Evaluation of different heat transfer conditions on an automotive turbocharger

This paper presents a combination of theoretical and experimental investigations for determining the main heat fluxes within a turbocharger. These investigations consider several engine speeds and loads as well as different methods of conduction, convection, and radiation heat transfer on the turbocharger. A one-dimensional heat transfer model of the turbocharger has been developed in combination with simulation of a turbocharged engine that includes the heat transfer of the turbocharger. Both the heat transfer model and the simulation were validated against experimental measurements. Various methods were compared for calculating heat transfer from the external surfaces of the turbocharger, and one new method was suggested. The effects of different heat transfer conditions were studied on the heat fluxes of the turbocharger using experimental techniques. The different heat transfer conditions on the turbocharger created dissimilar temperature gradients across the turbocharger. The results show that changing the convection heat transfer condition around the turbocharger affects the heat fluxes more noticeably than changing the radiation and conduction heat transfer conditions. Moreover, the internal heat transfers from the turbine to the bearing housing and from the bearing housing to the compressor are significant, but there is an order of magnitude difference between these heat transfer rates.The Swedish Energy Agency and KTH Royal Institute of Technology sponsored this work within the Competence Centre for Gas Exchange (CCGEx).Aghaali, H.; Angström, H.; Serrano Cruz, JR. (2015). Evaluation of different heat transfer conditions on an automotive turbocharger. International Journal of Engine Research. 16(2):137-151. doi:10.1177/1468087414524755S137151162Romagnoli, A., & Martinez-Botas, R. (2012). Heat transfer analysis in a turbocharger turbine: An experimental and computational evaluation. Applied Thermal Engineering, 38, 58-77. doi:10.1016/j.applthermaleng.2011.12.022Romagnoli, A., & Martinez-Botas, R. (2009). Heat Transfer on a Turbocharger Under Constant Load Points. Volume 5: Microturbines and Small Turbomachinery; Oil and Gas Applications. doi:10.1115/gt2009-59618Baines, N., Wygant, K. D., & Dris, A. (2010). The Analysis of Heat Transfer in Automotive Turbochargers. Journal of Engineering for Gas Turbines and Power, 132(4). doi:10.1115/1.3204586Serrano, J. R., Olmeda, P., Páez, A., & Vidal, F. (2010). An experimental procedure to determine heat transfer properties of turbochargers. Measurement Science and Technology, 21(3), 035109. doi:10.1088/0957-0233/21/3/035109Bohn, D., Heuer, T., & Kusterer, K. (2005). Conjugate Flow and Heat Transfer Investigation of a Turbo Charger. Journal of Engineering for Gas Turbines and Power, 127(3), 663-669. doi:10.1115/1.1839919Galindo, J., Luján, J. M., Serrano, J. R., Dolz, V., & Guilain, S. (2006). Description of a heat transfer model suitable to calculate transient processes of turbocharged diesel engines with one-dimensional gas-dynamic codes. Applied Thermal Engineering, 26(1), 66-76. doi:10.1016/j.applthermaleng.2005.04.010Sirakov, B., & Casey, M. (2012). Evaluation of Heat Transfer Effects on Turbocharger Performance. Journal of Turbomachinery, 135(2). doi:10.1115/1.4006608Serrano, J., Olmeda, P., Arnau, F., Reyes-Belmonte, M., & Lefebvre, A. (2013). Importance of Heat Transfer Phenomena in Small Turbochargers for Passenger Car Applications. SAE International Journal of Engines, 6(2), 716-728. doi:10.4271/2013-01-0576Larsson, P.-I., Westin, F., Andersen, J., Vetter, J., & Zumeta, A. (2009). Efficient turbo charger testing. MTZ worldwide, 70(7-8), 16-21. doi:10.1007/bf03226965Aghaali, H., & Ångström, H.-E. (2012). Turbocharged SI-Engine Simulation With Cold and Hot-Measured Turbocharger Performance Maps. Volume 5: Manufacturing Materials and Metallurgy; Marine; Microturbines and Small Turbomachinery; Supercritical CO2 Power Cycles. doi:10.1115/gt2012-68758Leufven, O., & Eriksson, L. (2012). Investigation of compressor correction quantities for automotive applications. International Journal of Engine Research, 13(6), 588-606. doi:10.1177/146808741243901

