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LES VERSUS k-ε TURBULENCE MODELLING OF LARGE UNDERGROUND ARCHAEOLOGICAL FACILITIES

Eng. Omar A.A. Abdel Aziz* and Prof.Dr.Essam E.Khalil.† Cairo University, Faculty of Engineering, Giza, Egypt1, 12613

CFD simulation of air flow inside ventilated or air-conditioned archaeological tombs allows the designer to select proper design criterion for better indoor air quality, comfort and hygiene conditions; nevertheless it allows for control and monitor of airflow effects on monuments inside it. The proper selection of turbulence model and mesh size ensures the reliable and appropriate prediction capabilities of the CFD simulations. In the present work a comparison between k-ε model and Large Eddy Simulations turbulence modelling techniques was made for Rameses VII tomb’s configuration. In addition, the mesh size effect on the solution was tested. It was noticed that as the number of mesh volumes decreases, the convergence criterion is easily achieved with computations typically performed on a personal computer with Pentium IV processor of 2.0 GHz clock and 400 MHz bus speed. Although CFD prediction is a great tool for studying the effect of various parameters on the proposed system design; it has a major drawback laid down by the validation procedure and questionable accuracy. Various software packages are available now; these software packages are designed to solve different governing equations through different numerical schemes. Furthermore, these packages are equipped with powerful mesh generator that is used to discretize the domain under investigation. In this case the designer should have the appropriate experience in addition to his engineering sense to properly identify the problem and select the suitable modelling governing equations along with the appropriate turbulence closure equations. Also, the designer should be able to apply the suitable numerical methods for his application. The present work made use of packaged CFD software, FLUENT® 6.2, to make use of the different built in numerical schemes and turbulence models. Basically, turbulence model and grid size are considered here for the tomb of Rameses VII. Full description of the parametric case studies is discussed in the paper. The primary objective of the present work is to provide a practical guide for the CFD simulations of this kind of applications and to quantify the difference between LES and k-ε turbulence model. The paper ends with a brief discussion and conclusion.

Nomenclature LES= Large Eddy Simulations k= Turbulent Kinetic Energy ε= Turbulent Dissipation Rate

I. Introduction VAC airside system design is a quite difficult task, especially when we are dealing with a critical situation

like that of conditioning an archaeological tomb. Severe restrictions are imposed by archeologists in order to preserve the tomb conditions from deteriorations. Air conditioning is defined as the conditioning of air to maintain specific conditions of temperature, humidity, and dust level inside an enclosed space. These conditions are to be maintained at specific levels dictated by the local environment, type, number of visitors, required climate, the required visitors comfort and last but not least property reservation. 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 The present work follows other earlier similar work 4-9, represents a numerical study that is used to assess the proposed airside ventilation system design of the tombs in terms of comfort and healthy conditions. The present work made use of FLUENT® 6.2 in the solution of the problem. Basically, turbulence models are considered here for the tomb of King Rameses VII (KV 1), including two different approaches: Reynolds averaging and LES. It is important to develop a solid understanding of the CFD

* Demonstrator, Mechanical Power Engineering Department, Faculty of Engineering Cairo University † Professor, Mechanical Power Engineering Department, Faculty of Engineering Cairo University, and AIAA Associate Fellow for second author.

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44th AIAA Aerospace Sciences Meeting and Exhibit9 - 12 January 2006, Reno, Nevada

AIAA 2006-1105

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

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simulation reliability in both cases in order to be able to determine which method to be used. The full description of the parametric cases’ parameters is discussed later. The primary objective of the present work is to assess the airflow characteristics, thermal pattern and relative humidity configuration in the different tomb ventilation configurations in view of basic known flow characteristics.

II. Problem Formulation The parametric studies made to develop the proper understanding of the acceptable turbulence model and the

grid size. Table II-1 show the different cases made.

Table II-1: Parametric Cases description. Case Turbulence model used Grid Size KV1-1keps Realizable k-ε 89746 KV1-1LES LES, with Smagorinsky-Lilly sub grid-scale model 89746 KV1-2keps Realizable k-ε 106213 KV1-2LES LES, with Smagorinsky-Lilly subgrid-scale model 106213 KV1-3keps Realizable k-ε 114147 KV1-3LES LES, with Smagorinsky-Lilly subgrid-scale model 114147 KV1-4keps Realizable k-ε 791696 KV1-4LES LES, with Smagorinsky-Lilly subgrid-scale model 791696

The volume was discretized using GAMBIT® mesh generator. The meshing was carried using the T-Grid

method. To obtain different mesh sizes for the same geometry the interval size was changed. Four different mesh sizes were used: 89746, 106213, 114147, and 791696 tetrahedral mesh volumes. The first three meshes are made in almost 10% increment. Furthermore, the last mesh was developed to make a very fine grid to compare with.

