The legend that the Syracuse tyrant Dionysius used this specific quarry to hear the voices of war prisoners through an aperture in the upper part of the innermost ...
XXX UIT HEAT TRANSFER CONFERENCE Bologna, Italy, June 25-27, 2012
NUMERICAL INVESTIGATION ON NATURAL CONVECTION CAUSED BY SOLAR HEATING IN THE EAR OF DIONYSIUS IN SYRACUSE Gino Iannace*, Luigi Menditto°, Sergio Nardini° and Amelia Trematerra* *Built Environment Control Laboratory Ri.A.S., Seconda Università degli Studi di Napoli, 81031 Borgo San Lorenzo Aversa (CE) °Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università degli Studi di Napoli, Via Roma 29, 81031 Aversa (CE)
ABSTRACT Only in the recent period it was found that the so-called Ear of Dionysius, an artificial grotto near the city of Syracuse, is connected to the outdoor by a narrow tunnel. The unbalance between temperature of outdoor and the large quarry surfaces can generate the flow of air through the tunnel from the lower grotto to the upper room. The mass transfer can improve sound propagation and validates the legend of the tyrant who heard the prisoners’ dialogues in the cavern. In this paper the results of a numerical investigation of natural convection in the Ear of Dionysius caused by the difference of temperature values among the upper room and the lower cavern walls. The Reynolds Navier-Stokes (RANS) modelling approach with the SST-k- turbulence model was used for the investigations. The steady-state governing equations were solved using the commercial CFD solver FLUENT©. From the numerical results obtained, it was noted that the temperature differences between the upper and lower cavities causes air flow from the lower part of the cavern entrance to the connecting tunnel. A dialogue in the cavern can be easy heard in the tunnel due to the aiding effect of mass transfer. The numerical results are confirmed by on-site measurements.
INTRODUCTION The Ear of Dionysius is a well-known artificial grotto carved out of the Temenite hill near the city of Syracuse in Sicily (Italy). During the period of tyranny at Syracuse (fourth century BC), the quarries were used as prisons for enemies captured during wars and for political opponents as well, who were compelled to work as stone cutters. So it is a consolidated belief that the Ear of Dionysius in Syracuse is a man-made cave; anyway, some doubts are cast over this traditional belief. The legend that the Syracuse tyrant Dionysius used this specific quarry to hear the voices of war prisoners through an aperture in the upper part of the innermost wall in the aim of discovering conspiracy against him has stimulated the curiosity of various visitors who wanted to check by themselves the truth. The most competent visitor was Wallace Clement Sabine, the pioneer of quantitative room-acoustics, [1]. About a century ago he visited personally the location and heard local people reporting him that the tyrant Dionysius had built the quarry with such an architectural skill to be able to realize an observation spot where he could see the prisoners and understand their speech even whispered. He explained that tyrant could hear the voices of prisoners for a trumpet-like effect (a horn for deaf people) rather than to a whispering gallery effect. Recently, the first author found a horizontal iron grille beyond which some steps of a stair were visible. Persons responsible of the management of the archaeological area confirmed that the stairs led to the listening window of the tyrant Dionysius and that since a long time the access was prohibited to visitors for safety reasons. Afterwards, Iannace et al. [2] performed acoustic measurements in the quarry that confirmed the possibility of listening even whispers from the upper tunnel. The listening windows is inside a narrow tunnel which connects the large quarry with the inlet room. This room has a prismatic shape with the tunnel entrance faced south. The
