Qi Liu

Sarra Tadrent

Christophe Proust

Francois Gomez

Anissa Khelfa

Denis Luart

Christophe Len

Theoretical analysis of the "green" synthesis of aniline by reduction of nitrobenzene

. In particular, activated carbon and water are used instead of hydrogen on a metal catalyst without a precise detail of the process. In the present paper, a theoretical analysis is proposed based on a step by step thermodynamic examination of elementary reactions. It is found that the Haber mechanism is theoretically possible but that due to the size of the pores of the carbon, inside which the reduction occurs, only the smallest molecules can move so that the "direct" path is favored. This can explain

2

why the yield is rather good.

1.Introduction:

Aniline (AN) is an important chemical intermediate used for instance to synthesize polyurethane [START_REF] Travis | Manufacture and uses of the anilines: A vast array of processes and products[END_REF], The traditional way to produce AN is to reduce nitrobenzene (NB) to AN using hydrogen over a metal catalyst can produce a 100 % selectivity towards AN at high pressure and temperature between 100 and 200°C [START_REF] Couto | Hydrogenation of nitrobenzene over a Pd/Al2O3 catalyst-mechanism and effect of the main operating conditions[END_REF], the process is particularly selective and efficient (about 67% yield) [START_REF] Varkolu | Nitrobenzene hydrogenation over Ni/TiO2 catalyst in vapour phase at atmospheric pressure: influence of preparation method[END_REF][START_REF] Wisniak | Reduction of nitrobenzene to aniline[END_REF]. 100 Years ago, Haber [START_REF] Haber | Gradual electrolytic reduction of nitrobenzene with limited cathode potential[END_REF] proposed a reaction pathway (Figure 1) for the reduction of NB according to which the "direct three steps" reduction of the NB molecule is competes a "condensation/reduction" route implying larger molecules. Note that the traditional production route raises serious safety and environmental concerns. NB and hydrogen can produce very severe explosions [START_REF] Tong | 3, 4-Dichloroaniline autoclave incident[END_REF] and AN is toxic [START_REF] Gheewala | Biodegradation of aniline[END_REF], which would increase the accident consequence in case of a primary explosion of the reactor.

The presence of metal in the products of the reaction is also to be avoided because of environmental concerns.

In this regard, the scientific community looks for an alternative process for the hydrogenation of nitro compounds in which hydrogen is produced in situ by a water-gas shift reaction (WGSR).

Hydrogen is produced by the conversion of a mixture of carbon monoxide and water vapor into a mixture of carbon dioxide and hydrogen. Hydrogen is then continuously consumed by the NB. But this hydrogenation process still requires the use of metal catalysts [START_REF] Pardey | The reduction of nitrobenzene as catalyzed by poly (4-vinylpyridine)-immobilized [Rh (COD)(amine) 2](PF6) complexes under WGSR conditions[END_REF][START_REF] Pardey | Water gas shift reaction and nitrobenzene reduction catalysis by tetracarbonyldi-μ-chlorodirhodium (I) complex immobilized on poly (4vinylpyridine)[END_REF][START_REF] Sivcev | Efficient reduction of nitroarenes using supercritical alcohols as a source of hydrogen in flowtype reactor in the presence of alumina[END_REF]. Recently, our group proposed and tested a new process successfully, also involving a WGSR without requiring the use of a catalyst [START_REF] Tadrent | Metal-free reduction of nitrobenzene to aniline in subcritical water[END_REF]. This new "green" chemical process is briefly recalled below with some typical results. But the details of the chemical reaction scheme were not clearly known and the present paper is an attempt to clarify this. To do this, a totally new "chemical equilibrium simulator", CIRCE, developed by the present team, is used which is described below also.

Some Experimental Details

The environmentally friendly approach for the reduction of NB to AN promoted by carbon catalyst was achieved successfully using activated carbon in water under subcritical water conditions. Hydrogen is generated and consumed in situ, and the synthesis temperature needed is lower (300 °C under 90 bars), which limits the risk of explosion. Furthermore, there is no need to use a catalyst. Only some representative results of the experimental work were selected. A 10 mmol of NB (1.23 g) was dissolved in 55 mL (55 g, 3 moles) of water and mixed with 6 g of carbon. This "carbon" is charcoal either activated or not. For the present study, "untreated carbon" under the form of graphite powder "chemically" activated carbon Dacarb PC1000 and "physically" activated carbon Norit Gac 12-40 were used under the form of powders with a particle size on the order of 50 µm. One of the main features of activated carbon is porosity. The graphite powder is not porous and its specific surface is that of the particle (about 30 m 2 /g). Activated carbons are intrinsically porous (Figure 3) with a specific surface of about 900 m 2 /g for Dacarb PC 1000 and Norit Gac 12-40. Pores usually characterized by their diameter: micro < 2 nm, meso 2-50 nm and macropores > 50 nm. For Dacarb and Norit, most (90%) of the porosity is meso and micro. At the end of the reaction, the autoclave is cooled down to 40 °C. The condensates are extracted and analyzed. All experiments were repeated at least three times and the scattering (in the compositions) was less than 5%. Two parameters are considered hereafter : the "progress" of the reaction which is the number of reacted moles of NB divided by the initial number of moles of NB (in %) and the "yield" of the reaction which is the number of moles of AN divided by the initial number of moles of NB (in % also named conversion rate of NB into AN).

A parametric investigation was performed and in particular the influence of the temperature. The influence of the reaction temperature on the rates is shown in Table 1 for Norit activated carbon.

It is observed that the yield increases with the temperature and to reach a maximum of 63% at 310 °C. About the influence of the nature of the carbon, graphite is clearly less efficient (Table 2). phases and many products. Gibbs showed that whatever the complexity, the final thermodynamic equilibrium is reached when the Gibbs energy of the system is minimum [START_REF] Gibbs | The collected works of J. Willard Gibbs[END_REF]. Some software [START_REF] Gordon | Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications[END_REF]Liu et al., submitted in 2019;[START_REF] Plus | Aspen technology. Inc[END_REF] were developed to solve this sort of "Gibbs problem". We have shown elsewhere that they usually fail when 3 phases are present (Liu et al., 2019(Liu et al., , submitted in 2019)).

Because of this, our team developed a new software, CIRCE, able to deal with such very complex situations. The code is described elsewhere [START_REF] Liu | Improving the predictability of chemical equilibrium software[END_REF]. The group theory of UNIFAC [START_REF] Fredenslund | Computerized design of multicomponent distillation columns using the UNIFAC group contribution method for calculation of activity coefficients[END_REF] and the LCVM [START_REF] Boukouvalas | Prediction of vapor-liquid equilibrium with the LCVM model: a linear combination of the Vidal and Michelsen mixing rules coupled with the original UNIF[END_REF] equation of state are used to implement as accurately as possible the influence of the non-idealities (activity coefficients, compressibility...). The code can be used to find the thermodynamic equilibrium in various conditions, at constant temperature and pressure as done hereafter, but also in a variety of adiabatic conditions. It can also be used to calculate the evolution of the Gibbs energy of a given reaction ΔGreaction (P, T) as a function of T or P:

. A-> b. B + c. C (1)
where A, B C are chemicals products and a, b, c the stoichiometric molar ratios.

