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Investigation of Gas Explosions in Open Geometries using EXSIM S. Mogensen, B. H. Hjertager, and T. Solberg Aalborg University Esbjerg, Niels Bohrs Vej 8, DK-6700 Esbjerg, Denmark and Telemark Technological R&D Centre, Kjølnes Ring, N-3914 Porsgrunn, Norway. Abstract The Joint Industry Project (JIP) on Blast and Fire Engineering for Topside Structures  revealed that computational fluid dynamic (CFD) modelling of gas explosions in highly con- gested and open geometries still remains a challenge. In the present study, the three realistic field scale explosion experiments specified by the Explosion Model Evaluation Project (EME)  are investigated using the explosion simulator, EXSIM. The influence of spatial and tem- poral resolutions on the gas explosion predictions is examined by varying the calculation do- main, number of control volumes and Courant number. For gas explosions in open geome- tries, the calculations show that the Courant number appears in particular to be influential in open geometries. Introduction u.c om Since the Piper Alpha disaster in 1988 where an oilrig was totally damaged by ow a gas explosion, and 167 persons were killed, much attention has been given to Com- 5g putational Fluid Dynamic (CFD) modelling of gas explosions. Today, CFD gas ex- .9 plosion models are well established for assessment of gas explosion hazards in the oil ww and gas industry. Gas explosion computer codes are even commercially available. A recent review of computer codes and physical models has been given by Hjertager & Solberg . w In order for industry and regulatory authorities to gain confidence in CFD gas explosion models, attention has recently been directed towards establishing a formal validation procedure for such models. Within the major industrial hazards research programme funded by the Council of the European Communities (CEC), a Model Evaluation Group on Gas Explosions (MEGGE) was initiated. The expert working group published a Gas Explosion Model Evaluation Protocol , which suggests a methodology for validating gas explosion models. The MEGGE work was continued by the Explosion Model Evaluation Project (EME)  sponsored by the CEC under the Fourth Framework programme. The EME project aimed at developing evaluation protocol, specifying test cases and performing protocol evaluation exercise for gas explosion models. A detailed evaluation of gas explosion models ability to predict explosions at full scale was performed in a Joint Industry Project (JIP) on Blast and Fire Engineering for Topside Structures . The JIP project was sponsored by ten oil and gas companies operating in the North Sea and the Health & Safety Executive in U.K. Gas explosion tests were performed in a rig designed to represent the scale and equipment layout of typical offshore modules. The influence of both equipment con- gestion and module confinement was investigated during the tests. Another part of the project was an explosion evaluation exercise following the MEGGE protocol, 1 where modellers were invited to participate by doing blind predictions of the gas ex- plosion tests. The objective of the present paper is to investigate gas explosions in highly congested and open geometries using the EXSIM computer code [4-8]. The JIP proj- ect revealed that such geometries still remain a challenge for CFD gas explosion mod- els. The three realistic field scale explosions specified in the EME project is therefore added to the EXSIM validation database [7,8]. The test rigs C1 and C2 are highly congested and open geometries typical for onshore gas storage and processing site. The test rig C3 is a highly congested and confined offshore platform module where focus is on the effect of the blast wave on two external vessels. The influence of spa- tial and temporal resolutions on the gas explosion predictions is examined by varying the calculation domain, number of control-volumes and Courant number. Geometry of case C1, C2 and C3 The realistic field scale explosion test rigs C1, C2 and C3 of the Explosion Model Evaluation Project (EME)  are generated from accompanying CHAOS ge- ometry files. The geometries are imported into ACADR14, which is used as pre- processor for EXSIM. u.c om 5g ow ww .9 w Figure 1: Visualisation of the computer model implementation of the C1 geometry. The test rig C1 shown in Figure 1 represents a typical onshore gas storage or processing site. The rig comprises a single, cuboidal congested region of pipework, vessels and support structures. The total number of obstacles is 734. The dimension of the rig is 5.3m long, 8.3 m wide and 3.5 m high. At the time of ignition, the entire rig is filled with a stoichiometric mixture of propane in air. The ignition point is placed centrally at ground level. 