heating of this wall causes a flow from the cold large quarry to upper room through the connecting tunnel. Measurements of air velocity in the listening windows have confirmed a flow from the lower cavern to the upper room. Velocity values were in the order of the meter per second. This may explain the fact that even whispers are heard at the listening windows. In the chamber of listening, the speech understanding also increases by the effects of thermal gradient and the wind speed. In fact, if the wind vertical gradient increases, also increases the sound speed in the wind direction, and the sound rays will tend to concentrate at the top with the possibility of a concentration of sound energy [3]. Mass flow rate of air moved from an ambient to another by the effect of the solar heating, the so-called solar chimney, is a topic widely investigated in particular in the bioclimatic design of buildings [4-6]. Configurations that are closer to the one investigated in this paper are the gable roofs integrated with solar chimneys to form the roof solar collectors [7-9]. Natural ventilation in atria buildings can be achieved with solar-driven, buoyancy-induced airflows through the use of an atrium space, a solar chimney channel or a combination of both. In the past the use of solar chimneys or an atrium space in buildings has been examined i.e., see Refs. [10-17].Currently computational fluid dynamics (CFD) techniques are being increasingly employed for predicting building air flows and testing natural ventilation strategies, e.g., see Refs. [6,18-22]. With the recent advances in computing power, the process of creating a CFD model and analyzing the results has become much less labor-intensive, reducing the time and therefore the cost. In the submitted paper will be presented the results of a numerical investigation on natural convection in the Ear of Dionysius caused by the solar heating of the walls of the upper cavity. The results will be discussed in terms of temperature and velocity fields and profiles. Comparisons among data from
(A) Enttrance of the Upp per Room ( Entrance of th (B) he Quarry
Figure 1A Aerial view off the Ear of Diionysius numeerical investiggation and from m measuremen nts on site willl be perfo ormed.
THE E SITE Figure 1 shows an aerial view w of the Archaaeological Park rk of Syraccuse where (A A) is the locattion of the horizontal iron ggate that closes c the fligght of stairs leeading to the observation o p oint of thee tyrant and (B B) is the locatioon of the entraance of the Eaar of Dion nysius cave. F Figure 2 show ws the entran nce to the Earr of Dion nysius from booth an externaal point of view w and an interrnal one. Figure F 3 show ws the window w of the tyrant looking from m the wind dow to the groound of the grootto and vice versa. The grrotto has a funnel-shapeed section having the heightt of about 29 m at the en ntrance and 322 m at the inneermost part. Itt extends for 665 m with an open S patttern that has a width varyin ng between 5 and 11 m, m Fig.4. The sinuous wallls converge at the top intoo an ogivaal shape. At thhe inner end off the cave, at th he height of abbout 30 m, m is a tunnel haaving a trapezzoidal section which w is abouut 10 m lon ng and 2.0 m hhigh. It opens to the stairs th hat lead to thee top of th he Greek Theeatre of Syraccuse. The totaal volume off the grotto o is about 100000 m3.
Fig gure 3 The win ndow of the tyyrant: (A) view w from the wiindow to the ground g of the grotto; (B) viice versa. the heating of seeveral walls oof an adjacen nt smaller room is con nsidered. The T numerical domain wass realized by means m of GAM MBIT taken soft ftware starting g from the geeometrical measurements m onssite by means of a Laser scaanner. The T numerical results weree obtained by the model repported in Fig. F 5. A brick k was located aabove the upp per room in ordder to sim mulate the outd door ambient aabove. The T steady-staate governing equations weere solved usinng the com mmercial CFD D solver FLUE UENT 6.3.26 [23]. [ The flow w was assu umed to be three-dimensio t onal, turbulen nt, incompresssible. All fluid therm mo-physical prroperties werre assumed to t be con nstant, except for the deependence of density onn the tem mperature (Boussinesq apprroximation) which w gives riise to the buoyancy forrces.
NUM MERICAL M MODEL DESC CRIPTION A computationnal analysis of o a three-dim mensional moodel conceerning with naatural convection in a large cavity c inducedd by
32 m
51 m
Figu ure 2 Views oof the entrancee of the Ear off Dionysius: (A A) external point of view; (B B) internal point of view.
Fig gure 4 Longitu udinal and a trransversal secctions of the grrotto.
Y
Figure 7 Grid in the room and connecting tunnel volumes. Figure 5 three-dimensional computational domain.
