negative $T_{wb}$, the water-ice layer becomes more wet as the mixed water-ice cloud transfers heat (enthalpy of freezing) to the surface until it reaches 0°C.

If the surface is heated, the water-ice layer will also reach the phase change temperature of 0°C, but contrary to the non-heated case, heat continues to be transferred to the water-ice layer. This additional heat generates a temperature gradient in the water-ice layer. When ice starts accreting, the ice layer insulates the surface from incoming ice particles and cold air, similar to the shield used before starting the cloud. Due to the constant heat flux from the substrate or in cases with positive wet bulb temperature in non-heated cases due to warm airflow, the majority of the ice in contact with the substrate melts and ultimately the substrate temperature rises to an equilibrium/steady-state temperature above 0°C as can be seen in Fig. 13 where the surface temperature hovers at around 1°C even though the ice layer has already accreted on the surface.

Therefore, heated test cases do not always show a perfectly flat temperature equilibrium curve, because the substrate temperature depends on a delicate thermodynamic equilibrium, on the airspeed, and on the accretion/shedding ice mass balance on the airfoil.

### 3.2.1.1. Variation of the surface temperature.
Fig. 14 (a) shows the equilibrium temperature at the leading edge plotted against the heat flux. The results are color and size mapped for a range of IWC. All test cases considered in this plot reached the equilibrium temperature at some time, from which point onward ice accretion could start.

Increasing the heat flux from 0 to 1.2 W cm⁻² creates a nearly linear increase of the surface temperature from approx. 0.5°C to approx. 2.5°C. On heated surfaces, the equilibrium temperature is always larger than on unheated surfaces, even accounting for the latent heat of crystallization released by supercooled melt water. The melt ratio close to the surface increases until only liquid water is available. This liquid layer is then heated to a temperature above the melting phase change temperature and even for small heat fluxes at equilibrium the temperature of the water layer at the surface is always >0°C and no ice is present immediately next to the surface. This is in line with the recent findings on ice crystal accretion inception on heated surface by Malik et al. (Malik et al., 2023).

The equilibrium temperature takes different values for the same heat flux (Fig. 14), since it depends on a set of experimental parameters. The IWC color mapping for heat fluxes between 0 and approx. 0.6 W cm⁻²

reveals that for the tests run at higher IWC the temperatures tend to lie on the lower end of the data cloud. We conclude that in this range of heat fluxes, larger IWC tend to cool the surface more strongly due to an increased mass of glaciated ice crystals. For a constant heat flux this leads to a thinner liquid layer and to a lower melt ratio in the water-ice layer. This trend seems to be lost for heat fluxes approx. >0.6 W cm⁻², where the supplied heat seems to be sufficient to melt all ice crystals, independently of the IWC used in our study. More test data points are needed, though, to confirm this observation.

Fig. 14 (b) shows the equilibrium temperature plotted vs. the heat flux, this time color-mapped is for the largest accreted area. A trend similar to that for IWC is observed here and the data points of the larger ice accretions roughly condense on the lower end of the data cloud. The above observations hold only in the range of heat fluxes used here, from low to moderate values. For larger heat fluxes, the melting rate of ice crystals is such that we observed always complete runback and no ice could accrete on the heated surfaces. It is important to point out here that the higher end of the plots with larger surface temperature corresponds to the cases with positive wet bulb temperature as the probability of melt water generation in those cases is higher due to the combined influence of melt water generated from the heat transfer between substrate and ice crystals as well as natural melting of ice layer due to warm airflow which makes the ice layers more prone to growth as well as shedding.

The melt water at the interface controls the probability of ice shedding events. Thick water layers favor a detachment of the ice layer from the heated surface. This threshold for the onset of shedding was modelled for non-heated surfaces by Kintea et al. (Kintea et al., 2016c).

### 3.2.1.2. Coupling effects of heat flux with influential parameters.
Fig. 15 (a) illustrates the maximum accreted area plotted vs. the heat flux for a range of airspeed at negative $T_{wb}$. The maximum ice accretion decreases for increasing airspeed. Within each airspeed field (differently colored dots) ice accretions tends to grow with increasing heat flux. This can be rationalized by the enhanced amount of heat transfer and potentially mass transport of melt water from the substrate interface to the outermost ice layer surface. This, in turn, increases the sticking efficiency of the incoming ice crystals and allows more ice to grow.

Fig. 15 (b) shows the results for positive $T_{wb}$. Contrary to negative $T_{wb}$, the maximum accreted area decreases with increasing heat flux which stems from a critical heat flux beyond which the tendency is inverted (i.e. plateau like behavior). This is due to the coupled influence of $T_{wb}$ and heat transfer from the surface. On non-heated surfaces, ice accretion depends only on the natural melting of the ice crystals before

<figure><img src="image_17.png" /><figcaption>**Fig. 14.** Surface temperature vs. heat flux for all heated and non-heated surfaces at negative and positive $T_{wb}$. a) Color- and size-mapped by IWC and b) Color- and size-mapped by largest accreted area. The angle of attack of all tests was 0° and the cloud consisted solely of glaciated ice crystals, which might have partially melted on the way to the surface.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 15.** Heat flux vs. largest accreted area for all heated and non-heated surfaces at negative (a) and positive (b) T<sub>wb</sub>. The angle of attack of all tests was 0° and the cloud consisted solely of glaciated ice crystals, which might have partially melted on the way to the surface.</figcaption></figure>

the impact, so that the melt ratio of the water-ice layer is favorable for ice accretion, but high airspeed keeps the accreted area small due to cyclic shedding. Increasing the heat flux increases the melt ratio of the water-ice layer, which becomes more slushy and more mobile and keeps ice accretions small. For the largest heat fluxes, the water-ice layer melt ratio reaches unity and only runback water is observed.

Fig. 16-1 shows the ratio of the total lost area and the total accreted area plotted against the heat flux with a color mapping for airspeed. At negative T<sub>wb</sub>, the ice detaching from the surface has a larger area for higher airspeed across the whole range of heat fluxes. For lower

airspeed, increasing the heat flux leads to decreasing the shed area, which means that ice accretions have a high coherence and a high adhesion to the surface.

At positive T<sub>wb</sub>, the slushy nature of the accreted ice layer leads to higher probability of complete detachment. The aerodynamic force required to overcome cohesive and adhesive forces is significantly lower than at negative T<sub>wb</sub>. This graph can be considered complementary to Fig. 15 (b): ice can detach only where it has previously accreted. Heat flux does not seem to have an influence on the detached ice mass in relation to the accreted ice mass in the range of the test conditions used,

<figure><img src="image_19.png" /><figcaption>**Fig. 16.** 1) Ratio of total lost area and total accreted area vs. heat flux for all heated and non-heated surfaces at negative (a) and positive (b) T<sub>wb</sub>. 2) Ratio of total shed area and total lost area vs. heat flux for all heated and non-heated surfaces at negative (a) and positive (b) T<sub>wb</sub>. The plots are color- and size-mapped by the airspeed. The angle of attack of all tests was 0° and the cloud consisted solely of glaciated ice crystals, which might have partially melted on the way to the surface.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 15.** Heat flux vs. largest accreted area for all heated and non-heated surfaces at negative (a) and positive (b) $T_{wb}$. The angle of attack of all tests was 0° and the cloud consisted solely of glaciated ice crystals, which might have partially melted on the way to the surface.</figcaption></figure>

the impact, so that the melt ratio of the water-ice layer is favorable for ice accretion, but high airspeed keeps the accreted area small due to cyclic shedding. Increasing the heat flux increases the melt ratio of the water-ice layer, which becomes more slushy and more mobile and keeps ice accretions small. For the largest heat fluxes, the water-ice layer melt ratio reaches unity and only runback water is observed.

Fig. 16-1 shows the ratio of the total lost area and the total accreted area plotted against the heat flux with a color mapping for airspeed. At negative $T_{wb}$, the ice detaching from the surface has a larger area for higher airspeed across the whole range of heat fluxes. For lower

airspeed, increasing the heat flux leads to decreasing the shed area, which means that ice accretions have a high coherence and a high adhesion to the surface.

At positive $T_{wb}$, the slushy nature of the accreted ice layer leads to higher probability of complete detachment. The aerodynamic force required to overcome cohesive and adhesive forces is significantly lower than at negative $T_{wb}$. This graph can be considered complementary to Fig. 15 (b): ice can detach only where it has previously accreted. Heat flux does not seem to have an influence on the detached ice mass in relation to the accreted ice mass in the range of the test conditions used,

<figure><img src="image_19.png" /><figcaption>**Fig. 16.** 1) Ratio of total lost area and total accreted area vs. heat flux for all heated and non-heated surfaces at negative (a) and positive (b) $T_{wb}$. 2) Ratio of total shed area and total lost area vs. heat flux for all heated and non-heated surfaces at negative (a) and positive (b) $T_{wb}$. The plots are color- and size-mapped by the airspeed. The angle of attack of all tests was 0° and the cloud consisted solely of glaciated ice crystals, which might have partially melted on the way to the surface.</figcaption></figure>
meaning that at any positive $T_{wb}$ any airspeed will cause the detachment of potentially accreted ice at some point.

Fig. 16-2 shows the ratio of the total shed area and the total lost area plotted against the heat flux with a color mapping for the airspeed. At negative $T_{wb}$, mildly heated surfaces experience less shedding and ice mass loss is dominated by erosion, melting, or sliding. An increasing heat flux shifts the mass loss mechanism to nearly complete shedding. At positive $T_{wb}$, the situation is complementary to the negative $T_{wb}$ case: if nearly all accretions already shed off on non-heated surfaces at all airspeed, the situation does not change upon increasing heat flux, apart from more generation of runback water.

### 3.2.2. Influence of wet bulb temperature

At positive $T_{wb}$, the natural melting of ice particles during flight leads to mixed-phase icing. We observed that wetting of the airfoil surface or of the outer surface of the ice layer led to the fast growth of slushy ice accretions over large airfoil areas due to the increased sticking efficiency of the ice crystals resulting from capillary force. This is in line with earlier research (Bucknell et al., 2018; Baumert et al., 2018; Struk et al., 2011; Currie et al., 2014a; Malik et al., 2022).

At negative $T_{wb}$, the ice crystals remain glaciated throughout the flight until they impinge on the surface. The conditions necessary to initiate ice accretion are dictated by the melt water produced at the interface due to the heat transfer between the heated surface and the ice crystals. The melt water layer first increases the sticking efficiency of ice crystals and then imbibes the forming porous ice layer at the outermost ice layer surface, further compacting it (Köbschall et al., 2021). Ice layers formed at negative $T_{wb}$ therefore have a stronger cohesion and adhesion to the surface compared with the slushy ice layers formed at positive $T_{wb}$ (Kintea et al., 2016b).

