Periodic Viscous Flows Research Articles

Longitudinally periodic viscous flows generated by a near-wall volume force

Two-dimensional steady-state flows of a viscous incompressible fluid over a fixed flat boundary, generated by a periodic near-wall volume force, are studied. The corresponding boundary-value problems for the Navier - Stokes equations are calculated using the expansion of the required solutions in a Fourier series in the longitudinal coordinate and a second-order finite-difference approximation in the vertical coordinate. The dependence of the far flow field on the force parameters is investigated.

An implicit and adaptive nonlinear frequency domain approach for periodic viscous flows

An implicit nonlinear Lower–Upper symmetric Gauss–Seidel (LU-SGS) solver has been extended to the adaptive Nonlinear Frequency Domain method (adaptive NLFD) for periodic viscous flows. The discretized equations are linearized in both spatial and temporal directions, yielding an innovative segregate approach, where the effects of the neighboring cells are transferred to the right-hand-side and are updated iteratively. This property of the solver is aligned with the adaptive NLFD concept, in which different cells have different number of modes; hence, should be treated individually. The segregate analysis of the modal equations prevents assembling and inversion of a large left-hand-side matrix, when high number of modes are involved. This is an important characteristic for a selected flow solver of the adaptive NLFD method, where a high modal content may be required in highly unsteady parts of the flow field. The implicit nonlinear LU-SGS solver has demonstrated to be both robust and computationally efficient as the number of modes is increased. The developed solver is thoroughly validated for the laminar vortex shedding behind a stationary cylinder, high angle of attack NACA0012 airfoil, and a plunging NACA0012 airfoil. An order of magnitude improvement in the computational time is observed through the developed implicit approach over the classical modified 5-stage Runge–Kutta method.

Orientation dynamics of weakly Brownian particles in periodic viscous flows

Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but nonzero Brownian rotations. The equations are based on a multiple time scale approach that allows fast computation of the relaxation processes leading to statistical equilibrium. The approach has been applied to the calculation of the effective viscosity of a thin disk suspension in an oscillating strain flow.

Immersed boundary approach to stability equations for a spatially periodic viscous flow

An efficient numerical method for the linear stability equations of a spatially periodic channel flow is presented. The method is based on global Fourier-Chebyshev approximation of a disturbance velocity field. The physical flow domain is embedded in a larger computational domain and the boundary conditions are re-formulated as internal conditions imposed at immersed boundaries. The advantage of this approach is an avoidance of domain mapping, leading to tremendous complication of governing equations and to excessive computational cost. The results of numerical tests are presented. Favorable convergence properties with respect to the length of the Fourier expansions are demonstrated.

Three-dimensional long-wave instability of unidirectional spatially periodic viscous flows

The long-wave instability of unidirectional spatially periodic flows is investigated by means of asymptotic expansions. It is shown that the wavevector of the most dangerous disturbances is generally inclined to the direction of the basic stream. A new type of long-wave oscillatory instability is discovered, and a comparison with results of previous investigations is performed.

Numerical calculation of periodic viscous flow through a circular hole

Periodic viscous flows through a circular hole driven by fluctuating far field pressure are studied numerically. The time dependent incompressible Navier-Stokes equations formulated with orthogonal curvilinear co-ordinates are solved by using a finite difference method. The flow patterns and acoustic impedance of the circular hole are investigated for various combinations of the pressure/viscous force ratio, frequency and hole edge thickness. Numerical calculations revealed some interesting facts, as follows. First, the flow patterns are classified into three regimes by fluctuating pressure amplitude and frequency: flows with no laminar separation (high-frequency-low-pressure range), flows with an attached separation bubble (intermediate frequency and pressure range) and flows with detached vortex rings (low-frequency-high-pressure range). Second, the flow resistance of the circular hole is proportional to the acoustic particle velocity but independent of the viscosity of the fluid, and almost invariant with the frequency for the low-frequency-high-pressure range. On the other hand, for the high-frequency-low-pressure range, the flow resistance is independent of the periodic pressure amplitude and varies directly with the 2 3 power of the frequency. Finally, the predicted circular hole impedance is in good agreement with the experimental data for the orifice impedance of Ingard and Ising.

Periodic viscous flow through a circular hole(With laminar separation).

The N-S equations formulated with the orthogonal curvilinear coordinate system have been solved numerically for periodic viscous flows through a circular hole driven by fluctuating far field pressure. The flow patterns and acoustic impedance of the circular hole are investigated for various combinations of pressure/viscous force ratio, fluctuating frequency and hole edge thickness. For the high frequency and low pressure range, there is no laminar separation, and the resistance is independent of the periodic pressure amplitude. For the intermediate frequency and pressure range, an attached separation bubble is generated near the downstream side of the hole edge, and the resistance is larger for smaller hole edge thickness and smaller force ratio. For the low frequency and high pressure range, the separation bubble grows to a detached vortex ring and the resistance is proportional to the square root of the pressure amplitude but independent of the viscousity of the fluid and almost invariant with the frequency.

Periodic viscous flow through a circular hole.

Periodic viscous flows through a circular hole driven by a fluctuating far field pressure are numerically studied. The time-dependent incompressible N-S equations formulated with orthogonal curvilinear coordinates are solved by using a finite difference method. Numerical examples compared with the potential theory predictions are presented. The acoustic impedances of a circular hole are calculated for various combinations of the pressure/viscous force ratio, frequency and the hole edge thickness.