Laurent Selle

Laurent Benoit

Thierry Poinsot

Franck Nicoud

Werner Krebs

Joint use of compressible large-eddy simulation and Helmholtz solvers for the analysis of rotating modes in an industrial swirled burner

Keywords: Large-Eddy Simulation, Acoustics, Helmholtz solver, complex geometry

Rotating modes are instabilities which are commonly observed in swirling flows.

This paper shows that, in complex geometry swirled combustors, such modes can appear for both cold and reacting conditions but that they have different sources: while the cold flow rotating mode is essentially hydrodynamic and corresponds to the well-known PVC (Precessing Vortex Core) observed in many swirled unconfined flows, the rotating structure observed for the reacting case inside the combustion chamber is not hydrodynamically but acoustically controlled. The two transverse acoustic modes of the combustion chamber couple and create a rotating motion of the flame which leads to a self-sustained turning mode which has the features of a classical PVC but a very different source (acoustics and not hydrodynamics). These

Introduction

Large-Eddy Simulation (LES) methodologies constitute intermediate steps between steady state calculations (RANS) and Direct Numerical Simulation (DNS) [START_REF] Poinsot | Theoretical and numerical combustion[END_REF]. During the past ten years, LES results have proved to be predictive for non-reacting flows [2 -6] and more recently also for reacting flows [7 -12]. These results suggest that LES could be used in configurations as complex as aero and industrial gas-turbines for the prediction of mean reacting flows properties but also of flow instabilities. However, the CPU cost and the restitution time of LES in these configurations do not yet meet industrial requirements. Consequently, simpler tools must be developped so that their joint use with LES enables a deeper understanding of the physics, thus reducing the number of LES calculations. One such class of codes is Helmholtz solvers which are commonly found in many research centers and companies involved in thermacoustics research [1, 13 -15]. These codes try to predict the frequencies and the structure of eigenmodes of the flow in the combustor assuming harmonic perturbations around a frozen mean state [START_REF] Poinsot | Theoretical and numerical combustion[END_REF][START_REF] Crighton | Modern methods in analytical acoustics[END_REF]. Obviously, Helmholtz appproaches require significant simplifications for the flow and cannot be expected to provide LES-like accuracy for the flow. However, the acoustic analysis offered by Helmholtz methods is more complete than the LES results: Helmholtz solvers provide all possible modes frequencies and structure as well as their growth rates while LES will only evidence the modes which appear for one given regime. Moreover, doing parametric studies is impossible with LES: knowing for example which exhaust nozzle or which Helmholtz resonator can damp a given combustion instability is out of reach of LES but can be done with Helmholtz solvers.

Obviously, LES and Helmholtz codes are complementary methods to study combustion instabilities and more generally unsteady combustion. In this paper, the power of these combined tools is illustrated by considering a question which is the subject of multiple discussions in the combustion community: the existence and importance of rotating modes in swirling combustion [12,[START_REF] Evesque | 9th AIAA / CEAS Aeroacoustics Conference and Exhibit[END_REF][START_REF] Krebs | [END_REF].

It is well known that non-reacting swirling flows exhibit a variety of unstable modes [18 -20]: the Precessing Vortex Core (PVC) is one of these modes (Fig. 1) for which the vortex axis destabilizes and spirals around the vortex initial direction. Such instabilities are observed for unconfined non-reacting flows [18] and also in the wakes of aircrafts [21 -23] but also in confined combustion chambers where they often dominate the turbulent activity in the absence of combustion [12]. Because these instabilities appear so clearly for non-reacting flows, it is often assumed that they also dominate the reacting cases. For example, gas turbine burner flows are often tested with water to determine residence times and try to predict possible instabilities from the observation of the cold flow modes. Whether modes observed in such water channel experiments can be extrapolated to instabilities in the real combusting situation is an important question. Note that PVCs are hydrodynamic instabilities which usually do not couple with the acoustics of the chamber. In reacting configurations, the acoustic generation due to the flame excites many modes of the chamber, sometimes leading to rotating modes which look like PVC but are actually due to the combination of transverse acoustic modes and not to a hydrodynamic instability. This paper describes such a situation in a swirled complex geometry combustor. The configuration is first presented. The LES and the Helmholtz solvers are then rapidly described. Cold flow results are discussed before presenting the computations for the reacting case.

Configuration

An important objective of this study is to present a methodology for the investigation of flame / acoustics interactions and combustion instabilities in realistic geometries. Therefore an industrial gas turbine burner (Fig. 2) mounted on a square laboratory combustion chamber in Karlsruhe [START_REF] Schildmacher | ASME TURBO EXPO[END_REF] is considered. This burner is fed by two coaxial swirlers respectively called axial and diagonal swirler. The axial swirler, including its vanes, is fully computed in the LES, whereas the computational domain of the diagonal swirler begins at the trailing edge of the swirling vanes [12]. This burner is mounted on an combustion chamber with a square cross section (Fig. 3).

Meshes

The computational domain is the same for both solvers (LES and Helmholtz) but the number of mesh points can be drastically reduced for the computation of acoustic modes with the Helmholtz solver: indeed, the spatial resolution needed for LES is much higher than it is for the resolution of the first acous-tic modes of the configuration in the Helmholtz computation. The grid for the reacting LES calculation contains 2,381,238 cells while the grid for the Helmholtz solver contains only 70,214 cells. Consequently, the computational cost of the Helmholtz solver is almost neglegible compared to the LES. The computational time for the reacting LES is 280 CPU hours for one period of the high-frequency instability on a SGI O3800, whereas the computation of the first 13 acoustic modes with the Helmholtz code takes less than 10 CPU hours on the same machine.

Boundary conditions

For such a study, boundary conditions must be well defined in terms of mean flow but also of acoustic impedances which must be the same in both computations (LES and Helmholtz). In this prospective study, purely reflecting boundary conditions are imposed at the inlets and outlet of the computational domain: the velocity profile is imposed at both axial and diagonal inlets (Fig. 2) and the pressure is imposed at the outlet of the combustion chamber (Fig. 3).

Numerical tools

LES solver

The solver used in this study (www.cerfacs.fr/cfd/avbp.html) has already been validated and used in numerous studies for turbulent flows both non-reacting [START_REF] Schlüter | [END_REF]6,[START_REF] Schlüter | ASME TURBO EXPO 2001 Land, Sea and Air[END_REF][START_REF] Prière | 1st Int. Workshop on Trends in Numerical and Physical Modeling for Turbulent Processes[END_REF] and reacting [12, 27 -30]. A description of the parallel solver can be found in [START_REF] Moureau | [END_REF] and its key features for this study are as follows. The code solves the compressible Navier-Stokes equations which allows to take into account acoustics. The Thickened Flame model for turbulent combustion [12,28] enables the resolution of the flame front on typical LES meshes (whose characteristic cell size are usually much larger than flame thicknesses) while allowing ignition and extinction. This feature is of major interest in the computation of combustion instabilities since parts of the flame front can alternatively be quenched and re-ignited during the instability cycle. Accurate boundary conditions [29,32] are mandatory for the prediction of unstable regimes since the acoustic impedances at the boundary drive the acoustic losses. Characteristic boundary conditions are used in the LES for all inlets, outlets and walls [START_REF] Moureau | [END_REF]33]. The use of unstructured meshes enables the computation of complex geometries. The use of a high order numerical scheme [34] with minimal dispersion and dissipation is a key feature for the computation of turbulent flows, but also for the accurate resolution of the acoustic waves.

