A H Fakra
email: fakra@univ-reunion.fr

H Boyer

F Miranville

D Bigot

A simple evaluation of global and diffuse Luminous Efficacy for all sky conditions in tropical and humid climate

Keywords: Global and diffuse luminous efficacy, different sky conditions, solar irradiance, solar illuminance

This paper presents initial values of global and diffuse luminous efficacy at Saint-Pierre (Reunion Island). Firstly, data used were measured for a period of 6 months, from February to June 2008. During this period, all defined day-types have been studied (clear, cloudy and intermediate). Generally, the meteorological database of Reunion does not contain information for illuminance values. On the other hand, the local meteorological center has a 60-years-old database for solar irradiance (W.m -2 ). So it is important to determine Luminous Efficacy in order to find illuminance from solar irradiance (or luminance from solar radiance). The measured data were analyzed, and empirical constant models were developed and presented in this paper in order to determine luminous efficacy under different sky conditions. A comparison between these empirical constants (models) and existing models has been made. The method used to define sky conditions (overcast, intermediate and clear) and day-types characterization as well as classification will be presented in this work.

Introduction

Daylighting is recognized as an important and useful strategy in the design of energy efficient buildings. It is particularly useful in hot climates since it reduces the use of artificial lighting and thus electricity demand. Luminous efficacy is the parameter used to determine outdoor illuminance. In fact, many regions of the world work on this parameter to meet the needs imposed by problematic environments (from a meteorological point of view). For example, illuminance values (in lux or lm.m -2 ) can be simulated from the solar irradiance (W.m -2 ) and luminous efficacy. Therefore, it is important to know theses values of luminous efficacy for a given location and this is the reason for this study at Reunion Island.

Most meteorological stations in La Reunion have a sizeable database for solar irradiance (going back about 60 years) but these stations unfortunately do not have illuminance data.

Another reason that prompts us to study these luminous efficacy values is that simulation software for buildings needs specific climatic data, particularly on outdoor illuminance.

Hence, luminous efficacy models introduced in the software enables illuminance values simulation using solar irradiance databases.

Firstly, empirical (or experimental) constant luminous efficacy (global and diffuse models) for this location (at 21°19'S, 55°28'E) is introduced. Materials, methods and experimental procedures are then presented. Results obtained confirm the accuracy of models. This work was done for a PhD thesis 1 and results obtained are used in CODYRUN 2 simulation software for predicted illuminance values in Reunion Island.

Literature review

The luminous efficacy of daylight (in lm/W) is defined as the ratio of daylight illuminance to solar irradiance. With the availability of the measured horizontal and/or vertical solar data, luminous efficacy for horizontal and/or vertical surfaces can be determined respectively. This gives building designers an indication of the relationship between daylight illuminance and solar irradiance. The bibliography is restricted to horizontal luminous efficacy cases only. This evaluation method of luminous efficacy is an experimental one: it is the ratio between outdoor illuminance and solar irradiance data (or luminance/radiance ratio).

Various research teams around the world had carried out similar studies to determine the luminous efficacy constants.

Among the earliest are the works of Pleijel 3 in Scandanavia, Blackwell 4 at Kew, England, Dogniaux 5 in Uccle, Belgium and Drummond 6 in Pretoria, South Africa. Blackwell concluded that global efficacy varied between 105 and 128 lm/W for average sky conditions. Although no diffuse efficacy values were available at that time, hence a combination of Backwell's irradiance measurements with corresponding illuminance values for Kew (outlined by McDermott and Gordon -Smith for nearby Teddington), 7 led Hopkinson 8 to propose a constant value of 125 lm/W for diffuse efficacy. Muneer and Angus (respectively 9 and 10) suggested allsky, average global and diffuse luminous efficacy values of 110 and 120 lm/W, respectively. Darula and Kittler 11, Joseph 12 or Dumortier 13 has given more information on the comparison of the different luminous efficacy found all over the world.

According to Darula 14, each region has its own constant of luminous efficacy. Indeed, in his work, the author demonstrated that these variables are heavily dependent on local climate (precipitation, temperature, etc.), geography location (latitude, longitude, etc.) and meteorological phenomena observed on the site (hurricanes, volcanoes, etc.).

Generally, the maximum average value for global luminous efficacy is 180 lm/W (in Norway) and the minimum average value is 98 lm/W (in Japan) 13. More recent research in this field has been carried out for Cucumo 15 for different locations and Ana 16, Spain.

In this paper, similar work has been done to determine the constant values for Reunion Island.

Methodology and experimental overview

The experimental station is located on the rooftop of an experimental test cell located at the University of Technology of Saint Pierre (University of Reunion) and is free from obstructions. In 2008, an experimental station was set up to measure horizontal solar irradiance and outdoor illuminance. The instrumentation of the station consists of two pyranometers and two illuminance sensors for horizontal solar irradiance and daylight illuminance data measurements. All sensors are installed on the rooftop in a position which is relatively free from any external obstructions, and is readily accessible for inspection and general cleaning.

Location of the meteorological station

The experimental station is located at 21°19'S, 55°28'E, and 70,40m above sea level (see Fig. 1 and2). The field environment consists of an experimental set up (the LGI cell 17) and meteorological station (see Fig. 3). Illuminance sensors fitted to the roof of the LGI cell. Measurements of solar irradiance were given by the pyranometer of the local meteorological station.

Experimentation set-up

Data collection starts before sunrise and ends after sunset. All measurements are referred to using true solar time (TST). Pyranometers (CM11), manufactured by Kipp & Zonen, was used to carry out the measurements of solar irradiance on a horizontal plane. The diffuse irradiance pyranometer was fitted with a shadow ring 55 mm wide and 620 mm in diameter, which shades the thermopile from the direct beam. The shadow ring is painted black to minimize the effect of multiple reflections. The two pyranometers were connected to a data acquisition system, which calculated the irradiance at intervals of one minute. The data from the system were sent by cable to a microcomputer for storage. The measurements of global and diffuse outdoor illuminance on a horizontal plane were made by means of two illuminance sensors (see Fig. 3). The two silicon photovoltaic cells have cosine and colour correction. Again, a shadow ring was used to stop the direct component to obtain the diffuse illuminance measurement. The measured results were converted into digital signals by an analogue to digital converter before being transferred into a microcomputer for storage. These data were measured at one-second intervals and averaged over one-minute intervals. For measurements of overall illuminance (i.e., direct beam, skydiffuse and ground -reflected components), one illuminance sensor of the same model type was used. The sensor is connected to another analogue to digital converter and linked to a computer for data conversion and data logging. The data collection method was the same one as that for horizontal illuminance measurements. Quality control tests were carried out to eliminate spurious data and inaccurate measurements resulting from the cosine response error of the pyranometers and illuminance sensors.

Irradiance was measured using a pyranometer (CM11 Kipp & Zonen secondary standard pyranometer) connected to a data logger of the CAMPBELL brand; while measurements associated with illuminance (FLA613VLM luxmeter and corresponding data logger) were done using equipment by the AHLBORN Company. Synchronization of the two experiments was necessary in order to get results of measurements for illuminance and irradiance simultaneously. Their respective manufacturers provide technical specifications for each instrument.

Methods and experimental data

Hubbard 18 demonstrated that the length of data series should be more than one year to characterize a seasonal pattern. Gueymard 19 recommended that, in order to validate irradiance-estimation models, long-term dataset is needed. Data collected every minute for 6 months (February -July) on horizontal plane, measured at the city of Saint-Pierre, were used for the analysis. Two seasons (winter and summer) were observed during this period of the year. In fact, in Reunion Island February correspond to summer season and June winter season.

It is often noticed some short periods of missing data due to various reasons including instrumentation malfunctioning and power failure. Considerable effort was made to obtain 12000 and 23000 minute reading, respectively, for each global and diffuse solar irradiance and daylight illuminance. Graphical representation is a simple and direct approach to analyze and interpret the recorded solar data.

Classification of day-type conditions

Sky conditions are generally classified into three categories, namely: clear, intermediate and overcast. It is important to have information about the occurrence of clear and cloudy days. In fact, the originality of this study is that three typical day-types (or day conditions) have been defined instead of three sky conditions: intermediate (Fig. 5), clear (Fig. 6) and overcast (Fig. 7) days. Global illuminance (sum of direct and diffuse illuminance) is the only variable used to classify the day-types defined. Indeed, testing classification models on diffuse illuminance cannot provide information on the day-type. These day-types (clear, intermediate and overcast) were observed during the 6 months measurement.

Classification assessment began at sunrise and finished at sunset. The frequency distribution of each sky type determines the day classification. In 2002, Kittler finally showed that K T was not appropriate for the study of classification of sky types 20. However, it is important to determine whether this index could be applied to classify daytypes or not. Other indices are generally used for studies of classification sky types. The aim of this study is also to verify the possibility of using the indices for the characterization of sky types on day-types, which were previously defined.

