CFD simulations of smoke detection in rooms with high ceilings

Transcription

1 Frédéric Conte CFD simulations of smoke detection in rooms with high ceilings SP AR 2002:30 Brandteknik Borås 2002 Ecole Nationale Supérieure d'ingénieurs de Mécanique Energétique de Valenciennes

2 2 Abstract In industry, there is usually a detection system placed to initiate the release of extinguishing media or s an alarm to the fire brigade in case of a fire. Fires in industrial buildings can generally cause serious damage so an early detection system is needed. Heat and smoke detectors are the most common. The detection time deps on the detector and the fire scenario. This report is included in a larger project "Early detection in rooms with high ceilings". This project consists of the study of smoke production, smoke detectors, and two problems detecting fires and will be finished by full-scale experiments. The objective of this report was to examine several scenarios which could prevent an early detection of smoke in rooms with high ceilings. Two different problems were studied: the effects of the existence of a temperature gradient on the smoke spread in a room and the effects of a ventilation system on the smoke spread in big industrial buildings. During the five-month placement, several simulations have been performed with the CFD software SOFIE. Three stages can be distinguished: determining the best model for the smoke source, the simulations of the temperature gradient and the ventilation system. A lot of time was spent to determine the best model for the smoke source doing experiments in a laboratory, and carrying out a parametric study with SOFIE to fit the experiments. The work for the simulations of the temperature gradient and the ventilation system was to find the manner to simulate a temperature gradient in SOFIE and to reach the best model for these two problems. The three different parts of this study are presented in this report. Key words: Smoke, detection, CFD, ventilation, temperature gradient. SP Sveriges Provnings- och Forskningsinstitut SP Swedish National Testing and Research Institute SP AR 2002:30 SP AR 2002:30 Borås 2002 Postal address: Box 857, SE BORÅS, Sweden Telephone: Telex: Testing S Telefax: info@sp.se

3 3 Preface This report is the result of a five-month placement carried out at Brandteknik, the department of fire technology of SP (Swedish national testing and research institute). This placement was a part of my engineer formation in France at the ENSIMEV (High institute of mechanical engineering of Valenciennes). This study was done with the collaboration of my supervisor at SP Petra Andersson who gave good advice and suggestions during the placement.

4 4 Table of contents Abstract 2 Preface 3 Table of contents 4 A - Problem position 7 1 Problems with detecting fires 7 2 Smoke source Pyrolysis Smouldering combustion 8 3 Presentation of SOFIE CFD SOFIE 10 B - Preparatory study 12 4 Parametric study Reference case The different changes and effects Conclusion 12 5 Experiments Experimental protocol Results 15 6 Tuning in the smoke source Basic script Results Boundary values Geometry Model Conclusion 23 C - Smoke spread in a room with a temperature gradient 24 7 The model in SOFIE Geometry Models and constants Interior values Solving 29 8 Results Temperature gradient in the small room Temperature gradient in the large room 34 9 Conclusion 39

5 5 D - Smoke spread in a room with a ventilation system The model Geometry Models and constants Boundary Solving Results Smoke source placed in the middle of four inflows Smoke source placed just under an inflow Conclusion Summary References Acknowledgements 54 Appix 55 A1 Results of the experiments 55 A2 Command files used in SOFIE 57 A2.1 Temperature gradient 57 A2.1 Ventilation system 61

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7 7 A - Problem position 1 Problems with detecting fires Usually in industry, there are some detectors placed to initiate the release of extinguishing media or s an alarm to the fire brigade in case of a fire. Heat and smoke detectors, are the most common. The detection time deps on the detector and the fire scenario. Early detection in rooms with ventilation and/or high ceilings is a difficult task. A simple fire can cause severe damage in many cases and therefore smoke detectors should be placed at locations where the smoke reaches the detector at an early stage of the fire. In order to calculate when a detector will be activated one should know the smoke production from the fire. Further, we need to know how the smoke is transported and the sensitivity of the detector. Fires in electrical equipment and packaging materials are relatively common in industries [1]. The smoke production from these is usually not known, especially when in the beginning of the fire there is a smouldering combustion. There is data available in the literature on smoke production from mainly pure fuels and usually from flaming combustion. Usually when doing smoke spread calculations a uniform temperature profile in the room is assumed together with no airflow before the fire starts. This is not the case in the reality, in rooms with high ceiling there is usually a significant temperature gradient and the airflow in the room can be rather large due to the ventilation system [2]. There is also the problem of other heating sources in the room that causes airflows. These problems cannot be modelled in, for instance, two zone models. In general they require CFD type of simulations. Only a very limited number of simulations of this kind have been published. Working with a CFD model, several cases can be simulated. This type of calculation is the cheapest way to undertake investigations in the smoke spread domain. In the last ten years, calculations using CFD have known a big development. The computers powerful increasing, the CFD calculations have got good results and are used nowadays in many cases. A final experiment can be carried out to conclude a study, to check and develop rules and advice.

8 8 2 Smoke source Different things can be at the origin of the smoke production. Smoke sources without flames, studied in this report, often existing before the real fire, can product a lot of smoke. Most common materials give less smoke with flaming combustion [3]. The smoke production often comes from some packaging materials and electrical equipment, in industrial buildings. 2.1 Pyrolysis The different kind of plastic used for packaging materials or electrical equipment can be an important smoke source when they are heated. When heating plastic, the plastic reaches high temperatures, melts, evaporates and so some gases are produced. In this case, the smoke consists of gases from chemical decomposition of the plastics; there are very few oxidations. The pyrolysis can be the origin of real fire. The pyrolysis is, by definition [4], an irreversible chemical decomposition of a material under the only action of the heat. It is produced by a rise of temperature without reaction with the oxygen. It should be distinguished from the combustion, which requires a contribution of oxygen and releases a lot of heat. 2.2 Smouldering combustion Only porous materials which form a solid carbonaceous char when heated can undergo selfsustained smouldering combustion. Included are a wide range of materials of vegetable origin such as paper, cellulosic fabrics, sawdust, fibreboard and latex rubber, as well as some thermosetting plastics in expanded form [3]. A smouldering combustion is combustion without flames, by oxidation, with smoke and char formation often occurring before fire. Figure 1 Photo of a polyethylene sample pyrolysis.

