×

zbMATH — the first resource for mathematics

Exploration of digital-filter and forward-stepwise synthetic turbulence generators and an improvement for their skewness-kurtosis. (English) Zbl 1410.76075
Summary: The performance of four synthetic turbulence generators that represent the majority of capabilities of (i) digital-filter-based (DFM) and (ii) forward-stepwise-based (FSM) generator categories is evaluated prior to transferring generator outputs into computational fluid dynamics simulations. In addition, a cheap-to-run and easy-to-code piecewise closed-form function that transforms one-spatial-point skewness-kurtosis of a synthetic time-series to a target value is derived and presented. The two main purposes of the study are to support model users in their decision process for choosing the most convenient type and their understanding of the models through a systematic exploration of model variables and modeling stages, and to extend the Gaussian nature of these models at a spatial point into non-Gaussianity for the first time. The evaluation test-bed contains three benchmarks, each of which focuses on an isolated aspect of turbulent flows: (i) decaying homogeneous isotropic turbulence, (ii) homogeneous shear turbulence and (iii) plane channel flow with smooth walls. The results obtained reveal that:
(i)
the original DFM provides the highest level of reconstruction for input one-spatial-point second-order correlation tensors and two-spatial/temporal-point correlation functions;
(ii)
FSM yields the best trade-off between the computational cost and the level of reconstruction;
(iii)
the use of exponential-form correlation functions as a model approximation is more advisable than that of Gaussian-form, as the former removes the premature, sharp, flow-type-independent drop in power spectra observed for the latter;
(iv)
the proposed non-Gaussian functionality reconstructs the target one-spatial-point skewness-kurtosis pairs of the test-bed flows virtually without altering their already-embedded statistics;
(v)
the Lund transformation changes existing statistics only in statistically inhomogeneous lateral directions of a flow when anisotropic Reynolds stresses are present; and
(vi)
a spatial variation of correlation functions on turbulence generation plane improves the overall reconstruction fidelity in terms of correlation functions and power spectra.
MSC:
76F55 Statistical turbulence modeling
76F65 Direct numerical and large eddy simulation of turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Rosales, C.; Meneveau, C., Anomalous scaling and intermittency in three-dimensional synthetic turbulence, Phys Rev E, 78, 1, 016313, (2008)
[2] AL-Bairmani, S.; Li, Y.; Rosales, C.; Xie, Z.-T., Subgrid-scale stresses and scalar fluxes constructed by the multi-scale turnover Lagrangian map, Phys Fluids, 29, 4, 045103, (2017)
[3] Gong, K.; Chen, X., Influence of non-Gaussian wind characteristics on wind turbine extreme response, Eng Struct, 59, 727-744, (2014)
[4] Berg, J.; Natarajan, A.; Mann, J.; Patton, E. G., Gaussian vs non-Gaussian turbulence: impact on wind turbine loads, Wind Energy, 19, 11, 1975-1989, (2016)
[5] Dhamankar, N. S.; Blaisdell, G. A.; Lyrintzis, A. S., Overview of turbulent inflow boundary conditions for large-eddy simulations, AIAA J, 1-18, (2017)
[6] Tabor, G. R.; Baba-Ahmadi, M. H., Inlet conditions for large eddy simulation: a review, Comput Fluids, 39, 4, 553-567, (2010) · Zbl 1242.76084
[7] Wu, X., Inflow turbulence generation methods, Annu Rev Fluid Mech, 49, 1, 23-49, (2017) · Zbl 1359.76162
[8] Mann, J., Spectral velocity tensor in moderately complex terrain, J Wind Eng Ind Aerodyn, 88, 2-3, 153-169, (2000)
[9] Kraichnan, R. H., Diffusion by a random velocity field, Phys Fluids, 13, 1, 22, (1970) · Zbl 0193.27106
[10] Lee, S.; Lele, S. K.; Moin, P., Simulation of spatially evolving turbulence and the applicability of taylor’s hypothesis in compressible flow, Phys Fluids A, 4, 7, 1521-1530, (1992) · Zbl 0825.76346
[11] Druault, P.; Lardeau, S.; Bonnet, J.-P.; Coiffet, F.; Delville, J.; Lamballais, E., Generation of three-dimensional turbulent inlet conditions for large-eddy simulation, AIAA J, 42, 3, 447-456, (2004)