Computational fluid dynamics assessment of subcooled flow boiling in internal-combustion engine-like conditions at low flow velocities with a volume-of-fluid model and a two-fluid model

The use of subcooled flow boiling is a convenient option for the thermal management of downsized engines, but proper control of the phenomenon requires the accurate prediction of heat transfer at the coolant side, for which the use of computational fluid dynamics is a suitable alternative. While in most of the applications found to engine cooling a single-fluid equivalent method is used, in this paper the performance of a twofluid method is evaluated in engine-like conditions with special interest in the low velocity range. The results indicate that the description of the process at low velocities provided by the two-fluid method is better than that of a single-fluid model, while model calibration is simpler and more robust and the computational cost is substantially reduced.The equipment used in this work was partially supported by FEDER project funds 'Dotacion de infraestructuras cientifico tecnicas para el Centro Integral de Mejora Energetica y Medioambiental de Sistemas de Transporte' (grant number FEDER-ICTS-2012-06), framed in the operational program of the unique scientific and technical infrastructure of the Ministry of Science and Innovation of Spain. This work was partially supported by Senacyt Panama (Omar Cornejo, grant 797-7-2)Torregrosa, AJ.; Olmeda González, PC.; Gil Megías, A.; Cornejo, O. (2015). Computational fluid dynamics assessment of subcooled flow boiling in internal-combustion engine-like conditions at low flow velocities with a volume-of-fluid model and a two-fluid model. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering. 229(13):1830-1839. https://doi.org/10.1177/0954407015571674S1830183922913Pang, H. H., & Brace, C. J. (2004). Review of engine cooling technologies for modern engines. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 218(11), 1209-1215. doi:10.1243/0954407042580110Burke, R. D., Brace, C. J., Hawley, J. G., & Pegg, I. (2010). Review of the systems analysis of interactions between the thermal, lubricant, and combustion processes of diesel engines. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 224(5), 681-704. doi:10.1243/09544070jauto1301Steiner, H., Brenn, G., Ramstorfer, F., & Breitschadel, B. (2011). Increased Cooling Power with Nucleate Boiling Flow in Automotive Engine Applications. New Trends and Developments in Automotive System Engineering. doi:10.5772/13489Li, Z., Huang, R.-H., & Wang, Z.-W. (2011). Subcooled boiling heat transfer modelling for internal combustion engine applications. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 226(3), 301-311. doi:10.1177/0954407011417349Hawley, J. G., Wilson, M., Campbell, N. A. F., Hammond, G. P., & Leathard, M. J. (2004). Predicting boiling heat transfer using computational fluid dynamics. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 218(5), 509-520. doi:10.1243/095440704774061165Li, G., Fu, S., Liu, Y., Liu, Y., Bai, S., & Cheng, L. (2009). A homogeneous flow model for boiling heat transfer calculation based on single phase flow. Energy Conversion and Management, 50(7), 1862-1868. doi:10.1016/j.enconman.2008.12.029Chen, J. C. (1966). Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow. Industrial & Engineering Chemistry Process Design and Development, 5(3), 322-329. doi:10.1021/i260019a023Torregrosa, A. J., Broatch, A., Olmeda, P., & Cornejo, O. (2014). Experiments on subcooled flow boiling in I.C. engine-like conditions at low flow velocities. Experimental Thermal and Fluid Science, 52, 347-354. doi:10.1016/j.expthermflusci.2013.10.004Robinson, K., Hawley, J. G., & Campbell, N. A. F. (2003). Experimental and modelling aspects of flow boiling heat transfer for application to internal combustion engines. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 217(10), 877-889. doi:10.1243/095440703769683289Lee, H. S., & O’Neill, A. T. (2009). Forced convection and nucleate boiling on a small flat heater in a rectangular duct: Experiments with two working fluids, a 50–50 ethylene glycol—water mixture, and water. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 223(2), 203-219. doi:10.1243/09544070jauto1008Biswas, R., & Strawn, R. C. (1998). Tetrahedral and hexahedral mesh adaptation for CFD problems. Applied Numerical Mathematics, 26(1-2), 135-151. doi:10.1016/s0168-9274(97)00092-5Hernandez-Perez, V., Abdulkadir, M., & Azzopardi, B. J. (2011). Grid Generation Issues in the CFD Modelling of Two-Phase Flow in a Pipe. The Journal of Computational Multiphase Flows, 3(1), 13-26. doi:10.1260/1757-482x.3.1.13Pioro, I. L., Rohsenow, W., & Doerffer, S. S. (2004). Nucleate pool-boiling heat transfer. II: assessment of prediction methods. International Journal of Heat and Mass Transfer, 47(23), 5045-5057. doi:10.1016/j.ijheatmasstransfer.2004.06.020Saiz Jabardo, J. M. (2010). An Overview of Surface Roughness Effects on Nucleate Boiling Heat Transfer~!2009-10-31~!2010-01-01~!2010-04-16~! The Open Transport Phenomena Journal, 2(1), 24-34. doi:10.2174/1877729501002010024Podowski, M. Z. (2012). TOWARD MECHANISTIC MODELING OF BOILING HEAT TRANSFER. Nuclear Engineering and Technology, 44(8), 889-896. doi:10.5516/net.02.2012.720Lo, S., & Osman, J. (2012). CFD Modeling of Boiling Flow in PSBT 5×5 Bundle. Science and Technology of Nuclear Installations, 2012, 1-8. doi:10.1155/2012/795935Del Valle, V. H., & Kenning, D. B. R. (1985). Subcooled flow boiling at high heat flux. International Journal of Heat and Mass Transfer, 28(10), 1907-1920. doi:10.1016/0017-9310(85)90213-3Cole, R. (1960). A photographic study of pool boiling in the region of the critical heat flux. AIChE Journal, 6(4), 533-538. doi:10.1002/aic.69006040