The most important reason for selecting this index is that the meteorological station laboratory can give input (variables) data and parameters to determine the index. Classification of the daylight data into three-day conditions is given by the four indexes shown in Table 3. Analytical form index and respective typical conditions to characterize day-types is given by:

 Perez's Clearness index  :    d h  d es d h       1.041 Z 3 11.041 Z 3
Tests conditions are:

 0  I N  0.05  Overcast 0.05  I N  0.9  Intermediate 0.9  I N  1  Clear       Kittler's index KT :  K T  G h G o (1) (3)
(5)

(2) (4)

Tests conditions are:

 0  K T  0.3  Overcast 0.3  K T  O.65  Intermediate K T  0.65  Clear       Sky Ratio index SR :  SR  d h G h
Tests conditions are:

 SR  0.8  Overcast 0.3  SR  0.8  Intermediate SR  0.3  Clear     
The application of these indices on different day-types (defined previously) and the comparison of the results obtained between the selected sky classifications indices are given in Fig. 8. For each index, associated tests conditions, enables us to define day-types (see tests conditions for relations (2), ( 4), ( 6) and ( 8)). Finally, the reliability of each index was checked, which describes day-types previously defined.

Analysis of the graphs showed that:  Finally, it is noted that Kittler's index does not suit these day-types. The only variable in the analytic form of the index is the global horizontal terrestrial-irradiance. The extraterrestrial solar irradiance stays constant. So, it is not possible to characterize correctly random cloud phenomenon for each defined day (overcast, intermediate and clear).

 Using Perraudeau's index,
To conclude, Perez's index can characterize day-types (defined previously) up to a certain extent (only clear and overcast days) in contrast with the SR index that is more appropriate to characterize day-types defined. Kittler's and Perraudeau's indices are not suitable to Reunion Island.

Fig. 8. Results of comparisons and application of different indices for day-type classification (clear, intermediate and overcast)

Comparisons of luminous efficacy models with measurements (Results)

Statistical errors indicators

The accuracy of the constants models was determined using statically indicators: the coefficient of determination R 2 , the Mean Bias Deviation (MBD) and the Root Means Square Deviation (RMSD). MBD demonstrates the model's tendency to underestimation or overestimation. RMSD offers a deviation measure from the predicted

(7) (6) (8)
values in relation to the measured values. Using the correlation coefficient R 2 , the MBD, and the RMSD determined the accuracy of the models as statistical estimators 25. They are defined as follows:

 RMSD  1 E mean        E mod,i  E meas,i   2 i1 N  N             1/ 2 and  MBD  E mod,i  E meas,i   i1 N  N  E mean 100
Where:

E meas,i : Measured value of the dependent variable corresponding to a particular set of values of the independent variables. In this study, it is the measured values for horizontal illuminance / irradiance; E mod,i : Predicted dependent variable value for the same set of independent variables above (these values are obtained from the model), In this case, it is the illuminance predicted values from the constant (global or diffuse) luminous efficacy;

E mean : Mean value of the dependent variable testing data set and N (number of records of data in the testing set) or the E meas,i mean values;

In order to increase accuracy, some statistical indicators also need to be defined as follows:

 R 2  E mod,i  E mean   2 i1 N  E meas,i  E mean   i1 N  2
Where  R 2 is the coefficient of correlation.

The definition of the following value at Mean Percentage Deviation (MPD) and Root Mean Square percentage deviation (RMS) between the calculated data and the experimental data, is given by 15: Diffuse luminous efficacy value remains constant during the day, except at sunrise and sunset where it varies considerably. Indeed, this value is function of the solar elevation. This explains the errors obtained when reducing this value to a constant.

 MPD  E mod,i  E meas,i   E meas,i
The results obtained for global luminous efficacy showed a fairly stable value throughout the day. It is true that this value is related to direct and diffuse luminous efficacy, and that these variables dependent on solar elevation (refer to 26, 27 and 28) but, similar studies showed that, generally, the diffuse luminous efficacy increases when the direct luminous efficacy decreases (and vice versa) in proportions that depend on the aerosol content of the atmosphere 13. Therefore, these two (direct and diffuse luminous efficacy) values tend to an equilibrium value (global luminous efficacy). This probably explains the small variations observed in the experimental value of global luminous efficacy (dependent direct and diffuse luminous efficacy). Errors obtained from the constant global luminous efficacy can be explained by the fact that this value varies solely on solar altitude. Indeed, other parameters such as the amount of aerosol contained in the atmosphere or the distribution of clouds in the sky can significantly influence this constant.

By taking experimental errors (of +/-1-3%) into consideration (given by the material manufacturer), it is concluded that the luminous efficacy values obtained experimentally are reasonable.

In addition, the constants found are in conformity with international references. For example, the value of global luminous efficacy was found to be 121.5 lm /W. This corresponds to a value between 98-180 lm/W (see reference 13).

Application: simulation in CODYRUN

CODYRUN is a dynamical building simulation code developed by the L.P.B.S. laboratory 2. The software uses a multiple-model approach to simulate the building system (thermal, airflow and humidity aspects in multizones buildings). The laboratory developed this program for two types of users:

 Building designers and operators

 Building physics researchers (14) (15)
Thereafter, several works have been investigated to improve the computer tools. Thus, in this scope, many physical models were introduced then tested into the software in order to make it even more powerful and more diversified (reference 29, 30 and 31).

Recently, improvements were made to the calculation code for simulating exterior daylighting from the meteorological database. In fact, two constants (global and diffuse) luminous efficacy to simulate illuminance values were used. Figs. 11 and 12 illustrate comparisons between the simulated results and measured ones obtained at Saint-Pierre, in the case of comparison for diffuse illuminance (see Fig. 11), showing four successive random days. In the case of comparison for global illuminance (see Fig. 12), three typical days were selected (clear, intermediate and overcast) to compare measured and simulated values. Errors between measurements and simulation are:

 RMSD = 5.04 %, MBD= 0.16 % and R 2 = 0.75 for the diffuse illuminance comparison and,  RMSD = 5.30 %, MBD= -1.45 % and R 2 = 0.74 for the global illuminance comparison.

These results showed that the constant model of global and diffuse luminous efficacy predicted better illuminance values at Saint-Pierre.

Outdoor daylighting obtained from luminous efficacy allows the simulation of indoor daylighting values at any point of a building. In fact, models introduced in CODYRUN enable the determination of indoor daylight values at any point on a virtual surface grid representing a interior horizontal surface (including the work plane or the roof).

Experiments done on the LGI cell (fig. 13) allowed the comparison of simulated daylight values with those measured experimentally. Measurements of internal illuminance were made at five points (A 1 , A 2 , A 3 , A 4 and A 5 ) in roofing (of height 0.01 meter above the floor). The sensors were aligned to the central axis of the building (cutting the glazing into two symmetrical parts) and perpendicular to single glazing plane (Fig. 14). In this case, Mean Relative Error between simulation and measurements is 9.9 % in dynamic conditions. It is important to know that it is very difficult to characterize dynamic conditions for indoor illuminance phenomenon (see reference 32 and 33). So, the result obtained is correct. For more information about this study, refer to Fakra's thesis 1. The detailed study of the indoor daylighting simulation from the software CODYRUN and the associated experimental validation will be submitted soon.

Conclusion

Generally, meteorological station in the Indian Ocean does not measure solar illuminance. So it is very difficult to study visual comfort in the building or reduce energy consumption from indoor electrical lighting.

The objective of this study is to give the possibility for the software CODYRUN to be able to simulate outdoor solar illuminance starting from the knowledge of the luminous efficacy and data of solar irradiance. This would make it possible to study visual comfort and energy consumption in the building.

Two parts are presented in this paper. On one hand, this work defines three typical day-types (overcast, clear and intermediate) and the method used to classify these days. Four indices (found in the scientific bibliography and used in sky conditions) for classification have been used to determine specific day-types (overcast, intermediate and clear). To conclude SR (Sky Ratio) index can be used to characterize typical days at Saint Pierre (Reunion Island).

On the other hand, average values for global and diffuse luminous efficacy were determined. Measurements of outdoor illuminance and solar irradiance data over six months have been analysed to establish constant average global and diffuse luminous efficacy at Saint-Pierre (Reunion Island). All climatic seasons are represented in this period. The average values of global and diffuse luminous efficacy for typical day conditions are 121,5 lm/W and 139,98 lm/W respectively.

These constants were introduced into the CODYRUN software in order to simulate outdoor daylighting. A comparison between the measured values at Saint-Pierre and simulated values, on the same site, showed that the software accurately predicted illuminance values.

It is intended to develop, in the future, analytical models of luminous efficacy (global and diffuse) for Reunion Island in order to compare the simulation results with other existing models.

A similar study for the characterization of day-types conditions will be applied to other regions including Indian Ocean Island (Mauritius, Seychelles, Madagascar, Comoros, etc) using locally available database.

