Kevin W. Cassel

A comparison of Navier-Stokes solutions with the theoretical description of unsteady separation

Numerical solutions of the unsteady two–dimensional boundary–layer and Navier–Stokes equations are considered for the flow induced by a thick–core vortex above an infinite plane wall in an incompressible flow. Vortex–induced flows of this type generally involve unsteady separation, which results in an eruption of high–vorticity fluid within a narrow streamwise region. At high Reynolds numbers, the unsteady separation process is believed to pass through a series of asymptotic stages. The first stage is governed by the classical non–interactive boundary–layer equations, for which solutions are given, and terminate in the Van Dommelen singularity. As an eruption develops, the boundary layer thickens and provokes a viscous–inviscid interaction leading to the second stage of unsteady separation. The third stage occurs when the normal pressure gradient becomes important locally within the boundary layer. In order to identify these asymptotic stages at large, but finite, Reynolds numbers, solutions of the full Navier–Stokes equations are obtained for the flow induced by a thick–core vortex. These results generally support this sequence of events; however, a large–scale viscous–inviscid interaction is found to begin at a time much earlier than allowed for by the asymptotic theory; that is it begins to occur prior to the formation of a spike within the boundary layer. Some consequences of these results on our understanding of unsteady separation are discussed.

Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions

Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtls solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.

Characteristic differences in cephalic arch geometry for diabetic and non-diabetic ESRD patients

BACKGROUND Fistula access in chronic haemodialysis patients is recommended. The first and second choice for location of fistula placement is radial-cephalic followed by the brachiocephalic fistula. Fistula access using the cephalic vein often results in cephalic arch stenosis that is less common in diabetics for unclear reasons. The objective of the current study is to determine if geometry of the cephalic arch differs between diabetics and non-diabetics. METHODS In a retrospective design, 57 patients with brachiocephalic fistula access had radiology films of the cephalic arch reviewed for geometric analysis. Twelve patients were excluded from final analysis because of stent placement in the cephalic arch. Measurements made included diameter of the cephalic vein, minimum radius of curvature and angle of the arch. Demographics were statistically analysed to determine the association with the geometric measurements. RESULTS Global and local measurements showed evidence of two arch types. Wider arch angles and larger R/d were associated with diabetes by univariate (P < 0.05) and multivariate analyses (P < 0.05). A wider arch angle was also associated with a history of right permcath access by multivariable analysis (P = 0.042). CONCLUSIONS Based on this study, it was found that there are two distinct types of cephalic arch geometries. Patients having diabetes mellitus show a significant probability of having a larger R/d ratio and wider arch angle. This study has given insight into structural alterations in geometry of the cephalic arch of diabetics with brachiocephalic fistula access.

On the ejection-induced instability in Navier-Stokes solutions of unsteady separation

Numerical solutions of the flow induced by a thick-core vortex have been obtained using the unsteady, two-dimensional Navier–Stokes equations. The presence of the vortex causes an adverse pressure gradient along the surface, which leads to unsteady separation. The calculations by Brinckman and Walker for a similar flow identify a possible instability, purported to be an inviscid Rayleigh instability, in the region where ejection of near-wall vorticity occurs during the unsteady separation process. In results for a range of Reynolds numbers in the present investigation, the oscillations are also found to occur. However, they can be eliminated with increased grid resolution. Despite this behaviour, the instability may be physical but requires a sufficient amplitude of disturbances to be realized.

Detachment of the Dynamic-Stall Vortex Above a Moving Surface

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 dynamic-stall vortex is modeled as a thick-core vortex above an infinite plane surface. Numerical solutions of the unsteady Navier-Stokes equations are obtained to determine the nature of the unsteady separation and vortex detachment processes and the influence of a moving wall. Whereas the unsteady separation process evolves very differently within two Reynolds number regimes, the detachment process is observed to be very similar over the range of Reynolds numbers considered. A moving wall has a significant influence on both processes