On calibrated weights in stratified sampling

In this paper, we propose a calibration estimator of population mean in stratified sampling using the known mean and variance information from multi-auxiliary variables. The problem of determining the optimum calibrated weights is formulated as a Nonlinear Programming Problem (NLPP) that is solved using the Lagrange multiplier technique. Numerical example with real data is presented to illustrate the computational details of the proposed estimator. A comparison study is also carried out using real and simulated data to evaluate the performance and the usefulness of the proposed estimator. The study reveals that the proposed estimator with multi-auxiliary information is more efficient estimator of the population mean as it provides least estimated variance and highest gain in relative efficiency (RE). References Jean Claude Deville and Carl Erik Sarndal. Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418):376–382, 1992. doi:10.1080/01621459.1992.10475217. Victor M Estevao and Carl Erik Sarndal. Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74(2):127–147, 2006. doi:110.1111/j.1751-5823.2006.tb00165.x Patrick J Farrell and Sarjinder Singh. Model-assisted higher-order calibration of estimators of variance. Australian and New Zealand Journal of Statistics, 47(3):375–383, 2005. doi:10.1111/j.1467-842X.2005.00402.x Wolfram Research, Inc. Mathematica, Version 11.3. Champaign, IL, 2018. Jong Min Kim, Engin A Sungur, and Tae Young Heo. Calibration approach estimators in stratified sampling. Statistics and probability letters, 77(1):99–103, 2007. doi:10.1016/j.spl.2006.05.015 Phillip S Kott. Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32(2):133, 2006. Dinesh K Rao. Mathematical programing in stratified random sampling. PhD thesis, School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Fiji, February 2017. Dinesh K. Rao, Tokaua. Tekabu, and Mohammad G M Khan. New calibration estimators in stratified sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering, pages 66–70. IEEE, 2016. Gurmindar K Singh, Dinesh K Rao, and Mohammed GM Khan. Calibration estimator of population mean in stratified random sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), pages 1–5. IEEE, 2014. Sarjindar Singh, Stephen Horn, and Frank Yu. Estimation of variance of general regression estimator: Higher level calibration approach. Survey Methodology, 24:41–50, 1998. Sarjinder Singh. Advanced Sampling Theory With Applications: How Michael "Selected" Amy, volume I and II. Kluwer Academic Publishers, Netherlands, 2003. Sarjinder Singh. On the calibration of design weights using a displacement function. Metrika, 75(1):85–107, 2012. doi:10.1007/s00184-010-0316-6 Sarjinder Singh, Stephen Horn, Sadeq Chowdhury, and Frank Yu. Theory and methods: Calibration of the estimators of variance. Australian and New Zealand Journal of Statistics, 41(2):199–212, 1999. doi:10.1111/1467-842X.00074 D S Tracy, S Singh, and R Arnab. Note on calibration in stratified and double sampling. Survey Methodology, 29(1):99–104, 2003. Changbao Wu and Randy R Sitter. A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96(453):185–193, 2001. doi:10.1198/01621450175033305

