Karsten Kusterer

Jens Dickhoff
email: dickhoff@bub-agema.de

René J Braun

Ryozo Tanaka

Tomoki Taniguchi

Dieter Bohn

Conjugate Heat Transfer Simulations for a Film Cooled Nozzle Guide Vane of a High-efficiency, Industrial Gas Turbine

Keywords:

Great efforts are still put into the design process of advanced film-cooling configurations. In particular, the vanes and blades of turbine front stages have to be cooled extensively for a safe operation. The conjugate heat transfer (CHT) calculation technique is used for the three-dimensional thermal load prediction of an extensively cooled 1 st nozzle test vane installed in a highest-efficient industrial gas turbine. With the CHT approach it is possible to take the interaction of internal flows, external flow, and heat transfer into account without estimation of heat transfer coefficients. The utilized numerical model contains all geometrical features (e.g. pin-fins, ribs, impingement sheets etc.) of the real test vane without simplifications. The comparison with thermal index paint measurements inside the test engine shows that a qualitatively and quantitatively good agreement between the CHT and the measurements results can be found. A consideration of advanced-shaped film cooling holes at the vane platforms also offers high potential to further reduce the material temperatures and decrease thermal stresses by lowering of platform temperatures and homogenization of the temperature distribution

INTRODUCTION

In order to achieve high process efficiencies for the economic operation of stationary gas turbines and aero engines, extremely high turbine inlet temperatures at adjusted pressure ratios are applied. However, the allowable hot gas temperature is limited by the material temperature of the hot gas path components, in particular the vanes and blades of the turbine. Intensive cooling is required to guarantee an economically acceptable life span of the components (e.g. combustor walls, turbine vanes and blades, disks, etc.) that are in contact with the hot gas. The initial design process of the cooled vanes and blades still depends on fast design procedures for the temperature field determination in the blade sections based on 1D and 2D calculation models for the internal flow path (1D network model) and the external flow of hot gas around the airfoil (2D boundary-layer code or 2D RANS calculation) coupled to a solid body heat conduction code by application of heat transfer correlations. However, the Conjugate Heat Transfer method for fully coupled three-dimensional flow field, heat transfer and heat conduction achieved more and more attention in the design process for modern gas turbines. With regard to the inter-relations between the external fluid flow, the internal fluid flow and the heat conduction, it is obvious that a coupled calculation can lead to a higher accuracy in thermal load predictions during the design process. Among others [START_REF] Li | A Coupled FVM/BEM Approach to Conjugate Heat Transfer in Turbine Blades[END_REF][START_REF] Rigby | Conjugate Heat Transfer Analysis of Internally Cooled Configurations[END_REF], Bohn et al. [3 -5] has developed a coupling approach at the Institute of Steam and Gas Turbines (IDG), RWTH Aachen University, which takes these considerations into account. It follows a homogeneous coupling procedure for the Conjugate Heat Transfer (CHT) calculations to be applied for thermal load prediction of cooled components in gas turbines. The method involves the direct coupling of the fluid flow and the solid body using the same discretization and numerical principle for both zones. This makes it possible to have an interpolation-free crossing of the heat fluxes between the neighboring cell faces. The detailed description of the conjugate calculation technique and its validation is provided by Bohn et al. in [START_REF] Bohn | Conjugate Heat Transfer: An Advanced Computational Method for the Cooling Design of Modern Gas Turbine Blades and Vanes[END_REF]. Today, the conjugate heat transfer procedure as explained above already became a standard application option in almost all modern commercial Computational Fluid Dynamics (CFD) tools. Furthermore, the CHT simulations of the cooled vanes and blades represent a state-of-the-art technology and an important step in the design process for the modern gas turbines. Depending on the kind of applied grid structures, such models today may include more than 60 million cells enabling the designers to take more and more geometric details into account within the simulation models. Due to an application of the technology, it is possible to detect deficiencies of the cooling design process in an early stage. The deficits are caused by complex three-dimensional flow phenomena and uncertainties of applied heat transfer conditions. Their impacts cannot be considered by the simpler design approaches. The improved design based on the CHT technology contributes to the advanced design of the hot gas components by reducing the cooling air amount required to fulfil the cooling task and, as a result, it also contributes to the increase in thermal efficiency of the gas turbine cycle. Therefore, modern industrial gas turbines can achieve thermal cycle efficiencies above 40%. The recently developed Kawasaki L30A 30MWel gas turbine can be given as one example, claiming for the presently highest efficiency in its class [START_REF] Tanaka | Development of High Efficient 30 MW Class Gas Turbine: The Kawasaki L30A[END_REF].

In the present study an extensively cooled state-the-art 1 st stage nozzle guide vane is investigated. The vane has been analyzed based on the CHT technology under boundary conditions as to be expected in the gas turbine engine, i.e. realistic high temperature combustion gas flow. All details of the internal cooling structure (cooling chambers, impingement cooling, pin fins, ribs etc.) have been modelled without simplifications. Furthermore, the test configuration has been implemented into a test engine at the Kawasaki Akashi plant and operated under a typical load condition of the gas turbine. Thermal Index Paint (TIP) measurements have been carried out and allowed the determination of the thermal load distributionqualitatively as well as quantitatively. Within the following sections, the numerical and experimental results are compared. Furthermore, the potential to improve the external vane cooling by application of advanced-shaped film cooling holes (NEKOMIMI-shaped configurations [START_REF] Kusterer | The NEKOMIMI Cooling Technology: Cooling Holes with Ears for High-efficient Film Cooling[END_REF]) is presented. Besides others, the NEKOMIMI-shaped film cooling holes have shown the potential, to establishing antivortex film cooling structures and improve the film cooling effectiveness with respect to cylindrical but also to conventional laidback fan-shaped film cooling configurations.

INVESTIGATED GEOMETRY 1.1 Test Nozzle Guide Vane

The test vane investigated within the present paper represents a state-of-the-art nozzle guide vane for industrial gas turbines. It includes an internal convective cooling scheme with impingement cooling for further enhancement of the heat transfer on the internal walls. Numerous geometric features like ribs and pin fins also contribute to the advanced design for enhanced internal heat transfer. The leading edge of the vane is extensively film cooled by a showerhead cooling design consisting of several rows of inclined cooling holes. Additional film cooling is established along the suction side. A trailing edge injection of cooling air is provided through modern type cutback slots.

Advanced-Shaped Film Cooling Holes

Besides the improvement of every single gas turbine component, the efficient cooling of the hot gas path components is a major measure in order to reach a high efficiency of the gas turbine cycle. Film cooling is widely used for vanes and blades of turbine front stages in gas turbines in order to reduce material temperatures as far as necessary to ensure an acceptable life span of the components. As the cooling fluid is extracted from the compressor on high pressure levels, the reduction of the amount of cooling fluid for the cooling task leads to increased thermal efficiencies of the gas turbine. Furthermore, film cooling leads to mixture losses and a reduced temperature of the hot combustion gas flow.

Improvements can be achieved by reducing the cooling fluid amount and by establishing a more homogenous distribution of the cooling fluid on the surface. Today it is well-known that film cooling effectiveness degradation is caused by secondary flows inside the cooling jets, i.e. the Counter-Rotating Vortices (CRV) or also named kidney-vortices, which induce a jet lift-off. The cooling fluid injection through a hole leads to a 'Jet in Cross flow' situation.

The vortices are generated due to the interaction between the coolant jet and the cross flow.

A large number of publications deal with the experimental visualization or numerical calculation of these vortices. The publications of Bergeles et al. [START_REF] Bergeles | The Prediction of Three-dimensional Discrete-hole Cooling Processes[END_REF], Leylek and Zerkle [START_REF] Leylek | Discrete-Jet Film Cooling: A Comparison of Computational results with Experiments[END_REF], and Walters and Leylek [START_REF] Walters | A Detailed Analysis of Film-Cooling Physics Part I: Streamwise Injection with Cylindrical Holes[END_REF] are mentioned as examples.

In order to establish anti-counter rotating vortices (ACRV) as major secondary flow phenomenon and enhance the film cooling effectiveness, Kusterer et al. [START_REF] Kusterer | Double-Jet Ejection of Cooling Air for Improved Film-cooling[END_REF] have introduced the Double-Jet Film Cooling (DJFC) technology. It utilizes the interaction between two separate inclined injection holes and the main flow. In 2011 Kusterer et al. presented a novel film cooling hole design derived from the DJFC-Concept -the patented NEKOMIMI technology (Japanese for "cat ears"), which has been patented [START_REF] Khi | [END_REF] (see Figure 2).

Figure 2. NEKOMIMI design concept

Like for conventional shaped film cooling holes, the diffusor part of the NEKOMIMI is intended to reduce the local momentum flux ratio at the hole exit and the penetration of the coolant into the main flow. Simultaneously, ACRV can be established and their intensity adjusted in order to keep the mixing between hot gas and coolant low. The technology has shown potential to break the limits of conventional shaped film cooling holes in terms of the overall film cooling effectiveness.

EXPERIMENTAL MEASURMENT

In order to evaluate the surface temperatures of the test vane, Thermal Index Paint (TIP) measurements have been conducted. Today, TIP measurements are common practice for the investigation of the thermal load of gas turbine parts, which are exposed to high temperatures. The technology is based on the thermal activation of chemical reactions between metal elements and special pigments (mineral compounds) [START_REF] Lempereur | Surface temperature measurement on engine components by means of irreversible thermal coatings[END_REF]. Metallic elements are provided by the test object itself (e.g. the nozzle vane body), while the pigments are part of the paint (mixture of solvents, binding agents and mineral fillers). By exposing the painted surfaces to high temperatures, the chemical reaction between metal and pigments changes the light reflection spectra. Thus, the human eye perceives a color change, which can be translated back to the local surface temperature of the test object. The reaction itself is irreversible, which means, that the resulting temperature distribution obtained from a TIP measurement represents only a composition of local peak temperatures occurred during the test run. This should be kept in mind while analyzing the measurement results. It also becomes clear, that it is of high importance to ensure constant boundary conditions during the test run without fluctuations. The technology allows an optical assessment of the resulting color of the tested gas turbine components offline only, after dismantling of the machine.

