AIAA-2006-4095

† Ph.D. (Eng. Research Associate), Consultant CEB, Cairo, Egypt ‡ Professor of Mechanical Engineering, Faculty of Engineering, Cairo University, Chairman CEB, Cairo, Egypt * B.Sc. (Eng. Research Associate), Faculty of Engineering, Cairo University, Cairo, Egypt Copyright © 2006by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved

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AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS

ON INDOOR AIRFLOW PATTERNS PREDICTIONS USING CFD IN THREE- DIMENSIONAL CONFIGURATIONS

Ramiz Kameel†, Essam E. Khalil‡, Nermeen Ramzy*

ABSTRACT

Airflow characteristics in enclosures play an important role in attainment of recommended human comfort level. This paper is devoted to the predictions of airflow patterns and turbulence characteristics in room enclosures with occupants. The present paper introduces a non-commercial developed Computational Fluid Dynamics (CFD) program to predict the airflow characteristics in the enclosures. The turbulence characteristics were represented in the present work to account for Reynolds and shear stresses and near-wall functions. The numerical scheme solves the differential equations governing the transport of mass, three momentum components, and energy in full three dimensional configurations. The present paper represents part of a more comprehensive work that aims at developing scientific and educational numerical models and programs. The present paper is the third reporting of work in progress documentations. The paper introduced a more comprehensive validation of the numerical scheme, grid dependence, beside the velocity and temperature validations and utilized turbulence models. The obtained results are compared with the steady-sate results obtained with 3DHVAC modified version to highlight the merits of each turbulence modelling assumptions relative to the standard two equation k- e model. The error sources are classified and introduced in this paper with several recommendations for analysis and modification procedures. Keywords: Air Conditioning, Air Flow Patterns, Simulation

I. INTRODUCTION AND COMPUTATIONAL METHOD DESCRIPTION To design an optimum HVAC airside system that provides comfort and air quality in the air-conditioned spaces with efficient energy consumption is a great challenge. Air conditioning can be identified as the conditioning of the air to maintain specific conditions of temperature, humidity, and dust level inside an enclosed space. The conditions to be maintained are dictated by the function of the space, type of users and the required users comfort. So, the air conditioning embraces more than cooling or heating. The comfort air conditioning is defined as “the process of treating air to control simultaneously its temperature, humidity, cleanliness, and distribution to meet the comfort requirements of the occupants of the conditioned space” 1. Air conditioning, therefore, includes the entire heat exchange operation as well as the regulation of velocity, thermal radiation and quality of air, as well as the removal of foreign particles and vapours 2. A successful HVAC design is that energy efficient design in addition to all previous factors The present model is packaged as a Computational Fluid Dynamics (CFD) program and is named under the title 3DTHVAC. This program is the advanced version of the 3DHVAC 1-4.The present paper introduces a brief description of the present 3DTHVAC program and its validation with steady state results 2, 5. This will be followed by the assessment of the airflow characteristics and energy consumption in the different four air-conditioned configurations. The paper ends with a brief discussion and conclusion. The program solves the differential equations governing the transport of mass, three momentum components, energy, relative humidity, and the air age in 3D configurations under unsteady conditions. The different governing partial differential equations are typically expressed in a general form as:

ΦΦΦΦ +⎟⎟⎠

⎞⎜⎜⎝

⎛∂Φ∂

Γ∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂Φ∂

Γ∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛∂Φ∂

Γ∂∂

+=Φ∂∂

+Φ∂∂

+Φ∂∂

+Φ∂∂ S

zzyyxxW

zV

yU

xt effeffeff ,,,ρρρρ (1)

4th International Energy Conversion Engineering Conference and Exhibit (IECEC)26 - 29 June 2006, San Diego, California

AIAA 2006-4095

Copyright © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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

Table 1: Terms of Partial Deferential Equations (PDE)

Φ ΓΦ,eff SΦ Continuity 1 0 0 X-momentum U µeff -∂P/∂x + SU Y-momentum V µeff -∂P/∂y + SV Z-momentum W µeff -∂P/∂z+ρgβ∆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) C1 = 1.44, C2 = 1.92, Cµ = 0.09 σH = 0.9, σRH = 0.9, στ = 0.9, σk = 0.9, σε = 1.225