Fig

  Fig. 1. Global view of the experimental platform

Fig

  Fig. 4. Global (Gh), diffuse (dh) and direct (Dh) fluctuations (irradiance) for three typical days

  beam normal terrestrial-irradiance (W.m -2 )   Z : The zenithal angle (rd)   G o : Extraterrestrial horizontal solar irradiance or solar constant (W.m -2 )    : Solar elevation or altitude angle (°) used to characterize day-types (overcast, clear and intermediate).

  classified in categories: overcast, intermediate overcast, intermediate mean, intermediate blue and clear. In our study, we have combined the three intermediate sky categories into a single category. This allows us to work with three day-types only, instead of five, and they are:

Fig. 9 .Fig. 10 .

 910 Fig. 9. Diffuse illuminance as a function of diffuse irradiance on the horizontal surface at Saint-Pierre

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Comparisons between measured and CODYRUN-simulated constant diffuse illuminance values atSaint-Pierre.

Fig. 13 .

 13 Fig. 13. An Internal view of LGI (test room)and indoor luxmeter

Figure 15

 15 Figure15shows two curves obtained at point A 3 on the ground for a given day in a dynamical behaviour of illuminance with hourly time step. The curve ('Measures.' curve) shows the measured values at point A 3 and the curve ('CODYRUN' curve) represents the simulated values in CODYRUN at this particular point, from global luminous efficacy model.

Fig. 15 .

 15 Fig. 15. Simulation (CODYRUN) / Measurement comparisons for indoor daylighting in LGI cell at pointA 3

. CM11 pyranometer specifications.

  Table. 1 And 2 show these errors values.

	Spectral range	305-2800 nm (50% points)
	Sensitivity	4-6 V/W/m 2
	Inpedance (nominal)	700-1500 
	Response time (95%)	15 sec.
	Non-linearity	<  0.6 % (<1000 W/m 2 )
	Operating temperature	-40°C to +80°C
	ISO-9060 Class	Secondary Standard
	Tab. 1Measuring range	0 -170 Klux
	Spectral sensitivity	360 -760 nm
	Dome	PMMA
	Cosine error	< 3 %
	Linearity	< 1 %
	Absolute error	< 10 %
	Directional error	<  10 W/m 2 (beam 1000 W/m 2 )
	Operating temperature	-20°C to +60°C

Temp. dependence of sensitivity <  1 % (-10 to +40 °C) Directional error <  10 W/m 2 (beam 1000 W/m 2 ) Tilt error None Zero-offset due to temp. changes <  2 W/m 2 at 5 K/h temp. change Tab. 2. FLA613VLM luxmeter specifications Fig. 3. Global illuminance sensor

  Figs. 9 and 10 show a linear relation between illuminance and irradiance, and consequently, the following simplified correlations of empirical average constant diffuse and global luminous efficacy for Saint-Pierre have been obtained by : Where K d is the empirical constant diffuse luminous efficacy, K g is the empirical constant global luminous efficacy, I d and I h are respectively the diffuse and global terrestrial-illuminance (in lux) on the horizontal surface. d h and G h are respectively the diffuse and global terrestrial-irradiance (in W.m -2 ).

		4.2. Simplified correlations of luminous efficacy for Saint-Pierre (a simple constant luminous efficacy in Reunion
		Island)
								(9)
		K d 	I d d h	 139.98 (lm/W)
		With: MPD= 0.41 %, RMS=6.95 %
		And,
								(10)
		K	g 	I	h		 121.5 (lm/W)
				G
					h
		With: MPD= 8.58 %, RMS=13.69 %
	
								(11)
					N		
					   i1 	   100	(12)
								N
		and
		RMS 	E      i1   N   	mod,i  E E meas,i meas,i		100  2   	   	(13)
						N	
					  	  
	

Acknowledgments

This research was supported by Région Réunion. Special thanks are extended to the Région Réunion for financial support of the experimental equipment.


H Boyer

F Miranville

D Bigot

S Guichard

I Ingar

A P Jean

A H Fakra

D Calogine

T Soubdhan

Heat Transfer in Buildings: Application to Solar Air Collector and Trombe Wall Design

Introduction

The aim of this paper is to briefly recall heat transfer modes and explain their integration within a software dedicated to building simulation (CODYRUN). Detailed elements of the validation of this software are presented and two applications are finally discussed. One concerns the modeling of a flat plate air collector and the second focuses on the modeling of Trombe solar walls. In each case, detailed modeling of heat transfer allows precise understanding of thermal and energetic behavior of the studied structures. Recent decades have seen a proliferation of tools for building thermal simulation. These applications cover a wide spectrum from very simplified steady state models to dynamic simulation ones, including computational fluid dynamics modules [START_REF] Clarke | Energy simulation in building design[END_REF]. These tools are widely available in design offices and engineering firms. They are often used for the design of HVAC systems and still subject to detailed research, particularly with respect to the integration of new fields (specific insulation materials, lighting, pollutants transport, etc.).

General overview of heat transfer and airflow modeling in CODYRUN software

Thermal modeling

This part is detailed in reference [START_REF] Boyer | Thermal building simulation and computer generation of nodal models[END_REF]. With the conventional assumptions of isothermal air volume zones, unidirectional heat conduction and linearized exchange coefficients, nodal analysis integrating the different heat transfer modes (conduction, convection and radiation) achieve to establish a model for each constitutive thermal zone of the building (one zone being a room of a group of rooms with same thermal behaviour). For heat conduction in walls, it results from electrical analogy that the nodal method leads to the setting up of an electrical network as shown in Fig. 1, the number of nodes depending on the number of layers and spatial discretization scheme : comes from the thermo-convective balance of the dry-bulb inside air temperature T ai , taking into account an air flow m $ through outside (T ae ) to inside. (4) represents the radiative equilibrium for the averaged radiative node temperature, T rm . The generic approach application implies a building grid-construction focus. Following the selective model application logic developed (Boyer, 1999), an iterative coupling process is implemented to manage multi-zone projects. From the first software edition, some new models were implemented. They are in relation with the radiosity method, radiative zone coupling (short wavelength, though window glass) or the diffuse-light reduction by close solar masks [START_REF] Lauret | A validation methodology aid for improving a thermal building model : how to account for diffuse radiation in a tropical climate[END_REF]. Another example of CODYRUN evolution capacity could be illustrated by a specific study using nodal reduction algorithms [START_REF] Berthomieu | Intégration de la réduction équilibrée à un code de simulation hygro-thermo-aéraulique de bâtiments[END_REF]. To resolve it, a new implementation was done: the system was modified into a canonic form (in state space).

From a user utilization point of view, this thermal module exit is mainly linked to the discretizated elements temperatures, the surfacic heat flows, zone specific comfort indices, energy needs, etc.

Airflow modeling

Thermal and airflow modules are coupled to each other thanks to an iterative process, the coupling variables being the air mass flows. It is useful to implement the inter zones flows with the help of a matrix m $ . The terms [, ] mi j $ then qualifies the mass transfer from the zone i to the zone j, as it is depicted .

Fig. 3. Interzonal airflow rates matrix

Then, a pressure model for calculating previous airflow rates is set and takes into account wind effect and thermal buoyancy. To date, the components are integrated ventilation vents, small openings governed by the equation of crack flow, as :

n m=CdS( P) $ (5)
S is aperture surface, Cd and n (typically 0.5-0.67) depends on airflow regime and type of openings and P Δ the pressure drop. Therefore, the following scheme can be applied for encountered cases.

Outdoor

Indoor Indoor Taking into account the inside air volume incompressibility hypothesis, the mass weight balance should be nil. Thus, in the established system, called pressure system, the unknowns are the reference pressure for each of the zones. Mechanical ventilation is simply taken into account through its known airflow values. In this way, ventilation inlets are not taken into detailed consideration which could have been the case owing to their flowpressure characteristics.

= =≠ = =≠ =- = ⎧ += ⎪ ⎪ ⎪ ⎪ += ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ += ⎪ ⎩ ∑ ∑ ∑ $$ $$ $$ iN i0 , i1 iN i0 , i2 iN1 i0 m( m ( 1 ) 0 m( m ( 2 ) 0 ... m( m ( N ) 0 vmc vmc vmc i,1) i,2) i,N) (6) k $ m( ) vmc
is the flow extracted from zone k (by vents) and N the total number of zones.

After the setting up of this non linear system, its resolution is performed using a variant of the Newton-Raphson (under relaxed method). This airflow model has recently been supplemented by a CO 2 propagation model in buildings [START_REF] Calogine | Identification of parameters in building concentration dispersion model[END_REF].

Humidity transfers

For decoupling reasons, zones dry temperatures, as well as inter zone airflows, have been previously calculated. At this calculation step, for a given building, each zone's specific humidity evolution depends on the matricial equation :

=+ $ .. hh h Cr Ar B (7)
According to Duforestel's model, an improvement of the hydric model (Lucas, 2003) was given by the use of a hygroscopic buffer. If we consider N as the number of zones, a linear system of dimension 2N is obtained and a finite difference scheme is used for numerical solution.

