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AIAA-2003-0859

THE PREDICTION OF AIRFLOW REGIMES IN SURGICAL OPERATING THEATRES: A COMPARISON OF DIFFERENT

TURBULENCE MODELS Ramiz Kameel†, Essam E. Khalil‡

Mechanical Engineering Department Faculty of Engineering Cairo University, Egypt

ABSTRACT

The air quality of the indoor environment is capable of affecting human comfort in a multitude of ways, depending on the contaminant. Airborne contaminants range from toxic substances such as carbon monoxide to nuisance matter such as large dust particles. There are literally thousands of air contaminants, each of them affects on the human body. It is necessary to understand how the body handles pollutants as well as the contaminants themselves and the symptoms they inflict on the human body. The airborne contaminant affects human health at different levels depending on the nature and type of contaminant.

Hospitals and other health care facilities are complex environments that require ventilation for comfort and to control hazardous emissions for patients, personnel and visitors. Indoor air quality is more critical in health care facilities than in most other indoor environments due to many dangerous microbial and chemical agents present and due to the increased susceptibility of the patients, especially immunosuppressed persons. To arrange ventilation capable of efficiently fulfilling all, often-even contradictory, needs is a great challenge; adequate solutions have not yet been found for many indoor air quality problems. In addition, the importance of good indoor climate is not yet unanimously recognized. Therefore, nosocomial infections due to contaminated air continue to cause unnecessary costs and sufferings, and health care personnel remains subject to several occupational exposure risks. In addition, indoor climate fails often to be comfortable, Healthy Building 2000.

Proper predictions of airflow regimes inside the healthcare applications, especially the surgical operating theatre, enhance our design decisions of the HVAC systems or even the earlier architecture design. Proper turbulence models can aid in that task, which lead engineers to accurate description of the airflow characteristics inside the surgical operating theatres. The present work is devoted to predict the airflow regimes inside different configurations of surgical operating theaters, using three different turbulence models. These three models are; namely standard k-ε model (Launder and Spalding), RNG model and the phenomenological model of (Li and Zhao) that based on DNS (Directly Numerical Simulation) data. The three models were utilized to predict the airflow regimes, turbulence heat transfer interactions. The obtained results suggest the use of the approximate model for engineering purpose. The k-ε model is superior in predicting flow characteristics in near wall and steep gradient zones.

† Research Associate, M.Sc ‡ Professor of Mechanical Engineering, M. ASME, ASHRAE, Associate Fellow AIAA Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

41st Aerospace Sciences Meeting and Exhibit6-9 January 2003, Reno, Nevada

AIAA 2003-859

Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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1. INTRODUCTION

Since the 1970s CFD building service engineers and others to examine air velocity, temperature and contaminant concentration distributions, references 1-36, Alamdari et al1, Chen and Xu 4, and Yuan et al 35 has increasingly used techniques. A review of CFD in this context is given by Jones and Whittle 8. In order to use CFD in both an efficient and meaningful way it is necessary to generate a suitable grid, accurately specify boundary conditions and to use an appropriate turbulence model. This paper concentrates on the choice of turbulence models for ventilated rooms, Holmes et al 7.

Surgical operating theatres are very important applications in the healthcare field, so the choice of the suitable prediction model is so complex, especially regarding the vertical downward flow displacement, which recommended in surgical operating theatres, Kameel and Khalil 13-19.

For such reason, this work discusses in

more details, the preceding attempts to obtain the optimum turbulence model capable to obtain the airflow characteristics in enclosures ventilated by downward flow. And then, the present work will analyze the chosen models of turbulence to predict the airflow characteristics and the airborne contaminant age.

The attempts to obtain the optimum turbulence model to predict the airflow characteristics were started in the late seventies and the early eighties of the twentieth century. Most of previous attempts agreed that incorporating the same concept of low Reynolds number version of k-ε model is acceptable in the prediction of the airflow characteristics in the ventilated enclosures, with slight changes of the model constants according to the empirical or experimental observations.

