Comparative Analysis of Velocity Decomposition Methods for Internal Combustion Engines
Affiliation(s)
Department of Aerospace Engineering and Mechanics, The University of Alabama, Tuscaloosa, USA. Department of Mechanical Engineering, The University of Alabama, Tuscaloosa, USA.
Department of Aerospace Engineering and Mechanics, The University of Alabama, Tuscaloosa, USA. Department of Mechanical Engineering, The University of Alabama, Tuscaloosa, USA.
ABSTRACT
Different signal processing technique performances are compared to each other with regard to separating the mean and fluctuating velocity components of a simulated one-dimensional unsteady velocity signal comparable to signals observed in internal combustion engines. A simulation signal with known mean and fluctuating components was generated using experimental data and generic turbulence spectral information. The simulation signal was generated based on observations on the measured velocity data obtained using LDV in a motored Briggs-and-Stratton engine at about 600 RPM. Experimental data was used as a guide to shape the simulated signal mean velocity variation; fluctuating velocity variations with specified spectrum and standard deviation was used to mimic the turbulence. Cyclic variations were added both to the mean and the fluctuating velocity signals to simulate prescribed cyclic variations. The simulated signal was introduced as input to the following algorithms: ensemble averaging; high-pass filtering; Proper-Orthogonal Decomposition (POD); Wavelet Decomposition (WD) and Wavelet Decomposition/Principal Component Analysis (WD/PCA). The results were analyzed to determine the best method in correctly separating the mean and the fluctuating velocity information, indicating that the WD/PCA performs better compared to other techniques.
Different signal processing technique performances are compared to each other with regard to separating the mean and fluctuating velocity components of a simulated one-dimensional unsteady velocity signal comparable to signals observed in internal combustion engines. A simulation signal with known mean and fluctuating components was generated using experimental data and generic turbulence spectral information. The simulation signal was generated based on observations on the measured velocity data obtained using LDV in a motored Briggs-and-Stratton engine at about 600 RPM. Experimental data was used as a guide to shape the simulated signal mean velocity variation; fluctuating velocity variations with specified spectrum and standard deviation was used to mimic the turbulence. Cyclic variations were added both to the mean and the fluctuating velocity signals to simulate prescribed cyclic variations. The simulated signal was introduced as input to the following algorithms: ensemble averaging; high-pass filtering; Proper-Orthogonal Decomposition (POD); Wavelet Decomposition (WD) and Wavelet Decomposition/Principal Component Analysis (WD/PCA). The results were analyzed to determine the best method in correctly separating the mean and the fluctuating velocity information, indicating that the WD/PCA performs better compared to other techniques.
Cite this paper
S. Ölçmen, M. Ashford, P. Schinestsky and M. Drabo, "Comparative Analysis of Velocity Decomposition Methods for Internal Combustion Engines," Open Journal of Fluid Dynamics, Vol. 2 No. 3, 2012, pp. 70-90. doi: 10.4236/ojfd.2012.23008.
S. Ölçmen, M. Ashford, P. Schinestsky and M. Drabo, "Comparative Analysis of Velocity Decomposition Methods for Internal Combustion Engines," Open Journal of Fluid Dynamics, Vol. 2 No. 3, 2012, pp. 70-90. doi: 10.4236/ojfd.2012.23008.