Some elements of CODYRUN validation

Inter model comparison

A large number of comparisons on specific cases were conducted with various softwares, whether CODYBA, TRNSYS for thermal part, with AIRNET, BUS, for airflow calculation or even CONTAM, ECOTECT and ESP. To verify the correct numerical implementation of models, we compared the simulation results of our software with those from other computer codes (Soubdhan, 1999). The benchmark for inter-comparison software is the BESTEST procedure (Judkoff, 1983), (Judkoff, 1995). This procedure has been developed within the framework of Annex 21 Task 12 of the Solar Heating and Cooling Program (SHC) by the International Energy Agency (IEA). This tests the software simulation of the thermal behavior of building by simulating various buildings whose complexity grows gradually and comparing the results with other simulation codes (ESP DOE2, SERI-RES, CLIM2000, TRNSYS, ...). The group's collective experience has shown that when a program showed major differences with the so-called reference programs, the underlying reason was a bug or a faulty algorithm.

IEA BESTEST cases

The procedure consists of a series of buildings carefully modeled, ranging progressively from stripped, in the worst case, to the more realistic. The results of numerical simulations, such as energy consumed over the year, annual minimum and maximum temperatures, peak power demand and some hourly data obtained from the referral programs, are a tolerance interval in which the software test should be. This procedure was developed using a number of numerical simulation programs for thermal building modeling, considered as the state of the art in this field in the US and Europe. After correction of certain parts of CODYRUN, an example output from this confrontation is the following concerns and energy needs for heating over a year, for which the results of our application are clearly appropriate.

Fig. 5. Exemple of BESTEST result

The procedure requires more than a hundred simulations and cases treated with CODYRUN showed results compatible with most referral programs, except for a few. We were thus allowed to reveal certain errors, such as the algorithm for calculating the transmittance of diffuse radiation associated with double glazing and another in the distribution of the incident radiation by the windows inside the envelope. As in the reference codes, two points are to remember: the majority of errors came from a poor implementation of the code and all the efficiency of the procedure BESTEST is rechecked, errors belonging to modules that have been used for years. The tests are designed for testing the capability of building energy simulation programs to predict the ventilation characteristics including wind effect, buoyancy and mechanical fan. CODYRUN passed all the test cases.

TN51 airflow case

In [START_REF] Orme | Applicable ventilation model for air infiltration and ventilation calculations[END_REF], a test case composed of a building with three storeys is described and first published in [START_REF] Tuomala | Combined air flow and thermal simulation of buildings[END_REF]. All boundary conditions are imposed (wind, external temperature) and indoor conditions are constant, i.e. in steady state. CODYRUN's results were added on the figure extracted from the paper [START_REF] Orme | Applicable ventilation model for air infiltration and ventilation calculations[END_REF].

Fig. 7. Intermodel airflow comparison

As it can be seen, in terms of numerical results, CODYRUN gives nearly the same values as the other codes, little differences being linked to numerical aspects as algorithms or convergence criteria used.

Experimental confrontation

As part of measurement campaigns on dedicated cells and real homes, a set of elements of models have been to face action (and for some improved), mostly concerning thermal and humidity aspects. Not limited to, some of these aspects are presented in the articles [START_REF] Lauret | A validation methodology aid for improving a thermal building model : how to account for diffuse radiation in a tropical climate[END_REF]) (Lucas, 2001) and (Mara, 2001), [START_REF] Mara | Parametric Sensitivity Analysis of a Test Cell Thermal Model Using Spectral Analysis[END_REF].

Two applications of the software 4.1 Air solar collector

An air solar collector is used to heat air from solar irradiation. More precisely, it allows to convert solar energy (electromagnetic form) into heat (Brownian motion). This type of system can be used to heat buildings or to preheat air for drying systems. Air solar collector is constituted by an absorber encapsulated into an isolated set-up (Fig. 8). To avoid heat loss by the incoming flux side, a glass is located above the absorber, letting a gap between them. This glass allowing to catch long wavelength emitted by the set-up when its temperature rises-up. Air temperature improvement is mostly done by air convection at the absorber interface. This heat is then carried by air in the building or in the drying system.

Fig. 8. Air solar collector principle, adapted from (Sfeir, 1984) The enclosure is not strictly speaking a building, but the generic nature of the software allows to study this device. This is a zone (within the captation area), a glazed windows, exterior walls and an inner wall of absorber on which it is possible to indicate that solar radiation is incident.

It should be noted that this is part of a class simulation exercise allowing students to learn collector physics basis.

Collector modeling and description of the study

It is assumed that before initial moment, there is no solar irradiation and the collector is at thermal equilibrium, i.e. outside air temperature is the set-up temperature. At t=0, an irradiation flux Dh is applied without interactions with the outside air temperature. In a simplified approach, a theoretical study is easily obtained. Some equations below are used to understand the functioning of the collector. In steady state, the incoming irradiation flux reaching the absorber is fully converted and transmitted to the air (assumed to uniform temperature):

ai as as 0 h p ai ae as ai ae dT C V = D -K S(T -T )-mC (T -T ) dt τ $ (8)
Where K p is the thermal conductance (W.m -2 .K -1 ) of each wall through which losses can pass, m dot is a constant air mass flow through the collector, T ai is the inside air temperature, T ae is the outside air temperature, and as (1.2 kg.m -3 ) and C as (1000 J.kg -1 .K -1 ) are respectively the air thermal conductivity and density. By knowing initial conditions (at t=0, T ai =T ae ), the solution of equation ( 8) appears:

( )

V C K t h ae ai as as e K D T t T ρ τ / 0 1 ) ( - - + = (9)
The power delivered by the collector is given by ua s a i a e

P= m C ( T -T ) $

(10)

The studied collector is horizontal, the irradiated face has a surface of 1m², and an air gap thickness of 0.1m. The meteorological file is constituted of a constant outside air temperature (25°C) and a constant direct horizontal solar irradiation of 500W (between 6 am and 7 pm). It is assumed (and further verified) that the steady state is reached at the end of the day.

Concerning the building description file, the collector is composed by 1 zone, 3 boundaries (1 for the upper face, 1 for the lower face, and 1 for all lateral faces), and 4 components (glass, lateral walls, lower wall and absorber). Walls are made -from inside to outside -of wood (1cm), polystyrene (5cm) and wood (1cm). Wood walls have a short wave absorptivity of = 0.3. The glass type is a single layer ( 0 τ = 0.85), and the absorber is a metallic black sheet of 2mm ( = 0.95). The solar irradiation absorption model of the collector is a specific one. This has to be chosen in CODYRUN, because traditionally in buildings the solar irradiation doesn't impact directly an internal wall (absorber), but the floor. Even if this solar air heater is considered as a very simple one, the following figure gives some details about heat exchanges in the captation area.

Simulation results in the case of forced convection in air gaps

An air flow of 1 m 3 .h -1 is set. After running simulations, the following graph is obtained for two identical days : Fig. 10. Evolution of air temperature at the output of the solar collector with forced convection (1m 3 .h -1 ).

Simulation results are consistent with simplified study, but not exactly identical. In fact, CODYRUN model is more precise than those use in eq. 8: thermal inertia of walls are taken into account, superficial exchanges are detailed, exchange coefficients are depending on inclination, glass transmittance is depending on solar incidence, … With a low air flow rate of 1 m 3 .h -1 , the collector output power is about 22W and its efficiency about 4.5%. A solution to improve efficiency is to increase air flow rate (see Fig. 11), in link with the fact that conductive thermal losses are decreasing when internal temperature is decreasing. Increase of flow rate leads to a lower air output temperature (and also to change convection exchange coefficients). In some cases like some drying systems where a minimal air output temperature should be needed, this can be problematic. In these cases, CODYRUN can help to choose the best compromise between air output temperature and collector power or efficiency. Many other simulations could be conducted, in particular in the case of natural convection. Some of these cases could be applied to air pre-heating in case of passive building design, as for next application.