[12] Jarrin, N.; Benhamadouche, S.; Laurence, D.; Prosser, R., A synthetic-eddy-method for generating inflow conditions for large-eddy simulations, Int J Heat Fluid Flow, 27, 4, 585-593, (2006)
[13] Klein, M.; Sadiki, A.; Janicka, J., A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations, J Comput Phys, 186, 2, 652-665, (2003) · Zbl 1047.76522
[14] Xie, Z. T.; Castro, I. P., Efficient generation of inflow conditions for large eddy simulation of street-scale flows, Flow Turbul Combust, 81, 3, 449-470, (2008) · Zbl 1257.76040
[15] Borgman, L. E., Ocean wave simulation for engineering design, Technical report, (1967), Hydraulic Engineering Laboratory Berkeley, California
[16] Nobach, H., Verarbeitung stochastisch abgetasteter signale, (1997), University of Rostock Germany, Ph.d. thesis
[17] Lund, T. S.; Wu, X.; Squires, K. D., Generation of turbulent inflow data for spatially-developing boundary layer simulations, J Comput Phys, 140, 2, 233-258, (1998) · Zbl 0936.76026
[18] di Mare, L.; Klein, M.; Jones, W. P.; Janicka, J., Synthetic turbulence inflow conditions for large-eddy simulation, Phys Fluids, 18, 2, 025107, (2006)
[19] di Mare, L.; Jones, W. P., Algebraic and operator methods for generation of inflow data for LES and DNS, Proceedings of the fourth international symposium on turbulence and shear flow phenomena (TSFP4). Williamsburg, Virginia, 687-692, (2005)
[20] Fathali, M.; Klein, M.; Broeckhoven, T.; Lacor, C.; Baelmans, M., Generation of turbulent inflow and initial conditions based on multi-correlated random fields, Int J Numer Methods Fluids, 57, 1, 93-117, (2008) · Zbl 1388.76095
[21] Kempf, A.; Klein, M.; Janicka, J., Efficient generation of initial- and inflow-conditions for transient turbulent flows in arbitrary geometries, Flow Turbul Combust, 74, 1, 67-84, (2005) · Zbl 1113.76346
[22] Fru, G.; Janiga, G.; Thévenin, D., Direct numerical simulation of highly turbulent premixed flames burning methane, (Kuerten, H., ERCOFTAC Series, 15, (2011), Springer-Verlag Eindhoven, The Netherlands), 327-332
[23] Dhamankar, N. S.; Martha, C. S.; Situ, Y.; Aikens, K. M.; Blaisdell, G. A.; Lyrintzis, A. S., Digital filter-based turbulent inflow generation for jet aeroacoustics on non-uniform structured grids, Proceedings of the 52nd aerospace sciences meeting, 1-35, (2014), American Institute of Aeronautics and Astronautics Reston, Virginia, USA
[24] Allegrini, J.; Carmeliet, J., Evaluation of the filtered noise turbulent inflow generation method, Flow Turbul Combust, 98, 4, 1087-1115, (2017)
[25] Kim, Y.; Castro, I. P.; Xie, Z. T., Divergence-free turbulence inflow conditions for large-eddy simulations with incompressible flow solvers, Comput Fluids, 84, 56-68, (2013) · Zbl 1290.76044
[26] Ewert, R., The simulation of slat noise applying stochastic sound sources based on solenoidal digital filters (SDF), Proceedings of the Euromech colloquium 467: turbulent flow and noise generation, July 18-20, 2005, (2005), American Institute of Aeronautics and Astronautics Reston, Virigina
[27] Smirnov, A.; Shi, S.; Celik, I., Random flow generation technique for large eddy simulations and particle-dynamics modeling, J Fluids Eng, 123, 2, 359, (2001)
[28] Jiménez, J., Turbulent velocity fluctuations need not be Gaussian, J Fluid Mech, 376, (1998) · Zbl 0922.76234
[29] Moser, R. D.; Kim, J.; Mansour, N. N., Direct numerical simulation of turbulent channel flow up to reτ=590, Phys Fluids, 11, 4, 943-945, (1999) · Zbl 1147.76463
[30] Touber, E.; Sandham, N. D., Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble, Theor Comput Fluid Dyn, 23, 2, 79-107, (2009) · Zbl 1234.76033
[31] Breuer, S.; Schmidt, M., Extended synthetic turbulence inflow generator within a hybrid LES-URANS methodology for the prediction of non-equilibrium wall-bounded flows, Flow Turbul Combust, 95, 4, 669-707, (2015)
[32] Anupindi, K.; Sandberg, R. D., Implementation and evaluation of an embedded LES-RANS solver, Flow Turbul Combust, 98, 3, 697-724, (2017)
[33] Okaze, T.; Mochida, A., Cholesky decomposition-based generation of artificial inflow turbulence including scalar fluctuation, Comput Fluids, 159, 23-32, (2017) · Zbl 1390.76204
[34] Ihme, M.; See, Y. C., LES flamelet modeling of a three-stream MILD combustor: analysis of flame sensitivity to scalar inflow conditions, Proc Combust Inst, 33, 1, 1309-1317, (2011)
