Long-channel nonlinear hydrodynamic stability of zero-mean oscillatory flows and its effect on heat transfer under quasi-steady condition

Conference · Thu Jul 01 04:00:00 EDT 1999

OSTI ID:20030486

Li, P; Yang, K T

Under certain appropriate conditions, high heat transfer enhancement from heated walls can be expected in zero-mean oscillatory flows in ducts, as compared to the corresponding steady forced-convection unidirectional flows. When the duct vertical characteristic lengths are small compared to the duct length, the duct end conditions lose their effects, even though heat-transfer enhancement may persist. In this case, it is known qualitatively that this enhancement is the result of nonlinear hydrodynamic instabilities and subsequent transition to turbulence at sufficiently high oscillatory-flow Reynolds numbers. Despite the general interests in this long-duct unsteady flow phenomena and their corresponding effects on the forced-convection heat transfer, very little is known beyond the determination of critical Reynolds numbers for the limit of linear stability. Even in this case, widely scattered critical Reynolds numbers have been reported based on various experimental studies and theoretical analyses of linear instabilities for laminar zero-mean oscillatory flows. The purpose of the present study is a theoretical attempt to understand the early nonlinear phenomena for zero-mean oscillatory flows in a long channel beyond the limits of linear instability. The analysis is based on direct numerical simulations of the Navier-Stokes equations by means of a finite-difference technique, in which the evolution of the flow in the presence of a prescribed set of infinitesimal disturbances is followed in time. The initial disturbances are determined under quasi-steady conditions of the unsteady base flow, based on the solutions to the Orr-Sommerfeld equation along with the base-flow velocity profiles at three time instants in the deceleration part of the oscillatory cycle, where the first amplifications of the disturbances have been observed in experiments. The time-dependent growth rates of the disturbances at each of the base-flow time instants have been determined, along with the power spectra of the velocity field. It is shown that early transition happens near the wall and that the flow that is nonlinearly more unstable is the one that is linearly more stable. It has also been demonstrated that the nonlinearly unstable flows lead to rapid increases in the fully-developed Nusselt numbers.

• Research Organization: Vickers Inc., Jackson, MS (US)
• OSTI ID: 20030486
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
AUGMENTATION
DUCTS
HEAT TRANSFER
INSTABILITY
LAMINAR FLOW
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
NUSSELT NUMBER
UNSTEADY FLOW