Author
J. R. Womersley
Bio: J. R. Womersley is an academic researcher. The author has contributed to research in topics: Separable partial differential equation & Exponential integrator. The author has an hindex of 4, co-authored 4 publications receiving 2029 citations.
Papers
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TL;DR: The experiments of McDonald and his co-workers have shown that in the larger arteries of the rabbit and the dog there is a reversal of the flow, and the simple mathematical treatment has strong similarities with the theory of the distribution of alternating current in a conductor of finite size.
Abstract: The experiments of McDonald and his co-workers (McDonald, 1952, 1955; Helps & McDonald, 1953) have shown that in the larger arteries of the rabbit and the dog there is a reversal of the flow. Measurements of the pressure gradient (Helps & McDonald, 1953) showed a phase-lag between pressure gradient and flow somewhat analogous with the phase-lag between voltage and current in a conductor carrying alternating current, and the simple mathematical treatment given below has strong similarities with the theory of the distribution of alternating current in a conductor of finite size.
1,675 citations
01 Jan 1957
TL;DR: In this article, the authors developed the concept of a thin walled elastic tube as a rough working model of an artery, and from a solution of the equations of motion of such a tube, filled with viscous liquid, a number of relationships are deduced that can be tested experimentally.
Abstract: : This work develops the concept of a thin walled elastic tube as a rough working model of an artery, and from a solution of the equations of motion of such a tube, filled with viscous liquid, a number of relationships are deduced that can be tested experimentally. The theory of pulse-wave transmission, and the relationships between pulse pressure, rate of flow, and radial expansion, are demonstrated as parts of a single logical structure. Some comparisons with experimental results are made and new experiments are proposed, as tests of the adequacy of the theory.
401 citations
TL;DR: In this paper, the authors give a way of applying it to partial differential equations in two independent variables with certain types of boundary conditions, which is particularly suited to the differential analyser, though it is also practicable for numerical work.
Abstract: The development of mechanical means of evaluating solutions of ordinary differential equations, in the form of the differential analyser of Dr. Bush (Bush 1931; Hartree 1935), has made it feasible to undertake the investigation of many problems of scientific and technical interest leading to differential equations which have no convenient formal solution, and which are too elaborate, or for which the range of solutions required is too extensive, for calculation of the solutions by numerical methods to be practicable. The practical success of this machine, and the wide range of equations to which it can be applied, have led to the hope that it may be found possible to apply it to partial differential equations, which are usually regarded as less amenable to numerical methods than ordinary equations. The present paper gives one way of applying it to such equations in two independent variables with certain types of boundary conditions. As will appear, the possibility of applying this method depends more on the form of the boundary conditions than on the exact form of the equations. The method is particularly suited to the differential analyser, though it is also practicable for numerical work.
84 citations
7 citations
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01 Jan 1947
TL;DR: In this paper, the authors present methods of evaluating numerical solutions of the non-linear partial differential equation to the boundary conditions A, k, q are known constants, where q is the rate of heat generation.
Abstract: This paper is concerned with methods of evaluating numerical solutions of the non-linear partial differential equationwheresubject to the boundary conditionsA, k, q are known constants.Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2).
2,613 citations
Book•
01 Sep 2013
TL;DR: In this article, the authors discuss the properties of high-temperature gas dynamics, including the effects of high temperature on the dynamics of Viscous Flow and Vibrational Nonequilibrium Flows.
Abstract: Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.
1,960 citations
TL;DR: The study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow.
Abstract: Blood flow in arteries is dominated by unsteady flow phenomena. The cardiovascular system is an internal flow loop with multiple branches in which a complex liquid circulates. A nondimensional frequency parameter, the Womersley number, governs the relationship between the unsteady and viscous forces. Normal arterial flow is laminar with secondary flows generated at curves and branches. The arteries are living organs that can adapt to and change with the varying hemodynamic conditions. In certain circumstances, unusual hemodynamic conditions create an abnormal biological response. Velocity profile skewing can create pockets in which the direction of the wall shear stress oscillates. Atherosclerotic disease tends to be localized in these sites and results in a narrowing of the artery lumen—a stenosis. The stenosis can cause turbulence and reduce flow by means of viscous head losses and flow choking. Very high shear stresses near the throat of the stenosis can activate platelets and thereby induce thrombosis, which can totally block blood flow to the heart or brain. Detection and quantification of stenosis serve as the basis for surgical intervention. In the future, the study of arterial blood flow will lead to the prediction of individual hemodynamic flows in any patient, the development of diagnostic tools to quantify disease, and the design of devices that mimic or alter blood flow. This field is rich with challenging problems in fluid mechanics involving three-dimensional, pulsatile flows at the edge of turbulence.
1,336 citations
TL;DR: Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented and are found to be in excellent agreement with theory.
Abstract: In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M
2), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density ρ is the independent dynamic variable. The incompressible Navier–Stokes equations are derived from the incompressible LB model via Chapman–Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.
1,115 citations
TL;DR: A more direct form of enquiry is to measure the oscillatory stress-strain relationships at any required frequency, which has previously been done with strips and rings cut from arteries and recently with intact vessels in vivo.
Abstract: Although the response of the arterial tree to relatively slow changes in blood pressure is determined by its static elastic properties (Bergel, 1961), the rapid pressure changes occurring at each heart beat will result in rather different behaviour. This is due to the visco-elastic properties of the arterial wall. The mechanical response of a visco-elastic material depends both on the force applied (elastic response) and on the time it acts (viscous response). These substances display 'creep' (continuing extension at constant load) and stress relaxation (tension decay at constant length). The properties of such a material can be defined by measurements of either of these phenomena, but it is difficult to infer from this the response to a rapid stress. A more direct form ofenquiry is to measure the oscillatory stress-strain relationships at any required frequency, which has previously been done with strips and rings cut from arteries and recently with intact vessels in vivo (Petersen, Jensen & Parnell, 1960). When using intact vessels it is necessary to measure simultaneously the amplitude and the phase relationships of oscillatory pressure and radius changes. As arteries change very little in length with each heart beat (Lawton & Greene, 1956) they should be held at their natural length.
926 citations