[35] Kim, Y.; Xie, Z. T.; Castro, I. P., A forward stepwise method of inflow generation for LES, AIP conference proceedings, 1376, 134-136, (2011), American Institute of Physics
[36] Schmidt, S.; Breuer, M., Source term based synthetic turbulence inflow generator for eddy-resolving predictions of an airfoil flow including a laminar separation bubble, Comput Fluids, 146, 1-22, (2017) · Zbl 1390.76218
[37] Veloudis, I.; Yang, Z.; McGuirk, J. J.; Page, G. J.; Spencer, A., Novel implementation and assessment of a digital filter based approach for the generation of LES inlet conditions, Flow Turbul Combust, 79, 1, 1-24, (2007) · Zbl 1200.76103
[38] Kempf, A. M.; Wysocki, S.; Pettit, M., An efficient, parallel low-storage implementation of klein’s turbulence generator for LES and DNS, Comput Fluids, 60, 58-60, (2012) · Zbl 1365.76088
[39] Smith, S. W., The scientist & engineer’s guide to digital signal processing, (1999), California Technical Pub
[40] Taylor, G. I., The spectrum of turbulence, Proc R Soc A: Math Phys Eng Sci, 164, 919, 476-490, (1938) · JFM 64.1454.02
[41] Booton, R. C., Nonlinear control systems with random inputs, IRE Trans Circuit Theory, 1, 1, 9-18, (1954)
[42] Grigoriu, M., Crossings of non-Gaussian translation processes, J Eng Mech, 110, 4, 610-620, (1984)
[43] Johnson, N. L., Systems of frequency curves generated by methods of translation, Biometrika, 36, 1-2, 149-176, (1949) · Zbl 0033.07204
[44] Gurley, K. R.; Tognarelli, M. A.; Kareem, A., Analysis and simulation tools for wind engineering, Probab Eng Mech, 12, 1, 9-31, (1997)
[45] Yamazaki, F.; Shinozuka, M., Digital generation of non-Gaussian stochastic fields, J Eng Mech, 114, 7, 1183-1197, (1988)
[46] Smallwood, D. O., Generation of partially coherent stationary time histories with non-Gaussian distributions, Shock and vibration symposium, (1996), U.S. Department of Energy, Office of Scientific and Technical Information Monterey, CA, USA
[47] Bowman, K. O.; Shenton, L. R., Johnson’s system of distributions, Encyclopedia of statistical sciences, 4, 303-314, (1982), John Wiley & Sons, Inc. Hoboken, NJ, USA
[48] Tuenter, H. J.H., An algorithm to determine the parameters of SU-curves in the Johnson system of probabillity distributions by moment matching, J Stat Comput Simul, 70, 4, 325-347, (2001) · Zbl 1098.62523
[49] Flynn, M. R., On the moments of the 4-parameter lognormal distribution, Commun Stat - Theory and Methods, 34, 4, 745-751, (2005) · Zbl 1080.62005
[50] OpenFOAM user guide. The open source CFD toolbox. OpenCFD Ltd (ESI Group). 2017. URL http://www.openfoam.com/.
[51] Comte-Bellot, G.; Corrsin, S., Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, isotropic turbulence, J Fluid Mech, 48, 2, 273-337, (1971)
[52] Tavoularis, S.; Corrsin, S., Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. part 2. the fine structure, J Fluid Mech, 104, 349-367, (1981)
[53] Sagaut, P., Large eddy simulation for incompressible flows: an introduction, (2006), Springer Berlin, Heidelberg · Zbl 1091.76001
[54] Baggett, J. S.; Jiménez, J.; Kravchenko, A. G., Resolution requirements in large-eddy simulation of shear flows, Annual research briefs - 1997, 51-66, (1997), Stanford University Stanford, CA, USA
[55] Issa, R. I., Solution of the implicitly discretised fluid flow equations by operator-splitting, J Comput Phys, 62, 1, 40-65, (1986) · Zbl 0619.76024
[56] NIST-SEMATECH, NIST/SEMATECH E-handbook of statistical methods, (2003), National Institute of Standards and Technology
[57] Jiménez, J.; Wray, A. A.; Saffman, P. G.; Rogallo, R. S., The structure of intense vorticity in isotropic turbulence, J Fluid Mech, 255, 65-90, (1993) · Zbl 0800.76156
[58] Farge, M.; Schneider, K., CVS decomposition of 3D homogeneous turbulence using orthogonal wavelets, 305-317, (2000), Center for turbulence research
[59] Dietzel, D.; Messig, D.; Piscaglia, F.; Montorfano, A.; Olenik, G.; Stein, O. T., Evaluation of scale resolving turbulence generation methods for large eddy simulation of turbulent flows, Comput Fluids, 93, 116-128, (2014) · Zbl 1391.76214
[60] Tavoularis, S.; Corrsin, S., Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. part 1, J Fluid Mech, 104, EM6, 311-347, (1981)
[61] Moser R.D.. DNS data for turbulent channel flow. 2007. URL http://bit.ly/2rJeQ3u.