Hemodynamics in the cephalic arch of a brachiocephalic fistula

The care and outcome of patients with end stage renal disease (ESRD) on chronic hemodialysis is directly dependent on their hemodialysis access. A brachiocephalic fistula (BCF) is commonly placed in the elderly and in patients with a failed lower-arm, or radiocephalic, fistula. However, there are numerous complications such that the BCF has an average patency of only 3.6 years. A leading cause of BCF dysfunction and failure is stenosis in the arch of the cephalic vein near its junction with the axillary vein, which is called cephalic arch stenosis (CAS). Using a combined clinical and computational investigation, we seek to improve our understanding of the cause of CAS, and to develop a means of predicting CAS risk in patients with a planned BCF access. This paper details the methodology used to determine the hemodynamic consequences of the post-fistula environment and illustrates detailed results for a representative sample of patient-specific anatomies, including a single, bifurcated, and trifurcated arch. It is found that the high flows present due to fistula creation lead to secondary flows in the arch owing to its curvature with corresponding low wall shear stresses. The abnormally low wall shear stress locations correlate with the development of stenosis in the singular case that is tracked in time for a period of one year.

Increased Inlet Blood Flow Velocity Predicts Low Wall Shear Stress in the Cephalic Arch of Patients with Brachiocephalic Fistula Access

Background An autogenous arteriovenous fistula is the optimal vascular access for hemodialysis. In the case of brachiocephalic fistula, cephalic arch stenosis commonly develops leading to access failure. We have hypothesized that a contribution to fistula failure is low wall shear stress resulting from post-fistula creation hemodynamic changes that occur in the cephalic arch. Methods Twenty-two subjects with advanced renal failure had brachiocephalic fistulae placed. The following procedures were performed at mapping (pre-operative) and at fistula maturation (8–32 weeks post-operative): venogram, Doppler to measure venous blood flow velocity, and whole blood viscosity. Geometric and computational modeling was performed to determine wall shear stress and other geometric parameters. The relationship between hemodynamic parameters and clinical findings was examined using univariate analysis and linear regression. Results The percent low wall shear stress was linearly related to the increase in blood flow velocity (p < 0.01). This relationship was more significant in non-diabetic patients (p < 0.01) than diabetic patients. The change in global measures of arch curvature and asymmetry also evolve with time to maturation (p < 0.05). Conclusions The curvature and hemodynamic changes during fistula maturation increase the percentage of low wall shear stress regions within the cephalic arch. Low wall shear stress may contribute to subsequent neointimal hyperplasia and resultant cephalic arch stenosis. If this hypothesis remains tenable with further studies, ways of protecting the arch through control of blood flow velocity may need to be developed.

Unsteady separation in vortex-induced boundary layers.

This paper provides a brief review of the analytical and numerical developments related to unsteady boundary-layer separation, in particular as it relates to vortex-induced flows, leading up to our present understanding of this important feature in high-Reynolds-number, surface-bounded flows in the presence of an adverse pressure gradient. In large part, vortex-induced separation has been the catalyst for pulling together the theory, numerics and applications of unsteady separation. Particular attention is given to the role that Prof. Frank T. Smith, FRS, has played in these developments over the course of the past 35 years. The following points will be emphasized: (i) unsteady separation plays a pivotal role in a wide variety of high-Reynolds-number flows, (ii) asymptotic methods have been instrumental in elucidating the physics of both steady and unsteady separation, (iii) Frank T. Smith has served as a catalyst in the application of asymptotic methods to high-Reynolds-number flows, and (iv) there is still much work to do in articulating a complete theoretical understanding of unsteady boundary-layer separation.

Gaseous Hydrogen and Muon Accelerators

Ionization cooling, a method for shrinking the size of a particle beam, is an essential technique for future particle accelerators that use muons. In this technique, muons lose energy in all three directions by passing through an absorber while only the longitudinal energy is regenerated by RF cavities. Thus the beam phase space area decreases down to the limit of multiple scattering in the energy absorber. Hydrogen is the material of choice for ionization cooling because of its long radiation length relative to its energy loss. In the application discussed here, dense gaseous hydrogen also suppresses RF breakdown by virtue of the Paschen effect, thereby allowing higher accelerating gradients and a shorter and less‐expensive cooling channel. As described in this paper, a channel of RF cavities pressurized with about 3 tons of cold hydrogen gas could provide transverse muon cooling for a Muon Collider or Neutrino Factory. The present status of this research effort and several issues related to the use of h...

Progress in absorber R & D for muon cooling

A stored-muon-beam neutrino factory may require transverse ionization cooling of the muon beam. We describe recent progress in research and development on energy absorbers for muon-beam cooling carried out by a collaboration of university and laboratory groups.