9 9 3 Presentation of SOFIE There has been considerable growth in the development and application of Computational Fluid Dynamics to all aspects of fluid dynamics and heat transfer. CFD has made an increasingly significant contribution to many branches of engineering since its emergence in the mid 1970 s as a practical design and analysis tool. As part of the research, design and development process, CFD programs are now considered to be standard numerical tools, widely utilised within industry. Several different CFD models exist today, general purpose codes like FLUENT and PHOENICS, or fire purpose codes such as JASMINE or SOFIE. SOFIE (Simulation Of Fires In Enclosures) is a field model using CFD written in Fortan and in C. SOFIE 3 has been written by Pr Rubini at Cranfield University. It has been developed under the sponsorship of a Consortium comprising a number of European fire research laboratories; FRS, HSE, Cranfield University and Home Office (UK); SP Borås and Lund University (Sweden); VTT (Finland); and CSTB (France). The major interest of the simulation is its low use cost. But it cannot replace experiments; it is necessary to compare the two ways to obtain the best results. 3.1 CFD CFD codes are structured around the numerical algorithms that can tackle fluid flow problems. All the field models using CFD use the same method. They first define a domain in space, the computational domain, where the simulation will be carried out. This domain is divided into a large number of small control volumes called cells, which can define a solid or a certain volume of fluid. The problem geometry and boundary conditions can be defined. Then, CFD technique is applied in order to solve a set of non-linear partial differential equations from basic laws of nature. In order to make the calculation possible, complex real phenomena are modelled. In the case of fire, a combustion model is used to simulate the course of combustion, a turbulence model is required and usually a buoyancy modified k-ε model is used to predict the turbulent flow. There are also others models for the radiation, the soot or the fire spread. Governing equations All the models solve the conservation equations for mass, movement, energy, and evaluate the species in each control volume [5]. All the conservation equations follow the same formula: t ( ρφ ) + div ( ρuφ ) = div ( Γgrad ( φ )) + S I II III IV φ Where φ is an arbitrary depent variable, I is the rate of change of φ in the control volume, II is the change of φ due to convection, III is the change of φ due to diffusion, IV is a source term.

10 10 In CFD calculations about control volumes are used with the finite volume method and it is also often possible to take advantages of symmetries in the room, using symmetry conditions, so that only a part of it needs to be simulated. The governing equations for 3D fluid flow are treated in the same way as above except that the integration is carried out over a three-dimensional control volume. The result is a set of algebraic equations, which in SOFIE is solved with for example a TDMA solver (line-by-line tridiagonal matrix algorithm) [6]. 3.2 SOFIE SOFIE solves the Reynolds averaged Navier-Stokes equation using a finite volume procedure like the other CFD models The interface Figure 2 Main menu of SOFIE. SOFIE uses a text interface pre-processor [7]. It uses five main menus: file where data exchanges (to export or to import the solutions) are dealt with, setup where the model is defined, run where the problem is solved, print where solutions can be visualized, and control where all the solver parameters are accessible. The databases are in specific files, and contain information on material and species properties that are required in order to solve the problem. Usually one writes a command file. The required type of solution is then specified. The different models for combustion, radiations, turbulence et cetera, are chosen. Then the geometry is defined. It can be imported from different software, like AC3D, where it can be defined easily. The boundary types and values are specified at the. The simulation can be run in steady state or in transient mode. The results from the simulation can be exported to visualisation software like Fieldview or Smokeview The k-ε turbulence model The k-ε turbulence model, the main model used in SOFIE for this report, is brievly presented in the following paragraph. The k-ε turbulence model is a two equation model implying that two additional transport equations, partial differential equation, are employed to determine the local turbulent viscosity, µ(x, y, z, t). Deping on the flow, different transport equations have to be used. Therefore, the k-ε model can be divided into high Reynolds number and low Reynolds number k-ε model.

11 11 The k-ε model focuses on the mechanisms that affect the turbulent kinetic energy. k is the turbulent kinetic energy and ε is the rate of dissipation of turbulent kinetic energy [8]. In words the equations are: Rate of change of k or ε Transport Transport Rate of + of k or ε by = of k or ε by + production - convection diffusion of k or ε Rate of destruction of k or ε The equation contain five adjustable constants C µ, σ k, σ ε, C 1ε and C 2ε. The values generally taken are: C µ = 0.09; σ k = 1.00; σ ε = 1.30; C 1ε = 1.44; C 2ε = Advantages: Simplest turbulence model for which only initial and/or boundary conditions need to be supplied Excellent performance for many industrially relevant flows Well established; the most widely validated turbulence model Disadvantages: More expensive to implement than mixing length model Poor performance in some cases: - Some unconfined flows - Flows with large extra strains - Rotating flows - Fully developed flows in non-circular ducts

12 12 B - Preparatory study 4 Parametric study To begin this preparatory study, a parametric study was carried out in order to determine the important parameters in the simulation of smoke spread, and to give an idea of the values of these parameters. The study consisted of trying different means of letting the smoke in as a conserved scalar and comparing them. The different changes were carried out on the parameters that can affect the results, like smoke velocity, surface temperature and area of the smoke generator. The parametric study was performed by changing one parameter at a time from the reference case i.e. the first setup of parameters. 4.1 Reference case The smoke generator was placed in the middle of a closed room 4 m high, 10 m long and 6 m wide. The simulation was done on a quart of this room with SOFIE. A box modelled the smoke source, and the smoke rose through the square top surface (20 cm x 20 cm by default). The smoke source represented a pyrolysis or smouldering combustion as explained preciously. An inflow modelled the source with a certain velocity (0.5m/s), a certain temperature at the surface (900K) and passive scalars represented the smoke. To simulate the airflow in SOFIE, the turbulent model high-re k-e was chosen. There were no combustion, no radiation, only heat transfer. Only a quart of the room was simulated in SOFIE. Mirrors in SOFIE can simulate the symmetry conditions in order to save computing time. 4.2 The different changes and effects The smoke spread was simulated for a surface temperature of 600, 750, 900, and 1200 K. The surface temperature (t_f) affected the smoke spread a lot. Indeed, the smoke spread was faster and bigger when the temperature was low, but the temperature of the room was not affected. Concerning the velocity, the values used were 0.3, 0.5 and 0.7 m/s. The smoke spread was logically faster for a high velocity, and also, the temperature of the room increased with higher velocity. Then the value of the generator surface was studied. When the smoke was generated by a larger surface, the temperature of the room increased a lot and the smoke spread is much faster. A heating part around the source, modelling the top face of the heating cone used in the next experiments called ovan, was tested. This element had almost no effects on the smoke spread, except to make the smoke plume a bit wider. 4.3 Conclusion So the important parameters to simulate a smoke spread in a room are the surface temperature, the inlet velocity, and the area of the smoke source. The values of the temperature and the velocity have to be known by doing experiments for example. The area is to some extent known by the geometry of the source.

