# Air Flow in Places of Worship.

INTRODUCTION

Over the past 100 years many research efforts have been devoted to developing indexes and models predicting the thermal sensation of people. Thermal comfort prediction models generally are mathematical models of the relationship between one or more environmental factors and certain occupant factors. The main aim of comfort models is to provide a single index that encompasses all relevant parameters. However A universal definition of comfort is almost impossible because of people's variable preferences, and the particular characteristics of different climates which affect the sensation of thermal comfort. ASHRAE standard (2010) and ISO 7730 (2005) have been widely adopted as international thermal comfort standards. These standards are based on a human energy balance obtained by assuming steady-state conditions. Those are deduced from the experiments conducted by Fanger (1972) in climatic chambers, using predicted mean vote (PMV) and Predicted Percentage Dissatisfied (PPD) to estimate the human mean response to the thermal environment from six thermal variables.These related indices are based on a combination and interaction between Environmental and personal parameters as follows:

* Environmental parameters comprise:

** Air velocity

** Air temperature

** Air relative humidity or vapor pressure

** Radiant (globe) temperature

* Personal parameters that are related to occupant adaptability to the local climate comprise:

** Metabolic rate

** Clothing insulation

By applying PMV model on an indoor environment, it predicts the average comfort vote of a group of occupants on the ASHRAE scale of thermal sensation and by further calculation the percentage of people dissatisfied regarding thermal environment. The model uses inputs of four environmental variables, air temperature, mean radiant temperature, air velocity and humidity, with two personal variables, metabolic rate and the insulation of the clothing ,Fanger, (1972,2010) Human life requires a deep-body temperature of a range between 35(95F) and 40[degrees]C(104F), for which 37 [degrees]C (98F) is the proxy mean. Skin temperature is normally between 31[degrees]C (88F) and 34[degrees]C (94F). If heat is to be lost, then the temperature of the surrounding environment must be less than skin temperature. However, temperature is not the only indicator, a number of factors influence the various heat exchange processes on the body surface which affect the sensation of comfort or discomfort It is usually noted that the PMV needs a steady state condition, it is not sensitive enough for fluctuating environmental conditions, and it does not take into consideration the adaptability of the occupants to improve their thermal comfort, to some extent, if needed (de Dear and Fountain, (1994). Also there were arguments that the PMV model under-estimates individuals' thermal sensation levels in indoor spaces of hot and dry climatic conditions, Al-ajmi, (2010).

Cairo climate

In Egypt, climate as a sample case is considered as a Hot and Dry climate while the north region adjacent to Mediterranean Sea is hot and humid climate due the effects of sea. Summer season is obvious in Egypt which most probably starts from June to August. Sometimes it can be quite unbearable in summer season in Cairo, as outdoor temperature may soar to 35[degrees]C (95F) or even more. Respectively, an outdoor averaged relative humidity levels may range from 30 to 35 %.The most important variable to determine human comfort is air temperature. Thus, based on climatic conditions In Egypt, air conditioning for indoor spaces becomes more a common in practice in order to achieve a better comfort conditions accepted by occupants.

Why Mosques?

A mosque is the building in which Muslims worship God. Throughout Islamic history, the mosque was considered as the Centre of the community and also towns formed around this high spiritual, pivotal building. Nowadays, especially in Muslim countries mosques are found on nearly every street corner, making it a simple matter for Muslims to attend the five daily prayers. In the West, mosques are integral parts of Islamic centers that also contain teaching and community facilities.

Review on Muslims Prayer

In the mosque, five obligatory prayers are performed daily; the average period of time for any prayer lasts from around fifteen to twenty minutes. When performing a congregational prayer in mosques, Muslims are guided by a leader called 'Imam'. The "Imam" is standing at the front wall of the mosque facing "Mihrab" which is a semi-circular niche in the wall of a mosque and indicates the "Qibla" that is, the direction of the "Ka'ba" in "Mecca" and hence the direction that all Muslims should face when praying. During Prayer, the 'Imam' is performing movements including postures such as standing, bowing and sitting. Verses or chapters from the holy Qur'an are being recited while standing .Therefore, for all intents the activities of all the participant prayers are synchronized behind 'Imam', and may be considered to be the same. Therefore, within accepted Muslim practice, any intentional action resulting from unaccepted indoor thermal conditions or any movement departing from the actual performance of the prayer is not allowed and would make a person's prayer invalid or unaccepted by God "Allah" SWT. However, in Egypt and most other Islamic countries, participation in congregational prayer in mosques is very common. With some exceptions, all the mosques are normally occupied by males only, because females are highly encouraged to pray in their home, especially the five obligatory prayers.