2 Figure 2: Visualisation of the computer model implementation of the C2 geometry. The test rig C2 shown in Figure 2 represents again a typical onshore gas stor- age or processing site. Now, the rig comprises a single, long, thin congested region of pipework, vessels and support structures. The total number of obstacles is 1584. The dimension of the rig is 29 m long, 4.7 m wide and 2.5 m high. At the time of igni- tion, the entire rig is filled with a mixture of natural gas in air and oxygen. The measured composition is 9.5 % v/v methane and 21.9 % v/v oxygen. This mixture is assumed equivalent to methane in air with an equivalence ratio of 1.1. The ignition point is located 1.2 m above ground level at the far left of Figure 2. u.c om Figure 3: Visualisation of the computer model implementation of the C3 geometry. 5g ow The test rig C3 shown in Figure 3 represents at full scale a single module .9 within an offshore platform. The measurements include the loading received by two ww vessels placed approximately 25 m away from the module. The module itself is 25.6 w m long, 8 m wide and 8 m high. The entire module is filled with premixed methane in air at an equivalence ratio of 1.08. A single ignition point, placed in the middle of the module, is considered. Modelling approach Before the gas explosion predictions can be performed, the geometry must be interpreted by the gas explosion computer code. Since turbulence generated by flow interactions with obstacles determines the flame acceleration mechanism, the obstacle representation on the numerical grid is a key feature in CFD modelling of gas explo- sions. The obstacle representation is also decisive for how grid dependent the nu- merical solution is. Gas explosion scenarios interesting to industry involve obstacles with dimensions over a wide range of scales. If the evolving shear layers behind the obstacles are numerically resolved, the obstacles are said to be fully resolved. Such obstacles are well represented on the numerical mesh and will not cause any grid ef- fects. Fully resolved obstacles are, however rare in practical gas explosion scenarios. If the obstacle dimensions are significantly smaller than the mesh size, the obstacles are said to be unresolved. Unresolved obstacles are handled in CFD modelling of gas explosions by volume averaging the governing transport equations. The unresolved obstacles affect the gas explosion by introducing additional flow blockage through volume and area porosities. Additional flow resistance through sub-grid models for 3 momentum, energy, turbulence and combustion is also introduced. If the averaging procedure and the sub-grid models are well defined, unresolved obstacles should not cause any grid effects. In practical gas explosion scenarios, however, several obsta- cles will only be partly resolved. For such obstacles will some grid effects be inevita- ble. In an attempt to control undesired grid effects, a fixed grid resolution, for which the gas explosion models are tuned, is therefore often recommended. The Joint Industry Project (JIP) on Blast and Fire Engineering for Topside Structures  clearly indicated that sub-grid models for flame area enhancement and successive flame acceleration in case of multiple obstacles in a control-volume are important for CFD modelling of gas explosions in highly congested geometries. These sub-grid models are strongly grid dependent, because they depend on the num- ber of obstacles contained in each control-volume. In EXSIM, there is work in prog- ress to eliminate this grid dependence in the combustion sub-grid models. Observed parameters CFD gas explosion codes can offer detailed information of the flow field as full spatial and temporal variations are provided for all variables. Owing to storage re- quirements, the program output is usually limited to time histories for a few variables at selected monitoring points and to a few variable fields at selected time steps. The following time histories are provided by EXSIM: • • Maximum overpressure anywhere u.c om ow Overpressure at monitoring points • 5g Kinetic energy at monitoring points • Product fraction at monitoring points • .9 Average pressure on monitoring walls ww w The strength of the explosion can be characterised by the maximum overpres- sure anywhere in the calculation domain. For structural response calculations, the pressure impulse is as important as the explosion strength. The pressure impulse can be found from the pressure-time histories. In addition to the maximum overpressure and time to maximum overpressure, the pressure pulse rise time and duration are im- portant parameters characterising the pressure impulse. Typical pressure-time histo- ries for an explosion in test rig C1 are illustrated in Figure 4. Here, the pressure is monitored at 4 internal sensors. 