For the present TIP measurements a multicolor TIP has been applied to the nozzle vane surfaces. The typical layer thickness of such coatings is approximately 40µm [START_REF] Lempereur | Surface temperature measurement on engine components by means of irreversible thermal coatings[END_REF]. Thus, the interference with the thermal behavior of the test object as well as the impact to the surrounding flow is minor.

The TIP measurement has been conducted on the gas turbine test rig at Kawasaki Akashi Plant, Japan (see Figure 3). More information about the test procedure, accuracy and calibration are given in [START_REF] Taniguchi | Application of an Optical Pyrometer to Newly Developed Industrial Gas Turbine[END_REF])

Figure 3.
L30A on the Heavy duty gas turbine test rig at Kawasaki Akashi Plant, Japan

NUMERICAL METHOD

The CHT calculations have been carried out with the commercial CFD tool Star-CCM+ and the following calculation procedure and physical settings:  three dimensional  steady  turbulent  multi-component gas  non-reacting  ideal gas The solver, calculation setup, procedure and mesh-settings have been benchmarked on basis of the well-known MARK II test case in 2012 [START_REF] Kusterer | 20 Years of of Experiences for the Conjugate Heat Transfer Analysis of Convection-cooled Turbine Vanes[END_REF]. Conjugate heat transfer calculations of the internally cooled blade, have been performed with Star-CCM+ as well as with the in-house code CHTflow [START_REF] Bohn | Combined Aerodynamic and Thermal Analysis of a High-pressure Turbine Nozzle Guide Vane[END_REF]. The fluid domain considers a two gas component model, which handles the hot combustion gas and pure cooling air fluid properties separately. The dynamic viscosity, specific heat and thermal conductivity of the hot combustion gas are considered as polynomial functions in dependency of the static gas temperature in order to represent the gas composition inside the test engine behind the can-combustors. The corresponding gas properties of pure air are related to the static temperature and the static pressure. They are deposited in a user library and correspond to the REFPROP data (NIST Reference Fluid Thermodynamic and Transport Properties Database) [START_REF] Lemmon | NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP[END_REF]. The material properties used for the solid region of the test vane represents a modern, state-of-the-art superalloy. In the CHT simulation, the thermal behavior is modelled by temperature dependent polynomial functions for the specific heat capacity and the thermal conductivity. The turbulence is considered based on RANS (Reynolds-Averaged Navier-Stokes) equations and the k-ω SST turbulence model. In order to capture the heat transfer also in regions with wall y+ values above one, an all y+ wall treatment has been utilized, which automatically selects an appropriate wall treatment depending on the local y+ value. The profile as well as the inner and the outer platform of the vane are coated with a ceramic layer (see Figure 1). Such thermal barrier coatings (TBC) are distinguished by a very low thermal conductivity. By its application, it is intended to reduce the heat input to the substrate and reduce the thermal loading of the coated component. Within the numerical model, the TBC layer has been considered as contact resistance (CR [m²K/W]), applied to the corresponding solid-fluid interfaces:

𝐶𝑅 = 𝑡 𝜆 (1)

Computational Domain

The computational domain of the CHT calculation is illustrated in The thermal load in the upstream region of the platforms is significantly influenced by the sealing air injection. Therefore, two sealing air inlets have been modelled infront of the test vane. The shape of the inner and outer cooling air chambers corresponds to the cavities inside the vane carrier.

Boundary Conditions

The CHT calculations have been performed with boundary conditions in accordance to operating conditions in the test engine. At the main flow inlet of the fluid region, hot combustion gas is entering the domain. The velocity components have been prescribed to be boundary normal. A total pressure, a total temperature and a boundary normal flow direction have been prescribed. The end of the main flow passage is represented by the main flow outlet and modelled with a static pressure boundary. The normalized radial profiles of total temperature at the main flow inlet and the static pressure at the main flow outlet are illustrated in Figure 5. The maximum total temperature is located at approx. 75% span. The absolute value drops by approx. 7% towards the inner and outer shroud platform. The static pressure profile at the main flow outlet is almost linear. The highest value is located close to the upper shroud. At the lower shroud the static pressure value is reduced to approx. 0.92*p st,max . For the solid region most of the surfaces are defined as fluidsolid interfaces. However, a few surfaces are in contact with the vane carrier or gasket ring structure when the vane is mounted into the gas turbine. An estimation of appropriate heat transfer coefficients for these surfaces is challenging. Furthermore the heat transfer at these surfaces is rather small. Therefore, the walls have been considered to be adiabatic, which corresponds to the assumption of an infinite contact resistance.

A heat transfer coefficient with corresponding reference temperature was defined at the blunt surface of the outer shroud (see Figure 6). The surface is located outside the fluid region of the computational domain but in contact with hot gas/sealing air in the real gas turbine. The HTC value has been derived with an estimation approach based on the VDI Heat Atlas [START_REF][END_REF], which is valid for fully turbulent flows inbetween two flat plates (gap flow).

Computational Mesh

The mesh of the computational domain (fluid and solid region) consists of unstructured polyhedral cells and has been generated in STARCCM+ 9.06. On the interfaces, prism layers are in use (on fluid side only) to keep the wall y+ values low and improve the heat transfer prediction accuracy. Figure 7 gives an impression of the mesh. As visible the number and height of the prism layers have been adjusted to the current flow properties at the corresponding interfaces. Hence, on the outer airfoil interfaces, 20 prism layers with a total thickness of 0.189mm were applied. The cell closest to the wall has a height of 3E-4mm. The stretching factor between the PL cells is 1.3. On interfaces between the internal cooling devices, the hot gas side of the inner and outer shroud interfaces and inside the film cooling holes, 15 prism layers were meshed (height of the wall near cell: 8E-4mm). An application of PL to the cooling devices was not possible due to the high complexity of the structures. This has been accepted, since an all y+ treatment was used for all CHT simulations (see chapter 2) and due to the fact, that the heat transfer enhancement intended by application of ribs and pin-fins is mainly caused by their turbulence and vorticity augmentation. Thus, the heat transfer is also increased on the interspaces between the cooling devices -not only at the walls of the devices. Additional prism layers can be found on the interface between the outer cooling chamber and the outer shroud platform. Here, a minimum cell height of 6E-3mm is sufficient to achieve wall y+ values below or close to 1, due to the relatively low velocities within the cavity.

The resulting mesh consists of approximately 14 million cells.

On the external and internal surfaces in-between the cooling devices, y+ values below or close to one could be achieved.

RESULTS

Validation of the CHT calculation procedure

Within the following section, the CHT results are compared and analyzed to the experimentally obtained data. A qualitative illustration of the surface temperature distribution on the pressure side of the vane is given in Figure 8. The TIP results (right hand side of the figure) show distinct temperature zones. At approx. 50% chord length, the temperature increases over the complete profile span within a short axial distance. This is also represented in the CHT simulation (zone (2) in Figure 8). The high temperature gradient results from the different cooling schemes utilized inside the vane for the rear and front part. In the rear, a pin-fin array is placed, while the front part of the vane is cooled more intensively by impingement jets.

The TIP measurement furthermore shows relatively low temperatures in upstream regions of the upper and lower shroud platforms due to sealing air injections located in-front of the shrouds (zone (1) and ( 3)). This is in good agreement with the temperature distribution obtained from the CHT simulation.

Figure 8. Surface temperature of the test vane -TIP measurement and CHT results

However, a zone with slightly increased surface temperatures (yellow) is located at the outer shroud platform towards the pressure side of the test vane, which is not captured by the CHT simulation. It can be presumed, that this is due to an inhomogeneous sealing air outflow in circumferential direction, but it might also be a result of the TIP measurement technique. As stated above, the color change of the paint is irreversible. Thus, the locally measured temperature corresponds to the maximum temperature occurred during the complete test run. Zones with increased temperatures might have been exposed to significantly higher temperature for a relatively short time period. However, the temperature distribution of the CHT simulation represents a time averaged surface temperature at all positions. A view on Figure 9 reveals that the discussed temperature increase around 50% chord is also represented on the suction side (see zone ( 2)), but according to the temperature distribution obtained from the CHT simulation, the magnitude of the temperature increase is noticeably smaller. Furthermore the TIP measurement result suggests that the temperatures are higher at the inner part of the profile. Close to the trailing edge, measurement and calculation show small areas with increased temperatures, distributed over the profile span (zone (4)). The position is influenced by the cutback slot geometry on the pressure side of the vane. On the opposite side of the lands in-between the cutback slots, the solid temperatures are locally increased (see Figure 9). Positions, which can be cooled more intensively by the ejected coolant, reveal a reduced thermal load (between the locations with increased temperatures -opposite side of the cutback slots). A detailed view on the surface temperature distribution on the outer shroud platform is illustrated in Figure 10. Generally, the numerically obtained temperature distribution is in good agreement with the measurement results, but it should be kept in mind, that the result of the TIP measurement represents an ensemble of local maximum peak temperatures, while the surface temperatures obtained from the CHT analysis represent averaged values under ideal conditions and without fluctuations. Local differences in terms of the surface temperature are consequently not avoidable. Two relatively cold zones, one located behind the sealing air injection in-front of the platform (zone ( 1)) and one close to the pressure side of the vane (zone ( 2)) are visible for the CHT and the TIP approach. Furthermore, a region with moderate temperatures (colored yellow) starts from the leading edge of the vane and propagates towards the end of the platform. As presented by the CHT simulation result, the temperature gradually increases in axial direction. However, the rough division of the TIP measurement colorbar suggests a more rapid change of the temperatures close to the trailing edge of the platform, which easily leads to a misinterpretation. This is a good example, which shows how CHT and TIP results can complement each other in order to improve the design of gas turbine components exposed to high temperatures. The measurement serves as validation basis for the numerical results. And the CHT simulation allows a deeper insight into flow phenomena in order to increase the understanding for the obtained resulting temperature distribution on the part surfaces.