13 13 5 Experiments The objective of the experiments was to measure the temperature and the velocity of the smoke above the source. These measurements were carried out in order to determine the boundary values to be used in the simulations. 5.1 Experimental protocol The sample used for the experiments was a square polyethylene sample, 10 cm wide. A heating cone formed by a resistance placed 2.5 cm above the sample heated it. The heating cone produced an even thermal radiation on the sample surface. It was the same type of cone calorimeter used in general in fire technology. The sample was placed, below the cone, on the top face of a metal box (figure3) containing a thermal insulator and an aluminium sheet. So, heating the plastic sample, some smoke was produced and rose through the hole of the cone. Figure 3 Plastic sample in the metal box. The temperature was measured at 6 different heights at the centre of the plume, by K thermocouples. The velocity was measured at 3 different heights, using a Pitot tube. A sampler collected all the data and transmitted them to the computer. Six tests were carried out: - Test 1: checking test - Test 2: velocity measures at 66.5 cm - Test 3: velocity measures at 66.5 cm - Test 4: velocity measures at 46.5 cm - Test 5: velocity measures at 26.5 cm - Test 6: velocity measures at 26.5 cm The first test was done to check if all the instruments worked. The plastic sample was put in place below the cone after a one-minute pre-measuring time, and then the surface temperature increased quickly. The temperature was measured at all the heights during all the tests. The temperature was measured at 1.065m, 86.5cm, 66.5cm, 46.5cm, 26.5cm, and at the sample surface.

14 14 Experimental device Figure 4 Photo of the experimental device. The photo of the experimental device is explained on the drawing below: Figure 5 Experimental device.

15 Results Figure 6 Smoke spread in the experiments. The experimental measurements for the temperature and the velocity were studied to extract some average values, which were used to compare with the simulations. Thus, getting the right parameters, the simulations could fit the experiments Temperature measures The temperature was measured at six heights during five tests. The ambient temperature was about 17 ºC. The results of the test 6 are displayed below:

16 16 temperature (C) Test 6 surface 26.5 cm 46.5 cm 66.5 cm cm 86.5 cm Time (s) Figure 7 Temperature profiles of the test 6. The results obtained were similar for all the tests (the results of all the tests are presented in appix). The values extracted below, from measures, are averages of all the tests. Surface temperature When the plastic sample was put in place under the cone after one minute, the surface temperature increased quickly. After four minutes, the temperature rose quite steadily during six minutes, and then reached a maximum of about 440 ºC, when almost the entire sample was consumed. However, it was very difficult to measure the surface temperature, so, these results have to be used carefully. At a height of 26.5 cm All the temperatures measured by thermocouples above the source fluctuated a lot. At 26.5 cm, on average, the temperature increased and reached, after 8 minutes, a level of 160ºC that was maintained. But, this value has to be used carefully because the thermocouple was close to the source and the cone could heat it. For the others thermocouples, the temperature measurements had the same profile, they increased and reached, after 8 or 9 minutes a level that was maintained. The average reached temperatures, for each height, are summed up in the following table:

17 17 Height (cm) Temperature (ºC) Velocity measures The velocity was measured at 3 heights with a Pitot tube: - At 66.5 cm: test 3 - At 46.5 cm: test 4 - At 26.5 cm: test 5 and 6 The Pitot tube measures a pressure difference P. The Bernoulli theorem is applied on the Pitot P tube placed at the centre of the plume, so the velocity is: V = 2. The density ρ deps ρ on the temperature. The law of Mariotte can be applied to the smoke, ρ T = P r, and as the pressure was almost constant, = ρ 0 T ρ 0 (with T 0 = K and ρ 0 = kg/m 3 ). So the T 2 P T velocity was calculated using V = ρ0 T0 It was very difficult to measure velocity because the values fluctuated a lot, especially at low velocities there were a lot of errors. The wanted value was the average of the reached velocity in the permanent state. At a height of 26.5 cm The results of the test 6 with the velocity measurements at 26.5 cm are displayed below:

18 18 test velocty (m/s) Time (s) Figure 8 Velocity profiles of the test 6. Two tests were carried out at this height. The velocity increased and reached on average 0.95 m/s and stayed on this value. At the two other heights, the velocity had the same profile. The average reached velocities, for each height, are summed up in the following table: Height (cm) Velocity (m/s) The results of all the tests are joined in appix.

19 19 6 Tuning in the smoke source In order to find the best way to simulate the smoke source, a parametric study was performed. The study was done modifying parameters one after one. The different changes were carried out on the boundary values, the geometry, and the model. Each of them was discussed in section 6.3, 6.4 and 6.5 below. 6.1 Basic script The simulation was done on a quart of the room at the beginning. Indeed, the symmetry conditions can be used to build mirrors in SOFIE to save computing time. To simulate the airflow in SOFIE, the turbulent model high-re k-e was chosen. There was no combustion, only heat transfer. An inflow modelled the source with a certain velocity, a certain temperature at the surface and passive scalars represent the smoke (scalar1_f = 1). The ambient temperature used was 290K like in the experiments. 6.2 Results Many simulations were carried out for this parametric study. The main results are displayed below to show the different changes. The different values were measured in the centre of the plume. There are two graphs, for the temperature and the velocity, and the simulations are briefly presented by the main parameters. temperature (K) a - 12cmx12cm; 723K; 0.15m/s 440 b - 8cmx8cm; 723K; 0.15m/s 430 c - 8cmx8cm; 723K; 0.25m/s 420 d - 8cmx8cm; 723K; 0.25m/s in the whole room 410 e - 8cmx8cm; 823K; 0.25m/s 400 f - laminar model; 723K; 0.15m/s g - 8cmx8cm; 773K; 0.25m/s in the whole room; prandtl number +10% for enthalpy 370 experiments height (m) Figure 9 Temperature profiles from the simulations.