Contrary to the fast ice growth rates at positive $T_{wb}$ due to high wetness level at the outermost surface of the accreting ice layer, growth rates are slower at negative $T_{wb}$ - even when the surface is heated. In fact, the melt water at the outermost ice layer surface needs time to imbibe and transfer heat to/melt the porous ice layer formed by impacting ice crystals. Unless the ice layer is not fully imbibed and stabilized by water, the dry porous ice crystals structure is more prone to be eroded by other impacting ice crystals. With increasing ice layer thicknesses the heat balance at the outermost ice layer surface should change to a favorable full freezing and a stagnation of ice growth. Nevertheless, in some cases unlimited growth over the entire test time was observed. This could mean that the substrate heat was not yet dominated by the incoming ice particle cooling and even at larger ice layer thicknesses of several millimeters the ice layer could be regarded as quasi one dimensional in

terms of heat distribution.

Fig. 17 (left) shows that for increasing $T_{wb}$ the largest overall accreted area also increased.

Similar to accretion, shedding shows a similar trend for increasing $T_{wb}$ (Fig. 17 (right)). Glaciated ice layers formed at negative $T_{wb}$ strongly adhere to the surface and are less prone to shedding. Ice layers formed on heated surfaces are strongly cohesive. They shed off the surface only by a combination of interfacial water film formed by heating and increasing aerodynamic force exerted on the growing ice layers.

The results thus show that the ice accretion and shedding process in fully glaciated conditions at negative $T_{wb}$ is different from the one in mixed-phase conditions at positive $T_{wb}$ which is why they are separately analyzed.

### 3.2.3. Influence of airspeed

Before the statistical influence of the airspeed is investigated, a visual aid is given in Fig. 18 to identify the qualitative differences in ice accretion “slushiness” and shapes. Four side view ice accretion cross section tracings at the respective largest ice accretion are illustrated. The two pairs of tracings have similar conditions respectively and each show two superposed ice accretions, one at an airspeed of $20 \text{ ms}^{-1}$ and the other at $40 \text{ ms}^{-1}$. It must be noted that the chosen ice accretion tracings do not represent the full envelope of test condition combinations. Nevertheless, for the respective conditions several observations can be made. At wet bulb temperatures above freezing and without substrate heating the ice accretion is very limited. Lower airspeeds lead to larger ice accretions. The shape seems to stay similar. At wet bulb temperatures below freezing and with a controlled substrate heat flux the ice accretion is generally larger and more irregular. As in the other case, larger airspeeds lead to a reduced ice accretion, but the shape seems to be more complex than at low airspeeds as the ice seems to wander in multiple directions. It was observed that for larger airspeeds the ice accretion moves more dynamically on the airfoil. Furthermore, as can be seen in Fig. 18 uniform ice accretion was observed that spanned the heated leading edge of the airfoil as perceived from the oblique perspective for positive and negative wet bulb temperatures and for low and moderate airspeeds alike.

The influence of the airspeed on the largest accreted area is shown in Fig. 19. For all $T_{wb}$, an increasing airspeed leads to decreasing largest accreted areas. At a low airspeed, ice accretions are extensive with highly irregular mushroom like shapes. At a larger airspeed, ice accretions are smaller and form conical shapes, as reported also in other studies (Baumert et al., 2018; Malik et al., 2022).

The trajectories of the ice particles (primary impacts and rebounds)

<figure><img src="image_20.png" /><figcaption>Fig. 17. Largest accreted area (left) and largest shed area (right) plotted against $T_{wb}$ for the three test campaigns for all heated and unheated cases. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>
meaning that at any positive $T_{wb}$ any airspeed will cause the detachment of potentially accreted ice at some point.

Fig. 16-2 shows the ratio of the total shed area and the total lost area plotted against the heat flux with a color mapping for the airspeed. At negative $T_{wb}$, mildly heated surfaces experience less shedding and ice mass loss is dominated by erosion, melting, or sliding. An increasing heat flux shifts the mass loss mechanism to nearly complete shedding. At positive $T_{wb}$, the situation is complementary to the negative $T_{wb}$ case: if nearly all accretions already shed off on non-heated surfaces at all airspeed, the situation does not change upon increasing heat flux, apart from more generation of runback water.

### 3.2.2. Influence of wet bulb temperature

At positive $T_{wb}$, the natural melting of ice particles during flight leads to mixed-phase icing. We observed that wetting of the airfoil surface or of the outer surface of the ice layer led to the fast growth of slushy ice accretions over large airfoil areas due to the increased sticking efficiency of the ice crystals resulting from capillary force. This is in line with earlier research (Bucknell et al., 2018; Baumert et al., 2018; Struk et al., 2011; Currie et al., 2014a; Malik et al., 2022).

At negative $T_{wb}$, the ice crystals remain glaciated throughout the flight until they impinge on the surface. The conditions necessary to initiate ice accretion are dictated by the melt water produced at the interface due to the heat transfer between the heated surface and the ice crystals. The melt water layer first increases the sticking efficiency of ice crystals and then imbibes the forming porous ice layer at the outermost ice layer surface, further compacting it (Köbschall et al., 2021). Ice layers formed at negative $T_{wb}$ therefore have a stronger cohesion and adhesion to the surface compared with the slushy ice layers formed at positive $T_{wb}$ (Kintea et al., 2016b).

Contrary to the fast ice growth rates at positive $T_{wb}$ due to high wetness level at the outermost surface of the accreting ice layer, growth rates are slower at negative $T_{wb}$ - even when the surface is heated. In fact, the melt water at the outermost ice layer surface needs time to imbibe and transfer heat to/melt the porous ice layer formed by impacting ice crystals. Unless the ice layer is not fully imbibed and stabilized by water, the dry porous ice crystals structure is more prone to be eroded by other impacting ice crystals. With increasing ice layer thicknesses the heat balance at the outermost ice layer surface should change to a favorable full freezing and a stagnation of ice growth. Nevertheless, in some cases unlimited growth over the entire test time was observed. This could mean that the substrate heat was not yet dominated by the incoming ice particle cooling and even at larger ice layer thicknesses of several millimeters the ice layer could be regarded as quasi one dimensional in

terms of heat distribution.

Fig. 17 (left) shows that for increasing $T_{wb}$ the largest overall accreted area also increased.

Similar to accretion, shedding shows a similar trend for increasing $T_{wb}$ (Fig. 17 (right)). Glaciated ice layers formed at negative $T_{wb}$ strongly adhere to the surface and are less prone to shedding. Ice layers formed on heated surfaces are strongly cohesive. They shed off the surface only by a combination of interfacial water film formed by heating and increasing aerodynamic force exerted on the growing ice layers.

The results thus show that the ice accretion and shedding process in fully glaciated conditions at negative $T_{wb}$ is different from the one in mixed-phase conditions at positive $T_{wb}$ which is why they are separately analyzed.

### 3.2.3. Influence of airspeed

Before the statistical influence of the airspeed is investigated, a visual aid is given in Fig. 18 to identify the qualitative differences in ice accretion “slushiness” and shapes. Four side view ice accretion cross section tracings at the respective largest ice accretion are illustrated. The two pairs of tracings have similar conditions respectively and each show two superposed ice accretions, one at an airspeed of $20 \text{ ms}^{-1}$ and the other at $40 \text{ ms}^{-1}$. It must be noted that the chosen ice accretion tracings do not represent the full envelope of test condition combinations. Nevertheless, for the respective conditions several observations can be made. At wet bulb temperatures above freezing and without substrate heating the ice accretion is very limited. Lower airspeeds lead to larger ice accretions. The shape seems to stay similar. At wet bulb temperatures below freezing and with a controlled substrate heat flux the ice accretion is generally larger and more irregular. As in the other case, larger airspeeds lead to a reduced ice accretion, but the shape seems to be more complex than at low airspeeds as the ice seems to wander in multiple directions. It was observed that for larger airspeeds the ice accretion moves more dynamically on the airfoil. Furthermore, as can be seen in Fig. 18 uniform ice accretion was observed that spanned the heated leading edge of the airfoil as perceived from the oblique perspective for positive and negative wet bulb temperatures and for low and moderate airspeeds alike.

The influence of the airspeed on the largest accreted area is shown in Fig. 19. For all $T_{wb}$, an increasing airspeed leads to decreasing largest accreted areas. At a low airspeed, ice accretions are extensive with highly irregular mushroom like shapes. At a larger airspeed, ice accretions are smaller and form conical shapes, as reported also in other studies (Baumert et al., 2018; Malik et al., 2022).

The trajectories of the ice particles (primary impacts and rebounds)

<figure><img src="image_20.png" /><figcaption>Fig. 17. Largest accreted area (left) and largest shed area (right) plotted against $T_{wb}$ for the three test campaigns for all heated and unheated cases. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>**Fig. 18.** Two sets of ice accretion tracings at different wet bulb temperatures, each with two airspeeds superposed (red area: $U = 20 \text{ ms}^{-1}$ and blue area: $U = 40 \text{ ms}^{-1}$), left: $T_{wb} > 0^{\circ}\text{C}$ [Params.: $T_{wb} = 2.5^{\circ}\text{C}$, IWC = $4 \text{ g}^{-3}$, $q = 0 \text{ W cm}^{-2}$], right: $T_{wb} < 0^{\circ}\text{C}$ [Params.: $T_{wb} = -10^{\circ}\text{C}$, IWC = $3.5 \text{ g}^{-3}$, $q = 0.57 \text{ W cm}^{-2}$]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

are partly responsible for the shape change of the ice layer, because they influence the balance between sticking efficiency and erosion. Whereas erosion is minimal for normal particle impacts on an ice layer, sticking efficiency is maximum. When particles impact at shallower angles, erosion dominates over sticking efficiency (Kott et al., 2020; Charton et al., 2020).

Upon the impact of ice crystals, the airspeed influences the transport of liquid water formed as a result of melting and the motion of accreted ice on the airfoil. The melt water at and around the leading edge decreases in size with an increasing airspeed. The higher airspeed results in stronger splashing and particle fragmentation, as well as larger aerodynamic drag carrying away large amounts of liquid water. As a consequence, the water layer on the surface becomes thinner and the sticking efficiency is reduced. Similarly, also the water film on top of the ice layer is thinner and incoming ice crystals stick less leading to reduced accreted areas.

The largest shed area as a function of airspeed shows a similar trend, Fig. 19 (right). In fact, since accretions reduce in size with increasing airspeed and only accreted ice can shed off, shed ice pieces also reduce in size.

