AIAA-2008-1163

1 American Institute of Aeronautics and Astronautics

Numerical Investigations of Energy Exchange and Fluid Flow Patterns inside Air Conditioned Amphitheater

Gamal El-Hariry, Essam E. Khalil and Waleed Abdel-Samee

Faculty of Engineering, Cairo University Cairo –EGYPT

ABSTRACT

The present paper is devoted to numerically investigate the influence of location and number of ventilation and air conditioning supply and extract openings on air flow characteristics in large cinema theatres. This work focuses on air flow patterns, thermal behaviour and carbon dioxide dispersion in cinema theatres where large number of guests are seated. The effectiveness of an air flow system is commonly determined by the successful removal of sensible and latent loads from occupants with additional of attaining air pollutants at a prescribed level to attain the human thermal comfort conditions and improve the indoor air quality; this is the main target during the present work.

A numerical study was carried out to define the optimum airside design of the HVAC systems that provides the optimum air flow and energy utilization. The present model is packaged as a Computational Fluid Dynamics (CFD) program embedded in code. Numerical computations were carried out with more than 600,000 orthogonal three dimensional control volumes. Grid nodes were densely located in the vicinity of the heat sources and accounts for sensible and latent heat load from individual humans. The paper ends with a brief discussion and conclusion. INTRODUCTION This paper attempts to predict the air flow characteristics in a large cinema theatre with numerically technique and compared with the existing thermal comfort standards, such as ASHRAE standard [1] and ANSI/ASHRAE standard 62–2004 [2] to specify the best required comfort conditions in the occupancy region. ASHRAE standard [1] represents the general design criteria for fully air-conditioned commercial and public buildings; for cinema theatres and auditoriums within the occupied zones, air conditions should be maintained as; relative humidity is held below 55%, temperatures are held within the 68 to 72 °F range, the air movement below 25 fpm to maintain the concentration of contamination at an acceptable level, and 8 to 12 ACH design. While ANSI/ASHRAE standard 62–2004 [2], limited the indoor CO2 concentration up to 1000 ppm in order to satisfy a healthy environment. Indoor Air Quality basics and parameters, measuring and assessments techniques for such variables are outlined in references [3 to 6].

CFD SIMULATION TECHNIQUES The present numerical investigation was based on solving the governing equations that described airflow inside the cinema theatre by a CFD program FLUENT 6.2

46th AIAA Aerospace Sciences Meeting and Exhibit7 - 10 January 2008, Reno, Nevada

AIAA 2008-1163

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

AIAA-2008-1163

2 American Institute of Aeronautics and Astronautics

(commercially available CFD program). This numerical approach solves the partial differential equations governing the transport of mass, three momentum, energy and species in a fully turbulent three dimensional domain under steady state conditions in addition to standard k – ε model equations for turbulence closure. An orthogonal three-dimensional grid was superimposed on the solution domain and comprised more than 600000 numerical cells. Details of the present numerical technique, governing equations, boundary and inlet conditions can be found in reference [7], where reference should be made regarding grid independency tests, convergence and numerical stability. The different governing partial differential equations are typically expressed in a general form as:

ΦΦΦΦ +⎟⎟⎠

⎞⎜⎜⎝

⎛∂Φ∂

Γ∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂Φ∂

Γ∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂Φ∂

Γ∂∂

=Φ∂∂

+Φ∂∂

+Φ∂∂ S

zzyyxxW

zV

yU

x effeffeff ,,,ρρρ … (1)

ρ = Air density, kg/m3 Φ = Dependent variable. SΦ = Source term of Φ. U, V, W = Velocity vectors. ΓΦ,eff = Effective diffusion coefficient. The effective diffusion coefficients and source terms for the various differential equations are listed in the table 1.

Table 1: Terms of Partial Differential Equations (PDE) equation 1

Φ ΓΦ,eff SΦ Continuity 1 0 0

X-momentum U µeff -∂P/∂x +ρg+ SU Y-momentum V µeff -∂P/∂y+ρg + SV Z-momentum W µeff -∂P/∂z+ρg(1+β∆t) +SW H-equation H µeff/σH SH

RH-Equation RH µeff/σRH SRH τ-age equation τ µeff/στ ρ

k-equation k µeff/σk G - ρ ε ε-equation ε µeff/σε C1 ε G/k – C2 ρ ε2/k

µeff = µlam + µ t µ t = ρ Cµ k2 / ε G = µt [2{(∂U/∂x)2 +(∂V/∂y)2 +(∂W/∂z)2}+(∂U/∂y + ∂V/∂x)2 +(∂V/∂z + ∂W/∂y)2 +(∂U/∂z + ∂W/∂x)2] SU = ∂/∂x(µeff ∂Φ/∂x)+∂/∂y(µeff ∂Φ/∂x)+∂/∂z(µeff ∂Φ/∂x) SV = ∂/∂x(µeff ∂Φ/∂y)+∂/∂y(µeff ∂Φ/∂y)+∂/∂z(µeff ∂Φ/∂y) SW = ∂/∂x(µeff ∂Φ/∂z)+∂/∂y(µeff ∂Φ/∂z)+∂/∂z(µeff ∂Φ/∂z) Turbulence model constants C1 = 1.44, C2 = 1.92, Cµ = 0.09 σH = 0.9, σRH = 0.9, στ = 0.9, σk = 0.9, σε = 1.225 INITIAL AND BOUNDARY CONDITIONS