20 20 Velocity (m/s) a - 12cmx12cm; 723K; 0.15m/s b - 8cmx8cm; 723K; 0.15m/s c - 8cmx8cm; 723K; 0.25m/s d - 8cmx8cm; 723K; 0.25m/s in the whole room e - 8cmx8cm; 823K; 0.25m/s f - laminar model; 723K; 0.15m/s g - 8cmx8cm; 773K; 0.25m/s in the whole room; prandtl number +10% for enthalpy experiments height (m) Figure 10 Temperature profile from the simulations. The main changes, which were carried out to reach a better agreement, are summed up in the following table. The different effects are quantified, a percentage is indicated to give an idea, but this value deps on all the parameters. Changes A B C D E F G H I Increasing T_f (+25%) Increasing V_f (+67%) Decreasing area (-55%) In the whole room Tke=10 Ted=0.05 cµ=0.18 cbuoy=0.8 5 Prandtl number + 10% for enthalpy Laminar model With ovan T values + (+4%) ++ (+13%) - (-2%) + (+2%) -- (-6%) - (-3%) + (+3%) +++ (+20%) O Effects T profile V values O O X O O X O XXX O + (+5%) ++ (+29%) -- (-21%) - (-4%) -- (-14%) -- (-27%) O (+5%) V profile O O X O XX XX O XX O Remarks It affected only the centre of the plume V increased on all the height Profile: O No significant effect X Small effect XX remarkable effect XXX Strong effect Values: O No significant effect + (-) increased (decreased) a bit the values ++ (--) increased (decreased) remarkably the values +++ (---) increased (decreased) strongly the values

21 Boundary values The first parameters which could be changed according to the experiment results, were the boundary values. First, the inlet velocity and the surface temperature were studied. The surface temperature measured in the experiments was about 450 C, but it was difficult to measure this temperature with a good accuracy, so this result had to be used carefully (The pyrolysis temperature of polyethylene, is reported in literature as 505 C). A first observation was that when increasing the surface temperature (t_f) in the simulation, the temperature and the velocity of the plume increased a little. Two simulations were done for example with 723K and 823K (e and c). It was more difficult to choose the inlet velocity because it was not possible to measure it experimentally. The maximum velocity observed was 0.95m/s. So the inflow velocity could be chosen changing it until the predicted maximum velocity reached the expected value of 0.95m/s. The smoke velocity increased obviously, increasing the inlet velocity (b and c). But, the temperature increased too. Thus, the temperature and the velocity of the plume were linked, and so these parameters had to be chosen together to fit the right values. But to have high temperatures with a low velocity like in the experiments, other things had to be changed. Other parameters could be studied more precisely like tke (turbulent kinetic energy) and the ted (rate of dissipation per unit turbulent kinetic energy). For the source, the chosen values were tke = 10 and ted = The temperature and the velocity of the plume obtained were compared in the previous table and the results were interesting, the temperature and the velocity were enough low compared with other values tried for tke and ted. 6.4 Geometry Some things about the geometry could be changed to match better the experiments. Indeed, like in the parametric study, the area of the surface of the smoke generator affected a lot the results. In the experiments, the used sample had an area of 100 cm 2, and the smoke raised through the hole of the cone which had an area almost three time smaller. Decreasing this area, the temperature in the plume decreased a bit and the velocity decreased a lot. A quite good result was obtained with a square 8 cm wide (64 cm 2 ). A heating part around the source, modelling the top face of the heating cone in the experiment, that was called ovan in the script, was tested in the simulations. But it did not affect so much the results, so it was not chosen. The simulations were carried out on a quart of the room and the different values were measured in the middle of the plume, so on the mirror. But, there was a difference about these values when the simulation was carried out on the whole room. This difference was due to an interpolation error. So when the interest was the values in the middle, it was better to carry out the simulation on the whole room. The mesh of the room was modified to get a better agreement. Building a finer mesh, the results of the simulation are more accurate and can match better the experiments. First of all, it was important to avoid the errors which could be created by a bad mesh. So the grid was taken finer above the smoke source on the width, but also on the height because the cells had to have, as mush as it was possible, a square shape. The ratio between the height and the width has to be

22 22 inferior to 10. There must not be also a too big difference between the sizes of the cells, so there can be some difficulties in big rooms. Figure 11 The used vertical mesh Figure 12 The vertical mesh built by the SOFIE s grid generator Figures 11 and 12 present the difference between the default mesh in the SOFIE and the mesh chosen for the simulations above the smoke source. 6.5 Model Finally, some parameters concerning the model could be modified to get a better accuracy. To try to get high temperatures with low velocities in the plume, the laminar model was tested instead of the turbulent one, without success. The results were very different; the velocity for example increased on all the height. A study on numerical simulation of thermal plumes done by Nam & Bill in 1992 has shown the used model can be modified, changing constants (C µ and C buoy ) responsible for the turbulent velocity in the energy equation, to get a better accuracy [9]. The advised values for these constants, in this study, were here C µ = 0.18 and C buoy = Indeed, This change made the velocity decrease a lot, and the temperature did not decrease so much. A last parameter was modified to try to improve the accuracy of the simulation. Following a peace of advise from Pr Rubini (author of SOFIE 3), the Prandtl number of the enthalpy was increased 10%. The result was better because there were no effects on the velocity but the temperature was a bit higher.

23 Conclusion Several simulations were done to determine the right parameters which had to be used to model the smoke source. This study was done comparing the results with the measurements of the experiments. The different changes were carried out on the boundary values, the geometry, and the model. The question of the mesh was also investigated to have more accurate results. This study allowed getting a good agreement with the experiments. To conclude, according to this study, the best parameters, to fit the experiments, could be chosen. These parameters are displayed below: - Surface temperature t_f = 773 K - Inlet velocity V_f = 0.25 m/s - Area of the source of 64 cm 2 - Scalar1_f = 1 - tke = 10 and ted = C µ = 0.18 and C buoy = The prandtl number of the enthalpy is increased 10% These parameters were used for all the simulations to model the smoke source.