In 3.1.2 we showed that at positive $T_{wb}$ the shed areas of slushy ice are generally larger than the shed areas of glaciated ice at negative $T_{wb}$. Accretion and shedding plots in Fig. 19 (bottom) permits drawing a similar conclusion. Almost all ice accretions above a few hundred square micrometers shed off in one piece and thus both the accreted (left plot) and shed (right plot) areas share similar distributions around the visual guidelines.

At negative $T_{wb}$, shedding events were more rare and data points are distributed close to the x-axis.

### 3.2.4. Influence of ice water content

The IWC determines the amount of glaciated ice particles impacting on the surface (Köbschall et al., 2021). To study the influence of IWC we

keep the airspeed constant. At negative $T_{wb}$ (Fig. 20), the overall largest accreted area initially increases with increasing IWC, and then drops again for high values of IWC. This indicates that a critical IWC seems to exist, where ice accretion is maximum. The water-ice composition of the ice layer is the driver for this phenomenon. An increasing heat flux increases the water content in the ice layer. For increasing IWC on a heated surface, the melting ratio balance of the water-ice layer changes from a purely liquid water layer to a mixed layer, which favors ice accretion until reaching a maximum. Further increasing IWC moves the balance to a fully glaciated layer, which is characterized by a low sticking efficiency and is prone to be eroded by incoming ice crystals (Karpen et al., 2022; Malik et al., 2022). Shed areas are overall smaller than accreted areas, which can be explained by the stronger adhesion and cohesion of the ice layer.

At Airbus CRT, the accretion (and thus shedding) is limited due to higher flow velocities with a dominant influence of aerodynamic stresses and erosion. Moreover, for positive $T_{wb}$, the scatter around IWC of $4 \text{ g}/\text{m}^3$ results from the different heating powers of some of the cases leading to a larger maximum accreted area or lack thereof. Further, accreted and shed areas are similar in both graphs which suggests that in most cases all ice shed off. This underlines the trend seen in Fig. 9 b). Due to the natural melting of ice crystals at the outermost surface of the ice layer the largest accreted and shed area are expected to show a growing trend. However, more data points would be required to explicitly draw a clear trend for the influence of the ice water content. The described trends are similar for the small and the large NACA0012 airfoils.

### 3.2.5. Comparability to real engine conditions

Compared to ice crystal icing in engines with accretion happening at impact speeds up to $200 \text{ ms}^{-1}$, the observed erosion in the experiments might be too dominant as the results of this study drop off at $60 \text{ ms}^{-1}$ as shown in section 3.1.2. This emphasizes the sensitivity of the ice accretion to a variation of the median ice crystal sizes and in turn that in real ice crystal icing events the MVD therefore must be much smaller than $100 \text{ µm}$, and/or that the standard deviation of the size distribution is much tighter than in the experiments. In fact, other studies showed that the MVD could be as small as $30 \text{ µm}$ after passing through several fragmentation stages inside the engine and before sticking to thw walls inside the low pressure compressor. Smaller particles can lead to higher sticking efficiency promoting ice accretion growth.

While the ice particles generated at the TUBS facility represent atmospheric particles, the ACRT ice particles are ground down once during the collection in the chest freezer. Both ice particle types do not represent the particles which would be apparent at the impact location in the low pressure compressor, in size and shape. Apart from the smaller sizes, the real particles are more round as they are fragmented multiple times prior to their sticking. Nevertheless, studies found that the shape does not necessarily alter the ice accretion behaviors significantly due to the stochastic mechanisms of the impact (Hauk et al., 2015; Reitter et al., 2021; Karpen et al., 2021).

Increasing altitude (or decreasing ambient pressure) promotes evaporation and therefore leads to a reduction in $T_{wb}$ for a given level of air temperature and relative humidity. Therefore, for a comparison of a ground test with an altitude test the $T_{wb}$ is critical. Furthermore, at a constant airspeed, increasing altitude leads to decreasing aerodynamic force, and will therefore tend to reduce the frequency of ice shedding. In order to be more comparable to altitude tests this force should be kept constant by setting a similar dynamic pressure and therefore decreasing the airspeed. However, decreasing the airspeed will lead to a decrease in the ice crystal mass flux and thus the rate of erosion. To compensate for these two phenomena, the TWC and the ice crystal diameter could be increased. Finally, even though potential parameter variations for a comparison with altitude tests are qualitatively given, defining exact scaling rules is very difficult.
<figure><img src="image_21.png" /><figcaption>**Fig. 18.** Two sets of ice accretion tracings at different wet bulb temperatures, each with two airspeeds superposed (red area: $U = 20 \text{ ms}^{-1}$ and blue area: $U = 40 \text{ ms}^{-1}$), left: $T_{wb} > 0^{\circ}\text{C}$ [Params.: $T_{wb} = 2.5^{\circ}\text{C}$, IWC = $4 \text{ g}^{-3}$, $q = 0 \text{ W cm}^{-2}$], right: $T_{wb} < 0^{\circ}\text{C}$ [Params.: $T_{wb} = -10^{\circ}\text{C}$, IWC = $3.5 \text{ g}^{-3}$, $q = 0.57 \text{ W cm}^{-2}$]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

are partly responsible for the shape change of the ice layer, because they influence the balance between sticking efficiency and erosion. Whereas erosion is minimal for normal particle impacts on an ice layer, sticking efficiency is maximum. When particles impact at shallower angles, erosion dominates over sticking efficiency (Kott et al., 2020; Charton et al., 2020).

Upon the impact of ice crystals, the airspeed influences the transport of liquid water formed as a result of melting and the motion of accreted ice on the airfoil. The melt water at and around the leading edge decreases in size with an increasing airspeed. The higher airspeed results in stronger splashing and particle fragmentation, as well as larger aerodynamic drag carrying away large amounts of liquid water. As a consequence, the water layer on the surface becomes thinner and the sticking efficiency is reduced. Similarly, also the water film on top of the ice layer is thinner and incoming ice crystals stick less leading to reduced accreted areas.

The largest shed area as a function of airspeed shows a similar trend, Fig. 19 (right). In fact, since accretions reduce in size with increasing airspeed and only accreted ice can shed off, shed ice pieces also reduce in size.

In 3.1.2 we showed that at positive $T_{wb}$ the shed areas of slushy ice are generally larger than the shed areas of glaciated ice at negative $T_{wb}$. Accretion and shedding plots in Fig. 19 (bottom) permits drawing a similar conclusion. Almost all ice accretions above a few hundred square micrometers shed off in one piece and thus both the accreted (left plot) and shed (right plot) areas share similar distributions around the visual guidelines.

At negative $T_{wb}$, shedding events were more rare and data points are distributed close to the x-axis.

### 3.2.4. Influence of ice water content

The IWC determines the amount of glaciated ice particles impacting on the surface (Köbschall et al., 2021). To study the influence of IWC we

keep the airspeed constant. At negative $T_{wb}$ (Fig. 20), the overall largest accreted area initially increases with increasing IWC, and then drops again for high values of IWC. This indicates that a critical IWC seems to exist, where ice accretion is maximum. The water-ice composition of the ice layer is the driver for this phenomenon. An increasing heat flux increases the water content in the ice layer. For increasing IWC on a heated surface, the melting ratio balance of the water-ice layer changes from a purely liquid water layer to a mixed layer, which favors ice accretion until reaching a maximum. Further increasing IWC moves the balance to a fully glaciated layer, which is characterized by a low sticking efficiency and is prone to be eroded by incoming ice crystals (Karpen et al., 2022; Malik et al., 2022). Shed areas are overall smaller than accreted areas, which can be explained by the stronger adhesion and cohesion of the ice layer.

At Airbus CRT, the accretion (and thus shedding) is limited due to higher flow velocities with a dominant influence of aerodynamic stresses and erosion. Moreover, for positive $T_{wb}$, the scatter around IWC of $4 \text{ g}/\text{m}^3$ results from the different heating powers of some of the cases leading to a larger maximum accreted area or lack thereof. Further, accreted and shed areas are similar in both graphs which suggests that in most cases all ice shed off. This underlines the trend seen in Fig. 9 b). Due to the natural melting of ice crystals at the outermost surface of the ice layer the largest accreted and shed area are expected to show a growing trend. However, more data points would be required to explicitly draw a clear trend for the influence of the ice water content. The described trends are similar for the small and the large NACA0012 airfoils.

### 3.2.5. Comparability to real engine conditions

Compared to ice crystal icing in engines with accretion happening at impact speeds up to $200 \text{ ms}^{-1}$, the observed erosion in the experiments might be too dominant as the results of this study drop off at $60 \text{ ms}^{-1}$ as shown in section 3.1.2. This emphasizes the sensitivity of the ice accretion to a variation of the median ice crystal sizes and in turn that in real ice crystal icing events the MVD therefore must be much smaller than $100 \text{ µm}$, and/or that the standard deviation of the size distribution is much tighter than in the experiments. In fact, other studies showed that the MVD could be as small as $30 \text{ µm}$ after passing through several fragmentation stages inside the engine and before sticking to thw walls inside the low pressure compressor. Smaller particles can lead to higher sticking efficiency promoting ice accretion growth.

While the ice particles generated at the TUBS facility represent atmospheric particles, the ACRT ice particles are ground down once during the collection in the chest freezer. Both ice particle types do not represent the particles which would be apparent at the impact location in the low pressure compressor, in size and shape. Apart from the smaller sizes, the real particles are more round as they are fragmented multiple times prior to their sticking. Nevertheless, studies found that the shape does not necessarily alter the ice accretion behaviors significantly due to the stochastic mechanisms of the impact (Hauk et al., 2015; Reitter et al., 2021; Karpen et al., 2021).

Increasing altitude (or decreasing ambient pressure) promotes evaporation and therefore leads to a reduction in $T_{wb}$ for a given level of air temperature and relative humidity. Therefore, for a comparison of a ground test with an altitude test the $T_{wb}$ is critical. Furthermore, at a constant airspeed, increasing altitude leads to decreasing aerodynamic force, and will therefore tend to reduce the frequency of ice shedding. In order to be more comparable to altitude tests this force should be kept constant by setting a similar dynamic pressure and therefore decreasing the airspeed. However, decreasing the airspeed will lead to a decrease in the ice crystal mass flux and thus the rate of erosion. To compensate for these two phenomena, the TWC and the ice crystal diameter could be increased. Finally, even though potential parameter variations for a comparison with altitude tests are qualitatively given, defining exact scaling rules is very difficult.
<figure><img src="image_22.png" /><figcaption>**Fig. 19.** Largest overall accreted area (left) and largest shed area (right) plotted versus the airspeed for the three test campaigns for all heated and unheated surfaces at negative (top) and positive (bottom) $T_{wb}$. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

The range of tested conditions does not fully cover real engine ice crystal icing conditions. The results obtained in this study therefore represent only part of the total image. One goal was to compare critical parameters in relation to other conditions and highlight the importance of cross interactions. These cross interactions will be observable throughout the entire possible range, and potentially play an even bigger role in the engine ice crystal conditions (larger airspeed, lower pressure).

