PROOF COPY 012403JFG PROOF COPY 012403JFG Marko Hoc ˇ evar* e-mail: marko.hocevar@fs.uni-lj.si Phone: +386 1 4771 774 Fax: +386 1 2518 567 Brane S ˇ irok e-mail: brane.sirok@fs.uni-lj.si Phone: +386 1 4771 410 Fax: +386 1 2518 567 Faculty of Mechanical Engineering, Hydraulic Machines Laboratory, University of Ljubljana, As ˇkerc ˇeva 6, P.O. Box 394, SI-1000 Ljubljana, Slovenia Igor Grabec e-mail: igor.grabec@fs.uni-lj.si Faculty of Mechanical Engineering, Laboratory of Technical Physics, University of Ljubljana, As ˇkerc ˇeva 6, P.O. Box 394, SI-1000 Ljubljana, Slovenia Phone: +386 1 4771 605 Fax: +386 1 2518 567 Experimental Turbulent Field Modeling by Visualization and Neural Networks Turbulent flow field was modeled based on experimental flow visualization and radial- basis neural networks. Turbulent fluctuations were modeled based on the recorded con- centration at various locations in the Karman vortex street, which were used as inputs and outputs of the neural network. From the measured and the modeled concentration the power spectra and spatial correlation functions were calculated. The measured and the modeled concentration power spectra correspond well to the -5/3 turbulence decay law, and exhibit the basic spectral peak of fluctuation power at the same frequency. The predicted and measured correlation functions of concentration exhibit similar behavior. DOI: 10.1115/1.1760534 1 Introduction Our purpose was to model the concentration in a Karman vor- tex street using an experimental modeling technique. The experi- mental method was based on measurements of concentration by a visualization technique, and modeling using a radial-basis neural network RBNN. Recently, some attempts have been made to apply artificial neu- ral networks ANNs to problems in fluid dynamics. Faller et al. 1,2 utilized an ANN to predict separation pressure on an aircraft foil after training it with existing unsteady airfoil data obtained at different pitch rates. Jacobson and Reynolds 3 used two different ANN controllers to alter the shear stress on the wall of a modeled boundary layer, and deduced a skin friction reduction of 8%. ANNs are also increasingly being applied in pattern recognition problems, and their application has been extended to particle im- age velocimetry and similar techniques Jambunathan et al. 4, Grant and Pan 5, Kimura et al. 6. Dibike et al. 7 applied ANNs in generation of wave equations from hydraulic data. Blackwelder 8 and Ferre-Gine et al. 9 used ANNs for turbulent eddy classification and detection of eddy patterns. A velocity field flow prediction was attempted by Delgado et al. 10, Zhang et al. 11, and Giralt et al. 12. Neural networks were applied towards the formulation of accurate and wide-range calibration methods for such flow-diagnostics instruments as multi-hole and cross-wire probes 13,14. For flow control applications, ANNs offer a possibility of adap- tive controllers that are simpler and potentially less sensitive to parameter variations as compared to conventional controllers Gad-el-Hak 15, Lee et al. 16. The controller does not neces- sarily require velocity field information, but also accepts other quantities, which characterize the structure of the flow field, for example flow visualization pictures Gillies, 1998 17. We con- sidered a turbulent flow of the Karman vortex street. Its properties were characterized by the power spectra and correlation functions of an added passive tracer concentration. Experimental conditions were selected such that a common ex- ample of turbulent field was obtained. In this case, the effect of the molecular diffusivity and the kinematic viscosity could be neglected. These occur at wavenumbers of fluctuating flow that are much smaller than the dissipation cut-off k d and the diffusion cut-off k c ( k k c ; k k d ). The scalar variance spectrum was then described by the well known power law McComb 18 F  k  =   -1/3 k -5/3 . (1) Here  is the Obukhov-Corrsin constant,  is variance of scalar concentration field, and  is turbulent kinetic energy dissipation rate. It was pointed out by Batchelor 19, that the proposed dif- fusion cut-off k c is only valid for viscosities smaller than the diffusion coefficient v D. In the following we show that our experimental arrangement provided for the generation of a turbu- lent field with this power spectrum, and demonstrate that the mod- eled field exhibited the same property. It is convenient to describe the statistical properties of the tur- bulent field based upon the correlation between two concentra- tions. The simultaneous measurements of concentration at two locations in the image permit to obtain directly the space autocor- relation coefficient Q, from which the Taylor length scale  c for concentration is deduced. The autocorrelation coefficient for con- centration can be approximated by a parabolic function in a simi- lar way as shown by Hinze 20 for velocity Q r  =1 - r 2  c 2 +O r 3  (2) for very small values of separation r. Our goal was to solve the following problem: Provided that the flow in some region is given, how can the flow in the surrounding region be forecast? We used a method that is similar to the rec- ognition of patterns by intelligent beings and is based on statistical modeling. This method was based on the information provided by past observations of the same phenomenon in equivalent environ- *Corresponding author. Contributed by the Fluids Engineering Division for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received by the Fluids Engineering Division March 20, 2003; revised manuscript received January 5, 2004. Associate Editor: M. V. O ¨ tu ¨gen. Copyright © 2004 by ASME Journal of Fluids Engineering MAY 2004, Vol. 126 Õ 1 PROOF COPY 012403JFG