= . , + . , -. ,

When P and T are such that the Gibbs energy of the reaction is positive, the reaction cannot proceed. where , are chemical potentials of product 'a'.

Thermodynamic analysis

This analysis is conducted in two steps. In the first one, the thermodynamics of each potential elementary reaction is investigated thermodynamically, and in the second step, the Gibbs energy of the reaction is minimized taking into account of only the products likely to appear.

Elementary reactions

Qi and al. (Liu et al., submitted in 2018) developed a simple method to identify, which reaction is possible as a function of the T, P conditions. To summarize this method, CIRCE can propose

the list of all the potential stable products, which could be formed based on the atomic composition of the reactant. Note that radicals do not appear "naturally". In the present situation, radicals where ignored. Based on this product database, the balanced reaction can be built, starting from the raw molecules. The process is continued with the molecules resulting from this first step up to the smallest.

Cyclic compounds are known to be very stable and difficult to decompose at low temperature.

In particular, aromatic compounds, in which all ring atoms participate in a network of bonds, present an unusual stability. For instance, the thermal decomposition of benzene has been shown

by [START_REF] Zanetti | The Thermal Decomposition of Benzene[END_REF]) to start at 500 °C. NB start to decompose at 356 °C [START_REF] Condit | Thermal Decomposition of Nitroxylene and Nitrobenzene[END_REF]. Nevertheless, NB is very stable and can only generate into benzenebased compounds [START_REF] Matveev | Kinetics and mechanism of the decomposition of nitrobenzene in the gas phase[END_REF]. The possibility to condensate 2 aromatic cores was given to test this chemical route for producing AN. On these bases, from the list of potential products proposed by CIRCE only the following ones remain: H2, O2, N2, CO, CO2, C6H7N, C6H7NO, C6H5NO2, C6H5NO, C12H10N2, C12H10N2O, H2O, C6H7N, C6H7NO, C6H5NO, C12H10N2, C12H10N2O, C. Starting from the raw compounds, the first elementary reactions are:

+ ! " → " + ! (3) " + ! " → CO ! + ! (4) % & '" ! + ! → % & '" + ! " (5)
% & '" ! + ! " → % % + '" (

% & '" ! + ! → % ) ' + " ! (7)

% & '" ! + ! " → % % " + '" ! (8)
The evolution of the Gibbs energy of all these reactions as a function of the temperature at 80 bars is shown in Figure 5. Those for which the Gibbs energy is positive are thermodynamically very limited in terms of yield, and among the thermodynamically favored reactions (negative Gibbs energy), those with the smaller Gibbs energy should typically dominate although this is not a sufficient condition (kinetics needs also be considered). 3) Reaction ( 4) Reaction ( 5) Reaction ( 6) Reaction ( 7) Reaction ( 8) Consider first the hydrogenation reactions of NB (reactions 5 to 8). Clearly, reactions ( 5) is strongly favored so that the others would be hardly perceptible. Consider now the production of hydrogen which, in the context of the present experiments, is supposed to proceed from an oxidation of C by water (reactions ( 3) and ( 4)). Unfortunately, reaction (3) has got a positive Gibbs energy in the targeted temperature domain so that only very small quantities can be produced. But reaction (4) has a negative Gibbs energy so that the imbrication of both reactions may be able to produce enough hydrogen for the reduction of NB. This point was investigated separately simulating (using CIRCE) this water gas shift reaction (reactions ( 3) and ( 4)) in the present experimental conditions but without considering the presence of NB and associated compounds.

Only reactions (3) and ( 4) are thus considered. The results are presented in Figure 6. Note the whole range of pressure and temperature is presented since, in the experiments, the reactive mixture is heated from ambient to about 600 K is a closed reactor so that both the temperature and the pressure vary. The ordinate is the total number of moles of hydrogen produced. Remember that only 0.01 mole of NB is available. According to the Haber reaction mechanism, 3 moles of hydrogen are required to transform 1 mole of NB into 1 mole of AN. So, in the present context, only 0.03 mole of H2 is enough. Clearly, reactions (3) and ( 4) have the thermodynamic capability of producing enough H2 provided enough time is left for the reaction to proceed. The next reaction steps are elaborated based on the products issued from the feasible reactions of the preceding steps.

The second step is:

% & '" + ! → % ) '" (9)
% & '" + % ) '" → *! *+ ' ! " + ! " (10)
% & '" + ! " → % % + '" ! (11) Reactions ( 9) and ( 10) are clearly favored but not reaction (11).

The third step would be: The reactions ( 12) and ( 13) are both favored.

% ) '" + ! → % ) ' + ! 0 (12)
*! *+ ' ! " + ! → *! *+ ' ! + ! " (13
The last step would be: The reactions ( 14) and ( 15) are particularly unfavorable so that tiny quantities of AN can be expected from this reaction path. Since aromatic cycles are stable, no further reaction step is included. Following, the reaction scheme obtained this way is represented in Figure 10. This scheme only partly corroborates the Haber mechanism. The thermodynamic analysis suggests that C12H10N2 cannot be easily reduced into AN. C12H10N2 appears as a byproduct.

*! *+ ' ! + ! → *! *! ' ! (14) *! *! ' ! + ! → 2 % ) ' ! (

Simulating the chemical equilibrium

To simulate the chemical equilibrium, an isothermal reaction implying 10 mmol of NB (1.23 g) dissolved in 55 mL (55 g, 3 moles) of water and mixed with 6 g of carbon in a constant 100 mL vessel is considered to mimic the experimental conditions. The reaction temperature is varied in the range of 250°C -300°C. The calculation of thermodynamic equilibrium can be done with the CIRCE software. (Liu et al., submitted in 2019) From the preceding analysis, the selected final products are gases (H2O, H2, O2, CO, CO2, C6H7N, C6H7NO, C6H5NO2, C6H5NO, C12H10N2O, C12H10N2, C12H12N2), liquids (H2O, C6H7N, C6H7NO, C6H5NO, C12H10N2O, C12H10N2, C12H12N2) and solid carbon (to mimic the char which contains more than 90% m/m fixed carbon). Clearly, the simulation results look very different from the experimental results, although the list of products, as mentioned above, is reasonable (Figure 10). It is known that chemical equilibrium calculations using the Gibbs method provide the best possible yield of a reactive medium. If experimental results are "better" than simulated, it means that products are lacking in the database or too much of them are present.