On calibrated weights in stratified sampling

In this paper, we propose a calibration estimator of population mean in stratified sampling using the known mean and variance information from multi-auxiliary variables. The problem of determining the optimum calibrated weights is formulated as a Nonlinear Programming Problem (NLPP) that is solved using the Lagrange multiplier technique. Numerical example with real data is presented to illustrate the computational details of the proposed estimator. A comparison study is also carried out using real and simulated data to evaluate the performance and the usefulness of the proposed estimator. The study reveals that the proposed estimator with multi-auxiliary information is more efficient estimator of the population mean as it provides least estimated variance and highest gain in relative efficiency (RE). References Jean Claude Deville and Carl Erik Sarndal. Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418):376–382, 1992. doi:10.1080/01621459.1992.10475217. Victor M Estevao and Carl Erik Sarndal. Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74(2):127–147, 2006. doi:110.1111/j.1751-5823.2006.tb00165.x Patrick J Farrell and Sarjinder Singh. Model-assisted higher-order calibration of estimators of variance. Australian and New Zealand Journal of Statistics, 47(3):375–383, 2005. doi:10.1111/j.1467-842X.2005.00402.x Wolfram Research, Inc. Mathematica, Version 11.3. Champaign, IL, 2018. Jong Min Kim, Engin A Sungur, and Tae Young Heo. Calibration approach estimators in stratified sampling. Statistics and probability letters, 77(1):99–103, 2007. doi:10.1016/j.spl.2006.05.015 Phillip S Kott. Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32(2):133, 2006. Dinesh K Rao. Mathematical programing in stratified random sampling. PhD thesis, School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Fiji, February 2017. Dinesh K. Rao, Tokaua. Tekabu, and Mohammad G M Khan. New calibration estimators in stratified sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering, pages 66–70. IEEE, 2016. Gurmindar K Singh, Dinesh K Rao, and Mohammed GM Khan. Calibration estimator of population mean in stratified random sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), pages 1–5. IEEE, 2014. Sarjindar Singh, Stephen Horn, and Frank Yu. Estimation of variance of general regression estimator: Higher level calibration approach. Survey Methodology, 24:41–50, 1998. Sarjinder Singh. Advanced Sampling Theory With Applications: How Michael "Selected" Amy, volume I and II. Kluwer Academic Publishers, Netherlands, 2003. Sarjinder Singh. On the calibration of design weights using a displacement function. Metrika, 75(1):85–107, 2012. doi:10.1007/s00184-010-0316-6 Sarjinder Singh, Stephen Horn, Sadeq Chowdhury, and Frank Yu. Theory and methods: Calibration of the estimators of variance. Australian and New Zealand Journal of Statistics, 41(2):199–212, 1999. doi:10.1111/1467-842X.00074 D S Tracy, S Singh, and R Arnab. Note on calibration in stratified and double sampling. Survey Methodology, 29(1):99–104, 2003. Changbao Wu and Randy R Sitter. A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96(453):185–193, 2001. doi:10.1198/01621450175033305

Multiscale computational homogenization: review and proposal of a new enhanced-first-order method

