Bolus Contaminant Dispersion for Oscillatory Flow in a Curved Tube

1996 ◽  
Vol 118 (3) ◽  
pp. 333-340 ◽  
Author(s):  
Yahong Jiang ◽  
James B. Grotberg
Keyword(s):  
Stokes Equations ◽  
Time History ◽  
Local Maximum ◽  
Effective Diffusivity ◽  
Axial Position ◽  
Radius Of Curvature ◽  
Local Concentration ◽  
Straight Tube ◽  
Molecular Diffusivity ◽  
Curved Tube

The dispersion of a bolus of soluble contaminant in a curved tube during volume-cycled oscillatory flows is studied. Assuming a small value of δ (the ratio of tube radius to radius of curvature), the Navier-Stokes equations are solved by using a perturbation method. The convection-diffusion equation is then solved by expanding the local concentration in terms of the cross-sectionally averaged concentration and its axial derivatives. The time-averaged dimensionless effective diffusivity, 〈Deff/D〉, is calculated for a range of Womersley number α and different values of stroke amplitude A and Schmidt number Sc, where D is the molecular diffusivity of contaminant. For the parameter values considered, the results show that axial dispersion in a curved tube is greater than that in a straight tube, and that it has a local maximum near α = 5 for given fixed values of Sc = 1, A = 5 and δ = 0.3. Finally it is demonstrated how the time history of concentration at a fixed axial position can be used to determine the effective diffusivity.

Oscillatory flow and mass transport in a curved tube

1988 ◽  
Vol 188 ◽  
pp. 509-527 ◽  
Author(s):  
David M. Eckmann ◽  
James B. Grotberg
Keyword(s):  
Oscillatory Flow ◽  
Equations Of Motion ◽  
Radius Of Curvature ◽  
Straight Tube ◽  
Perturbation Scheme ◽  
Regular Perturbation ◽  
Order Unity ◽  
Curved Tube ◽  
Soluble Material ◽  
Flow And Mass Transport

Transport of soluble material is analysed for volume-cycled oscillatory flow in a curved tube. The equations of motion are solved using a regular perturbation method for small ratio of tube radius to radius of curvature and order unity amplitude over a range of the Womersley parameter. The transport equation is similarly solved by a regular perturbation scheme where uniform steady end concentrations and no wall flux are assumed. The time-average axial transport of solute is calculated. There is substantial modification of transport compared to the straight-tube case and the results are interpreted with respect to pulmonary gas exchange.

Augmentation of Axial Dispersion by Intermittent Oscillatory Flow

1998 ◽  
Vol 120 (3) ◽  
pp. 405-415 ◽  
Author(s):  
G. Tanaka ◽  
Y. Ueda ◽  
K. Tanishita
Keyword(s):  
Stationary Phase ◽  
High Frequency ◽  
Oscillatory Flow ◽  
Effective Diffusivity ◽  
Axial Dispersion ◽  
High Frequency Oscillation ◽  
Gas Transfer ◽  
Straight Tube ◽  
Gas Dispersion ◽  
Molecular Diffusivity

The efficiency of axial gas dispersion during ventilation with high-frequency oscillation (HFO) is improved by manipulating the oscillatory flow waveform such that intermittent oscillatory flow occurs. We therefore measured the velocity profiles and effective axial gas diffusivity during intermittent oscillatory flow in a straight tube to verify the intermittency augmentation effect on axial gas transfer. The effective diffusivity was dependent on the flow patterns and significantly increased with an increase in the duration of the stationary phase. It was also found that the ratio of effective diffusivity to molecular diffusivity is two times greater than that in sinusoidal oscillatory flow. Moreover, turbulence during deceleration or at the beginning of the stationary phase further augments axial dispersion, with the effective diffusivity being over three times as large, thereby proving that the use of intermittent oscillatory flow effectively augments axial dispersion for ventilation with HFO.