The geometry of the impact surface and the boundary conditions upstream and downstream of the impact surface play an important role in the ice accretion and shedding process. Other studies (Fuleki et al., 2019) pursued a more realistic geometry to achieve the most realistic ice accretion and shedding possible including melt water / slushy ice run back, re-emitted and re-impacting fragments. However, separating and quantifying individual influences is then rendered more difficult. While with a NACA0012 model some of these important factors are lost, the quantification of the ice accretion and erosion caused by primary and measurable parameters is enabled. Similar methodologies were pursued by other studies (Currie and Fuleki, 2016). In a holistic view, all the known phenomena inside the compressor stages should be individually investigated with quantifiable in- and out-put parameters and later linked. The NACA0012 ice accretion and shedding experiments of this study are just one of these many individual phenomena tests.

The obtained data could be used to feed fundamental icing physics models. In combination with results of other studies models could inter- and extrapolate the currently untested ranges. Ideally, these ranges will be experimentally tested in the future with icing wind tunnels that overcome the limitations apparent in this study and elsewhere. Models

could also help to find scaling rules to better compare laboratory experiments with real engine icing conditions.

## 4. Main observations and conclusions

The analysis of the collected data from sensors and videos led to the definition of accretion and shedding parameters in order to characterize observations and to rationalise results. Ice crystal accretion and shedding phenomena on non-heated surfaces were investigated by prior studies and for a limited range of test parameters. This study agreed well with the previous findings and extended the parameter range. The investigations on heated surfaces constituted the most relevant novelty of this work.

A total of three test campaigns were carried out at Airbus CRT and TU Braunschweig with two NACA-0012 airfoils of different sizes, wherein the influence of governing parameters, namely airspeed, wet bulb temperature, icing water content, and heat power density on accretion and shedding process was investigated. A good agreement of the findings of the three campaigns with overlapping test parameters was observed. The results generally confirmed findings from past studies, taking into account the stochastic behavior of the ice accretion and shedding processes and the strong coupling effects of all test parameters.

* For negative $T_{wb}$, the necessary condition for the onset of ice accretion was heating of the surface. For the range of tested conditions we observed that upon increasing the airspeed the area covered by ice accretions decreased, leading in turn to less ice shed from the
<figure><img src="image_22.png" /><figcaption>**Fig. 19.** Largest overall accreted area (left) and largest shed area (right) plotted versus the airspeed for the three test campaigns for all heated and unheated surfaces at negative (top) and positive (bottom) $T_{wb}$. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

The range of tested conditions does not fully cover real engine ice crystal icing conditions. The results obtained in this study therefore represent only part of the total image. One goal was to compare critical parameters in relation to other conditions and highlight the importance of cross interactions. These cross interactions will be observable throughout the entire possible range, and potentially play an even bigger role in the engine ice crystal conditions (larger airspeed, lower pressure).

The geometry of the impact surface and the boundary conditions upstream and downstream of the impact surface play an important role in the ice accretion and shedding process. Other studies (Fuleki et al., 2019) pursued a more realistic geometry to achieve the most realistic ice accretion and shedding possible including melt water / slushy ice run back, re-emitted and re-impacting fragments. However, separating and quantifying individual influences is then rendered more difficult. While with a NACA0012 model some of these important factors are lost, the quantification of the ice accretion and erosion caused by primary and measurable parameters is enabled. Similar methodologies were pursued by other studies (Currie and Fuleki, 2016). In a holistic view, all the known phenomena inside the compressor stages should be individually investigated with quantifiable in- and out-put parameters and later linked. The NACA0012 ice accretion and shedding experiments of this study are just one of these many individual phenomena tests.

The obtained data could be used to feed fundamental icing physics models. In combination with results of other studies models could inter- and extrapolate the currently untested ranges. Ideally, these ranges will be experimentally tested in the future with icing wind tunnels that overcome the limitations apparent in this study and elsewhere. Models

could also help to find scaling rules to better compare laboratory experiments with real engine icing conditions.

## 4. Main observations and conclusions

The analysis of the collected data from sensors and videos led to the definition of accretion and shedding parameters in order to characterize observations and to rationalise results. Ice crystal accretion and shedding phenomena on non-heated surfaces were investigated by prior studies and for a limited range of test parameters. This study agreed well with the previous findings and extended the parameter range. The investigations on heated surfaces constituted the most relevant novelty of this work.

A total of three test campaigns were carried out at Airbus CRT and TU Braunschweig with two NACA-0012 airfoils of different sizes, wherein the influence of governing parameters, namely airspeed, wet bulb temperature, icing water content, and heat power density on accretion and shedding process was investigated. A good agreement of the findings of the three campaigns with overlapping test parameters was observed. The results generally confirmed findings from past studies, taking into account the stochastic behavior of the ice accretion and shedding processes and the strong coupling effects of all test parameters.

* For negative $T_{wb}$, the necessary condition for the onset of ice accretion was heating of the surface. For the range of tested conditions we observed that upon increasing the airspeed the area covered by ice accretions decreased, leading in turn to less ice shed from the
<figure><img src="image_23.png" /><figcaption>**Fig. 20.** Largest overall accreted area (left) and largest shed area (right) plotted versus IWC for the three test campaigns for all heated and unheated cases at negative (top) and positive (bottom) $T_{wb}$. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

substrate. Increasing the surface heat flux led to the formation of larger accreted and shed areas, while

* for positive $T_{wb}$ large ice accretions were primarily driven by natural melting of the ice crystals during flight or after impact. For a given TWC, increasing the airspeed led to higher shedding frequency due to increasing aerodynamic loads, since the accreted ice layers were slushy in consistence and thus with lower cohesion and adhesion strength to the surface. Upon additionally heating the surface, the accretion efficiency dropped with small ice pockets observed for moderate heat flux cases and runback water formed at high heat fluxes.

* At positive $T_{wb}$, larger surface heat fluxes led to less shedding, but increased melting, sliding and erosion processes.

* At negative $T_{wb}$, larger surface heat fluxes led to more frequent ice shedding due to increased surface temperatures, leading to higher melt ratios of the water-ice layer.

* Increasing IWC led to a lower surface temperature. Further, the ice accretion and shed area increased with the IWC until the IWC became too large resulting in lower sticking efficiency and a thus decreased accretion and shed area.

* At negative $T_{wb}$ and airspeed between 20 and 40 m/s, increasing airspeed led to more frequent shedding. Shedding or mass loss of ice further increased at higher airspeed until 80 m/s, mainly due to increasing erosion and aerodynamic loads.

* For all experimental conditions tested in this work, a critical ice accretion area threshold (a few hundred square millimeters) was identified beyond which ice either started accreting continuously or

shed off completely. Further testing and modeling is required to better understand this critical parameter.

* For all experimental conditions tested in this work, larger ice accretions had a stronger tendency to shed as one piece, while smaller ice accretions were more efficiently removed by melting, sliding, or erosion.

From qualitative observation of experimental runs two shedding regimes were identified namely continuous and cyclic shedding regime. For cases with high liquid fraction (i.e. mainly for $T_{wb} > 0$) continuous shedding regime was identified which resulted from the runback of a mixed phase film composed of both liquid water and ice crystals. On the other hand, for cases with low to intermediate liquid fraction (i.e. mainly for $T_{wb} < 0$ with substrate heating) cyclic shedding regime was observed resulting in cyclic shedding of ice blocks due to aerodynamic forces superseding the adhesive forces.

The three test campaigns in the two facilities showed only a few minor disagreements and can otherwise be taken as a statement of universality. This study showed that investigations of ice crystal accretion and shedding in different facilities and over the course of several studies, although of significant stochastic nature, have specific underlying regularities. An attempt was made to quantify these, but future work must be done to correlate them further. The complexity of the problem is a major hurdle which could be tackled with more test cases and even more sophisticated detailed tests focused on single phenomena. Additionally, new experiments more closely simulating real conditions (in terms of particle size, airspeed, altitude) will be needed to confirm the physical mechanisms observed in this study.
<figure><img src="image_23.png" /><figcaption>**Fig. 20.** Largest overall accreted area (left) and largest shed area (right) plotted versus IWC for the three test campaigns for all heated and unheated cases at negative (top) and positive (bottom) $T_{wb}$. The angle of attack of all tests was 0° and the cloud consisted solely of ice crystals, which might have partially melted during flight depending on the respective test conditions. The dotted lines are visual guidelines without physical relevance.</figcaption></figure>

substrate. Increasing the surface heat flux led to the formation of larger accreted and shed areas, while

* for positive $T_{wb}$ large ice accretions were primarily driven by natural melting of the ice crystals during flight or after impact. For a given TWC, increasing the airspeed led to higher shedding frequency due to increasing aerodynamic loads, since the accreted ice layers were slushy in consistence and thus with lower cohesion and adhesion strength to the surface. Upon additionally heating the surface, the accretion efficiency dropped with small ice pockets observed for moderate heat flux cases and runback water formed at high heat fluxes.

* At positive $T_{wb}$, larger surface heat fluxes led to less shedding, but increased melting, sliding and erosion processes.

* At negative $T_{wb}$, larger surface heat fluxes led to more frequent ice shedding due to increased surface temperatures, leading to higher melt ratios of the water-ice layer.

* Increasing IWC led to a lower surface temperature. Further, the ice accretion and shed area increased with the IWC until the IWC became too large resulting in lower sticking efficiency and a thus decreased accretion and shed area.

* At negative $T_{wb}$ and airspeed between 20 and 40 m/s, increasing airspeed led to more frequent shedding. Shedding or mass loss of ice further increased at higher airspeed until 80 m/s, mainly due to increasing erosion and aerodynamic loads.

* For all experimental conditions tested in this work, a critical ice accretion area threshold (a few hundred square millimeters) was identified beyond which ice either started accreting continuously or

shed off completely. Further testing and modeling is required to better understand this critical parameter.

* For all experimental conditions tested in this work, larger ice accretions had a stronger tendency to shed as one piece, while smaller ice accretions were more efficiently removed by melting, sliding, or erosion.

From qualitative observation of experimental runs two shedding regimes were identified namely continuous and cyclic shedding regime. For cases with high liquid fraction (i.e. mainly for $T_{wb} > 0$) continuous shedding regime was identified which resulted from the runback of a mixed phase film composed of both liquid water and ice crystals. On the other hand, for cases with low to intermediate liquid fraction (i.e. mainly for $T_{wb} < 0$ with substrate heating) cyclic shedding regime was observed resulting in cyclic shedding of ice blocks due to aerodynamic forces superseding the adhesive forces.