On the platform near the suction side (zones ( 4), ( 6) and ( 7)), the CHT simulation result shows regions with increased temperatures. The TIP measurement technique is not able to resolve those locally increased temperatures due to the small number of temperature levels available. Every color represents a relatively wide temperature range. Additionally, cooling air may have been escaped from the lateral gap between two neighboring nozzle vanes in the experimental measurement, which can cause a temperature reduction in zone ( 6) and ( 7). This sealing air is not modelled within the CHT simulation (flanks of the solid vane body are considered as periodic surfaces). Thus, zones ( 3) and ( 4) propagate towards the neighboring vane and build zones ( 7) and ( 6) respectively. Zones ( 3) and ( 5) are reproduced by the measurement and the simulation result. Zone ( 5) is located at the very end of the outer shroud platform -downstream of the outer cooling chamber (OCC). An extensive cooling by the OCC is consequently not possible. Furthermore the bearing structure of the vane carrier is located above this part of the shroud platform when the nozzle vane is installed in the machine. Thus, the cooling effect by sealing air, which is injected behind the outer shroud platform, is small. However, on the blunt surface at the end of this platform, the sealing air is reducing the surface temperature. This is reproduced by the TIP measurement as well as by the CHT simulation result.

For zone (3), the CHT result shows, that the region with increased surface temperatures is rather small and the magnitude of the temperature is lower than obtained from the TIP measurement. This is more realistic than the rapid temperature change shown for the TIP result, in which the temperature is changing by two temperature steps from yellow to red (pink is not visible). A explanation reason is that the surface has been exposed to locally very high temperatures for a short time period, but it might also be a measurement or data acquirement failure. Upstream of zone (3), a double jet film cooling pair is located, but the CHT results display that the downstream effect is too small to avoid a temperature increase on the outer shroud platform towards the profile trailing edge. For the inner shroud platform, the measurement results also show increased surface temperatures close to the profile, beginning at approx. 50% span. This is reproduced by the CHT simulation result as well (cf. zones (3) and ( 4)). Downstream of zone (4), the results obtained from calculation show a strong temperature reduction caused by the double jet film cooling arrangement. Small regions with considerably low temperatures, resulting from the generated cooling air film, could be reproduced with the TIP measurement technique as well (colored in blue). Zone (1) is reproduced with both approaches, too. As discussed above, sealing air is injected in-front of the inner and outer shroud platforms resulting in a locally reduced surface temperature. For the CHT simulation, a coolant mass flow inlet has been modelled in-front of the vane. Over the circumference, a constant cooling air mass flow is injected in negative radial direction (fully homogenous mass flux dist. in circumferential direction). However, comparison between the cold zones (1) obtained from the experiment and the calculation, with respect to their shape, suggests that the sealing air outflow in the real gas turbine is not fully homogenous or even fluctuating. Zone ( 2) is not directly represented by the measurement results, due to the low number of temperature steps, but the yellow color indicates, that the sealing air injected in-front of the platforms is not capable of cooling this region that intensively. It is mixed out with hot combustion gas before reaching the position of zone (2).

Another region with increased temperatures is located at the downstream part of the inner shroud platform (zone ( 5)). As discussed for the outer shroud platform (zone (5) in Figure 10) the rear parts of the platforms cannot be cooled by the inner/outer cooling chambers. Furthermore, it is challenging to establish a high heat transfer on the surfaces, which are opposed to those in contact with the main flow passage, due to the position of the connected nozzle vane support structure (e.g. vane carrier).

Application of Advanced-Shaped Film Cooling Holes

On the platforms of the tested 1 st nozzle guide vane, double jet film cooling (DJFC) holes have been utilized. This leads to a sufficient cooling with respect to the maximum allowable wall temperature on the platforms. The DJFC technology has been invented with the intention to establish anti-counter rotating vortices (ACRV) and thus augment the film cooling effectiveness. As mentioned in section 1.2, this advanced film cooling technology consists of a pair of cylindrical cooling holes. The relative position and orientation between the two holes and the approach flow direction is a key parameter to establish the desired ACRV. Precise knowledge of the exact flow direction close to the platform surfaces is consequently essential but difficult to predict without modern measurement or calculation techniques. In Figures 12 and13 A comparison between the TBC discoloration and the CHT results shows that the calculated flow directions are in very good agreement with the ones inside the real gas turbine. Additionally both results show potential for the improvement of the DJFC hole orientation. However, due to the complex supply situation (connection to the inner/outer cooling chamber), the possibilities for variation of the DJFC hole arrangement and orientation are limited.

To compensate this drawback of the DJFC technology, the NEKOMIMI-shaped film cooling holes have been invented. With one main supply hole, the transfer of the cooling air from the cooling chamber to the hot external surfaces of the gas turbine parts has been simplified significantly.

It should be noted, that the following numerical comparison between the double jet and the NEKOMIMI film cooling approach, has been carried out on the basis of slightly different boundary conditions with respect to the simulations presented in section 4.1 and 4.2. The two simulations carried out for the present section -one with DJFC and one with NEKOMIMI-shaped film cooling holes -correspond to another load state of the engine. Figure 14 shows the mass fraction of the coolant inside the gas mixture on the inner and outer shroud platform. These values give an indication of the adiabatic film cooling effectiveness on the walls. The local temperature of the fluid inside the cooling film is influenced by the thermal conduction inside the fluid, radiation and the mixing between hot combustion gas and cooling air. The latter leads to a changed coolant mass fraction and governs the fluid temperature -especially within the region close to the film cooling hole, where the mixing process is strong (cf. [START_REF] Kusterer | Nekomimi film cooling hole configurations under conjugate heat transfer condition[END_REF]). Furthermore the footprints of the coolant mass fraction behind the film cooling holes give a good indication whether the NEKOMIMI is properly oriented or not (see Figure 14). Additionally, this result allows a comparison between the more theoretical studies on the NEKOMIMI technology based on the typical test case with ideal boundary conditions and on a flat surface without cross flows or pressure gradients on the test section (e.g. [START_REF] Kusterer | The NEKOMIMI Cooling Technology: Cooling Holes with Ears for High-efficient Film Cooling[END_REF] or [START_REF] Kusterer | Improvement of the NEKOMIMI Film Cooling Technology by Application of an Automated Optimization Algorithm[END_REF]).

The current setup consists of two NEKOMIMI types, which are visible on the inner and outer shroud platforms. The main difference is the lateral distance (regulated with the angle β; cf. Figure 2) between the ears and the laidback angle (δ; cf. Figure 2). A higher lateral distance leads to a wide film cooling footprint (configuration presented in the center of Figure 14). Thus, the film cooling air remains close to the wall and covers a relatively wide part of the hot shroud surface. Furthermore, a bimodal pattern is formed for this type of NEKOMIMI holes, which is desired, promotes the generation of ACRV and therewith further enhances the film cooling effectiveness. However, a high lateral distance between the NEKOMIMI ears lowers the robustness of the film cooling hole against compound angles between the NEKOMIMI orientation and the approach flow. Thus, the orientation becomes more challenging. Otherwise the coolant mass flow may be distributed uneven inside the diffusor part and the bimodal pattern cannot establish. The NEKOMIMI-shapes with smaller lateral and streamwise propagation are more robust with regard of compound approach flow angles and perform better, when the orientation is not optimal due to restriction by the supply air situation or if the holes are located in regions with high static pressure gradients on the wall. The latter has an impact to the coolant mass flux distribution inside the diffusor of the shaped hole.

From these considerations it becomes clear, that the orientation and selection of adequate shaped film cooling holes for the application inside a gas turbine is challenging and requires profound knowledge about the technology.

Figure 15 shows the surface temperature on the outer shroud platform for the DJFC and the NEKOMIMI configuration. As shown in section 4.1, two zones with increased temperatures are located close to the trailing edge (zones (3) and ( 1)), which propagate towards the neighboring vane (zones ( 2) and ( 4)). On the inner shroud platform (see Figure 16) the DJFC holes inside zone (4) lead to a significant reduction of the temperatures, but this also leads to increased temperature gradients due to the locally very restricted effect of the DJFC holes. With the implementation of NEKOMIMI cooling holes, the temperature gradients could be reduced, but the maximum wall temperature is still on the same level as obtained for the DJFC configuration and located at the end of the platform. Due to the complex supply situation it is not possible to reposition the cooling hole exits towards higher axial positions to compensate the increased temperatures. In total three additional NEKOMIMI film cooling holes have been added to the test vane with regard to the number of DJFC holes -two to the inner and one to the outer shroud platform. One film cooling hole has been removed. However, the total coolant consumption for platform cooling could be reduced by 27%, while the surface temperature distributions on the inner and outer shroud platform have been significantly improved.

CONCLUSION

The present paper discusses the calculation procedure and the accuracy of conjugate heat transfer calculations for a modern, extensively cooled 1 st nozzle guide test vane in comparison to thermal index paint measurements. In general, numerical results are in good agreement with the experimental test engine data in terms of the wall temperature distribution and the direction of the coolant propagation after ejection through double jet film cooling holes, which are located on the inner and outer shroud platform. The paper furthermore shows how CHT simulations and TIP measurements can complement each other in order to obtain detailed information about the external and internal wall temperature distribution of gas turbine components exposed to high temperatures. The understanding of flow phenomena can be deepened and reasons for zones with increased temperatures can be figured out, which is essential in order to improve the design. The application of the NEKOMIMI film cooling holes on the inner and outer shroud platforms is one example for a successful design improvement.

