• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.3
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• pp.319-325
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• 2003

We investigate the spectra and the pseudospectra in plane Poiseuille flow, plane Couette flow and Blasius flow. At subcritical Reynolds number, the spectra are lied strictly inside the stable complex half-plane, but the pseudospectra are lied in the unstable half-plane, reflecting the large linear transient growth that certain perturbations may excite. It means that the smooth flows may become to turbulent even though all the eigenmodes decay monotonically. We found that pseudospectra is one reason that causes subcritical transition in plane Poiseuille flow and plane Couette flow and bypass transition in Blasius flow.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.691-694
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• 2002

The most unstable situation of laminar plane Poiseuille flow for transition to turbulence is investigated by using a pseudo-spectral method. A number of various disturbance modes are tested and it is found that the flow is the most unstable when it is disturbed by an oblique wave with an angle of $29.7^{\circ}$.

• Journal of the Korean Society of Visualization
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• v.17 no.3
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• pp.12-18
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• 2019

Direct numerical simulation of a fully developed turbulent plane Couette-Poiseuille flow with a two-dimensional (2-D) rod-roughened wall is performed to investigate the impacts of the surface roughness. It is shown that the logarithmic region in the mean velocity profile over the rough wall Couette-Poiseuille flow is significantly shortened by the surface roughness compared to that over a turbulent Couette-Poiseuille flow with smooth wall. The Reynolds shear stress over the rough wall Couette-Poiseuille flow is decreased compared to that for a smooth case in the outer layer. These results are attributed to weakened turbulence activity or roll-cell mode over the rough wall Couette-Poiseuille flow near the channel centerline due to suppressed development of u'-structure on the top wall, as documented through spanwise energy spectra of the streamwise velocity fluctuations. Inspection of congregation motion near the bottom wall and time evolution of u'-structure reveal weakened co-supporting cycle for the rough wall case.

• Journal of Advanced Marine Engineering and Technology
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• v.17 no.4
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• pp.28-37
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• 1993

Flow characteristics within the three-dimensional square cavity are studied experimentally by adopting PIV(Particle Image Velocimetry). A new method for tracking the same particle pairs in the consecutive flow image is suggested resulting in more effective acquisition of the velocity vectors. Two methods for supplying the shearing stress within the cavity are developed by continuous moving belt and 2-dimensional plane Poiseuille flow. The effect of TGL vortex in the case of belt-moving flow is remarkable owing to the distribution of the kinetic energy in the spanwise direction. But, for the plane Poiseuille flow, velocity profiles similar to a forced vortex are obtained and its tendency increases with the Reynolds number.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.766-772
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• 2003

The pseudospectral method for stability analysis was used to find the most influential disturbance mode for transition of plane channel flows and Blasius flow at their critical Reynolds numbers. A number of various oblique disturbance waves were investigated for their pseudospectra and resolvent norm contours in each flow, and an exhaustive search method was employed to find the disturbing waves to which the flows become most unstable. In plane Poiseuille flow an oblique disturbance with a wavelength of 3.59h (where h is the half channel width) at an angle $28.7^{\circ}$ was found to be the most influential for the flow transition to turbulence, and in plane Couette flow it is an oblique wave with a wavelength of 3.49h at an angle of $19.4^{\circ}$. But in Blasius flow it was found that the most influential mode is a normal wave with a wavelength of $3.44{\delta}_{999}$. These results imply that the most influential disturbance mode is closely related to the fundamental acoustic wave with a certain shear sheltering in the respective flow geometry.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.233-238
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• 2010

A two-dimensional laminar flow past a vertical plate in a microchannel is investigated. At far upstream and downstream from the plate in the microchannel, the plane Poiseuille flow exists. The Stokes flow for this microchannel is investigated analytically and then the laminar flow by numerical method. For the Stokes flow analysis, the method of eigenfunction expansion is used. From the results, the streamline pattern and the pressure distribution are plotted, and the additional pressure drop induced by the plate and the force exerted on the plate are calculated as functions of the length of the plate. For the laminar flow, finite difference method (FDM) is used to obtain the vorticity and the stream function. When the Reynolds number exceeds a critical value, a pair of viscous eddies appears behind the plate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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• pp.73-86
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• 2009

The problem of thermal stability of an exothermic reactive viscous fluid between two parallel walls in the plane Poiseuille and Couette flow configurations is investigated for different thermal boundary conditions. Neglecting reactant consumption, the closed-form solutions obtained from the momentum equation was inserted into the energy equation due to dissipative effect of viscosity. The resulting energy equation was analyzed for criticality using the variational method technique. The problem is characterized by two parameters: the Nusselt number(N) and the dynamic parameter($\Lambda$). We observed that the thermal and dynamical boundary conditions of the wall have led to a significant departure from known results. The influence of the variable pre-exponential factor, due to the numerical exponent m, also give further insight into the behavior of the system and the results expressed graphically and in tabular forms.

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.66.3-66.3
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• 2008

• Korea-Australia Rheology Journal
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• v.21 no.1
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• pp.47-58
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• 2009

We have investigated the transient behavior of 1D fully developed Poiseuille viscoelastic flow under finite pressure gradient described by the Oldroyd-B and Leonov constitutive equations. For analysis we employ a simple $2^{nd}$ order discretization scheme such as central difference for space and the Crank-Nicolson for time approximation. For the analysis of the Oldroyd-B model, we also apply the analytical solution, which is obtained again in this work in terms of elementary solution procedure simpler than the previous one (Waters and King, 1970). Both models demonstrate qualitatively similar solutions, but their eventual steady flowrate exhibits noticeable difference due to the absence or presence of shear thinning behavior. In the inertialess flow, the flowrate instantaneously attains a large value corresponding to the Newtonian creeping flow and then decreases to its steady value when the applied pressure gradient is low. However with finite liquid density the flow field shows severe fluctuation even accompanying reversals of flow directions. As the assigned pressure gradient increases, the flowrate achieves its steady value significantly higher than its value during oscillations after quite long period of time. We have also illustrated comparison between 1D and 2D results and possible mechanism of complex 2D flow rearrangement employing a previous solution of [mite element computation. In addition, we discuss some mathematical points regarding missing boundary conditions in 2D modeling due to the change of the type of differential equations when varying from inertialess to inertial flow.

• Journal of Ocean Engineering and Technology
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• v.12 no.1
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• pp.113-119
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• 1998

An experimental study was carried out in a three-dimensional cubic cavity driven by 2-dimensional plane Poiseuille flow for three kinds of Reynolds number, $10^4$, 3 $\times$ $10^4$ and 5 $\times$ $10^4$ based on the cavity width and cavity inlet mean flow velcoity. Instant simultaneous velocity vectors at whole field were measured by 2-D PIV system. Laser based illumination and two-frame grey-level cross correlation algorithm are adopted. Severe unsteady flow fluctuation within the cavity are remarkable at above Re = 3 $\times$ $10^4$ Reynolds numbers and sheared mixing layer phenomena are also found at the region where inlet driving Poiseuille flow is collided with the clock-wise rotating main primary vortex at upper center area. Instant velocity profiles reveal that deformed forced vortex formation is observed throughout the separate two areas.