The second option is investigated here, remembering that activated carbons are porous.

The larger molecules such as C12H10N2O are nanometers large so that they may hardly move or even be created in the micro-meso pores constituting most of the reactive surface of activated carbons. For this reason, it can be assumed that the direct reaction path would be favored (C6H5NO2->C6H5NO->C6H7NO->C6H7N).

The simulations were reprocessed after removing all the C12 molecules (Figure 10). The considered products are gases (H2O, H2, CO, CO2, C6H7N, C6H7NO, C6H5NO2, C6H5NO), liquids (H2O C6H7N, C6H7NO, C6H5NO2, C6H5NO) and solid (C).

Figure 1 .

 1 Figure 1. Potential reaction scheme for the reduction of nitrobenzene to aniline according to

Figure 2 .

 2 Figure 2. The proposed "green" process for the metal-free reduction of nitrobenzene to aniline on

Figure 3 .

 3 Figure 3. The structure of active carbon.

Figure 4 .

 4 Figure 4. Type of autoclave used to perform the experiments.

Figure 5 .

 5 Figure 5. Gibbs energy as a function of the temperature for reactions (3) to (8) (calculated using

Figure 6 .

 6 Figure 6. Calculated evolution of the maximum number of H2 moles produced during the heating

Figure 7 .

 7 Figure 7. Gibbs energy as a function of the temperature for reactions (9) to (11) (atmospheric

Figure 8 .

 8 Figure 8. Gibbs energy as a function of the temperature for reactions (12) and (13) (atmospheric

Figure 9 .

 9 Figure 9. Gibbs energy as a function of the temperature for reactions (14) and (15) (atmospheric

Figure 10 .

 10 Figure 10. The revised potential scheme for the reduction of nitrobenzene into aniline.

Figure 11 .

 11 Figure 11. Comparison between the simulation results in red (obtained with CIRCE with all 13

Figure 12 .

 12 Figure 12. Comparison between the simulation results in red (obtained with CIRCE with the

Table 1 .

 1 Influence of the reaction temperature (1.23 g nitrobenzene, 55 g water, 6 g Norit Gac 12-

	40).
	Entry	T (°C)	Yield. (%)	Progress. (%)
	1	275	33	82
	2	300	62	100
	3	310	66	100
	4	320	53	100

Table 2 .

 2 Influence of the nature of the carbon source (6 g carbon, 1.23 g nitrobenzene, 55 g water,

	310 °C).
	Entry	Carbon materials	Yield (%)	Progress (%)
	1	Graphite	35,5	100

Some details about the theoretical tools and methods

  It was shown during the experiments that the equilibrium was reached. The idea is to use the theories of the thermodynamic equilibria to investigate what could have happened in the chemical process. The process is particularly complex, involving several reactions, several

aspect of the carbon is a very important aspect, and the present calculations helped to understand this.

Acknowledgment

The authors thank the Ministère de l'Enseignement Supérieur et de la Recherche for its constant supports.

All of this suggests that not only the possibility to reduce NB to AN in subcritical water with carbon is viable but also that the yield of the reaction is favored by the porous nature of the carbon.

Obviously, other catalyst effects need to be accounted for [START_REF] Blaser | Selective catalytic hydrogenation of functionalized nitroarenes: an update[END_REF] but nevertheless, the diffusional/mechanical aspects of the reaction may explain a lot about the reaction.

Conclusion

The synthesis of AN by reducing NB is studied numerically, and the results are compared to experimental values in view of interpreting the results. The novelty of this synthesis path is that no added hydrogen, nor catalyst are used but the reduction is obtained using carbon and subcritical water. The latter reactants are supposed to produce hydrogen in situ, which is used to perform the reduction. Note that porous activated carbon is used.

To do the simulations, the in-house developed software CIRCE was used. CIRCE (LIU et al., submitted in 2018) is capable of providing the list of all products of a reaction (from the atomic composition of the reactants) and can calculate the multiphase chemical equilibrium.

The thermodynamic analysis or the elementary reactions suggests that the Haber reaction mechanism is only partly possible involving a direct path involving only C6 molecules and an indirect path involving C12 molecules. It is found that this second path is much less likely.

If both pathways are implemented, the calculated conversion rate of NB in AN is only about 30%, which is much less than measured with activated carbons (65%). Note this calculated yield is very much in line with the measurements when non-porous graphite is used instead of activated carbons. When the C12 molecules are withdrawn, the calculated yield is much closer to those measures with activated carbons. The interpretation is that large C12 molecule could hardly move inside the pores so that may not be produced or react. This would suggest that the mechanical

AUTHOR INFORMATION

Corresponding Author *E-mail: christophe.proust@ineris.fr

Notes

The authors declare no competing financial interest.


Hatim Belkhou
email: hatim.belkhou@imt-lille-douai.fr

Serge Russeil

Talib Dbouk

Mohammed Mobtil

Daniel Bougeard

Nicolas-Yoan Francois

Large Eddy Simulation of boundary layer transition over an isolated ramp-type micro roughness element

Keywords: LES, Boundary layer, CFD, Hairpin vortices, Roughness element, Laminar-turbulent transition

Boundary layer transition over an isolated surface roughness element is investigated by means of numerical simulation. Large Eddy Simulation (LES) flowmodeling approach is employed to study flow characteristics and transition phenomenon past a roughness element immersed within an incoming developing boundary layer, at a height-based Reynolds number of 1170. LES numerical results are compared to experimental data from literature showing the timeaveraged velocity distribution, the velocity fluctuation statistics and the instantaneous flow topology. Despite slight difference in the intensity of streamwise velocity fluctuations, the present LES results and experimental data show very good agreement. The mean flow visualization shows streamwise counter-rotating vortices pairs formation downstream of the obstacle. The primary pair induces an upwash motion and a momentum deficit that creates a Kelvin-Helmholtz type flow instability. The instantaneous flow topology reveals the formation of coherent K-H vortices downstream that produce turbulent fluctuations in the wake of the roughness element. These vortices are streched and lifted up when moving downstream. The velocity fluctuations results show that the onset of the turbulence is dominated by the energy transfer of large-scale vortices.

Introduction

Boundary layer transition is a known phenomenon occurring in a large range of industrial configurations and applications, and thus its prediction is of major importance and remains a crucial issue.

In a developing boundary layer flow, the transition regime from laminar to turbulent is an uncertainty state, which makes the boundary layer transition prediction a major subject of many studies. The flow over a smooth flat plate is expected to remain laminar until a certain distance range from the leading edge, but the presence of roughness structures triggers instabilities that can cause significant momentum transport. In separation control applications and aero-thermal problems theses disturbances and their impact on the momentum distribution normal to the wall are of great importance. Thus, the interaction between a boundary layer and structures immersed in it represents an interesting and complex problem.