AIAA-2008-1163

3 American Institute of Aeronautics and Astronautics

The initial conditions of the solving domain are taken to represent the actual value of each variable Φ . The boundary conditions represent the wall, inlet, and outlet conditions. The detailed treatment of boundary conditions can be found in the literature, Khalil [8]. Near the wall, the log-law of the wall function is applied to correct and find the values of turbulence and dissipation. The velocity of the airflow tends to be zero at the wall surface. The effect of buoyancy forces was included. CONVERGENCE AND STABILITY The simultaneous and non-linear characteristics of the finite difference equations necessitate that special measures are employed to procure numerical stability (convergence): these include under relaxation of the solution of the momentum and turbulence equations by under relaxation factors which relate the old and the new values of Φ as follows: ( ) oldnew 1 Φγ−+Φγ=Φ … (2) Where: γ is the under-relaxation factor. It was varied between 0.2 and 0.3 for the three velocity components as the number of iteration increases. For the turbulence quantities, γ was taken between 0.2 and 0.4 and for other variables between 0.2 and 0.6. The required iterations for convergence are based on the nature of the problem and the numerical conditions (grid nodes, under-relaxation factor, initial guess, etc.). So the time (on the computer processor) required to obtain the results is based on many factors. The computational number of iterative steps is selected according space cell (spatial difference) to yield converged solutions [9]. The validity of the present computational technique was assessed previously in the open literature, for example in references [8-10]. where reference should be made for more detailed readings. THEATRE GEOMETRICAL CONFIGURATIONS The present study was performed on cinema theatre whose dimensions were 30.0 m long, 20.0 m wide, with varied ceiling height of 10.0 m at screen to 8.0 m at the rear. This is clearly indicated in figure 1. This case describes the air flow characteristics at ceiling air supply with 20 square supply air ports distributed uniformly at the ceiling but two of the air supply ports concentrated at front of the cinema theatre to satisfy the required air conditions for the exhibit area (optional) and nine square supply air ports from sub-ceiling (bottom of the balcony partition), while 12 extract ports from both side walls (wall of X-Z plane at Y = 0, and wall of X-Z plane at Y = 20 ) mounted at nearly the seating levels. Table 1 summarizes the boundary conditions and related air openings areas for this designated case of the cinema theatre. This case designed with 12 air changes per hour, air enters theatre volume through air supply ports with CO2 concentration of 0.00038 (380 ppm) [6] and the surface temperature of all internal walls assumed to be at 298 K.

AIAA-2008-1163

4 American Institute of Aeronautics and Astronautics

All supply velocities were normal to supply grills with assumed 5 % turbulence intensity according to measured and practical values and 0.6 m turbulence length scale [3], which is the smallest dimension for the supply grill opening.

Figure 1: The cinema theatre Configuration.

Table 1: Theatre boundary conditions.

Inlet Air Conditions Supply grilles

descriptions Extract grilles descriptions

VS, m/s TS, K RHS, % Modules (Ports) Area, m2 Modules

(Ports) Area, m2

2.5 m/s for S10 to S20 289 60 11 0.6 × 0.6 1 m/s for S1 to S9 289 60 9 0.6 × 0.6

1 m/s for balcony sub-ceiling ports 289 60 9 0.6 × 0.6

12 1.8 × 0.6

• S1 to S9: The nine ceiling air supply diffusers are located above the balcony zone. • S10 to S20: The eleven ceiling air supply diffusers issue air directly to the floor level

(remotely from the balcony partition).

MODELING OF AUDIENCE PRESEENSE Due to the difference in human skin surface temperature and indoor environment temperature, there is heat exchange between human body and the indoor environment.

AIAA-2008-1163

5 American Institute of Aeronautics and Astronautics

In air-conditioned spaces, a steady-state thermal equilibrium is usually maintained between the human body and the indoor environment. So, all metabolic heat production is released. The human body and face is modeled according to the description of figure 2 and treated as a wall at a constant temperature of its skin temperature. The skin temperature is a function of its metabolic rate [4]; then the skin temperature is 34 oC according to 60 W/m2 of metabolic rate [5] generated from human body seated at rest. While the human face dissipated species mass fraction of 0.042 kgw / kgd.a at 37 oC (temperature of body core) in order to consider the moisture gain from the audience respiration to the theatre airflow, and zero diffusive sweat mass flux from skin surface is assumed.