Helmholtz solver

If the reactive Navier Stokes equations are linearized around a mean state (index 0), the general form of the Helmholtz equation is obtained [START_REF] Poinsot | Theoretical and numerical combustion[END_REF][START_REF] Crighton | Modern methods in analytical acoustics[END_REF]:

∇ • c 2 ∇p ′ - ∂ 2 ∂t 2 p ′ = -(γ -1) ∂ ωT ∂t -γp 0 ∇ u : u (1)
where p ′ is the pressure perturbation, ωT is the unsteady local heat release, p 0 is the average pressure and c is the local sound speed. c changes considerably in a reacting flow: it depends on the local value of γ, on the mean molecular weight W and on temperature: c = (γRT /W ) 1/2 where R = 8.32uSI. The two forcing terms in the RHS of Eq. 1 are related to the outsteady combustion and turbulent noise respectively. To obtain this equation, the following assumptions are needed:

• Low Mach number flow

• No volume forces

• Linear acoustics (i.e. small perturbations)

• Large scale fluctuations.

• Homogeneous mean pressure.

• Constant polytropic coefficient γ.

The wave equation is usually not solved in the time domain but in the frequency domain by assuming harmonic pressure variations at frequency f = ω/(2π) for pressure and for local heat release perturbations:

p ′ = ℜ(P ′ (x, y, z) exp(-iωt)) (2)
ωT = ℜ(Ω ′ T (x, y, z) exp(-iωt)) (3)
with i 2 = -1

Introducing Eq. (3) into Eq. ( 1) and neglecting the turbulent noise compared to the combustion forcing leads to the Helmholtz equation where the unknown quantities are the complex pressure oscillation amplitude P ′ at frequency f and the heat release amplitude field Ω ′ T :

∇ • c 2 ∇P ′ + ω 2 P ′ = iω(γ -1)Ω ′ T ( 4
)
This equation is the basis of three-dimensional Helmholtz codes. Knowing the sound speed (c) distribution, i.e. knowing the local composition and temper-ature, it provides the eigen frequencies ω k and the associated structure of the mode P ′ k (x, y, z). At this point, two approaches of increasing complexity are found :

• First, the effects of the unsteady combustion can be neglected by setting Ω ′ T = 0. This is equivalent to finding the eigenmodes of the burner, taking into account the presence of the flame through the mean temperature field but neglecting the flame effect as an acoustic active element.

• In a second step, the active effect of combustion can be taken into account if a model linking Ω ′ T and P ′ can be derived to close Eq. ( 4). This is usually the difficult part of the modeling because it requires the determination of the transfer function between acoustics and flame.

For the present study, the active efffects of the flame were neglected (Ω ′ T = 0) and a parallel iterative solver was used to solve Eq. 4 on hybrid meshes [35].

The required mean fields of sound speed is obtained by post-processing the LES results for the reacting flow so that the effect of the flame through the mean temperature field is properly accounted for. Details about solving Eq. 4

with general boundary conditions and acoustically active flame are discussed in [START_REF] Martin | Proc of the Sum[END_REF]37].

Non-reacting flow: low-frequency rotating mode

For the non-reacting regime, pure air is injected in both axial and diagonal swirlers. The air is pre-heated to T cold = 323 K. The LES results have been successfully compared to experimental data in a previous paper [12] in terms of mean and rms values for both axial and tangential velocities. The agreement between LES calculations and experimental results is good for the mean flow and the focus is set here on the analysis of unsteady phenomena and especially of turning modes.

To begin this analysis, the acoustic modes of the configuration, computed with the Helmholtz solver for the non-reacting regime are first listed in Tab. 1:

• Modes number 1 and 2 correspond respectively to the 1/4 wave (Fig. 4) and 3/4 wave (Fig. 5) longitudinal modes of the configuration.

• Modes number 3 and 4 (Fig. 6 and7) are the two 1/2 wave tranverse and 1/4 wave longitudinal modes of the combustion chamber: their frequencies are equal because the chamber has a square cross-section and the burner is axisymetric.

• Mode number 5 (Fig. 8) is the 5/4 wave longitudinal mode.

• Modes number 6 and 7 (Fig. 9 and 10) are the two 1/2 wave tranverse and 3/4 wave longitudinal modes of the configuration.

Considering now the LES results, the first obvious observation is that the instantaneous flow does not follow the symmetries of the geometry: since the burner axis is on axis of symmetry for the burner and the chamber, one would expect the radial components of the velocity (v and w) to be zero on the burner axis, apart from turbulent fluctuations. However, plotting the third component of the velocity at point A i.e. on the burner axis (Fig. 3) shows that the symmetry is broken by a strong harmonic oscillation (Fig. 15 in [12]).

The frequency of this oscillation is f cold = 275 Hz. This mode was also observed in the experiment at Karlsruhe University [START_REF] Schildmacher | ASME TURBO EXPO[END_REF] at the frequency f exp = 255 Hz.

The frequency f cold of the velocity oscillation on the burner axis does not match any of the frequencies listed in Tab. 1 showing that this oscillation is not an acoustic mode. It is thus suggested that the unsteadiness is caused by a hydrodynamic mode, which can be caracterized in terms of Strouhal number: St = f D/u bulk , where f is the frequency of the instability, D the burner diameter and u bulk the bulk velocity. For the present mode St = 0.62, which is typical of PVC in swirl flows [18 -20]. Fig. 1 presents a generic PVC:

the vortex due to the swirling motion, originally aligned with the burner axis breaks down at point S in a spiral form. This structure rotates, as a block, around the burner axis. The PVC can be tracked in the LES (Fig. 11) by the low pressure region near the vortex axis. In this configuration, the sense of winding of the spiral is opposite to that of the swirl (which is the same for axial and diagonal swirlers). However, the whole structure precesses in the same direction as the global rotation of the flow. In conclusion, the cold flow is dominated by a hydrodynamic mode (PVC) in which acoustics play no role.

Reacting flow: high frequency rotating mode

For the regime considered here, the diagonal swirler is fed with premixed methane/air while the axial swirler injects pure air. Both flows are pre-heated to 673 K and the global equivalence ratio is φ = 0.5.

Analysis of LES results

The 275 Hz PVC evidenced in the cold flow is not present any more in the reacting regime which is considered here [12]. However, plotting w at point A, after the PVC has vanished (Fig. 12) shows that the symmetry of the flow is still broken by a strong harmonic oscillation. This oscillation dominates the turbulent fluctuations and its frequency is determined through a FFT of the velocity signal on the burner axis (Fig. 13): f hot = 1198 Hz. Plotting the pressure field in a plane normal to the burner axis (Fig. 14) shows that this high frequency oscillation now corresponds to a rotating transverse mode: the points of minimum and maximum pressure are rotating around the burner axis at the frequency f hot . Even though this mode is "turning" like the PVC observed without combustion, it is not hydrodynamically but acoustically controlled.

Its frequency is not determined through a Strouhal scaling based on the burner dimension but through the acoustic eigenmodes of the chamber as shown in the next section.

Reconstruction of the rotating mode using acoustic eigenmodes

As for the cold flow, the list of the first eigen frequencies in the reacting regime are presented in Tab. 2. Though the frequencies are different (due to the increase in the temperature), the structure of these modes is exactly the same as for the cold flow (c.f. Sec. and4). The pressure fluctuations induced by modes 3 and 4 can respectively be written:

p ′ 3 (x, y, z, t) = A 3 cos (ω 3 t + φ 3 ) F 3 (x, y, z) (5)
p ′ 4 (x, y, z, t) = A 4 cos (ω 4 t + φ 4 ) F 4 (x, y, z) (6)
where F i is the mode shape, A i the amplitude and φ i the phase for mode number i. Combining Eq. 5 and 6 with equal amplitudes (A 3 = A 4 = A) but shifting mode 4 by 90 (φ 3 = 0; φ 4 = -π/2) leads to:

p ′ (x, y, z, t) = A (F 3 (x, y, z) cos (ω 3 t) + F 4 (x, y, z) cos (ω 4 t -π/2)) (7)
As the mode shape is a direct output of the Helmholtz solver, the result of Eq. 7 can be reconstructed to generate the temporal evolution of the mode.