This is a copy of the author 's final draft version of an article published in the Archives of computational methods in engineering. The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-016-9205-0The continuous increase of computational capacity has encouraged the extensive use of multiscale techniques to simulate the material behaviour on several fields of knowledge. In solid mechanics, the multiscale approaches which consider the macro-scale deformation gradient to obtain the homogenized material behaviour from the micro-scale are called first-order computational homogenization. Following this idea, the second-order FE2 methods incorporate high-order gradients to improve the simulation accuracy. However, to capture the full advantages of these high-order framework the classical boundary value problem (BVP) at the macro-scale must be upgraded to high-order level, which complicates their numerical solution. With the purpose of obtaining the best of both methods i.e. first-order and second-order, in this work an enhanced-first-order computational homogenization is presented. The proposed approach preserves a classical BVP at the macro-scale level but taking into account the high-order gradient of the macro-scale in the micro-scale solution. The developed numerical examples show how the proposed method obtains the expected stress distribution at the micro-scale for states of structural bending loads. Nevertheless, the macro-scale results achieved are the same than the ones obtained with a first-order framework because both approaches share the same macro-scale BVP.Peer ReviewedPostprint (author's final draft

Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and \v{S}ejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.Comment: 28 pages, 14 figure

Acoustic characteristics of a ported shroud turbocompressor operating at design conditions