Lam et al 25 stated that no one, earlier than 1981, had pinpointed the causes for the observed discrepancies between predictions and measurements to be due to weakness in the basic model equations or in the wall

function formula. They considered that modified modeling assumptions near the wall leads to obtain the correct airflow characteristics in general. They presented a general modification on the wall function to obtain better airflow characteristics.

Thies and Tam 34 stated that the k-ε model has proven, over the years, to be a useful engineering approach for the prediction of the mean velocity profiles of turbulent flows.

Chen 4 studied the prediction results of several different k-ε models to obtain the indoor airflow characteristics for the down flow configuration. Also, Lin et al 28 investigated the prediction results of their CFD model in the vertical displacement flow configuration, as a part of their validation of CFD model for a research into displacement ventilation applications. They found that the prediction results of the Re-Normalization Group (RNG) k-ε model, in the vertical displacement ventilation matches the measured data very well, Yuan et al 35 and Lin et al 28.

Also, Chow et al 5 investigated the airflow characteristics numerically in a surgical operating theatre follows the HTM 2025, NHS Estates 29, depending on the Re-Normalization Group (RNG) k-ε model. Chow et al 5 agreed with Chen 3 and Lin et al 28 in the appropriately of the Re-Normalization Group (RNG) k-ε model to predict the downward airflow configuration.

Holmes et al 7 investigated the assessment of a range of turbulence models when predicting room ventilation for two idealized rooms. They studied the vertical and horizontal displacement ventilation models, which were initially examined by Buchanan 2, He et al 6, and Holmes et al 7 found that the predicted flow of the vertical displacement ventilation appears fairly insensitive to the turbulence choice.

Zhao et al 36 introduced three-dimensional CFD code under the name STACH-3 that was developed by Tsinghua University to simulate non-isothermal indoor airflow more quickly and presumably

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more correctly. They used zero-equation turbulence model that was developed by Chen and Xu 4.

Zhao et al 36 pointed out that many applications and validations show that k-ε turbulence model can adequately simulate isothermal indoor airflow well. But different types of indoor airflow, such as flows with stratified temperature filed, require different turbulence models, according to Nielsen 30. Zhao et al 36 claimed that their new turbulence model can adequately simulate natural convection and mix convection quickly and accurately.

The present work displays the comparisons among the standard low-Reynolds k-ε model (present work model), RNG k-ε model, and STACH-3 model, on the configuration of Kameel and Khalil 17-19 and Chow et al 5.

2. NUMERICAL METHODS 2.1. Mathematical Equations

Computational Fluid Dynamics (CFD) is used to model airflow by numerically solving equations based on fundamental physical principles. Three time averaged velocity components in X, Y, and Z coordinate directions were obtained by solving the governing equations using a "SIMPLE Numerical Algorithm" [Semi Implicit Method for Pressure Linked Equation] described earlier in the work Spalding and Patankar 32, Launder and Spalding 26, Khalil 21. The turbulence characteristics in the present work were represented by standard low-Reynolds k-ε model, RNG k-ε model, while the STACH-3 model was used to account for normal and shear stresses and near-wall functions. The present work made use of the Computer Program 3DHVAC, which was developed, by Khalil 22-24 and modified later by Kameel 9,10, and by Kameel and Khalil 11-14. The program solves the differential equations governing the transport of mass, three momentum components and energy in three-dimensional configurations. The different

governing partial differential equations are typically expressed in a general form as: Where: ρ = Air density, kg/m3 Φ = Dependent variable. V = Velocity vector. ΓΦ,eff = Effective diffusion coefficient. SΦ = Source term of Φ.

The effective diffusion coefficients and source terms for the various differential equations are listed in Table 1. The Computational Fluid Dynamics (CFD) model utilizes the following approximations in calculating the turbulence quantities, such as isotropic turbulence and the Boussinesq eddy viscosity concept.

