Entry flow in a curved pipe

1974 ◽  
Vol 65 (3) ◽  
pp. 517-539 ◽  
Author(s):  
M. P. Singh
Keyword(s):  
Secondary Flow ◽  
Dynamic Pressure ◽  
Steady Motion ◽  
Practical Interest ◽  
Initial Development ◽  
Curved Pipe ◽  
Curved Tube ◽  
Entry Condition ◽  
Pulsatile Flows ◽  
Inlet Conditions

This paper deals with the development of the flow in a curved tube near the inlet. The solution is obtained by the method of matched asymptotic expansions. Two inlet conditions are considered: (i) the condition of constant dynamic pressure at the entrance, which may be of practical interest in applications to blood flow in the aorta; and (ii) a uniform entry condition. It is shown that the geometry and the nature of the entry condition appreciably influence the initial development of the flow. The effect of the secondary flow due to the curvature on the wall shear is discussed and it is shown that the cross-over between shear maxima on the inside and the outside of the tube occurs at a downstream distance which is 1·9 times the radius of the tube for entry condition (i) while in the case of entry condition (ii) it is 0·95 times the radius, which is half the distance required in case (i). It is found that the pressure distribution is not significantly influenced by the secondary flow during the initial development of the motion. The analysis, which is developed for steady motion, can be extended to pulsatile flows, which are of greater physiological interest.

Motion of a fluid in a curved tube

1968 ◽  
Vol 307 (1488) ◽  
pp. 37-53 ◽  
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Outer Boundary ◽  
Steady Motion ◽  
Circular Cross Section ◽  
Polar Angle ◽  
Straight Tube ◽  
Curved Tube ◽  
Series Development

Dean’s work on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended. A method using a Fourier-series development with respect to the polar angle in the plane of cross-section is formulated and the resulting coupled non­linear equations solved numerically. The results are presented in terms of a single variable D = 4 R √(2 a/L ), where R is the Reynolds number, a the radius of cross-section of the tube, and L the radius of the curve. The results cover the range of D from 96 (the upper limit of Dean’s work) to over 600. From these it is found that the secondary flow becomes very appreciable for D = 600, moving the position of maximum axial velocity to a distance less than 0.38 a from the outer boundary, and decreasing the flux by 28% of its value for the straight tube. These calculations fill a large part of the gap in existing knowledge of secondary flow patterns, which lies in the upper range of Reynolds number for which flow is laminar. This range is of particular interest in the investigation of the cardiovascular system

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

Computational modelling and analysis of haemodynamics in a simple model of aortic stenosis

2018 ◽  
Vol 851 ◽  
pp. 23-49 ◽  
Author(s):  
Chi Zhu ◽  
Jung-Hee Seo ◽  
Rajat Mittal
Keyword(s):  
Simple Model ◽  
Aortic Stenosis ◽  
Secondary Flow ◽  
Pressure Fluctuation ◽  
Computational Modelling ◽  
Maximum Pressure ◽  
Cardiac Auscultation ◽  
Curved Pipe ◽  
Free Jet ◽  
Wall Pressure Fluctuation

In a study motivated by considerations associated with heart murmurs and cardiac auscultation, numerical simulations are used to analyse the haemodynamics in a simple model of an aorta with an aortic stenosis. The aorta is modelled as a curved pipe with a$180^{\circ }$turn, and three different stenoses with area reductions of 50 %, 62.5 % and 75 % are examined. A uniform steady inlet velocity with a Reynolds number of 2000 is used for all of the cases and direct numerical simulation is employed to resolve the dynamics of the flow. The poststenotic flow is dominated by the jet that originates from the stenosis as well as the secondary flow induced by the curvature, and both contribute significantly to the flow turbulence. On the anterior surface of the modelled aorta, the location with maximum pressure fluctuation, which may be considered as the source location for the murmurs, is found to be located around$60^{\circ }$along the aortic arch, and this location is relatively insensitive to the severity of the stenosis. For all three cases, this high-intensity wall pressure fluctuation includes contributions from both the jet and the secondary flow. Spectral analysis shows that for all three stenoses, the Strouhal number of the vortex shedding of the jet shear layer is close to 0.93, which is higher than the shedding frequency of a corresponding free jet or a jet confined in a straight pipe. This frequency also appears in the pressure spectra at the location postulated as the source of the murmurs, in the form of a ‘break frequency.’ The implications of these findings for cardiac auscultation-based diagnosis of aortic stenosis are also discussed.

scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

Experimental Investigations and Numerical Validation of an Outlet Guide Vane With an Engine Mount Recess

2008 ◽  
Author(s):  
Johan Hja¨rne ◽  
Valery Chernoray ◽  
Jonas Larsson
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Guide Vane ◽  
Test Facility ◽  
Experimental Investigations ◽  
Flow Angle ◽  
Sst Model ◽  
Engine Mount ◽  
Inlet Conditions ◽  
Secondary Flow Field

This paper presents experiments and CFD calculations of a Low Pressure Turbine/Outlet Guide Vane (LPT/OGV) equipped with an engine mount recess (a bump) tested in the Chalmers linear LPT/OGV cascade. The investigated characteristics include performance for the design point in terms of total pressure loss and turning as well as a detailed description of the downstream development of the secondary flow field. The numerical simulations are performed for the same inlet conditions as in the test-facility with engine-like properties in terms of Reynolds number, boundary-layer thickness and inlet flow angle. The objective is to validate how accurately and reliably the secondary flow field and losses can be predicted for an LPT/OGV equipped with a bump. Three different turbulent models as implemented in FLUENT, the k-ε realizable model, the kω-SST model and the RSM are validated against detailed measurements. From these results it can be concluded that the kω-SST model predicts both the secondary flow field and the losses most accurately.

Fluid Kinetic Energy Based Limits in the Design of Control Valves and Valve-Related Systems

2007 ◽  
Author(s):  
Sanjay V. Sherikar ◽  
Vinay Nagpal
Keyword(s):  
Kinetic Energy ◽  
Dynamic Pressure ◽  
Practical Interest ◽  
Energy Criterion ◽  
Engineering Practice ◽  
Solid Particle Erosion ◽  
Control Valves ◽  
Reliable Performance ◽  
Flowing Stream ◽  
Vibration Noise

The term 1/2ρV2 represents kinetic energy per unit volume; it is also known as dynamic pressure, or velocity head, in flowing fluids and has units of pressure. It is one of the primary parameters in many wide-ranging phenomenon of practical interest in control valves and valve-related systems. The phenomena of interest include vibration, noise, solid particle erosion, liquid impingement erosion, cavitation and more. The description of the extent of these phenomena through their physics, as relating to acceptability of the system performance, is closely tied to the magnitude of the kinetic energy of the flowing stream; this permits use of this parameter as a criterion for reliable performance of control valves and valve-related systems. Kinetic energy criterion is a more general approach, when compared to the older engineering practice of specifying velocity limits only, because it takes into account the effect of fluid density which can be different by orders of magnitude depending on the process. The robustness of this criterion is confirmed by the results of its application in solving valve problems. Its main advantages are simplicity while staying close to the phenomena of interest.

scholarly journals Secondary flow in a curved tube

1973 ◽  
Vol 57 (1) ◽  
pp. 167-176 ◽  
Author(s):  
D. Greenspan
Keyword(s):  
Nonlinear System ◽  
Incompressible Fluid ◽  
Cross Section ◽  
Finite Differences ◽  
Entire Range ◽  
Steady Motion ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Curved Tube ◽  
Computer Calculations

The work of Dean and that of McConalogue & Srivastava on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended through the entire range of Reynolds numbers for which the flow is laminar. The coupled nonlinear system of partial differential equations which defines the motion is solved numerically by finite differences. Computer calculations are described and physical implications are discussed.

scholarly journals Design of Compressor Endwall Velocity Triangles

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Kiran Auchoybur ◽  
Robert J. Miller
Keyword(s):  
Dynamic Pressure ◽  
Three Dimensional ◽  
Flow Region ◽  
Degree Of Freedom ◽  
Diffusion Limit ◽  
Local Geometry ◽  
Operating Range ◽  
Blade Row ◽  
Inlet Conditions ◽  
Separation Size

