Haecheon Choi

Direct numerical simulation of turbulent flow over riblets

Direct numerical simulations of turbulent flows over riblet-mounted surfaces are performed to educe the mechanism of drag reduction by riblets. The computed drag on the riblet surfaces is in good agreement with the existing experimental data. The mean-velocity profiles show upward and downward shifts in the log–law for drag-decreasing and drag-increasing cases, respectively. Turbulence statistics above the riblets are computed and compared with those above a flat plate. Differences in the mean-velocity profile and turbulence quantities are found to be limited to the inner region of the boundary layer. Velocity and vorticity fluctuations as well as the Reynolds shear stresses above the riblets are reduced in drag-reducing configurations. Quadrant analysis indicates that riblets mitigate the positive Reynolds-shear-stress-producing events in drag-reducing configurations. From examination of the instantaneous flow fields, a drag reduction mechanism by riblets is proposed: riblets with small spacings reduce viscous drag by restricting the location of the streamwise vortices above the wetted surface such that only a limited area of the riblets is exposed to the downwash of high-speed fluid that the vortices induce.

Control of laminar vortex shedding behind a circular cylinder using splitter plates

Laminar vortex shedding behind a circular cylinder and its control using splitter plates attached to the cylinder are simulated. The vortex shedding behind a circular cylinder completely disappears when the length of the splitter plate is larger than a critical length, and this critical length is found to be proportional to the Reynolds number. The Strouhal number of the vortex shedding is rapidly decreasing with the increased plate length until the plate length (l) is nearly the same as the cylinder diameter (d). On the other hand, at 1<l/d<2, the control shows two different behaviors for the Reynolds numbers investigated. The net drag is significantly reduced by the splitter plate, and there exists an optimum length of the plate for minimum drag at a given Reynolds number. From an examination of the instantaneous flow fields, it is found that the Strouhal number modification by the splitter plate is closely related to the size of the primary vortex behind the cylinder and the length of the plate.

Feedback control for unsteady flow and its application to the stochastic Burgers equation

Mathematical methods of control theory are applied to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. The procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory is presented using model problems through the formalism and language of control theory. Then we present a suboptimal control and feedback procedure for general stationary and time-dependent problems using methods of calculus of variations through the adjoint state and gradient algorithms. This suboptimal feedback control procedure is applied to the stochastic Burgers equation. Two types of controls are investigated : distributed and boundary controls. The control inputs are the momentum forcing for the distributed control and the boundary velocity for the boundary control. Costs to be minimized are defined as the sum of the mean-square velocity gradient inside the domain for the distributed control or the square velocity gradient at the wall for the boundary control; and in both cases a term was added to account for the implementation cost. Several cases of both controls have been numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs. Another version of the feedback procedure more effective for practical implementation has been considered and implemented, and the application of this algorithm also shows significant reductions of the costs. Finally, dependence of the control algorithm on the time-discretization method is discussed.

Drag reduction by polymer additives in a turbulent channel flow

Turbulent drag reduction by polymer additives in a channel is investigated using direct numerical simulation. The dilute polymer solution is expressed with an Oldroyd-B model that shows a linear elastic behaviour. Simulations are carried out by changing the Weissenberg number at the Reynolds numbers of 4000 and 20 000 based on the bulk velocity and channel height. The onset criterion for drag reduction predicted in the present study shows a good agreement with previous theoretical and experimental studies. In addition, the flow statistics such as the r.m.s. velocity fluctuations are also in good agreement with previous experimental observations. The onset mechanism of drag reduction is interpreted based on elastic theory, which is one of the most plausible hypotheses suggested in the past. The transport equations for the kinetic and elastic energy are derived for the first time. It is observed that the polymer stores the elastic energy from the flow very near the wall and then releases it there when the relaxation time is short, showing no drag reduction. However, when the relaxation time is long enough, the elastic energy stored in the very near-wall region is transported to and released in the buffer and log layers, showing a significant amount of drag reduction.

