Fluid Dynamics at Connections in Paediatric Cardiac Surgery*

The modified Blalock-Taussig shunt is a connection created between the systemic and pulmonary arterial circulations to improve pulmonary perfusion in children with congenital heart diseases. Survival of these patients is critically dependent on blood flow distribution between the pulmonary and systemic circulations, that in turn depends upon the fluid dynamic behaviour of the shunt. Computational fluid dynamics, structural analyses as well as in vitro experiments were carried out to derive a quantitative relationship between the shunt flow and the corresponding pressure drop. While computational fluid dynamics simulations were based on the assumption of rigid wall for the shunt and the arteries, proper distensible conduits were used in the in vitro study and the structural analysis of the anastomosis deformation. The results indicated that the internal pressure combined with wall distensibility modifies the cross-sectional area of the distal anastomosis (between the shunt and the pulmonary artery). This fact affects the pressure drop across the shunt, especially at low pressures. Based on the results from the computational analyses and the in vitro experiments, a relationship between pressure drop and flow in the shunt was obtained, which matches data from clinical measurements.     

Application of Uniform Asymptotics to the Second Painlevé Transcendent

In this work we propose a new method for investigating connection problems for the class of nonlinear second‐order differential equations known as the Painlevé equations. Such problems can be characterized by the question as to how the asymptotic behaviours of solutions are related as the independent variable is allowed to pass towards infinity along different directions in the complex plane. Connection problems have been previously tackled by a variety of methods. Frequently these are based on the ideas of isomonodromic deformation and the matching of WKB solutions. However, the implementation of these methods often tends to be heuristic in nature and so the task of rigorising the process is complicated. The method we propose here develops uniform approximations to solutions. This removes the need to match solutions, is rigorous, and can lead to the solution of connection problems with minimal computational effort. Our method relies on finding uniform approximations of differ ential equations of the generic form as the complex‐valued parameter . The details of the treatment rely heavily on the locations of the zeros of the function F in this limit. If they are isolated, then a uniform approximation to solutions can be derived in terms of Airy functions of suitable argument. On the other hand, if two of the zeros of F coalesce as , then an approximation can be derived in terms of parabolic cylinder functions. In this paper we discuss both cases, but illustrate our technique in action by applying the parabolic cylinder case to the “classical” connection problem associated with the second Painlevé transcendent. Future papers will show how the technique can be applied with very little change to the other Painlevé equations, and to the wider problem of the asymptotic behavio ur of the general solution to any of these equations. (Accepted May 15, 1997)     

Use of caged fluorescent dyes for the study of turbulent passive scalar mixing

The non-intrusive initialization of a flow field with distinct and spatially segregated scalar components represents a significant experimental difficulty. Here a new technique is described which makes possible the non-intrusive initialization of a spatially binary passive scalar field in a laminar or turbulent flow field. This technique uses photoactivatable (caged) fluorescent dyes dissolved in the flow medium. The scalar field within the flow field is tagged or initialized by uncaging the appropriate regions with an ultraviolet excimer laser. Mixing between the tagged and untagged regions is quantified using standard laser induced fluorescence techniques. The method is currently being used to study mixing in a turbulent pipe flow.     

Some theorems in the theory of small deformations superimposed on a finite deformation of a hyperelastic material of grade 2

The equations for small deformations superimposed on large deformations of a hyperelastic material of grade 2 are formulated and applied to derive a basic integral relation that is used to establish generalized Betti, Clapeyron, work and energy theorems. Theorems of minimum and complementary energy are deduced essentially from an energy criterion of super-stability, and these are used to prove uniqueness of solutions to the static and dynamic, mixed incremental boundary value problems. These results use a certain generalized kinetic energy functional that is assumed positive definite; and this property and the reciprocal and energy principles are exploited further to establish some theorems in the theory of small free vibrations.     

Investigation of temperature distribution in a piecewise-homogeneous seam with pressed-in hot fluid

Temperature distribution in a piecewise-homogeneous finiteseam exposed to hot fluid and the effect of inhomogeneity in the permeability and thermal properties of separate zones of a seam on the redistribution of temperature fields for flat parallel or axial flow of a pressed-in hot liquid are studied. The differential equations which describe the process of temperature distribution in accordance with [1] are solved for various initial and boundary conditions. Exact analytic formulas are obtained which are useful in numerical computations. The problem under consideration is related to important engineering problems in hydrology, geothermy, as well as in the development of oil or gas fields [2–4, 5].     

Thermohydrodynamic conditions at the peak flux of horizontal heaters in superfluid liquid helium II at zero net mass flow

Measurements of the peak flux (at the onset of film boiling) in He II are used as a diagnostic tool to investigate the non-classical thermohydrodynamics of superfluid liquid helium for horizontal heaters at zero net mass flow. Data for the single horizontal cylinder in a large pool of He II are approximately accounted for by a power law describing the dimensionless nonclassical superfluid transport number as a function of the fourth root of the dimensionless thermo-mechanical driving potential. Results for transport in narrow vertical cylinders (with insulated walls and lower end closed) are approximately described on the basis of the Gorter-Mellink transport equations. The saturation hypothesis is used which postulates local onset of boiling when vapor-liquid equilibrium is reached at the heater.     

Jacobi's multiplier for Poincaré's equations

In this paper we use Poincaré's equations in group variables to describe the motion of a holonomic mechanical system and to determine Jacobi's multiplier for the equations of motion.     

Wall-shear-stress and near-wall turbulence measurements up to single pixel resolution by means of long-distance micro-PIV

A digital large-format long-distance micro-particle image velocimetry system (μ-PIV) was developed to measure the wall-shear-stress and the near-wall flow properties in a laminar, transitional and turbulent boundary layer flow along a flat plate, non-intrusively with high accuracy and spatial resolution. To achieve the desired measurement accuracy and spatial resolution, all experimental limitations associated with the seeding, light-sheet, out-of-focus particles, optical aberrations and distortions were successfully solved and various spatial correlation image analysis approaches based on the two-point or single-pixel ensemble correlation were developed, analyzed and compared with the state-of-the-art spatial correlation techniques. The instrument is well suited to prove fundamental fluid mechanical hypotheses such as the universality of the constants κ and B of the logarithmic law. However, for the analysis of flows at large Reynolds and Mach numbers, where small spatial dimensions and strong flow gradients prevent accurate measurements, this technique can be applied as well.     

Determining stress intensity factors in orthotropic composites from far-field measured temperatures

We demonstrate the ability to determine stress intensity factors in orthotropic materials directly from measured temperatures away from the crack and using far-field expressions for the stresses. This is advantageous, recognizing that recorded thermoelastic data can be very unreliable near the tip of a crack. In addition to singular terms that govern in the immediate vicinity of the crack tip, the present series expressions for the stresses contain higher-order finite terms. Little measured input information is needed and data acquisition positions can be selected largely at the user's discretion.