COMPUTATIONAL GRID GENERATION The present program utilizes the modified hyperbolic formula 6 for grid node generation. The present formula creates non-uniform orthogonal grid. The present program is also designed to simulate the airflow domain using up to 500,000 cells to obtain grid independent predictions with efficient cost. NUMERICAL SCHEME The present program utilizes the power-law scheme that proposed and recommended 7 to avoid the simple first-order upwind difference scheme 8. The power-law scheme is not particularly expensive to compute and provides an extremely good representation of the exponential behaviour 7. Although the power-law scheme is only first-order accurate on the basis of truncation error, the power-law difference scheme is a conservative formulation and does not have the problem of numerical oscillations. The drawback of the scheme is the inherent numerical diffusion. In the recirculating zones, the effective diffusion will be replaced by a numerical cross-flow diffusion in regions of the solution domain where the flow is not aligned with the grid-lines 8,9. INITIAL AND BOUNDARY CONDITIONS The initial conditions of the solving domain are taken to represent the actual value of each variable Φ the time t=0. The boundary conditions represent the wall, inlet, and outlet conditions. The detailed treatment of boundary conditions can be found in the literature that describes the 3DTHVAC program 4. 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. CONVERGENCE AND STABILITY The convergence should be attained over the time step. The simultaneous and non-linear characteristics of the finite difference equations necessitate that special measures are employed to procure numerical stability (convergence):

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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 within the time step as follows:

( ) oldnew 1 Φγ−+Φγ=Φ (2) Where γ is the under-relaxation factor, which 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.).

II.COMPUTATIONAL TECHNIQUE’S ASSESSMENTS This section demonstrates a sample of the likely comparisons between experimental results in the literature previously investigated and reported by others for relevant configurations and those of obtained in the present work using 3DTHVAC; the comments on the likely agreements and discrepancies observed during the validation process are discussed. VALIDATION WITH NIELSEN ET AL’S EXPERIMENTS Extensive velocity measurements in a rectangular parallelepiped scaled model of a room (H = 89.3 mm) in which the isothermal airflow is expected to be almost two-dimensional was carried out 11 as shown in Figure 1. The length of the model (L = 3H). The conditions parameters are based on inlet Reynolds number (Re = 5000) 11. Detailed measurements of velocity profiles are provided along different locations through the central vertical plane located at Y = W/2 (at X = H and X = 2H), and (at Z = 0.972H and Z = 0.028H) 11. In the present work, the same configuration was simulated using 3DTHVAC and the comparisons are presented in the Figure 1. The comparisons indicate good agreement especially in the jet downstream with discrepancies of the order of 5 – 7.5%. The comparison also shows some discrepancies in the prediction at the recirculation zones, especially near the floor. These predicted discrepancies occurred as the airflow velocity tends to zero near the wall, and can be attributed to the effect of the wall function of the turbulence model.

X = H X = 2H

Figure 1: Comparison with Experiments [11] VALIDATION WITH CHOW ET AL’S WORK The investigations of Chow et al 12 were the important investigations reported in that field. Their investigation was mainly concerned to evaluate the effect of the HVAC conditions on the airflow regimes in a surgical operating

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theatre. Indeed, they carried out three numerical investigations to obtain the effect of air supply velocity and effect of supply partial wall on the value of airflow velocities at the operating area. In this section, comparisons between the present numerical results for their cases and their results are shown. It should be noted here that the present work made use of the one equation Zhao et al 14 model is used in the present work to be compared to the RNG- turbulence model of Chow et al 12. From figure 2, good agreement can be observed between the predictions using the present k-ε model, and that of Zhao et al 14 and those of RNG model in the region between ceiling and the level of Z/H = 0.35. Actually the results of STACH-3 Model gave predicted velocity values to be less than the other two models. In the vicinity of the floor downstream the supply jet, STACH-3 model introduced a good agreement with the present model. The RNG model represents a pronounced penetration of the supply flow. It seems that the effect of vertical displacement factor in the RNG model is more significant than the effect of the wall. STACH-3 model gave good results near the wall due to the presence of the wall effect drastically in the zero-equation model. The results of local mean age of air from the CFD model are compared with the numerical results of Chow et al 12. They studied the airflow characteristics for an empty surgical operating theatre. They performed field measurements to record the air velocities at respectively the supply diffuser, extract grilles. They evaluated the operating theatre across three numerical cases. Conditions details for the three cases were presented in Chow et al 12. They used in their CFD analysis the Re-Normalization Group (RNG) k-ε model. The present work simulates the three cases for the same operating theatre of Chow et al 12, and presents the result at centre of the supply diffusers. The comparisons presented here are shown at different positions in Figure 2. In the figure Z/H is the normalized height of the room ,N-W is the normalized velocity and NLMA is the normalized local mean age of the air. Where, Normalized Local Mean Age = NLMA = [τp-τmin] / [τmax-τmin] .From the NLMA comparisons, it can observe that there are some differences of the normalized local mean age of the air near the floor of the room. The comparisons show a qualitative agreement with a maximum difference around 15%. The comparisons of normalized local mean age in the operating area had shown a good agreement. There are some differences occurred in near the ceiling especially in the case 3, which contain fixed partial walls.