[EN] In this article, the acoustic characterisation of a turbocharger compressor with ported shroud design is carried out through the numerical simulation of the system operating under design conditions of maximum isentropic efficiency. While ported shroud compressors have been proposed as a way to control the flow near unstable conditions in order to obtain a more stable operation and enhance deep surge margin, it is often assumed that the behaviour under stable design conditions is characterised by a smooth, non-detached flow that matches an equivalent standard compressor. Furthermore, research is scarce regarding the acoustic effects of the ported shroud addition, especially under the design conditions. To analyse the flow field evolution and its relation with the noise generation, spectral signatures using statistical and scale-resolving turbulence modelling methods are obtained after successfully validating the performance and acoustic predictions of the numerical model with experimental measurements. Propagation of the frequency content through the ducts has been estimated with the aid of pressure decomposition methods to enhance the content coming from the compressor. Expected acoustic phenomena such as `buzz-saw¿ tones, blade passing peaks and broadband noise are correctly identified in the modelled spectrum. Analysis of the flow behaviour in the ported shroud shows rotating structures through the slot that may impact the acoustic and vibration response. Further inspection of the pressure field through modal decomposition confirms the influence of the ported shroud cavity in noise generation and propagation, especially at lower frequencies, suggesting that further research should be carried out on the impact these flow enhancement solutions have on the noise emission of the turbocharger.The project was sponsored and supported by BorgWarner Turbo Systems and the Regional Growth Fund (RGF Grant Award 01.09.07.01/1789C). The authors would like to thank BorgWarner Turbo Systems for permission to publish the results presented in this article. The support of the HPC group at the University of Huddersfield is gratefully acknowledged.Sharma, S.; Broatch, A.; Garcia Tiscar, J.; Allport, JM.; Nickson, AK. (2020). Acoustic characteristics of a ported shroud turbocompressor operating at design conditions. International Journal of Engine Research. 21(8):1454-1468. https://doi.org/10.1177/1468087418814635S14541468218Sundström, E., Semlitsch, B., & Mihăescu, M. (2017). Generation Mechanisms of Rotating Stall and Surge in Centrifugal Compressors. Flow, Turbulence and Combustion, 100(3), 705-719. doi:10.1007/s10494-017-9877-zGonzalez, A., Ferrer, M., de Diego, M., Piñero, G., & Garcia-Bonito, J. . (2003). Sound quality of low-frequency and car engine noises after active noise control. Journal of Sound and Vibration, 265(3), 663-679. doi:10.1016/s0022-460x(02)01462-1Brizon, C. J. da S., & Bauzer Medeiros, E. (2012). Combining subjective and objective assessments to improve acoustic comfort evaluation of motor cars. Applied Acoustics, 73(9), 913-920. doi:10.1016/j.apacoust.2012.03.013Teng, C., & Homco, S. (2009). Investigation of Compressor Whoosh Noise in Automotive Turbochargers. SAE International Journal of Passenger Cars - Mechanical Systems, 2(1), 1345-1351. doi:10.4271/2009-01-2053Figurella, N., Dehner, R., Selamet, A., Tallio, K., Miazgowicz, K., & Wade, R. (2014). Noise at the mid to high flow range of a turbocharger compressor. Noise Control Engineering Journal, 62(5), 306-312. doi:10.3397/1/376229Torregrosa, A. J., Broatch, A., Margot, X., García-Tíscar, J., Narvekar, Y., & Cheung, R. (2017). Local flow measurements in a turbocharger compressor inlet. Experimental Thermal and Fluid Science, 88, 542-553. doi:10.1016/j.expthermflusci.2017.07.007Broatch, A., Galindo, J., Navarro, R., García-Tíscar, J., Daglish, A., & Sharma, R. K. (2015). Simulations and measurements of automotive turbocharger compressor whoosh noise. Engineering Applications of Computational Fluid Mechanics, 9(1), 12-20. doi:10.1080/19942060.2015.1004788Raitor, T., & Neise, W. (2008). Sound generation in centrifugal compressors. Journal of Sound and Vibration, 314(3-5), 738-756. doi:10.1016/j.jsv.2008.01.034Galindo, J., Tiseira, A., Navarro, R., & López, M. A. (2015). Influence of tip clearance on flow behavior and noise generation of centrifugal compressors in near-surge conditions. International Journal of Heat and Fluid Flow, 52, 129-139. doi:10.1016/j.ijheatfluidflow.2014.12.004Broatch, A., Galindo, J., Navarro, R., & García-Tíscar, J. (2014). Methodology for experimental validation of a CFD model for predicting noise generation in centrifugal compressors. International Journal of Heat and Fluid Flow, 50, 134-144. doi:10.1016/j.ijheatfluidflow.2014.06.006Semlitsch, B., & Mihăescu, M. (2016). Flow phenomena leading to surge in a centrifugal compressor. Energy, 103, 572-587. doi:10.1016/j.energy.2016.03.032Sundström, E., Semlitsch, B., & Mihăescu, M. (2018). Acoustic signature of flow instabilities in radial compressors. Journal of Sound and Vibration, 434, 221-236. doi:10.1016/j.jsv.2018.07.040Torregrosa, A. J., Broatch, A., Margot, X., & García-Tíscar, J. (2016). Experimental methodology for turbocompressor in-duct noise evaluation based on beamforming wave decomposition. Journal of Sound and Vibration, 376, 60-71. doi:10.1016/j.jsv.2016.04.035Nicoud, F., & Ducros, F. (1999). Flow, Turbulence and Combustion, 62(3), 183-200. doi:10.1023/a:1009995426001Chow, P., Cross, M., & Pericleous, K. (1996). A natural extension of the conventional finite volume method into polygonal unstructured meshes for CFD application. Applied Mathematical Modelling, 20(2), 170-183. doi:10.1016/0307-904x(95)00156-eKaji, S., & Okazaki, T. (1970). Generation of sound by rotor-stator interaction. Journal of Sound and Vibration, 13(3), 281-307. doi:10.1016/s0022-460x(70)80020-7Sivagnanasundaram, S., Spence, S., & Early, J. (2013). Map Width Enhancement Technique for a Turbocharger Compressor. Journal of Turbomachinery, 136(6). doi:10.1115/1.4007895Aubry, N. (1991). On the hidden beauty of the proper orthogonal decomposition. Theoretical and Computational Fluid Dynamics, 2(5-6), 339-352. doi:10.1007/bf00271473Wold, S., Esbensen, K., & Geladi, P. (1987). Principal component analysis. Chemometrics and Intelligent Laboratory Systems, 2(1-3), 37-52. doi:10.1016/0169-7439(87)80084-9LIANG, Y. C., LEE, H. P., LIM, S. P., LIN, W. Z., LEE, K. H., & WU, C. G. (2002). PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY. Journal of Sound and Vibration, 252(3), 527-544. doi:10.1006/jsvi.2001.4041Abdi, H., & Williams, L. J. (2010). Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2(4), 433-459. doi:10.1002/wics.101Nikiforov, V. (2007). The energy of graphs and matrices. Journal of Mathematical Analysis and Applications, 326(2), 1472-1475. doi:10.1016/j.jmaa.2006.03.07

Direct simulation of liquid-gas-solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid-gas-solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary -- in particular if the bubble-particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble-particle interaction at a size ratio of 1-2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than $100\,000$ fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully-resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble-particle interaction problems correctly.Comment: submitted to International Journal of Computational Fluid Dynamic