Pressure coupling was treated using the SIMPLE algorithm. The second-order upwind scheme was used to discretize the momentum, turbulent kinetic energy, dissipation rate and energy conservation equations. The body force weighted scheme was used to discretize pressure-velocity coupling. These were solved in a segregated manner. The under relaxation factors for pressure, density, momentum, turbulence kinetic energy, turbulence dissipation rate, turbulent viscosity, energy 0.3, 1, 1, 0.7, 0.8, 0.8, 1, 1 respectively were used to get the solution converged. In order to assign the boundary conditions onsite measurements by means of the Infrared Camera Nek TH 7102 MV were taken. In Fig. 6 the temperature field on a part of the southern and western room walls are reported. The measurements were taken at 11 a.m. hence the western wall was not yet heated. Outdoor temperature was equal to 18°C, hence the difference between the southern wall temperature and the outdoor one was nearly equal to 7°C. On the base of these observations the thermo-physical properties of the fluid were evaluated at the outdoor temperature, To, which was assumed to be equal to 300K. In order to taking into account the surfaces heating by means of solar radiation the southern room wall was at 310K, the eastern and eastern walls room and the horizontal wall above the room were at 305 K. In order to investigate the effect of the difference wall temperature values of the upper and lower cavity, a case-2 with the surface temperature of the upper cavity equal to 300K was analyzed. In both the investigated configurations the surfaces temperature of the lower cavity, that is the large cave, was considered equal to 290K.
Computation started with zero values of velocities and with pressure and temperature values equal to the outdoor ambient ones. The convergence criteria of 10-6 for the residuals of velocity components and of 10-8 for the residuals of the energy were assumed. A grid dependence test was accomplished to realize the more convenient grid size by monitoring variables like average wall heat flux on the southern room wall. Three mesh grids were analyzed, by doubling the number of nodes in the room and connecting tunnel. It was observed a variation of about 2% in terms of average wall heat flux by doubling the number of the nodes in the tunnel and upper room. The chosen mesh size was characterized by 27290 nodes in the entire domain and it was employed in this investigation because it ensured a good compromise between the computational time and the accuracy requirements. A particular of the grid in the room and connecting tunnel is reported in Fig.7. The validation of results was accomplished by comparing the numerical simulation with the onsite measurements.
RESULTS The difference among the temperatures of both outdoor ambient temperature and cave walls causes a natural flow motion from the cave entrance to open room surface. In particular, the Fig.8 shows the x-component of velocity field at the cavern entrance. It is worth noticing that the outdoor air enters from the lover part of the entrance whereas it exits from the upper one. This denotes the presence of a backflow and then a recirculating cell in the cave. This is clear by observing pathlines of particles released from the quarry entrance, which are reported in Fig.9a. Only a little part of the air entering the quarry crosses it and moves to the upper tunnel, a large recirculating cell is present under the
WesternWall
Southern Wall
Figure 6 Temperature field on the Western and Southern room walls from an Infrared Camera
Figure 8 x-component of velocity at the cavern entrance.
0 0
a)
Cave Entrance
0.4
0.6
-1
Vx [m/s]
Listening Window
0.2
-0.5
a)
-1.5 -2 -2.5 -3
b)
Location on the horizontal window mid-line [m]
Cave Entrance
0 Listening Window
0
0.2
0.4
0.6
0.8
1
Vx [m/s]
-0.5
Figure 9 Pathlines colored by velocity magnitude: a) particles released from the quarry entrance; b) particles which cross the listening windows.