Case 1

Figure 2a: Comparisons between different computational procedures and turbulence models

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Case 2

Case 3

Figure 2b,c: Comparisons between different computational procedures and turbulence models

III.PARAMETRIC FLOW INVESTIGATIONS Several attempts were carried out to assess the different ventilation systems; many researchers depended on the CFD to assess the ventilation strategies in different room configurations 13. In the present paper, four different basic room flow configurations are subjected to validation and assessment, as shown in Figure 3. The various conditions and parameters of the parametric cases are indicated in Table 2. Different arrangements of the internal obstacle can also be considered in practice to represent the effect of the furniture on the flow pattern arrangements and consequently their effect on the comfort, health, and energy utilization. The present parametric cases are a part of the complete investigation study, which aims at enhancing our knowledge of the best design of airside systems.

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METHOD OF ANALYSES In the present work, comparisons between various airside system designs are carried out with and without presence of the internal obstacles; comparisons were carried out based on the numerical results obtained with the aid of the present developed program in addition to several analytical formulations that were incorporated to account for jet configurations in the present study. These formulations are selected and proposed in an attempt to better describe the ventilation efficiency and energy exchange patterns. 5,13,14

Figure 3: Geometrical Configuration of Various Parametric Cases

Table 2: Conditions of Parametric Cases

Space Dimensions: Length L=2H , Width WD=1.33H m, Height H=3 m In Vertical Obstacle Arrangements The obstacle height is half of the space height, The obstacle width is equal the space width WD, The obstacle is located at longitudinal distance X = H Case MFM The obstacle length is half of the space length , The obstacle width is equal the space width WD, The obstacle is located at height Z = H/2 Case PFM The obstacle length is half of the space length, The obstacle width is equal WD/4, The obstacle is located at Z = H/2 Operation Conditions: Air Changes per Hour ACH=20, Supply Area = 0.06 of Wall Area, Supply Area = 0.03 of Ceiling Area (cases PF, PFM) , Supply Temp. = 13 oC, Target Temp. = 23 oC, Heat transmission to the room from the all surfaces, It is assumed that the all walls maintain at 23 oC , Extraction Temperature is floating , No Slip condition at the wall , Initial condition of temperature is 23 oC

In this work, the thermal performance is evaluated using two different indices. These indices assessed the heat removal efficiencies and the energy efficiency. 5 The energy efficiency evaluates the performance of the airside design for air utilization in the enclosure. This index is proposed to evaluate the airside design, and the effectiveness of the extraction port(s) location. The airflow distribution is assessed using the air-exchange efficiency. Heat removal Index (Eh) : Eh = (Te - Ti) / (Tm - Ti) (3) Energy Efficiency (Ee) (proposed in earlier works) 5 Ee = (Te - Ti) / (Tt - Ti) (4) Where: i, e, m, t = inlet, extraction, mean, target Air exchange Index (Ea) Ea = τn / 2τm

(5) τn = nominal time = enclosure volume/supply flow rate τm = local mean age average of the room

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NUMERICAL RESULTS The airflow distribution for the parametric cases is investigated using the 3DTHVAC program , with the aid of the RNG k-ε turbulence mode and with grid size of 500000 grid node after grid independency test revealed that results are grid independent with 4%. The predicted airflow distribution of the proposed parametric cases, shown in Figure 4 represented that the recirculated nature of the proposed main four designs (DF, CF, MF, and PF). Also, one can conclude that the extraction port location has a minimal effect on the main airflow distribution in the enclosure in the first three cases. The piston flow doesn’t provide the optimal solution due to the dependence on multi supply outlets. The recirculation zones in the enclosures can be minimized using the proper locations of the supply outlets and extraction ports. Their relative position can be the prime factor affecting the development of recirculation zone .

DF CF

MF PF

Figure 4: Airflow Distribution at Mid- Depth Plane The temperature distribution is displayed, in Figure 5, at half way Y =WD/2 i.e. at the mid depth plane. The temperature distribution in the occupancy zone is shown to have temperatures that can satisfy comfort levels. It can be seen that the general temperature patterns can be influences by the locations of inlets and extracts. The cavity flow configuration provides the most uniform temperature in the occupancy zone. The MF and PF configurations provided the poorest temperature distribution of the temperature in the occupancy zone. The temperature distribution evaluation is supported by the local-mean-age distribution evaluation, as shown in Figure 6. The air exchange and heat removal efficiency results are represented in the Figures 7and 8 for the flow situations in the geometry indicated in Table 2.

