3,987 research outputs found
Skin friction in zero-pressure-gradient boundary layers
A global approach leading to a self-consistent solution to the
Navier-Stokes-Prandtl equations for zero-pressure-gradient boundary layers is
presented. It is shown that as , the dynamically
defined boundary layer thickness and the
skin friction . Here and are the wall shear stress and
free stream velocity, respectively. The theory is formulated as an expansion in
powers of a small dimensionless parameter
in the limit
The Last Stages of Terrestrial Planet Formation: Dynamical Friction and the Late Veneer
The final stage of terrestrial planet formation consists of the cleanup of
residual planetesimals after the giant impact phase. Dynamically, a residual
planetesimal population is needed to damp the high eccentricities of the
terrestrial planets after the giant impact stage. Geochemically, highly
siderophile element (HSE) abundance patterns inferred for the terrestrial
planets and the Moon suggest that a total of about 0.01 M_Earth of chondritic
material was delivered as `late veneer' by planetesimals to the terrestrial
planets after the end of giant impacts. Here we combine these two independent
lines of evidence for a leftover population of planetesimals and show that: 1)
A residual planetesimal population containing 0.01 M_Earth is able to damp the
eccentricities of the terrestrial planets after giant impacts to their observed
values. 2) At the same time, this planetesimal population can account for the
observed relative amounts of late veneer added to the Earth, Moon and Mars
provided that the majority of the late veneer was delivered by small
planetesimals with radii <10m. These small planetesimal sizes are required to
ensure efficient damping of the planetesimal's velocity dispersion by mutual
collisions, which in turn ensures that the planets' accretion cross sections
are significantly enhanced by gravitational focusing above their geometric
values. Specifically we find, in the limit that the relative velocity between
the terrestrial planets and the planetesimals is significantly less than the
terrestrial planets' escape velocities, that gravitational focusing yields an
accretion ratio Earth/Mars~17, which agrees well with the accretion ratio
inferred from HSEs of 12-23. For the Earth-Moon system, we find an accretion
ratio of ~200, which is consistent with estimates of 150-700 derived from HSE
abundances that include the lunar crust as well as mantle component. (Abridged)Comment: accepted for publication in ApJ, 9 pages, 4 figures; minor
corrections, additional references adde
Experimental Investigation of the Problem of Surface Roughness
Based on the universal laws of turbulent velocity distribution at rough and smooth walls, there is in the present work presented a method that allows surface roughness tests and in particular, measurements on the roughness of ship surfaces to be carried out in a much simpler manner. The types of roughness investigated were in the form of flat, rough plates installed in a square-section rectangular channel, the other three walls always being smooth. Twenty-one plates of various roughness were investigated, the roughness elements being the following: spheres of diameter 0.41 and 0.21, respectively, spherical segments, cones, and "short" and "long" angles
Airfoil Theory at Supersonic Speed
A theory is developed for the airfoil of finite span at supersonic speed analogous to the Prandtl airfoil theory of 1918-1919 for incompressible flow. In addition to the profile and induced drags, account must be taken at supersonic flow of still another drag, namely, the wave drag, which is independent of the wing aspect ratio. Both wave and induced drags are proportional to the square of the lift and depend on the Mach number, that is, the ratio of flight to sound speed. In general, in the case of supersonic flow, the drag-lift ratio is considerably less favorable than is the case for incompressible flow. Among others the following examples are considered: 1) lifting line with constant lift distribution (horseshoe vortex); 2) computation of wave and induced drag and the twist of a trapezoidal wing of constant lift density; 3) computation of the lift distribution and drag of an untwisted rectangular wing
Amplitude distribution and energy balance of small disturbances in plate flow
The distribution of the correlation coefficient and of the amplitude of the disturbance velocities is calculated as a function of the distance from the wall for two neutral disturbances, one at the lower and one at the upper branch of the neutral stability curve. The energy balance of the disturbance motion is also investigated and it is found that as required for neutral stability the energy of the disturbance motion that is dissipated by viscosity is equal to the energy transferred to the disturbance motion from the main flow during one cycle
The Dornier Wind Tunnel
After completion of the required calibrations, the Dornier open-throat tunnel is now in operation. With an elliptic test section of 3 by 4 m (9.84 by 3.12 ft.), its length is 7 m (22.97 ft.), its maximum horsepower 800, and its maximum air speed 60 m/s (134.2 mph). As to local uniformity of velocity, static pressure as well as jet direction, and turbulence factor, this tunnel is on par with those of the good German and foreign research labs
Is turbulent mixing a self convolution process ?
Experimental results for the evolution of the probability distribution
function (PDF) of a scalar mixed by a turbulence flow in a channel are
presented. The sequence of PDF from an initial skewed distribution to a sharp
Gaussian is found to be non universal. The route toward homogeneization depends
on the ratio between the cross sections of the dye injector and the channel. In
link with this observation, advantages, shortcomings and applicability of
models for the PDF evolution based on a self-convolution mechanisms are
discussed.Comment: 4 page
Integral analysis of laminar indirect free convection boundary layers with weak blowing for Schmidt no. ~ 1
Laminar natural convection at unity Schmidt number over a horizontal surface
with a weak normal velocity at the wall is studied using an integral analysis.
To characterise the strength of the blowing, we define a non-dimensional
parameter called the blowing parameter. After benchmarking with the no blowing
case, the effect of the blowing parameter on boundary layer thickness, velocity
and concentration profiles is obtained. Weak blowing is seen to increase the
wall shear stress. For blowing parameters greater than unity, the diffusional
flux at the wall becomes negligible and the flux is almost entirely due to the
blowing.Comment: 10 pages, published in International Communications in heat and mass
transfer,Vol31,No8, 2004, pp 1199 -120
Morphological instability of the solid-liquid interface in crystal growth under supercooled liquid film flow and natural convection airflow
Ring-like ripples on the surface of icicles are an example of morphological
instability of the ice-water interface during ice growth under supercooled
water film flow. The surface of icicles is typically covered with ripples of
about 1 cm in wavelength, and the wavelength appears to be almost independent
of external temperature, icicle radius, and volumetric water flow rate. One
side of the water layer consists of the water-air surface and growing ice is
the other. This is one of the more complicated moving phase boundary problems
with two interfaces. A recent theoretical work [K. Ueno, Phys. Rev. E 68,
(2003) 021603] to address the underlying instability that produces ripples is
based on the assumption of the absence of airflow around icicles. In this
paper, we extend the previous theoretical framework to include a natural
convection airflow ahead of the water-air surface and consider whether the
effect of natural convection airflow on the wavelength of ripples produced on
an ice surface is essential or not.Comment: 19 pages, 5 figure
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