A Numerical Study of the Impact of Wavy Walls on Steady Fluid Flow Through a Curved Tube

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Chekema Prince ◽  
Mingyao Gu ◽  
Sean D. Peterson
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Perturbation Expansion ◽  
Analytical Investigation ◽  
Navier Stokes ◽  
Radius Of Curvature ◽  
Navier Stokes Equations ◽  
Curved Tube ◽  
Small Tube ◽  
The Impact

In this paper, we discuss the impact of a wavy-walled pipe cross-section on steady flow in a curved tube at moderate Dean numbers and small tube radius-to-radius-of-curvature ratios. Parameters investigated include the protrusion height, the number of protrusions around the tube circumference, and the pipe curvature. This work extends a previous analytical investigation that employed a double perturbation expansion to elucidate the flow field as a function of these parameters. Due to the rapid growth in the solution complexity as the number of terms in each expansion increases, the analytical work is relegated to small wall perturbations and low Dean numbers. These barriers are removed in the present study by numerically solving the Navier–Stokes equations at Dean numbers up to 2500. The impact on the axial and secondary flow structures are emphasized, along with the resulting wall shear stress distributions.

Investigation and Development of Proposed General Pressure Drop and Heat Transfer Correlations for Laminar Flow in a Toroidal Coiled Tube System

2004 ◽  
Author(s):  
Anthony J. Bowman ◽  
Hyunjae Park
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Radius Of Curvature ◽  
Straight Tube ◽  
Coiled Tube ◽  
Tube Heat Exchanger ◽  
Curved Tube

In this paper, the laminar flow pressure drop and heat transfer correlations published and applied to plain, coiled tube heat exchanger systems are extensively investigated. It was found that most correlations obtained for toroidal geometric systems have been applied to the analysis of helical and spiral tube systems. While toroidal (and helical) coils have a constant radius of curvature about the coil center-point (and center-line), spiral coils have a continuously varying radius of curvature, in which the flow does not reach a typical fully developed flow condition. The centrifugal forces, arising from the curved flow path, contribute to the enhancement of heat transfer (at the cost of additional pressure drop) over straight tube heat exchangers of the same length. In this paper, using published correlations and available experimental test data for pressure drop and heat transfer in toroidal tube systems, the proposed general correlations are developed by using a filtered-mean multiple regression method. The Coiling Influence Factors for the friction factor and heat transfer, CIFf and CIFh, respectively; defined and used in the authors’ previous works [1,2,3] it was found that the deviations between the proposed and published correlations are within about 3% for friction factor and 5–20% for heat transfer, depending on working fluid. In order to assess the validity of applying the generalized correlations developed in this work for toroidal tube systems, onto other curved tube systems, a numerical analysis of toroidal coil systems, using the commercially available CFD package (Fluent 6) has been explicitly performed. A comparison is made between the CFD result for average heat transfer (CIFh) with that predicted by the proposed general correlation for toroidal coils and available experimental data. As an extension of this work, a comparison of curved tube over straight tube heat exchanger effectiveness is made to highlight its use as a design optimization parameter and motivation for additional coiled tube heat exchanger research.

Shear dispersion and anomalous diffusion by chaotic advection

1994 ◽  
Vol 280 ◽  
pp. 149-172 ◽  
Author(s):  
S. W. Jones ◽  
W. R. Young
Keyword(s):  
Effective Diffusivity ◽  
Axial Dispersion ◽  
Slip Condition ◽  
Chaotic Advection ◽  
Local Analysis ◽  
Axial Position ◽  
Solid Boundary ◽  
Transverse Mixing ◽  
Molecular Diffusivity ◽  
Shear Dispersion

