Basil N. Antar

The Rayleigh–Taylor and Kelvin–Helmholtz stability of a viscous liquid–vapor interface with heat and mass transfer

Linear stability analysis of a liquid–vapor interface under adverse gravitational field and velocity streaming is considered. The liquid is assumed viscous, incompressible, and motionless over a vapor layer with a uniform horizontal velocity. It is shown that while the coupled viscosity‐phase change mechanism of former studies adds considerably to the stability of the Rayleigh–Taylor problem, it has a deleterious effect on the Kelvin–Helmholtz mode of stability.

Penetrative double‐diffusive convection

The onset of double‐diffusive convection is studied for an infinite fluid layer possessing a density maximum in its interior. Linear stability analyses are performed on a basic state with constant temperature and concentration gradients in which the density‐temperature relationship is quadratic. Regions of stability and instability to both steady and oscillatory modes are delineated in the positive quarterplane of the Rayleigh and solutal Rayleigh numbers plane. It is found that decreasing the position of maximum density in the vertical leads to an increased stability range and also increased regions of oscillatory instability in that quadrant. It is also found that the extent of penetration of the convective motion into the stable region is diminished with increased solute concentration. The effects of both the rigid–rigid and the free–free boundary conditions on the instabilities are investigated. Both conditions lead to dynamically similar motions with significant quantitative differences.

Temporal eigenvalue spectrum of the Orr–Sommerfeld equation for the Blasius boundary layer

A search for the eigenvalue spectrum of the Orr–Sommerfeld equation for the Blasius boundary layer is conducted. The investigation is numerical involving two different numerical methods. The resulting spectrum is found to depend on the finite interval of integration chosen for the numerical scheme. This spectrum is shown to be infinite and discrete whenever it is identified with the aid of numerical integrations. The spectrum belonging to the exact semi‐infinite problem is inferred from the asymptotic behavior of the same spectrum. This is shown to be comprised of a finite discrete set and a continuous portion.

Flow boiling in low gravity environment

An experimental procedure for examing flow boiling in low gravity environment is presented. The procedure involves both ground based and KC‐135 flight experiments. Two experimental apparati were employed, one for studying subcooled liquid boiling and another for examining saturated liquid boiling. For the saturated experiments, liquid nitrogen was used while freon 113 was used for the subcooled experiments. The boiling phenomenon was investigated in both cases using flow visualization techniques as well as recording wall temperatures. The flow field in both cases was established by injecting cold liquid in a heated tube whose temperature was set above saturation values. The tubes were vertically supported with the liquid injected from the lower end of the tube. The results indicate substantial differences in the flow patterns established during boiling between the ground based, (1‐g), experiments and the flight experiments, (low‐g). These differences in the flow patterns will be discussed and some explana...

Viscous Nongeostrophic Baroclinic Instability

Abstract Calculations have been performed of the (linear) stability of a baroclinic flow to three-dimensional perturbations. Both the simple Eady basic state and the rotating Hadley cell of Antar and Fowlis are considered. The independent influences of the Richardson (Ri), thermal Rossby (baroclinicity), Ekman, and Prandtl numbers are examined, as well as the influences of the angle of orientation of the horizontal wave vector and the wavelength. It is shown that if the wavelength is allowed to vary freely, disturbances of the Eady type are preferred (i.e., have greatest growth rate) unless Ri and Ekman numbers are small enough and the thermal Rossby number is large enough. In the latter case, disturbances whose angles of orientation are almost symmetric and whose wavelengths are mesoscale are preferred. If, on the other hand, the wavelength is fixed at a mesoscale size, only the symmetric and almost symmetric modes have growth. By allowing the wave vector orientation to deviate from purely symmetric, we ...

Viscosity Measurement Using Drop Coalescence in Microgravity

We present in here validation studies of a new method for application in microgravity environment which measures the viscosity of highly viscous undercooled liquids using drop coalescence. The method has the advantage of avoiding heterogeneous nucleation at container walls caused by crystallization of undercooled liquids during processing. Homogeneous nucleation can also be avoided due to the rapidity of the measurement using this method. The technique relies on measurements from experiments conducted in near zero gravity environment as well as highly accurate analytical formulation for the coalescence process. The viscosity of the liquid is determined by allowing the computed free surface shape relaxation time to be adjusted in response to the measured free surface velocity for two coalescing drops. Results are presented from two sets of validation experiments for the method which were conducted on board aircraft flying parabolic trajectories. In these tests the viscosity of a highly viscous liquid, namely glycerin, was determined at different temperatures using the drop coalescence method described in here. The experiments measured the free surface velocity of two glycerin drops coalescing under the action of surface tension alone in low gravity environment using high speed photography. The liquid viscosity was determined by adjusting the computed free surface velocity values to the measured experimental data. The results of these experiments were found to agree reasonably well with the known viscosity for the test liquid used.