Case study

This portion of article covers A numerical study performed on "Nabiha Yaken" mosque which is an archaeological mosque Located in "sayda zieneb" ("garden city" district) downtown Cairo, Egypt. And as most public buildings in Cairo, The mosque is air-conditioned.Nabiha Yaken" mosque with an averaged area 820 [m.sup.2] (8815 f[t.sup.2] )and 6m (20 ft) height is considered as a moderate capacity mosque if compared with other archaeological or modern mosques. However, mosques in general are considered to be a high capacity occupied building type, so to design an optimum HVAC system that provides comfort and air quality in such a high capacity occupied spaces with efficient energy consumption is a great challenge. Especially if the number of occupants within a space increases, the need for an indoor Air Quality and better thermal comfort environment increases too, Khalil, (2012) and ISO (1998).

MATHEMATICAL MODELLING

Governing Equations

Air motion in 3D configurations is treated as an incompressible fluid flow governed by continuity equation which is described in vector form as follows:

[[[partial derivative][rho]]/[[partial derivative]t]] + div ([rho]u)=0

Other main governing equations are three momentum components (Navier stokes equations), energy, and species concentrations which are described as follows:

x--momentum: [[[partial derivative]([rho]u)]/[[partial derivative]t]] + div([rho]vu) = - [[[partial derivative]p]/[[partial derivative]x]] + div([mu] grad u) + [S.sub.Mx]

y--momentum: [[[partial derivative]([rho]v)]/[[partial derivative]t]] + div([rho]vu) = - [[[partial derivative]p]/[[partial derivative]y]] + div([mu] grad v) + [S.sub.My]

z--momentum: [[[partial derivative]([rho]w)]/[[partial derivative]t]] + div([rho]wu) = - [[[partial derivative]p]/[[partial derivative]z]] + div([mu] grad w) + [S.sub.Mz]

energy [[[partial derivative]([rho]i)]/[[partial derivative]t]] + div([rho]iu) = - p div u + div (k grad T) + [PHI] + [S.sub.i]

species [mathematical expression not reproducible]

Turbulence Modeling

K-[epsilon] model is the most commonly used turbulence model for HVAC applications as it leads to stable calculations that converge relatively easily. The following (simplified) model equation for k is commonly used:

[mathematical expression not reproducible]

And the following (simplified) model equation for [epsilon] is commonly used:

[[sigma].sub.k]=1.0; [[sigma].sub.[epsilon]=1.3; [C.sub.[epsilon]1]=1.44; [C.sub.[epsilon]2]=1.92;

The objective of thermal radiation modeling is to obtain the total volumetric absorption and emission. The spectral radiative transfer equation (RTE) can be simplified by Discrete Transfer Radiation approach which is the commonly used radiation model for HVAC applications this is done by Using ray-tracing technique to integrate radiant intensity along each ray:

[mathematical expression not reproducible]

Thermal Comfort Factors

Thermal comfort Factors were described in ASHRAE Standard ,(2010) and ISO 7730,(2005). The most important parameters of global comfort were considered to be Fanger, (1972, 2010):

* PMV -- Predicted Mean Vote

* PPD -- Predicted Percentage Dissatisfied

PMV is calculated from the formula:

[mathematical expression not reproducible]

The Predicted Percentage Dissatisfied expresses the heat sensations of a group of people dissatisfied with the thermal conditions in a given space. It is calculated from the formula:

PPD = 100-95*e(-0,03353*PM[V.sup.4]-0,2179*PM[V.sup.2])

PMV is clipped to lie between -3 and +3 based on the ASHRAE-seven point thermal sensation scale and is defined as: (-3) cold, (-2) cool, (-1) slightly cool, (0) neutral, (1) slightly warm, (2) warm, and (3) hot. Thus, PPD is in the range from 0% to +99.12%. This range is used because ISO data reaches these levels. For further information about comfort terms and definitions as Radiant (Globe) temperatures refer to the standards mentioned above or their latest editions in case of being obtainable.