The dispersion of passive scalars by the steady viscous flow through a twisted pipe is both a simple example of chaotic advection and an elaboration of Taylor's classic shear dispersion problem. In this article we study the statistics of the axial dispersion of both diffusive and perfect (non-diffusive) tracer in this system.For diffusive tracer chaotic advection assists molecular diffusion in transverse mixing and so diminishes the axial dispersion below that of integrable advection. As in many other studies of shear dispersion the axial distribution ultimately becomes Gaussian as t → ∞. Thus there is a diffusive regime, but with an effective diffusivity that is enhanced above molecular values. In contrast to the classic case, the effective diffusivity is not necessarily inversely proportional to the molecular diffusivity. For instance, in the irregular regime the effective diffusivity is proportional to the logarithm of the molecular diffusivity.For perfect tracer chaotic advection does not result in a diffusive process, even in the irregular regime in which streamlines wander throughout the cross-section of the pipe. Instead the variance of the axial position is proportional to t in t so that the measured diffusion coefficent diverges like In t. This faster than linear growth of variance is attributed to the trapping of tracer for long times near the solid boundary, where the no-slip condition ensures that the fluid moves slowly. Analogous logarithmic effects associated with the no-slip condition are well known in the context of porous media.A simple argument, based on Lagrangian statistics and a local analysis of the trajectories near the pipe wall, is used to calculate the constants of proportionality before the logarithmic terms in both the large- and infinite-Péclet-number limits.

scholarly journals Steady flow separation patterns in a 45 degree junction

2000 ◽  
Vol 411 ◽  
pp. 1-38 ◽  
Author(s):  
C. ROSS ETHIER ◽  
SUJATA PRAKASH ◽  
DAVID A. STEINMAN ◽  
RICHARD L. LEASK ◽  
GREGORY G. COUCH ◽  
...  
Keyword(s):  
Flow Separation ◽  
Stokes Equations ◽  
Bypass Graft ◽  
Three Dimensional ◽  
Symmetry Plane ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Measured Velocity ◽  
Curved Tube

Numerical and experimental techniques were used to study the physics of flow separation for steady internal flow in a 45° junction geometry, such as that observed between two pipes or between the downstream end of a bypass graft and an artery. The three-dimensional Navier–Stokes equations were solved using a validated finite element code, and complementary experiments were performed using the photochromic dye tracer technique. Inlet Reynolds numbers in the range 250 to 1650 were considered. An adaptive mesh refinement approach was adopted to ensure grid-independent solutions. Good agreement was observed between the numerical results and the experimentally measured velocity fields; however, the wall shear stress agreement was less satisfactory. Just distal to the ‘toe’ of the junction, axial flow separation was observed for all Reynolds numbers greater than 250. Further downstream (approximately 1.3 diameters from the toe), the axial flow again separated for Re [ges ] 450. The location and structure of axial flow separation in this geometry is controlled by secondary flows, which at sufficiently high Re create free stagnation points on the model symmetry plane. In fact, separation in this flow is best explained by a secondary flow boundary layer collision model, analogous to that proposed for flow in the entry region of a curved tube. Novel features of this flow include axial flow separation at modest Re (as compared to flow in a curved tube, where separation occurs only at much higher Re), and the existence and interaction of two distinct three-dimensional separation zones.

A Study of a Sharp 90 Degree Curved Flow

1992 ◽  
Author(s):  
R. H. Kim
Keyword(s):  
Turbulence Model ◽  
Ideal Gas ◽  
Radius Of Curvature ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Algebraic Stress Model ◽  
Finite Difference Technique ◽  
Curved Tube ◽  
Kinetic Energy Loss ◽  
The Ideal

Abstract An investigation of air flow along a 90 degree elbow-like tube is conducted to determine the velocity and temperature distributions of the flow. The tube has a sharp 90 degree turn with a radius of curvature of almost zero. The flow is assumed to be a steady two-dimensional turbulent flow satisfying the ideal gas relation. The flow will be analyzed using a finite difference technique with the K-ε turbulence model, and the algebraic stress model (ASM). The FLUENT code was used to determine the parameter distributions in the passage. There are certain conditions for which the K-ε model does not describe the fluid phenomenon properly. For these conditions, an alternative turbulence model, the ASM with or without QUICK was employed. FLUENT has these models among its features. The results are compared with the result computed by using elementary one-dimensional theory including the kinetic energy loss along the passage of the sharp 90 degree curved tube.