Laminar flow past a rotating circular cylinder

The present study numerically investigates two-dimensional laminar flow past a circular cylinder rotating with a constant angular velocity, for the purpose of controlling vortex shedding and understanding the underlying flow mechanism. Numerical simulations are performed for flows with Re=60, 100, and 160 in the range of 0⩽α⩽2.5, where α is the circumferential speed at the cylinder surface normalized by the free-stream velocity. Results show that the rotation of a cylinder can suppress vortex shedding effectively. Vortex shedding exists at low rotational speeds and completely disappears at α>αL, where αL is the critical rotational speed which shows a logarithmic dependence on Re. The Strouhal number remains nearly constant regardless of α while vortex shedding exists. With increasing α, the mean lift increases linearly and the mean drag decreases, which differ significantly from those predicted by the potential flow theory. On the other hand, the amplitude of lift fluctuation stays nearly constant with in...

Suboptimal control of turbulent channel flow for drag reduction

Two simple feedback control laws for drag reduction are derived by applying a suboptimal control theory to a turbulent channel flow. These new feedback control laws require pressure or shear-stress information only at the wall, and when applied to a turbulent channel flow at Re τ =110, they result in 16–22% reduction in the skin-friction drag. More practical control laws requiring only the local distribution of the wall pressure or one component of the wall shear stress are also derived and are shown to work equally well.

Immersed boundary method for flow around an arbitrarily moving body

For the simulation of flow around an arbitrarily moving body, an immersed boundary method is developed in a non-inertial reference frame that is fixed to the body. The Navier-Stokes equation is formulated in a conservative form such that the force terms due to the rotation and the translational and rotational accelerations are included in the nonlinear term. In order to satisfy the no-slip condition on the body surface, momentum forcing and mass source/sink are applied on the body surface or inside the body. The numerical method is based on a finite volume approach on a staggered mesh together with a fractional-step method. The present numerical method is applied to both the forced motion and fluid-structure interaction problems. In the latter, we solve fully coupled Navier-Stokes and dynamic equations for the moving body without introducing any iteration. Four different flow problems are tested and the results are in excellent agreements with previous numerical and experimental ones.

Grid-point requirements for large eddy simulation: Chapman’s estimates revisited

Resolution requirements for large eddy simulation (LES), estimated by Chapman [AIAA J. 17, 1293 (1979)], are modified using accurate formulae for high Reynolds number boundary layer flow. The new estimates indicate that the number of grid points (N) required for wall-modeled LES is proportional to ReLx, but a wall-resolving LES requires NReLx13/7, where Lx is the flat-plate length in the streamwise direction. On the other hand, direct numerical simulation, resolving the Kolmogorov length scale, requires NReLx37/14.

Direct numerical simulation of turbulent thermal boundary layers

In this paper, a method of generating realistic turbulent temperature fluctuations at a computational inlet is proposed and direct numerical simulations of turbulent thermal boundary layers developing on a flat plate with isothermal and isoflux wall boundary conditions are carried out. Governing equations are integrated using a fully implicit fractional-step method with 352×64×128 grids for the Reynolds number of 300, based on the free-stream velocity and the inlet momentum thickness, and the Prandtl number of 0.71. The computed Stanton numbers for the isothermal and isoflux walls are in good agreement with power-law relations without transient region from the inlet. The mean statistical quantities including root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and skewness and flatness of temperature fluctuations agree well with existing experimental and numerical data. A quadrant analysis is performed to investigate the coherence between the velocity and temperature...

An immersed-boundary finite-volume method for simulation of heat transfer in complex geometries

An immersed boundary method for solving the Navier-Stokes and thermal energy equations is developed to compute the heat transfer over or inside the complex geometries in the Cartesian or cylindrical coordinates by introducing the momentum forcing, mass source/sink, and heat source/sink. The present method is based on the finite volume approach on a staggered mesh together with a fractional step method. The method of applying the momentum forcing and mass source/sink to satisfy the no-slip condition on the body surface is explained in detail in Kim, Kim and Choi (2001, Journal of Computational Physics). In this paper, the heat source/sink is introduced on the body surface or inside the body to satisfy the iso-thermal or iso-heat-flux condition on the immersed boundary. The present method is applied to three different problems : forced convection around a circular cylinder, mixed convection around a pair of circular cylin-ders, and forced convection around a main cylinder with a secondary small cylinder. The results show good agreements with those obtained by previous experiments and numerical simulations, verifying the accuracy of the present method.