This result is plotted in Fig. 15 and shows exactly the same structure as the rotating mode evidenced in the LES even though the pressure field obtained by LES displays slightly more complex patterns probably due to turbulence (Fig. 14). This proves that the high-frequency rotating mode evidenced in the LES of the reacting regime is the combination of the first two transverse acoustic modes of the combustion chamber, with equal amplitudes and a phase difference of π/2. Despite the fact that this result does not say why there transverse modes combine in this manner, it proves the acoustic nature of the turning mode for the reacting case.

Influence of the rotating mode on the flame shape

The objective of this section is to show that in the LES, the shape of the flame is strongly affected by acoustic velocity fluctuations. The 1198 Hz mode is not simply forced by combustion. It also affects the flame itself leading to a self-sustained three-dimensional oscillation. These perturbations can be reconstructed from the Helmholtz solver results using the mass conservation

u ′ = ∇p ′ iρω (8)
Combining Eq. 7 and Eq. 8 allows the reconstruction of the velocity perturbations corresponding to the acoustic rotating mode. Fig. 16 is a plot of axialvelocity fluctuations at the burner mouth generated by the rotating mode.

At a given phase φ = ωt of the oscillation, the amplitude of the fluctuation is maximum at two locations close to the burner outer side and on opposite sides of the burner axis. At these two spots the axial velocity fluctuations have opposite signs. This pattern rotates around the burner axis at the frequency

f hot = 1198 Hz.
The axial velocity fluctuations induced by the rotating acoustic mode occur at a critical location in the flow field: the burner mouth. Such fluctuations at a sudden expansion are known to generate vortex rings which can distort the flame front. This occurs in the present configuration: as shown in Fig. 19 the flame is distorted by a coherent structure in phase with the acoustic mode.

The vortex is not toroidal as for vortex rings but has a spiral form which is the combination of two motions:

(1) the rotating mode

(2) and the convection by the mean flow field.

For a final quantitative validation of the structure of this mode, the phase of the axial velocity fluctuations from LES and Helmholtz solvers are now compared. Fig. 17 presents the pressure fluctuations at point C (Fig. 3) which is used as the phase reference to synchronize LES result with Eq. 7. Fig. 18 is the comparison of axial velocity fluctuations at point B (Fig. 3). The average ve-locity is substracted from the LES signal, and the fluctuations are normalized with a unique normalisation:

• The phases for the two solvers match exactly showing the power of the Helmholtz solver to predict acoustically induced velocity fluctuations.

• The fluctuations of u are strongly dominated by the acoustics showing that this flow is not dominated by turbulence but by acoustics.

• This result has implications for simulation: as this flow is obviously acoustically driven, the accurate computation of acoustic waves (low dispersion of numerical scheme, accurate boundary conditions) may be as critical as the modeling of the subgrid-scale turbulence.

Conclusion

Large-Eddy Simulations (LES) of an industrial-size burner mounted on an academic combustion chamber were conducted in both reacting and non-reacting regimes. The work focuses on the analysis of rotating modes evidenced in both LESs (cold and reacting). The joint use of a compressible LES solver and a Helmholtz solver enables the determination of the nature of these instabilities:

• For the cold flow the rotating mode is due to an hydrodynamic instability typical of swirling flows: Precessing Vortex Core (PVC). The Helmholtz solver shows that the frequency of this instability (275 Hz) does not correspond to an eigenmode of the configuration but can be predicted using a

Strouhal scaling based on the bulk velocity and the burner mouth dimension.

• In the reacting regime, the flow still exhibits a rotating mode but at 1198

Hz. This mode is not hydrodynamic: it is acoustically controlled by a combination of the first two transverse modes of the combustor at 1192 Hz. The identification of the rotating mode as an acoustic mode is confirmed by the pressure fluctuation field: the complex structure of this mode evidenced in the LES can be successfully reconstructed from Helmholtz solver results.

This study suggests that a numerical prediction of turbulent combustion instabilities in a gas turbine requires:

(1) A compressible LES solver: though the non-reacting part of this study could have been conducted with an incompressible solver, taking into account the acoustic waves is mandatory for the reacting case.

(2) The joint use of two solvers (i.e. LES and Helmholtz). The Helmholtz solver explains the acoustic structure evidenced in the LES simulations by allowing the identification of all possible modes.

In the case of turning modes in swirled combustors, these two tools show that such modes can indeed be observed both for cold and reacting flows but that their nature is very different: for the cold flow, the rotating mode is an hydrodynamic mode but it becomes acoustically controlled when combustion is activated. Such an information is useful to understand the behavior of the combustor but also to help design which is often based on cold flow observation to study instabilities.

Acknowledgments

This work has been supported by SIEMENS PG. The numerical simulations have been conducted on the computers of the French national computing cen-

  4 and Fig. 4 to 10); and they are not repeated here. Modes 3 and 4 are transverse modes sharing the same frequency, 1192 Hz, very close to that observed in the LES. It is possible to show that the rotating mode observed in the LES is actually the combination of these two modes (3

Fig. 1 .

 1 Figures

Fig. 2 Fig. 3 .Fig. 4 .

 234 Fig. 2. Burner.

Fig. 5 .

 5 Fig. 5. Mode number 2 is the 3/4 wave longitudinal acoustic mode (P ′ modulus).

Fig. 6 .

 6 Fig. 6. Mode number 3 is the 1/2 wave transverse in y direction, 1/4 wave longitudinal acoustic mode (P ′ modulus).

Fig. 7 .

 7 Fig. 7. Mode number 4 is the 1/2 wave transverse in z direction, 1/4 wave longitudinal acoustic mode (P ′ modulus).

Fig. 8 .

 8 Fig. 8. Mode number 5 is the 5/4 wave longitudinal acoustic mode (P ′ modulus).

Fig. 9 .

 9 Fig. 9. Mode number 6 is the 1/2 wave transverse in y direction, 3/4 wave longitudinal acoustic mode (P ′ modulus).

Fig. 10 .

 10 Fig. 10. Mode number 7 is the 1/2 wave transverse in z direction, 3/4 wave longitudinal acoustic mode (P ′ modulus).

Fig. 11 . 31 -Fig. 12 .Fig. 13 .

 11311213 Fig. 11. Visualisation of the PVC in the LES by a pressure iso-surface.

Fig. 17 .

 17 Fig. 17. Normalised pressure fluctuations at point C in the LES (solid) and from the Helmholtz solver (dashed).

Fig. 18 .