0,50 0,40 Overpressure (bar) 0,30 0,20 P1 P2 0,10 P3 P4 0,00 50 100 150 200 250 -0,10 Time (msec) -0,20 4 Figure 4: Typical pressure-time histories for 4 internal pressure monitoring points in test rig C1. The time histories of kinetic energy can provide information of the drag forces subjected by the blast wave on for instance pipes. Likewise, the time histories of av- erage pressure on monitoring walls can give the loads subjected on blast walls by the explosion. Finally, the production fraction at monitoring points can be used as ioni- sation gaps to monitor the flame position as function of time. Simulations of case C1 The gas explosion scenario for test rig C1 has been investigated for different spatial and temporal resolutions. Predictions have been performed for three different grid sizes and for three different Courant numbers (CFL). Besides, the influence of the boundary conditions is investigated by doing predictions with two different com- putational domains. The maximum predicted overpressures are listed in Table 1. In comparison, the maximum measured overpressure is 360 mbar. Table 1: Maximum predicted overpressure (mbar), test rig C1. Shaded case gives “best” agreement with experiment. om Cell size CFL Domain 1 Domain 2 u.c 0.5 49 51 0.25 m 1.0 31 38 2.0 0.5 5g ow 11 397 15 400 .9 0.50 m ww 1.0 2.0 191 22 201 22 w 0.5 1100 1137 1.0 m 1.0 411 426 2.0 34 43 The predictions are seen to be strongly dependent on grid refinements. The combustion sub-grid models are most likely responsible for this deficiency. As the mesh becomes coarser, the number of obstacles contained in each control volume in- creases. Accordingly, the combustion sub-grid models become increasingly more in- fluential. For the present obstacle configuration, a grid size of about 0.5 m appears to be optimal. A similar strong dependence is also observed by reducing the Courant number. The numerical algorithm is implict, so that there are no formal stability requirements on the time stepping. Nevertheless, the time stepping must be small enough to resolve the appropriate pressure waves. Clearly, a Courant number larger than one is not ap- propriate for open geometries. Even a Courant number of one, which means that a gas particle can move one grid cell during one time step, seems to be too large. A Courant number of 0.5 appears to be optimal for open geometries. Since we are not interesting in resolving acoustic waves, the Courant number should not be much smaller than one. A comparison of pressure-time histories for two simulations with different Courant numbers is given in Figure 5. 5 Changing the computational domain appears to have little effects on the pre- dictions. Apparently, a computational domain, which extends one rig length in each direction, is sufficient for test rig C1. A scatter-plot with maximum predicted against maximum observed overpres- sure at all the 19 pressure sensors in case C1 is shown in Figure 6. At 17 out of 19 sensors, the maximum predicted overpressure is within a factor of two of the maxi- mum observed overpressure. The remaining two sensors are external ones which measure the far field blast wave. 0,40 0,30 Overpressure (bar) 0,20 CFL=0.5 CFL=1 0,10 0,00 0 50 100 150 200 250 -0,10 time (msec) Figure 5: Comparison of pressure-time histories at internal pressure sensor 1 for two different Courant numbers (CFL), test rig C1. u.c om 1000 5g ow .9 Max predicted overpressure (mbar) 100 w ww 10 Case C1 Wanted factor of 2 1 1 10 100 1000 Max observed overpressure (mbar) Figure 6: Scatter-plot for the 19 pressure sensors in case C1, Courant number (CFL) of 0.5. Simulations of case C2 Like test rig C1, the gas explosion scenario for test rig C2 has been investi- gated for different spatial and temporal resolutions. Predictions have been performed for two different grid sizes and for three different Courant numbers (CFL). Since the polythene sheeting covering the entire obstacle arrangement in the experiments was not cut prior to ignition and was left to fail as a result of the overpressures generated by the explosion, predictions both with and without polythene sheeting have been 6 conducted. The maximum predicted overpressures are listed in Table 2. In compari- son, the maximum measured overpressure is 220 mbar. However, one pressure trans- ducer placed in the region where the highest pressure occurred was reported to be out of order. The predictions of case C2 exhibit very much the same behaviour as for case C1 with respect to spatial