The three test campaigns in the two facilities showed only a few minor disagreements and can otherwise be taken as a statement of universality. This study showed that investigations of ice crystal accretion and shedding in different facilities and over the course of several studies, although of significant stochastic nature, have specific underlying regularities. An attempt was made to quantify these, but future work must be done to correlate them further. The complexity of the problem is a major hurdle which could be tackled with more test cases and even more sophisticated detailed tests focused on single phenomena. Additionally, new experiments more closely simulating real conditions (in terms of particle size, airspeed, altitude) will be needed to confirm the physical mechanisms observed in this study.
Overall, the analyzed large dataset presented in this research work provides a sound basis for development of accurate accretion and robust shedding models.

### CRediT authorship contribution statement

**Yasir A. Malik:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization. **Norbert Karpen:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization. **Elmar Bonaccuro:** Conceptualization, Supervision, Methodology, Writing – review & editing, Funding acquisition. **Ilia Roisman:** Supervision. **Jeanette Hussong:** Supervision. **Philippe Villedieu:** Conceptualization, Methodology, Writing – review & editing, Project administration, Funding acquisition.

### Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests.

Yasir Malik reports financial support and travel were provided by European Union. Norbert Karpen reports financial support and travel

were provided by European Union. Elmar Bonaccuro reports financial support and travel were provided by European Union. Ilia Roisman reports financial support and travel were provided by European Union. Jeanette Hussong reports financial support and travel were provided by European Union. Philippe Villedieu reports financial support and travel were provided by European Union.

### Data availability

Data will be made available on request.

### Acknowledgments

The authors acknowledge the contribution of Rémy Huneke who helped with the experimental setups and with icing experiments conducted at TU Braunschweig. We would also like to acknowledge technical input from Stephan Sattler (TU Braunschweig), Thomas Bürger (ACRT) and Bodo Haffner (ACRT) for the design and the manufacturing of the test articles and experimental setups. Louis Reitter and Kilian Köbschall (TU Darmstadt) invaluably contributed with their skills during data processing and analysis.

This research work received funding from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No 767560.

## Appendix A. Characterisation of test article layers

<table><caption>Table A.3
Properties of the materials composing the heatable NACA0012 airfoil.</caption><thead><tr><td>Material</td><td>ρ [kg.m<sup>-3</sup>]</td><td>c<sub>p</sub> [J.kg<sup>-1</sup>.K<sup>-1</sup>]</td><td>λ [W.m<sup>-1</sup>.K<sup>-1</sup>]</td></tr></thead><tbody><tr><td>Aluminum</td><td>2700</td><td>900</td><td>237</td></tr><tr><td>Teflon</td><td>2200</td><td>1000</td><td>0.25</td></tr><tr><td>Thermally conductive adhesive</td><td>2500</td><td>900</td><td>5.8</td></tr><tr><td>Kapton heaters</td><td>2700</td><td>900</td><td>0.8</td></tr><tr><td>Multitherm insulation</td><td>2800</td><td>787</td><td>0.023</td></tr></tbody></table>

### References

Addy, J., Veres, J., 2011. An Overview of NASA Engine Ice-Crystal Icing Research. https://doi.org/10.4271/2011-38-0017.

Ayra, E.S., Sanz, Á.R., Valdés, R.A., Comendador, F.G., Cano, J., 2020. Detection and warning of ice crystals clogging pitot probes from total air temperature anomalies. Aerosp. Sci. Technol. 102, 105874.

Bansmer, S.E., Baumert, A., Sattler, S., Knop, I., Leroy, D., Schwarzenboeck, A., Jurkat-Witschas, T., Voigt, C., Pervier, H., Esposito, B., 2018. Design, construction and commissioning of the Braunschweig icing wind tunnel. Atmos. Meas. Tech. 11 (6), 3221–3249.

Bartkus, T., Tsao, J.-C., Struk, P., 2019. Analysis of Experimental Ice Accretion Data and Assessment of a Thermodynamic Model During Ice Crystal Icing. https://doi.org/10.4271/2019-01-2016.

Baumert, A., 2019. Experimental and Numerical Studies on Ice Crystal Icing of Civil Aircraft. Ph.D. thesis.

Baumert, A., Bansmer, S., Sattler, S., Pervier, H., Esposito, B., 2016. Simulating natural ice crystal cloud conditions for icing wind tunnel experiments-a review on the design, commissioning and calibration of the tu braunschweig ice crystal generation system. In: 8th AIAA Atmospheric and Space Environments Conference, p. 4053.

Baumert, A., Bansmer, S., Trontin, P., Villedieu, P., 2018. Experimental and numerical investigations on aircraft icing at mixed phase conditions. Int. J. Heat Mass Transf. 123 (08) https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.008.

Bucknell, A, McGilvray, M, Gillespie, DRH, Jones, G, Reed, A, Buttsworth, DR, 2017, June 26-30. Heat Transfer in the Core Compressor Under Ice Crystal Icing Conditions. In: Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. Volume 2D: Turbomachinery. Charlotte, North Carolina, USA, V02DT48A001. ASME. https://doi.org/10.1115/GT2017-63077.

Bucknell, A.J., McGilvray, M., Gillespie, D., Jones, G., Reed, A., Collier, B., 2018. Experimental studies of ice crystal accretion on an axisymmetric body at engine-realistic conditions. In: 2018 Atmospheric and Space Environments Conference, p. 4223. https://doi.org/10.2514/6.2018-4223.

Bucknell, A., McGilvray, M., Gillespie, D.R., Jones, G., Reed, A., Collier, B., 2020. Experimental studies of ice crystal accretion on axisymmetric bodies at aeroengine conditions. J. Propuls. Power 36 (6), 836–850.

Bucknell, A., McGilvray, M., Gillespie, D.R., Jones, G., Collier, B., 2021. A thermodynamic model for ice crystal accretion in aircraft engines: Emm-c. Int. J. Heat Mass Transf. 174, 121270. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121270.

Cao, Y., Tan, W., Wu, Z., 2018. Aircraft icing: an ongoing threat to aviation safety. Aerosp. Sci. Technol. 75, 353–385. https://doi.org/10.1016/j.ast.2017.12.028.

Charton, V., Senoner, J.-M., Trontin, P., Villedieu, P., 2020. Semi-Empirical Erosion Model with Particle Size and Liquid Water Content Effects for Ice Crystal Icing Simulations. https://doi.org/10.2514/6.2020-2827.

Currie, T.C., Fuleki, D., 2016. Experimental results for ice crystal icing on hemispherical and double wedge geometries at varying mach numbers and wet bulb temperatures. In: 8th AIAA Atmospheric and Space Environments Conference, p. 3740.

Currie, T., Struk, P., Tsao, J.-C., Fuleki, D., Knezevici, D., 2012a. Fundamental study of mixed-phase icing with application to ice crystal accretion in aircraft jet engines. In: 4th AIAA Atmospheric and Space Environments Conference, p. 3035. https://doi.org/10.2514/6.2012-3035.

Currie, T., Struk, P., Tsao, J.-C., Fuleki, D., Knezevici, D., 2012b. Fundamental study of mixed-phase icing with application to ice crystal accretion in aircraft jet engines. In: 4th AIAA Atmospheric and Space Environments Conference, p. 3035.

Currie, T.C., Fuleki, D., Knezevici, D.C., MacLeod, J.D., 2013. Altitude scaling of ice crystal accretion. In: 5th AIAA Atmospheric and Space Environments Conference, p. 2677.

Currie, T.C., Fuleki, D., Mahallati, A., 2014a. Experimental studies of mixed-phase sticking efficiency for ice crystal accretion in jet engines. In: 6th AIAA Atmospheric and Space Environments Conference, p. 3049. https://doi.org/10.2514/6.2014-3049.

Currie, T.C., Fuleki, D., Mahallati, A., 2014b. Experimental studies of mixed-phase sticking efficiency for ice crystal accretion in jet engines. In: 6th AIAA Atmospheric and Space Environments Conference, p. 3049.
Overall, the analyzed large dataset presented in this research work provides a sound basis for development of accurate accretion and robust shedding models.

### CRediT authorship contribution statement

**Yasir A. Malik:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization. **Norbert Karpen:** Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization. **Elmar Bonaccuro:** Conceptualization, Supervision, Methodology, Writing – review & editing, Funding acquisition. **Ilia Roisman:** Supervision. **Jeanette Hussong:** Supervision. **Philippe Villedieu:** Conceptualization, Methodology, Writing – review & editing, Project administration, Funding acquisition.

### Declaration of Competing Interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests.

Yasir Malik reports financial support and travel were provided by European Union. Norbert Karpen reports financial support and travel

were provided by European Union. Elmar Bonaccuro reports financial support and travel were provided by European Union. Ilia Roisman reports financial support and travel were provided by European Union. Jeanette Hussong reports financial support and travel were provided by European Union. Philippe Villedieu reports financial support and travel were provided by European Union.

### Data availability

Data will be made available on request.

### Acknowledgments

The authors acknowledge the contribution of Rémy Huneke who helped with the experimental setups and with icing experiments conducted at TU Braunschweig. We would also like to acknowledge technical input from Stephan Sattler (TU Braunschweig), Thomas Bürger (ACRT) and Bodo Haffner (ACRT) for the design and the manufacturing of the test articles and experimental setups. Louis Reitter and Kilian Köbschall (TU Darmstadt) invaluably contributed with their skills during data processing and analysis.

This research work received funding from the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No 767560.

## Appendix A. Characterisation of test article layers

<table><caption>Table A.3
Properties of the materials composing the heatable NACA0012 airfoil.</caption><thead><tr><td>Material</td><td>ρ [kg.m<sup>-3</sup>]</td><td>c<sub>p</sub> [J.kg<sup>-1</sup>.K<sup>-1</sup>]</td><td>λ [W.m<sup>-1</sup>.K<sup>-1</sup>]</td></tr></thead><tbody><tr><td>Aluminum</td><td>2700</td><td>900</td><td>237</td></tr><tr><td>Teflon</td><td>2200</td><td>1000</td><td>0.25</td></tr><tr><td>Thermally conductive adhesive</td><td>2500</td><td>900</td><td>5.8</td></tr><tr><td>Kapton heaters</td><td>2700</td><td>900</td><td>0.8</td></tr><tr><td>Multitherm insulation</td><td>2800</td><td>787</td><td>0.023</td></tr></tbody></table>

### References

Addy, J., Veres, J., 2011. An Overview of NASA Engine Ice-Crystal Icing Research. https://doi.org/10.4271/2011-38-0017.

