Dynamic stall occurs on helicopter blades and pitching airfoils when the
dynamic-stall vortex, which forms as a result of an unsteady boundary-layer
eruption near the leading edge, detaches from the surface and convects
into the wake of the airfoil. The detachment process is initiated by a vortex-induced eruption that
occurs due to the adverse pressure gradient induced by the dynamic-stall vortex. Solutions of the unsteady
Navier-Stokes equations for the flow induced by a thick-core vortex above an infinite plane surface are
investigated in order to determine the influence of a moving wall on the unsteady separation and vortex
detachment processes. It has been shown based on unsteady-boundary layer calculations that a moving wall can
delay unsteady separation and vortex detachment. For wall speeds above a critical value, unsteady separation
is completely suppressed. Based on numerical solutions of the Navier-Stokes equations, it has been shown in
this investigation that decreasing the Reynolds number decreases the critical wall speed. When unsteady
separation does occur, boundary-layer vorticity is ejected away from the surface and interacts with the
primary vortex, causing it to weaken due to a reduction in net circulation, and the primary vortex detaches
from the surface and convects downstream.
Funded by: Army Research Office.
Numerical solutions of the unsteady Navier-Stokes equations are considered for the flow induced
by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The
presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads
to the formation of a secondary recirculation region, followed, in the high Reynolds number cases, by a
narrow eruption of near-wall fluid. The locally thickening boundary layer in the vicinity of the
eruption then provokes an interaction between the viscous boundary layer and the outer inviscid flow.
Numerical solutions of the Navier-Stokes equations show that the interaction occurs on two distinct
streamwise length scales depending upon which of three Reynolds number regimes is being considered.
At high Reynolds numbers, the sharp spike leads to a small-scale interaction; at moderate Reynolds
numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the
growing spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or
subsequent small-scale interaction.
Funded by: Army Research Office.
The Neutrino Factory and Muon Collider Collaboration is an international
group of physicists and engineers
collaborating on the research and development necessary to build a next generation particle-physics experiment
known as
a neutrino factor that would eventually lead to construction of a muon collider.
The Fermi National Accelerator Laboratory near Chicago is coordinating the efforts necessary to demonstrate the
ionization cooling channel, which is one
of the critical portions of both the neutrino factory and the muon collider. The cooling channel is cooled
cryogenicly and is in a magnetic field supplied by superconducting magnetic coils. It consists of
alternating radio-frequency (RF) cavities and liquid-hydrogen absorbers through which the muon
beam passes. As the muon beam passes through the liquid hydrogen, heat is deposited that must be removed
continuously for the duration of the experiment. We are using computational fluid dynamics (CFD) and heat
transfer to provide simulations that are aiding in the development of a novel approach to cooling the liquid
hydrogen.
Funded by: Department of Energy,
Fermi National Accelerator Laboratory and the
Illinois Consortium for Accelerator Research.
Vortices are fundamental and common features in a wide variety of fluid flows. High-Reynolds number,
mixed-convective flows, such as those around bluff bodies like circular cylinders, airfoils and turbomachinery
blades, generate intense vorticity at the body surface. In addition, horseshoe vortices can form near the
intersection of a bluff body and an adjoining surface, and hairpin vortices in near-wall flows play a central
role in generating and sustaining turbulence. When vortices, whether induced by viscous or buoyancy forces,
interact with solid surfaces, the resulting unsteady boundary-layer flow exhibits a variety of flow phenomena
including reversed flow and a violent eruption of boundary-layer fluid. In order to investigate the effect of
such an event on surface and convective heat transfer as well as the influence of buoyant convection on the
unsteady boundary-layer separation process, numerical solutions of the unsteady mixed-convection boundary
layer induced by a rectilinear vortex above a heated plane surface were obtained. Here numerical solutions of
the mixed-convection boundary-layer equations were obtained in the Lagrangian coordinate system. The numerical
solutions for various values of the inclination angle of the surface and Grashof number show that there is a
strong coupling between the fluid flow and heat transfer within the boundary layer. Depending upon the
orientation of the surface, buoyancy forces can be significant enough to alter the character of the separating
boundary layer, and the boundary-layer eruption ejects heated near-wall fluid into the outer flow.