References
[1] L. J. Lumley, “Engines, an Introduction,” Cambridge University Press, Cambridge, 1999. doi:10.1017/CBO9781139175135 [2] E. P. Hassel and S. Linow, “Laser Diagnostics for Studies of Turbulent Combustion,” Measurement Science and Technology, Vol. 11, No. 2, 2000, pp. R37-R57. doi:10.1088/0957-0233/11/2/201 [3] A. Erdil, A. Kodal and K. Aydin, “Decomposition of Turbulent Velocity Fields in an SI Engine,” Flow, Turbulence and Combustion, Vol. 68, No. 2, 2002, pp. 91-110. doi:10.1023/A:1020467008591 [4] W. C. Choi and Y. G. Guezennec, “Experimental Investigation to Study Convective Mixing, Spatial Uniformity, and Cycle-to-Cycle Variation during the Intake Stroke in an IC Engine,” Journal of Engineering for Gas Turbines and Power, Vol. 122, No. 3, 2000, pp. 493-501. doi:10.1115/1.1286626 [5] A. R. Denlinger, Y. G. Guezennec and W. C. Choi, “Dynamic Evolution of the 3-D Flow Field during the Latter Part of the Intake Stroke in an IC Engine,” Analysis of Combustion and Flow Diagnostics (SP-1348), SAE Paper, 1998. [6] M. P. Patrie and J. K. Martin, “PIV Measurements of in-Cylinder Flow Structures and Correlation with Engine Performance,” Fall Technical Conference, 1997. [7] H. J. NeuBer, L. Spiegel and J. Ganser, “Particle Tracking Velocimetry-A Powerful Tool to Shape the in-Cylinder Flow of Modern Multi Valve Engine Concepts,” SAE Paper, 1995. [8] K. H. Lee, C. S. Lee, H. J. Park and D. S. Kim, “Effects of Tumble and Swirl Flows on the Turbulence Scale Near the TDC in 4 Valve SI Engine,” ICE Spring Technical Conference, 2001. [9] D. P. Towers and C. E. Towers, “Cyclic Variability Measurements of in-Cylinder Engine Flows Using HighSpeed Particle Image Velocimetry,” Measurement Science and Technology, Vol. 15, No. 9, 2004, pp. 19171925. doi:10.1088/0957-0233/15/9/032 [10] R. B. Rask, “Laser Doppler Anemometer Measurements in an Internal Combustion Engine,” SAE Paper, 1979. [11] S. Bopp, F. Durst and C. Tropea, “In-Cylinder Velocity Measurements with a Mobile Fiber Optic LDV System,” SAE Paper, 1990. [12] F. Durst, A. Naqwi and C. Tropea, “Development and Applications of LDA-systems in I.C. Engine Research,” International Symposium, Vol. 90, 1990, pp. 21-30. [13] H. Vigor, J. Pecheux and J. L. Peube, “Velocity Measurements Inside the Cylinder of an Internal Combustion Model Engine during the Intake Process,” Laser Anemometry, Vol. 1, 1991. [14] M. R. Himes and P. V. Farell, “Laser Doppler Velocimeter Measurements within a Motored Direct Injection Spark Ignited Engine,” University of Wisconsin-Madison, Madison, 1998. [15] K. Y. Kang and J. H. Baek, “Turbulence Characteristics of Tumble Flow in a Four-Valve Engine,” Experimental Thermal and Fluid Science, Vol. 18, 1998, pp. 231,243. [16] V. S. S. Chan and J. T. Turner, “Velocity Measurement Inside a Motored Internal Combustion Engine Using Three-Component Laser Doppler Anemometry,” Optics & Laser Technology, Vol. 32, 2000, pp. 557-566. [17] B. Kim, et al., “In-Cylinder Turbulent Measurements with a Spark Plug-In Fiber LDV,” 11th Symposia on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8-11 July 2002. [18] D. Park, P. Sullivan and J. Wallace, “Different Velocity Data Analysis for Flows Near a Spark Plug in the Combustion Chamber of a Spark Ignition Engine,” SAE Paper, 2004. [19] C. Arcoumanis and J. H. Whitelaw, “Fluid Mechanics of Internal Combustion Engines: A Review,” International Symposium on Flows in Internal Combustion Engines-III, Vol. 201, No. 1, 1985, pp. 57-74. [20] S. Roudnitzky, P. Druault, and P. Guibert, “Proper Orthogonal