The effect of roughness elements in promoting boundary layer transition is commonly [START_REF] Tani | Boundary-layer transition[END_REF][START_REF] Tani | Boundary-layer transition by isolated roughness[END_REF][START_REF] Von Doenhoff | The effect of distributed surface roughness on laminar flow[END_REF] linked to the height-based Reynolds number. This Reynolds number considers the roughness size as a characteristic length, so a roughness element with large enough size may greatly modify the transition mechanism for a developing laminar boundary layer, and accelerate the transition process. Till now, the structure details and creation of the turbulent-like boundary layers induced by different types of roughness elements are still not very well understood and analyzed.

Various flow disturbances may trigger this transition and act as an accelerating process source (i.e. natural, bypass, etc.). These disturbances are the sources of complex mechanisms which finally lead to turbulence. There are three main paths to turbulence:

• Natural: for smooth walls and flows with extremely low levels of dis-turbances (freestream turbulence, vibrations, etc.), boundary layer can remain laminar well beyond critical Reynolds values for bypass transition.

The transition results in this case from the amplification of unstable waves.

• Bypass: sufficient disturbances are present (such as in most engineering applications), so the flow transition occurs spontaneously and far upstream the natural transition location. In this case, the waves are no longer present and other instability structures are observed.

• Induced: It means that the laminar-to-turbulent transition is triggered by an element (wall-mounted obstacle, wall-roughness, etc.), which leads to instabilities and a rapid breakdown to turbulence.

In very common engineering applications, a wide range of heat exchangers are often used with complex surface geometries (surface obstacles used to enhance the overall efficiency), at various types of fluid and flow regimes. One of the major challenges in this framework is then to correctly model and simulate correctly the laminar-turbulent transition and thus capture the real physics behind. Indeed, laminar-to-turbulent transition can greatly influence several flow parameters like the pressure drop, drag coefficient and heat transfer efficiency.

Hence it is very important to understand these transition phenomenon in order to predict well transition processes.

For modeling transitional and turbulent flows, the Reynolds-Averaged Navier-Stokes (RANS) approach is one strategy mainly used for its reasonable computational time and simplified post-processing [START_REF] Corson | Industrial application of rans modelling: capabilities and needs[END_REF][START_REF]Progress in Hybrid RANS-LES Modelling, Notes on Numerical Fluid Mechanics and Multidisciplinary Design[END_REF]. The ability of RANS simulations to capture the laminar-to-turbulent transition is very limited and depends mainly on the flow unsteadiness and the predictive capability of the turbulence models.

In the work of Toubiana et al. [START_REF] Toubiana | Large eddy simulation and reynolds-averaged navier stokes modeling of flow in staggered plate arrays: Comparison at various flow regimes[END_REF], three modeling approaches were employed to study the evolution of three-dimensional transitional and turbulent flow characteristics and heat transfer in staggered plate arrays. Laminar, RANS and LES simulation have been compared for various Reynolds number ranging from 300 to 9000. A very significant deviation, up to 44% for friction factor and 27% for Colburn factor, in the transitional regime has been found when comparing all numerical approaches, showing that the various laminar and RANS models have great difficulties to predict the laminar-to-turbulent transition.

Zhang et al. [START_REF] Zhang | Fluid flow and heat transfer in plate-fin and tube heat exchangers in a transitional flow regime[END_REF] conducted numerical analysis of the unsteady behavior of transitional fluid flow and heat transfer in a plate-fin and tube heat exchanger.

The numerical results were compared to experimental results for the baseline plate-fin and tube heat exchanger for Reynolds number from 978 to 2257. Laminar, RANS standard k -ε (SKE) and LES approaches were used to simulate the transitional flow for a wide range of fin pitches. It has been found that the SKE model overestimates the heat transfer by at least 50% for all Reynolds numbers.

The laminar model shows good agreement for Reynolds numbers below 1000.

The LES is the only appropriate model for the analysis of flow and heat transfer in the transitional flow regime, where the laminar and SKE models failed.

Thus regarding the numerical studies of transitional flows, various RANS turbulence models were applied and showed their inability to accurately predict the transition location and its properties. Laminar to turbulent transition owing to instability processes cannot be predicted by statistical RANS models that average the turbulent structures. Thus, none of the turbulent structures are resolved in the RANS approach, and the Large Eddy Simulation (LES) appears as an interesting approach allowing to explicitly resolve a very wide range of time and eddies length scales (with DNS approach, which remains too costly for engineering applications). However, it is important to note that some RANS-based turbulence models were designed to predict the laminar-turbulent transition. Malan [START_REF] Malan | Calibrating the Gamma-Re theta Transition Model for Commercial CFD[END_REF] discusses the implementation and validation of the γ -Re θ , a Local Correlation based Transition Model (LCTM) based on the Shear Stress Transport (SST) k -ω model of Menter [START_REF] Menter | Two-equation eddy-viscosity turbulence models for engineering applications[END_REF] widely used for engineering applications.

Although the flow past obstacles and protrusions has been widely studied in turbulent and compressible boundary layers, supersonic and hypersonic flow regime [START_REF] Tirtey | Characterization of hypersonic roughness-induced boundary-layer transition[END_REF][START_REF] Sun | Numerical and experimental investigations of the supersonic microramp wake[END_REF][START_REF] Sun | Decay of the supersonic turbulent wakes from micro-ramps[END_REF][START_REF] Robinson | Coherent motions in the turbulent boundary layer[END_REF], surprisingly, the flow around an isolated obstacle immersed in a laminar and incompressible developing boundary layer has been reported in literature only in a few papers.

Ye et al. [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF] performed tomographic Particle Image Velocimetry (PIV) to study the influence of various isolated roughness elements on boundary layer transition at super-critical regime. Different roughness geometries mounted on a flat plate were studied, where the upcoming developing flow is laminar. The conducted PIV measurements enabled the analysis of the mean and instantaneous flow characteristics in the roughness wake. Flow instability is induced and leads to vortex systems generation and turbulent fluctuations, which are associated to the transition mechanism.

For similar flow configuration, Acarlar and Smith [START_REF] Acarlar | A study of hairpin vortices in a laminar boundary layer. part 1. hairpin vortices generated by a hemisphere protuberance[END_REF] undertook hot-film anemometry techniques to study discrete hairpin vortices and their induced flow patterns past a hemisphere protuberance placed in a stable developing laminar boundary. The authors concluded that the shear layer instability and related hairpin vortices play a significant role in the laminar-turbulent transition process, which confirms the PIV analysis of Ye et al. [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF].