Trombe wall modeling 4.2.1 Trombe-Michel wall presentation

A Trombe-Michel wall (often called Trombe wall), is a passive heating system invented and patented (in 1881) by Edward Morse. It takes its name from two French people who popularized it in 1964, one engineer and one architect, respectively Félix Trombe and Jacques Michel. A Trombe-Michel wall allows to store solar energy and distribute heat following simple physical principles. This system is composed of a vertical wall, submitted to the sunshine, which absorb and store the radiative energy as thermal energy by inertia. To improve its absorptivity, the wall can be paint in a dark color. Stored energy rises-up the wall temperature, inducing some heat transfer such as conduction (into the wall from outdoor to indoor side), radiation and convection (both with in/outdoor). To avoid outdoor losses, a glazing, which is not transmissive to ultraviolet and far infrared, is located few centimeters in front of the wall (outdoor side). So the glazing reduces outside losses by convection and traps wall's radiation due to its temperature (far infrared emission) into the building. But it also slightly reduces the solar incoming flux, because some of it is reflected or absorbed. Nota: Considering the glazing, the sunshine insulation (etc.), it is not easy to choose the optimal set-up configuration; this kind of situations are typical cases where CODYRUN simulations allow to find out. Heat transfer through the wall is done by conduction. According to the wall size and its composition, a thermal delay appears between heat absorption and emission. This characteristic allows to configure specifically the system in function of the needs. Considering the thermal delay, conductive transfer-mode is convenient to heat by night, but not by day. To palliate this lack, a faster transfer mode is brought by a variant of the Trombe-Michel wall, called recycling wall (Fig. 12). The recycling wall is obtained by holes addition at the top and the bottom of the wall. This variant allows to get a natural air flow, transferring energy by sensitive enthalpy between the system side of the wall (also called Trombe side) and the room. Indeed, as long as the glass is far enough of the wall, the temperature difference between them induces some air-convective movement, initiating the global air-circulation, so allowing heat distribution. [START_REF] Sfeir | Ingénierie des systèmes solaires, application à l'habitat[END_REF] Several variants of the Trombe-Michel wall can be used. These one usually evolve in function of the climatic need and can, for example, be defined by: the holes size and presence (or not), the characteristics of the storage wall (e.g. thickness, density, presence of fluid circulation or phase change materials, etc. ) or the glazing type (e.g. simple or double, treated surface, noble gas, etc.). Some technical indications about these considerations are given by Mazria (Mazria, 1975). Though two levels experimental design, [START_REF] Zalewski | Experimental thermal study of a solar wall composite type[END_REF] shows that external glazing emissivity, window type and wall absorptivity mainly characterize the system. Trombe-Michel system (and its variants) inspired numerous publications about temperate climate and proved their efficiency as passive heating system. By extension, there is also a lot of studies about similar system, as solar chimney [START_REF] Ong | A mathematical model of a solar chimney[END_REF], [START_REF] Awbi | Ventilation of buildings[END_REF].

There are several values usually used to describe Trombe-Michel wall functioning:

•

Transmitted energy through the wall by conduction,

•

Transmitted energy through the holes by sensitive enthalpy,

•

The system efficiency, defined as the rate between the energy received into the room over the total energy received by the North wall (South hemisphere) in the meantime.

•

The FGS (solar benefits fraction), defined as the rate between the benefits from the Trombe-Michel system and the energy needed by the room without it, for a room temperature of 22°C. Nota: Even if the FGS refers to active heating systems, it allows to compare easily passive heating systems between them and to other installations.

Presentation of Trombe-Michel wall simulations under CODYRUN

This numerical study is resolved by software simulations. The case study case presented here takes place in Antananarivo, Madagascar (Indian Ocean). The aim of the simulations conducted was to help this developing country to face low temperatures in classrooms during winter season. The word 'zone', used previously, is understood as CODYRUN vocable, correspond usually to one room. Into the actual description, isothermal air assumption is made into the capitation area. This consideration is taken as first approximation and can be possibly modified later to improve the model (e.g. replaced by linear gradient hypothesis, etc.). According to the bibliography, one of the main issues mentioned is about the convection coefficient into the Trombe side of the wall. Because of the system successively laminar and turbulent, convection correlation such as -Nu = f(Gr) -cannot be used. In this case, [START_REF] Zalewski | Experimental thermal study of a solar wall composite type[END_REF] says that the laminar coefficient evolve between 2 and 2.3 W.m -2 .K -1 and the turbulent one evolve between 2.25 and 3.75 W.m -2 .K -1 . So, in a first approach, we approximate the temperature-evolving value of the convection coefficient as the average of the turbulent and laminar values (2.9 W.m -2 .K -1 ). Considering thermo-circulation, the CODYRUN's airflow module allows to calculate air flows through wall's holes. This consideration and the case study description, the two areas (the Trombe system and the room) are studied coupled, which is a right physical representation of the reality. Results validity are certified by the fact that each module of CODYRUN, and their combinations, has been validated by comparison with experimental results, reference codes and BESTEST procedures. This multi-model code structure [START_REF] Boyer | Thermal building simulation and computer generation of nodal models[END_REF]) can be efficiently exploited by studies such as this one, where it is necessary to choose the convection coefficients by area or by wall, to mesh slightly the walls to calculate precisely the conductive fluxes, to choose a solar gains repartition model or equivalent sky temperature, etc. CODYRUN also creates numerous output simulation variables, in addition to the one related to the dry temperature area, such as sensible power outputs from mass exchange through wall holes, conductive fluxes through the wall, enthalpic zone balance and the PMV (Predictive Mean Vote, according to Gagge) of interior zone to quantify comfort conditions. It is also possible to explore the conductive flux through the Trombe-Michel wall glass. Simulation results are presented with meteorological data of Antananarivo coming from TRNSYS 16.0 software and its TMY2 documentation data file. According to this one, daily sunshine insulation annual average is about 5.5 kWh.m -2 . The one on the North and East walls are respectively 2.23 and 2.67 kWh.m -2 . Modified in function of the current albedo (0.3), the previous values become 3 and 3.46 kWh.m -2 . The simulated building represents a residence unit based on a geometric cell description (9 m² parallelepiped square base ground). Moreover, materials, thermo-physics characteristics and wall type are typical from Madagascar. The room is supposed to be constantly occupied by two persons and have a usual profile for intern lighting. This area is supposed to exchange air with the outside at a rate of 1 volume per hour. Finally, the system area is of 2 m 2 and is located on the North wall (South hemisphere).

Simulation

Passive heating oriented-simulations are made the first day of July (Julian calender days 181 and following). In a first time, the objective is to explain the set-up functioning. So, some hourly based analyses will be conducted. Finally, the last experiment will compare the same Trombe-Michel wall with and without the recycling variant.

Inverse thermo-circulation evidence

By night, over some system specific conditions (open holes) and in function of previous day insulations (e.g. low insulation), the flow evolution can sometime be the symmetric of the one by day (Fig. 13). In this configuration, the system functioning is reversed, cooling the room instead of heating it. Between points 19 and 32 (i.e. 7 pm to 8 am next day), the Trombe-area temperature is lower than the room temperature, inducing the inverse thermocirculation. This physical process can be illustrated by the negative part of the sensitive aeraulic benefits for the inside area. Even if the flux values by night are low, it is important to note the following point : the curves are obtained by assuming a sky temperature equal to the outside air temperature. This assumption reduces the impact of the system/sky radiation transfer, so involves an error. This error could be reduced by taking a sky temperature value more realistic, so by considering the night-sky wide wavelength emission and the high glass emissivity (0.9). A better approximation can be done by a sky temperature model such as T sky =T ae -K, where K=6.

Night hole closing system

Hole closing system strategy deserve a specific comment. This one can be done nicely from flow measurement, but a simpler and passive way to do it also exists. This one consists in a plastic foil, only attached on one side and occulting the holes preventing from inverse thermo-circulation. Into CODYRUN, the closure system is designed by the "little opening" component added to a hourly profile (i.e. 24 opening percentages), where the hole is closed by night and opened by day. However, the thermo-circulation (by system inertia) continues during the two first hours of the evening, so the profile includes this pattern too. Because of the small gap with the previous curves (Fig. 13), the results are firstly surprising. An explanation can be done by the small thermal gradient during the considered night. According to Mazria (Mazria, 1975) and Bansal [START_REF] Bansal | Passive Building design. A handbook of natural climatic control[END_REF], recycling variant are only useful into cold climates (winter averages: -1 °C to -7 °C). So, simulation results show the minor impact of the hole control in this study case. In other words, it seems that the mass flow have a very low sensibility to the opening state. This hypothesis is rejoined by another author [START_REF] Zalewski | Experimental thermal study of a solar wall composite type[END_REF] who have substantively the same conclusion for a North France located case.

Global Trombe wall functioning

To obtain the full power delivered by the wall, airflow and conductive heat transfer have to be summed. By night, it appears a constantly positive heat flux inducing a rise-up of the room temperature (Fig. 14). In the morning (e.g. 9am first day), the global flux becomes negative. A full curve interpretation is approached by airflow and conductive heat flux analyze through the wall (right part of Fig. 14). Early morning, the global heat flux inversion can be explained by highly negative conductive heat flux resulting certainly from the heat flux night inversion (around 9 to 14, so a delay of 4 hours). Drawn curves of the incoming heat flux through the wall confirm this hypothesis. As foreseeable (without simulation tools), the curves show the alternate functioning of the conductive and sensible airflow input power (the wall characteristics setting the shifting period). By night, the conductive heat flux through the wall rises-up the room temperature, whereas by day this action is done by the heat flux associated to air displacement, physically expressed by the natural air movement which is a priori synchronous with the sunlight distribution profile. The previous report allows to ask about the holes necessity. In fact, even if there is no heat transfer improvement, the main interest comes from the heat distribution and its timeevolving modulation into the building. To increase the room input power (i.e. the global heat flux), it could be simple to rise-up the wall surface and/or to add some reflectors to raise the incoming sunlight intensity.

