scholarly journals Modelling Compressible Blood Flow with Slip in a Constricted Rectangular Flow Domain

2021 ◽  
Author(s):  
Matthew DeClerico
Keyword(s):  
Blood Flow ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Rectangular Microchannel ◽  
Flow Features ◽  
Flow Through ◽  
Linear Differential ◽  
Momentum Integral

The abnormal narrowing of blood vessels is known to affect the characterization of blood flow through these constricted regions. Both theoretical and clinical research has suggested that these changes in flow are associated with cardiovascular related diseases. Analytic, numerical, and particle based methods have been employed to solve the Navier-Stokes momentum integral equations associated with compressible, Newtonian fluid flow. In this thesis, the Karman-Pohlhausen method is used to transform a system of partial differential equations into a single second-order, non-linear differential equation in terms of the density. Numerical solutions are presented and important flow features, including the role of slip and compressibility, are discussed. The choice to use a symmetric rectangular channel, rather than a cylindrical one, is largely motivated by the opportunity to compare the numerical solutions with experimental data collected from a rectangular microchannel. The numerical results also indicate similar trends in the flow characteristics for the rectangular channel as compared to previous results using cylindrical models.

scholarly journals Modelling Compressible Blood Flow with Slip in a Constricted Rectangular Flow Domain

2021 ◽  
Author(s):  
Matthew DeClerico
Keyword(s):  
Blood Flow ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Rectangular Microchannel ◽  
Flow Features ◽  
Flow Through ◽  
Linear Differential ◽  
Momentum Integral

The abnormal narrowing of blood vessels is known to affect the characterization of blood flow through these constricted regions. Both theoretical and clinical research has suggested that these changes in flow are associated with cardiovascular related diseases. Analytic, numerical, and particle based methods have been employed to solve the Navier-Stokes momentum integral equations associated with compressible, Newtonian fluid flow. In this thesis, the Karman-Pohlhausen method is used to transform a system of partial differential equations into a single second-order, non-linear differential equation in terms of the density. Numerical solutions are presented and important flow features, including the role of slip and compressibility, are discussed. The choice to use a symmetric rectangular channel, rather than a cylindrical one, is largely motivated by the opportunity to compare the numerical solutions with experimental data collected from a rectangular microchannel. The numerical results also indicate similar trends in the flow characteristics for the rectangular channel as compared to previous results using cylindrical models.

Flow Characteristics in a Three-Dimensional Rectangular Channel With a Pair of Ribs Placed Symmetrically at the Channel Walls

2000 ◽  
Author(s):  
M. Singh ◽  
P. K. Panigrahi ◽  
G. Biswas
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Complex Flow ◽  
Energy Equations

Abstract A numerical study of rib augmented cooling of turbine blades is reported in this paper. The time-dependent velocity field around a pair of symmetrically placed ribs on the walls of a three-dimensional rectangular channel was studied by use of a modified version of Marker-And-Cell algorithm to solve the unsteady incompressible Navier-Stokes and energy equations. The flow structures are presented with the help of instantaneous velocity vector and vorticity fields, FFT and time averaged and rms values of components of velocity. The spanwise averaged Nusselt number is found to increase at the locations of reattachment. The numerical results are compared with available numerical and experimental results. The presence of ribs leads to complex flow fields with regions of flow separation before and after the ribs. Each interruption in the flow field due to the surface mounted rib enables the velocity distribution to be more homogeneous and a new boundary layer starts developing downstream of the rib. The heat transfer is primarily enhanced due to the decrease in the thermal resistance owing to the thinner boundary layers on the interrupted surfaces. Another reason for heat transfer enhancement can be attributed to the mixing induced by large-scale structures present downstream of the separation point.

