Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-26T05:55:41.576Z Has data issue: false hasContentIssue false
  • English
  • Français

Spatial reconstruction of steady scalar sources from remote measurements in turbulent flow

Published online by Cambridge University Press:  14 May 2019

Qi Wang ,
Yosuke Hasegawa  and
Tamer A. Zaki Open the ORCID record for Tamer A. Zaki [Opens in a new window]
Qi Wang
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Yosuke Hasegawa
Affiliation:
Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
Tamer A. Zaki*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Identifying the source of passive scalar transported in a turbulent environment from remote measurements is an ill-posed problem due to the irreversibility of diffusive processes. A significant difficulty of the source reconstruction is due to different potential source locations generating very highly correlated signals at the sensor. A variational algorithm is formulated, which utilizes high-fidelity simulations to reconstruct the spatial distribution of the source. A cost functional is defined based on the difference between the true measurements and their prediction from the simulations with the estimated source. Using forward–adjoint looping, the gradient of the cost functional with respect to the source distribution is evaluated, and the estimate of the source is updated. The adjoint-variational approach naturally accommodates measurements from multiple sensors, with essentially the same computational cost. The algorithm is evaluated for scalar dispersion in turbulent channel flow. When a single sensor is placed directly downstream of the source, the reconstruction is accurate in the cross-stream directions and is elongated in the streamwise direction. The estimated source, however, can reproduce the measurements and the scalar plume downstream of the sensor location. In the channel centre and log layer, the scalar fields are dominated by dispersion, and therefore the reconstruction is better than in the near-wall regions, where the scalar fields are dominated by diffusion. When a sensor is placed near the wall, the accuracy of the source recovery deteriorates due to diffusive effects. By using more sensors that span the plume cross-section, improvement of performance can be demonstrated despite an enlarged domain of dependence.