However, in every cases the system have to be simulated for summer conditions. In order to reduce the external loss (illustrated by negative heat fluxes), a double glazing could be used, even if it reduces the incoming sunlight intensity (transmission loss). For reference, double glazing can be easily made from simple glazing. Another solution consists in isolating the indoor side of the wall.

Trombe-Michel wall and recycling variant comparison

The comparison, in the meantime, of the wall's holes presence (or not), expresses a gap between the global heat fluxes. The values corresponding to the recycling variant are shifted to the left compared to the classic Trombe-Michel wall (Fig. 15). The input power delivered with the holes is slightly superior, which confirms the hypothesis of low impact on section 4.2.3.2. A piece of explanation (checkable by simulation) can be given by the thermal gradient between the room and the Trombe system, the decrease of this one reducing the conductive transfer through the glazing. Predicted Mean Votes (PMV) curves (of the right of Fig. 15) express the comfort sensation which evolve between -3 and +3. By comparison, it can be affirmed that the holes improve the comfort sensation. This improvement is related to the previous comment (about the superior input power amount which led to a rise-up of the dry temperature), and to the higher indoor side wall temperatures.

Trombe wall simulation exercise conclusion

This example of CODYRUN use allows to find some interesting results about Trombe-Michel wall configurations for the specific location of Antananarivo. Results such as the interest of the recycling variant (which is almost not influenced by hole closing procedure), the time-repartition (and impact) of the airflow and conductive heat flow on the room temperature, (etc.) have been found. Considering the case study, much more informations could be deduced from other well designed simulations. The considerable amount of knowledge found was only deduced from simulations, so only following a numerical approach. From this consideration and the results precision, a good estimation about CODYRUN quality and level of development can be done.

Conclusion

This paper describes the models, validation elements and two applications of a general software simulation of building envelopes, CODYRUN. Many studies and applications have been conducted using this code and illustrate the benefits of this specific development.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Example of associated electrical network associated to wall conduction

Fig. 4 .

 4 Fig. 4. Exterior and interior small openings

  Concerning airflow validation, IEA multizone airflow test cases describe several theoretical and comparative test cases for the airflow including multizone cases. It was developed within the International Energy Agency (IEA) programs: Solar Heating and Cooling (SHC) Task 34 and Energy Conservation in Building and Community Systems (ECBCS) Annex 43.

Fig. 6 .

 6 Fig. 6. TN 51 Test case Next figure shows solution of 3 references codes, i.e. COMIS, CONTAM93 and BREEZE. CODYRUN's results were added on the figure extracted from the paper[START_REF] Orme | Applicable ventilation model for air infiltration and ventilation calculations[END_REF].

Fig. 9 .

 9 Fig. 9. Solar irradiation absorption process.

Fig. 11 .

 11 Fig. 11. Evolution of collector outputs regarding air flow rate.

  Fig. 12. Trombe-Michell recycling wall set-up[START_REF] Sfeir | Ingénierie des systèmes solaires, application à l'habitat[END_REF]

Fig. 13 .

 13 Fig. 13. Dry temperatures and sensible power balance through holes.

Fig. 14 .

 14 Fig. 14. Global and specific fluxes induced by the Trombe wall into the room.

Fig. 15 .

 15 Fig. 15. Input power and PMV comparisons

Conducted and sustained for over fifteen years, the specific developments made around CODYRUN led our team to be owner of a building simulation environment and develop connex themes such as validation or application to large scale in building architectural requirements. This evolving environment has enabled us to drive developments in methodological areas (Mara, 2001) (modal reduction, sensitivity analysis, coupling with genetic algorithms (Lauret, 2005), neural networks, meta models,...) or related to technological aspects (solar masks, integration of split-system, taking into account the radiant barriers products, ...). This approach allows a detailed understanding of the physical phenomena involved, the use of this application in teaching and capitalization within a work tool of a research team. Accompanied by the growth of computer capabilities, the subject of high environmental quality in buildings, our field becomes more complex by the integration of aspects other than those originally associated with the thermal aspects (environmental quality, including lighting, pollutants, acoustics, ...). Simultaneously, it is also essential to achieve a better efficiency in the transfer of knowledge and operational tools.


Olivier Glück
email: olivier.gluck@ens-lyon.fr

Jean-Christophe Mignot
email: jean-christophe.mignot@ens-lyon.fr

Splitting TCP for MPI applications executed on grids

In this paper, we first study the interaction between MPI applications and TCP on grids. Then, we propose MPI5000, a transparent applicative layer between MPI and TCP, using proxies to improve the execution of MPI applications on grids. Proxies aim at splitting TCP connections in order to detect losses faster and avoid to return in a slowstart phase after an idle time. Finally, we evaluate our layer executing the NAS Parallel Benchmarks on Grid'5000, the French research grid. The results show that our architecture reduces the number of idle timeout and of long-distance retransmissions for BT, SP and LU benchmarks. Using MPI5000, these applications can decrease their execution time by 35%, 28%, and, 15% respectively. A comparison with MPICH-G2 performances shows that our layer can even outperform a grid enabled MPI implementation.

Introduction

This paper deals with the execution of parallel applications on grid platforms. Many parallel applications are written with the Message Passing Interface (MPI) library. MPI [START_REF]MPI standard[END_REF] is a standard that defines communication primitives for parallel applications. It includes both point to point (MPI Send, MPI Recv...) and collective communication functions (like MPI Gather, MPI Alltoall...). While applications are well executed on clusters, as they are more and more resource-consuming, they need to be efficiently executed on grids.

Grids are a pool of computing resources like nodes or data servers connected together. But from the MPI point of view, they should be seen as an interconnection of clusters by a wide area network (WAN). As this WAN is shared by all grid users, applications must take care of concurrent traffic and fairly share the network. This is usually achieved thanks to TCP. The WAN bandwidth is usually much smaller than required to prevent congestion if all the nodes of one site send data to another site. It is consequently a bottleneck for the application. Moreover, the WAN la-tency is high and thus, costly. When using TCP, the time to detect a loss or repair it depends on the Round Trip Time (RTT) and is much more costly on a WAN than on a LAN.

To take these problems into account, we put forward MPI5000, a communication layer between the application (MPI for example) and TCP that can be used automatically and transparently. The idea is to introduce proxies at the LAN/WAN interface in order to: [START_REF]MPI standard[END_REF] Give the application the knowledge that the grid is an interconnection of clusters.

(2) Implement the TCP split: each end-to-end TCP connection (LAN-WAN-LAN) is replaced by 3 connections: LAN-LAN, WAN-WAN, LAN-LAN. (3) Take decisions and implement optimizations on proxies: bandwidth reservation between proxies, communication scheduling, parallel longdistance connections, use of a modified TCP.

This paper studies the advantages of TCP splitting for MPI applications executed on a grid and presents our architecture. It is organized as follows. Section 2 explains which problems are raised by using TCP for MPI communications on long-distance links. Then, Section 3 introduces the advantages of our approach and some implementation details. Section 4 presents the evaluation of MPI5000 on the french research grid, Grid'5000 [START_REF] Bolze | Grid'5000: a large scale and highly reconfigurable experimental Grid testbed[END_REF]. Section 5 discusses related works. Finally, we conclude and give some future researches we will work on in Section 6.

Interactions between Grids, MPI, and TCP

MPI applications alternate communication and computation phases. When a computation phase is finished, the application waits for new data to compute. MPI applications communicate with small to medium message size (usually less than 1 MB) and generate a bursty traffic [START_REF] Roy | MPICH-GQ: quality-of-service for message passing programs[END_REF]. These bursts are likely to fill the network equipment queues and generate losses and retransmissions. It ultimately increases the application completion time as the execution flow is usually waiting for the next message to continue its execution.

As explained in introduction, in grids, losses and retransmissions at TCP level are even more costly due to the high latency, the sharing of the WAN, and the bottleneck at the 1 WAN/LAN interface. Most losses occur while communicating on the WAN. Since the RTO timeout and the reception of DupACKs depends on the RTT, a loss on the WAN takes a longer time to be detected than on a LAN.

Moreover, the TCP congestion window limits the amount of data that can be sent at the same time. If the congestion window is not large enough, an MPI message can not be sent in one time but have to wait for ACKs to make this window increase and finish its sends. Due to the RTT, it is costly on high latency links. Moreover, as slowstart is activated again after an idle time, if an MPI application computes longer than the idle timeout, it will suffer from the reactivation of the slowstart mechanism. Thus, TCP congestion control is very costly for MPI applications executed on grids because an idle time may often occur and then highly increases the transfer time of MPI messages.