Figure 1 .

 1 Figure 1. Solid body of the test nozzle guide vane with thermal barrier coating (TBC)

  (t: thickness of the TBC layer [m]; 𝜆: thermal conductivity of the TBC [W/m-K])

Figure 4 .

 4 It consists of a solid (left) and a fluid region (right). Congruent surfaces are defined as in-place interface and allow modeling of the heat transfer. The solid region corresponds to the test vane geometry provided by KHI. Small geometrical features of the solid body have been removed as they are not affecting the fluid flow and have minor effect to the thermal behavior of the vane body.

Figure 4 .

 4 Figure 4. Computational Domain of the CHT simulationsolid and fluid body The fluid region illustrated on the right hand side of Figure 4 consists of the following surfaces:  one main flow inlet (MFI)  two sealing air inlets (SAI) in-front of the inner (IS) and outer shroud (OS) platforms  two cooling air inlets (CAI) -one at top (connected to the outer cooling chamber (OCC)) and one at the bottom of the domain (connected to the inner cooling air chamber (ICC))  one main flow outlet (MFO)  six periodic surfaces (main flow passage, inner cooling chamber and outer cooling chamber)  adiabatic walls (grey)  solid-fluid interfaces (light green)The thermal load in the upstream region of the platforms is significantly influenced by the sealing air injection. Therefore, two sealing air inlets have been modelled infront of the test vane. The shape of the inner and outer cooling air chambers corresponds to the cavities inside the vane carrier.

Figure 5 .

 5 Figure 5. Boundary conditions applied to the fluid region of the test vane (principal).

Figure 6 .

 6 Figure 6. Boundary conditions applied to the solid body of the test vane.

Figure 7 .

 7 Figure 7. Computational mesh of the fluid and solid regionoverview and mid-span section

Figure 9 .

 9 Figure 9. Surface temperature of the test vane -TIP measurement and CHT results

Figure 10 .

 10 Figure 10. Surface temperature on the outer shroud platform of the test vane -TIP measurement (left) and CHT results (right)

Figure 11 .

 11 Figure 11. Surface temperature on the inner shroud platform of the test vane -TIP measurement (left) and CHT results (right)

  the platforms of the test vane are shown after 4900 operating hours (right and left hand side of the two figures). The thermal barrier coating has changed its color. It gives a qualitative indication of the temperature on the shroud platforms and therewith information about the flow directions close to the walls downstream of the DJFC holes.

Figure 12 .

 12 Figure 12. Inner shroud platform of the test vane after 4900 operating hours (right and left) and the CHT result (center)with streamlines starting inside the film cooling holes.

Figure 13 .

 13 Figure 13. Outer shroud platform of the test vane after 4900 operating hours (left), of the thermal index paint measurement (right) and the CHT result (center) with streamlines starting inside the film cooling holes. The CHT simulation results are illustrated in the center of Figures 12 and 13. Streamlines indicate the direction of the film cooling air ejected through the DJFC pairs.A comparison between the TBC discoloration and the CHT results shows that the calculated flow directions are in very good agreement with the ones inside the real gas turbine. Additionally both results show potential for the improvement of the DJFC hole orientation. However, due to the complex supply situation (connection to the inner/outer cooling chamber), the possibilities for variation of the DJFC hole arrangement and orientation are limited.To compensate this drawback of the DJFC technology, the NEKOMIMI-shaped film cooling holes have been invented. With one main supply hole, the transfer of the cooling air from the cooling chamber to the hot external surfaces of the gas turbine parts has been simplified significantly.It should be noted, that the following numerical comparison between the double jet and the NEKOMIMI film cooling approach, has been carried out on the basis of slightly different boundary conditions with respect to the simulations presented in section 4.1 and 4.2. The two simulations carried out for the present section -one with DJFC and one with NEKOMIMI-shaped film cooling holes -correspond to another load state of the engine. Figure14shows the mass fraction of the coolant inside the gas mixture on the inner and outer shroud platform. These values give an indication of the adiabatic film cooling

Figure 14 .

 14 Figure 14. Coolant mass fraction on the inner and outer shroud platform

Figure 15 .

 15 Figure 15. Surface temperature obtained for the outer shroud platform with the double jet film cooling (DJFC) and the NEKOMIMI design.An improvement of the platform temperatures has been achieved by application of a NEKOMIMI hole close to zone (1), this region with increased temperatures could be avoided. Additionally, zone (3) has been weakened. The application of the shaped film cooling holes has led to a more homogenous temperature distribution on the complete pressure side of the outer shroud surface.In the downstream part of zone (3), an additional NEKOMIMI hole has been placed. The established cooling film proceeds towards the neighboring vane platform. Besides the temperature reduction in zone (3), this also leads to a reduction of the thermal load in zone (2). On the inner shroud platform (see Figure16) the DJFC holes inside zone (4) lead to a significant reduction of the temperatures, but this also leads to increased temperature gradients due to the locally very restricted effect of the DJFC holes.

Figure 16 .

 16 Figure 16. Surface temperature obtained for the inner shroud platform with the double jet film cooling (DJFC) and the NEKOMIMI design.

ACKNOWLEDGMENTS

The numerical simulations presented in this paper have been performed with the commercial software package STAR-CCM+ by CD-adapco. B&B-AGEMA and Kawasaki Heavy Industries would like to thank CD-adapco for their support


Matevž Dular
email: matevz.dular@fs.uni-lj.si

Hydrodynamic cavitation damage in water at elevated temperatures

Keywords: cavitation, erosion, thermodynamic effect, model, thermodynamic parameter

In the present study we show experimental campaign where cavitation erosion in water at different temperatures was investigated. In contrary to other studies, where cavitation is generated by ultrasound, we employed hydrodynamic cavitation, which more closely resembles the conditions in applications -it is known that the results obtained by ultrasonic cavitation can be misleading. The tests were performed in a radial flow test-section, which can generate very aggressive type of cavitation. Polished aluminum samples were used to investigate the damage. Temperatures in the range between 30 and 100°C were investigated. We found out that the temperature of the water significantly influences the cavitation aggressiveness -maximum aggressiveness was found at 60°C. In the last part of the work two theories were developed and tested. Micro-jet approach correctly predicted the trend but the influence of the temperature was marginal. On the other hand, the theory of the spherical bubble collapse with consideration of thermodynamic effects of cavitation produced a very good agreement to the experiments.

INTRODUCTION

Cavitation is a phenomenon characterized by vapor generation and condensation in high-speed liquid flows. It frequently occurs in industrial configurations such as rotating machinery, injectors, and other hydraulic devices. Most of the time it is accompanied by effects like vibrations, increase of hydrodynamic drag, changes in the flow hydrodynamics, noise, erosion, light effects such as sonoluminescence, and also thermal effects [START_REF] Dular | Thermodynamic effects during the growth and collapse of a single cavitation bubble[END_REF][START_REF] Petkovšek | IR measurements of the thermodynamic effects in cavitating flowOriginal Research Article[END_REF].

Thermodynamic effects become significant only when the critical-point temperature is close to the operating temperature of the fluid, as in the case of cryogenic fluids [START_REF] Stahl | Thermodynamic aspects of cavitation in centrifugal pumps[END_REF]. Therefore, the understanding and the prediction cavitation effects in such cases is crucial in many applications; for example the turbopumps for liquid hydrogen LH2 and oxygen LOX in space launcher engines need to have an inducer rotor installed upstream from the main impellers, in order to achieve high suction performance [START_REF] Kamijo | Developmental History of Liquid Oxygen Turbopumps for the LE-7 Engine[END_REF]. The inducer is designed to operate in moderate cavitating conditions, hence a minimum pressure level in the tanks must be ensured, in order to avoid the occurrence of large sheet cavities on the blades, which are often associated with large-scale instabilities. Particularity well known is the failure of the Japanese H-II rocket due to rotating cavitation in the LH2 turbopump [START_REF] Sekita | Lessons learned from H-2 failure and enhancement of H-2a project[END_REF].

The new generation of rocket engines will also feature the possibility of re-ignition while in orbit, hence long term operation of LH2 and LOX turbo-pumps under cavitation conditions is becoming an issue.

A wide range of studies related to various aspects of the cavitation erosion problem -bubble dynamics, model development, CFD prediction, material testing etc.have been performed in the past [START_REF] Lauterborn | Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary[END_REF][START_REF] Dular | Relationship between cavitation structures and cavitation damage[END_REF][START_REF] Pereira | Prediction of Cavitation Erosion: an Energy Approach[END_REF][START_REF] Franc | Incubation Time and Cavitation Erosion Rate of Work-Hardening Materials[END_REF][START_REF] Pelz | On the Kinematics of Sheet and Cloud Cavitation and Related Erosion[END_REF][START_REF] Edts | [END_REF][START_REF] Peters | Numerical modelling and prediction of cavitation erosion[END_REF]. They all aim at improving the physical understanding of the phenomenon. Yet it seems, that with every new step we find new phenomena and physical background, which prove that cavitation erosion process is even more complex and its prediction even more elusive [START_REF] Dular | On the mechanisms of cavitation erosion -Coupling high speed videos to damage patterns[END_REF]. The effects of medium temperature on the aggressiveness of cavitation erosion were studied as early as 1960's ans 70's when Garcia & Hammitt [START_REF] Garcia | Cavitation Damage and Correlations With Material and Fluid Properties[END_REF], Young & Johnston [START_REF] Young | Effect of temperature and pressure on cavitation damage to a cobalt base alloy in sodium, Characterization and Determination of Erosion Resistance[END_REF] and Plesset [START_REF] Plesset | Temperature Effects in Cavitation Damage[END_REF] conducted vibratory tests. They have concluded that the decrease in the damage observed at higher temperatures can be attributed to either the increase in vapor pressure or the fact that the condensation driven collapse of a bubble at a higher temperature is slower, since more heat needs to be conducted into the surrounding fluid as a result of higher vapor density -when the temperature and pressure of the uncondensed vapor are raised, they arrest the bubble collapse, decrease collapse pressures and consequently damage. More recently the effects of medium and its temperature on acoustic cavitation aggressiveness were studied by Hatori [START_REF] Hattori | Cavitation erosion of silver plated coatings in a low-temperature environment[END_REF][START_REF] Hattori | Cavitation erosion of silver plated coatings considering thermodynamic effect[END_REF]. While they show that both play significant role in the process, few conclusions on the physical background of the measured results are provided.