 18 Fig. 18. Normalised axial velocity fluctuations at point B in the LES (solid) and from the Helmholtz solver (dashed).

Table 1

 1 List of eigen frequencies for the non-reacting case.

	Stanford, 2004, p. 377-394.
	[37] Benoit, L. and Nicoud, F., International Journal For Numerical Methods
	in Fluids: (in press) (2005).
	List of Tables
	1	List of eigen frequencies for the non-reacting case.	23
	2	List of eigen-frequencies for the reacting case.	23
	List of Figures
	1	Schematic representation of a generic PVC.	24
	2	Burner.	25
	3	Computational domain.	26
	4	Mode number 1 is the 1/4 wave longitudinal acoustic mode
		(P ′ modulus).	27
	5	Mode number 2 is the 3/4 wave longitudinal acoustic mode
		(P ′ modulus).	27
		20

Table 2

 2 List of eigen-frequencies for the reacting case.


Thu Hien Tran

Alexandre Govin

René Guyonnet

Philippe Grosseau

Christine Lors

Denis Damidot

Olivier Devès

Bertrand Ruot

Olivier Deves

Duy Tan

Influence of the intrinsic characteristics of mortars on their biofouling by pigmented organisms: Comparison between

Keywords: mortar, biofouling, intrinsic properties, laboratory test, in-situ test

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The colonization of building facades by microorganisms is a subject that concerns more and more the civil engineering community. Indeed, this phenomenon changes the aesthetical appearance of materials and, in later stage, can even compromise the durability of structures by corrosion or by physical degradation induced by the microorganism [START_REF] Maury-Ramirez | Titanium dioxide based strategies to prevent algal fouling on cementitious materials[END_REF]. The type of microorganisms colonizing cement based building facades is diverse. But the analyses of in-situ samples show that algae are one of the initial and main colonizers [START_REF] Gaylarde | A comparative study of the major microbial biomass of biofilms on exteriors of buildings in Europe and Latin America[END_REF]. These microorganisms allow the successive implantation and the growth of other biological organisms such as lichens and bryophytes. If no solution is found, the pteridophytes and higher plants may also appear [START_REF] Perrichet | Développement de micro-organismes à la surface des bétons et enduits[END_REF][START_REF] Deruelle | Rôle du support dans la croissance des microorganismes[END_REF][START_REF] Barberousse | Etude de la diversité des algues et des cyanobactéries colonisant les revêtements de façade en France et recherche des facteurs favorisant leur implantation[END_REF]. The microbial development must be eliminated to avoid worse consequences to buildings. The more the cleaning maintenance activities are repeated the more expensive the cost.

Several factors such as the global climate, the local environment, the building design and the facade materials influence the biological fouling.

The rainfall, the wind and the temperature consist in the climatic parameters influencing together the water availability of facade materials which is an essential element to the microbial metabolism. A permanently wet facade promotes the growth of algae and higher plants [START_REF] Ariño | Factors affecting the colonization and distribution of cyanobacteria, algae and lichens in ancient mortars[END_REF][START_REF] Loh | Product development for green productivity -a case study / Development of algae resistant surface coating for building facades in the humid tropics[END_REF]. Therefore, the facades represent a higher susceptibility to biofouling in the rainy regions and during the heavy rainy season [START_REF] Young | Biological growth and their relationship to the physical and chemical characteristics of sandstones before and after cleaning[END_REF]). However, a high temperature induces water evaporation by heating the materials.

Similarly, the wind can cause a drying phenomenon.

The local environmental conditions, such as topography and nature of the ground, presence of moisture and/or industrial activities around the buildings, should be taken into account. As an example, a house roof, located close to seaside, can be totally colonized by nitrophilous lichens, characterized by the yellow or orange, in a few years [START_REF] Deruelle | Rôle du support dans la croissance des microorganismes[END_REF]. Indeed, sea sprays, by providing nitrogen to the building surface, favor the microorganism growth. In addition, the humid environments set near a lake, a river, trees or shrubs, are favorable to the appearance of stains on the walls.

The growth of biological fouling is also depending on the orientation of the facade. Indeed, the north-facing facades which are wetter and less sunny, get colonize faster [START_REF] Ariño | Factors affecting the colonization and distribution of cyanobacteria, algae and lichens in ancient mortars[END_REF][START_REF] Young | Biological growth and their relationship to the physical and chemical characteristics of sandstones before and after cleaning[END_REF][START_REF] Barberousse | Etude de la diversité des algues et des cyanobactéries colonisant les revêtements de façade en France et recherche des facteurs favorisant leur implantation[END_REF]. Similarly, a facade exposed to dominant winds seems to be colonized more easily than the other sides of the same building.

The wind can transport both the rain and the biological propagules at the facades promoting the biofouling.

Parts of building often moistened for long periods, or easily covered of propagules, are highly sensitive to the biological colonization [START_REF] Wee | Proliferation of algae on surfaces of buildings in Singapore[END_REF]. The biofouling often grows at the foot of walls, the junction of different coatings and the overhanging elements (cornices, moldings, balconies, etc.) [START_REF] Wee | Proliferation of algae on surfaces of buildings in Singapore[END_REF][START_REF] Cstb | Salissures de façade : comment les éviter ? Exemples de solutions techniques[END_REF][START_REF] Barberousse | Etude de la diversité des algues et des cyanobactéries colonisant les revêtements de façade en France et recherche des facteurs favorisant leur implantation[END_REF].

In addition to external conditions, the biological development is affected by the intrinsic characteristics of the facade, defined as its bioreceptivity [START_REF] Guillitte | Bioreceptivity: A new conception for building ecology studies[END_REF]. These characteristics can be divided into physical properties (porosity, roughness and hydrodynamic properties) and chemical ones (chemical composition, pH surface).

Since the last thirty years, several researches have been devoted to the study of the building-materials bioreceptivity. In all these studies, the experimental tests were conducted with more or less accelerated methods of the biological growth on materials. The goal of these accelerated methods was to reduce the test duration, which normally required many years in the real-world. The experimental parameters were thus optimized to favor the growth of microorganisms [START_REF] Dubosc | Characterization of biological stains on external concrete walls and influence of concrete as underlying material[END_REF][START_REF] Barberousse | Etude de la diversité des algues et des cyanobactéries colonisant les revêtements de façade en France et recherche des facteurs favorisant leur implantation[END_REF]. Different methodologies, concerning the preparation of materials, the process of inoculation and humidification, the temperature and the photoperiod of the test were developed [START_REF] Grant | A new method for assessing the resistance of stone to algal disfigurement and the efficacy of chemical inhibitors[END_REF][START_REF] Guillitte | Laboratory chamber studies and petrographical analysis as bioreceptivity assessment tools of building materials[END_REF][START_REF] Ohshima | A study on growth of fungus and algae on mortar[END_REF][START_REF] Dubosc | Characterization of biological stains on external concrete walls and influence of concrete as underlying material[END_REF][START_REF] Miller | Primary bioreceptivity: A comparative study of different Portuguese lithotypes[END_REF][START_REF] Miller | The influence of inherent properties of building limestones on their bioreceptivity to phototrophic microorganisms[END_REF][START_REF] De Muynck | Evaluation of strategies to prevent algal fouling on white architectural and cellular concrete[END_REF][START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF]. According to all these studies, the roughness of materials appears as one of the most important parameters. Indeed, the colonization of the building materials by microorganisms is promoted by the roughness of the surface. In fact the roughness provides many asperities and thus increases the physical anchorage of these micro-organisms [START_REF] Dubosc | Etude du développement de salissures biologiques sur les parements en béton: Mise au point d'essais accélérés de vieillissement[END_REF][START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF]. This effect of roughness on the biofouling was confirmed by observations of buildings in real conditions [START_REF] Wee | Proliferation of algae on surfaces of buildings in Singapore[END_REF][START_REF] Darlington | Ecology of walls[END_REF][START_REF] Pietrini | A reddish colour alteration caused by algae on stoneworks[END_REF]Joshi and Mukundan, 1997). The total porosity, the pore size distribution and the porous network, should be taken into account, because the absorption and the water retention of materials are controlled by these characteristics [START_REF] Warscheid | Studies on the temporal development of microbial infection of different types of sedimentary rocks and its effect on the alterioration of the physico-chemical properties in building materials[END_REF][START_REF] Ohshima | A study on growth of fungus and algae on mortar[END_REF][START_REF] Crispim | Algal and cyanobacterial biofilms on calcareous historic buildings[END_REF][START_REF] Miller | Primary bioreceptivity: A comparative study of different Portuguese lithotypes[END_REF][START_REF] Miller | The influence of inherent properties of building limestones on their bioreceptivity to phototrophic microorganisms[END_REF]. Furthermore, the inhibition of the algal growth by high pH of material surface is commonly mentioned [START_REF] Grant | Fouling of terrestrial substrates by algae and implications for control -a review[END_REF].

