Simplified Boundary Layer Model Research Articles

Mach reflection in steady supersonic flow considering wedge boundary-layer correction

Mach reflection in steady supersonic flow is an important phenomenon having received extensive studies, among which simplified theoretical models to predict the size of Mach stem and other flow structure are of particular interest. Past efforts for such models were based on inviscid assumption while in real cases the flow is viscous. Here in this paper we consider the influence of wedge boundary layer on the Mach stem height. This is done by including a simplified boundary layer model into a recently published inviscid model. In this viscous model, the wedge angle and the trailing edge height, which control the Mach stem height, are replaced by their equivalent ones accounting for the displacement effect of the wedge boundary layer, with the boundary layer assumed to be laminar or fully turbulent. This viscous model is shown to compare well with numerical results by computational fluid dynamics and gives a Mach stem height as function of the Reynolds number and Mach number. It is shown that due to the viscous effect, the Mach stem height is increased, through increasing the effective wedge angle.

Parametric design studies for propulsive fuselage aircraft concepts

Breaking with the classical separation of airframe and power plant system, new synergy effects may be rooted in close design coupling and the approach of distributing the production of thrust along the main components of the airframe. Beside greater configurational flexibility, airframe structural relief, improved noise shielding, and, the potential for control power augmentation, distributed propulsion is particularly interesting due to the reduced propulsive power demands expected from the notion of aircraft wake filling. In previous work, the concept of a propulsor encircling the aft fuselage with intent to entrain the fuselage boundary layer was identified to be one of the most promising concepts for aircraft wake filling. In this paper, the analytical basis for the quantification of efficiency benefits connected to the propulsive fuselage concept is discussed. Appropriate control volume and consistent efficiency chain definitions are introduced. A simplified boundary layer model is derived from axisymmetric fuselage CFD simulation and used to determine the momentum deficit ingested by the fuselage propulsor. Based on a novel figure of merit for vehicular efficiency, the energy-specific air range, ESAR, the dependency of aircraft cruise efficiency on basic propulsion system and aircraft design changes is parametrically investigated. Specifically, the sensitivities of vehicular efficiency w.r.t. wing aspect ratio and flow transition characteristics, propulsor size, and aircraft design cruise Mach number are studied.

Wind speed interpolation in the vicinity of the Panama Canal

AbstractA simplified boundary layer (SBL) model formulation is tested against the mesoscale meteorological model MM5 with respect to the 2 km interpolation of hourly surface wind station data for stations in the close vicinity of the Panama Canal. The required short computation time for the real time interpolation of the wind during air pollution incidents involving crossing cargo ships makes the use of simplified wind models an alternative to the full implementation of mesoscale models. The SBL model does take into consideration the land cover of the ground surface, which exhibits substantial variability in the study region. The SBL model produces features of wind speed that are similar to those of the MM5 simulation along the better‐observed Canal centreline. The presence of orographic features makes the applicability of the simplified formulation reasonable only near the Canal where the terrain has small undulations. The simulated wind fields show that the dry season (January to April) is more spatially and temporally coherent than the wet season and that it also has higher wind speeds than the wet season. The evening hours have higher wind speeds than the morning hours in both seasons. The simulated wind exhibits higher average wind speeds and higher frequencies of exceeding 5 m s−1 within the Gatun Lake on the Caribbean side of the Isthmus and the entrance/exit of the Canal on the Caribbean and Pacific coasts. These results are useful for the development of effective disaster mitigation strategies for air pollution events in the region. Copyright © 2011 Royal Meteorological Society

Forced convection in-tube steam condensation in the presence of noncondensable gases

An experimental and analytical investigation has been conducted to determine the effects of the presence of noncondensable gases on in-tube steam condensation under forced convection conditions. The local mixture Nusselt numbers were correlated in terms of the local mixture Reynolds number, mixture Jakob number, and the gas mass fractions or the mixture Schmidt number. Correlations including the mixture Schmidt number did better in representing the condensation process in the presence of one noncondensable gas. The experiments covered steam/gas mixture inlet Reynolds numbers from about 6000 to 26000, inlet helium mass fraction range from 0.022 up to 0.20, inlet air mass fraction range from 0.045 up to 0.20, and mixture inlet temperature of 100°C and 130°C (corresponding to a pressure range from 114 to 603 kPa). The ratios of the condensate film thermal resistance to the thermal resistance of the steam/noncondensable gas mixture at the same bulk temperature were calculated. In general, the condensate film thermal resistance was found to be significant for turbulent gas mixture conditions (Re > 6000) and relatively low gas mass fraction (W < 0.2). A diffusion-based, simplified boundary layer model has been developed. The steady-state radial diffusion equations of the mixture components were solved in order to obtain the steam mass flux at the interface between the condensate film and the mixture. The effect of the axial flow was included in terms of an effective boundary layer thickness which decreases with mixture Reynolds number. The model included the effect of more than one noncondensable gas on steam condensation. The model-predicted mixture heat transfer coefficients were favorably compared to the experimental results.

Structure of axisymmetric mantle plumes

Results of high‐resolution numerical calculations of axisymmetric thermal plumes in an infinite Prandtl number fluid with thermally activated viscosity are used to infer the structure of axisymmetric subsolidus thermal plumes in the Earth's lower mantle. We calculate the velocity and temperature distribution for axisymmetric convection above a heated disk in an incompressible fluid cylinder, 2400 km in height and 1200 km in diameter, initially at a uniform temperature T∞. The lower boundary, representing the plume source region near the core‐mantle boundary, is stress‐free and maintained at temperature Tc&gt; T∞. The upper boundary is permeable, allowing the plume to escape the cylinder. We determine the sensitivity of plume structure to viscosity variations η∞/ηc ranging from 102 to more than 104 and temperature differences ΔT = Tc ‐ T∞. in the range 400–850 K. Starting plumes consist of a large leading diapir and a trailing conduit connected to the thermal boundary layer above the heated surface. The leading diapir expands during ascent, to about 400 km diameter at 2200 km height. In steady state, the plume consists of a narrow, high‐velocity conduit imbedded within a broader thermal halo. The width of both these structures is proportional to height above the heated boundary and inversely proportional to ΔT and the viscosity ratio. Heat transport in the plume is nearly independent of viscosity variations. A simplified boundary layer model yields a heat transfer law, Nu ≈ Ra⅓ where Nu is the plume Nusselt number and Ra is the Rayleigh number based on, ΔT, η∞ and the radius of the heated circular region feeding the plume. Calculated steady state plume heat transports fit this law to within a few percent. We present several calculations of plumes with heat transport in the range 100–400 GW, similar to the advective heat transport by the Hawaiian hotspot. At the top of the lower mantle, plumes with large viscosity variations have high‐velocity conduits 50–60 km in diameter and 125‐km‐diameter thermal halos, a centerline temperature anomaly of about 500 K and a centerline velocity of about 75 cm yr−1. Plumes with weak viscosity variations are approximately twice as broad and have centerline temperature anomalies less than 160 K at the same height and much smaller velocity. Large viscosity variations and a minimum heat transport are both

A test of the boundary layer model in unsteady Czochralski growth

We compare a boundary layer model of unsteady Czochralski growth to a more comprehensive connective-diffusive model. Two test problems are considered: determining segregation effects due to the initial transient when a crystal starts growing at a constant rate and determining the segregation effects due to oscillatory crystal growth. In both instances, the results from the simplified boundary layer model are nearly identical to those from the connective-diffusive model. The simplified model is considerably easier to use. However, it is incomplete and requires a parameter Δ to be supplied externally. This parameter can be obtained from a steady state version of the connective-diffusive model.