Decomposition of in-Cylinder Engine Flow into Mean Component, Coherent Structures and Random Gaussian Fluctuations,” Journal of Turbulence, Vol. 7, No. 70, 2006, p. 70. [21] M. Fogleman, J. Lumley, D. Rempfer and D. Haworth, “Application of the Proper Orthogonal Decomposition to Datasets of Internal Combustion Engine Flows,” Journal of Turbulence, Vol. 5, No. 23, 2004, pp. 1-18. [22] P. Sullivan, R. Ancimer, J. Wallace, “Turbulence Averaging within Spark Ignition Engines,” Experiments in Fluids, Vol. 27, No. 1, 1999, pp. 92-101. doi:10.1007/s003480050333 [23] R. Ancimer, P. Sullivan and J. Wallace, “Decomposition of Measured Velocity Fields with Spark Ignition Engines Using Discrete Wavelet Transforms,” Experiments in Fluids, Vol. 30, No. 2, 2001, pp. 237-238. doi:10.1007/s003480000152 [24] F. S?derberg, B. Johansson, and B. Lindoff, “Wavelet Analysis of in-Cylinder LDV Measurements and Correlation Against Heat-Release,” SAE Paper, 1998. [25] A. Sen, G. Litak, R. Taccani and R. Radu, “Wavelet Analysis of Cycle-to-Cycle Pressure Variations in an Internal Combustion Engine,” Chaos, Solitons and Fractals, Vol. 38, No. 3, 2008, pp. 886-893. doi:10.1016/j.chaos.2007.01.041 [26] Z. Zhang, E. Tomita, S. Yoshiyama, Y. Hamamoto and H. Kawabata, “Wavelet Transform Analysis of Unsteady Turbulence and Turbulent Burning Velocity in a Constant-Volume Vessel,” JSME International Journal, Series B, Vol. 44, No. 4, 2001, pp. 608-615. doi:10.1299/jsmeb.44.608 [27] C. Arcoumanis, A. C. Enotiadis and J. H. Whitelaw, “Frequency Analysis of Tumble and Swirl in Motored Engines,” Journal of Automobile Engineering, Vol. 205, 1991, pp. 177-184. doi:10.1243/PIME_PROC_1991_205_168_02 [28] T. D. Fansler, “Turbulence Production and Relaxation in Bowl-in-Piston Engines,” SAE Paper, 1993. [29] A. C. Enotiadis, C. Vafidis and J. H. Whitelaw, “Interpretation of Cyclic Flow Variations in Motored Internal Combustion Engines,” Experiments in Fluids, Vol. 10, No. 2-3, 1990, pp. 77-86. [30] E. Esirgemez and M. S. ?l?men, “Spark-Plug LDV Probe for in-Cylinder Flow Analysis of Production IC Engines,” Measurement Science and Technology, Vol. 16, No. 10, 2005, pp. 2038-2047. doi:10.1088/0957-0233/16/10/020 [31] N. Kevlehan, J. C. R. Hunt and J. C. Vassilicos, “A Comparison of Different Analytical Techniques for Identifying Structures in Turbulence,” Applied Scientific Research, Vol. 53, No. 3-4, 1994, pp. 339-355. doi:10.1007/BF00849109 [32] H. E. Albrecht, M. Borys, N. Damaschke and C. Tropea, “Laser Doppler and Phase Doppler Measurement Techniques,” Springer-Verlag, 2003. [33] L. H. Benedict, H. Nobach and C. Tropea, “Estimation of Turbulent Velocity Spectra from Laser Doppler Data,” Measurement Science and Technology, Vol. 11, No. 8, 2000, pp. 1089-1104. doi:10.1088/0957-0233/11/8/301 [34] E. Konstantinidis, A. Ducci, S. Balabani and M. Yianneskis, “An Empirical Method for Efficient Spectrum Estimation from LDA Data,” 13th International Symposiaon Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 26-29 June 2006. [35] I. ?elik, I. Yavuz, A. Smirnov, J. Smith, E. Amin and A. Gel, “Prediction of in-Cylinder Turbulence for IC Enginess,” Combustion Science and Technology, Vol. 153, No. 1, 2000, pp. 339-368. doi:10.1080/00102200008947269 [36] “Matlab,” Version 7.7.0.471, The MathWorks Inc., Natick, 2008. [37] P. M. T. Broersen and S. de Waele, “Generating Data with Prescribed Power Spectral Density,” IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 4, 2003, pp. 1061doi:10.1109/TIM.2003.814824 [38] S. F. Al-Sharif, M. A. Cotton and