24 24 C - Smoke spread in a room with a temperature gradient Several simulations were carried out in order to simulate the smoke spread in a room with a temperature gradient. Two different sizes of rooms were tested. For each room, two different values of the temperature gradient were used: 0.5 C/m and 1 C/m. 7 The model in SOFIE The problem was modelled in SOFIE. A lot of simulations were carried out to reach good results, and the chosen model is displayed below. 7.1 Geometry The first case was a small room 4 m high, 6 m wide, and 10 m long. The geometry of the room was simple; there was nothing in the room, except the smoke source. There was only a small opening of 10 cm on the bottom of two opposed walls, to avoid an overpressure. The smoke source was modelled for the geometry by a simple square box 8 cm wide and 2 cm high, placed in the centre of the room. The smoke source 4 m 6 m 10 m Figure 13 Picture of the small room in AC3D. The computational domain had to be larger than the room in order to allow air inflow and outflow to the room. The computational domain was closed by a fixed pressure boundary simulating atmospheric conditions. The second case was a large room 10 m high, 15 m wide, 20m long. The room configuration was the same as the small room, and the same smoke source was used.

25 25 The smoke source 10 m 15 m 20 m Figure 14 Picture of the large room in AC3D. The question of the mesh SOFIE uses the finite volume method to solve the equations, so the computational domain was divided in small cells. According to the simple geometry, the chosen mesh should be the same everywhere. But as the smoke source had a small size compared with the room, the mesh had to be finer to improve the accuracy of the results increasing the number of calculations above the source where there were important physical phenomenon. Moreover, the number of cells had to be limited to avoid a too long time of calculation. So, for big rooms like the one, the cells had to be rather large in the room in general, but small around the source. But this difference of size could be at the origin of problems. Indeed, there could be some errors, like discontinuities. So to decrease the difference, there should be a transition, a space with cells which had a medium size. It was difficult to find a mesh with which the results were good. The shape of the smoke spread could be quite strange; it took square shapes due to the mesh SOFIE s Cartesian grid generator was used but a considerable amount of time was spent on constructing the grid in order to achieve reasonable accuracy of the main flows without too many cells. Figure 15 shows the chosen mesh for the small room. The outlines of the walls and the computational domain are displayed in grey. The mesh was finer in the middle of the room where the smoke source was, and it was less fine outside, where nothing important happened.

26 26 Figure 15 The mesh in the small room. The size of the different cells is exposed in the figure 16. The mesh is seen from a plan at a constant height. The mesh is the same on all heights. The cells have a height of 11 cm. The number of cells used in the computational domain for the small room is cm 3 cells 2.7 cm wide Cell 9.6 cm wide Figure 16 The horizontally mesh in the small room.

27 27 In the large room, the grid has the same structure; only the size of the cells changes. They have a height of 20 cm in the room, and the other dimensions are shown in the following picture. The number of cells used in this case is cm 3 cells 2.7 cm wide Cell 12 cm wide Figure 17 The horizontally mesh in the large room. 7.2 Models and constants In this problem, only heat transfers were considered. The radiation phenomenon was not taken into account because the smoke production occured without fire and flames. In addition no combustion model was used, only heat transfer. Likewise, the heat losses trough the walls were neglected because the room did not reach a high temperature compared with the ambient temperature. This means that all the walls and the ceiling were adiabatic and declared as inactive. The used turbulence model was the high-re k-e model which is the most common. The problem used the transient solution type and the buoyancy correction for the turbulence, and the smoke was modelled by passive scalars. According to the preparatory study ( tuning in the smoke source ) which was done to improve the accuracy of the simulation, some constants concerning the models had to be modified: C µ = 0.18 and C buoy = 0.85 for the turbulence, and the Prandtl number for the enthalpy had to be increased 10% (σ = 0.77). 7.3 Boundary There were two boundaries to close the computational domain. The first boundary was the smoke source which was simulated by a box with an inflow. Indeed, the smoke was simulated by an inflow with a velocity of 0.25 m/s and a temperature of 773 K. So, the smoke source was defined as a box which blew a hot smoke (simulated by passive scalars with a boundary values scalar1_f = 1). The turbulence parameters were defined at the boundary with the following values: tke_f = 10 and ted_f = 0.05.

28 28 The outside boundary was on top of the computational domain. This boundary was modelled by a surface declared as static pressure called static pressure boundary. Only one surface like this was necessary. Static pressure boundaries provided an unspecified flow direction and could act as either mass sources or sinks; they simulated ambient conditions. The following picture shows the pressure boundary above the room: Pressure boundary Figure 18 The static pressure boundary in AC3D. 7.4 Interior values The final solution of the governing transport equations only deps upon the boundary values specified. However, the rate at which a solution may be obtained, or even if one can be obtained at all, can be influenced by initial estimates for the value of solved variables within the interior of the computational domain. This SOFIE s menu allows interior values for all solved and variables to be specified. That is why in general a component of the velocity (here v) is estimated to make easier the calculations. The value has no importance. So here, a vertical velocity v = 0.1 m/s was set for all the cells in the fluid domain. Likewise, the temperature gradient could be built in this menu. Indeed, a certain temperature could be specified for each cell. So to define a temperature gradient, a certain temperature had to be set for all the cells which were at the same height and so on for each level. In the case of the small room 4 m high, there were 41 cells which had all the same height except the first four cells. For the temperature gradient of 0.5 C/m and 1 C/m, the differences of temperature over the height were 2 C and 4 C. A simulation was run for a problem of several minutes, with only the temperature gradient, without smoke production, and the temperature gradient was maintained.

29 29 The used script in SOFIE, for a level, is displayed below: The type of variable The type of cell The number of cells for each directions x, y, z The temperature Figure 19 Extract from a script file for SOFIE. The picture 20 shows the temperature gradient of 0.5 C/m made with SOFIE in the small room. Figure 20 Temperature gradient in the small room. 7.5 Solving All the simulations were performed with a transient solution type. The solutions were exported each 20 seconds, and 10 minutes of the problem was simulated. A timestep of 1 second was chosen to have a good accuracy and a good convergence. The iterations for one timestep were considered as converging when the mass residual was less than 0.1% or when 150 iterations were completed. If the mass residual criterion was reached before 30 iterations the solver was forced to continue until 30 iterations. The mass residual was defined as the average mass error over the whole solution domain, normalised by the total mass flow into the domain. To get quicker convergence, the relax values were taken for all the variables equal to 0.2.

30 30 8 Results 8.1 Temperature gradient in the small room Two simulations were carried out in the small room with a temperature gradient of 0.5 C/m and 1 C/m. The results are described and analysed in this part. The two cases are treated in two different paragraphs Temperature gradient of 0.5 C/m There was a temperature gradient of 0.5 C/m in the room. The smoke spread from the source in the centre of the room. Three different isosurfaces of smoke after 3 minutes (scalar1 = 0.002, 0.003, 0.004) are displayed in the figure 21. This picture shows the smoke spreading in a column and reaching the ceiling. Figure 21 Smoke spread Figure 22 shows the smoke fields on a surface in the centre of the plume after 3 minutes; the colour scale is displayed on the side. Figure 22 Smoke fields in the small room after 3 minutes.