The CFD simulations were made on an unsteady solver and the gradient formulations were made using the node-based option for better simulation for the tetrahedral cells. The boundary conditions for the above 8 cases were set all at the same values. The solutions were made up to a solution time of 300 seconds. Figure 1 below show the tomb structure and the outlets locations.

Figure II.1: KV1 structure details.

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III. Boundary Conditions Inlet Air Conditions The inlet air conditions are taken as the average day max of 40ºC and 30% relative humidity, Egyptian Code

[10], representing August conditions. If the air is allowed to freely enter the tomb, the turbulence intensity could be assumed to be 6% and the length scale is assumed to be 1 m. Furthermore, the flow is assumed to be normal to the inlet boundary.

Outlets The air outlet are set as outflow conditions where the specification of the flow rate weighing can differ from one

outlet to the other in order to allow more flexibility. More flow rate weighing is assigned to outlets near higher visitor population whereas less flow rate weighing is assigned for outlets near the tomb entrance or near lower visitor population.

Walls The walls are considered as a slab, as they are deep inside the earth, and hence are considered to be at a constant

temperature over the day equal to the wet bulb temperature of the outside air. Using the psychrometric chart it can be found that the outside air wet bulb temperature is 25ºC. Also it is assumed that the wall have zero water vapour diffusive flux. The no slip condition is enabled for all walls, while using the standard wall function for near wall treatment.

Visitors’ Bodies The visitors’ bodies are considered as isothermal walls kept at the human skin temperature of 37ºC due to the

weak clothing of the tourist in Luxor. Furthermore, it is assumed that there is no diffusive flux. These assumptions were made due to the absence of a heat flux model at these harsh room conditions. This is because all heat flux models are for humans inside air-conditioned rooms maintained at comfort conditions.

Visitors’ Faces The visitors’ faces are considered as isothermal walls kept at the human skin temperature of 37ºC as well. Also it

is assumed that there is a specified species mass fraction of 0.0411 kgw/kgd.a in order to take into account the sweat effect in moisture gain to the tomb airflow.

IV. Results and Discussions The following paragraphs describe the numerical predictions resulting from the various test cases with the two

turbulence models. Only few samples will be shown and discussed here for space limitations. It is usually very difficult to definitively decide which turbulence model is suitable to better and more adequately represent the flow configurations.

LES k-ε

Figure 2: Comparisons between the predicted velocity contours with the LES and k-ε models at z=1.8 m ,KV1-1

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Figures 2,3 and 4 showed comparisons between the two turbulence model predictions for the smallest grid of case KV1-1 of 89746 cells. The predicted velocities are similar in nature and differ in details. The two equation turbulence model predicted shorter penetration with lower temperatures near sarcophagus.

LES k-ε

Figure 3: Comparisons between the predicted temperature contours with the LES and k-ε models at z=1.8 m ,KV1-1

LES k-ε

Figure 4: Comparisons between the predicted relative humidity contours with the LES and k-ε models at z=1.8 m , KV1-1 Higher humidity was predicted by LES in the upper wall vicinity as indicated in figure 4. For a larger grid size ,case KV1-2 the same general trend was observed in figures 5,6 and 7 at time of 300 seconds with 106213 cells.

LES k-ε

Figure 5: Comparisons between the predicted velocity contours with the LES and k-ε models at z=1.8 m ,KV1-2

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LES k-ε

Figure 6: Comparisons between the predicted temperature contours with the LES and k-ε models at z=1.8 m ,KV1-2

LES k-ε Figure 7: Comparisons between the predicted relative humidity contours with the LES and k-ε models at z=1.8 m , KV1-2 In addition to the velocity contour plots, temperature and relative humidity distribution were also investigated in a vertical plane along the tomb axis. Again, the k- ε model showed to be robust and reliable; while the LES model results are still questionable. The predicted velocity, air temperature and relative humidity contours are also shown in figures 8, 9 and 10 for case KV1-3 with 114147 cells and also after 300 seconds of start of computations. Another drawback experienced with the LES turbulence model is that it resulted in high temperature regions where the temperature was higher than the inlet temperature (which is the maximum temperature in our case). This problem is only noticed in figures 6 and 9 after the sarcophagus region.