In contrary to other studies, where cavitation is generated by ultrasound, we employed hydrodynamic cavitation, which more closely resembles the conditions in space propulsion applications. Cavitation aggressiveness on aluminum samples in water with different temperatures (from low to significant level of thermodynamic effects) was observed. In the discussion we derive a bubble dynamics model, which explains the dependency between the temperature of the medium (its thermodynamic parameter cavitation aggressiveness. The present study is a step towards evaluation of erosion in cryogenic liquids under a scope of the continuous work for the European Space Agency (ESA).

EXPERIMENT

Cavitation tests were performed in a small cavitation tunnel at the Laboratory for Water and Turbine Machines, University of Ljubljana. The geometry was adopted from the facility at the LEGI Grenoble [START_REF] Franc | Incubation Time and Cavitation Erosion Rate of Work-Hardening Materials[END_REF][START_REF] Franc | Material and velocity effects on cavitation erosion pitting[END_REF]. A 4.5 kW pump (1) enables the variation of the rotation frequency in order to set the flow rate. Downstream of the pump, a partially filled tank (2) is installed for water heating and for damping the periodical flow rate and pressure fluctuations. Cavitation and its effects are observed in a test section [START_REF] Stahl | Thermodynamic aspects of cavitation in centrifugal pumps[END_REF]. The water enters the section axially through the nozzle and exits it by 8 flexible pipes. The tank further downstream (4) is used for cooling of the circulation water -a secondary cooling water loop is installed in it. The valves ( 5) and ( 6) enable easy and fast disconnection of the test section from the main loop. The flow rate is measured by an electromagnetic flow meter (7) ABB ProcessMaster 300 (DN 40) with a 2% uncertainty on measurements. Temperature is obtained with a type K thermocouple [START_REF] Pereira | Prediction of Cavitation Erosion: an Energy Approach[END_REF]. The reference pressure is measured 35 mm upstream from the test-section by an ABB 266AST pressure transducer (9) -the uncertainty of the measurements is 8 mbar. The pressure in the test rig is adjusted in the partially filled tank (2) connected to a compressor [START_REF] Pelz | On the Kinematics of Sheet and Cloud Cavitation and Related Erosion[END_REF] and a vacuum pump [START_REF] Edts | [END_REF]. The precisions of the pressure, velocity and temperature measurements result in a mean uncertainty of 3% for the cavitation number.

Test-section

To ensure a highly aggressive cavitation conditions one needs to develop a test section where i) the pressure recuperation is rapid and ii) cavitation clouds implode in the vicinity of the specimen. Both conditions are easily achieved in the so-called radial jet testsection shown schematically in Fig. 2. The flow enters the section axially at a high velocity through a nozzle with a diameter of 10 mm. It then forced to turn at an angle of 90°, which makes it cavitate. The radius of curvature of the feed nozzle exit is 0.75 mm. The gap between the front and back plates is 2 mm wide. As the fluid moves radially outwards between the plates the pressure recuperates rapidly and cavitation zone abruptly closes. The flow exits the section axially through 8 holes in the back plate. The position of the specimen center lies at a radial distance of 22.2 mm from the center of the feed nozzle.

Specimens

Specimens (Fig. 3) were manufactured out of aluminum. The diameter of the surface which was exposed to cavitation is 30 mm. The surface was polished down to 1 hardness was measured to be 65HV.

Observation of cavitation

For the purpose cavitation observation the front plate of the test-section was replaced with a transparent one. The idea of this test was to obtain some general characteristics of cavitation behavior inside the section.

High speed camera Fastec Imaging HiSpec4 2G mono was used for image acquisition. Figure 4 shows images of cavitation in the test section recorded at a frame rate of 50000 frames per second (only every 10th image is shown in Fig. 4). Images of cavitation were recorded at a resolution of 176×86 pixels. Our results relate well to the observations in the original design from LEGI laboratory [START_REF] Gavaises | Visualisation and les simulation of cavitation cloud formation and collapse in an axisymmetric geometry[END_REF]. As mentioned, the water begins to cavitate at a 90° bend as it enters the gap between the plates. Cavitation clouds separate from the attached cavity and travel radially outwards to a higher pressure region where they collapse -roughly 20 to 25 mm from the center of the plate. We expect the highest erosion rate in the region of cavitation cloud collapse -near the outer perimeter of cavitation zone. A circle in Fig. 4 shows the position of the specimen.

Test conditions

The test parameters included 8 conditions where the water temperature was varied between 30 and 100°C and specimens were exposed to cavitation for a period 120 minutes. For cases of water temperature of 30 and 40°C, four additional measurements were made where the specimens were exposed to cavitation for only of 30 and 60 minutes.

EROSION EVALUATION

After the exposure to cavitation the specimen was photographed with a TESA-VISIO 300 GL DCC system. To photograph the entire surface of the specimen about 80 images were taken, each covering the area of 5.5 by 4 mm at a pixel size of approximately 7 m.

The images can be stacked together to obtain a high resolution image of the whole specimen surface (Fig. 5). Comparing the two individual images the damaged area can clearly be seen. As expected the damage follows a circle with the center in the middle of the test-section -the maximum damage lies at a radius of about 22 mm -the same as the closure region of cavitation (Fig. 4).

The evaluation followed the pit-counting technique [START_REF] Dular | Relationship between cavitation structures and cavitation damage[END_REF][START_REF] Pelz | On the Kinematics of Sheet and Cloud Cavitation and Related Erosion[END_REF]. Pits are recognized as the darker regions in an image, while the brighter area is assumed to be undamaged surface. The pitcount method gives a distribution of the number and the area of the pits and consequently, the distribution of the magnitude of cavitation erosion on the surface.

Figure 6 shows a typical result of evaluation (again for the case where specimen was exposed to cavitation for 120 minutes in water at T=30°C). One can clearly see that the damage is concentrated along a circular pattern at a radial distance of approximately 22 mm from the center of the test-section. Figure 6 also shows how the results were averaged according to the radial distance from the center of the section. One can describe the averaging by:

       mm r mm r pit r A R r L r A 2 . 37 2 . 7 ) ( ) ( 1 ) ( (1)
where A pit is the damaged area within an evaluated band (shown as gray area), L is the evaluated arch length (depending of the distance from the section center) and R is the width of the evaluated band (about 0.1 mm). A(r) represents the part of the area covered by pits and is given in %. The definition of the cavitation aggressiveness is unified among the researchers -most commonly it is related to the pit volume or the deformation energy needed to form a pit. It was shown in several studies [START_REF] Reboud | Analysis of damaged surfaces: Part I: Cavitation mark measurements by 3D laser profilometry[END_REF][START_REF] Lohrberg | Analysis of Damaged Surfaces and Part II: Pit Counting by 2D Optical Techniques[END_REF][START_REF] Escaler | Cavitation Erosion Tests on a 2D Hydrofoil Using a Surface-Mounted Obstacles[END_REF][START_REF] Bachert | Comparison of Different Methods for the Evaluation of Cavitation Damaged Surfaces[END_REF][START_REF] Pelz | Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction[END_REF] that the measurement of the surface of the pit correlates well to the pit volume, the damage energy and consequently to cavitation aggressiveness. Our present observations of the surfaces did not reveal significant dependence between the topology of the pit and the medium temperature; hence the area A(r) can be used as an indicator of cavitation aggressiveness.

RESULTS

The results are presented in diagrams showing the percentage of the damaged surface as a function of radial distance from the center of the section (Fig. 6 and Eqn. 1). First tests where the samples were exposed to cavitation at a low temperature (30 and 40°C) and for different lengths of time are shown and discussed (Fig. 7). These tests were performed to determine the most suitable time of exposure and also to evaluate the method. One can see that at a maximum about 5-7% of the surface was covered by pits after 120 minutes of exposure. Such a value is well placed as it lies in a range where significant number of pits is accumulated for further statistical evaluation, but there is also not significant overlapping of the damage, which could distort the results [START_REF] Dular | Relationship between cavitation structures and cavitation damage[END_REF]. One can also see that the damage increases approximately linearly with time, which corresponds to our previous experiments [START_REF] Osterman | Time dependant measurements of cavitation damage[END_REF]. The maximum of the damage lies roughly 22 mm from the center of the section (in the middle of the specimen), which coincides with the cavity closure line (Fig. 4).

Figure 8 shows the results of measurements where the specimens were exposed to cavitation for a period of 120 minutes at water temperatures between 30 and 100°C. One can clearly see that cavitation aggressiveness is strongly dependent on the temperature of the medium. As the temperature was increased from 30°C also the damage extent rose. The maximum is achieved at around 60°C. The cavitation remains aggressive for water of 70°C, then it sharply drops to level below the one at 30°C. The effected region did not change significantly between the tests -most of the damage is concentrated around the cavity closure line at R=22 mm.