and temporal resolutions. Again, a grid size of 0.5 m and a Courant number of 0.5 appear to be optimal. Whether or not, the polythene sheeting is included in the computations appears to be unimportant. The numerical polythene sheeting is assumed to open cell-wise as the local overpressure exceeds 10 mbar. Table 2: Maximum predicted overpressure (mbar), test rig C2. Shaded case gives “best” agreement with experiment. Cell size CFL No polythene sheet Polythene sheet 0.5 428 482 0.50 m 1.0 179 254 2.0 23 Diverged 0.5 5639 5935 1.0 m 1.0 603 629 2.0 841 1231 om A scatter-plot with maximum predicted against maximum observed overpres- u.c sure at all the 8 pressure sensors in case C2 is shown in Figure 7. Five of the pre- dicted pressure sensors lie within 13% of the observed values. The remaining pre- ow dicted pressure sensors are within a factor of two of the observed values .9 5g 1000 www Max predicted overpressure (mbar) 100 10 Case C2 Wanted factor of 2 1 1 10 100 1000 Max observed overpressure (mbar) Figure 7: Scatter-plot for the 8 pressure sensors in case C2, Courant number (CFL) of 0.5. Simulations of case C3 As test rig C3 was part of the Joint Industry Project (JIP) on Blast and Fire Engineering for Topside Structures , the module geometry is already included in the EXSIM validation database. A new feature of the Explosion Model Evaluation Project (EME)  is the interaction of the blast wave with two cylindrical vessels lo- 7 cated outside the explosion test rig as indicated in Figure 3. The test rig C3 has been well predicted in the joint industry project with a cell size of 0.5 m. Only the influence of the Courant number has therefore been investi- gated here. A comparison of pressure-time histories for Courant numbers 0.5 and 2.0 is shown in Figure 8. In contrast to the open geometries C1 and C2, the internal peak pressure of the relatively confined geometry C3 is observed to be only moderately af- fected by the Courant number. The time to peak pressure occurs in all cases much earlier with a smaller Courant number. 4,00 3,50 3,00 Overpressure (bar) 2,50 2,00 1,50 CFL=0.5 CFL=2 1,00 0,50 0,00 0 100 200 300 400 500 -0,50 om Time (msec) Figure 8: Comparison of pressure-time histories at internal pressure sensor 1 for two different Courant numbers (CFL), test rig C3. ow u.c .9 5g ww Scatter-plots with maximum predicted against maximum observed overpres- sure at all the 67 pressure sensors in case C3 are shown in Figure 9 and 10 for Courant w numbers 0.5 and 2.0, respectively. A reduction of the Courant number appears to in- crease slightly the overpressure in all the pressure sensors. The effect is, however, most pronounced for the external pressure sensors at the two cylindrical vessels. Again, the external blast wave seems to be better predicted with a Courant number of 0.5. 10000 Max predicted overpressure (mbar) 1000 CFL=0.5 100 Wanted Factor of 2 10 1 1 10 100 1000 10000 Max observed overpressure (mbar) Figure 9: Scatter-plot for the 67 pressure sensors in case C3, Courant number (CFL) 8 of 0.5. 10000 Max predicted overpressure (mbar) 1000 CFL=2 100 Wanted Factor of 2 10 1 1 10 100 1000 10000 Max observed overpressure (mbar) Figure 10: Scatter-plot for the 67 pressure sensors in case C3, Courant number (CFL) of 2.0. om Overall performance of EXSIM u.c After having examined the effects of Courant number for the three realistic field scale explosion test rigs; C1, C2 and C3 of the Explosion Model Evaluation ow Project (EME) , a natural choice is to perform a similar examination of the EXSIM 5g validation database. Scatter-plots comparing the predicted maximum overpressure of .9 all pressure sensors with that observed experimentally are shown in Figure 11 and 12 ww for Courant numbers 0.5 and 2.0, respectively. The overall response to changes in the w Courant number for the EXSIM validation database is much the same as that for the test rigs C1, C2, and C3. If the Courant number is reduced, the maximum overpres- sure appears to increase slightly. The effect is again most pronounced when open geometries and external blast waves are considered. A statistical analysis evaluating explosion model performance has been sug- gested in the Gas Explosion Model Evaluation Protocol . By taking the ratio of the predicted value to the corresponding observed value and plotting the geometric vari- ance (VG) against the geometric mean (MG), the model performance is graphically identified. This is illustrated in Figure 13, where the EXSIM model performance is summarised. A solid parabola defining the minimum possible VG value for a given MG is also included in the graph. The two dotted lines represent a factor of two agreement between mean predictions and observations. A perfect model that is the predictions are in perfect agreement with the observation with no scatter is located in the point (1,1). Models located on the parabola are under- or over-predicting consis- tently by the same factor for all predictions, whereas models on the vertical abscissa under- and over-predict with roughly the same factor. EXSIM is observed to be a model of the last kind. The overall model performance of EXSIM is noticed not to be significantly changed by altering the Courant number. 