-1 -1.5
b)
-2 -2.5 -3
listening window as shown in Fig. 9b. The air enters into the connecting tunnel through the listening window with velocity values of several meters for second. Velocity magnitude field at the listening window is shown in Fig.10. In Fig. 11 the profiles of the x-component of the velocity as a function of location on the horizontal and vertical window mid-line, Fig. 11a and 11b respectively. These velocity values are sufficiently high to justify a good speech understanding. The onsite measurements of velocity magnitude in proximity of the listening windows confirmed values of about 4 m/s. Pathlines for particles released from the listening window and the parapet are reported in Fig. 12a and b respectively. The air coming from the quarry below enters through the listening window and moves to the room, Fig12a. The parapet is an obstacle to the air flow so a recirculating zone is present downstream it, Fig.12b. Figure 13 shows the pathlines in the upper room. The air from the connecting tunnel enters in the upper room with a such velocity that it impinges on the opposite wall. This generates a recirculating zone in the lower part of the room. This is also clear by observing the velocity vectors in the vertical plane at the middle of the room, which is reported in Fig. 14. In particular, the air jet coming from the tunnel
Location on the vertical window mid-line [m]
Figure 11 x-component of the velocity at the listening window vs: A) Location on the horizontal window mid-line; B) Location on the vertical window mid-line. impinges on the northern wall then it separates in two branches. One part exits from the room adjacent the northern wall. This causes the inflow of outdoor air close the heated southern wall. The other part moves down adjacent the northern wall generating a recirculating zone in the lower part of the cavity that extents in the tunnel. The presence of a jet is justified for the great mass flow rate of air coming from the Listening Window
a)
Parapet
Listening Window
b)
Horizontal window mid-line
Vertical window mid-line
Figure 10 Velocity magnitude at the listening window.
Parapet
Figure 12 Pathlines colored by velocity magnitude: a) particles released from the listening window; b) particles released from parapet.
100
q [Wm-2]
80 60 40 20 0 0
Figure 13 Pathlines in the upper room colored by velocity magnitude. lower quarry. The fact that the air coming from the cave is always in the upper part of the tunnel, that is at the location of an human ear, is particularly advantageous for sound propagation and listening. In Fig. 15 is shown the temperature field in the vertical mid-plane of the room. The effect of the heating is localized adjacent to the heated walls. Local heat flux profile on a vertical line on the southern room wall in the middle of it is reported in Fig. 16. Heat flux has a maximum value at about 0.5 m from the tunnel entrance. This indicates a weaker convective heat transfer in the lower part of southern wall due to the downward flow as shown in Fig. 14. In order to study the effect of solar heating on the walls of the room, the case of uniform temperature of 300K, equal to outdoor one, for all the room walls and for the horizontal wall above the room was investigated. In Fig.17 pathlines of particles released from the cave entrance and of the particles that cross the listening window are shown. The paths are very
0.5 1 1.5 2 Distance from the tunnel entrance [m]
2.5
Figure 16 Wall Heat flux on the vertical mid-line of southern room wall similar to the previous investigated case. Therefore also when the motion is only due to the difference between the temperatures of the room and cave walls the air enters into the quarry from the bottom and a large recirculating cell is present in the part of the cave under the connecting tunnel. The velocity of the air at the listening window is of the same order of magnitude of the previous case as may be observed from Fig.18 where the velocity magnitude field at the listening window is reported. This generates also in this case the impinging jet on the northern room wall as shown in Fig. 19.
CONCLUSION In this paper a numerical analysis by means the commercial code FLUENT has been carried out in order to investigate the effect of the solar heating on air flow in the Ear of Dionysius. The analysis was carried out employed a three-dimensional turbulent model. The results have shown that the solar chimney causes air flow from the lower part of the cavern entrance to the
Figure 14 Velocity vectors in the vertical mid-plane of the room.
Figure 15 Temperature field in the vertical mid-plane of the room
Figure 17 Pathlines colored by velocity magnitude-case 2: a) particles released from the quarry entrance; b) particles which cross the listening windows.
Figure 18 Velocity magnitude at the listening window, case-2.
Figure 19 Velocity vectors in the vertical mid-plane of the room, case-2.
connecting tunnel. The buoyancy-driven natural flow was such as that the velocity in the connecting window was of several meters per second even if the difference between the temperatures of the upper and lower wall cavities was equal to 10K. Air flow from the lower to the upper cavity aids the sound propagation and the speech understanding at the listening window. NOMENCLATURE q T To V x, y, z
Heat flux Temperature Outdoor temperature Velocity Spatial coordinates
W/m2 K K m/s m
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