Effect of a Time-Dependent Stenosis on Flow Through a Tube

1968 ◽  
Vol 90 (2) ◽  
pp. 248-254 ◽  
Author(s):  
D. F. Young
Keyword(s):  
Stokes Equations ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Arterial System ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Dependent Growth ◽  
Abnormal Tissue

A common occurrence in the arterial system is the narrowing of arteries due to the development of atherosclerotic plaques or other types of abnormal tissue development. As these growths project into the lumen of the artery, the flow is disturbed and there develops a potential coupling between the growth and the blood flow through the artery. A discussion of the various possible consequences of this interaction is given. It is noted that very small growths leading to mild stenotic obstructions, although not altering the gross flow characteristics significantly, may be important in triggering biological mechanisms such as intimal cell proliferation or changes in vessel caliber. An analysis of the effect of an axially symmetric, time-dependent growth into the lumen of a tube of constant cross section through which a Newtonian fluid is steadily flowing is presented. This analysis is based on a simplified model in which the convective acceleration terms in the Navier-Stokes equations are neglected. Effect of growth on pressure distribution and wall shearing stress is given and possible biological implications are discussed.

Modeling Transient Heat Transfer Through the Skin and Superficial Tissues—1: Surface Insulation

1986 ◽  
Vol 108 (2) ◽  
pp. 183-188 ◽  
Author(s):  
D. A. Hodson ◽  
G. Eason ◽  
J. C. Barbenel
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Transient Heat Transfer ◽  
Transient Problem ◽  
Finite Slab ◽  
Infinite Slab ◽  
Flow Through ◽  
Superficial Tissues

Two models of transient heat transfer through the skin and superficial tissues are presented. One model comprises a finite slab and semi-infinite slab, representing the epidermis and subdermal tissues, respectively, and a heat-generating interface representing the thermal effect of blood flow through the dermis. A model is also considered where the three tissue regions are represented more conventionally by three finite slabs. A transient problem arising from surface insulation is examined and analytical solutions derived from the first model are compared with numerical solutions derived from the second.

Numerical Solutions of the Navier-Stokes Equations for Axisymmetric Flows

1968 ◽  
Vol 10 (5) ◽  
pp. 389-401 ◽  
Author(s):  
D. R. Strawbridge ◽  
G. T. J. Hooper
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Labyrinth Seal ◽  
Taylor Vortex ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Taylor Vortex Flow ◽  
Concentric Cylinders ◽  
Flow Through

A numerical method is presented for the solution of the time dependent Navier-Stokes equations for the axisymmetric flow of an incompressible viscous fluid. The method is applied to the problems of Taylor-vortex flow about an enclosed rotating cylinder and between infinite concentric cylinders, and to the analysis of the flow through a labyrinth seal. The torque calculations, which show favourable agreement with experiment, and the resulting flow patterns are presented graphically.

Heat Transfer and Flow Characteristics of a Rib With a Slit

2003 ◽  
Author(s):  
Andallib Tariq ◽  
P. K. Panigrahi
Keyword(s):  
Heat Transfer ◽  
Shear Layer ◽  
Flow Behavior ◽  
Rectangular Channel ◽  
Flow Characteristics ◽  
Area Ratio ◽  
Open Area ◽  
Bottom Part ◽  
Turbulent Statistics ◽  
Flow Through

The present investigation is an experimental study of convective heat transfer in the entrance region of a rectangular channel with a single surface mounted slit rib. The open area ratios of the slit rib set during the experiment are equal to 10, 20, 30, 40 and 50%. Hotwire anemometry (HWA) and resistance thermometry (RTD) have been used for velocity and temperature measurement respectively. Both mean and turbulent statistics of the velocity and temperature fluctuations have been reported. Smoke visualization has also been carried out to obtain a qualitative picture of the flow field behind the rib. The surface Nusselt number has been determined from liquid crystal thermography (LCT). The Reynolds number based on the hydraulic diameter of the channel has been set at Re = 32,100. The nature of the flow through the slit and its interaction with the shear layer from the top of the rib depend on the size of the slit. For the slit rib with higher open area ratio (β = 40 and 50%), the bottom part of the slit rib behaves like an independent small rib with its own reattachment region. At smaller open area ratio (β = 10, 20 and 30%), the flow through the slit manipulates the reattaching shear layer from the top of the rib. The size of the slit and its location from the bottom channel surface are the primary parameters responsible for the modification and manipulation of the flow behavior of a slit rib in comparison to the solid rib.