NUMERICAL SIMULATION

In numerical simulation, ANSYS-Gambit software is used for creating mosque Geometry and also for Grid generation. While ANSYS-CFX software, (2011) is used for physical processing and solving comfort factors for the mosque case. The modeled mosque is considered as a relatively large size domain which was meshed with 1,709,152 tetrahedral elements. This was to avoid high skewness or meshing low quality problems. For this meshing criterion, the computation time may increase. Thus, a further more simplification is done by simulating a worshiper body as a vertical rectangular box 1.75 m (5,74ft) height x 0.25 m (10 inch) depth x 0.5 m (20 inch) width as shown in figure 1.

The Mosque is Air-Conditioned with 8 commercial floor free-standing units, each of cooling capacity 14.6 kW(cooling) ,(50000 BTU/Hr), with typical dimensions of 2 m height (6.55 ft) x 0.6 m width (2ft) x 0.4 m(1.31ft) depth. The units are mounted on the floor and distributed about the perimeter of the mosque as shown in figure 2.

By estimating roughly space portion per worshiper, the maximum number of worshipers within mosque was found to be 900 worshipers including the "Imam". Similarly, based on previous assumption for a worshiper body, a row of worshipers (standing shoulder to shoulder) is also modeled as a rectangular box with the same dimensions (height and width) while row length is as many times as a worshiper length depending on how many worshipers are standing in the row. In other words; behind the 'Imam', are standing 899 worshipers arranged in 23 rows guided by their leader 'Imam' and follow him by copying his ritual actions of worship as shown in figure 3.

BOUNDARY CONDITIONS

"Fanger's" model as a prediction tool for thermal comfort assumes a steady state conditions. Thus, Initial and boundary conditions are simply assumed according to moderate summer conditions, ASHREA (2009) in Cairo-Egypt as shown in table 1:

RESULTS

Results were plotted on an important vertical (YZ) plane in the middle of the mosque as shown in figure 4. The importance of this plane is due to being away as possible from Air-conditioning units. And also passing through the "Imam" and cutting the 23 following rows of worshipers.

Case Results are arranged such that the four predicted environmental parameters; air temperature, mean radiant temperature, air velocity and Relative humidity are shown in figures (5, 6, 7, and 8) respectively. While the other dependent global comfort factors: predicted mean vote and predicted percentage dissatisfied are shown in figures (9, 10).

Figures 5 to 10 represent a vertical section in mosque showing rows of prayers and demonstrating the counters of velocities, temperatures, relative humidity % and thermal comfort parameters .Comfort was maintained within the occupied zone as PMV values up to +1.0.

Another study was performed on "St Mary's" Orthodox Church which is located in Cairo, and houses more than 450 prayers. The main hall is of 17.2 m (57ft) x 18.2 m (60 ft) x height (X, Z, Y) which is variable with domes maximum of 9.3 m(30.5ft) , a total volume of 2424 [m.sup.3]. The inlet air conditions are taken as an average day max of 40[degrees]C (104F) and 30% relative humidity, representing August conditions. Predicted temperatures at 1.5 m (5 ft) are shown here in Figure 11 in comparisons with the experiments. Figure 11(b) depicted the predicted temperature contours in a vertical plane at x=4 m.

A final work covers a study on "The Grand" Mosque in Mecca, Saudi Arabia. The Grand Mosque houses 500000 prayers and is air conditioned. Figure (12) shows the predicted relative humidity in the Grand mosque in Mecca for sample lines of prayers. Relative humidity is high near the faces due to the breathing effect of prayers, 4000000 nodes were presently used to yield grid independent results.

CONCLUSIONS

The main conclusions from the study are summarized as follows:

* "Fanger" comfort model with its thermal sensation scales PMV and PPD can be used as a reliable method to predict the performance of HVAC system within a space, Khalil et al (2012).

* On applying PMV-PPD model for hot and dry climatic regions, the involved space under investigation must be Air-conditioned.

* The relative position between occupants and Air Outlets affects comfort levels within space.

