G. Danabasoglu

Computation of convective flow with gravity modulation in rectangular cavities

In this work, a computational study is presented for the investigation of gravity modulation (£-jitter) effects in thermally driven cavity flows at terrestrial and microgravity environments. The two-dimensional, time-dependent Navier-Stokes equations are numerically integrated by a time-split method using direct matrix solvers. Computations at terrestrial gravity are utilized to assess the effects of adiabatic side-wall boundary conditions as well as the full nonlinearity of the governing equations on the sinusoidally forced Benard problem studied by Gresho and Sani.1 The low-g calculations focus on the establishment of critical frequency ranges and consider the effects of modulation direction and randomness. The applicability of linear analysis in the excitable frequency range at low g is also discussed.

Spatial simulation of instability control by periodic suction blowing

The applicability of active control by periodic suction blowing in spatially evolving plane Poiseuille flow is investigated by the direct simulation of the three‐dimensional, incompressible Navier–Stokes equations. The results reveal that significant reductions in perturbation amplitudes can be obtained by a proper choice of the control wave amplitude and phase. The upstream influence of the control wave is shown to be confined to a region in the vicinity of the control slot with no apparent effect on the flow development.

Oscillatory flow with heat transfer in a square cavity

A computational study is presented for the flow inside an oscillatory cavity. The numerical scheme employs a semi‐implicit, time‐splitting method to integrate the two‐dimensional full Navier–Stokes equations satisfying continuity to machine accuracy. The efficient use of direct solvers for the uncoupled momentum and pressure equations is demonstrated. The oscillatory cavity flow is studied considering the effects of heat transfer, Reynolds number, and oscillatory Stokes number.

Spatial simulation of secondary instability in plane channel flow: comparison of K- and H-type disturbances

This study involves a numerical simulation of spatially evolving secondary instability in plane channel flow. The computational algorithm integrates the time-dependent, three-dimensional, incompressible Navier-Stokes equations by a mixed finitedifferencelspectral technique. In particular, we are interested in the differences between instabilities instigated by Klebanoff (K-) type and Herbert (H-) type inflow conditions, and in comparing the present spatial results with previous temporal models. It is found that for the present inflow conditions, H-type instability is biased towards one of the channel walls, while K-type instability evolves on both walls. For low initial perturbation amplitudes, H-type instability exhibits higher growth rates than K-type instability while higher initial amplitudes lead to comparable growth rates of both Hand K-type instability. In H-type instability, spectral analysis reveals the presence of the subharmonic two-dimensional mode which promotes the growth of the threedimensional spanwise and fundamental modes through nonlinear interactions. An intermodal energy transfer study demonstrates that there is a net energy transfer from the three-dimensional modes to the two-dimensional mode. This analysis also indicates that the mean mode transfers net energy to the two-dimensional subharmonic mode and to the three-dimensional modes.

Numerical simulation of spatially-evolving instability

A computational study of the spatial stability of plane Poiseuille flow is presented. The numerical scheme employs a time-splitting method to integrate the full Navier-Stokes equations using spectral collocation/finite-diiFerence discretization on a non-staggered mesh. The eigenvalue decomposition procedure is applied for the solution of the Poisson equations using the capacitance matrix technique. The buffer domain method is incorporated for the outflow boundary conditions. The input perturbation velocities are obtained by solving the Orr-Sommerfeld equation for the non-linear eigenvalue problem employing the companion matrix method. Computational results are compared with the linear theory for two-dimensional disturbances.

A Finite-Difference Method with Direct Solvers for Thermally-Driven Cavity Problems

In this paper, we present a computational study concerning the problem of buoyancy-driven flows in a shallow cavity with aspect ratio, Ar = 4. We investigate two cases with rigid and free-surface upper boundaries. For each of these cases, the effects of Grashof number is investigated for low Prandtl number fluids, namely Pr = 0 (conduction limit) and Pr = 0.015. The numerical results indicate the onset of oscillatory flow as well as some sudden transitions at higher Grashof numbers.

Simulation of instabilities in a boundary layer with a roughness element

The computational procedure which involves the multidomain method was successfully used to study the spatial development of instability waves in the presence of a two-dimensional, isolated roughness element.

A Spectral Multi-Domain Code for the Navier-Stokes Equations

A computational method to study the spatial stability of the Blasius boundary layer in the presence of a roughness element is developed. The numerical scheme uses a time- splitting, finite-difference/spectral method to integrate the full Navier-Stokes equations on a stretched grid. Time advancement is done by the Crank-Nicolson and the third-order compact Runge-Kutta methods. Difficulties associated with the singular corners are overcome by the application of the multi-domain method. The code is also used for Blasius boundary layer instability and the results are compared with the linear theory.