Direct Numerical Simulation of Cellular Blood Flow Through a Model Arteriole Bifurcation

2010 ◽  
Author(s):  
Daniel A. Reasor ◽  
Jonathan R. Clausen ◽  
Cyrus K. Aidun
Keyword(s):  
Numerical Simulation ◽  
Blood Flow ◽  
Direct Numerical Simulation ◽  
Volume Fraction ◽  
Flow Characteristics ◽  
Particle Level ◽  
Suspension Dynamics ◽  
Flow Through ◽  
Fahraeus Effect ◽  
The Continuum

Blood is composed of a suspension of red blood cells (RBCs) suspended in plasma, and the presence of the RBCs substantially changes the flow characteristics and rheology of these suspensions. The viscosity of blood varies with the hematocrit (volume fraction of RBCs), which is a result not seen in Newtonian fluids. Additionally, RBCs are deformable, which can alter suspension dynamics. Understanding the physics in these flows requires accurately simulating the suspended phase to recover the microscale, and a subsequent analysis of the rheology to ascertain the continuum-level effects caused by the changes at the particle level. The direct numerical simulation of blood flow including RBC migration effects has the capability to resolve the Fåhraeus effect of observing low hematocrit values near walls, the subsequent cell-depleted layer, and the presence of velocity profile blunting due to the distribution of RBCs.

The developing tangential velocity profile for axial flow in an annulus with a rotating inner cylinder

1968 ◽  
Vol 307 (1488) ◽  
pp. 55-69 ◽  
Keyword(s):  
Velocity Profile ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Axial Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Taylor Vortices ◽  
Flow Through ◽  
Momentum Integral ◽  
Tangential Velocity Profile

A method is described of predicting the growth of a tangential velocity profile in fully developed laminar axial flow through a concentric annulus when the inner surface is rotated at speeds which are insufficient to generate Taylor vortices. The treatment, which is based on simplification and subsequent solution of the Navier-Stokes equations, as Fourier-Bessel series, appears preferable to momentum-integral techniques through greater simplicity of expression and in requiring fewer assumptions about the developing tangential profile. The validity of the predictions is best at high axial Reynolds number.

NUMERICAL RESEARCH ON A SPECIAL FLUID PHENOMENON: RANQUE-HILSCH EFFECT

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1723-1726 ◽  
Author(s):  
J. Y. LIU ◽  
M. Q. GONG ◽  
Y. ZHANG ◽  
H. HONG ◽  
J. F. WU
Keyword(s):  
High Speed ◽  
Numerical Solutions ◽  
Vortex Tube ◽  
Flow Characteristics ◽  
Temperature Fields ◽  
Energy Separation ◽  
Separation Effect ◽  
Speed Flow ◽  
Flow Features ◽  
Numerical Research

An application of CFD model for the simulation of a strongly swirling and high speed flow in the vortex tube is presented in this paper. A partly modified standard K-ε turbulent model has been used to investigate the flow characteristics and energy separation effect in the vortex tube. It is found that there is an obvious energy separation effect in the vortex tube and the numerical solutions of the flow and temperature fields agree well with the experiments. More detailed flow features are obtained by the CFD calculation. Based on the validated numerical model, the influence of the cold flow fraction on the energy separation effect is also investigated and compared with experimental results.

The oblique ascent of a viscous vortex pair toward a free surface

1992 ◽  
Vol 236 ◽  
pp. 461-476 ◽  
Author(s):  
Hans J. Lugt ◽  
Samuel Ohring
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Vortex Pair ◽  
Nonlinear Boundary Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Directional Change ◽  
Secondary Vortices

The problem of a vortex pair, rising obliquely at an angle of 45° toward a deformable free surface in a viscous, incompressible fluid, is solved with the aid of the Navier—Stokes equations. The full nonlinear boundary conditions at the free surface are applied. The oblique interaction of the vortex pair with the free surface results in a number of novel features that have not been observed for the special case of a vertical rise, reported earlier. These features include the directional change of trajectories near the free surface and the occurrence of waves driven by the vortex pair. Moreover, surface tension can completely change the flow characteristics such as the direction of the trajectories and the generation of secondary vortices. Numerical solutions are presented for selected Reynolds, Froude, and Weber numbers.

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