LES k-ε

Figure 8: Comparisons between the predicted velocity contours with the LES and k-ε models at z=1.8 m ,KV1-3

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LES k-ε

Figure 9: Comparisons between the predicted temperature contours with the LES and k-ε models at z=1.8 m ,KV1-3

LES k-ε

Figure 10: Comparisons between the predicted relative humidity contours with the LES and k-ε models at z=1.8 m , KV1-3 The predicted velocity , air temperature and relative humidity contours are also shown in figures 11,12 and 13 for case KV1-4 with 791696 cells and also after 300 seconds of start of the computational cycle. More differences in details were observed as anticipated. The large eddy simulation had shown more detailed variations of flow field and thermal pattern in the middle section of the tomb.

LES k-ε

Figure 11: Comparisons between the predicted velocity contours with the LES and k-ε models at z=1.8 m ,KV1-4

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LES k-ε

Figure 12:Comparisons between the predicted temperature contours with the LES and k-ε models at z=1.8 m,KV1-4

LES k-ε

Figure 13: Comparisons between the predicted relative humidity contours with the LES and k-ε models at z=1.8 m , KV1-4 The k-ε model predictions are further extended at the largest grid of 791696 to cover various time intervals as shown in figure 14 for case KV1-4 at 60,120,180 and 240 seconds for velocity filed ( the predicted velocity contours at 300 seconds were shown earlier in figure 11). There is a similarity between the relative humidity distribution and the temperature distribution as the later is a dominant factor in calculating the relative humidity. However, the relative humidity is observed to be high in the vicinity of the visitors head as shown below. The corresponding temperature predictions are shown in figure 15 for the same flow configuration and at z=1.8 m. The critical issue in the tomb climate suitability for the preservation of the artifacts and the comfort of the visitors is the prevailing relative humidity. It is worth noting that the tomb wall materials are basically limestone with large affinity to water. Therefore the percentage relative humidity in the tombs should not exceed certain limits in order to preserve the contents. As the relative humidity is directly related to presence of humans. It is important to optimize the number of visitors per time interval; a final goal of the present invrestigation.Figure 16 indicated the relative humidity contours development with time in the tomb in summer and at the climatic conditions set up above. The optimum utilization of the air movement to ventilate and reduce temperature can be attained by locating the 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. Still all shown predictions clearly indicated the usefulness of floor extracts that do not disturb the archaeological value of the tomb and do not install any artificial materials in the tombs .The influence of the recirculation zones on the visitors’ occupancy zone and also on the fresh supplied air were investigated.

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60 seconds 120 seconds

180 seconds 240 seconds

Figure 14: Predicted velocity contours at various time intervals at Z=1.8 m ,KV1-4.

60 seconds 120 seconds

180 seconds 240 seconds

Figure 15: Predicted temperature Contours at various time intervals , z=1.8 ,KV1-4

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60 seconds 120 seconds

180 seconds 240 seconds

Figure 16: Predicted relative humidity Contours at various time intervals , z=1.8 , KV1-4 From the above results, it is depicted that the k- ε model is grid independent and can obtain reliable results for CFD simulation for airflow inside enclosures. However, the results for the LES showed that for the small grid sizes, the flow is mainly solved by the sub-grid scale model and that it started to simulate the flow as the grid size was reduced as in case KV1-4 LES. This means that LES simulation for the airflow inside enclosures is still very computationally expensive; case KV1-4 LES took about 170 computational hours on a PC to reach a converged solution at a flow time of 300 s.

V. Conclusion and Recommendation

The results shown hereinbefore showed that the k- ε model is superior in the applications concerning the airflow inside enclosures. However, the crawling model LES needs exceptional care when choosing the grid size in order to be able to get reliable output.

It is recommended to use the k- ε model if the grid size could not be increased in order to account for the turbulence length scales experienced throughout the flow domain. In addition, it is advised to perform experimental validation for the above problem in order to get a confident decision about the turbulence models in hand.

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Acknowledgments The authors would like to acknowledge FLUENT® for their kind sponsorship, the Supreme Council of

Antiquities, ministry of Culture, ARE and the CAPSCU of Cairo University for continuous support.

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2000, Finland, Vol. 2, Page 461. [5] Kameel, R., 2002, Computer aided design of flow regimes in air-conditioned operating theatres, Ph.D. Thesis work, Cairo

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2002, 181-184. [7] Kameel, R., and Khalil, E. E., 2003, Energy efficiency, air quality, and comfort in air-conditioned spaces, DETC2003 / CIE

– 48255, ASME 2003, Chicago, Illinois USA, 2003. [8] Abdel-Aziz, O.A. and Khalil, E.E., 2004, CFD-Controlled Climate Design Of The Archaeological Tombs Of Valley Of

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