Ayra, E.S., Sanz, Á.R., Valdés, R.A., Comendador, F.G., Cano, J., 2020. Detection and warning of ice crystals clogging pitot probes from total air temperature anomalies. Aerosp. Sci. Technol. 102, 105874.

Bansmer, S.E., Baumert, A., Sattler, S., Knop, I., Leroy, D., Schwarzenboeck, A., Jurkat-Witschas, T., Voigt, C., Pervier, H., Esposito, B., 2018. Design, construction and commissioning of the Braunschweig icing wind tunnel. Atmos. Meas. Tech. 11 (6), 3221–3249.

Bartkus, T., Tsao, J.-C., Struk, P., 2019. Analysis of Experimental Ice Accretion Data and Assessment of a Thermodynamic Model During Ice Crystal Icing. https://doi.org/10.4271/2019-01-2016.

Baumert, A., 2019. Experimental and Numerical Studies on Ice Crystal Icing of Civil Aircraft. Ph.D. thesis.

Baumert, A., Bansmer, S., Sattler, S., Pervier, H., Esposito, B., 2016. Simulating natural ice crystal cloud conditions for icing wind tunnel experiments-a review on the design, commissioning and calibration of the tu braunschweig ice crystal generation system. In: 8th AIAA Atmospheric and Space Environments Conference, p. 4053.

Baumert, A., Bansmer, S., Trontin, P., Villedieu, P., 2018. Experimental and numerical investigations on aircraft icing at mixed phase conditions. Int. J. Heat Mass Transf. 123 (08) https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.008.

Bucknell, A, McGilvray, M, Gillespie, DRH, Jones, G, Reed, A, Buttsworth, DR, 2017, June 26-30. Heat Transfer in the Core Compressor Under Ice Crystal Icing Conditions. In: Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. Volume 2D: Turbomachinery. Charlotte, North Carolina, USA, V02DT48A001. ASME. https://doi.org/10.1115/GT2017-63077.

Bucknell, A.J., McGilvray, M., Gillespie, D., Jones, G., Reed, A., Collier, B., 2018. Experimental studies of ice crystal accretion on an axisymmetric body at engine-realistic conditions. In: 2018 Atmospheric and Space Environments Conference, p. 4223. https://doi.org/10.2514/6.2018-4223.

Bucknell, A., McGilvray, M., Gillespie, D.R., Jones, G., Reed, A., Collier, B., 2020. Experimental studies of ice crystal accretion on axisymmetric bodies at aeroengine conditions. J. Propuls. Power 36 (6), 836–850.

Bucknell, A., McGilvray, M., Gillespie, D.R., Jones, G., Collier, B., 2021. A thermodynamic model for ice crystal accretion in aircraft engines: Emm-c. Int. J. Heat Mass Transf. 174, 121270. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121270.

Cao, Y., Tan, W., Wu, Z., 2018. Aircraft icing: an ongoing threat to aviation safety. Aerosp. Sci. Technol. 75, 353–385. https://doi.org/10.1016/j.ast.2017.12.028.

Charton, V., Senoner, J.-M., Trontin, P., Villedieu, P., 2020. Semi-Empirical Erosion Model with Particle Size and Liquid Water Content Effects for Ice Crystal Icing Simulations. https://doi.org/10.2514/6.2020-2827.

Currie, T.C., Fuleki, D., 2016. Experimental results for ice crystal icing on hemispherical and double wedge geometries at varying mach numbers and wet bulb temperatures. In: 8th AIAA Atmospheric and Space Environments Conference, p. 3740.

Currie, T., Struk, P., Tsao, J.-C., Fuleki, D., Knezevici, D., 2012a. Fundamental study of mixed-phase icing with application to ice crystal accretion in aircraft jet engines. In: 4th AIAA Atmospheric and Space Environments Conference, p. 3035. https://doi.org/10.2514/6.2012-3035.

Currie, T., Struk, P., Tsao, J.-C., Fuleki, D., Knezevici, D., 2012b. Fundamental study of mixed-phase icing with application to ice crystal accretion in aircraft jet engines. In: 4th AIAA Atmospheric and Space Environments Conference, p. 3035.

Currie, T.C., Fuleki, D., Knezevici, D.C., MacLeod, J.D., 2013. Altitude scaling of ice crystal accretion. In: 5th AIAA Atmospheric and Space Environments Conference, p. 2677.

Currie, T.C., Fuleki, D., Mahallati, A., 2014a. Experimental studies of mixed-phase sticking efficiency for ice crystal accretion in jet engines. In: 6th AIAA Atmospheric and Space Environments Conference, p. 3049. https://doi.org/10.2514/6.2014-3049.

Currie, T.C., Fuleki, D., Mahallati, A., 2014b. Experimental studies of mixed-phase sticking efficiency for ice crystal accretion in jet engines. In: 6th AIAA Atmospheric and Space Environments Conference, p. 3049.
Currie, T., Fuleki, D., Davison, C., 2015. Simulation of Ice Particle Melting in the Nrc Rafac Mixed-Phase Icing Tunnel, 2015-June. SAE International. https://doi.org/10.4271/2015-01-2107.

Esposito, B.M., Bachalo, W.D., Leroy, D., Schwarzenboeck, A., Jurkat, T., Voigt, C., Bansmer, S., 2019. Wind tunnel measurements of simulated glaciated cloud conditions to evaluate newly developed 2d imaging probes. https://doi.org/10.4271/2019-01-1981.

Eu Commission Page, 2012. High Altitude Ice Crystals. https://cordis.europa.eu/proje ct/id/314314.

Flegel, A., Oliver, M., 2016. Preliminary Results from a Heavily Instrumented Engine Ice Crystal Icing test in a Ground Based Altitude Test Facility. https://doi.org/10.2514/ 6.2016-3894.

Fontaine, E., Leroy, D., Schwarzenboeck, A., Delanoë, J., Protat, A., Dezitter, F., Grandin, A., Strapp, J.W., Lilie, L.E., 2017. Evaluation of radar reflectivity factor simulations of ice crystal populations from in situ observations for the retrieval of condensed water content in tropical mesoscale convective systems. Atmos. Meas. Tech. 10 (6), 2239-2252. https://doi.org/10.5194/amt-10-2239-2017.

Fontaine, E., Schwarzenboeck, A., Leroy, D., Delanoë, J., Protat, A., Dezitter, F., Strapp, J.W., Lilie, L.E., 2020. Statistical analysis of ice microphysical properties in tropical mesoscale convective systems derived from cloud radar and in situ microphysical observations. Atmos. Chem. Phys. 20 (6), 3503-3553. https://doi. org/10.5194/acp-20-3503-2020.

Fuleki, D., Neuteboom, M., Chalmers, J., 2019. Ice Crystal Icing Test Design and Execution for the alf502 Vane Segment in the Nrc Rafac Cascade Rig. https://doi. org/10.4271/2019-01-1925.

Gent, R., Dart, N., Cansdale, J., 2000. Aircraft icing. Philos. Trans. R. Soc. London. Ser. A Math. Phys. Eng. Sci 358, 2873-2911. https://doi.org/10.1098/rsta.2000.0689.

Guégan, P., Othman, R., Lebreton, D., Pasco, F., Villedieu, P., Meyssonnier, J., Wintenberger, S., 2011. Experimental investigation of the kinematics of post-impact ice fragments. Int. J. Impact Eng. 38 (10), 786-795. https://doi.org/10.1016/j. ijimpeng.2011.05.003.

Haggerty, J., Defer, E., de Laat, A., Bedka, K., Moisselin, J., Potts, R., Delanoë, J., Parol, F., Grandin, A., DiVito, S., 2019. Detecting clouds associated with jet engine ice crystal icing. Bull. Am. Meteorol. Soc. 100, 31-40. https://doi.org/10.1175/ bams-d-17-0252.1.

Han, Y., Soltis, J., Palacios, J., 2018. Engine inlet guide vane ice impact fragmentation. AIAA J. https://doi.org/10.2514/1.J056648.

Hauk, T., Strobl, T., Raps, D., 2013. Implementation and calibration of the icing and contamination research facility (icore). In: Proceedings of the 25th ILASS-Europe, pp. 921-928. URL https://ilasseurope.org/events/25th-ilass-europe/.

Hauk, T., Bonaccurso, E., Roisman, I., Tropea, C., 2015. Ice crystal impact onto a dry solid wall. particle fragmentation. Proc. R. Soc. Lond. A 471. https://doi.org/ 10.1098/rspa.2015.0399, 20150399.

Hauk, T., Bonaccurso, E., Villedieu, P., Trontin, P., 2016. Theoretical and experimental investigation of the melting process of ice particles. J. Thermophys. Heat Transf. 30 (10) https://doi.org/10.2514/1.T4886.

Hong, Y., Moon, K., 2017. Experimental research on ice particle impact on aluminum alloys. Wear 382-383, 102-106. https://doi.org/10.1016/j.wear.2017.04.024.

Karpen, N., Cuco, A., Kuenstler, D., Bonacurso, E., Reitter, L.M., Roisman, I.V., Tropea, C., 2021. Characterizing Microscopic Ice Particle Impacts onto a Rigid Surface: Wind Tunnel Setup and Analysis. https://doi.org/10.2514/6.2021-2671.

Karpen, N., Bonacurso, E., Roisman, I.V., Hussong, J., Tropea, C., 2022. Insights on Ice Particle Impacts Initializing the Ice Accretion Process during Ice Icing. https://doi.org/10.2514/6.2022-3680.

Kintea, D., Schremb, M., Roisman, I., Tropea, C., 2014. Numerical Investigation of Ice Particle Accretion on Heated Surfaces with Application to Aircraft Engines. https:// doi.org/10.2514/6.2014-2820.

Kintea, D., Hauk, T., Roisman, I., Tropea, C., 2015. Shape evolution of a melting nonspherical particle. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 92, 033012. https://doi.org/10.1103/PhysRevE.92.033012.

Kintea, D., Breitenbach, J., Gurumathy, V., Roisman, I., Tropea, C., 2016a. On the influence of surface tension during the impact of particles on a liquid-gaseous interface. Phys. Fluids 28, 012108. https://doi.org/10.1063/1.4939285.

Kintea, D., Roisman, I., Tropea, C., 2016b. Transport processes in a wet granular ice layer: Model for ice accretion and shedding. Int. J. Heat Mass Transf. 97, 461-472. https://doi.org/10.1016/j.ijheatmasstransfer.2016.01.076.

Kintea, D., Roisman, I., Tropea, C., 2016c. Transport processes in a wet granular ice layer: Model for ice accretion and shedding. Int. J. Heat Mass Transf. 97, 461-472.