Yanaoka et al. [START_REF] Yanaoka | Turbulence and heat transfer of a hairpin vortex formed behind a cube in a laminar boundary layer[END_REF] carried out three-dimensional direct numerical simulation (DNS) of a cube mounted on heated plate with an incoming laminar boundary layer to investigate the dynamics of the vortex structures formed in the wake and their impact on heat transfer. The numerical calculations were performed for a Reynolds number of 500 based on the cube size. A horseshoe and hairpin vortex system are generated behind the cube. Diaz-Daniel et al. [START_REF] Diaz-Daniel | Direct numerical simulations of a wall-attached cube immersed in laminar and turbulent boundary layers[END_REF] studied the flow past wall-attached cube immersed in laminar and turbulent boundary layers by means of DNS at various Reynolds numbers. The flow mechanisms and structures generated downstream of the wall-attached cube are analyzed through turbulence energy spectra. It was found that the flow around a wall-attached cube strongly depends on the upstream flow conditions and generates an additional low-frequency far-field peak for turbulent incoming boundary layers.

The state of knowledge regarding the induced flow transition process past an immersed isolated roughness is limited. For theses cases, the details of the laminar-turbulent transition onset and evolution are still in question. The case of an isolated wall-mounted roughness, although simplistic, may represent a reference scenario for incompressible boundary layer transition induced by an immersed obstacle. Such flows are encountered in various engineering applications (automotive heat exchangers, HVAC heat exchangers, airfoils, etc.).

One of the main objectives of the present paper is to develop and validate a numerical methodology based on Large Eddy Simulation (LES) technique, by comparing numerical results to experimental data obtained by tomographic PIV [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF][START_REF] Ye | Boundary layer transition mechanisms behind a micro-ramp[END_REF]. The LES approach is then used for an extensive analysis of the induced transitional regime focusing on the mean and instantaneous flow organization as well as the turbulent statistics.

Simulations overview

The developing air flow over a flat plate equipped with an isolated roughness element is investigated. The geometry of the protrusion studied in the present paper follows the experimental work previously published by Ye et al. [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF], that is the micro-ramp. The roughness element with a height of 2mm and a span width of 4mm is placed at 290mm from the leading edge inside a developing laminar boundary layer flow. The air freestream velocity u ∞ is equal to 10 m/s, which is equivalent to a local Reynolds number of Re x = 176, 000 calculated at the roughness streamwise position. It indicates a laminar regime upstream the roughness position. It is worth to note that the roughness element is immersed within the laminar boundary layer: the ratio between the roughness height and the undisturbed boundary-layer thickness is h/δ 99 = 0.61. In such wall-mounted obstacle configuration, the height-based Reynolds number, i.e. Re h = h.u∞ ν , is often taken as a criterion for being in sub-or super-critical regime. In [START_REF] Tani | Boundary-layer transition[END_REF], it was established that the critical Reynolds number for an isolated roughness element ranges from 600 to 900 times aspect ratio power 0.4: (h/c) 0.4 (from 455 to 682 for an aspect ratio of 0.5). The simulations were carried out at a Reynolds number of 1170 based on the roughness height, indicating a supercritical regime.

Mathematical model

In order to perform a precise study of the transitional flow past roughness element, LES calculations are carried out using finite volume approach by means of the CFD software STAR-CCM+ 12.02 R . The following considerations were made:

• three-dimensional and unsteady flow,

• isothermal flow,

• constant fluid (air) properties,

• negligible gravity and compressibility effects.

The LES approach resolves explicitly the large scales of turbulence while modeling the small scale motions, by means of a filtering operation applied to the Navier-Stokes equations. The governing equations of the present flow are the three-dimensional, unsteady, incompressible filtered Navier Stokes equations, given by:

∂ρ ∂t + ∂ ∂x i (ρ u i ) = 0 (1) ∂ ∂t (ρ u i ) + ∂ ∂x i (ρ u i u j ) = - ∂ p ∂x i + ∂σ ij ∂x j - ∂τ R ij ∂x j (2)
where the stress tensor is defined as follows:

σ ij = µ ∂ u i ∂x j + ∂ u j ∂x i - 2 3 µ ∂ u i ∂x i δ ij (3)
where τ R ij is the subgrid-scale stress tensor and represents the effect of the subgrid-scale motions on the resolved grid-scale velocities of the fluid [START_REF] Zikanov | Essential Computational Fluid Dynamics[END_REF].

τ R ij = ρ u i u j -ρ u i u j (4)
Boussinesq approximation assumes the exchange of turbulent energy in the cascading process of eddies is analogous to that of molecular viscosity. The subgrid-scale tensor is thus modeled using the turbulent viscosity as following:

τ R ij = 2ν t S ij + 1 3 τ kk δ ij (5)
where S ij is the filtered resolved strain-rate tensor (=

1 2 ∂ ui ∂xj + ∂ uj ∂xi
). In the present study, the subgrid-scale tensor is modeled by the Wall-Adapting Local Eddy-viscosity (WALE) model which is based on the square of the velocity gradient tensor and has a proper near wall behavior that takes into account the effects of strain and rotation rates [START_REF] Nicoud | Subgrid-scale stress modelling based on the square of the velocity gradient tensor[END_REF]. The WALE subgrid scale model provides the following mixing-length type formula for the subgrid scale viscosity:

ν t = (C w ∆) 2 (s d ij s d ij ) 3/2 ( S ij S ij ) 5/2 + (s d ij s d ij ) 5/4 ( 6
)
where ∆ is the the filter width and C w the non-universal model coefficient.

The deformation parameter is defined as:

s d ij = 1 2 g 2 ij + g 2 ji - 1 3 δ ij g 2 kk ( 7
)
where g ij = ∂ ui ∂xj .

Numerical Procedure

Computational Domain

The studied geometry and computational domain are illustrated in figure 1.

The roughness height (noted h) is set to 2mm and its span width (noted c) to 4mm.

The origin of the coordinate system is located at the center of the roughness element. The x, y, z axes correspond respectively to the streamwise, wallnormal and spanwise directions. The study is focused on the flow nearby the roughness element, and especially the flow topology in the wake. Therefore, the computational domain is chosen as a rectangular box with a length of 55h, based on the roughness height (h). The roughness element is installed 10h downstream of the inlet. The width of the domain is 20h and the height is set to 5h, allowing minimal influence of the boundary conditions applied to the domain sides. The choice of these values are based on the experimental region of interest chosen for flow topology visualization by [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF], see for example the green dashed line in figure 1 which represents the limit for experimental measurement domain height. In order to reduce the computational domain size, a two-dimensional laminar boundary layer profile is specified at the inlet boundary, which was set 270mm downstream the plate leading edge. The imposed profile is based on a Blasius 195 boundary layer velocity profile [START_REF] Schlichting | Boundary-layer theory[END_REF]. At the outlet boundary, an outlet-pressure boundary condition with a fixed pressure value is imposed. No-slip conditions are assumed at the roughness and plate surfaces. The remaining boundaries are set to walls with a slip boundary condition on the velocity.

