Effects of parietal suction and injection on the stability of the Blasius boundary-layer flow over a permeable, heated plate

Abstract

The main concern of this paper is to investigate the effects on the stability behavior of wall suction or injection for external boundary-layer flow over a heated, porous plate for a fluid with temperature-dependent viscosity. The wall suction or injection are applied to the flow by a simple modification for the no-penetration condition and the current boundary conditions on the flat plate. Liquid-type viscosities are found to entrain both the velocity and temperature profiles closer to the plate with increasing both temperature sensitivity and suction intensity, whereas gas-type viscosities are found to exhibit the reverse effect with increasing flow injection and decreasing temperature dependence. We present then the linear stability analysis and find that increasing both the temperature dependence (from gas-to liquid-type behavior) and suction intensity of the fluid leads to increasing critical Reynolds number to a point of maximum stability. We note also that increasing both the Prandtl number (Pr) and flow suction in the liquid-type behavior results in an increased critical Reynolds number. The magnitudes of the perturbation eigenfunctions are considered before utilising them to obtain solutions to an energy balance integral. We find that the eigenfunction profiles are imitative of the narrowing of their mean flow counterparts when increasing either the temperature dependence or the flow suction. Our results are then confirmed by the energy analysis, where we find a significant reduction in the energy produced by the disturbance with increasing suction intensity and ultimately leads to a more stable flow. Overall, there is a strong destabilizing effect with increasing injection and the temperature-dependent viscosity over a heated plate. In summary, the findings indicate that increasing the wall suction and temperature dependence results in significantly more stable flows. It is worth noting that application and extension of this study are considered in the context of chemical vapor deposition reactors.

Effects of the suction/injection and external free stream on the instability of a boundary layer over a rotating disk

“…We also observed that shifting from injection to suction stabilized the flow. However, our results are consistent with Al-Malki 41 for Blasius flow, in that suction causes a stabilisation of the type II cross-flow instability mode. When we compared the asymptotic results of types I with II modes, we concluded that increasing T s to a positive value destabilizes the type I modes and stabilizes the type II modes for a flow over a rotating disk and vice versa.…”

“…Collectively, increasing W * from negative to positive shifted the curves at type I and II upwards (figure ( 14)). Our data are consistent with Al-Malki 41 for Blasius flow, where suction stabilized the type I cross flow instability mode. Importantly, expanding the inviscid type I and viscous type II modes provided the capacity to consider non-parallel effects.…”

Non-ideal gas behavior matters in hydrodynamic instability

“…However, in the compressible scheme, the physics of the fluid largely stayed in the ideal gas regime due to the erstwhile aerodynamic demand. On the other hand, the O–S framework has been extended to account for temperature-dependent viscosity 17 , 18 , coupling with various controlling methods 19 . In line with the emphasis on viscosity, viscosity-stratified flows amount to a particular type that attracted significant attention 20 .…”

Competing roughness effects on the non-stationary crossflow instability of the boundary-layer over a rotating broad cone

“…An exponential map of the Gauss-Lobatto grid points is adopted for the Chebyshev polynomials at a number of points into the physical domain: 100 points are sufficient to achieve accurate results such as results of previous studies, which are validated by confirming 100 points distributed between the geometry surface z = 0 and the top of the domain η max = 20 using the spectral method based on Chebyshev polynomials such as. 5,[30][31][32] Our simulations were run with a variable number of collocation points e.g. 110 or 120 and also η max was varied e.g.…”

“…The delay of transition has a particular interest to stabilise laminar flows, where this idea has been investigated extensively. There is a number of interesting examples that include: suction, mean flow distortion, surface roughness and wave cancellation by superposition (see [2][3][4][5] ). These investigations could be intelligent strategies in most technological applications to delay the laminar-turbulent transition process in mechanism of fluid flow.…”