Thus, there are two kinds of problems: (1) due to a high latency on the grid, the application waits a longer time for DupACKs and for the TCP congestion window increase; (2) due to MPI application communication profile, there might be many RTO timeouts and many idle times. Table 1 shows some clue on these problems. It presents the number of DupAcks, RTOs and Idle timeouts that occur on long-distance connections while executing BT, FT and LU from the NAS Parallel Benchmarks [START_REF] Bailey | The NAS Parallel Benchmarks[END_REF] (NAS or NPB) suite. The experiments are performed on Grid'5000. The figures were obtained with Web100, as described in section 4.1. DupAcks and RTOs occur only with FT while the three applications are impacted by idle timeouts.

In order to solve some of these problems, we put forward in the next section an architecture based on LAN/WAN proxies that enables to split TCP connections, and thus to reduce the number of idle timeouts, and to faster detect losses and reduce their number.

MPI5000 layer

In order to control and improve MPI communications on grids, we propose MPI5000, a transparent layer to execute MPI applications on grids using proxies. It can be used with any MPI implementation by loading the MPI5000 library (i.e., set the environment LD PRELOAD variable) and launching the MPI5000 daemons (i.e., proxies). connections without MPI5000 while the plain green lines represent the MPI5000 connections. Thus, with MPI5000, each LAN-WAN-LAN connection is replaced by three connections: LAN-LAN, WAN-WAN, and LAN-LAN. N s,n is the node n of site s. P s,n,p is the process p executed on node n of site s. G s is the proxy of site s. Each process is connected to the proxy of its site and proxies are connected together. Proxies enable both a faster reaction in case of congestion and a transformation of MPI's bursty traffic into longer flows on long-distance links. Indeed, the WAN-WAN MPI5000 connection aggregates the traffic coming from all the processes of the same site. Thus, MPI5000 eliminates some RTO timeouts on longdistance and local links. It also retransmits DupACKs faster. Therefore, it reduces the TCP waiting time of MPI applications and improve their global performances. Our architecture also has an impact on the congestion window. Indeed, proxies help to keep the congestion window on the WAN connection closer to the real available bandwidth because they transmit more data than a single process and thus probe the network more regularly. If an application has computation phases on one process longer than the idle timeout but all processes do not communicate synchronously, the proxies avoid to go back in slowstart phase because other processes keep the congestion window widely opened.

MPI5000 overview

MPI5000 implementation

MPI5000 is based on two components (see Figure 2): a library linked to the application on nodes and a daemon program executed on proxies. The dashed red lines represent the data path from one node to another one without MPI5000 while the plain green lines represent it with MPI5000.

In order to route messages between nodes and proxies, MPI5000 adds a header to the MPI message as shown on Figure 3. The header contains a flag that identifies the message type (data or connection), the destination's id, the size of the MPI message and the source's id. An id is described using three numbers (see P s,n,p examples on Figure 1): the site's number (s or x), the node's number (n or y) and the process's number on the node (p or z).

The two components of MPI5000 are now briefly described. The first one, the MPI5000 library, is linked to the application through the mpirun command line (for example -env LD PRELOAD in mpich). Our library intercepts functions of socket API (bind, accept, connect, write/v, read/v, close) -in other words, we force the MPI program to call our library's functions instead of libc's -and adapt them to MPI5000's architecture. With this mechanism, it is possible to use our layer with any MPI implementation. When a bind() is called, the library connects the node to the proxy. When a connect() is intercepted, the library creates a MPI5000 message with the connection flag set and sends it to the proxy. When an accept() is called, it just waits for the matching connect(). The second component of MPI5000 is composed of the proxies. The proxies just wait for data and forward it to either another proxy or to local destination node, using the information included in the header. If the connection flag is set, the proxy establishes the connection to the matching node in order to free the pending accept(). Once this is done, this connection is closed and only the connection to the proxy remains.

Experimental evaluations

This section evaluates the architecture described in the previous section and is based on the elements discussed in Section 2. First, we present our experimental testbed. Then, a simple pingpong application is executed with MPI5000 in order to evaluate the raw proxy overhead. Finally, we evaluate MPI5000 performances when executing the NAS Parallel Benchmarks.

Experimental testbed

Our experiments are conducted on Grid'5000 [START_REF] Bolze | Grid'5000: a large scale and highly reconfigurable experimental Grid testbed[END_REF], which connects nine sites in France, with a RTT between 5ms to 21ms. Sites are connected by a dedicated WAN operated by RENATER at 1 or 10 Gbps. This architecture provides researchers a full reconfigurability feature to dynamically deploy and configure any OS on any host. This feature allows them to have administrator rights, to change TCP parameters for instance. Figure 4 shows our experimental testbed.

Proxies impact on a simple pingpong

In this section, we measure the overhead of MPI5000 executing a simple MPI pingpong. With MPI5000, the latency is increased by 141 µs (+1.5%) for 1 Byte messages. This time mainly includes the crossing of two MPI5000 proxies, one on each site. One proxy overhead (see Figure 1 and 2) is the sum of one extra LAN RTT (between the local switch and the proxy node) and the crossing time of proxy communication layers including four extra copies on the proxy (from the network interface card to the TCP buffer, from the TCP buffer to the MPI5000 daemon buffer and the same backwards). Bandwidth is decreased about 7% from 840 Mbps to 785 Mbps for 33 MB messages. Indeed, a higher message size increases the time to do extra copies.

Nas Parallel Benchmark performances

In this section, we execute the Nas Parallel Benchmarks (NPB [START_REF] Bailey | The NAS Parallel Benchmarks[END_REF]) to evaluate the MPI5000 performance using a panel of real applications. First, we present the NAS benchmarks and their communication features. Then, we give the completion time of each benchmark without and with MPI5000 and comment our results. We present further experiments showing that MPI5000 can improve application performances by decreasing the number of idle timeouts and losses on the long-distance link. Last, we compare our results with those of MPICH-G2, a well-known Gridenabled MPI implementation.

NPB communication features

The NPB are a set of eight programs (BT, CG, EP, FT, IS, LU, MG and SP) that have been designed to compare performances of supercomputers but are now also used to compare MPI implementations. The NPB give a good panel of the different parallel applications that could be executed on a cluster or a grid. We run each NPB three times and take the mean execution time. In order to understand the following experimental results, Table 3 presents a classification of NPB with regards to three communication metrics: the communication frequency is the mean time between two communication phases; the communication size is the average size of application messages; the burstiness indicates whether all the application processes send data synchronously or create bursty traffic (for instance, collective operations create bursty traffic) and has an impact on the congestion. LU sends small messages asynchronously but very often. CG and MG communicate very often with medium message size in a burstiness way. BT and SP communicate quite often with medium message size but not in a burstiness way. Lastly, FT and IS do not communicate often but in a very burstiness way with big messages.

NPB completion time results

Figure 5 shows the NPB completion time results with MPICH2, MPICH2 with MPI5000 and MPICH-G2. All the results are relative to MPICH2 results.

FT and IS show very bad performances with our layer. As mentioned in the previous section, FT and IS use big size collective operations. Thus, each time a collective operation is called, the MPI5000 proxies become a bottleneck and the copy overhead is too important compared to the expected gain (see Section 3) of our architecture. To strengthen our idea, we run a simple MPI Alltoall of 2 MB on 16 nodes without and with MPI5000. The completion time with MPI5000 is 2.74 higher than the one without MPI5000 which is similar to the result observed for FT on Figure 5 (2.86). The same conclusion could be done for IS, except that message sizes are smaller, and so is the overhead. The results obtained for LU and MG show that completion times with MPI5000 is a little higher than without MPI5000. We explain why in the next two sections. Finally, the BT, CG and SP results show that MPI5000 decreases their completion time and so is a valid solution to improve performances of some MPI applications executed on grids.

To conclude this section, firstly not all applications can benefit from MPI5000 but some of them really improve their execution time thanks to our proposition and secondly our MPI5000 proxies have to be optimized, which is not yet the case actually, in order to reduce their overhead.

MPI5000 benefits on idle timeouts

Table 4 shows the number of time the congestion window size is decreased without loss signal i.e., the number of idle timeouts we have measured with and without MPI5000 during the NPB execution. These figures are obtained thanks to the Web100 patch. The figures for MPICH2 without MPI5000 are a mean on all long-distance connections while for MPICH2 with MPI5000 they are taken on the proxy long-distance connection. As expected, all NAS show a smaller number of idle timeouts with MPI5000.

In order to confirm these results, we disabled the slowstart after idle TCP feature (an option in linux). The results are shown in Table 5. CG, LU and MG show a similar completion time with or without the slowstart after idle. Thus, reducing the number of idle timeouts can not improve their performances. These results confirm our classification pre- sented in Table 3 because CG, MG and LU often communicate. For BT and SP, disabling slowstart after idle improves completion time. These results confirm that MPI5000 reduces the number of idle timeouts and then improves the execution time of benchmarks which suffer from them.