[62] Fréchet, M. M., Sur quelques points du calcul fonctionnel, Rend Circolo Mat Palermo, 22, 1, 1-72, (1906) · JFM 37.0348.02
[63] Eiter, T.; Mannila, H., Computing discrete Fréchet distance, Technical report, (1994), Technische Universität Wien Wien
[64] Eiter, T.; Mannila, H., Distance measures for point sets and their computation, Acta Inform, 34, 2, 109-133, (1997) · Zbl 0865.51011
[65] Michaud-Agrawal, N.; Denning, E. J.; Woolf, T. B.; Beckstein, O., Mdanalysis: a toolkit for the analysis of molecular dynamics simulations, J Comput Chem, 32, 10, 2319-2327, (2011)
[66] Gowers, R. J.; Linke, M.; Barnoud, J.; Reddy, T. J.E.; Melo, M. N.; Seyler, S. L., Mdanalysis: a python package for the rapid analysis of molecular dynamics simulations, (Benthall, S.; Rostrup, S., Proceedings of the 15th Python in science conference, (2016)), 98-105
[67] Seyler, S. L.; Kumar, A.; Thorpe, M. F.; Beckstein, O., Path similarity analysis: a method for quantifying macromolecular pathways, PLoS Comput Biol, 11, 10, (2015)
[68] Thomas, D. B.; Luk, W.; Leong, P. H.W.; Villasenor, J. D., Gaussian random number generators, ACM Comput Surv, 39, 4, (2007)
[69] Marsaglia, G.; Tsang, W. W., The ziggurat method for generating random variables, J Geol Soc Lond, 5, 8, 1-7, (2000)
[70] Eddelbuettel D.. RcppZiggurat: ‘Rcpp’ integration of different “Ziggurat” normal RNG implementations. 2015.
[71] Leong, P. H.W.; Zhang, G.; Lee, D.-U.; Luk, W.; Villasenor, J. D., A comment on the implementation of the ziggurat method, J Stat Softw, 12, 7, 1-4, (2005)
[72] Claerbout, J. F., Multidimensional recursive filters via a helix, Geophysics, 63, 5, 1532-1541, (1998)
[73] Weisstein E.W. Fourier Transform-Gaussian. From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/FourierTransformGaussian.html.
[74] Weisstein E.W. Fourier Transform-Exponential Function. From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/FourierTransformExponentialFunction.html.
[75] Dickey, D. A.; Fuller, W. A., Distribution of the estimators for autoregressive time series with a unit root, J Am Stat Assoc, 74, 366, 427, (1979) · Zbl 0413.62075
[76] Grazzini, J., Analysis of the emergent properties: stationarity and ergodicity, Jasss, 15, 2, (2012)
[77] O’Neill, P. L.; Nicolaides, D.; Honnery, D. R.; Soria, J., Autocorrelation functions and the determination of integral length with reference to experimental and numerical data, Proceedings of the 15th Australasian fluid mechanics conference, 1, 1-4, (2004), The University of Sydney Sydney, Australia
[78] Welch, P. D., The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms, IEEE Trans Audio Electroacoust, 15, 2, 70-73, (1967)
[79] Cameron, P. J., Colour schemes, Technical Note, (1982), SRON Netherlands Institute for Space Research · Zbl 0501.05002
[80] Neidell, N. S., Deterministic deconvolution operators - 3 point or 4 point?, Geophysics, 37, 6, 1039-1042, (1972)
[81] Claerbout, J. F.; Karrenbach, M.; Balog, O., Earth soundings analysis: processing versus inversion, (1992), ISBN 978–0865422100.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.