31 31 The smoke reached the ceiling and then followed the walls downwards. The smoke went down until a certain height and then, by the airflow, filled the room area at that height. After 3 minutes the smoke reached all the walls. Then the smoke layer depth increased. Figure 23 displays the outlines of the walls and the boundaries of the computational domain, a vertical surface showing the temperature gradient, and an isosurface of the smoke (scalar1 = 0.001) in grey after 10 minutes. Figure 23 Smoke spread in the small room after 10 minutes. The isosurface of smoke had a horizontal shape, and the temperature gradient was maintained except in the plume. So the smoke spread with this temperature gradient in this room, was not so different in the form than without temperature gradient.

32 32 Figure 24 Smoke fields after 10 minutes. Figure 24 shows the smoke fields after 10 minutes. The smoke stayed mainly below the ceiling near the walls Temperature gradient of 1 C/m The simulation was carried out with a temperature gradient of 1 C/m. First the smoke spread like with the other temperature gradient: it raised and reached the ceiling after 1 minute (figure 25). Figure 25 Smoke field after 1 minute. After 2 minutes (figure 26), the smoke stopped to spread horizontally and went down until a certain height. Then the smoke spread just under the ceiling became slower and the smoke spread at this height. Indeed, until it reached the ceiling, the smoke followed the airflow and the temperature from the source. Then the smoke reached the high temperature of top of the room due to the temperature gradient. The smoke temperature was less high, so the smoke went down towards lower temperatures.

33 33 Figure 26 Smoke field after 2 minutes. The smoke spread on this height during a certain time. Then, the smoke spread at the same time under the ceiling and reached the walls (figure 30). Figure 27 Smoke field after 10 minutes. After 10 minutes (figure 27), the smoke reached all the walls and the entire ceiling. It did not stay at a certain height and filled all the space up to the ceiling, like with the other temperature gradient, but the smoke layer was less low. Figure 28 Smoke spread in the small room after 3 minutes.

34 34 Figure 29 Smoke spread in the small room after 5 minutes. Figure 30 Smoke spread in the small room after 10 minutes. The three previous pictures show the smoke spread in the room during 10 minutes. The pictures content a vertical surface showing the temperature, and an isosurface of smoke (scalar1 = 0.001). After 3 minutes (figure 28), the isosurface reached the ceiling went down and spread at a height of 3.15 m during 4 minutes. It began to fill all the space when it almost reached the farthest walls after 5 minutes (figure 29). Then the smoke reached the walls and the smoke layer went down regularly (figure 30). The smoke spread was slower than with the other temperature gradient. The pictures show that the temperature field changed a bit in 10 minutes. Indeed, the smoke source heated the room, and after several minutes the high temperatures on top of the room went down with the smoke. 8.2 Temperature gradient in the large room Two simulations were carried out in the large room with a temperature gradient of 0.5 C/m and 1 C/m. The results are described and analysed together in this part, because the two cases are similar and it is easier to compare them.

35 35 Figure 31 Smoke spread with the temperature gradient of 1 C/m after 3 minutes. There was a temperature gradient in the large room of 0.5 C/m or 1 C/m, so there was a difference of 5 C or 10 C over the height. The smoke spread from the same source as in the small room. Figure 32 illustrates a surface with the temperature gradient and the same isosurface of smoke (scalar1 = 0.001) as displayed for the small room, after 3 minutes. The smoke spread normally in the plume. When it reached a certain height, the smoke started to spread downwards or stopped. The smoke field had a shape of a mushroom; figure 32 shows clearly that the smoke did not reach the ceiling after 3 minutes. As the smoke reached a too high ambient temperature, it stopped. Figure 32 Smoke spread after 3 minutes with 0.5 C/ m Figure 33 Velocity pattern of the plume.

36 36 The velocity pattern of the plume is displayed in figure 33 together with the smoke field. The velocity vectors show that the smoke went a bit down after it reached the maximum point. This type of picture gives an idea about the airflow and the circulation around the plume; the air around the source followed the inflow of the source and went down on the side. Figure 34 Smoke spread after 3 minutes with 1 C/m. Figure 34 illustrates the isosurface in the same conditions as with 0.5 C/m after 3 minutes, so the two smoke spreads are comparable. With a temperature gradient of 1 C/m, the isosurface had not exactly the same shape, but it was the same phenomenon. After 3 minutes, the smoke did not reach as high as in the 0.5 case, but the smoke spread more horizontally. The temperature gradient is visible on the picture but the colour scale is not the same as in the 0.5 case.

37 m 6.35 m Figure 35 Smoke spread with the temperature gradient of 0.5 C/m after 10 minutes. Figure 35 still illustrates the same isosurface (scalar1 = 0.001). After 10 minutes, the maximum height reached by the smoke did not changed compared with after 3 minutes: it was about 6.35 m. The figure shows that the smoke stayed at a height of 4.75 m, after it reached the maximum point. These values explain why there was not this phenomenon in the small room with the same temperature gradient. Indeed, the height of the small room was 4 m, so the temperatures were not too high on the top of the room and the smoke could reach the ceiling m 5 m Figure 36 Smoke spread with the temperature gradient of 1 C/m after 10 minutes.

38 38 With a temperature gradient of 1 C/m, the smoke reached a maximum height of 5 m; with 0.5 the maximum height was 6.35 m. The smoke spread horizontally at an average height of 3.75m. The smoke spread is bigger for the 1 case when looking at the isosurface (scalar1 = 0.001). The heights marked in the figure explain why the phenomenon did not happen totally in the small room, the smoke could find enough high temperature at 3.75 m, but the smoke reached the ceiling because the height of the room was 4 m. Figure 37 Smoke spread after 10 minutes. For 0.5 C/m Figure 38 Smoke field after 10 minutes For 0.5 C/m Figure 39 Smoke spread after 10 minutes. For 1 C/m Figure 40 Smoke field after 10 minutes. For 1 C/m Figure 37 and 38 show the isosurface of smoke with scalar1 = With this isosurface, the smoke almost reached the walls. We can see that the smoke spread between two different heights, in a specific range, until it reached the walls. Figures 39 and 40 illustrate the smoke field after 10 minutes. The figures clearly show that the smoke spread out at certain heights. The smoke spread was smaller in height with a larger temperature gradient. It can be explained by the fact that the temperature increased two times faster with the height, so the smoke stayed in a smaller range. The high densities of smoke spread slower with 1 C/m compared with 0.5. But for the low densities the spread was similar for the two cases.