T. J. Craft, “Reynolds Stress Transport Models in Unsteady and Non-Equilibrium Turbulent Flows,” International Journal of Heat and Fluid Flow, Vol. 31, No. 3, 2000, pp. 401-408. doi:10.1016/j.ijheatfluidflow.2010.02.024 [39] S. He, C. Ariyaratne and A. E. Vardy, “A Computational Study of Wall Friction and Turbulence Dynamics in Accelerating Pipe Flows,” Computers & Fluids, Vol. 37, No. 6, 2008, pp. 674-689. doi:10.1016/j.compfluid.2007.09.001 [40] A. J. Revell, S. Benhamadouche, T. Craft and D. Laurence, “A Stress-Strain Lag Eddy Viscosity Model for Unsteady Mean Flow,” International Journal of Heat and Fluid Flow, Vol. 27, No. 5, 2006, pp. 821-830. doi:10.1016/j.ijheatfluidflow.2006.03.027 [41] Y. C. Liang, H. P. Lee, S. P. Lim, W. Z. Lin, K. H. Lee and C. G. Wu, “Proper Orthogonal Decomposition and Its Applications—Part I: Theory,” Journal of Sound and Vibration, Vol. 252, No. 3, 2002, pp. 527-544. [42] E. Zervas, “Correlations between Cycle-to-Cycle Variations and Combustion Parameters of a Spark Ignition Engine,” Applied Thermal Engineering, Vol. 24, No. 14-15, 2004, pp. 2073-2081. doi:10.1016/j.applthermaleng.2004.02.008 [43] W. C. Choi and Y. G. Guezennec, “Study of the Flow Field Development During the Intake Stroke in an IC Engine Using 2-D PIV and 3-D PTV,” International Congress and Exposition Detroit, Michigan, 1-4 March 1999. [44] T.-M. Liou and D. A. Santavicca, “Cycle Resolved LDV Measurements in a Motored IC Engine,” Journal of Fluids Engineering, Transactions of ASME, Vol. 107, 1985, pp. 232-240. [45] R. A. Fraser and F.V. Bracco, “Cycle-Esolved LDV Integral Length Scale Meaurements Investigating Clearance Height Scaling, Isotropy, and Homogeneity in an I.C. Engine,” International Congress and Exposition, Detroit, 27 February-3 March 1989. [46] C. W. Hong and D. G. Chen, “Direct Measurements of in-Cylinder Integral Length Scales of a Transparent Engine,” Experiments in Fluids, Vol. 23, No. 2, 1997, pp. 113-120. doi:10.1007/s003480050092 [47] R. B. Rask, “Comparison of Window, Smoothed-Ensemble, and Cycle-to-Cycle Data Reduction Techniques for Laser Doppler Anemometer Measurements of in-Cylinder Velocity,” In: T. Morel, R. P. Lohmann and J. M. Rackley, Eds., Fluid Mechanics of Combustion Systems, ASME, New York, 1981. [48] J. L. Lumley, “The Structure of Inhomogeneous Turbulence,” In: A. M. Yaglom and V. I. Tatarski, Eds., Atmospheric Turbulence and Wave Propagation, Nauka, Moscow, 1967, pp. 166-178. [49] A. Chatterjee, “An Introduction to the Proper Orthogonal Decomposition,” Current Science, Vol. 78, No. 7, 2000, pp. 808-817. [50] C. Tropea, A. L. Yarin and J. F. Foss, “Springer Handbook of Experimental Fluid Mechanics,” 2007. [51] C. Torrence, and G. P. Compo, “A Practical Guide to Wavelet Analysis,” Bulletin of the American Meteorological Society, Vol. 79, No. 1, 1998, pp. 61-78. doi:10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2 [52] M. Farge, K. Scheineder and P. Abry, “Analyzing and Compressing Turbulent Fields with Wavelets,” Institut Pierre Simon Laplace Publication, 2002. [53] M. Farge, “Wavelet Transforms and Their Applications to Turbulence,” Annual Review of Fluid Mechanics, Vol. 24, 1992, pp. 395-457. doi:10.1146/annurev.fl.24.010192.002143 [54] M. Misiti, Y. Misiti, G. Oppenheim and J.-M. Poggi, “Wavelet Toolbox? 4, User’s Guide,” 2008. [55] M. Aminghafari, N. Cheze and J.-M. Poggi, “Multivariate Denoising Using Wavelets and Principal Component Analysis,” Computational Statistics & Data Analysis, Vol. 50, No. 9, 2006, pp. 2381-2398. doi:10.1016/j.csda.2004.12.010
