S. H. Winoto

Free Convection in a Porous Wavy Cavity Based on the Darcy-Brinkman-Forchheimer Extended Model

A numerical investigation is carried out for steady, free convection inside a cavity filled with a porous medium. The cavity has vertical wavy walls which are isothermal. The top and bottom horizontal straight walls are kept adiabatic. The numerical method is based on the finite-volume method with body-fitted and nonorthogonal grids. A generalized model, which includes a Brinkman term, a Forcheimmer term, and a nonlinear convective term, is used. Studies are carried out for a range of wave ratio λ = 0 − 1.8, aspect ratio A = 1–5, Darcy number Da = 10−1–10−6, and Darcy-Rayleigh number Ra* = 10–105. Results are presented in the form of streamlines, isotherms, and local and average Nusselt numbers. The generalized model which considers viscous, inertia, and convective effects enables results to be obtained for a wider range of Darcy and Rayleigh numbers.

Development of boundary-layer flow in the presence of forced wavelength Görtler vortices

Hot-wire measurements in the boundary layer developing on a concave surface of 2.0 m radius of curvature in the presence of forced wavelength Gortler vortices have been conducted for a free-stream velocity of 3.0 m/s. The wavelengths of vortices were preset by vertical perturbation wires of 0.2 mm diameter located 10 mm upstream of the concave surface leading edge. The velocity contours in the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices that are similar to those found in the transitional flow field. It shows the occurrence of the second instability mode that is indicated by the formation of small horseshoe eddies generated between the two neighboring vortices traveling in the streamwise direction to form mushroom-like structures as a consequence of the nonlinear growth of the Gortler vortices. The breakdown of these structures before the boundary-layer flow becomes turbulent is also shown to qualitatively predict the start of the transition in the f...

On the linear and nonlinear development of Görtler vortices

The linear and nonlinear developments of Gortler vortices were experimentally investigated by means of hot-wire anemometer measurement. The wavelengths of the vortices were preset to be the most amplified using thin perturbation wires. Three different vortex wavelengths of 12, 15, and 20 mm were considered. These wavelengths were preserved downstream which confirm the prediction of the most amplified wavelength of Gortler vortices. The onset of the nonlinear region occurs at about the same Gortler number of 5.0 for all the wavelengths considered. In this nonlinear region, the secondary instability is initiated near the boundary layer edge, and it develops further downstream. The maximum turbulent intensity increases as the secondary instability becomes dominant in the flow. In the transition region, however, it slightly decreases before drastically increasing due to the onset of turbulence. Three maxima of intense turbulence are found in the turbulent intensity contours in the nonlinear region, which indi...

Visualizing Görtler Vortices

The development of Görtler vortices with pre-set wavelength of 15 mm has been visualized in the boundary-layer on a concave surface of 2.0 m radius of curvature at a free-stream velocity of 3.0 m/s. The wavelength of vortices was pre-set by vertical wires of 0.2 mm diameter located 10 mm upstream of the concave surface leading edge. The velocity contours in the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices. Three different regions can be identified based on different growth rate of the vortices. The occurrence of a secondary instability mode is indicated by the formation of a small horseshoe eddies generated between the two neighboring vortices traveling streamwise, to form mushroom-like structures as a consequence of the non-linear growth of the Görtler vortices.

Wall shear stress in Görtler vortex boundary layer flow

The development of wall shear stress in concave surface boundary layer flows in the presence of Gortler vortices was experimentally studied by means of hot-wire measurements. The wavelengths of the vortices were preset by thin vertical perturbation wires so to produce the most amplified wavelengths. Three different vortex wavelengths of 12, 15, and 20 mm were considered, and near-wall velocity measurements were carried out to obtain the “linear” layers of velocity profiles in the boundary layers. The wall shear stress coefficient Cf was estimated from the velocity gradient of the “linear” layer. The streamwise developments of boundary layer displacement and momentum thickness at both upwash and downwash initially follow the Blasius (laminar boundary layer) curve up to a certain streamwise location. Further downstream, they depart from the Blasius curve such that they increase at upwash and decrease at downwash before finally converge to the same value due to the increased mixing as a consequence of transi...