Table 1. Values of Φ, ΓΦ,eff, and SΦ for Partial Differential Equations

Φ ΓΦ,eff SΦ Continuity 1 0 0 X-momentum U µ - ∂P/∂x+ρgx Y-momentum V µ - ∂P/∂y+ρgy Z-momentum W µ - ∂P/∂z+ρgz+ρgβ∆t H-equation H µ / σH SH RH-equation RH µ / σRH SRH τ-age equation τ µ / στ ρ

µ = µlam + µ t µ t is calculated following the present models

σH = 0.9, σRH = 0.9, στ = 0.9 G = µ [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]

Boundary conditions are presented for the

present configurations, in Kameel and Khalil 17-19 and Chow et al 5.

2.2. Numerical Procedure

The Computer Program, 3DHVAC of Kameel and Khalil 11-14, was used to solve the time-independent (steady state) conservation equations together with the standard k-ε model as Launder and Spalding 26, and the corresponding boundary conditions. The numerical solution grid divided the space of the surgical operating theatre into discritized computational cells (80 x 60 x 30 grid nodes) using the modified hyperbolic equation of Kameel and Khalil 17, as in equation 2. The discrete finite

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difference equations were solved with the SIMPLE algorithm, Patankar 32. Solution convergence criteria, was applied at each iteration and ensured the summations of normalized residuals were less than 0.1% for flow, 1% for k and ε, and 0.1% for energy. 2.3. Models Validation

Previous comparisons between measured and predicted flow patterns , turbulence characteristics, and heat transfer was reported earlier in the open literature utilizing the present models. The predictions of flow and turbulence characteristics are in general qualitative agreement with the corresponding experiments and numerical simulations published by others, Chen 3, Lin et al 28, Kameel and Khalil 20, and Zhao et al 36.

3. PARAMETRIC CASES

The model rooms considered here are practical configurations of the surgical operating theatres exist already in the Hong Kong and Egypt, Figures 1 and 2. The two room-models (Kameel et al 20 and Chow et al 5 models respectively) represents two different types of the downward flow configurations. Actually, the two room models follow two different types of the HVAC system standards, review Chow et al 5 and Kameel and Khalil 20. The simulation of first configuration, figure 1, is obtained for the vacant room, while the simulation of second configuration, figure 2, is obtained with existing of the surgical operating table.

The boundary conditions of the different simulation cases are similar, with the same terminology, to the conditions that follows in the earlier published works of Chow et al 5 and Kameel and Khalil 20.

3.1. Kameel and Khalil configuration:

The room dimensions are 6.6 m in length (L), 4.0 m in width (w), and 3.0 m in height

(H). The operating table has a length of 2.0 m and a width of 0.5 m, and is 1.0 m high. Four ceiling square perforated supply air diffusers were located at the ceiling of the room with dimensions of 0.6 m x 0.6 m; their centers were located at X, Y equal to (1.7,1.3), (4.9,1.3), (4.9,2.7), and (1.7,2.7) as shown in Figure 1. The two extract ports were located on the left wall with dimensions of 0.5 m x 0.3 m and 0.5 m x 0.2 m; the larger, lower port center point is located at 0.75 m from the floor. The higher extract port center point is located at 2.25 m from the floor, Kameel 10.

The present predictions were obtained under the steady state conditions. The supply air conditions were measured as 0.31 m/s velocity and 19.5 oC, for more details of the experimental procedure, reference should be made to Kameel 10.

3.2. Chow et al configuration and cases:

Figure 2 shows the configuration of the operating theatre.

Case 1: this was based on the measured room conditions, i.e. at discharge and extract velocities of 0.287 and 0.475 m/s respectively.

Case 2: this was based on the measured room conditions as in Case 1, but with the addition of fixed partial walls.

Case 3: this was based on the flow conditions and partial walls fully complied with the HTM requirements.

4. RESULTS

Kameel and Khalil configuration was simulated numerically using the standard low-Reynolds k - ε model with the aid of 3DHVAC program and phenomenological zero equation model obtained with the aid STACH-3 program.