Funded by: NRC Postdoctoral Fellowship Program and
Army Research Office.
At high Reynolds numbers, fluid particles within a boundary layer experience a momentum deficit relative
to the external mainstream flow and are very susceptible to unsteady separation in regions of adverse external
pressure gradient. Because unsteady separation is prevalent in most flows near solid walls at high Reynolds
numbers, there has been intense interest for many years in understanding the physical processes and in
developing a theoretical explanation of the phenomena involved. The evolution of the separation process for
an unsteady two-dimensional boundary layer at high Reynolds number was considered for incompressible flows.
Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation
singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts
to separate from the surface, however, the external pressure distribution is altered through viscous-inviscid
interaction just prior to the formation of the separation singularity, giving rise to an interactive stage.
For many years a solution to this interactive stage was thought to be intractable using traditional techniques.
Here a numerical solution of this stage was obtained in Lagrangian coordinates, in which the trajectories of
a large number of fluid particles are computed. The solution was found to exhibit a high-frequency inviscid
instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability
was confirmed through a linear stability analysis. The implications of these results on the theoretical
description of unsteady boundary-layer separation remain unclear, but it is suggested that some other physical
effect becomes important much sooner than previously thought.
Funded by: Air Force Office of Scientific Research and the NDSEG Fellowship Program.
This investigation was concerned with the flow of a supersonic stream past a compression ramp at small
angles of inclination. This simple geometry provides a framework in which it is convenient to investigate
the effects of surface geometry on steady separation. For small ramp angles, the flow in the vicinity of
the corner is governed by the classical supersonic triple-deck structure which facilitates the interaction
between the viscous boundary layer and the inviscid outer flow necessary to account for the upstream influence
of the ramp. An algorithm was used which combines the interaction condition with the sublayer equations in
such a way as to circumvent the need for iteration between solutions in the viscous and inviscid regions.
In numerical solutions of the triple-deck formulation for ramp angles above a critical value, a reversed-flow
region is observed adjacent to the corner which increases in size as the ramp angle is increased, and a plateau
forms in the pressure distribution. It was found that as the ramp angle is increased further, an instability
in the form of a wave packet arises within the viscous sublayer of the triple deck. However, unlike the
convective instabilities observed in other triple-deck flows, the instability observed here is absolute and
remains stationary near the corner. The critical ramp angle at which the instability first appeared in the
numerical calculations was consistent with the criterion obtained from a linear stability analysis.
Funded by: Air Force Office of Scientific Research and the NDSEG Fellowship Program.
Due to the extreme temperatures experienced by hypersonic flight vehicles, it is often necessary to insulate
or actively cool certain critical surfaces of such vehicles. The objective of this investigation was to
determine the effect of wall cooling on separation and stability of the hypersonic flow over a compression
ramp. The flow in the vicinity of the corner is governed by a triple-deck structure similar to the classical
supersonic triple deck; therefore, the algorithm used in the supersonic flow study was extended to the
hypersonic case with wall cooling. Numerical solutions were obtained for both subcritical and supercritical
boundary-layer flows (as determined by the average Mach number across the boundary layer) over the compression
ramp geometry with various small ramp angles and levels of wall cooling. Wall cooling of subcritical boundary
layers was shown to have a strong destabilizing effect, while wall cooling of supercritical boundary layers
has a stabilizing effect. The influence of wall cooling on separation is also dramatic and depends upon
whether the boundary layer is subcritical or supercritical. In either case, a sufficient level of wall
cooling was found to eliminate separation altogether for the ramp angles considered.
Funded by: NASA Lewis Research Center, Air Force Office of Scientific Research and NDSEG Fellowship Program.