Grid generation

200

A structured non-uniform mesh combined with a mesh refinement in the wake region and a near-wall refinement are applied. In order to maintain a smooth transition between the refined wake region and the domain complemen-tary regions, transition regions are used. The detailed procedure of the wake refinement module can be found in the user guide [START_REF] Software | User guide Star-CCM+ version 12[END_REF]. Wall grid generation is applied to accurately capture the boundary layer and maximum y + is computed and found to be 0.96, thus respecting y + < 1. An example of the grid is shown in figure 2. A grid resolution study, to check the solution mesh-independence, was conducted using different three mesh sizes. The global skin friction coefficient is computed and used as a first indicator for the grid dependency. The refined mesh contains 7M cells. The coarse and medium meshes contain respectively 2.5M and 4.7M cells and the mean skin friction coefficient rate equals to 7.8% and 2.8% of the refined mesh mean skin friction coefficient. In this paper, the results based only on the 4.7M grid system are shown.

Moreover to further assess the mesh quality, we also adopted the most common criterion for LES found in the literature which is the index of resolution quality. This mesh quality index is defined as the ratio between the resolved turbulent kinetic energy and the total kinetic energy: LES IQ = kres ktot .

Celik [START_REF] Celik | Index of resolution quality for large eddy simulations[END_REF] suggested an estimation of this ratio, based on the Kolmogorov scale as the following:

LES IQ η = 1 1 + a η ( h η k ) m (8)
where a η and m are two parameters that will be determined later. In first ap-

proximation: h ≈ V 1 3
, where V corresponds to the cell volume. The Kolmogorov scale is defined as:

η k = ( ν 3 ε ) 1 4
, where ε corresponds to the total dissipation rate.

For the LES simulations, the total energy dissipation rate is computed as follows (sum of the resolved and modeled dissipation):

ε = ε res + ε mod = ν + ν t 2 ( ∂u i ∂x j + ∂u j ∂x i ) 2 (9)
In the literature, a LES simulation is usually considered as correctly resolved if 80% of the total kinetic energy is solved [START_REF] Pope | Ten questions concerning the large-eddy simulation of turbulent flows[END_REF]. According to Pope [START_REF] Pope | Turbulent flows[END_REF], the motions responsible for the dissipation have a larger scale than the Kolmogorov scale, with a ratio of 8 < h η k < 60, and a peak of dissipation of the turbulent kinetic energy located at h η k = 25. As Celik [START_REF] Celik | Index of resolution quality for large eddy simulations[END_REF] suggested, we consider that an index of resolution quality greater than 80% corresponds to a high-resolution LES and a value of 95% or more to a DNS. The parameters a η et m are determined by considering, for example, that h η k corresponds to a Direct Numerical Simulation (DNS) and h 25η k to a LES. Thus, the parameters a η = 0.05 / m = 0.5 are used in the study.

The local distribution of the index of resolution quality is shown in figure 3 for two characteristic planes. It is found that all IQ cell values are above 0.8 over the whole calculation domain. Thus, the considered mesh of 4.7M cells which details are shown in figure 2 was adopted for the present LES simulations.

Numerical methods

The equations governing the fluid flow are solved numerically using the Finite Volume Method (FVM) and the SIMPLE algorithm for pressure-velocity coupling [START_REF] Versteeg | An introduction to computational fluid 605 dynamics: the finite volume method[END_REF]. Spatial derivatives are discretized using a second-order central with the corresponding RANS simulation solution, and an integration of 500 h u∞ time units was used to reach a state that is independent on the initial conditions.

After an establishment period that ensures statistical convergence, data statistics for mean quantities are collected over 10,000 time steps (15 flow-through times) with a time step of 0.1 h u∞ . At each time step, solution convergence was achieved. It is worth to note that a convergence study for time averaging has been performed by comparing numerical results from a collection of 10,000 time steps and from an integration of 20,000 steps. Similar results of mean quantities were found, which consolidates our choice for this data processing time.

Time-averaged flow properties

Mean flow topology

The mean flow topology is examined by visualizing the distribution of the mean streamwise velocity u over three cross-sectional planes y-z located downstream of the obstacle. Moreover, a projection of the velocity streamlines on these planes was applied. Figure 4 illustrates the comparison of the mean flow topology between the LES simulations and the PIV experimental results [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF]. It should be mentioned that, in the present paper, the visualization domain of the LES simulation is adjusted so that its dimensions are equal to the experimental visualization domain (3hx10h). The mean streamwise velocity is normalized by the freestream magnitude. Downstream the obstacle, a pair of upwash vortices (TRP) is generated. In figure 4, a mushroom-like shape induced by the upwash movement as well as an axial velocity deficit in the plane of symmetry (z/h=0) are observed for both sets of results.

Moving downstream, the primary pair lifts up with a decrease of its intensity (x/h=15-25). As shown in figure 4, a second pair of induced counter-rotating vortices (SP) appears below the primary pair (x/h=15) in the near-wall vicinity.

The formation of such a system of vortex pairs is also observed by Ye et al. [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF].

The comparison between the LES and the PIV results shows a good agreement of the mean flow topology contours as well as the locations of the vortices at the different cross-sectional planes. It can be noticed that the downwash motion induced by the secondary pair produces a modification of the mean velocity profile in the symmetry plane (z/h=0): a velocity deficit at the saddle point located between the two pairs, below which the near-wall fluid is accelerated. The two swirling vortex pairs induces low and high momentum areas, corresponding to an increase of the shear stress which is associated with the generation of flow instabilities that leads to the transition from the laminar to the turbulent regime, as depicted in the following section.

Momentum deficit

Further comparisons are made by analyzing the momentum deficit via the local mean streamwise velocity profiles. These profiles are plotted in figure 5, superimposed with the experimental profiles as well as the undisturbed flat plate profiles (Blasius laminar profiles).

The results show a momentum deficit of velocity approximately equal to 0.6u ∞ located at y/h = 1.2 at the position x/h=5. Consequently, a strong inflection point bounded with two shear layers is produced. The lower zone is produced under action of the secondary pair of vortices, which transports the fluid of high moment towards the symmetry plane. The upper zone is produced by the trailing edge pair of the obstacle. The latter shear layer induces Kelvin-Helmholtz type instabilities, which leads to the formation of vortex structures.

When moving downstream (x/h=15 and 40), a decrease of the mean streamwise velocity deficit is observed, and the profile tends to flatten. This decay indicates the presence of a recovery process across the boundary layer. This process is dominated by the mixing of large swirling scales, referred to as the This movement is mainly attributable to the upwash motion of the main vortex structures (TRP, see figure 4). At the plane x/h=40, the intensity of the primary vortices is reduced and they are driven upwards by the upwash motion and are no longer detected within the visualization domain.