DISCUSSION

Studies agree that cavitation structures carry a significant amount of potential energy and can, at their collapse, emit pressure waves of magnitude of several MPa [START_REF] Wang | Shock wave development in the collapse of a cloud of bubbles[END_REF]. Yet it seems that the macroscopic cavitation cloud collapse itself cannot be a direct cause of erosion as its energy is not enough concentrated. Currently the most widely accepted explanation of the phenomenon is that the potential energy contained in a macro-cavity transformed into the radiation of acoustic pressure waves, and further on into the erosive power contained in the micro-scale cavitation structures or single bubbles that collapse in the vicinity of the material boundaries [START_REF] Fortes-Patella | A phenomenological and numerical model for scaling the flow aggressiveness in cavitation erosion[END_REF][START_REF] Bark | Application of principles for observation and analysis of eroding cavitation[END_REF]. Two theories describe the last stages of life of a micro-scale cavitation structure -the micro-jet and the spherical microbubble collapse [START_REF] Chahine | Modeling of Cavitation Dynamics and Interaction with Material[END_REF]. Since the scientific community is divided between the two, we have used both approaches for explaining the physics behind our experimental results.

Micro-jet

If we assume that the bubble will collapse in the form of a micro-jet we can estimate its velocity according to the theory by Plesset & Chapmann [START_REF] Plesset | Collapse of an innitially spherical vapour cavity in the neighbourhood of a solid boundary[END_REF] and to experimental and numerical work by Chahine [START_REF] Chahine | Modeling of Cavitation Dynamics and Interaction with Material[END_REF]:

 v mj p p k v     .
(

) 2
k is a constant, which was determined to be k= 4.6 by Chahine [START_REF] Chahine | Modeling of Cavitation Dynamics and Interaction with Material[END_REF]. It is common to obtain velocities of the micro-jet in the order of several hundred m/s. The pressure induced on the solid material is the water hammer pressure reduced by the efficiency of the impact, which lies at 60% [START_REF] Chahine | Modeling of Cavitation Dynamics and Interaction with Material[END_REF]:

mj wh v c p      6 . 0 , ( 3
)
where c is the liquid sonic velocity. One can easily calculate the great erosive potential of such collapse. To take the effect of the temperature into an account we only need to consider that the sonic velocity and the density of the liquid will change with temperature. Figure 9 shows the dependence of the water hammer pressure as a function of temperature compared to experimental results of measured damage (the part of the specimen surface which was covered by pits -Aint). We postulate that there is a relationship between the magnitude of water hammer pressure and damage [START_REF] Dular | On the mechanisms of cavitation erosion -Coupling high speed videos to damage patterns[END_REF][START_REF] Dular | Development of a cavitation erosion model[END_REF]. Since we do not have the means to determine the pressure difference in Eqn. 2 we present the result in its nondimensional form: (if we assume that the pressure difference is independent of the temperature, then the prediction is only a function of liquid sonic velocity and liquid density, which are both temperature dependent). Although we see that the micro-jet theory predicts the maximum to lie at 60°C, what agrees with experiments, the predicted temperature influence on cavitation aggressiveness is insignificant -only about 3%. Such a small variation in the predicted water hammer pressure cannot explain the obvious and dependence of cavitation aggressiveness on the medium temperature. On the basis of these results we can deem the micro-jet approach as questionable or even false in the present case.

Spherical collapse

The second widely accepted mechanism that takes place in creating a pit is the shock wave, which is emitted at a spherical collapse of an even smaller bubble. The pressure field, in terms of the distance from the bubble center and the time pcs(r,t), can be determined by solving the Reyleigh-Plesset equation, which, for the case of fluids with considerable themodynamic effect, needs to be modified [START_REF] Dular | Thermodynamic effects during the growth and collapse of a single cavitation bubble[END_REF][START_REF] Brennen | The dynamic behavior and compliance of a stream of cavitating bubbles[END_REF]:

  R R μ R R R p + p T p = ρ t R Σ + R + R R ρ γ g0 v l l      4 2S 2 3 3 0 2                   , (4)
where:

  l pl l v α T c ρ L ρ = Σ  2 2 (5)
is the thermodynamic parameter [START_REF] Brennen | The dynamic behavior and compliance of a stream of cavitating bubbles[END_REF] and it depends on the liquid temperature. Here T ∞ is the test temperature,  v is the vapor density,  l is the liquid density, L is the evaporative latent heat, c pl is the constant pressure specific heat of the liquid and  l is the thermal diffusivity of the liquid.

The pressure emitted at collapse can be calculated as [START_REF] Franc | Fundamentals of Cavitation[END_REF]:

                   4 4 2 2 4 2 ) , ( r R r R R r R R p t r p l sc     . ( 6
)
The results put the maximal pressure in an order of several hundred MPa or even GPa -again one can appreciate the high pressure and erosive potential of such collapse.

By investigating several boundary conditions we concluded that the choice of the initial bubble size and the ambient pressure evolution do not influence the general (non-dimensional) outcome of the calculation -although the bubble dynamics and shock wave magnitudes change significantly, the predicted dependency of the shock wave magnitude on the temperature does not change. Figure 10 shows the dynamics of cavitation bubble (its radius) in time as a function of the temperature. A bubble with an initial radius of 2 subjected to an oscillatory pressure field with amplitude. A constant pressure amplitude f p∞,max-pv(T)=1.4 bar and frequency of 25 kHz was used (this way constant cavitation conditions (constant cavitation number) in terms of the temperature were assured). We can see that the collapse occurs roughly between 17 and 20 s after the bubble is exposed to the oscillatory pressure field. The bubble reaches the greatest size in the case at 50°C -about 27 m, compared to, for example, only 12m for the case of 100°C. It is important to notice that the time taken for the collapse (from the instant when the bubble reaches its maximal size to the time of the first rebound) is almost the same to all temperatures -about 3 s. Hence, the velocity of the collapse strongly depends on the temperature of the medium. Equation 6states that the faster the collapse, the greater will the shock wave be.

Figure 11 shows the prediction of the shock wave amplitude as a function of temperature together with the measured integral damage (Aint) -again (as for the micro-jet approach presented in Fig. 9) we use a non-dimensional scale for the magnitude of the shock wave. A secondary x-axis gives the values of the thermodynamic parameter  (Eqn. 5). For the sake of comparison we again assume that a relationship between the magnitude of the shockwave and damage exists [START_REF] Dular | On the mechanisms of cavitation erosion -Coupling high speed videos to damage patterns[END_REF][START_REF] Dular | Development of a cavitation erosion model[END_REF]. When the spherical bubble collapse theory with the addition of thermodynamic effects is considered the predicted trend lies much closer to the experimental one. A considerable influence can be seen at higher temperatures (T>60°C) where the thermodynamic effects play a major role -according to Hattori [START_REF] Hattori | Cavitation erosion of silver plated coatings considering thermodynamic effect[END_REF] this is above >100 m/s 3/2 . The maximal magnitude of the shockwave is predicted at 50°C, which somewhat differs from the maximum of measured erosion (60°C). Also the prediction does not comply well with the experiment at lower temperatures, although the trend is correct. Nevertheless we conclude that the spherical bubble collapse theory with the addition of thermodynamic effects is a valuable tool for the prediction of cavitation aggressiveness in thermosensible fluids.

Interestingly the presented theory also complies with the measurements by Hattori et al. [START_REF] Hattori | Cavitation erosion of silver plated coatings in a low-temperature environment[END_REF] who have shown that acoustically generated cavitation erosion in liquid nitrogen is marginal -the thermodynamic parameter of LN2 lies in the range of  =3•10

CONCLUSIONS

Measurements of hydrodynamic cavitation erosion in water at different temperatures were performed. In addition two models (micro-jet and spherical bubble collapse) were developed and tested against the measurements. The following conclusions can be drawn:  As in the case of ultrasonic cavitation, in hydrodynamic cavitation the thermal effect on erosion aggressiveness needs to be considered when >100 m/s 3/2

.

 Micro-jet theory correctly predicts the trend but the influence of the temperature is marginal.  The theory of the spherical bubble collapse with consideration of thermodynamic effects of cavitation produced a very good agreement to the experiments.  The theory of the spherical bubble collapse with consideration of thermodynamic effects also agrees with measurements in LN2 by Hattori et al. [START_REF] Hattori | Cavitation erosion of silver plated coatings in a low-temperature environment[END_REF].

Figure 1 .

 1 Figure 1. The test-rig.

Figure 2 .

 2 Figure 2. Test section design with indicated general flow pattern.

Figure 3 .

 3 Figure 3. Dimensions of the specimen (in mm) and its picture prior to the exposure to cavitation.

Figure 4 .

 4 Figure 4. A single image (frontal view) and a high speed sequence showing cavitation in the test-section (T=30°C, v=20.5 m/s, p∞=4.305 bar). The position of the specimen is shown by dashed line.

Figure 5 .

 5 Figure 5. High resolution image of specimen surface, which has been exposed to cavitation for 120 minutes in water at T=30°C.

Figure 6 .

 6 Figure 6. A typical result of pit-count evaluation (Water temperature is 30°C, time of exposure is 120 min).

Figure 7 .

 7 Figure 7. Damage distributions for tests at 30 and 40°C for exposure

Figure 8 .

 8 Figure 8. Damage distributions for tests at temperatures from 30 to 100°C for exposure time of 120 minutes.

Figure 9 .

 9 Figure 9. Prediction according to the micro-jet theory.

Figure 10 .

 10 Figure 10. Predicted bubble radius as a function of time for temperatures between 30 and 100°C.

Figure 11 .