Most of previous studies propose only a qualitative evaluation of the biofouling or a comparison of very different materials. In order to accelerate the fouling, mortars are usually aged (by carbonation and/or leaching) to decrease the surface alkalinity. But the effect of the accelerated aging is rarely evaluated. Moreover, the experimental conditions of accelerated tests are significantly far from the real conditions. The investigations in field-scale are rarely conducted because of the long duration of the experiments [START_REF] Young | Biological growth and their relationship to the physical and chemical characteristics of sandstones before and after cleaning[END_REF][START_REF] Ohshima | A study on growth of fungus and algae on mortar[END_REF][START_REF] Lengsfeld | Microorganisms on facades -reasons, consequences and measures[END_REF]. Thus, the relationship between bench-scale experimental results and field-scale experimental results is scant.

This work aims to clarify the effect of porosity, roughness and carbonation, on the building-materials colonization by algae at laboratory and in-situ scale. One unique mortar formulation has been investigated. The kinetic of the biological colonization was studied.

Materials and methods

Preparation and characterization of samples

Portland cement (CEM I 52.5, Holcim), siliceous sand (Sibelco DU 0.1/0.35), calcareous filler (Omya) and cellulose ether (Hydroxylethyl Methyl Cellulose, SE-Tylose) were mixed according to the proportions summarized in Table 1 to prepare the studied samples. The water-to-cement ratio (w/c) (wt/wt) was fixed at 1 and 1.2. These two w/c were considered in order to modify the porosity without changing the chemical composition of mortars. The variation of sample surface pH was achieved by a curing process. Mortars were subjected (called carbonated mortars) or not (called uncarbonated mortars) to ageing by accelerated carbonation prior to the start of biofouling test.

After mixing, the fresh mortar was casted into 50 cm × 50 cm × 1 cm extruded polystyrene molds. The fresh mortar was stored at 21 ± 1 °C and 95 ± 5 % of relative humidity during 28 days for the uncarbonated samples. The mortar plates were then cut into samples of 20 cm × 8 cm × 1 cm and of 20 cm × 30 cm × 1 cm for the laboratory tests and the in-situ tests, respectively. For the carbonated samples, the fresh mortar was stored in the aforementioned conditions for only 7 days before being cut. This premature curing end aimed to shorten the total duration of specimen production and to obtain the closest total storage time as possible between carbonated and uncarbonated samples.

The samples were then exposed to pure CO 2 at 21 ± 1 °C and 65 ± 5 % of relative humidity until the complete carbonation. This carbonation process required 36 days. The pH was verified by spraying a phenolphthalein solution (0.2 % in ethanol) on the entire thickness of specimen. The discoloration of the solution indicated a diminution of pH to about 9 [START_REF] Thiery | Modélisation de la carbonatation atmosphérique des matériaux cimentaires; prise en compte des effets cinétiques et des modifications microstructuraleset hydriques[END_REF].

Moreover, the surface pH of mortar was measured by means of a surface electrode (WTW Sentix Sur). For each sample, six measurements were performed at six positions distributed over the sample surface. A constant volume of distilled water (0.1 ml) was deposed on the related position. The electrode was kept in contact with the sample surface during a fixed time of 30 seconds. The pH value was then recorded and the surface pH of sample was the average of these six values. The surface pH of sample was monitored twice a week during the carbonation process.

The pore size distribution and the total porosity of materials were determined using mercury intrusion porosimetry (Micromeritics Autopore IV 9400). Three samples were measured for each mortar formulation, i.e. w/c ratio of 1 and 1.2, both uncarbonated after 28 days of curing and carbonated after 7 days of curing and 36 days of accelerated carbonation.

They were beforehand dried by acetone to evacuate the open pores.

To obtain several surface roughnesses, three surface finishing methods were applied during the sample setting. The first one consisted in smoothing the surface of fresh mortars with a ruler and the two others in scratching the surface of the setting mortars with sponges of two different roughnesses.

The roughness of the mortar specimens was evaluated by means of an optical profilometer (CHR-150-L). The arithmetic average of the height R a was determined from the measurements of the surface profile [START_REF] Gadelmawla | Roughness parameters[END_REF]. Measurements consisted in analyze 161 profiles of 7 cm length and spaced of 500 µm. The data was recorded each 20 µm along each profile. The value Ra, representative of the sample roughness, corresponded to the average of 563.661 measuring points.

Each mortar was labeled by four codes. The first one corresponds to the w/c ratio, the second to the carbonation state, the third to the roughness and the last to the scale of the biofouling test. For example, a sample labeled 1UC-R1-Lab corresponded to the uncarbonated mortar prepared with a w/c ratio of 1 with the smoothest roughness and tested in the laboratory experiment.

Lab-scale and field-scale biofouling tests

The laboratory experiments consisted in an accelerated algal growth on cementitious materials. A closed device containing an algal suspension was set up. The microalgae Klebsormidium flaccidum was selected in this research basing on its representativeness and ease of liquid culture. The suspension was periodically sprinkled on the samples surface. The run-off period was fixed to 90 min every 12 h. The light was provided by two neon lamps during 12 h per day, and was set to start simultaneously with the run-off cycles. All the experimental configurations (rate of sprinkling, light intensity, temperature, initial concentration of the algal suspension and angle inclination of the samples) were kept constant. The details of the experimental approach were described in previous papers [START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF][START_REF] Tran | Avrami's law based kinetic modeling of colonization of mortar surface by algae Klebsormidium flaccidum[END_REF].

In laboratory experiments, specimens with dimension of 20 cm × 8 cm × 1 cm were tested in triplicate for each material. Carbonated and uncarbonated samples were tested separately.

Therefore, 18 samples were introduced in the test-chamber for each experiment.

The field-scale experiments consisted in a natural development of microorganisms on cementitious materials. The mortar samples were placed on a stainless steel frame in a private green park close to Grenoble, France. The sample dimensions were larger than the ones used in the laboratory test, i.e. 20 cm × 30 cm × 1 cm. The larger dimensions aimed to minimize all the non-representative effect resulted from the natural incidental events such as a random intense inoculation of microorganisms at an individual sample points, the deposition of bird droppings on the sample surface, etc.

The exposure of materials to the outdoor conditions started on 26 June 2009 and lasted one year and a half. The experimental configurations were chosen in order to favor the biological colonization of the sample surface. The samples were placed near trees, facing the north direction and inclined with an angle of 45 °. The specimens were arranged in two rows of which the first was located at 1 m above the ground to avoid splashing during rainy periods.

The contamination between specimens by water flow was also avoided (Fig. 1). Each material was tested in triplicates. The mortars with a w/c ratio of 1 were studied at carbonated and uncarbonated states, with the three roughnesses. For the samples with a w/c ratio equal to 1.2, only the carbonated mortars with the two highest roughnesses were examined.

Evaluation criteria of biofouling

The biological colonization of mortar surface was evaluated by means of image analysis and colorimetric measurements.

Concerning the image analysis, the surface of samples was digitized using Epson V300 office scanner. The images obtained in the RGB color space were converted into the YIQ color space. The distinction between the areas covered by algae and the surfaces of clean mortars were achieved on the Q channel [START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF]. The colonization rate (X(t) (%))

was then given by the ratio of the fouled areas to the total surface of the sample. The samples from the lab-scale and field-scale experiments were scanned every weekday and at least every two months, respectively.

