Wave Instability of Natural Convection Flow on Inclined Surfaces

Tzuoo, K. L.; Chen, T. S.; Armaly, Bassem F.

doi:10.1115/1.3247364

Cited by 20 publications

(9 citation statements)

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“…Moreover, for very small 0, the TollmienSchlichting travelling wave instability with streamwise variation but no spanwise dependence seems to be more unstable than the roll instability (Lloyd & Sparrow 1970). This has also been theoretically confirmed by Hwang & Cheng (1973), Haaland & Sparrow (1973), Kahawita & Meroney (1974), Iyer & Kelly (1974) and TZUOO, Chen & Armaly (1985) for various Prandtl numbers Pr and inclination angles 8. Kahawita & Meroney predicted that a t Pr = 0.72, the wave instability becomes dominant for 8 < 17" and Iyer & Kelly found that for water (Pr = 6.7), the crossover angle based on a parallel flow model is 8 = 4'.…”

Section: C Chen a Labhabi H-c Chang And R E Kellymentioning

confidence: 53%

“…In general, interaction between these two modes is most pronounced near the cross-over 8 when the critical Reynolds number R, for both instabilities become identical (see studies on interactions between Gortler vortices and TollmienSchlichting waves in curved channels by Daudpota, Hall & Zang (1988), between temperature-driven and solute-driven instabilities in the doubly-diffusive Marangoni problem by Ho & Chang (1988) and between even and odd convective patterns in Taylor-BBnard instability in a Hele-Shaw cell by Hwang & Chang (1989)). Also, computations by Tzuoo et al (1985) and experimental observations (Sparrow & Husar 1969) show that the dimensional streamwise wavelength of the wave instability is much longer than the spanwise wavelength of the roll instability. Consequently, if the growth rate of the wave instability is small, the roll instability will most likely evolve independently from the wave instability even for near-vertical plates where the wave instability destabilizes first.…”

Section: C Chen a Labhabi H-c Chang And R E Kellymentioning

confidence: 99%

“…For this particular flow, its use allows the fact that the velocity component normal to the plate is inwards at the edge of the boundary layer to be taken into account, which is vital to the analysis of long-wavelength disturbances. Gebhart & Mahajan (1982) and Tzuoo et al (1985) also employed the same approximations to study streamwise TollmienSchlichting waves in the same flow. The analogous parallel-flow linear theories for spanwise Gortler instability have been scrutinized by Hall (1983).…”

Section: Av/al"+ V -mentioning

confidence: 99%

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Spanwise pairing of finite-amplitude longitudinal vortex rolls in inclined free-convection boundary layers

et al. 1991

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Buoyancy-driven flow on a heated inclined plate can become unstable to static longitudinal roil instability at a critical distance, measured by $\tilde{R}_{\rm c}$, from the leading edge. Experiments in water by Sparrow & Husar (1969) indicate that these rolls undergo a second transition further downstream such that adjacent rolls merge and their spanwise wavelength is doubled. We study this secondary bifurcation phenomenon here with a set of model equations by first constructing the full eigenspectrum and eigenfunctions with a Chebyshev–Tau spectral method and then deriving the pertinent amplitude equations. By stipulating that the dimensional cross-stream wavelength of the rolls remains constant beyond $\tilde{R}_{\rm c}$, which is consistent with experimental observation, we show that the finite-amplitude primary rolls are destabilized by the ½ subharmonic mode at another critical distance $\tilde{R}_{\frac{1}{2}}$ from the edge. This ½ mode is shown to have an asymmetric spatial phase shift of ½π relative to the original 1 mode of the primary rolls, thus explaining the unique dislocation of tracer streaks after the rolls coalesce in the experiments. Also consistent with experimental observation is the theoretical result that the merged rolls are annihilated downstream by a saddle-node bifurcation before further wavclength doubling can occur. Simple amplitude criteria and critical distances from the leading edge for the various transitions are derived and compared to experimental values.

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Section: C Chen a Labhabi H-c Chang And R E Kellymentioning

confidence: 53%

Section: C Chen a Labhabi H-c Chang And R E Kellymentioning

confidence: 99%

Section: Av/al"+ V -mentioning

confidence: 99%

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Spanwise pairing of finite-amplitude longitudinal vortex rolls in inclined free-convection boundary layers

et al. 1991

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“…The properties of such buoyancy-driven instabilities have been extensively studied (for example Gill &Davey 1969 andTzuoo, Chen &Armaaly 1985, as well as Bergholz 1978) and further investigation is outside the scope of this paper. It is interesting to speculate, however, that these perturbations may play a role in the transition to turbulence observed in high-Ra flows of this kind.…”

Section: Discussionmentioning

confidence: 99%

Transient features of natural convection in a cavity

1990

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Comparisons of numerical and experimental results for transient two-dimensional natural convection initiated by instantaneously heating and cooling the opposing vertical walls of a square cavity containing a stationary and isothermal fluid are presented. The good comparisons indicate that the simulation is capturing the important features of the flow. Several features are identified and discussed in detail; in particular, the presence of travelling wave instabilities on the vertical-wall boundary layers and horizontal intrusions, the existence of a rapid flow divergence in the region of the outflow of the intrusions, and the presence of cavity-scale oscillations, caused by the interaction of the intrusions with the opposing vertical boundary layer. The utilization of both numerical and experimental investigations has allowed a more complete exploitation of the available resources than would have been possible had each been conducted separately.

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“…Tzuoo et al [4] carried on with the existing studies regarding problems of natural convection on a vertical plate with turbulent regime improving the methods of turbulence measurements; they obtained a critical value of the local Grashof number of 6.2 × 10 6 .…”

Section: Introductionmentioning

confidence: 99%