 11 Figure 11. Prediction according to the spherical collapse theory.

5 m/s 3 / 2 -

 32 looking at the diagram in Fig.11one can indeed predict very gentle cavitation.

ACKNOWLEDGMENTS

The work was performed in the scope of the project "Cavitation in Thermosensible Fluids" financially supported by the European Space Agency (ESA).


Tewfik Ziadi
email: tewfik.ziadi@lip6.fr

Lom Messan Hillah

Software Product Line Extraction from Bytecode based applications

Keywords: Software Product Line, Bytecode, Analysis

This paper presents a Software Product Line (SPL) extraction approach to handle legacy software systems running on the Java Virtual Machine (JVM), for which the source code is unavailable, and factor in all input programming languages for the JVM. The approach extracts from the bytecode of a collection of software variants created using the Clone-And-Own approach a full SPL with its feature model. We provide a full implementation and integration in the BUT4Reuse framework. An early experiment was carried out on the ArgoUML case study and preliminary results are discussed.

I. INTRODUCTION

Software Product Lines Engineering (SPLE) [START_REF] Van Der Linden | Software product lines in action -the best industrial practice in product line engineering[END_REF] defines two phases: domain and application engineering [START_REF] Apel | Feature-Oriented Software Product Lines -Concepts and Implementation[END_REF]. Domain engineering defines the scope of the SPL, and specifies the commonality and variability among products using the concepts of features and feature models [START_REF] Apel | Feature-Oriented Software Product Lines -Concepts and Implementation[END_REF]. A feature is a prominent or distinctive characteristic, quality or user-visible aspect of a software system or systems [START_REF] Kang | Feature-Oriented Domain Analysis (FODA) Feasibility Study[END_REF]. Feature models (FM) are popular in SPLE to describe both variability and commonalities in a family of product variants [START_REF] Benavides | Automated analysis of feature models 20 years later: A literature review[END_REF]. Figure 1 shows a feature model illustrating a simplified example of an electronic shop. The E-Shop FM consists of a mandatory feature Catalogue, two possible Payment methods from which one or both could be selected, an alternative between two Security levels, and an optional Search feature.

Adopting an SPL approach and designing SPL variability is a major challenge for companies [START_REF] Krueger | Easing the transition to software mass customization[END_REF], [START_REF] Kästner | Variability mining: Consistent semi-automatic detection of product-line features[END_REF]. Berger et al. showed that around 50% of companies participating in industrial SPL Engineering cannot adopt SPL proactively [START_REF] Berger | A survey of variability modeling in industrial practice[END_REF]. On the one hand, the variability is discovered as customers' needs emerge over time; so, it is tough, if not impossible, to anticipate all the variations from the beginning. On the other hand, companies already have created product variants using opportunistic adhoc reuse to quickly respond to different customers' needs. As a consequence, instead of adopting an SPL, many companies clone an existing product and modify it to fit new customer needs [START_REF] Dubinsky | An exploratory study of cloning in industrial software product lines[END_REF]. This approach, called Clone-and-Own, is popular because it is faster and more efficient to start with an already developed and tested set of artifacts [START_REF] Dubinsky | An exploratory study of cloning in industrial software product lines[END_REF].

The Clone-and-Own approach incurs a severe drawback which is the high cost of managing and maintaining many variants at the same time [START_REF] Berger | A survey of variability modeling in industrial practice[END_REF]. For instance, when a bug is identified and fixed in one variant, the question of propagating the bug fix onto all existing variants becomes very difficult and error-prone when the number of variants increases. One solution to deal with this problem is to migrate these existing variants into an SPL.

Although the migration is a well-known challenge [START_REF] Lopez-Herrejon | Second international workshop on reverse variability engineering (REVE 2014)[END_REF], several approaches, referred to as extractive or bottom-up approaches, have been proposed for source code artifacts [START_REF] Linsbauer | Variability extraction and modeling for product variants[END_REF], [START_REF] Ziadi | Towards a language-independent approach for reverse-engineering of software product lines[END_REF] or models [START_REF] Martinez | Automating the extraction of model-based software product lines from model variants (T)[END_REF]. In this work, we focus on the Java Virtual Machine Bytecode [START_REF] Lindholm | The Java R Virtual Machine Specification[END_REF] and propose an end-to-end solution for dealing with what is referred to in an SPL extractive approach as Feature identification. Feature identification consists in analyzing and comparing the existing product variants to identify commonality and variability in terms of features.

Instead of considering the source code of the product variants, we analyze the bytecode to identify features. This approach allows a generic end-to-end solution that can: i) Support any programming language based on the bytecode (e.g., Java, Scala, Groovy, Kotlin, etc.); ii) Perform feature identification on legacy systems where the source code is not available. We implemented our solution inside the BUT4Reuse tool [START_REF] Martinez | Bottomup technologies for reuse: automated extractive adoption of software product lines[END_REF].

This paper thus makes the following contributions: i) an original approach for commonality and variability identification between the bytecode of a set of product variants; ii) a full integration of the approach with an existing framework for SPL extraction, BUT4Reuse. This solution reuses a set of techniques for feature identification and location, reusable asset construction, variability model synthesis, and visualization; iii) an assessment of the proposed approach with one real case study. The paper is structured as follows: Section II presents the background concepts and states our motivations. Section III details the technical workflow of our solution. Section IV reports on the evaluation of the solution with an industrial case study. Section V reports on related work. Finally, Section VI sketches the perspectives to this work.

II. BACKGROUND AND MOTIVATIONS

A. Software Product Line Extraction with BUT4Reuse

In previous work, we introduced BUT4Reuse (Bottum-Up-Technologies for Reuse) [START_REF]Bottom-up adoption of software product lines: a generic and extensible approach[END_REF], [START_REF]Bottom-up technologies for reuse: automated extractive adoption of software product lines[END_REF], a generic and extensible framework for extractive SPL adoption. It is generic by enabling its use in different scenarios with product variants of different software artifact types (e.g., source code in Java, C, models, requirements, or plugin-based architectures). It is extensible by combining different concrete techniques for the relevant activities of extractive SPL adoption (i.e., feature identification, feature location, mining feature constraints, extraction of reusable assets, feature model synthesis and visualizations). Several validation studies of BUT4Reuse using different software artifact types or different extensions have already been published [START_REF] Martinez | Automating the extraction of model-based software product lines from model variants (T)[END_REF], [START_REF] Li | Mining families of Android applications for extractive SPL adoption[END_REF].

BUT4Reuse relies on adapters to support different artifact types. These adapters are the main extensible, pluggable components of the framework. An adapter is responsible for decomposing each artifact type into the constituting, distinct and atomic elements. It also defines how a set of elements should be constructed to create a reusable asset. Designing an adapter for a given artifact type requires three main tasks. The first task is to identify the elements that compose an artifact, at a selected granularity level. For the same artifact type, we can select from coarse to fine granularity (e.g., package level versus statement level for source code). The second task is to define a similarity metric between any pair of elements. An element comparing its similarity with another element returns as output a value ranging from zero (completely different) to one (identical). The last task is to identify structural dependencies for the elements. When the artifact type is structured, the elements will have containment relations. In the case of source code, program dependence graphs usually capture this information.

B. Bytecode as a universal JVM representation

The Java Virtual Machine (JVM) [START_REF] Lindholm | The Java R Virtual Machine Specification[END_REF] is a widely spread implementation of abstract computing machines [START_REF] Diehl | Abstract machines for programming language implementation[END_REF], originally designed to interpret programs written in Java. Its defining feature as a platform (hardware / operating system)independent execution environment comes from its instruction set, the Java Bytecode. Programs in several popular programming languages can compile to the Java Bytecode (e.g., Java, Kotlin, Scala, etc.).

Many libraries, such as ASM [START_REF] Bruneton | Asm: A code manipulation tool to implement adaptable systems[END_REF], provide an abstraction for manipulating the bytecode. ASM allows to handle the elementary instructions described above from a high-level model. Figure 2 illustrates a partial view of this model. It follows an object orientation, presenting concepts such as ClassNode that abstracts the bytecode to represent a class. Each ClassNode is composed of MethodNode and FieldNode, that abstract, respectively, methods and fields. The AbstractInsNode element abstracts the bytecode related to the statements inside a method.

III. SOFTWARE PRODUCT LINE EXTRACTION FROM BYTECODE VARIANTS

Figure 3 illustrates our approach, which runs in four steps. a) Decomposition in Atomic Bytecode Elements and identification of dependencies: This step takes as input the bytecode of a collection of system variants created using the Clone-And-Own approach. It decomposes each variant as a set of Atomic Bytecode Elements (ABEs). ABEs correspond to the main elements in the ASM model partially presented in Fig. 2. In addition, dependencies between elements are inferred at this stage. To implement this step, our approach uses the different visitors proposed by ASM to go through the bytecode and identify the ABEs.

b) Block Identification: We reuse our algorithm, called Interdependent Elements [START_REF] Ziadi | Feature identification from the source code of product variants[END_REF], which automatically identifies sets of ABEs that correspond to the distinguishable features from the model variants. We named Blocks these sets of ABEs. The detailed description of this algorithm was presented in [START_REF] Ziadi | Feature identification from the source code of product variants[END_REF] and [START_REF] Martinez | Automating the extraction of model-based software product lines from model variants (T)[END_REF]. We only underline in the following the important principles. The algorithm computes the interdependence among ABEs. Given a set of bytecode variants BVs, two ABEs abe 1 and abe 2 (of models from BVs) are interdependent if the two following conditions are fulfilled:

1

) ∃B ∈ BVs abe 1 ∈ B ∧ abe 2 ∈ B; 2) ∀B ∈ BVs abe 1 ∈ B ⇔ abe 2 ∈ B.
A Block is thus a set of interdependent ABEs that are distinguishable in the bytecode variants.