Knezevici, D., Fuleki, D., Currie, T., MacLeod, J., 2012. Particle size effects on ice crystal accretion. In: 4th AIAA Atmospheric and Space Environments Conference, p. 3039.

Knezevici, D.C., Fuleki, D., Currie, T.C., Galeote, B., Chalmers, J., MacLeod, J., 2013a. Particle Size Effects on ice Crystal Accretion - Part II. https://doi.org/10.2514/ 6.2013-2676.

Knezevici, D.C., Fuleki, D., Currie, T.C., Galeote, B., Chalmers, J., MaCleod, J.D., 2013b. Particle size effects on ice crystal accretion-Part II. In: 5th AIAA Atmospheric and Space Environments Conference, p. 2676.

Köbschall, K., Oberreuter, J., Breitenbach, J., Roisman, I.V., Tropea, C., Hussong, J., 2021. Melting of and imbibition in a granular ice layer on a heated substrate. In: Icing 2021 Forum. AIAA. https://doi.org/10.2514/6.2021-2682.

Kott, B., Struk, P., Bartkus, T., 2020. A Study of Ice-Crystal Icing Erosion Using the Nasa Icing Research Tunnel and Propulsion Systems Laboratory. https://doi.org/10.2514/ 6.2020-2842.

Leroy, D., Fontaine, E., Schwarzenboeck, A., Strapp, J.W., Korolev, A., Mcfarquhar, G.M., Dupuy, R., Gourbeyre, C., Lilie, L., Protat, A., Delanoë, J., Dezitter, F., Grandin, A., 2017. Ice crystal sizes in high ice water content clouds. Part 2: Statistics of mass diameter percentiles in tropical convection observed during the HAIC/HIWC project.

Journal of Atmospheric and Oceanic Technology 34 (1), 117-136. https://doi.org/ 10.1175/jtech-d-15-0246.1. URL https://hal.archives-ouvertures.fr/hal-01980993.

Löwe, J., Kintea, D., Baumert, A., Bansmer, S., Roisman, I.V., Tropea, C., 2016a. Inception of ice accretion by ice crystal impact. J. Phys. Conf. Ser. 745, 032013 https://doi.org/10.1088/1742-6596/745/3/032013.

Löwe, J., Kintea, D., Baumert, A., Bansmer, S., Roisman, I.V., Tropea, C., 2016b. Inception of ice accretion by ice crystal impact. In: Journal of Physics: Conference Series, 745. IOP Publishing, p. 032013.

Malik, Y., Bennani, L., Vorgias, A., Trontin, P., Villedieu, P., 2022. Experimental and Numerical Investigation of Ice Crystal Icing on a Heatable naca0012 Airfoil. https:// doi.org/10.2514/6.2022-3534.

Malik, Y.A., Bennani, L., Bansmer, S., Trontin, P., Villedieu, P., 2023. Experimental and numerical investigation of accretion inception and heat transfer physics in ice crystal icing. Int. J. Heat Mass Transf. 214, 124364. https://doi.org/10.1016/j. ijheatmasstransfer.2023.124364. URL https://www.sciencedirect.com/science/ article/pii/S0017931023005100.

Mason, J., Strapp, W., Chow, P., 2006. The ice particle threat to engines in flight. In: 44th AIAA Aerospace Sciences Meeting and Exhibit, p. 1. https://doi.org/10.2514/ 6.2006-206.

Mason, J.G., Chow, P., Fuleki, D.M., 2011. Understanding ice crystal accretion and shedding phenomenon in jet engines using a rig test. J. Eng. Gas Turbines Power 133 (4). https://doi.org/10.1115/1.4002020.

Mazzawy, R.S., 2007. Modeling of ice accretion and shedding in turbofan engines with mixed phase/glaciated (ice crystal) conditions. In: 2007 SAE Aircraft and Engine Icing International Conference, SAE Technical Paper 2007-01-3288, pp. 1-14. https://doi.org/10.4271/2007-01-3288.

Nilamideen, S., Neuteboom, M., Shah, S., Stokes, J., Aliaga, C., Chalmers, J., Davison, C., Fuleki, D., 2021. Icing Simulation Studies on the Nrc Rotating Rig. https://doi.org/ 10.2514/6.2021-2663.

Norde, E., Senoner, J.-M., Weide, E., Trontin, P., Hoeijmakers, H., Villedieu, P., 2018. Eulerian and lagrangian ice-crystal trajectory simulations in a generic turbofan compressor. J. Propuls. Power 35, 1-15. https://doi.org/10.2514/1.836916.

Oliver, M.J., 2014. Validation ice crystal icing engine test in the propulsion systems laboratory at nasa glenn research center. In: 6th AIAA Atmospheric and Space Environments Conference. https://doi.org/10.2514/6.2014-2898.

Oliver, M., 2015. Ice crystal icing engine testing in the nasa glenn research center's propulsion systems laboratory: Altitude investigation. SAE Int. J. Aerosp. 8 (1), 33-37. https://doi.org/10.4271/2015-01-2156.

Razak, A., 2007. Industrial Gas Turbines: Performance and Operability. Elsevier.

Reitter, L., Lohmann, H., Schremb, M., Roisman, I., Hussong, J., Tropea, C., 2021. Impact of an ice particle onto a dry rigid substrate: Dynamic sintering of a residual ice cone. Cold Reg. Sci. Technol. 194, 103416. https://doi.org/10.1016/j. coldregions.2021.103416.

Roisman, I.V., 2022. Hydrodynamic model of a collision of a spherical plastic ice particle with a perfectly rigid substrate. Int. J. Impact Eng. 159, 104019. https://doi.org/ 10.1016/j.ijimpeng.2021.104019.

Roisman, I., Tropea, C., 2015. Impact of a crushing ice particle onto a dry solid wall, Proceedings of the Royal Society a: Mathematical. Phys. Eng. Sci. 471 (2183), 20150525. https://doi.org/10.1098/rspa.2015.0525.

Senoner, J.-M., Trontin, P., Reitter, L.M., Karpen, N., Schremb, M., Vargas, M., Villedieu, P., 2022. Ice particle impact on solid walls: size modeling of reemitted fragments. Int. J. Impact Eng. 169, 104322. https://doi.org/10.1016/j. ijimpeng.2022.104322.

Soubrié, T., Senoner, J.-M., Villedieu, P., Neuteboom, M.O., 2022. Ice Crystal Trajectory Simulations in the ICE-MACR Compressor rig: Fragmentation and Melting Dynamics. https://doi.org/10.2514/6.2022-3535.

Struk, P., Currie, T., Wright, W.B., Knezevici, D.C., Fuleki, D., Broeren, A., Vargas, M., Tsao, J.-C., 2011. Fundamental Ice Crystal Accretion Physics Studies, 06. https://doi. org/10.4271/2011-38-0018.

Struk, P.M., King, M.C., Bartkus, T.P., Tsao, J.-C., Fuleki, D., Neuteboom, M., Chalmers, J., 2018. Ice crystal icing physics study using a naca 0012 airfoil at the national research council of canada's research altitude test facility. In: 2018 Atmospheric and Space Environments Conference, p. 4224.

Stull, R., 2011. Wet-bulb temperature from relative humidity and air temperature. J. Appl. Meteorol. Climatol. 50 (11), 2267-2269.

Tippmann, J.D., Kim, H., Rhymer, J.D., 2013. Experimentally validated strain rate dependent material model for spherical ice impact simulation. Int. J. Impact Eng. 57, 43-54. https://doi.org/10.1016/j.ijimpeng.2013.01.013.

Trontin, P., Villedieu, P., 2018. A comprehensive accretion model for glaciated icing conditions. Int. J. Multiphasas. Flow 108 (07). https://doi.org/10.1016/j. ijmultiphaseflow.2018.06.023.

Trontin, P., Blanchard, G., Villedieu, P., 2016. A comprehensive numerical model for mixed-phase and glaciated icing conditions. In: 8th AIAA Atmospheric and Space Environments Conference, p. 3742.

Tsao, J.-C., Struk, P.M., Oliver, M.J., 2014. Possible mechanisms for turbofan engine ice crystal icing at high altitude. In: 6th AIAA Atmospheric and Space Environments Conference, p. 3044.

van Diedenhoven, B., Fridlind, A.M., Cairns, B., Ackerman, A.S., 2014. Variation of ice crystal size, shape, and asymmetry parameter in tops of tropical deep convective clouds. J. Geophys. Res. Atmos. 119 (20), 11,809-11,825. https://doi.org/10.1002/ 1041J0D22385.

Vargas, M.M., Struk, P.M., Kreeger, R.E., Palacios, J., Iyer, K., Gold, R.E., 2014. Ice Particle Impacts on a Moving Wedge. https://doi.org/10.2514/6.2014-3045.
Currie, T., Fuleki, D., Davison, C., 2015. Simulation of Ice Particle Melting in the Nrc Ratafc Mixed-Phase Icing Tunnel, 2015-June. SAE International. https://doi.org/10.4271/2015-01-2107.

Esposito, B.M., Bachalo, W.D., Leroy, D., Schwarzenboeck, A., Jurkat, T., Voigt, C., Bansmer, S., 2019. Wind tunnel measurements of simulated glaciated cloud conditions to evaluate newly developed 2d imaging probes. https://doi.org/10.4271/2019-01-1981.

Eu Commission Page, 2012. High Altitude Ice Crystals. https://cordis.europa.eu/projec/t/id/314314.

Flegel, A., Oliver, M., 2016. Preliminary Results from a Heavily Instrumented Engine Ice Crystal Icing test in a Ground Based Altitude Test Facility. https://doi.org/10.2514/6.2016-3894.

Fontaine, E., Leroy, D., Schwarzenboeck, A., Delanoë, J., Protat, A., Dezitter, F., Grandin, A., Strapp, J.W., Lilie, L.E., 2017. Evaluation of radar reflectivity factor simulations of ice crystal populations from in situ observations for the retrieval of condensed water content in tropical mesoscale convective systems. Atmos. Meas. Tech. 10 (6), 2239-2252. https://doi.org/10.5194/amt-10-2239-2017.

Fontaine, E., Schwarzenboeck, A., Leroy, D., Delanoë, J., Protat, A., Dezitter, F., Strapp, J.W., Lilie, L.E., 2020. Statistical analysis of ice microphysical properties in tropical mesoscale convective systems derived from cloud radar and in situ microphysical observations. Atmos. Chem. Phys. 20 (6), 3503-3553. https://doi.org/10.5194/acp-20-3503-2020.

Fuleki, D., Neuteboom, M., Chalmers, J., 2019. Ice Crystal Icing Test Design and Execution for the alf502 Vane Segment in the Nrc Ratafc Cascade Rig. https://doi.org/10.4271/2019-01-1925.