* Initial and boundary conditions and other physical variables play an important role and must be carefully specified

to reflect reality to avoid meaningless .Verification with experiments was found to be necessary and should be adopted whenever reliable sets of measurements are available.

* CFD techniques are an effective tool for Predicting thermal comfort factors for Practical Engineering applications.

NOMENCLATURE

[rho] Fluid density, kg/[m.sup.3]

P Fluid pressure, Pa;

T Fluid temperature, oK;

U Velocity component in X direction, m/s;

V Velocity component in Y direction, m/s;

W Velocity component in Z direction, m/s;

[PHI] Scalar quantity (species transport);

[S.sub.M] Source term for body forces;

[S.sub.i] Source term for energy;

[S.sub.[PHI]] Source term for species transport;

[GAMMA] Turbulent diffusivity, [m.sup.2]/[s.sup.2];

k Turbulent Kinetic Energy, [m.sup.2]/[s.sup.2];

[epsilon] Dissipation rate of turbulent K.E;

[micro] Dynamic viscosity, N.s/[m.sup.2];

[[micro].sub.t] Turbulent viscosity, N.s/[m.sup.2];

[I.sub.v] Spectral radiation intensity depends on (r, s);

(r, s) r: position and s: direction;

[I.sub.v o] Radiation Intensity leaving a boundary;

[I.sub.b v] Blackbody emission intensity;

[K.sub.a v] absorption coefficient;

[K.sub.s v] scattering coefficient;

S Path length;

M metabolic rate, W/[m.sup.2];

[t.sub.a] Air temperature, [degrees]C;

[t.sub.mrt] Mean radiant temperature, [degrees]C;

[v.sub.ar] Relative air velocity, m/s;

REFERENCES

Al-ajmi, F. F. 2010, Thermal comfort in air-conditioned mosques in the dry desert climate. Building and Environment, Vol.45 (11), 2407-2413

ANSYS-CFX. 2011, CFX-Solver Theory Guide.

ASHRAE. 2009, ASHRAE Fundamentals Handbook.

ASHRAE. 2010, ASHRAE Standard 55. Thermal Environmental Conditions for Human Occupancy.

ISO standard 7730, 2005, Ergonomics of the thermal environment-Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria.2005

De Dear, R.J. and Fountain, M.E., 1994, "Field experiments on occupant comfort and office thermal environments in a hot-humid climate", ASHRAE Transactions 100 (2) (1994) 457-475.

Fanger, P.O., 1972, Thermal Comfort: Analysis and Application in Environmental Engineering, McGraw-Hill, New York.

Fanger, P.O., 2003, Ventilation for health, comfort and productivity, Proceedings of the 2003 4th International Symposium on Heating, Ventilating and Air Conditioning, 1, 1-7

ISO standard 7726, 1998, Ergonomics of the thermal environment-Instruments for measuring physical quantities. 1998.

Khalil, E.E., 2012, Energy Efficient Hospitals Air conditioning Systems, OJEE, Open Journal of Energy Efficiency, 1, pp.1-8, June 2012

Khalil, E.E., El-Bialy, E.M., 2012. Experimental and Numerical Investigation of Indoor Environmental Quality in a Subway Station. ASHRAE Transactions, 118 (PART 1), 199-206.

Essam E.Khalil, PhD

Fellow ASHRAE

Gamal Elhariry, PhD

Omar A. Huzayyin, PhD

Ramy H. Ragab

Essam E.Khalil is a professor, Gamal Elhariry and Omar A.Huzzain are assistant professors in the Department of Mechanical Engineering, Cairo University, Cairo, Egypt. Ramy H. Ragab is a Research Mechanical Engineer at Cairo University, Cairo, Egypt.
```Table 1. Boundary conditions and occupant data details

Boundary           value          Occupant Data        value

Roof temperature   306 [K]        Gender               Male
Walls temperature  305 [K]        Activity type        Standing, relaxed
Floor temperature  302 [K]        Metabolic rate       1.2 [met]
Outlet air         286 [K]        Skin temperature     307 [K]
temperature
Outlet air            3.15 [m/s]  Clothing type        Light summer
velocity                                               clothing
Initial air        304 [K]        Clothing insulation  0.073 [m2*K/w]
temperature
```
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