The colorimetric measurements were performed using colorimeters (Minolta CM-2600d

for the laboratory tests and Konica Minolta Chroma CR-410 for the in-situ tests). For each specimen, the measurements were conducted at fixed positions spread over the whole sample surface. Thirty six and eighteen measurements were monitored on a lab sample and an in-situ one, respectively. The sample area of each measurement was of 0.5 cm 2 and 19.6 cm 2 , respectively. The CIE Lab color space data (L*, a*, b* coordinates) were collected. The data was monitored three times a week on the lab specimens and at least every two months for the field-scale specimens. In order to evaluate the color changes of the test specimens, for each color coordinate (L*, a*, b*), the difference between sample at a given time and the same sample at the initial time (uncolonized sample) was determined (∆L*, ∆a*, ∆b*).

Results

Characterization of materials

The porosity, the surface pH and the roughness of each mortar are given in Table 2. For the samples made with w/c ratio equal to 1 (i.e. uncarbonated and carbonated), the values of the porosity, the surface pH and the roughness R1 were those of a previous paper [START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF]. The total porosity of uncarbonated mortars varied from 37 to 39 %, which is coherent with the literature [START_REF] Monge | Fissuration des mortiers en couches minces -Effets de l'hydratation, du séchage et de la carbonatation[END_REF]). The mortars with the highest w/c ratio were slightly more porous.

According to [START_REF] Lafhaj | Correlation between porosity, permeability and ultrasonic parameters of mortar with variable water/cement ratio and water content[END_REF], the porosity increases non-linearly with the w/c ratio. When this w/c ratio is high, its effect on the total porosity is attenuated.

The carbonated mortars were less porous than the uncarbonated ones, i.e. 32 % for 1C against 37 % for 1UC and 36 % for 1.2C against 39 % for 1.2UC. It is known that the carbonation leads to a reduction of pore volume. [START_REF] Houst | Diffusion de gaz carbonatation et retrait de la pâte de ciment durcie[END_REF] noted that this reduction of the total porosity is even more enhanced by a low w/c ratio.

Depending on the curing process, two levels of surface pH were obtained. The surface pH reached 11 with the standard curing (uncarbonated samples) and 9 by accelerated carbonation.

Moreover, no effect of the w/c ratio on the surface pH was detected. Indeed, the same value of surface pH was measured for both w/c ratios.

Three levels of roughness were obtained whatever the curing process and the w/c ratio. The smoothest surface (R1), without reliefs, was achieved by the method of finishing to the rule.

The rougher surfaces were obtained by scratching the sample surfaces with sponges. Both strong reliefs and asperities appeared on the roughest surface (R3). Moreover, a remarkable discrimination between the highest roughness (R3) and the intermediate one (R2) was observed. In fact, the R a values were 2.5 to 5 times higher for R3 than for R2. As a comparison, the difference between the R2 and R1 was only about 1.5 times. The same latency time was observed by [START_REF] Dubosc | Etude du développement de salissures biologiques sur les parements en béton: Mise au point d'essais accélérés de vieillissement[END_REF] and [START_REF] Young | Biological growth and their relationship to the physical and chemical characteristics of sandstones before and after cleaning[END_REF] for carbonated mortars and sandstone samples, respectively. The biological development accelerated during the autumn period (August to November, i.e. 13 to 17 months of exposure). The same observation was made by [START_REF] Warscheid | Studies on the temporal development of microbial infection of different types of sedimentary rocks and its effect on the alterioration of the physico-chemical properties in building materials[END_REF] on stone samples exposed to outdoor conditions in different locations in Germany.

Biological colonization of cementitious materials in laboratory and field test

The propagules of microorganisms might be already settled on the mortar surface since the spring. In the lab test, the algal colonization curve was of sigmoid type. Three steps can be identified: a latency step, an exponential growth step and a step of stagnation. For each roughness (R1, R2 and R3), no effect of the w/c ratio was identified on algal coverage. In fact, for the roughest mortars (R3), the fouling rate evolved quite identically. The algal colonization appeared after 6 testing days and the entire surface was covered after 30 days.

Effect of w/c ratio

For the two other roughnesses, with such experimental standard deviation, the colonization rate of the less porous mortars (1C) could be considered similar to the one of the more porous mortars (1.2C).

Unlike in the accelerated test, in the real conditions, an effect of the w/c ratio was detected.

Indeed, the mortars made with a w/c ratio of 1.2 presented a faster microbial development than the ones prepared with a w/c ratio of 1. For the 1.2C-R3 samples, the biofouling appeared between 11 and 13 months of exposure. At the same moment, no algal colonization was observed on the mortar 1C. The following measures, realized two months later, showed a coverage area of 80 % for 1.2C mortars against only 30 % for 1C mortars. For the intermediate roughness (R2), the effect of w/c ratio was less important. 30 % of the mortars 1C was colonized while it was 2 times higher on the mortar 1.2C. One month later, only the more porous mortar was totally colonized.

The color changes of the roughest mortar confirmed the results obtained from the images analyses (Fig. 5). Indeed, the color intensity of 1.2C-R3-Field mortars evolved faster than the one of 1C-R3-Field mortars. Furthermore, the change in color intensity between these two mortars occurred after 13 months of exposure. Concerning the bench-scale experiments, the evolution of the color and the colonization rate coincided perfectly regardless of the w/c ratio.

Indeed, an increase in the color intensity was detected between 4 and 28 days of exposure.

Then, no color evolution was observed since the 28th days of testing, corresponding to the necessary time for a complete biofouling.

Effect of the roughness

For the bench-scale test, the biofouling rate was obviously influenced by the surface roughness of samples (Fig. 6a). The effect of the three levels of roughness tested on the biofouling were quite distinct, whatever the w/c ratio (1 and 1.2). The smoothest roughness (R1) exhibited the lowest colonization rate and the highest latency time. Indeed, the latency time was around 18 days of testing for roughness R1, against 9 and 6 days for roughness R2 and R3, respectively. Similarly, the complete colonization was achieved more quickly on the rougher mortars, i.e. in 30 days for R3, against 51 and 56 days for R2 and R1, respectively.

Furthermore, the curve slope evolved in the same way as the roughness during the exponential growth phase. The more the roughness was high, the more the colonization was quick.

The roughness impacted also the biological development of mortars exposed in the realworld (Fig. 6b). However, unlike bench-scale test, only two grades of roughness (i.e. rough and smooth) were observed. The mortars of very different roughness, R2 and R3, showed no difference in bioreceptivity to visible photosynthetic organisms. This result was particularly obvious for w/c = 1. Conversely, a transition from a smooth surface (R1) to a rough one (R2)

remarkably increased the bioreceptivity of mortars. Indeed, the colonization appeared slower for the mortar R1 than for the two others. The entire surface of samples R2 and R3 was colonized after 17 months (November 2010). For the same duration, only 60 % of mortar surface R1 was colonized. Beyond this time, a decrease in the covered area was noticed for all samples. It has been assigned to detachment of algae. The detachment rate was similar for all mortars of w/c equal to 1. However, for mortar of w/c equal to 1.2, smooth surface showed a faster decrease in the coverage area compared to the rough one. Hence, the effect of roughness on the microbial detachment rate remains difficult to analyze. The carbonation seemed to be the most decisive parameter on the bioreceptivity of materials for the accelerated fouling test. It significantly shortened the latency time, and accelerated the rate of algal colonization. As showed in the Fig. 7, the latency time of 1C-R1 mortar was of 18 days. This value was 2.6 times less than that of 1UC-R1 mortar (46 days).