Figure 2: The human body modeling.

ANSI/ASHRAE Standard 62-2004 [2] specified the rate of CO2 generation from human byproduct respiration with the physical person activity. For the present work, CO2 concentration in the human respiration equal 0.03125 LCO2 /La. Modeling of audience presence inside the theatre will be developed with full audience load, which appear on the floor and balcony regions as shown in figure 3.

AIAA-2008-1163

6 American Institute of Aeronautics and Astronautics

Figure 3: Modeling of audience presence inside the theatre. RESULTS AND DISCUSSION Figures 4 to 7 show the complete predictions of air velocity, temperature, relative humidity and CO2 concentration inside the theatre. All of theses predictions are developed with tilted planes parallel with floor and balcony levels at 1.7 m from the floor and balcony levels [1].

(a) (b)

Figure 4: Velocity magnitude contours (m/s), at a plane at 1.7 m above

(a) Theatre floor level (b) balcony level

AIAA-2008-1163

7 American Institute of Aeronautics and Astronautics

(a) (b)

Figure 5: Predicted air Temperatures Contours (K) at a plane at 1.7 m above (a) Theatre floor level (b) balcony level

(a) (b)

Figure 6: Predicted air Relative Humidity Contours, Rh% at a plane at 1.7 m above

(a) Theatre floor level (b) balcony level

AIAA-2008-1163

8 American Institute of Aeronautics and Astronautics

(a) (b)

Figure 7: Predicted CO2 Concentration Contours at a plane at 1.7 m above

(a) Theatre floor level (b) balcony level From the displayed results, for study of air flow patterns, it's clear that there is insufficient supply air flow rate at zones of above and below the balcony partition as indicated by most significant dead zones appears within it. While good and uniform air distribution in front part of the occupied zone on the floor with average air velocity 0.18 m/s, which is slightly higher than the comfort range value but may be accepted due to this value decreases within the humans face level. Also as air flow study, the thermal study of this case indicated uncomfortable high temperature magnitudes and low relative humidity magnitudes at above and below the balcony occupied zones, especially near the rear wall zones. While good air temperature and relative humidity magnitudes in front part of the occupied zone on the floor with 293 K average air temperature and 55 % average relative humidity which fall within the comfort range values [1]. While for the predicted CO2 concentrations at the same planes, these predictions indicated poor fresh air at above and below the balcony occupied zones where the average CO2 concentration within these zones is 1100 ppm which is higher than the threshold limit [2] while good CO2 concentrations within front part of the occupied zone on the floor with 750 ppm average CO2 concentration which indicated a healthier zone. CONCLUSIONS AND RECOMMENDATIONS From all predictions of air flow characteristics in the cinema theatre designed case, it is clear that the front part of the occupied zone on the floor satisfied the comfort conditions within it. However predictions in regions above and below the balcony occupied zones indicated uncomfortable air conditions due insufficient air flow rate at these zones. So, this case requires more enhancements through increasing the fresh air flow rate within above and below the balcony occupied zones in order to specify the comfort conditions in all theatre occupied zones. More supply air diffusers should be located near the above mentioned regions to provide more comfort.

AIAA-2008-1163

9 American Institute of Aeronautics and Astronautics

REFERENCES [1] ASHRAE Handbook, HVAC Applications, 2007. [2] ASHRAE, " ASHRAE Standard 62-2004: ventilation for acceptable indoor air quality ", American Society of Heating, Refrigerating and Air Conditioning Engineers, Atlanta, USA, 2004. [3] FLUENT 6.2 Documentation, © Fluent Inc. 2005. [4] INNOVA, Air Tech Instruments Booklet. Web site:http//www.innova.com [5] ASHRAE FUNDAMENTALS, HVAC Applications, 2006. [6] UIG, Universal Industrial Gases, Inc. Web site: http//www.UIG.com [7] Abdel-Samee, W.” Numerical Investigations of Flow Patterns and Thermal Comfort in Air-Conditioned Cinema Theatres”.Cairo University, September 2007. [8] Khalil, E.E.,”Energy Performance of Commercial Buildings in Egypt: A New Direction", Proceedings, Energy2030, Abu Dhabi, November 2006. [9] Kameel, R.A., and Khalil, E.E., (2007),”Computer Aided Design Of Indoor Air Quality And Air Flow In Surgical Operating Theatres, Proceedings Roomvent2007, Paper 1217, June 2007. [10] Khalil, E.E., (2007),”Numerical Simulation of Flow Regimes and Heat Transfer Interactions in Complex Geometries”, Proceedings, 5th IECEC, St. Louis, AIAA-2007-4726, June 2007.