9 EXSIM v3.0, CFL=0.5 10000 1000 Simulated data (mbar) 100 Test cases Wanted Factor of 2 Series4 10 1 1 10 100 1000 10000 Experimental data (mbar) Figure 11: Scatter-plot for all test cases, Courant number (CFL) of 0.5. EXSIM v3.0, CFL=2 10000 u.c om ow 1000 Simulated data (mbar) 100 .9 5g Test cases ww C1, C2, C3 Wanted 10 Factor of 2 1 1 w 10 100 1000 10000 Experimental data (mbar) Figure 12: Scatter-plot for all test cases, Courant number (CFL) of 2.0. Scatter diagram VG 10 CFL=2 CFL=0.5 Minimum scatter Factor of -2 1 Factor of +2 0,1 1 10 MG 10 Figure 13: Minimum scatter diagram, comparing two different Courant numbers Conclusion The three realistic field scale explosion test rigs C1, C2 and C3 specified in the Explosion Model Evaluation Project (EME)  have been added to the EXSIM vali- dation database. The test rigs C1 and C2 are highly congested and open geometries typical for onshore gas storage and processing site. The test rig C3 is a highly con- gested and confined offshore platform module where the blast wave on two external vessels is a key feature. The influence of spatial and temporal resolutions on the gas explosion calcu- lations has been investigated by varying the calculation domain, number of control volumes and Courant number. For highly congested geometries, the influence of grid resolution has been found to be significant. The combustion sub-grid models for flame area enhancement and successive flame acceleration due to multiple obstacles are most likely responsi- ble for this deficiency since they are strongly dependent on the number of obstacles contained in each control-volume. For a coarser grid, more obstacles are contained in each control-volume, and the combustion sub-grid models become more influential. For open geometries and external blast waves, the influence of the Courant om number has been found to be important. While the Courant number can be above one u.c for confined geometries, the Courant number must be below one for open geometries in order to predict the peak pressure correctly. A Courant number of 0.5 appear to be optimal for the test rigs considered. 5g ow The overall model performance of EXSIM is investigated by using the statisti- .9 cal analysis suggested in the Gas Explosion Model Evaluation Protocol  on the ww peak pressure. EXSIM is found to predict on average the observed peak pressure, but EXSIM tends to under- and over-predict with the same factor. w Acknowledgement The work on gas explosions at Aalborg University Esbjerg and Telemark Technologi- cal R&D Centre has been financially supported by Shell Research Ltd. UK. References 1 “Gas Explosion Model Evaluation Protocol, Model Evaluation Group”, European Communities, Directorate-General XII, Science Research and Development, January 1996. 2 “Explosion Model Evaluation Project (EME), Model Evaluation Group”, Euro- pean Communities, Directorate-General XII, Science Research and Development, June 1998. 3 “Joint Industry Project on: Blast and Fire Engineering for Topside Structures, Phase 2”, Eds. Selby, C.A. & Burgan, B.A., SCI-P-253, The Steel Construction Institute, Ascot, UK, 1998. 4 Hjertager B.H., “Simulation of Transient Compressible Turbulent Reactive Flows”, Combustion Science and Technology, Vol. 41, pp. 159-170, 1982. 11 5 Hjertager, B.H. Numerical Simulation of Flame and Pressure Development in Gas Explosions. SM Study No. 16, University of Waterloo Press, Ontario, Can- ada, pp. 407-426, 1982. 6 Hjertager, B.H., Solberg, T. & Nymoen, K.O., “Computer Modelling of Gas Ex- plosion Propagation in Offshore Modules, J. Loss Prev. Process Ind., Vol. 5, No. 3, pp. 165-174, 1992. 7 Sæter, O., Solberg, T. & Hjertager, B.H., “Validation of the EXSIM-94 Gas Ex- plosion Simulator”, Proceedings 4th International Conference and Exhibition "Offshore Structures - Hazards, Safety and Engineering", London, UK, December 12-13, 1995. 8 Hjertager, B.H. & Solberg, T., “A Review of Computational Fluid Dynamics (CFD) Modelling of Gas Explosions”, in Prevention of Hazardous Fires and Ex- plosions, Eds. Zarko, V.E. et al., Kluwer Academic Publishers, pp. 77-91, 1999. u.c om 5g ow ww .9 w 12
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