Figure 3 shows the prediction of the present configuration using the 3DHVAC and STACH-3 programs. The velocity results in the vicinity of the supply air diffuser located at (X=4.9, Y=1.3) indicated poor agreement between the different models. On the other hand, the velocity

( ) ( )( ) ( ) )2(]

2/Cosh/2/Sinh)5.0n/I(Cosh/)5.0n/I(Sinh

1[L5.0LX

11

i1i1

i1kk

αβα−αβ−α

++= −

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results in the vicinity of the surgical operating theatre at the center of the theatre concluded excellent agreement. The results of temperature and relative humidity have the same general qualitative trend, actually, with some discrepancies in the details, but such differences were attributed mainly due to the great influence of buoyancy modeling effect in the STACH-3 . Indeed, the buoyancy effect is considered in the two models, but its influence is significantly pronounced in the STACH-3

Chow et al 5 had obtained their numerical results in the section X-X as indicated in figure 2. They found in the first two cases that the velocity at the operating plane (1.0 m height from the floor) is 0.2 m/s, and in the third case is 50% higher (i.e. 0.3 m/s). In the present case, it was found that velocity is different in the three cases; i.e. 0.16 m/s, 0.18 m/s, and 0.28 m/s for the cases 1, 2, and 3 respectively. There are differences, 20%, 10%, and 6.7% for the cases 1, 2, and 3 respectively. Figure 4 represents the comparison between the data obtained by Chow et al 5 using the RNG k-ε model and the data obtained in the present work. On the other hand, the airflow characteristics in the same configuration of Chow et al 5 were obtained and reported here using the model of Zhao et al 36.

Good agreement was shown in Figure 4 between the present predictions 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. Generally, the present model of 3DHVAC

program introduces acceptable comparative results.

The results of local mean age of air obtained from the CFD model are compared with the numerical results of Chow et al 5 who had evaluated the operating theatre performance for the three numerical cases. The present work simulates also the three cases for the same operating theatre of Chow et al 5, and presents the result at center of the supply diffusers. The comparison presented here showed at (X/L = 0.07, 0.14, 0.2), where X is the longitudinal direction and L is the length of the room at that section in the room. Figures 5, 6 and 7 show the comparison results. In the figure Z/H is the normalized height of the room, 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 be observed that there are some differences of the normalized local mean age in 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 indicated good agreements. Discrepancies were also observed in vicinity of the ceiling especially in the case 3, which contain fixed partial walls.

5. DISCUSSION AND CONCLUSION The aim of this study was to assess turbulence models when modeling ventilated downward flow configurations such as the surgical operating theatres. From the present investigation one can observe that the downward flow is divided to different regions depending mainly on the dimensions of the supply airflow diffusers or plenum and its relative position to the theatre. The low-Reynolds k - ε model and RNG k - ε model succeeded to distinguish between the different zones, in contrast, the zero-equation model failed to predict the real flow characteristics. The zero-equation

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model was developed on phenomenological bases on DNS (Directly Numerical Simulation) data. Fairly, this dependency will not inherent the all-internal prediction capabilities of the DNS model and its data to this simple equation. Maybe, the zero-equation model succeeded in some cases but that doesn’t overshadow doubts of its general capabilities. Finally, it is found that the low-Reynolds k - ε model and RNG k - ε model do not differ in their treatments of the downward flow. So we can support the conclusions of Holmes et al 7, that the prediction of downward flow configurations characteristics appears insensitive to the selection of the higher order turbulence models.

REFERENCES

1. Alamdari, F., Bennet, K. M., and Rose, P. M., 1994, Airflow and temperature distribution within an open-plan office building space using a displacement ventilation system, Roomvent'94, Fourth International Conference, Vol. 1, 481-495.

2. Buchanan, C., 1997, CFD characterisation of a mechanically ventilated office room: the effects of room design on ventilation performance, Ph.D. thesis, University of California.