It can be seen from figure 5 that the recovery process is found to be slightly faster (between the planes x/h=5 and x/h=15) in the case of the numerical simulation LES compared to the experimental data [START_REF] Ye | Boundary layer transition mechanisms behind a micro-ramp[END_REF].

In order to quantify this momentum recovery process, a maximum velocity deficit rate is defined as the following: |u(y)-u BL (y)|max u∞ , where u BL is the Blasius streamwise velocity and u ∞ the freestream velocity.

As shown in figure 6, velocity deficit rate drops from 0.6 to 0.1 between the two positions x/h=5 and x/h=40. Downstream this position, experimental results show that the deficit is located in the upper zone of the boundary layer and its value remains constant.

For turbulent boundary layers, theoretical work [START_REF] Tennekes | A first course in turbulence[END_REF] and experimental studies [START_REF] Sun | Decay of the supersonic turbulent wakes from micro-ramps[END_REF] have shown that the maximum momentum deficit between the wake and the free stream follows a power-law decay. The validity of this law has been verified by Ye et al. [START_REF] Ye | Boundary layer transition mechanisms behind a micro-ramp[END_REF] for the micro-ramp roughness geometry in the range x/h= [7:27] that corresponds to a range dominated by swirling vortices.

The numerical momentum deficit rate is then computed from the present LES simulation results at different streamwise positions. A power-law fitting (black line) is done for the blue plot from figure 6 in the range x/h= [7:27] and is given by:

|u(y) -u BL (y)| max u ∞ = 4.0073 x h -1.084 . ( 10
)
The power exponent corresponds to the recovery rate of the momentum deficit.

It is an indicator of the large-scale momentum mixing efficiency. The numerical recovery rate found with our numerical simulation 1.084 is close to the experimental value reported by Ye et al. [START_REF] Ye | Boundary layer transition mechanisms behind a micro-ramp[END_REF] that is equal to 1.06, with a relative error of 2.3% which indicates a good agreement between both set of results which indicates a good agreement between both set of results.

Instantaneous flow

The instantaneous flow analysis is another important flow feature, because it is directly associated with the flow instability generated by the two main vortices pairs. The instantaneous flow topology is expected to differ from the mean topology, as large scale fluctuations induced by the micro-ramp and the Kelvin-Helmholtz (K-H) instability takes place. The dynamic characterization of the roughness-induced transition phenomenon is carried out by inspecting the temporal and spatial evolution of coherent vortex structures. This can be achieved by using the well known λ 2 criterion [START_REF] Jeong | On the identification of a vortex[END_REF], that allows the inspection of vortex organization within the flow. In order to highlight the accelerated and decelerated flow regions, and to allow a better comparison of numerial results with the experimental PIV data [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF], the isocontours of λ 2 are coloured by streamwise velocity. The attached supplementary material (movie 1) shows the perspective view of the time-evolution instantaneous flow organization that is analyzed in the following paragraphs.

The results show that the backflow region behind the micro-ramp (x/h≤4) is dominated by the trailing edge pair of vortices (TRP). The near-wake flow exhibits a quasi-steady behavior without any significant instabilities or fluctuations. Downstream this zone (x/h=5), Kelvin-Helmholtz instability mechanism appears and leads to the formation of vortex structures and fluctuations in the upper shear layer. These fluctuations are in agreement with the presence of a momentum deficit (inflection point) observed in figure 5.

As show in figure 7 by a detailed zoom near x/h=6, a primary hairpin vortex (PHV) system is formed. These structures are composed of a head portion (with a spanwise rotation) and a leg portion (quasi-streamwise rotation). While moving downstream, the swirling hairpin vortices are stretching and distorting.

The hairpin vortices break down and their geometrical shape moves from hairpin to ring. The vortex structures lift up due to the upwash motion of the leg portion of the vortices. For a hairpin vortex system, the head breaks down and the feet of the structure connect together and form a full ring vortex (see figure 7(b)).

The upwash movement of the legs brings high-speed flow down and lifts up low-speed flow. Far from the roughness element (x/h=20-30), the formation of a new near-wall vortex systems due to interaction between low-momentum and outer flow fluid is observed. These lateral hairpin-shape secondary struc- tures develop downstream while moving away from the symmetry plane z/h=0 and moving upward, forming a turbulent wedge. The interaction between the primary and secondary vortical structures is the mechanism that yields to the 375 turbulence onset and a complex flow structure.

The coherent structures lead to an energy cascade, which ensures energy transfer from the mean kinetic energy to the turbulent kinetic energy. The head portion of the primary hairpin vortices (PHV) contributes to the maximum peak of velocity fluctuations at the upper shear layer, as it will be shown in the next section in figure 8.

Power spectrum. Instantaneous visualizations from the LES simulations using the λ 2 criterion have been presented and analyzed in the previous section. The momentum deficit due to the shear layer modification showed to induce a flow instability, that leads to the creation of hairpin vortices. Now, the dynamic structures will be analyzed by visualizing the energy spectrum of the streamwise velocity component. The power spectral density is plotted versus the Strouhal number (St = f h u∞ ) in figure 8. The probes 1 and 2 from figure 8(a) correspond to local points from the calculation domain located at (x/h=5h; y/h=1.25h; z/h=0) and (x/h=40h; y/h=1.25h; z/h=0), respectively.

At the probe 1 location, the flow is dominated by the formation of hairpin vortex structures. These unsteady structures appear as a single peak in the turbulence energy spectrum in figure 8(b). The Strouhal number associated with this main peak is equal to 0.242. The hairpin shedding Stouhal number (0.242) lies between 0.2 and 0.37, range reported by Acarlar and Smith [START_REF] Acarlar | A study of hairpin vortices in a laminar boundary layer. part 1. hairpin vortices generated by a hemisphere protuberance[END_REF] for a hemisphere protuberance in similar flow configuration.

The instantaneous visualizations presented in figure 7 suggest that the flow structures are much more complex at the probe 2 location than at the probe 1 location. According to energy spectrum analysis results, the magnitude of the peak in the power spectrum decreases while moving downstream. At probe 2 location, the vortex structures break down and flow interaction produce several secondary motions as previously depicted and thus a more disorganized distribution of flow perturbations and energy spectrum peaks are produced. Based on the energy spectrum in figure 8, it can be stated that the flow instability become non-linear at the probe 2 position and the flow behavior becomes turbulent. For that reason in this section, the appearance of oscillatory movements, their growth and the onset of turbulence will be represented and discussed through the velocity profiles, amplitude of streamwise velocity fluctuations and turbulence production.

