Yunpeng Wang and Roger E. Khayat
The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface tension…
Abstract
Purpose
The purpose of this study is to examine theoretically the axisymmetric flow of a steady free-surface jet emerging from a tube for high inertia flow and moderate surface tension effect.
Design/methodology/approach
The method of matched asymptotic expansion is used to explore the rich dynamics near the exit where a stress singularity occurs. A boundary layer approach is also proposed to capture the flow further downstream where the free surface layer has grown significantly.
Findings
The jet is found to always contract near the tube exit. In contrast to existing numerical studies, the author explores the strength of upstream influence and the flow in the wall layer, resulting from jet contraction. This influence becomes particularly evident from the nonlinear pressure dependence on the upstream distance, as well as the pressure undershoot and overshoot at the exit for weak and strong gravity levels, respectively. The approach is validated against existing experimental and numerical data for the jet profile and centerline velocity where good agreement is obtained. Far from the exit, the author shows how the solution in the diffusive region can be matched to the inviscid far solution, providing the desired appropriate initial condition for the inviscid far flow solution. The location, at which the velocity becomes uniform across the jet, depends strongly on the gravity level and exhibits a non-monotonic behavior with respect to gravity and applied pressure gradient. The author finds that under weak gravity, surface tension has little influence on the final jet radius. The work is a crucial supplement to the existing numerical literature.
Originality/value
Given the presence of the stress singularity at the exit, the work constitutes a superior alternative to a computational approach where the singularity is typically and inaccurately smoothed over. In contrast, in the present study, the singularity is entirely circumvented. Moreover, the flow details are better elucidated, and the various scales involved in different regions are better identified.
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Marianne Obé and Roger E. Khayat
The purpose of this paper is to investigate the thermal convection inside a spatially modulated domain.
Abstract
Purpose
The purpose of this paper is to investigate the thermal convection inside a spatially modulated domain.
Design/methodology/approach
The governing equations are mapped onto an infinite strip, allowing Fourier expansion of the flow and temperature in the streamwise direction.
Findings
Similar to Rayleigh‐Benard convection, conduction is lost to convection at a critical Rayleigh number, which depends strongly on both the modulation amplitude and the wavenumber. The effect of modulation is found to be destabilizing (stabilizing) for conduction for relatively large (small) modulation wavelength. Oscillatory convection sets in as the Rayleigh number is increased.
Originality/value
This paper presents novel results.
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Rahim M Khorasany, Roger E Khayat and Mohammad Niknami
The purpose of this paper is to determine the thermo-gravitational convective state of a non-Fourier fluid layer of the single-phase-lagging type, heated from below. Unlike…
Abstract
Purpose
The purpose of this paper is to determine the thermo-gravitational convective state of a non-Fourier fluid layer of the single-phase-lagging type, heated from below. Unlike existing methodologies, the spectral modes are not imposed arbitrarily. They are systematically identified by expanding the spectral coefficients in terms of the relative departure in the post-critical Rayleigh number (perturbation parameter). The number and type of modes is determined to each order in the expansion. Non-Fourier effects become important whenever the relaxation time (delay in the response of the heat flux with respect to the temperature gradient) is of the same order of magnitude as process time.
Design/methodology/approach
In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A perturbation approach is developed to solve the nonlinear spectral system in the post-critical range.
Findings
The Nusselt number increases with non-Fourier effect as suggested in experiments in microscale and nanofluid convection.
Originality/value
Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection.
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Xundong Qin and Roger E. Khayat
This numerical study explores the influence of the time dependence of material fluid parameters on the transient temperature evolution during the growth of fluid shells. The shell…
Abstract
This numerical study explores the influence of the time dependence of material fluid parameters on the transient temperature evolution during the growth of fluid shells. The shell is spherical, the fluid is Newtonian, and the flow is induced by a constant driving pressure. The coupled heat and flow equations are solved numerically using the cobody (Lagrangian) transformation and a central difference discretization in space. The range of material values is adjusted from existing experiments. It is generally found that the variation in viscosity, surface tension and specific heat can have a significant influence on both the growth rate and temperature evolution. Thermal conductivity is found to be of little influence.
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Mohammad Niknami, Zahir Ahmed, Bashar Albaalbaki and Roger E Khayat
The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below…
Abstract
Purpose
The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues.
Design/methodology/approach
In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered.
Findings
It is found that very small Prandtl numbers (Pr < 0.1) can change the Nusselt number, when terms to O(ε5/2) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualitative agreement is observed, even far from the linear threshold.
Originality/value
Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection. The number and type of modes to be included are directly related to the post-critical Rayleigh number. The method is not limited to the weakly nonlinear range.