3. Chen, Q., 1995, Comparison of different k-ε models for indoor airflow computations, Numerical Heat Transfer, Part B. Vol. 28, 353-369.

4. Chen, Q., and Xu, W., 1998, A zero-equation turbulence model for indoor airflow simulation, Energy and Buildings, Vol. 28 (2), 137-144.

5. Chow T. T., Ward, S., Liu, J. P., and Chan, F. C. K., 2000, Airflow in hospital operating theatre: the Hong Kong experience, Proceedings of Healthy Buildings 2000, Vol. 2, 419-424.

6. He, P., Kuwahara, R., and Mizutani, K., 1999, Numerical study on air-conditioned indoor airflow by

dynamic large eddy simulation, Proc. Indoor Air 1999, Vol. 1, 714-719.

7. Holmes, S. A., Jouvary, A., and Tucker, P. G., 2002, An assessment of a range of turbulence models when predicting room ventilation, Proceedings of Healthy Buildings 2000, Vol. 2, 401-406.

8. Jones, P. J., and Whittle, G. E., 1992, Computational fluid dynamics for building airflow prediction – current status and capabilities, Building and Environment, Vol. 27(3), 321-338.

9. Kameel, R., 2000, Computer aided design of flow regimes in air-conditioned spaces, M.Sc. Thesis, Cairo University.

10. Kameel, R., 2002, (In progress), Computer aided design of flow regimes in air-conditioned operating theatres, Ph.D. Thesis work, Cairo University.

11. Kameel, R., and Khalil, E. E., 2000 a, Computer aided design of flow regimes in air-conditioned Spaces, Proc. ESDA2000 ASME 5th Biennial Conference on Engineering Systems Design & Analysis, Montreaux 2000.

12. Kameel, R., and Khalil, E. E., 2000 b, Fluid flow and heat transfer in air-conditioned spaces, International Conference of Energy Systems, 2000, ICES, 2K. Page 188 –200, Amman, 25th – 28th, Sept. 2000.

13. Kameel, R., and Khalil, E. E., 2001 a, Numerical computations of the fluid flow and heat transfer in air-conditioned spaces, NHTC2001-20084, 35th National Heat Transfer Conference, Anaheim, California.

14. Kameel, R., and Khalil, E. E., 2001 b, Operating parameters affecting air quality in operating theatres: a numerical approach, Clima 2000/Napoli 2001 World Congress – Napoli (I), 15-18 September 2001.

15. Kameel, R., and Khalil, E. E., 2001 c, Air quality appraisal in air-conditioned operating theatres: numerical analysis, Clima 2000/Napoli

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2001 World Congress – Napoli (I), 15-18 September 2001.

16. Kameel, R., and Khalil, E. E., 2001 d, Air quality appraisal in air-conditioned spaces: numerical analyses, Proc.4th IAQVEC Conference, Changsha, China, Page 287-297.

17. Kameel, R., and Khalil, E. E., 2002 a, Generation of the grid node distribution using modified hyperbolic equations, 40th Aerospace Sciences Meeting & Exhibit, Reno, Nevada, AIAA-2002-656, 12-15 January 2002.

18. Kameel, R., and Khalil, E. E., 2002 b, Experimental investigations of airflow regimes in air-conditioned operating theatres, Roomvent 2002

19. Kameel, R., and Khalil, E. E., 2002 c, Predictions of flow, turbulence, heat transfer and humidity patterns in operating theatres, Roomvent 2002

20. Kameel, R., and Khalil, E. E., 2002 d, Predictions of turbulence behavior using k-ε model in operating theatres, Roomvent 2002

21. Khalil, E. E., 1978, “Numerical Procedures as a tool to Engineering Design”, Proc. Informative 78, Yugoslavia.

22. Khalil, E. E., 1994, Three-dimensional flow pattern in enclosures, Interim Report, Egyptalum, Egypt.

23. Khalil, E. E., 1999, “Fluid Flow Regimes Interactions in Air Conditioned Spaces”, Proc. 3 rd Jordanian Mech. Engineering Conference, pp. 79, Amman, May 1999.

