TY - GEN

T1 - Input-output analysis of the 2D/3C model in channel flows of viscoelastic fluids

AU - Hoda, Nazish

AU - Jovanović, Mihailo R.

AU - Kumar, Satish

PY - 2008

Y1 - 2008

N2 - Energy amplification in streamwise constant channel flows of viscoelastic fluids is studied from an input-output point of view by analyzing the responses of the velocity components to spatio-temporal body forces. These inputs into governing equations are assumed to be harmonic in spanwise direction and stochastic in the wall-normal direction and in time. An explicit Reynolds number scaling of frequency responses from different input to different output components is developed. It is found that some of the components of frequency response peak at nonzero temporal frequencies. This is in contrast to the Newtonian fluids, where peaks are always observed at zero frequency, suggesting that viscoelastic effects introduce additional timescales and promote development of flow patterns with smaller time constants than in Newtonian fluids. The frequencies, corresponding to the peaks in the components of frequency response, decrease with an increase in viscosity ratio and show maximum for non-zero elasticity number. At low Reynolds numbers, the energy density decreases monotonically when the elasticity number is sufficiently small, but shows a maximum when the elasticity number becomes sufficiently large, suggesting that elasticity can amplify disturbances even when inertial effects are weak.

AB - Energy amplification in streamwise constant channel flows of viscoelastic fluids is studied from an input-output point of view by analyzing the responses of the velocity components to spatio-temporal body forces. These inputs into governing equations are assumed to be harmonic in spanwise direction and stochastic in the wall-normal direction and in time. An explicit Reynolds number scaling of frequency responses from different input to different output components is developed. It is found that some of the components of frequency response peak at nonzero temporal frequencies. This is in contrast to the Newtonian fluids, where peaks are always observed at zero frequency, suggesting that viscoelastic effects introduce additional timescales and promote development of flow patterns with smaller time constants than in Newtonian fluids. The frequencies, corresponding to the peaks in the components of frequency response, decrease with an increase in viscosity ratio and show maximum for non-zero elasticity number. At low Reynolds numbers, the energy density decreases monotonically when the elasticity number is sufficiently small, but shows a maximum when the elasticity number becomes sufficiently large, suggesting that elasticity can amplify disturbances even when inertial effects are weak.

KW - Input-output analysis

KW - Reynolds-number scaling

KW - Transition to turbulence

KW - Viscoelastic fluids

UR - http://www.scopus.com/inward/record.url?scp=62949229258&partnerID=8YFLogxK

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U2 - 10.1109/CDC.2008.4739444

DO - 10.1109/CDC.2008.4739444

M3 - Conference contribution

AN - SCOPUS:62949229258

SN - 9781424431243

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 841

EP - 846

BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 47th IEEE Conference on Decision and Control, CDC 2008

Y2 - 9 December 2008 through 11 December 2008

ER -