Steady Flow in the Transition Length of a Straight Tube

1942 ◽  
Vol 9 (2) ◽  
pp. A55-A58 ◽  
Author(s):  
Henry L. Langhaar
Keyword(s):  
Velocity Field ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Straight Tube ◽  
Pressure Function ◽  
Navier Stokes Equations ◽  
Dimensionless Constant ◽  
The Family ◽  
Transition Length

Abstract By means of a linearizing approximation, the Navier-Stokes equations are solved for the case of steady flow in the transition length of a straight tube. The family of velocity profiles is defined by Bessel functions, and the parameter of this family is tabulated against the axial co-ordinate in a dimensionless form. Hence, the length of transition is obtained. The curves give a comparison of the author’s calculations of the velocity field with those of other investigators, and with the experimental data of Nikuradse. The pressure function is derived from the computed velocity field by means of the energy equation, and the pressure drop in the transition length is defined by a dimensionless constant m, which is computed to be 2.28. A discussion of this constant is given in the conclusions.

The effective long-time diffusivity for a passive scalar in a Gaussian model fluid flow

1978 ◽  
Vol 89 (2) ◽  
pp. 241-250 ◽  
Author(s):  
R. Phythian ◽  
W. D. Curtis
Keyword(s):  
Diffusion Processes ◽  
Fluid Velocity ◽  
Gaussian Model ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Random Motion ◽  
Velocity Correlation ◽  
Molecular Diffusivity ◽  
Velocity Correlation Function ◽  
Long Time

The problem considered is the diffusion of a passive scalar in a ‘fluid’ in random motion when the fluid velocity field is Gaussian and statistically homogeneous, isotropic and stationary. A self-consistent expansion for the effective long-time diffusivity is obtained and the approximations derived from this series by retaining up to three terms are explicitly calculated for simple idealized forms of the velocity correlation function for which numerical simulations are available for comparison for zero molecular diffusivity. The dependence of the effective diffusivity on the molecular diffusivity is determined within this idealization. The results support Saffman's contention that the molecular and turbulent diffusion processes interfere destructively, in the sense that the total effective diffusivity about a fixed point is less than that which would be obtained if the two diffusion processes acted independently.

Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 1. Linear stability analysis

2013 ◽  
Vol 721 ◽  
pp. 268-294 ◽  
Author(s):  
L. Talon ◽  
N. Goyal ◽  
E. Meiburg
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Variable Density ◽  
Local Concentration ◽  
Miscible Displacements ◽  
Instability Modes ◽  
Finger Tip

AbstractA computational investigation of variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells is presented. As a first step, two-dimensional base states are obtained by means of simulations of the Stokes equations, which are nonlinear due to the dependence of the viscosity on the local concentration. Here, the vertical position of the displacement front is seen to reach a quasisteady equilibrium value, reflecting a balance between viscous and gravitational forces. These base states allow for two instability modes: first, there is the familiar tip instability driven by the unfavourable viscosity contrast of the displacement, which is modulated by the presence of density variations in the gravitational field; second, a gravitational instability occurs at the unstably stratified horizontal interface along the side of the finger. Both of these instability modes are investigated by means of a linear stability analysis. The gravitational mode along the side of the finger is characterized by a wavelength of about one half to one full gap width. It becomes more unstable as the gravity parameter increases, even though the interface is shifted closer to the wall. The growth rate is largest far behind the finger tip, where the interface is both thicker, and located closer to the wall, than near the finger tip. The competing influences of interface thickness and wall proximity are clarified by means of a parametric stability analysis. The tip instability mode represents a gravity-modulated version of the neutrally buoyant mode. The analysis shows that in the presence of density stratification its growth rate increases, while the dominant wavelength decreases. This overall destabilizing effect of gravity is due to the additional terms appearing in the stability equations, which outweigh the stabilizing effects of gravity onto the base state.

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