JFM classification

Turbulent Flows: Turbulence control Mathematical Foundations: Variational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 316 - 352
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abe, H., Antonia, R. A. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.Google Scholar
Alapati, S. & Kabala, Z. J. 2000 Recovering the release history of a groundwater contaminant using a non-linear least-squares method. Hydrol. Process. 14 (6), 1003–1016.Google Scholar
Atmadja, J. & Bagtzoglou, A. C. 2001 Pollution source identification in heterogeneous porous media. Water Resour. Res. 37 (8), 2113–2125.Google Scholar
Bieringer, P. E., Rodriguez, L. M., Vandenberghe, F., Hurst, J. G., Bieberbach, G. Jr, Sykes, I., Hannan, J. R., Zaragoza, J. & Fry, R. N. Jr 2015 Automated source term and wind parameter estimation for atmospheric transport and dispersion applications. Atmos. Environ. 122, 206–219.Google Scholar
Brereton, C. A., Joynes, I. M., Campbell, L. J. & Johnson, M. R. 2018 Fugitive emission source characterization using a gradient-based optimization scheme and scalar transport adjoint. Atmos. Environ. 181, 106–116.Google Scholar
Cerizza, D., Sekiguchi, W., Tsukahara, T., Zaki, T. A. & Hasegawa, Y. 2016 Reconstruction of scalar source intensity based on sensor signal in turbulent channel flow. Flow Turbul. Combust. 97 (4), 1211–1233.Google Scholar
Colaço, M. J., Orlande, H. R. B. & Dulikravich, G. S. 2006 Inverse and optimization problems in heat transfer. J. Braz. Soc. Mech. Sci. Engng 28 (1), 1–24.Google Scholar
Gorelick, S. M., Evans, B. & Remson, I. 1983 Identifying sources of groundwater pollution: an optimization approach. Water Resour. Res. 19 (3), 779–790.Google Scholar
Hajieghrary, H., Tomás, A. F. & Hsieh, M. A. 2015 An information theoretic source seeking strategy for plume tracking in 3D turbulent fields. In 2015 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), pp. 1–8. IEEE.Google Scholar
Hasegawa, Y. & Kasagi, N. 2009 Low-pass filtering effects of viscous sublayer on high Schmidt number mass transfer close to a solid wall. Intl J. Heat Fluid Flow 30 (3), 525–533.Google Scholar
Houweling, S., Kaminski, T., Dentener, F., Lelieveld, J. & Heimann, M. 1999 Inverse modeling of methane sources and sinks using the adjoint of a global transport model. J. Geophys. Res. 104 (D21), 26137–26160.Google Scholar
Huang, C.-H., Li, J.-X. & Kim, S. 2008 An inverse problem in estimating the strength of contaminant source for groundwater systems. Appl. Math. Model. 32 (4), 417–431.Google Scholar
Jelly, T. O., Jung, S. Y. & Zaki, T. A. 2014 Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26 (9), 095102.Google Scholar
Joynes, I. M.2014 Proof-of-concept inverse micro-scale dispersion modelling for fugitive emissions quantification in industrial facilities. PhD thesis, Carleton University.Google Scholar
Kang, W. & Xu, L. 2012 Optimal placement of mobile sensors for data assimilations. Tellus A 64 (1), 17133.Google Scholar
Keats, A., Yee, E. & Lien, F.-S. 2007 Bayesian inference for source determination with applications to a complex urban environment. Atmos. Environ. 41 (3), 465–479.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
Lee, J., Jelly, T. & Zaki, T. A. 2015 Effect of Reynolds number on turbulent drag reduction by superhydrophobic surface textures. Flow Turbul. Combust. 95, 277–300.Google Scholar
Lee, J., Sung, H. J. & Zaki, T. A. 2017 Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 819, 165–187.Google Scholar
Liu, X. & Zhai, Z. 2007 Inverse modeling methods for indoor airborne pollutant tracking: literature review and fundamentals. Indoor Air 17 (6), 419–438.Google Scholar
Mahar, P. S. & Datta, B. 1997 Optimal monitoring network and ground-water-pollution source identification. J. Water Resour. Plann. Manag. 123 (4), 199–207.Google Scholar
Mahar, P. S. & Datta, B. 2000 Identification of pollution sources in transient groundwater systems. Water Resour. Manag. 14 (3), 209–227.Google Scholar
Mahar, P. S. & Datta, B. 2001 Optimal identification of ground-water pollution sources and parameter estimation. J. Water Resour. Planning Manag. 127 (1), 20–29.Google Scholar
Masson, J. B., Bechet, M. B. & Vergassola, M. 2009 Chasing information to search in random environments. J. Phys. A 42 (43), 434009.Google Scholar
Mons, V., Chassaing, J.-C. & Sagaut, P. 2017 Optimal sensor placement for variational data assimilation of unsteady flows past a rotationally oscillating cylinder. J. Fluid Mech. 823, 230–277.Google Scholar
Neupauer, R. M. & Wilson, J. L. 2001 Adjoint-derived location and travel time probabilities for a multidimensional groundwater system. Water Resour. Res. 37 (6), 1657–1668.Google Scholar
Nolan, K. P. & Zaki, T. A. 2013 Conditional sampling of transitional boundary layers in pressure gradients. J. Fluid Mech. 728, 306–339.Google Scholar
Pudykiewicz, J. A. 1998 Application of adjoint tracer transport equations for evaluating source parameters. Atmos. Environ. 32 (17), 3039–3050.Google Scholar
Quadrio, M. & Luchini, P. 2003 Integral space–time scales in turbulent wall flows. Phys. Fluids 15 (8), 2219–2227.Google Scholar
Rosenfeld, M., Kawak, D. & Vinokur, M. 1991 A fractional step solution method for the unsteady incompressible Navier–Stokes equations in generalized curvilinear coordinate systems. J. Comput. Phys. 94, 102–137.Google Scholar
Skaggs, T. H. & Kabala, Z. J. 1994 Recovering the release history of a groundwater contaminant. Water Resour. Res. 30 (1), 71–79.Google Scholar
Skaggs, T. H. & Kabala, Z. J. 1995 Recovering the history of a groundwater contaminant plume: method of quasi-reversibility. Water Resour. Res. 31 (11), 2669–2673.Google Scholar
Vergassola, M., Villermaux, E. & Shraiman, B. I. 2007 ‘Infotaxis’ as a strategy for searching without gradients. Nature 445 (7126), 406–409.Google Scholar
Woodbury, A., Render, F. & Ulrych, T. 1995 Practical probabilistic ground-water modeling. Ground Water 33 (4), 532–538.Google Scholar
Woodbury, A. D. 1997 A probabilistic fracture transport model: application to contaminant transport in a fractured clay deposit. Can. Geotech. J. 34 (5), 784–798.Google Scholar
Woodbury, A. D. & Ulrych, T. J. 1993 Minimum relative entropy: forward probabilistic modeling. Water Resour. Res. 29 (8), 2847–2860.Google Scholar
Zaki, T. A. 2013 From streaks to spots and on to turbulence: exploring the dynamics of boundary layer transition. Flow Turbul. Combust. 91 (3), 451–473.Google Scholar
Zaki, T. A. & Saha, S. 2009 On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers. J. Fluid Mech. 626, 111–147.Google Scholar