Velocity profiles

A possible way to detect the onset of tubulence is to plot the wall-normal semi-logarithmic velocity profiles. These profiles may be compared to the loglaw profiles for turbulent boundary layer [START_REF] Coles | Computation of turbulent boundary layers[END_REF]. Mean velocity profiles along the symmetry plane are thus plotted versus the non-dimensional wall-normal position, see figure 9.

Turbulent boundary layer is characterized by a logarithmic law of the wall in the overlap region [START_REF] Kármán | Mechanical similitude and turbulence[END_REF]:

u + = 1 κ lny + + B + , ( 11
)
where κ is the Von Kármán constant and B + a constant. u + is the dimensionless streamwise velocity and y + is the dimensionless distance to the wall. The results

show that from x/h=5 to x/h=25, the velocity profiles exhibit a large deficit region. At x/h=40, the velocity profile become fuller and its upper part fits with a log-law profile in the range y + ∈ [400 : 2000] corresponding to a straight line on the semi-log graph (figure 9). Thus, the velocity profile displays a logarithmic behavior that characterizes a turbulent state, at a distance of 40h downstream the obstacle.

Velocity fluctuations

The ity fluctuations lifts up due the primary vortices upwash motion when moving downstream the obstacle. Also, the fluctuations magnitude is decreased due to the recovery process. Furthermore it can be seen that beneath the primary region at x/h=15, the downwash movement of secondary vortices transports high A turbulent wedge originating at the roughness is produced, where large-scale hairpin vortices transfer mean flow energy into turbulence. Thus, it promotes the laminar-to-turbulent transition.

It can be stated from the spatial distribution of the streamwise velocity fluctuations that region of maximum RMS intensity is less spread by LES at x/h=5 and the RMS intensity is slightly overestimated by LES at x/h=40 compared to tomographic PIV data [START_REF] Ye | Boundary layer transition mechanisms behind a micro-ramp[END_REF].

Conclusion

In this contribution, Large-Eddy Simulations (LES) were carried out to investigate the induced transitional flow phenomenon over a ramp-type wallmounted roughness element immersed in a developing boundary layer at a supercritical regime. The results present several transition flow features that are compared to tomographic PIV experimental data from [START_REF] Ye | Geometry effect of isolated roughness on boundary layer transition investigated by tomographic piv[END_REF][START_REF] Ye | Boundary layer transition mechanisms behind a micro-ramp[END_REF]. The comparisons show that the present LES methodology is well adapted for this type of transitional flow, and makes it possible to account numerically for the various physical phenomenon involved.

The mean flow analysis indicates the formation of a primary contra-rotating pair of vortices (TRP) at the trailing edge of the obstacle, which consequently generates an upwash motion and a streamwise momentum deficit. The shear layer becomes unstable, and a hairpin-like vortex system is generated due to Kelvin-Helmholtz type instability. These vortices are formed in the near-wake of the micro-ramp, and are stretched when moving downstream. A second pair of vortices is formed in the near-wall. The break down of the primary hairpin system produces new near-wall vortices propagating in the spanwise direction.

The head of the hairpin vortices and the secondary vortices are found to generate a local high-turbulence zones, associated with the velocity fluctuations.

In our study, the instantaneous flow topology shows that the flow down- The boundary layer induced-transition phenomenon past an immersed microramp can then be summarized in four main stages:

• Formation of longitudinal vortices in the very near wake of the obstacle with a quasi-steady shear flow.

• Development of Kelvin-Helmholtz instabilities and formation of transverse hairpin vortex structures.

• Evolution of vortices to a hairpin or ring shape, and vortex merging.

• Generation of new vortex structures in the near-wall and lateral propagation (turbulent wedge).

The boundary layer transition is therefore associated with the modified shear layer induced by the vortices past the obstacle, as well as the inflectional velocity profile.

It would be fruitful to pursue further research about the effect of an immersed roughness element placed in laminar flow on a heated plate in order to assess the thermal enhancement of a such configuration.

Figure 1 :

 1 Figure 1: Roughness geometry and boundary conditions

Figure 2 :

 2 Figure 2: Schematic of the chosen grid.

Figure 3 :

 3 Figure 3: Index of resolution quality.

Figure 4 :

 4 Figure 4: Color contours visualization of the non-dimensional mean velocity superimposed with projected streamlines at three streamwise positions y-z : x/h=5, 15, 25. (TRP) trailingedge pair, (SP) secondary pair.

Figure 5 :

 5 Figure 5: Profiles of mean streamwise velocity component in the center plane at three positions: x/h=5; 15; 40.

Figure 6 :

 6 Figure 6: Streamwise evolution of maximum velocity deficit rate.

Figure 7 :

 7 Figure 7: Instantaneous flow organization color coded by u/u∞ ; (a,b) perspective views at precise streamwise locations.

Figure 8 :

 8 Figure 8: Energy spectrum analysis of the flow past a micro-ramp roughness with a laminar incoming boundary layer, at different positions x, y. a) schematic view of the probe positions. b) power spectral density for the probe 1 x=5h; y=1.25h. c) power spectral density for the probe 1 x=40h; y=1.25h.

Figure 9 :

 9 Figure 9: Semi-logarithmic non-dimensional velocity profiles at several streamwise positions

  spatial distributions of the root mean square (RMS) values of streamwise velocity component are illustrated in figure 10 for several y-z cross-planes (x/h = 5, 15, 25 and 40). The RMS of the velocity fluctuations are good indicator of the turbulence intensity. According to figure 10, peak velocity fluctuations are found to be located at the head portion of the coherent vortex structures (hairpin and ring) where the flow instability is produced. At x/h=5, a peak fluctuation is observed as a result of the upper shear layer instability (peak (I)). The RMS contours shape could be interpreted as the elongated hairpin vortices formed downstream the roughness element. The concentrated RMS values locations are the zones where the local velocity profile has an inflection point in the wall-normal direction, that is, ∂ 2 u ∂y 2 = 0. It indicates that the fluctuations result from a Kelvin-Helmholtz-type instability mechanism in the wall-normal direction. The maximum of veloc-

Figure 10 :

 10 Figure 10: Cross-sectional contours of streamwise velocity fluctuations.

  stream the obstacle is dominated by Kelvin-Hemholtz vortices, which are generated in the form of hairpin. A study of the velocity fluctuations shows that the maximum values of turbulence production are concentrated at the head of the haiprin vortex structures, and at the edges of the turbulent wake created downstream of the obstacle. The coherent structures are mainly organized into hairpin vortices shed from the near-roughness wake region and wall-attached vortices generated at both sides of the micro-ramp wake.The streamwise mean velocity, turbulent fluctuations and instantaneous vortex visualization are in relatively good agreement with experiments. A discrepancy in the streamwise turbulent fluctuations intensity is observed, and can be ascribed to the experimental PIV resolution, the discretization scheme and the subgrid scale model.