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

A three-dimensional linear stability analysis of a baroclinic flow for Richardson number Ri of order unity is presented. The model considered is a thin, horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the Navier–Stokes and energy equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in closed form. The stability analysis is also based on the Navier–Stokes and energy equations; and perturbations possessing zonal, meridional and vertical structures were considered. Numerical methods were developed for the solution of the stability problem, which results in an ordinary differential eigenvalue problem. The objectives of this work were to extend the previous theoretical work on three-dimensional baroclinic instability for small Ri to a more realistic model involving the Prandtl number σ and the Ekman number E , and to finite growth rates and a wider range of the zonal wavenumber. The study covers ranges of 0.135 [les ] Ri [les ] 1.1, 0.2 [les ] σ [les ] 5.0, and 2 × 10 −4 [les ] E [les ] 2 σ 10 −3 . For the cases computed for E = 10 −3 and σ ≠ 1, we found that conventional baroclinic instability dominates for Ri > 0.825 and symmetric baroclinic instability dominates for Ri E [ges ] 5 × 10 −4 and σ = 1 in the range 0.3 [les ] Ri [les ] 0.8, conventional baroclinic instability always dominates. Further, we found in general that the symmetric modes of maximum growth are not purely symmetric but have weak zonal structure. This means that the wavefronts are inclined at a small angle to the zonal direction. The results also show that as E decreases the zonal structure of the symmetric modes of maximum growth rate also decreases. We found that when zonal structure is permitted the critical Richardson number for marginal stability is increased, but by only a small amount above the value for pure symmetric instability. Because these modes do not substantially alter the results for pure symmetric baroclinic instability and because their zonal structure is weak, it is unlikely that they represent a new type of instability.

Baroclinic Instability of a Rotating Hadley Cell

Abstract The stability of a thin fluid layer between two rotating plates which are subjected to a horizontal temperature gradient is studied. First, the solution for the stationary basic state is obtained in a closed form. This solution identifies Ekman and thermal layers adjacent to the plates and interior temperature and velocity fields which are almost linear functions of height. Then the stability of that basic state with respect to infinitesimal zonal waves is analyzed via the solution of the complete viscous linear equations for the perturbations. The character of the growth rates is found to be similar to the growth rates of the classical baroclinic waves. The neutral stability curves for these waves possessed a knee in the Rossby-Taylor number plane to the left of which all perturbations are stable. The region of instability is found to depend on the Prandtl number, the vertical stratification parameter, and both the meridional and zonal wavenumbers. It is found in general that the flow is unstabl...

Utilization of low gravity environment for measuring the viscosity of highly viscous liquids

Abstract The method of drop coalescence is utilized for determining the viscosity of highly undercooled liquids. Low gravity environment is necessary in order to avoid problems connected with droplet deformation due other body forces that are present under terrestrial conditions. The drop coalescence method is preferred over the drop oscillation technique since the latter method can only be applied for liquids with vanishingly small viscosities. The technique developed relies on both the highly accurate solution of the equations of motion for fluid flows as well as on data from experiments conducted in near zero gravity environment. Results are presented for method validation experiments performed recently on board the NASA/KC-135 aircraft. These experiments gave excellent results which will be discussed together with plans for implementing the method in a shuttle flight experiment.

Influence of solidification on surface tension driven convection

The effect of solidification on the onset of surface tension driven convection in a reduced gravity environment is studied. Two simple but physically realistic configurations representing the solidification of a simple material are analyzed. The analysis shows that as a result of the solidification process the critical Marangoni number is shifted to lower values indicating that solidification has a destabilizing effect upon the liquid. From this result it is concluded that convection can be brought about in the liquid phase at lower Marangoni numbers when solidification is present than when it is not. The effects of other parameters introduced by the solidification process are analyzed and discussed.