DF CF

MF PF

Figure 5: Temperature Distribution at Mid- Depth Plane

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These were obtained with the aid of the RNG k-ε model and figure 7 indicated the air exchange efficiency for the various configurations. These configurations provide the most economic airside design among the proposed design in the presented work. The room configurations designation MFM, CFL, and CFU refer to Mixed Flow with horizontal partition, Cavity flow with vertical partitions as indicated in Table 2.The PF configuration has the lowest heat removal efficiency among the other configurations. The proposed energy efficiency measures the capability of the airside design to utilize the all supplied air and the capability of the design to extract the target air temperature only. When the system extracts the target temperature, one can consider that the ideal system that has the maximum energy consumption utilization. The energy efficiency results are displayed in Figure 8. It is found that the MFM, CFL, and CFU configurations have the highest energy utilization efficiencies. It is found that the MFM, CFU, and PFM configurations have the highest air exchange efficiencies among the all designs. From the all-previous indices, one can observe that the MFM, CFL, and CFU configurations are the most proper airside designs. The gross efficiency is a driven factor from the multiplication of the heat removal, energy, and air exchange efficiencies . This new index supports the latter observation.

IV.DISCUSSIONS AND CONCLUSIONS

The main flow pattern of the supply jet in (DF, CF, and MF) types is slightly influenced by the extraction port location. For each obstacle location, there is a proper airside design. Basically, the airside design should provide the optimum utilization of the supplied air.

DF CF

MF PF

Figure 6: Local Mean Age Distribution at Mid- Depth Plane

The optimum utilization of the supplied air can be attained by locating the supply outlets and extraction ports to minimize the recirculation zone and prevent the air short circuits. Ideally, the optimum airside design system can be attained, if the airflow is directed to pass all the enclosure areas before the extraction, Such as the MF and CF configurations. The proposed indices do not ,as yet ,completely provide adequate evaluation of the airside system designs. The gross efficiency is proposed here to overcome this problem by composing all efficiencies in one factor. Still, the present attempt has some notable deficiencies, such as the evaluation of the local mean age of the extracted air, and the influence of the design on the occupancy zone patterns. The proposed evaluation indices exhibit some shortcomings to fully describe the influence of the recirculation zones on the occupancy zone and also on the fresh supplied air. The optimum airside design system can be attained, if the airflow is directed to pass all the occupancy areas before being extracted. The air flow in any room requires careful design consideration, not only to provide temperature, relative humidity and avoid excessive air drafts and turbulence, but also to efficiently utilize the available energy.

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Figure 7: Heat Removal Index Eh Figure 8: Energy Efficiency Ee

V. REFERENCES [1] ASHRAE Handbook, Fundamentals 2005, ASHRAE, Atlanta, USA. [2] Stoecker, W. F., and Jones, J. W., 1985, Refrigeration and air conditioning, Second Edition, TATA McGraw-Hill Publishing Company LTD., 1985. [3] Khalil, E. E., 2000, Computer aided design for comfort in healthy air conditioned spaces, Proceedings of Healthy Buildings 2000, Finland, Vol. 2, Page 461. [4] Kameel, R., 2002, Computer aided design of flow regimes in air-conditioned operating theatres, Ph.D. Thesis work, Cairo University. [5] Kameel, R., and Khalil, E. E., 2002, Verification of numerical prediction of 3-D air-conditioned flow behaviour in full and reduced scale room models, 40th Aerospace Sciences Meeting & Exhibit, Reno, Nevada, AIAA-2002-654, 12-15 January 2002. [6] Kameel, R., and Khalil, E. E., 2002, Generation of the grid node distribution using modified hyperbolic equations, 40th Aerospace Sciences Meeting & Exhibit, Reno, Nevada, AIAA-2002-656, 12-15 January 2002. [7] Patankar, S. V. 1980, Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, WDC. [8] Sorensen, D. N., and Nielsen, P. V., 2003, Quality control of computational fluid dynamics in indoor environments, Indoor Air, Volume 12 No.1, page 2. [9] Leonard, B. P., and Drummond, J. E., 1995, Why you should not use ‘hybrid’, ‘power-law’ or related exponential schemes for connective modelling – there are much better alternatives, International Journal for Numerical Methods in Fluids, 20, 421-442, 1995.

[10] Anderson, D. A., Tannehill, J. C., and Pletdher, R. H., 1980, Computational fluid mechanics and heat transfer, Hemisphere 1980.

[11] Nielsen, P. V., Restivo, A. and Whitelaw, J. H., 1978, The velocity characteristics of ventilated rooms, J. Fluids Eng., 100, 291–298.

[12] Chow, T. T., Ward, S., Liu, J. P., and Chan, F. C. K., 2000, Airflow in hospital operating theatre: the Hong Kong experience, Proceeding of Healthy Buildings, Vol. 2, Finland.

[13] Cho, Y., Awbi, H. B., and Karimipanah, T., 2002, A comparison between four different ventilation systems, ROOMVENT 2002, 181-184.

[14] Kameel, R., and Khalil, E. E., 2003, Energy efficiency, air quality, and comfort in air-conditioned spaces, DETC2003 / CIE – 48255, ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, Illinois USA, 2003.