39 39 9 Conclusion Different cases were simulated to show the effects of a temperature gradient on a smoke spread in a room. Two different rooms were tested, a small room 4 m high and a large room 10 m high. The chosen mesh for each room gave good results. Two values of the temperature gradient were chosen: 0.5 C/m and 1 C/m. The smoke source was modelled in order to get the best results matching the experiments. The simulations took several days, for the large room almost one week. The different simulations showed that the smoke spread could be affected by the existence of a temperature gradient in the room. In rooms with high ceilings or large temperature gradient, the temperature just under the ceiling was superior to the smoke temperature and therefore could the smoke not reach the ceiling. Therefore, the smoke stayed at a certain height (4.75 m for a temperature gradient of 0.5 C/m and 3.75 m for 1 C/m). The smoke spread had a mushroom shape, and the smoke almost reached the walls in the large room after 10 minutes. This phenomenon happened only in the large room where the room was height enough. This phenomenon can prevent the detectors from detecting the smoke. In general, the smoke detectors are placed in the ceiling in industrial buildings, so it can be difficult, when there is a temperature gradient in the room, in the summer for example, to detect the smoke early. It is an important problem because small smoke sources like smouldering combustion can be the origin of a real fire and an early detection of this type of smoke production can avoid a disaster.

40 40 D - Smoke spread in a room with a ventilation system The smoke spread was simulated in a room with a ventilation system. Two cases were modelled in a big building ventilated by a system of small inflows. The objective of these simulations was to see the effects of the ventilation system on the smoke spread, especially if the smoke did reach the ceiling. In the first case, the smoke source was placed in the middle of four inflows. In the second case, the source was placed just under a inflow. 10 The model The simulations were simulated with SOFIE and the chosen model is explained below Geometry The room, which was studied here, was a very big building 12 m high, 165 m wide and 200 m long. This room had the same features as the room where the experiments will take place in the future. The ventilation system of this room was composed of 68 vertical fans which were placed at a height of 10.3 m with a flow of 178 l/s per inflow, and an outflow placed in one of the corner 7.5 m above the floor with a flow of l/s. In the first case, the smoke source was placed in the middle of the room in the middle of four inflows (figure 21). According to the huge size of the building, only a quart of the room was simulated to save computing time. However, there were no symmetry conditions because there was only one outflow in a corner but despite this fact, one outflow was taken for each quart of room with a flow four times lower. Indeed the simulation of one quart of the room was the only way to get a result without sping to much computing time. 100 m 82.5 m 12 m Figure 41 Geometry of the quart of the room used in the first case. Figure 42 shows the distribution of the inflows in the room which was chosen to be simple and well spread out in the room. So there were 17 inflows on the quart of the room.

41 41 Smoke source 16 m 8 m 24 m Inflow 22.5 m Outflow Figure 42 Distribution of the inflows. Inflows have a circular area in reality, but square areas 22 cm wide were used in the simulation since these are easier to construct using Cartesian coordinates. The outflow taken into account in the quart of room had the same surface as the real outflow but it had a velocity four times lower. The smoke source was exactly the same as used with the temperature gradient in the room. 22 cm 22 cm 2.3 m 2.7 m 5 cm 1.8 m Figure 43 An inflow. Figure 44 The outflow in the corner. In the second case, the smoke source was placed just under an inflow. In order to save computing time, the chosen geometry was not the same. Indeed, the same distribution of inflow was taken but with only four inflows in the centre of the room. So a whole room was taken into account but with only 4 inflows and one outflow. The room 12 m high, 48 m long and 32 m wide could simulate a similar case than with a smoke source under a inflow in a corner of the real room. The

42 42 outflow taken for this case had the same velocity as in the first case, but it had a smaller area, i.e. the length was only 54 cm. Outflow Inflow 32 m 16 m 24 m 12 m 48 m Smoke source Figure 45 Geometry of the room in the second case. The question of the mesh The mesh building was a difficult task in these two cases. Indeed, the studied room had huge dimensions compared with the smoke source size or the inflow size. So a compromise had to be found between the big cells which had to structure the room and the small cells which had to describe the small phenomenon near the inflow and the smoke source. First, SOFIE s Cartesian grid generator was used to build a first grid with a big number of cells. The same method as presented in the previous chapter was used to make a transition between the fine and coarse grid. A grid of 9 cells had to be used to define the surface of the smoke source like with the temperature gradient, despite the fact that the cells had a very small width, because with 4 cells the shape of the plume was too bad. A finer mesh was used at the height of the outflow too.

43 43 Figure 46 The two different meshes used in the first case. Two simulations were done in order to check if the results were indepent to the grid. Figure 46 shows the two different meshes used in the first case in order to compare the results from two different meshes, i.e. a coarse grid at the top of the figure and a finer grid below. The coarse mesh used cells to simulate a quart of this big room. The biggest cells, which were the more numerous, were cubes 1.1 m wide. The finer mesh used cells, so almost twice as many cells, the biggest cells were cells 90 cm wide, 90 cm long and 66 cm high; this mesh was finer than the other one near the smoke source. The simulations showed that the results from the two meshes were similar, and so the doarse mesh brought good results compared with the computing time for each simulation. However, the results presented in the next part come from the finer mesh. However, if other simulations are carried out in the future, the coarse mesh can be used bringing good results. Figure 47 The coarse mesh on a quart of the room.

44 44 Figure 48 shows the mesh used in the second case. It is the same type of mesh as the coarse mesh used in the case 1. About cells were used. Figure 48 The mesh chosen in the second case Models and constants The same model was used for the two cases studied. The same model as used in the temperature gradient case was used for both cases studied with the ventilation system. Only heat transfers were considered, no radiation phenomenon and no combustion. Likewise, the heat losses trough the walls were neglected so all the walls and the ceiling were adiabatic and declared as inactive. The used turbulence model was the high-re k-e model with the buoyancy correction. The problem used the transient solution type and the smoke was modelled by passive scalars. According to the preparatory study ( tuning in the smoke source ) which was done to get a better agreement with the experiments, some constants concerning the models had to be modified: C µ = 0.18 and C buoy = 0.85 for the turbulence, and the Prandtl number for the enthalpy had to be increased 10% (σ = 0.77) Boundary The boundary conditions for the two cases were almost the same, so they are treated together. There were a lot of boundaries to close the computational domain. For each case, the computation domain was exted in order to allow air inflow and outflow. A first boundary, like with the temperature gradient was the smoke source which was simulated by a box with an inflow with a velocity of 0.25 m/s and a temperature of 773 K. The turbulence parameters were defined at the boundary with the following values: tke_f = 10 and ted_f = 0.05.