During this step, we also extract requires and exclusionmutual dependencies between blocks based on the ABEs dependencies. This extraction is defined as follows:

1) a block B1 requires another block B2 iff ∃abe 1 ∈ B1 and ∃abe 2 ∈ B2 and abe 1 requires abe 2 ; 2) a block B1 is in mutual-exclusion dependency with and block B2 iff ∃abe 1 ∈ B1 and ∃abe 2 ∈ B2 and abe 1 is in mutual-exclusion dependency with abe 2 .

c) Feature Identification: This step is a semi-automatic process where domain experts manually review the elements from the identified blocks to map them with the functionalities (i.e., features) of the system. BUT4Reuse integrates VariCloud [START_REF] Martinez | Name suggestions during feature identification: The VariClouds approach[END_REF], a technique that analyzes the elements inside each block and extracts words that help domain expert to identify features. VariCloud uses information retrieval techniques, such as the IF-TDF (frequency-inverse document frequency), to analyze the text describing elements inside blocks. The descriptions used by BUT4Reuse to build word clouds are thus provided by the specific adapter. For our bytecode adapter, words correspond to the names of classes, fields, and methods. d) Feature Model Synthesis: Once features are identified, the last step is to synthesize the feature model. Feature model synthesis represents itself an independent research field [START_REF] She | Efficient synthesis of feature models[END_REF]. BUT4Reuse integrated many simple techniques such as the alternatives before hierarchy. This technique is based on calculating first the alternative constructions from the mutual exclusion constraints, and then creating the hierarchy using the requires constraints. Constraints not included in the hierarchy are added as cross-tree constraints.

IV. EVALUATION

ArgoUML is an open source tool for modeling using UML diagrams. Variants for this tool originate from its Java codebase by removing specific features [START_REF] Couto | Extracting software product lines: A case study using conditional compilation[END_REF]. These features are mainly related to the tool support for the edition of different kinds of UML diagrams. We considered the bytecode of the original ArgoUML and the seven variants related to diagram edition support (8 artifacts in total). Table I shows these variants along with their the number of lines and atomic bytecode elements. As an example, the first row, ActivityDisabled, means that this tool variant contains all the features related to UML diagrams edition except for Activity diagrams.

Figure 4 shows the distribution of the identified blocks (colored stripes) over the artifacts (vertical bars) of the eight variants of ArgoUML. Block 0 (first stripe in all variants) is the most common one, representing the core of the ArgoUML product line. Figure 5 shows the distribution of the identified blocks over the eight ArgoUML variants. Again Block 0 is present in all variants, while Block 4 is present in all variants except CollabDisabled, which corresponds to the ArgoUML variants without the support of Collaboration diagrams. Figure 6 shows the VariClouds for Block 3 (above the black line) and Block 4 (below the black line). Their contents reveal that Block 3 (fourth stripe in Fig. 4) implements the support of Sequence diagrams, while Block 4 (fifth stripe in Fig. 4) implements the support of Collaboration diagrams. This confirms why Block 4 is missing in the CollabDisabled variant, as shown in Fig. 5.

Table II shows the identified blocks and their respective sizes in terms of ABEs. ArgoUML variants' specific implementing features can be easily identified in the first seven blocks, by manually inspecting their corresponding VariClouds, as illustrated in Fig. 6. The other remaining blocks contain fewer ABEs. After analysis of these remaining blocks, we identified them as blocks implementing the concept named feature interaction. Indeed, to implement any pair of two distinct features, it is common to add some implementation elements to glue these features.

The outcomes of our experiment are available online 1 , to allow the reader to reproduce the same experiment.

V. RELATED WORK

The JVM Bytecode has been subject to an important body of research investigations for a wide range of purposes, such as bug, vulnerability, malware detection, program verification and automatic testing, code obfuscation, and so on. The closest research line in our context studies code clone detection. Code clones may share a syntactic or functional similarity. Syntactic similarity arises with similar code patterns. There are three types of clones in this category. Type-1 clones are exact copies, with perhaps differences in whitespace, comments, or layout. In Type-2 clones, variables or functions have been renamed, 1 https://pages.lip6.fr/Tewfik.Ziadi/iceccs18.html or types have changed. Type-3 clones have added or deleted statements. Type-3 clones are also termed gapped clones [START_REF] Ueda | On detection of gapped code clones using gap locations[END_REF]. Functional similarity refers to semantic similarity in Type-4 clones, regardless of syntactic code patterns. Approaches in code clone detection generally fall into six categories according to the underlying technique: text-based [START_REF] Svajlenko | Fast and flexible large-scale clone detection with cloneworks[END_REF], token-based [START_REF] Wang | CCAligner: a token based large-gap clone detector[END_REF], tree-based [START_REF] White | Deep learning code fragments for code clone detection[END_REF], graphbased [START_REF] Higo | Incremental code clone detection: A pdg-based approach[END_REF], metrics-based [START_REF] Choi | Extracting code clones for refactoring using combinations of clone metrics[END_REF], and hybrid [START_REF] Jia | KClone: A Proposed Approach to Fast Precise Code Clone Detection[END_REF]. Some code clone detection techniques have considered the bytecode as the primary artifact [START_REF] Yu | Detecting java code clones with multi-granularities based on bytecode[END_REF]- [START_REF] Cuomo | Cd-form: A clone detector based on formal methods[END_REF], to detect Type 3 and 4 clones.

X X X X X X X X X X X X X X
The Clown-and-Own paradigm in SPLE yields clones that span across the four types. In Type-1, product variants may share the same code, except for whitespace, comments, and layout. This type of clones is rare in the context of meaningful SPLE. In Type-2, some product variants might have renamed, even changed the types of some variables and functions. In Type-3, some product variants might have enhanced, updated, added, or removed some features of the product line according to the products development strategy and customers' needs. Finally, in Type-4, some algorithms might have been redesigned (e.g., changing or tuning a sorting algorithm for performance reasons), or the developers might have switched to other programming languages to craft the same features.

We would classify our solution as targeting all types of clones. However, it bears some notable differences with other code clone detection approaches. Firstly, it is semi-automated, and each instance of extraction is domain-specific: the developer is always in the loop since s/he writes the corresponding adapter in the BUT4Reuse framework. Secondly, our solution is more generic and flexible, as it allows the product line engineer to adapt the extraction procedure to the semantics of similarity s/he considers. We believe this flexibility is relevant in many industrial contexts. We experimented an extraction approach where statements in methods' bodies were considered (not reported in this paper) and another where they were discarded. In terms of granularity in extracting feature-implementing blocks, we consider methods and classes (thus identified thanks to their signature) as first-class units of decomposition. Finally, there is no single tool that can comprehensively handle all four types of clones, the costs of complexity and scalability just being too high. Hence the flexibility of our approach makes it amenable to business context-focused applications, without paying a costly upfront investment.

VI. CONCLUSION

The extraction of product lines from software artifacts has demonstrated its relevance in leveraging a more systematic, model-based product-line approach in developing large families of related software. It can help increase productivity in companies and Open Source communities who produce large code bases using a clown-and-own approach. The main trend of the extraction paradigm is to consider source code. This paper presented an extraction approach from the Java Virtual Machine (JVM) Bytecode, to handle legacy software systems for which the source code is unavailable, and factor in all input programming languages for the JVM. An early experiment was carried out on the ArgoUML case study and preliminary results discussed.

The first perspective to this work is to consider the behavior of methods, as mentioned in the previous section. To this aim, we will adapt traditional clone detection techniques that deal with programs semantics. The second perspective is to have our adapter propose different options regarding the flexibility of the bytecode decomposition approach, related to different granularities of extraction. Last, we will enrich the evaluation with various product families implemented in several JVMbased languages.

Fig. 1 .

 1 Fig. 1. E-Shop feature model

  Fig. 2. ASM Model

Fig. 3 .

 3 Fig. 3. Our approach

Fig. 4 .

 4 Fig. 4. Bars represent the artifacts of the eight variants, stripes the distribution of blocks over the artifacts

Fig. 5 .Fig. 6 .

 56 Fig. 5. Distribution of identified blocks over the ArgoUML variants

TABLE I ARGOUML

 I VARIANTS: NUMBER OF LINES OF CODE AND INSTRUCTIONS IN THE BYTECODE.

		LOC	ABEs
	ActivityDisabled	118,066	24282
	CollabDisabled	118,769	26085
	DeployDisabled	117,201	25912
	Loggingdisabled	118,189	26010
	Original	120,348	26289
	SequenceDisabled	114,969	25570
	StateDisabled	116,431	25687
	UsecaseDisabled	117,636	25906

TABLE II NUMBER

 II OF ATOMIC BYTECODE ELEMENTS PER BLOCK AND IDENTIFIED FEATURES IN THE ARGOUML CASE STUDY

		ABEs	Identified feature
	Block 0	21310	Core
	Block 1	243	Cognitive
	Block 2	376	Use cases
	Block 3	688	Sequence
	Block 4	195	Collaboration
	Block 5	588	State
	Block 6	370	Deployment
	Block 7	2440	Activity

CollabDisabled X X X X X X X X X X X X X X X X DeployDisabled X X X X X X X X X X X X X X X X X LoggingDisabled X X X X X X X X X X X X X X Original X X X X X X X X X X X X X X X X X X X X SequenceDisabled X X X X X X X X X X X X X X X X StateDisabled X X X X X X X X X X X X X X X X X UsecaseDisabled X X X X X X X X X X X X X X X X X

ACKNOWLEDGEMENT

This work was partially supported by the ITEA3 15010 REVaMP2 project: FUI the Ile-de-France region and BPI in France. Special thanks to our students Koita Demba and Lazovic Sasa for their active involvement in implementing the adapter.