Gent, R., Dart, N., Cansdale, J., 2000. Aircraft icing. Philos. Trans. R. Soc. London. Ser. A Math. Phys. Eng. Sci 358, 2873-2911. https://doi.org/10.1098/rsta.2000.0689.

Guégan, P., Othman, R., Lebreton, D., Pasco, F., Villedieu, P., Meyssonnier, J., Wintenberger, S., 2011. Experimental investigation of the kinematics of post-impact ice fragments. Int. J. Impact Eng. 38 (10), 786-795. https://doi.org/10.1016/j.ijimpeng.2011.05.003.

Haggerty, J., Defer, E., de Laat, A., Bedka, K., Moisselin, J., Potts, R., Delanoë, J., Parol, F., Grandin, A., DiVito, S., 2019. Detecting clouds associated with jet engine ice crystal icing. Bull. Am. Meteorol. Soc. 100, 31-40. https://doi.org/10.1175/bams-d-17-0252.1.

Han, Y., Soltis, J., Palacios, J., 2018. Engine inlet guide vane ice impact fragmentation. AIAA J. https://doi.org/10.2514/1.J056648.

Hauk, T., Strobl, T., Raps, D., 2013. Implementation and calibration of the icing and contamination research facility (icore). In: Proceedings of the 25th ILASS-Europe, pp. 921-928. URL https://ilasseurope.org/events/25th-ilass-europe/.

Hauk, T., Bonaccurso, E., Roisman, I., Tropea, C., 2015. Ice crystal impact onto a dry solid wall. particle fragmentation. Proc. R. Soc. Lond. A 471. https://doi.org/10.1098/rspa.2015.0399, 20150399.

Hauk, T., Bonaccurso, E., Villedieu, P., Trontin, P., 2016. Theoretical and experimental investigation of the melting process of ice particles. J. Thermophys. Heat Transf. 30 (10) https://doi.org/10.2514/1.T4886.

Hong, Y., Moon, K., 2017. Experimental research on ice particle impact on aluminum alloys. Wear 382-383, 102-106. https://doi.org/10.1016/j.wear.2017.04.024.

Karpen, N., Cuco, A., Kuenstler, D., Bonacurso, E., Reitter, L.M., Roisman, I.V., Tropea, C., 2021. Characterizing Microscopic Ice Particle Impacts onto a Rigid Surface: Wind Tunnel Setup and Analysis. https://doi.org/10.2514/6.2021-2671.

Karpen, N., Bonacurso, E., Roisman, I.V., Hussong, J., Tropea, C., 2022. Insights on Ice Particle Impacts Initializing the Ice Accretion Process during Ice Icing. https://doi.org/10.2514/6.2022-3680.

Kintea, D., Schremb, M., Roisman, I., Tropea, C., 2014. Numerical Investigation of Ice Particle Accretion on Heated Surfaces with Application to Aircraft Engines. https://doi.org/10.2514/6.2014-2820.

Kintea, D., Hauk, T., Roisman, I., Tropea, C., 2015. Shape evolution of a melting nonspherical particle. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 92, 033012. https://doi.org/10.1103/PhysRevE.92.033012.

Kintea, D., Breitenbach, J., Gurumathy, V., Roisman, I., Tropea, C., 2016a. On the influence of surface tension during the impact of particles on a liquid-gaseous interface. Phys. Fluids 28, 012108. https://doi.org/10.1063/1.4939285.

Kintea, D., Roisman, I., Tropea, C., 2016b. Transport processes in a wet granular ice layer: Model for ice accretion and shedding. Int. J. Heat Mass Transf. 97, 461-472. https://doi.org/10.1016/j.ijheatmasstransfer.2016.01.076.

Kintea, D., Roisman, I., Tropea, C., 2016c. Transport processes in a wet granular ice layer: Model for ice accretion and shedding. Int. J. Heat Mass Transf. 97, 461-472.

Knezevici, D., Fuleki, D., Currie, T., MacLeod, J., 2012. Particle size effects on ice crystal accretion. In: 4th AIAA Atmospheric and Space Environments Conference, p. 3039.

Knezevici, D.C., Fuleki, D., Currie, T.C., Galeote, B., Chalmers, J., MacLeod, J., 2013a. Particle Size Effects on ice Crystal Accretion - Part II. https://doi.org/10.2514/6.2013-2676.

Knezevici, D.C., Fuleki, D., Currie, T.C., Galeote, B., Chalmers, J., MaCleod, J.D., 2013b. Particle size effects on ice crystal accretion-Part II. In: 5th AIAA Atmospheric and Space Environments Conference, p. 2676.

Köbschall, K., Oberreuter, J., Breitenbach, J., Roisman, I.V., Tropea, C., Hussong, J., 2021. Melting of and imbibition in a granular ice layer on a heated substrate. In: Icing 2021 Forum. AIAA. https://doi.org/10.2514/6.2021-2682.

Kott, B., Struk, P., Bartkus, T., 2020. A Study of Ice-Crystal Icing Erosion Using the Nasa Icing Research Tunnel and Propulsion Systems Laboratory. https://doi.org/10.2514/6.2020-2842.

Leroy, D., Fontaine, E., Schwarzenboeck, A., Strapp, J.W., Korolev, A., Mcfarquhar, G.M., Dupuy, R., Gourbeyre, C., Lilie, L., Protat, A., Delanoë, J., Dezitter, F., Grandin, A., 2017. Ice crystal sizes in high ice water content clouds. Part 2: Statistics of mass diameter percentiles in tropical convection observed during the HAIC/HIWC project.

Journal of Atmospheric and Oceanic Technology 34 (1), 117-136. https://doi.org/10.1175/jtech-d-15-0246.1. URL https://hal.archives-ouvertures.fr/hal-01980993.

Löwe, J., Kintea, D., Baumert, A., Bansmer, S., Roisman, I.V., Tropea, C., 2016a. Inception of ice accretion by ice crystal impact. J. Phys. Conf. Ser. 745, 032013 https://doi.org/10.1088/1742-6596/745/3/032013.

Löwe, J., Kintea, D., Baumert, A., Bansmer, S., Roisman, I.V., Tropea, C., 2016b. Inception of ice accretion by ice crystal impact. In: Journal of Physics: Conference Series, 745. IOP Publishing, p. 032013.

Malik, Y., Bennani, L., Vorgias, A., Trontin, P., Villedieu, P., 2022. Experimental and Numerical Investigation of Ice Crystal Icing on a Heatable naca0012 Airfoil. https://doi.org/10.2514/6.2022-3534.

Malik, Y.A., Bennani, L., Bansmer, S., Trontin, P., Villedieu, P., 2023. Experimental and numerical investigation of accretion inception and heat transfer physics in ice crystal icing. Int. J. Heat Mass Transf. 214, 124364. https://doi.org/10.1016/j.ijheatmasstransfer.2023.124364. URL https://www.sciencedirect.com/science/article/pii/S0017931023005100.

Mason, J., Strapp, W., Chow, P., 2006. The ice particle threat to engines in flight. In: 44th AIAA Aerospace Sciences Meeting and Exhibit, p. 1. https://doi.org/10.2514/6.2006-206.

Mason, J.G., Chow, P., Fuleki, D.M., 2011. Understanding ice crystal accretion and shedding phenomenon in jet engines using a rig test. J. Eng. Gas Turbines Power 133 (4). https://doi.org/10.1115/1.4002020.

Mazzawy, R.S., 2007. Modeling of ice accretion and shedding in turbofan engines with mixed phase/glaciated (ice crystal) conditions. In: 2007 SAE Aircraft and Engine Icing International Conference, SAE Technical Paper 2007-01-3288, pp. 1-14. https://doi.org/10.4271/2007-01-3288.

Nilamideen, S., Neuteboom, M., Shah, S., Stokes, J., Aliaga, C., Chalmers, J., Davison, C., Fuleki, D., 2021. Icing Simulation Studies on the Nrc Rotating Rig. https://doi.org/10.2514/6.2021-2663.

Norde, E., Senoner, J.-M., Weide, E., Trontin, P., Hoeijmakers, H., Villedieu, P., 2018. Eulerian and lagrangian ice-crystal trajectory simulations in a generic turbofan compressor. J. Propuls. Power 35, 1-15. https://doi.org/10.2514/1.836916.

Oliver, M.J., 2014. Validation ice crystal icing engine test in the propulsion systems laboratory at nasa glenn research center. In: 6th AIAA Atmospheric and Space Environments Conference. https://doi.org/10.2514/6.2014-2898.

Oliver, M., 2015. Ice crystal icing engine testing in the nasa glenn research center's propulsion systems laboratory: Altitude investigation. SAE Int. J. Aerosp. 8 (1), 33-37. https://doi.org/10.4271/2015-01-2156.

Razak, A., 2007. Industrial Gas Turbines: Performance and Operability. Elsevier.

Reitter, L., Lohmann, H., Schremb, M., Roisman, I., Hussong, J., Tropea, C., 2021. Impact of an ice particle onto a dry rigid substrate: Dynamic sintering of a residual ice cone. Cold Reg. Sci. Technol. 194, 103416. https://doi.org/10.1016/j.coldregions.2021.103416.

Roisman, I.V., 2022. Hydrodynamic model of a collision of a spherical plastic ice particle with a perfectly rigid substrate. Int. J. Impact Eng. 159, 104019. https://doi.org/10.1016/j.ijimpeng.2021.104019.

Roisman, I., Tropea, C., 2015. Impact of a crushing ice particle onto a dry solid wall, Proceedings of the Royal Society a: Mathematical. Phys. Eng. Sci. 471 (2183), 20150525. https://doi.org/10.1098/rspa.2015.0525.

Senoner, J.-M., Trontin, P., Reitter, L.M., Karpen, N., Schremb, M., Vargas, M., Villedieu, P., 2022. Ice particle impact on solid walls: size modeling of reemitted fragments. Int. J. Impact Eng. 169, 104322. https://doi.org/10.1016/j.ijimpeng.2022.104322.

Soubrié, T., Senoner, J.-M., Villedieu, P., Neuteboom, M.O., 2022. Ice Crystal Trajectory Simulations in the ICE-MACR Compressor rig: Fragmentation and Melting Dynamics. https://doi.org/10.2514/6.2022-3535.

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flight icing due to high altitude ice crystals. SAE Int. J. Adv. & Curr. Prac. in Mobilit. 2, 78–89. https://doi.org/10.4271/2019-01-1962.

Widhalm, M., 2015. Lagrangian trajectory simulation of rotating regular shaped ice particles. In: SAE 2015 International Conference on Icing of Aircraft, Engines, and Structures. SAE International, p. 14. https://doi.org/10.4271/2015-01-2141.