45 45 Figure 49 The static pressure boundary in the second case. The outside boundary was on top of the computational domain. This boundary was modelled by a surface declared as static pressure called static pressure boundary. Only one surface like this was necessary. Static pressure boundaries provide an unspecified flow direction and can act as either mass sources or sinks; they simulate ambient conditions. The different element of the ventilation system are the others boundaries. In the first case where one quart of the room was simulated, there were 17 inflows with a flow of 178 l/s, so they had a velocity of m/s for the vertical component. The inflow temperature was 15 C. The outflow was simulated in SOFIE as an extract boundary. Indeed, the air went out with a certain velocity which was fixed at The flow was four times lower than the real one (12500 l/s), because this case simulated four outflows for the whole room. The second case had the same boundary types. There were four inflows with still the same velocity ( m/s). The outflow velocity was maintained as in the previous case but the area was decreased to match the inflow. The temperature of the air inflow was 15 C. Figure 50 exposes the velocity pattern in the first case with the inflows in green and the outflow in yellow. Smoke source Figure 50 Velocity pattern in the first case.

46 Solving For the interior values, the same technique as in the previous chapter was used, i.e. all velocities in the V direction were set to -0.1 m/s in order to improve the solution. All the simulations were performed with a transient solution type. The solutions were exported each 20 seconds, and 15 minutes of the problem was simulated. A timestep of 1 second was chosen to have a good accuracy and a good convergence. The iterations for one timestep were considered as converging when the mass residual was less than 0.1% or when 150 iterations were completed. If the mass residual criterion was reached before 30 iterations the solver was forced to continue until 30 iterations. These were the same conditions as with the temperature gradient. The relax values were taken to 0.2 for all variables equal. In the first case, with the finer mesh, one iteration took 22 s, and with the other mesh, 12 s. For the second case, it was about 10 s.

47 47 11 Results 11.1 Smoke source placed in the middle of four inflows. This paragraph presents the results for the first studied case where the smoke source was placed in the middle of four inflows. These results come from the simulations done with the finer mesh presented previously. Figure 51 The smoke spread in the first case after 3 minutes. Figure 51 exposes two different isosurfaces of smoke (scalar1 = and ), a surface with the vertical velocity (v) fields for the inflows with the colour scale and with the u (perpicular to the outflow) velocity fields for the outflow. The velocity fields show the high velocity under the inflows and the air which went out by the outflow, so the ventilation system worked. The smoke spread normally and reached the ceiling after 3 minutes, at least for scalar1 = Indeed, the smoke source was simulated between four inflows which were quite far (8 and 12 m), so the smoke was not hampered by the air flow. The same isosurface of smoke (scalar1 = ) is displayed in the figure 52 at two different moments. The grey surface shows the smoke after 10 minutes, and the blue one after 15 minutes. For this value of scalar1 ( ) the smoke stayed above the inflows. The blue surface (15 minutes) was smaller than the grey the one. There was a phenomenon which happened after 10 minutes above the fans. The higher density of smoke spread above the inflows so they should not be affected by the ventilation system. Nevertheless, after 15 minutes, the area reached by the isosurfaces became smaller. The smoke was affected by the inflow because of the under pressure created by the inflow.

48 48 Figure 52 Isosurfaces of smoke after 10 and 15 minutes. Figure 53 shows an isosurface of (scalar1 = ) smoke and a surface with smoke fields to see the different densities of smoke. For this value of scalar1, the smoke was blown by the nearest inflows and so went down to the floor after 15 minutes. When the smoke reached the nearest inflow, the smoke reached quickly the floor and spread on the floor. The smoke fields show that the higher density of smoke stays above the inflows, just under the ceiling. Figure 53 Smoke spread after 15 minutes in the first case.

49 49 The room studied was very big so the smoke did not reach all the inflows and the walls after 15 minutes. But the smoke reached a big part of the ceiling Smoke source placed just under an inflow This paragraph presents the results for the second studied case where the smoke source was placed just under an inflow. The simulation was carried out in a special small room with only four inflows. Figure 54 Small spread in the second case after 3 minutes. Figure 54 shows two isosurfaces of smoke (scalar1 = and ) and the velocity fields for two inflows (with the colour scale) and the outflow. The velocity fields illustrate that the ventilation system worked. The inflow on the right was better described than the other in flow because it used the same fine mesh as the smoke source. After 3 minutes, the smoke stayed on the floor, blown by the inflow. More precisely, the smoke spread on the floor and began to rise on the sides. The smoke began to rise on all the sides in the same manner. No direction was chosen. After 15 minutes, the smoke managed to rise on the sides and reached the ceiling. Reaching the ceiling, a big quantity of smoke was released. An isosurface of smoke (scalar1 = ) and a surface with the smoke fields are displayed in the figure 55. The smoke reached the ceiling rising in a column on a side. The smoke reached several walls and a big part of the ceiling. The smoke fields show that the higher densities of smoke were above the inflows, just under the ceiling. There was also some smoke on the floor under each fan.

50 50 Figure 55 Small spread in the second case after 15 minutes. Figure 56 shows the velocity pattern and the smoke field above the smoke source, the surface was not taken in the middle of the plume but one metre ahead of the plume to avoid the big velocity vectors of the fan on the figure. Figure 57 illustrates the two same isosurfaces as figure 13 but after 15 minutes. After 10 minutes, the smoke chose a direction to rise and after 15 minutes, the smoke rose in a column to reach the ceiling. The velocity pattern shows that the air blew the smoke on a side and the smoke reached the ceiling. This figure illustrates the velocity directions but does not explain why this direction for the smoke was chosen. Anyway in reality, the geometry is not perfectly symmetric so the smoke chooses a direction to rise. Figure 56 Velocity pattern and smoke fields Figure 57 Smoke spread after 15 minutes