Effect of the accelerated carbonation

Similarly, the colonization of 1C-R3 mortar began after 7 days against 26 days for 1UC-R3 mortar. The complete colonization was reached in 30 days for the 1C-R3 mortar against 51 days for the 1UC-R3 one. It is worth noting that, the total colonization of 1UC-R1 was not obtained because of a precocious stop of testing. Nevertheless, basing on the roughest mortars, the slope of the curve was greater for carbonated mortars than for uncarbonated ones.

In the field-scale test, it seems that the accelerated carbonation did not result in different growth profiles. The biofouling evolved quite identically on carbonated and uncarbonated mortars. For both mortars 1UC and 1C, and of roughness R1 or R3, the colonization by microorganisms began at the same moment, i.e. after 13 months. Then, 4 months later (November, corresponding to 17 months of exposure), the entire surface of all rough samples (R3) was colonized. At this same time, the algal colonization reached a common rate of around 60 % for smoothest samples (R1), carbonated or uncarbonated. From 18 months (December 2010), a decrease of fouled area was observed on the entire surface due to the microbial detachment. It seems that the detachment rate was not dependent on the initial carbonation state of mortars.

Discussion

The results obtained from the color measurements and the image analysis, are coherent and complementary. Indeed, the effect of intrinsic characteristics of mortars on their bioreceptivity was found identical by these two methods. Due to monitoring the entire surface of samples, the color changes are well representative of the fouled area.

The color evolution of the surface of the samples, for both laboratory and in-situ tests, was quite identical, i.e. more and more dark, green and yellow. The fouling of the in situ samples is thus presumably associated to green algae. These microbial species are the primary and main colonizers on building facades as noticed by several authors [START_REF] Wee | Proliferation of algae on surfaces of buildings in Singapore[END_REF][START_REF] Grant | Fouling of terrestrial substrates by algae and implications for control -a review[END_REF][START_REF] Ortega-Calvo | Factors affecting the weathering and colonization of monuments by phototrophic microorganisms[END_REF][START_REF] Tomaselli | Biodiversity of photosynthetic microorganisms dwelling on stone monuments[END_REF][START_REF] Barberousse | Etude de la diversité des algues et des cyanobactéries colonisant les revêtements de façade en France et recherche des facteurs favorisant leur implantation[END_REF].

The influence of w/c ratio on the accelerated fouling was negligible. The reason is related to experimental conditions rather than to modest difference in porosity between two studied mortars. Indeed, the relative humidity in the laboratory test chamber is permanently very high (i.e. from 80 to 100 %) (Fig. 8). In this condition, the water content into the samples is always abundant and so is sufficient to the algal development. In order to verify this assumption, the filling rate of pore by water (ε (%)) was calculated [START_REF] Dubosc | Etude du développement de salissures biologiques sur les parements en béton: Mise au point d'essais accélérés de vieillissement[END_REF]. It corresponds to q/p ratio, where p (%) is the sample porosity, and q (%) is the amount of water absorbed by a unit of sample volume, calculated as follows:

V water : volume of water absorbed by the sample (cm 3 );

V sample : apparent volume of the sample (cm 3 ), calculated from three dimensions of sample;

m water : amount of water absorbed by the sample (g) that is equal to the difference between the mass of sample in the humid condition and in the dry one.

ρ water : density of water (1 g.cm -3 )

The humid sample weight was measured 6 times along the diurnal cycle and 2 times along the nocturnal one. Before the start of accelerated fouling test, the sample was dried at 40 o C until obtaining constant weight. This weight was considered as the mass of dry sample.

The amount of water absorbed by the sample reached a maximum value just after the sprinkling cycle and remained constant during all the nocturnal period. During the diurnal period, the water evaporated under the warming effect induced by neon lights. However, the amount of evaporated water was weak. Indeed, at the end of the diurnal period, the remaining water into the mortars filled at least 75 % and 60 % of the porosity of uncarbonated and carbonated samples, respectively.

The water, being an indispensable element for the biological metabolism, is thus no longer a limiting factor for the biological development. This observation was confirmed by previous studies regarding two mortars made with w/c ratios equal to 0.5 and 1 [START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF]2013). Despite of the considerable difference in porosity, these mortars exhibited completely identical bioreceptivity.

In natural condition, the impact of the w/c ratio on the colonization rate of samples was exhibited. The microbial fouling seemed to be favored by the highest w/c ratio (1.2).

To evaluate the porous network of mortars, analyses were performed after 17 months of exposure to the outdoor conditions. PIM's results indicate a modification of the porous network. Indeed, the total porosity of the 1C-R3 and 1.2C-R3 mortars increased from 32 to 36 % and from 36 to 38 %, respectively. Moreover, the single peak characterizing the pore entrance diameter shifted to larger diameters (Fig. 9). Indeed, the pore inlet diameter, that was equal to 0.3 µm at the beginning of outdoor exposure, was about 0.5 µm at the end of the experiment for the 1C mortar. For the 1.2C mortar, the pore inlet diameter evolved from 0.75 to 1.6 µm. The enlargement of the pore entrance diameter could be due to the leaching effect by rain and to the activities of biological agent such as bacterial communities and/or fungi [START_REF] Warscheid | Biodeterioration of stone: a review[END_REF]. These results, which corresponded to the average values of the entire thickness of samples, might be amplified at the surface.

the results of laboratory tests, the in-situ samples of the roughness R3 should have been firstly colonized, successively followed by mortars of the roughness R2 and then R1. However, in the in-situ test, the season, the external relative humidity and temperature could impact the colonization and thus hided the roughness effect.

In the natural conditions, only two grades of roughness were observed. The two roughest mortars showed the same bioreceptivity to pigmented organisms despite considerably different roughness. This tendency remains coherent with that obtained in laboratory test. In fact, a nonlinear relationship between roughness and algal fouling rate is noticed. A close bioreceptivity was observed between mortars of high roughness [START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF]. The nondifferentiation in the outdoor test could be induced by a natural inoculation much less intense than in accelerated tests.

Concerning the accelerated carbonation, this intrinsic characteristic of the samples appeared as the most important parameter which affected the biological growth in the accelerated fouling test. Unlike the effect of roughness which favors the ability of algae to physically cling to the surface, the pH and/or carbonation disturbs the biological metabolism.

Carbonation leads to a decrease in the surface pH of samples and to a lower increase in pH of the algal suspension flowing on test specimens. Consequently, the K. flaccidum algal cells are in less alkaline conditions and thus in less stressful environment for their growth with carbonated samples than with uncarbonated ones. Indeed, K. flaccidum is known as an acidophilic microorganism. The ability of attaching and growth of algae on a surface are thus promoted by the carbonated of samples [START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF]2013).

The growth of the algal spots on the sample surface is the consequence of the vegetative and cellular multiplication which is favored at low pH (Škaloud, 2006). The attachment of algae on the surface of the substrate is governed by adaptive metabolic interactions between algal cells and the substrate [START_REF] Fattom | Hydrophobicity as an adhesion mechanism of benthic cyanobacteria[END_REF][START_REF] Finlay | The influence of surface wettability on the adhesion strength of settled spores of the green alga Enteromorpha and the diatom Amphora[END_REF][START_REF] Barberousse | Capsular polysaccharides secreted by building façade colonisers: characterisation and adsorption to surfaces[END_REF]. The algal extracellular polysaccharides could play the role of glue [START_REF] Robins | Mucilage acts to adhere cyanobacteria and cultured plant cells to biological and inert surfaces[END_REF][START_REF] Gantar | Role of extra-cellular polysaccharides in the colonization of wheat (Triticum vulgarie L.) roots by N 2 -fixing cyanobacteria[END_REF][START_REF] Barberousse | Capsular polysaccharides secreted by building façade colonisers: characterisation and adsorption to surfaces[END_REF]. These metabolites depend on the algal species considered and the substrate. They are involved in the initial contact between the cell and the surface, and act over time [START_REF] Barberousse | Capsular polysaccharides secreted by building façade colonisers: characterisation and adsorption to surfaces[END_REF].