The operating range of a compressor is usually limited by the rapid growth of three-dimensional (3D) separations in the endwall flow region. In contrast, the freestream region is not usually close to its diffusion limit and has little effect on overall range. In light of these two distinct flow regions, this paper considers how velocity triangles in the endwall region should be designed to give a more balanced spanwise failure across the span of a blade row. In the first part of this paper, the sensitivity of 3D separations in a single blade row to variations in realistic multistage inlet conditions and endwall geometry is investigated. It is shown that a blade's 3D separation size is largely controlled by the dynamic pressure within the incoming endwall “repeating stage” boundary layer and not the detailed local geometry within the blade row. In the second part of this paper, the traditional design process is “flipped.” Instead of redesigning a blade's endwall geometry to cope with a particular inlet profile into the blade row, the endwall region is redesigned in the multistage environment to “tailor” the inlet profile into downstream blade rows, giving the designer a new extra degree-of-freedom. This extra degree-of-freedom is exploited to balance freestream and endwall operating range, resulting in a compressor having an increased operating range of ∼20%. If this increased operating range is traded with reduced blade count, it is shown that a design efficiency improvement of ∼0.5% can be unlocked.

Secondary Flow Structure Induced by Physiologically Relevant Waveform in a Curved Tube

2009 ◽  
Author(s):  
Chekema N. Prince ◽  
Sean D. Peterson ◽  
Michael W. Plesniak
Keyword(s):  
Secondary Flow ◽  
Blood Vessels ◽  
Complex Geometry ◽  
Vascular System ◽  
Flow Regimes ◽  
Flow Conditions ◽  
Complex Flow ◽  
Curved Tube ◽  
Secondary Flow Structure ◽  
The Impact

The complex geometry of the vascular system can induce the development of complex primary and secondary flow regimes within blood vessels. Recent literature has focused on the impact of these complex flow regimes on endothelial cells (EC), which line blood vessels, and their role on the progression of vascular disease. One such disease, atherosclerosis has been linked to the reaction of ECs to flow conditions. Atherosclerosis is often treated by stent implantation to return the vessel lumen to its native diameter. It is hypothesized that stent struts may alter the development of secondary flow within the vessel and cause re-stenosis and/or thrombosis distal to the stent.

Formation and interaction of multiple secondary flow vortical structures in a curved pipe: transient and oscillatory flows

2019 ◽  
Vol 876 ◽  
pp. 481-526 ◽  
Author(s):  
Mohammad Reza Najjari ◽  
Christopher Cox ◽  
Michael W. Plesniak
Keyword(s):  
Secondary Flow ◽  
Initial Conditions ◽  
Inlet Section ◽  
Vortex Identification ◽  
Navier Stokes Equation ◽  
Cross Sectional ◽  
Oscillatory Flows ◽  
Axis Orientation ◽  
Vortical Structures ◽  
Curved Pipe

Transient, steady and oscillatory flows in a $180^{\circ }$ curved pipe are investigated both numerically and experimentally to understand secondary flow vortex formation and interactions. The results of numerical simulations and particle image velocimetry experiments are highly correlated, with a low error. To enable simulations in a smaller domain with shorter inlet section, an analytical solution for the unsteady Navier–Stokes equation is obtained with non-zero initial conditions to provide physical velocity profiles for the simulations. The vorticity transport equation is studied and its terms are balanced to find the mechanism of vorticity transfer to structures in the curved pipe. Several vortices are identified via various vortex identification (ID) methods and their results are compared. Isosurfaces of the $\unicode[STIX]{x1D706}_{2}$ vortex ID are used to explain the temporal and spatial evolution of vortices in the curved pipe. Eigenvalues and eigenvectors of the velocity gradient tensor are calculated for the swirling strength vortex ID method, which also determines vortex axis orientation. The classical Lyne vortex in oscillatory flow with an inviscid core is also revisited and its results are compared with the transient and steady flows. These in-depth analyses provide a better understanding and characterization of vortical structures in the curved pipe flow. Our findings show that, although there are some visual similarities between cross-sectional views of steady/transient flows and oscillatory flows, the structure herein designated as Lyne-type vortex detected in the cross-sections (under steady, transient and pulsatile flows) is not the same as the classical Lyne vortex pair (in oscillatory flows).

Sign in / Sign up

Export Citation Format

Share Document