[1] L. J. Lumley, “Engines, an Introduction,” Cambridge University Press, Cambridge, 1999. doi:10.1017/CBO9781139175135 [2] E. P. Hassel and S. Linow, “Laser Diagnostics for Studies of Turbulent Combustion,” Measurement Science and Technology, Vol. 11, No. 2, 2000, pp. R37-R57. doi:10.1088/0957-0233/11/2/201 [3] A. Erdil, A. Kodal and K. Aydin, “Decomposition of Turbulent Velocity Fields in an SI Engine,” Flow, Turbulence and Combustion, Vol. 68, No. 2, 2002, pp. 91-110. doi:10.1023/A:1020467008591 [4] W. C. Choi and Y. G. Guezennec, “Experimental Investigation to Study Convective Mixing, Spatial Uniformity, and Cycle-to-Cycle Variation during the Intake Stroke in an IC Engine,” Journal of Engineering for Gas Turbines and Power, Vol. 122, No. 3, 2000, pp. 493-501. doi:10.1115/1.1286626 [5] A. R. Denlinger, Y. G. Guezennec and W. C. Choi, “Dynamic Evolution of the 3-D Flow Field during the Latter Part of the Intake Stroke in an IC Engine,” Analysis of Combustion and Flow Diagnostics (SP-1348), SAE Paper, 1998. [6] M. P. Patrie and J. K. Martin, “PIV Measurements of in-Cylinder Flow Structures and Correlation with Engine Performance,” Fall Technical Conference, 1997. [7] H. J. NeuBer, L. Spiegel and J. Ganser, “Particle Tracking Velocimetry-A Powerful Tool to Shape the in-Cylinder Flow of Modern Multi Valve Engine Concepts,” SAE Paper, 1995. [8] K. H. Lee, C. S. Lee, H. J. Park and D. S. Kim, “Effects of Tumble and Swirl Flows on the Turbulence Scale Near the TDC in 4 Valve SI Engine,” ICE Spring Technical Conference, 2001. [9] D. P. Towers and C. E. Towers, “Cyclic Variability Measurements of in-Cylinder Engine Flows Using HighSpeed Particle Image Velocimetry,” Measurement Science and Technology, Vol. 15, No. 9, 2004, pp. 19171925. doi:10.1088/0957-0233/15/9/032 [10] R. B. Rask, “Laser Doppler Anemometer Measurements in an Internal Combustion Engine,” SAE Paper, 1979. [11] S. Bopp, F. Durst and C. Tropea, “In-Cylinder Velocity Measurements with a Mobile Fiber Optic LDV System,” SAE Paper, 1990. [12] F. Durst, A. Naqwi and C. Tropea, “Development and Applications of LDA-systems in I.C. Engine Research,” International Symposium, Vol. 90, 1990, pp. 21-30. [13] H. Vigor, J. Pecheux and J. L. Peube, “Velocity Measurements Inside the Cylinder of an Internal Combustion Model Engine during the Intake Process,” Laser Anemometry, Vol. 1, 1991. [14] M. R. Himes and P. V. Farell, “Laser Doppler Velocimeter Measurements within a Motored Direct Injection Spark Ignited Engine,” University of Wisconsin-Madison, Madison, 1998. [15] K. Y. Kang and J. H. Baek, “Turbulence Characteristics of Tumble Flow in a Four-Valve Engine,” Experimental Thermal and Fluid Science, Vol. 18, 1998, pp. 231,243. [16] V. S. S. Chan and J. T. Turner, “Velocity Measurement Inside a Motored Internal Combustion Engine Using Three-Component Laser Doppler Anemometry,” Optics & Laser Technology, Vol. 32, 2000, pp. 557-566. [17] B. Kim, et al., “In-Cylinder Turbulent Measurements with a Spark Plug-In Fiber LDV,” 11th Symposia on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8-11 July 2002. [18] D. Park, P. Sullivan and J. Wallace, “Different Velocity Data Analysis for Flows Near a Spark Plug in the Combustion Chamber of a Spark Ignition Engine,” SAE Paper, 2004. [19] C. Arcoumanis and J. H. Whitelaw, “Fluid Mechanics of Internal Combustion Engines: A Review,” International Symposium on Flows in Internal Combustion Engines-III, Vol. 201, No. 1, 1985, pp. 57-74. [20] S. Roudnitzky, P. Druault, and P. Guibert, “Proper Orthogonal