Investigation of intermittency measurement methods for transitional boundary layer flows

Abstract Three turbulent intermittency methods, namely the u , TERA (turbulent energy recognition algorithm), and M-TERA (modified turbulent energy recognition algorithm) methods, for identifying the intermittent flow characteristics associated with boundary layer transition from laminar to turbulent were considered and compared. The data used were obtained from hot-wire measurements in transitional boundary layer flows on a concave surface with a 2-m radius of curvature and on a flat plate. Comparisons show that the u and TERA methods are more sensitive to the choice of threshold constants than the M-TERA method. In terms of the intermittency distribution across the boundary layer, the values obtained by the u and TERA methods are unrealistically high in the near-wall region, while those obtained by the M-TERA method are more realistic. In the outer boundary layer region and outside the boundary layer, the u and M-TERA methods give reasonable intermittency values, whereas the TERA method produces unrealistically high values in the region outside the boundary layer. In addition, the M-TERA method provides a sharper definition of theend of transition.

Secondary instability in forced wavelength Görtler vortices

From an experimental study on the onset of secondary instability in forced wavelength Gortler vortices, it is found that the breakdown process of the Gortler vortices is due to the development of varicose and sinuous mode instabilities. The development of the varicose mode is characterized by the formation of horseshoe vortices that evolve downstream to form mushroom-like structures. This phenomenon is then followed by meandering of the vortices as an indication of the onset of sinuous mode instability, prior to turbulence. The spectrum analysis applied to the fluctuating velocity component shows the occurrence of peak frequency of about 150Hz, which is attributed to the fundamental secondary instability mode with its wavelength comparable to the spanwise wavelength of the primary Gortler vortices, at the location where the mushroom-like structures are clearly depicted in the mean velocity contours on the y-z plane. This confirms that the secondary instability is of the varicose type at the onset that is ...

Mass Transport in a Microchannel Bioreactor With a Porous Wall

A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier-Stokes equation; for the porous medium region, the generalized Darcy-Brinkman-Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis-Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.

Forced Convection Over a Backward-Facing Step with a Porous Floor Segment

Forced convection after a backward-facing step, with a porous floor segment, is investigated numerically using the SIMPEC method. The Brinkman-Forcheimmer extended model is used to govern the flow in the porous-medium region. At the interface, the flow boundary condition imposed is a shear stress jump, which includes the inertial effect, together with a continuity of normal stress. The thermal interfacial condition is continuities of temperature and heat flux. Results are presented for Reynolds number up to 800 and Darcy number up to 10−1. Also varied are the length and depth of the porous segment. Compared with the case with no porous floor, the local heat transfer is augmented after the porous floor. Within the porous floor, the heat transfer is reduced, but this may be offset by using a porous medium of higher conductivity than the fluid. To obtain good heat enhancement after the porous segment, it should approximately match the length of the recirculation region. The porous segment should have large permeability (Darcy number around 10−1), but it is not necessary that it be of great depth. The interfacial stress jump coefficients β and β 1 are varied from − 5 to + 5, and some effects are observed on the local Nusselt numbers, velocity profile, and temperature distribution.

Development of most amplified wavelength Görtler vortices

The development of most amplified wavelength Gortler vortices is studied by means of varying the spanwise spacing of thin vertical wires located upstream of the leading edge of a concave surface. The free-stream velocity is set so as to provide the value of the dimensionless parameter of that for the most amplified vortex wavelength. The resulting uniform vortex wavelengths were determined by the wire spacings and they were preserved downstream prior to turbulence. The spectrum study of the fluctuating velocity component was able to detect the fundamental frequency of the secondary instability mode with the streamwise wavelengths comparable to the wire spacing, which confirm that the wavelength of the vortices observed is the most amplified one. The intermittency study of the boundary layer flow in the presence of the most amplified wavelength Gortler vortices of 15.0 mm using Turbulent Energy Recognition Algorithm method shows the transition onset in the upwash regions, which coincides with the onset of ...