MPI5000 benefits on RTO and DupACK

The previous experiments do not explain the impact of MPI5000 on CG, LU and MG. Moreover, the Web100 results on these NPB show that there is no loss signal (neither duplicate ACK or RTO). Thus, the expected advantages of MPI5000 -that are to detect and repair losses faster, to reduce number of idle timeouts, to keep the congestion window closer to the available bandwidth -can not improve performances of CG, LU and MG in our previous experiments because neither idle timeouts nor losses appear.

In order to see what MPI5000 can improve under congestion conditions, we add cross-traffic, carried out with two iperf TCP flows at 1 Gbps on four extra nodes.

Figure 6 shows that BT, LU, and, SP benefit from MPI5000 in case of cross-traffic. However, CG decreases its performance compared to the case without cross traffic. This is probably due to a congestion window that do not increase fast enough but further investigation is needed on this point.

Table 6 shows the number of congestion signals without and with MPI5000 in case of cross-traffic. In the MPI5000's case, local refers to connections from one node to one proxy and distant refers to the connection between the proxies. As expected, the results show that MPI5000 deletes a lot of long distance RTO and DupACKs. However, despite of the cross-traffic, the number of losses measured on MG is not high enough to overlap the proxy overhead. But, its relative completion time is reduced compared to the case without cross-traffic. SP is also even better in this case than without cross-traffic and shows an improving completion time by 35% thanks to MPI5000.

Comparison with a Grid-enabled MPI implementation

Both Figure 5 is valid for MPI application executions on the grid and that MPI5000 is a complementary solution to grid-enabled MPI implementations. In future works, we should execute MPICH-G2 or GridMPI with MPI5000 to emphasize that MPICH-G2 or GridMPI on one side and MPI5000 on the other side do not address the same problems and are complementary.

Related works

Many MPI implementations are available for the grid like MPICH2 [START_REF] Gropp | MPICH2: A New Start for MPI Implementations[END_REF], OpenMPI [START_REF] Gabriel | Open MPI: Goals, Concept, and Design of a Next Generation MPI Implementation[END_REF], GridMPI [START_REF]GridMPI Project[END_REF] or MPICH-G2 [START_REF] Karonis | MPICH-G2: A Grid-Enabled Implementation of the Message Passing Interface[END_REF]. Some of them need tuning to be efficiently executed with TCP in a grid [START_REF] Hablot | Comparison and tuning of MPI implementations in a grid context[END_REF]. Splitting TCP connections [START_REF] Kopparty | Split TCP for mobile ad hoc networks[END_REF] has already been done in wireless or satellite networks but never in wire grid networks. We show in this paper that it is also useful for wired connections, mostly in the context of MPI application traffic features and with RTT values less than satellite's ones. Several past propositions [START_REF] Takano | High Performance Relay Mechanism for MPI Communication Libraries Run on Multiple Private IP Address Clusters[END_REF] [12] [START_REF] Gabriel | Implementing MPI with optimized algorithms for metacomputing[END_REF] introduce proxies at the LAN/WAN interfaces to improve performance but the detailed propositions, the proxy level or usage are different from us. Even if we focalized on MPI applications, our proposition is not specific to MPI applications because it is at the socket level and thus, it would apply to any grid application executed above TCP.

Conclusion

The execution of MPI applications on grids faces new problems. We first show in this paper how MPI deals with TCP on grids. We conclude that (1) a high latency on the grid makes the application wait a longer time for DupACKs and for the TCP congestion window increase, (2) many RTO timeouts and idle times occur due to MPI application communication pattern. To take these problems into account, we propose MPI5000, a transparent layer that alleviates TCP's drawbacks by adding proxies at the LAN/WAN interfaces. It better manages the long-distance traffic and connections by splitting each LAN-WAN-LAN TCP connection in three distinct connections: LAN-LAN, WAN-WAN and LAN-LAN. Our proposition allows one to detect losses faster by avoiding RTO timeouts. MPI5000 also helps to avoid the slowstart phase after an idle time (time without communication on a link).

Finally, we evaluate MPI5000 on the french research grid, Grid'5000. Not all applications can benefit from MPI5000 but some of them really improve their execution time. Our evaluations confirm that MPI5000 effectively decreases the number of long-distance DupACKs and RTOs, the number of idle timeouts and thus the application execution time. The comparison with MPICH-G2 proves that MPI5000 can outperform a grid enabled MPI implementation. In conclusion, splitting TCP connections is a valid approach to better execute MPI applications on grids and MPI5000 can improve application performances.

In future works, we will reduce the MPI5000 proxy overhead by implementing a kernel version of the proxies to avoid two extra copies in user space. We should also study the scalability of proxy processes. Finally, we will implement and evaluate further optimizations now available thanks to MPI5000: bandwidth reservation between proxies, communication scheduling, parallel long-distance connections, use of an optimized/modified TCP protocol on the WAN.

Figure 1 Figure 1 .

 11 Figure 1 illustrates how MPI5000 splits the TCP connections. The dashed red lines on the figure represent the

Figure 2 Figure 3 .

 23 Figure 2. MPI5000 architecture.

Figure 4 .

 4 Figure 4. Experimental testbed.

Figure 5 .

 5 Figure 5. Relative completion time of NPB normalized to MPICH2.

Figure 6 .

 6 Figure 6. Relative completion time of NPB normalized to MPICH2 with cross-traffic.

Table 1 . Number of DupACKs, RTOs, and Idle timeouts while executing some NPB on grids.

 1

	Application DupACK RTO Idle timeout
	BT	1	0	5668
	FT	275	20	905
	LU	1	0	760

Table 2 . NPB communication features on the long-distance link.

 2

		Communication Amount Number/size
		type	of data	of long-distance writes
	BT	Point to Point	2.8 GB	9648 writes of 26 kB + 16112 writes of 160 kB
	CG	Point to Point	2.37 GB 15800 writes of 150 KB
	FT	Collective	5.9 GB	600 writes<200 B + 2816 writes>2 MB
	IS	Collective	0.74 GB 1151 writes<400 B + 0.5 MB<1400 writes<0.6 MB
	LU	Point to Point	0.62 GB 200000 writes of 1 KB + 2000 writes of 200 KB
	MG Point to Point	0.19 GB 8842 * diff. sizes from 40 B to 135 KB
	SP	Point to Point	5.1 GB	45 KB<19248 writes<54 KB + 100 KB<32112 writes<160 KB
					Classification level
				Low	Medium	High
			Comm.	>1s	between 0.1s and 1s	<0.1s
			frequency	FT, IS	BT, SP	CG, MG, LU
		Metric	Comm. size	<1KB LU	between 1KB and 200KB BT, SP, CG, MG	>200KB FT, IS
			Burstiness BT, SP, LU	CG, MG	FT, IS

Table 3 . Classification of NPB with regards to three communication features.

 3

Table 2

 2 summarizes the long-distance communication features of NPB 2.4 for B class problem on 16 nodes. We obtain these figures by logging each TCP write size on WAN connections during one NPB execution. We do not care about EP because it mostly computes and does very few communications. FT and IS mainly use collective communication primitives: MPI Alltoall for FT, MPI Allreduce and MPI Alltoallv for IS.

Table 4 . Number of idle timeouts in the NPB without and with MPI5000.

 4

		MPICH2	MPICH2
	NAS	without MPI5000	with MPI5000
	BT	331	323
	CG	725	427
	LU	185	179
	MG	73	70
	SP	487	426

Table 5 . Comparison of NPB execution time with and without slowstart after idle.

 5

		MPICH2 without MPI5000	MPICH2 with MPI5000
		Execution time	Execution time	Execution time
	NAS	(s)	without slowstart	(s)
			after idle (s)
	BT	204	171	147
	CG	122	122	116
	LU	66	71	74
	MG	11	11	14
	SP	242	203	221

Table 6 . DupACK and RTO without and with MPI5000 in case of cross-traffic.

 6

		and 6 show the MPICH-G2 performances
	with the NPB. They are very similar to MPICH2 per-
	formances except for IS due to grid-optimized collective
	operations of MPICH-G2. MPI5000 results outperform
	MPICH-G2 for BT, SP and LU in the same manner that it
	does for MPICH2. These results confirm that our approach
		MPICH2		MPICH2
		without MPI5000		with MPI5000
		Distant	Local		Distant
	NAS	DupAck	RTOs	DupAck	RTOs	DupAck	RTOs
	BT	757	56	4	1	320	1
	LU	327	232	0	0	174	41
	MG	94	53	7	0	48	4
	SP	1409	778	8	0	667	131

Acknowledgment

Experiments presented in this paper were carried out using the Grid'5000 experimental testbed, being developed under the INRIA ALADDIN development action with support from CNRS, RENATER and several Universities as well as other funding bodies (see https://www.grid5000.fr).