Decomposition of in-Cylinder Engine Flow into Mean Component, Coherent Structures and Random Gaussian Fluctuations,” Journal of Turbulence, Vol. 7, No. 70, 2006, p. 70. [21] M. Fogleman, J. Lumley, D. Rempfer and D. Haworth, “Application of the Proper Orthogonal Decomposition to Datasets of Internal Combustion Engine Flows,” Journal of Turbulence, Vol. 5, No. 23, 2004, pp. 1-18. [22] P. Sullivan, R. Ancimer, J. Wallace, “Turbulence Averaging within Spark Ignition Engines,” Experiments in Fluids, Vol. 27, No. 1, 1999, pp. 92-101. doi:10.1007/s003480050333 [23] R. Ancimer, P. Sullivan and J. Wallace, “Decomposition of Measured Velocity Fields with Spark Ignition Engines Using Discrete Wavelet Transforms,” Experiments in Fluids, Vol. 30, No. 2, 2001, pp. 237-238. doi:10.1007/s003480000152 [24] F. S?derberg, B. Johansson, and B. Lindoff, “Wavelet Analysis of in-Cylinder LDV Measurements and Correlation Against Heat-Release,” SAE Paper, 1998. [25] A. Sen, G. Litak, R. Taccani and R. Radu, “Wavelet Analysis of Cycle-to-Cycle Pressure Variations in an Internal Combustion Engine,” Chaos, Solitons and Fractals, Vol. 38, No. 3, 2008, pp. 886-893. doi:10.1016/j.chaos.2007.01.041 [26] Z. Zhang, E. Tomita, S. Yoshiyama, Y. Hamamoto and H. Kawabata, “Wavelet Transform Analysis of Unsteady Turbulence and Turbulent Burning Velocity in a Constant-Volume Vessel,” JSME International Journal, Series B, Vol. 44, No. 4, 2001, pp. 608-615. doi:10.1299/jsmeb.44.608 [27] C. Arcoumanis, A. C. Enotiadis and J. H. Whitelaw, “Frequency Analysis of Tumble and Swirl in Motored Engines,” Journal of Automobile Engineering, Vol. 205, 1991, pp. 177-184. doi:10.1243/PIME_PROC_1991_205_168_02 [28] T. D. Fansler, “Turbulence Production and Relaxation in Bowl-in-Piston Engines,” SAE Paper, 1993. [29] A. C. Enotiadis, C. Vafidis and J. H. Whitelaw, “Interpretation of Cyclic Flow Variations in Motored Internal Combustion Engines,” Experiments in Fluids, Vol. 10, No. 2-3, 1990, pp. 77-86. [30] E. Esirgemez and M. S. ?l?men, “Spark-Plug LDV Probe for in-Cylinder Flow Analysis of Production IC Engines,” Measurement Science and Technology, Vol. 16, No. 10, 2005, pp. 2038-2047. doi:10.1088/0957-0233/16/10/020 [31] N. Kevlehan, J. C. R. Hunt and J. C. Vassilicos, “A Comparison of Different Analytical Techniques for Identifying Structures in Turbulence,” Applied Scientific Research, Vol. 53, No. 3-4, 1994, pp. 339-355. doi:10.1007/BF00849109 [32] H. E. Albrecht, M. Borys, N. Damaschke and C. Tropea, “Laser Doppler and Phase Doppler Measurement Techniques,” Springer-Verlag, 2003. [33] L. H. Benedict, H. Nobach and C. Tropea, “Estimation of Turbulent Velocity Spectra from Laser Doppler Data,” Measurement Science and Technology, Vol. 11, No. 8, 2000, pp. 1089-1104. doi:10.1088/0957-0233/11/8/301 [34] E. Konstantinidis, A. Ducci, S. Balabani and M. Yianneskis, “An Empirical Method for Efficient Spectrum Estimation from LDA Data,” 13th International Symposiaon Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 26-29 June 2006. [35] I. ?elik, I. Yavuz, A. Smirnov, J. Smith, E. Amin and A. Gel, “Prediction of in-Cylinder Turbulence for IC Enginess,” Combustion Science and Technology, Vol. 153, No. 1, 2000, pp. 339-368. doi:10.1080/00102200008947269 [36] “Matlab,” Version 7.7.0.471, The MathWorks Inc., Natick, 2008. [37] P. M. T. Broersen and S. de Waele, “Generating Data with Prescribed Power Spectral Density,” IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 4, 2003, pp. 1061doi:10.1109/TIM.2003.814824 [38] S. F. Al-Sharif, M. A. Cotton and