As a consequence, carbonated mortars are highly receptive to colonization by microorganisms. Algal colonization begins much earlier, and occurs faster compared to the uncarbonated mortars.

In the field-scale test, the influence of carbonation was not highlighted. Indeed, the biofouling of mortars, carbonated or uncarbonated, was detected at the same moment.

Perhaps, the favorable climatic conditions and sufficient inoculation conditions were not met at the beginning of testing. In fact, the samples were exposed through the summer. Therefore, spring, the most favorable season for the microorganism spreading and their growth was past.

Hence, the microbial colonization of carbonated samples was not initiated despite a favorable surface pH. After one year of exposure, the mortars were aged and weathered by leaching and natural carbonation. Consequently, the same surface pH (pH = 8) was measured for all the samples whatever their initial carbonation state. The bioreceptivity of mortars is thus identical when favorable conditions to the biological development have been in place. Therefore, the influence of the initial surface pH on biofouling is completely inhibited.

Conclusion

The present research has investigated the effect of the intrinsic parameters (porosity, roughness and carbonation) of mortars on their biofouling by photosynthetic organisms. This study was conducted by both laboratory accelerated tests and in-situ ones.

The impact of porosity on the biofouling of mortars is different for the two experimental test scales. This parameter has no effect on the biofouling rate in laboratory tests due to the experimental conditions. However, although more experiments of verification still required for the field-scale tests, high porosity seems to favor the biological colonization.

For the both test scales, the influence of the roughness is evidenced. A rough surface enhances the biological attachment. The discrimination of roughness grades was better in the accelerated tests than in the field-scale ones. This result could be explained by the fact that the accelerated test is performed in a closed circuit with an intense inoculation while the in-situ test involves natural inoculation.

Thanks to its experimental configuration, the laboratory tests allow revealing the role of the accelerated carbonation. It is considered as a decisive parameter in the accelerated fouling.

Indeed, carbonated mortars lead to a lower pH value of the mortar surface and the algal suspension in the test chamber. The algal development is thus significantly promoted and so the colonization rate is remarkably accelerated in the case of carbonated mortars. While in the natural conditions, due to numerous uncontrolled and random environmental factors, the effect of the carbonation was not observed. The evolution of biofouling is identical on the both carbonated and uncarbonated mortars. Due to the long exposure time and progressive ageing by lixiviation and carbonation, the surface pH, and thus the alkalinity, of carbonated and uncarbonated samples is the same.

The divergence of results between the laboratory and field-scale tests, prevent to correlate the two experimental scales. These dissimilarities could be remediated by improving the experimental protocol. In the accelerated test, a drying phase of samples between two sprinkling cycles could allow highlighting the role of porosity. A reasonable choice of the beginning of sample exposure to natural environment could highlight the effect of carbonation. The effect of roughness in accelerated test could be closer than that in natural test by decreasing the inoculation intensity. This decrease in inoculation process could be achieved by reducing, either the initial concentration of the algal suspension or either the runoff.

Fig. 1 .

 1 Fig. 1. Experimental set-up for the in-situ tests.

Fig. 2 Fig. 3 .

 23 Fig. 2 illustrates the biological fouling of specimens investigated in the accelerated tests

Fig. 4 .Fig. 5 .

 45 Fig. 4. Monthly average air temperature and cumulative precipitation during the in-situ test.

Fig. 6 Fig. 6

 66 Fig.6shows the influence of the w/c ratio (1 and 1.2) on the biofouling rate of carbonated

Fig. 7 Fig. 7 .

 77 Fig. 7 illustrated the evolution of the colonization rate for carbonated and uncarbonated

Fig. 8 .

 8 Fig. 8. Daily cycle of temperature and relative humidity in the test chamber.

Table 1

 1

	Mortar formulation
	Component	Cement	Sand	Calcareous Filler	Admixture a
	% mass of dry mixture	30	65	5	0.27
	a in addition to dry mixture (cement, sand and filler)

Table 2

 2

	Characteristics of mortars
		Ratio	Porosity	Surface		Code	R a (µm)
		w/c	(%)	pH
	Uncarbonated	1	37.2 ± 0	11 ± 0.4	Roughness 1	1UC-R1	29 ± 5
					Roughness 2	1UC-R2	47 ± 6
					Roughness 3	1UC-R3	70 ± 8
		1.2	38.9 ± 0.3 11.0 ± 0.3	Roughness 1	1.2UC-R1	29 ± 5
					Roughness 2	1.2UC-R2	47 ± 6
					Roughness 3	1.2UC-R3	123 ± 9
	Carbonated	1	32.1 ± 1.9 9.0 ± 0.1	Roughness 1	1C-R1	29 ± 5
					Roughness 2	1C-R2	47 ± 6
					Roughness 3	1C-R3	138 ± 15
		1.2	36.2 ± 0.1 8.9 ± 0.1	Roughness 1	1.2C-R1	32 ± 4
					Roughness 2	1.2C-R2	47 ± 6
					Roughness 3	1.2C-R3	145 ± 18

The mortars made with a w/c ratio of 1.2 were more porous than those formulated with a w/c ratio of 1 and exhibited a greater bioreceptivity. The effect of porosity on the biofouling rate of samples exposed outdoor are in agreement with the literature [START_REF] Warscheid | Studies on the temporal development of microbial infection of different types of sedimentary rocks and its effect on the alterioration of the physico-chemical properties in building materials[END_REF][START_REF] Ohshima | A study on growth of fungus and algae on mortar[END_REF][START_REF] Crispim | Algal and cyanobacterial biofilms on calcareous historic buildings[END_REF][START_REF] Prieto | Estimation of the potential bioreceptivity of granitic rocks from their intrinsic properties[END_REF][START_REF] Miller | Primary bioreceptivity: A comparative study of different Portuguese lithotypes[END_REF][START_REF] Miller | The influence of inherent properties of building limestones on their bioreceptivity to phototrophic microorganisms[END_REF].

Previous studies highlighted an important role of roughness on the biological colonization [START_REF] Prieto | Estimation of the potential bioreceptivity of granitic rocks from their intrinsic properties[END_REF][START_REF] Miller | Primary bioreceptivity: A comparative study of different Portuguese lithotypes[END_REF][START_REF] Miller | The influence of inherent properties of building limestones on their bioreceptivity to phototrophic microorganisms[END_REF][START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF][START_REF] Tran | Avrami's law based kinetic modeling of colonization of mortar surface by algae Klebsormidium flaccidum[END_REF]. By providing asperities, the roughness favors the physical attachment of microorganisms which is dispersed by the water flow or the wind. Consequently, the rougher the surface is, earlier the biological fouling begins and faster the colonization is. The recent accelerated fouling experiments allow confirming the effect of roughness. Indeed, the three grades of roughness studied induced a discriminating effect on the colonization rate. The same results were noticed by [START_REF] Tran | Influence of the intrinsic characteristics of mortars on biofouling by Klebsormidium flaccidum[END_REF] on others mortars mixed with a w/c ratio of 0.5.

For in-situ samples, the visible biofouling due to phototrophic organisms appeared approximately at the same moment whatever the roughness of mortars. Indeed, for all the roughnesses, the first spots were detected after about 13 and 15 months of exposure. Based on