24. Khalil, E. E., 2000, Computer aided design for comfort in healthy air conditioned spaces, Proceedings of Healthy Buildings 2000, Finland, Vol. 2, Page 461-466.

25. Lam, C. K. G., and Bremhorst, K., 1981, A modified form of the k-ε model for predicting wall turbulence, Transactions of the ASME, Vol. 103, 456-460

26. Launder, B. E., and Spalding D. B., 1974, “The Numerical Computation

of Turbulent Flows”, Computer Methods App. Mech., pp. 269-275.

27. Li, X., and Zhao, B., 1999, Report of STACH-3, Department of Thermal Engineering, Tsinghua University.

28. Lin, Z., Chow, T. T., Fong, K. F., et al, 1999, Validation of CFD model for research into application of displacement ventilation to Hong Kong Buildings, Proceedings of the 3rd International Symposium on Heating, Ventilation and Air Conditioning –ISHVAC ’99, Vol. 2, 602-613.

29. NHS Estates, 1994, Health Technical Memorandum 2025: Ventilation in healthcare, Premises, HMSO: London.

30. Nielsen, P. V., 1989, Numerical Prediction of air distribution in rooms, ASHRAE, Building systems: room air and air contaminant distribution, 1989.

31. Nielsen, P. V., 1998, The selection of turbulence models for prediction of room airflow, ASHRAE Transactions, Vol. 104, 1119-1126.

32. Patankar, S. V. 1980, Numerical heat transfer and fluid flow, 1980 Hemisphere, WDC.

33. Spalding, D. B., and Patankar, S. V., 1974, “A Calculation Procedure for Heat, Mass and Momentum Transfer in Three Dimensional Parabolic Flows”, Int. J. Heat & Mass Transfer, 15, pp. 1787.

34. Thies, A. T. and Tam, C. K. W., 1996, Computation of turbulent axisymmetric and nonaxisymmetric jet flows using the k-ε model, AIAA Journal, Vol. 34, No. 2, 309-316.

35. Yuan, X., Chen, Q., and Glicksman, L. R., 1999, Models for prediction of temperature difference and ventilation effectiveness with displacement ventilation, ASHRAE Transactions, Vol. 105, 353-367.

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Congress – Napoli (I), 15-18 September 2001.

NOMENCLATURE

k Turbulence kinetic energy, m2/s2. p Pressure, Pascal. U,V,W Instantaneous components of velocity in

three directions, m/s. X,Y,Z Coordinate directions. H Room Height SΦ Source term of entity Φ, Φ = U, V, W, … NLMA Normalized Local Mean Age N-W Normalized W velocity N-T Normalized Temperature N-RH Normalized Relative Humidity

Figure 1: Layout of Kameel and Khalil 20 δij Kronecker delta function. ε Turbulence dissipation rate. Φ Entity. Γ Molecular viscosity. µ Absolute viscosity of air, kg/ms. ρ Density of air, kg/m3.

σ Effective Prandtl number. Subscripts

i,j,k Denoting Cartesian coordinate direction takes the values of axes X, Y, Z.

t Turbulent property. o Outlet Supply (related to supply). i Inner room (related to return outlets).

Figure 2: Layout of Chow et al 5 Configuration

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Figure 4: Comparison among three turbulent models, configuration of Chow et al 5

A - Results in the vicinity of the supply diffusers

B - Results in the vicinity of the operating table (center of the theatre) Figure 3: Comparison of Kameel and Khalil 20 configuration results, using 3DHVAC and STACH-3

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Figure 5. Local Mean Age Comparison of the Case 1 of Chow et al. 5

Figure 6. Local Mean Age Comparison of the Case 2 of Chow et al. 5

Figure 7: Local Mean Age Comparison of the Case 3 of Chow et al. 5