T. J. Craft, “Reynolds Stress Transport Models in Unsteady and Non-Equilibrium Turbulent Flows,” International Journal of Heat and Fluid Flow, Vol. 31, No. 3, 2000, pp. 401-408. doi:10.1016/j.ijheatfluidflow.2010.02.024 [39] S. He, C. Ariyaratne and A. E. Vardy, “A Computational Study of Wall Friction and Turbulence Dynamics in Accelerating Pipe Flows,” Computers & Fluids, Vol. 37, No. 6, 2008, pp. 674-689. doi:10.1016/j.compfluid.2007.09.001 [40] A. J. Revell, S. Benhamadouche, T. Craft and D. Laurence, “A Stress-Strain Lag Eddy Viscosity Model for Unsteady Mean Flow,” International Journal of Heat and Fluid Flow, Vol. 27, No. 5, 2006, pp. 821-830. doi:10.1016/j.ijheatfluidflow.2006.03.027 [41] Y. C. Liang, H. P. Lee, S. P. Lim, W. Z. Lin, K. H. Lee and C. G. Wu, “Proper Orthogonal Decomposition and Its Applications—Part I: Theory,” Journal of Sound and Vibration, Vol. 252, No. 3, 2002, pp. 527-544. [42] E. Zervas, “Correlations between Cycle-to-Cycle Variations and Combustion Parameters of a Spark Ignition Engine,” Applied Thermal Engineering, Vol. 24, No. 14-15, 2004, pp. 2073-2081. doi:10.1016/j.applthermaleng.2004.02.008 [43] W. C. Choi and Y. G. Guezennec, “Study of the Flow Field Development During the Intake Stroke in an IC Engine Using 2-D PIV and 3-D PTV,” International Congress and Exposition Detroit, Michigan, 1-4 March 1999. [44] T.-M. Liou and D. A. Santavicca, “Cycle Resolved LDV Measurements in a Motored IC Engine,” Journal of Fluids Engineering, Transactions of ASME, Vol. 107, 1985, pp. 232-240. [45] R. A. Fraser and F.V. Bracco, “Cycle-Esolved LDV Integral Length Scale Meaurements Investigating Clearance Height Scaling, Isotropy, and Homogeneity in an I.C. Engine,” International Congress and Exposition, Detroit, 27 February-3 March 1989. [46] C. W. Hong and D. G. Chen, “Direct Measurements of in-Cylinder Integral Length Scales of a Transparent Engine,” Experiments in Fluids, Vol. 23, No. 2, 1997, pp. 113-120. doi:10.1007/s003480050092 [47] R. B. Rask, “Comparison of Window, Smoothed-Ensemble, and Cycle-to-Cycle Data Reduction Techniques for Laser Doppler Anemometer Measurements of in-Cylinder Velocity,” In: T. Morel, R. P. Lohmann and J. M. Rackley, Eds., Fluid Mechanics of Combustion Systems, ASME, New York, 1981. [48] J. L. Lumley, “The Structure of Inhomogeneous Turbulence,” In: A. M. Yaglom and V. I. Tatarski, Eds., Atmospheric Turbulence and Wave Propagation, Nauka, Moscow, 1967, pp. 166-178. [49] A. Chatterjee, “An Introduction to the Proper Orthogonal Decomposition,” Current Science, Vol. 78, No. 7, 2000, pp. 808-817. [50] C. Tropea, A. L. Yarin and J. F. Foss, “Springer Handbook of Experimental Fluid Mechanics,” 2007. [51] C. Torrence, and G. P. Compo, “A Practical Guide to Wavelet Analysis,” Bulletin of the American Meteorological Society, Vol. 79, No. 1, 1998, pp. 61-78. doi:10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2 [52] M. Farge, K. Scheineder and P. Abry, “Analyzing and Compressing Turbulent Fields with Wavelets,” Institut Pierre Simon Laplace Publication, 2002. [53] M. Farge, “Wavelet Transforms and Their Applications to Turbulence,” Annual Review of Fluid Mechanics, Vol. 24, 1992, pp. 395-457. doi:10.1146/annurev.fl.24.010192.002143 [54] M. Misiti, Y. Misiti, G. Oppenheim and J.-M. Poggi, “Wavelet Toolbox? 4, User’s Guide,” 2008. [55] M. Aminghafari, N. Cheze and J.-M. Poggi, “Multivariate Denoising Using Wavelets and Principal Component Analysis,” Computational Statistics & Data Analysis, Vol. 50, No. 9, 2006, pp. 2381-2398. doi:10.1016/j.csda.2004.12.010