Bradley Rogers

Mixed Convection in an Annulus of Large Aspect Ratio

Mixed convection in an annulus of large aspect ratio is studied. At an aspect ratio of 100, the effect of wall curvature is minimal, and both the base flow and the stability characteristics approach those of a two-dimensional channel flow. The linear-stability results demonstrate that the fully developed flow is unstable in regions of practical interest in an appropriate parameter space. Consequently, commonly assumed steady parallel countercurrent flows in many idealized numerical and analytical studies are unlikely to be observed experimentally.

Natural convection in a heated annulus

Abstract Natural convection in a heated vertical concentric annulus is studied. A constant heat-flux is applied to the inner cylinder and the outer cylinder is insulated. Under these conditions, the mean temperature of the fluid increases linearly while, at the same time, heat diffuses from the heated surface into the fluid, resulting in a temperature distribution on the cross-section. Subtracting this steadily increasing temperature from the total temperature results in a steady temperature stratification on the cross-section which drives fluid motion. The mathematical form of the scaled problem is shown to be identical to that of a fluid in an annulus with uniformly distributed heat sources, with the inner cylinder maintained at constant temperature and the outer cylinder insulated. At low heat addition rates, the fluid motion is steady and parallel, and heat is transferred by conduction between the fluid layers. As the rate of heating increases, the flow becomes unstable and recirculating eddies appear, which transfer heat by convection. The onset of convection is determined by linear-instability analysis of the basic-state. The results demonstrate that when the Prandtl number is small, the dominant instability obtained energy primarily from shear production. On the other hand, when the Prandtl number is large, an instability that obtains kinetic energy from buoyant production is pre-eminent. Weakly nonlinear instability theory is used to analyze finite-amplitude effects. The results show that both types of linear instabilities are supercritical.

Finite-amplitude instability of mixed-convection in a heated vertical pipe

Abstract The instability of flow in a heated vertical pipe is studied using weakly nonlinear instability theory for both stably and unstably stratified cases. It is found that the dominant instability for stably stratified flow is a thermal-buoyant instability, while that of the unstably stratified case is a Rayleigh-Taylor instability. The weakly nonlinear theory predicts supercritical instability for the stably stratified case, in agreement with experimental observations. In this case, it is found that a wide band of wave numbers are linearly unstable soon after the onset of the initial instability. This limits the range for which the weakly nonlinear results are accurate in this case since the theory considers the growth of a single dominant wave. The results of the weakly nonlinear calculations for unstably stratified flow indicate that the flow is potentially subcritically unstable, again in agreement with the experimental observations. On the other hand, the theory predicts that a large amplitude disturbance will be necessary to initiate subcritical instability, while the amplitude of a supercritical disturbance will grow quickly as the magnitude of Ra increases. Therefore, another possible flow transition that is consistent with experimental observations involves rapid growth of the first azimuthal mode of a supercritical Rayleigh Taylor instability, followed by secondary instabilities that lead quickly to turbulence. Analysis of energy transfer in the fundamental wave demonstrates that the thermal-buoyant instability is supercritical because increases in the viscous dissipation rate and the rate of transfer of energy from the fundamental wave back into the mean flow overcome the destabilizing effect of an increase in the rate of buoyant production. Subcritical instability occurs with the Rayleigh-Taylor mode when the disturbance amplitude increases to the point that the combined destabilizing effects caused by a change in the shape of the fundamental wave induced by nonlinear effects become larger than the stabilizing effects due to the production of the harmonic wave and the distortion of the mean-flow. The increase in heat transfer rates due to instability predicted by the weakly nonlinear theory is smaller than the experimental observations. However, it is demonstrated that experimentally observed increases in Nu are predicted if the effects of additional waves are included in an approximate manner.

Finite-amplitude instability of mixed convection

The finite-amplitude instability of mixed convection of air in a vertical concentric annulus with each cylinder maintained at a different temperature is studied by use of weakly nonlinear instability theory and by direct numerical simulation. A strictly shear instability and two thermally induced instabilities exist in the parameter space of Reynolds and Grashof numbers. The first thermal instability occurs at low Reynolds numbers as the rate of heating increases, and is called a thermal-shear instability because it is a shear-driven instability induced by thermal effects. The second thermal instability occurs at larger Reynolds number as heating increases, and is also a thermally induced shear instability called the interactive instability. The weakly nonlinear results demonstrate that the thermal-shear instability is supercritical at all wavenumbers. With the shear and interactive instabilities, however, both subcritical and supercritical branches appear on the neutral curves. The validity of the weakly nonlinear calculations are verified by comparison with a direct simulation. The results for subcritical instabilities show that the weakly nonlinear calculations are accurate when the magnitude of the amplification rate is small, but the accuracy deteriorates for large amplification rates. However, the trends predicted by the weakly nonlinear theory agree with those predicted by the direct simulations for a large portion of the parameter space. Analyses of the energy sources for the disturbance show that subcritical instability of the shear and interactive modes occurs at larger wavenumbers because of increased gradient production of disturbance kinetic energy. This is because, at shorter wavelengths, the growth of the wave causes the shape of the fundamental disturbance to change from that predicted by linear instability theory to a shape more favourable for shear-energy production. The results also show that many possibly unstable modes may be present simultaneously. Consequently, all of these modes, as well as all of the possible wave interactions among the modes, must be considered to obtain a complete picture of mixed-convection instability.

The effect of mixed convection instability on heat transfer in a vertical annulus

Abstract The hydrodynamic stability of mixed convection in an annulus is studied. The linear stability limit for forced flow up a vertical annulus with a constant heat flux applied to the inner wall and the outer wall insulated is determined. The result indicates that the fully-developed flow is thermally unstable in most regions of an appropriate parameter space. The magnitudes of the finite amplitude disturbances in the unstable region are determined by utilizing Stuarts shape assumption. Distorted mean flow profiles are obtained and the increase in heat transfer rates due to these disturbances are calculated from the results and agree well with the experimental data.

Creation of security engineering programs by the Southwest Surety Institute

The Southwest Surety Institute includes Arizona State University (ASU), Louisiana State University (LSU), New Mexico Institute of Mining and Technology (NM Tech), New Mexico State University (NMSU), and Sandia National Laboratories (SNL). The universities currently offer a full spectrum of post-secondary programs in security system design and evaluation, including an undergraduate minor, a graduate program, and continuing education programs. The programs are based on the methodology developed at Sandia National Laboratories over the past 25 years to protect critical nuclear assets. The programs combine basic concepts and principles from business, criminal justice, and technology to create an integrated performance-based approach to security system design and analysis. Existing university capabilities in criminal justice (NMSU), explosives testing and technology (NM Tech and LSU), and engineering technology (ASU) are leveraged to provide unique science-based programs that will emphasize the use of performance measures and computer analysis tools to prove the effectiveness of proposed systems in the design phase. Facility managers may then balance increased protection against the cost of implementation and risk mitigation, thereby enabling effective business decisions. Applications expected to benefit from these programs include corrections, law enforcement, counter-terrorism, critical infrastructure protection, financial and medical care fraud, industrial security, and border security.