Collapse of Arteries Subjected to an External Band of Pressure

1980 ◽  
Vol 102 (1) ◽  
pp. 8-22 ◽  
Author(s):  
A. M. Hecht ◽  
H. Yeh ◽  
S. M. K. Chung
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Cylindrical Shell ◽  
Orthotropic Cylindrical Shell ◽  
Reynolds Numbers ◽  
Intraluminal Pressure ◽  
Collapse Pressure ◽  
Vessel Size ◽  
Flow Reynolds Number ◽  
Small Band

Collapse of arteries subjected to a band of hydrostatic pressure of finite length is analyzed. The vessel is treated as a long, thin, linearly elastic, orthotropic cylindrical shell, homogeneous in composition, and with negligible radial stresses. Blood in the vessel is treated as a Newtonian fluid and the Reynolds number is of order 1. Results are obtained for effects of the following factors on arterial collapse: intraluminal pressure, length of the pressure band, elastic properties of the vessel, initial stress both longitudinally and circumferentially, blood flow Reynolds number, compressibility, and wall thickness to radius ratio. It is found that the predominant parameter influencing vessel collapse for the intermediate range of vessel size and blood flow Reynolds numbers studied is the preconstricted intraluminal pressure. For pressure bands less than about 10 vessel radii the collapse pressure increases sharply with increasing intraluminal pressure. Initial axial prestress is found to be highly stabilizing for small band lengths. The effects of fluid flow are found to be small for pressure bands of less than 100 vessel radii. No dramatic orthotropic vessel behavior is apparent. The analysis shows that any reduction in intraluminal pressure, such as that produced by an upstream obstruction, will significantly lower the required collapse pressure. Medical implications of this analysis to Legg-Perthes disease are discussed.

An Experimental Investigation of the Effect of Freestream Turbulence on the Wake of a Separated Low-Pressure Turbine Blade at Low Reynolds Numbers

1999 ◽  
Vol 122 (2) ◽  
pp. 431-433 ◽  
Author(s):  
C. G. Murawski ◽  
K. Vafai
Keyword(s):  
Reynolds Number ◽  
Turbine Blade ◽  
Turbulence Intensity ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Freestream Turbulence ◽  
Suction Surface ◽  
Low Reynolds Numbers ◽  
Low Pressure Turbine ◽  
Flow Reynolds Number

An experimental study was conducted in a two-dimensional linear cascade, focusing on the suction surface of a low pressure turbine blade. Flow Reynolds numbers, based on exit velocity and suction length, have been varied from 50,000 to 300,000. The freestream turbulence intensity was varied from 1.1 to 8.1 percent. Separation was observed at all test Reynolds numbers. Increasing the flow Reynolds number, without changing freestream turbulence, resulted in a rearward movement of the onset of separation and shrinkage of the separation zone. Increasing the freestream turbulence intensity, without changing Reynolds number, resulted in shrinkage of the separation region on the suction surface. The influences on the blade’s wake from altering freestream turbulence and Reynolds number are also documented. It is shown that width of the wake and velocity defect rise with a decrease in either turbulence level or chord Reynolds number. [S0098-2202(00)00202-9]

Pulsatile Blood Flow in a Channel of Small Exponential Divergence—III. Unsteady Flow Separation

1977 ◽  
Vol 99 (2) ◽  
pp. 333-338 ◽  
Author(s):  
Daniel J. Schneck
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Steady State ◽  
Flow Separation ◽  
Reynolds Numbers ◽  
Critical Value ◽  
Flow Oscillation ◽  
Pulsatile Blood Flow ◽  
Steady Streaming ◽  
Flow Through

Analysis of pulsatile flow through exponentially diverging channels reveals the existence of critical mean Reynolds numbers for which the flow separates at a downstream axial station. These Reynolds numbers vary directly with the frequency of flow oscillation and inversely with the rate of channel divergence. Increasing the Reynolds number above its critical value results in a rapid upstream displacement of the point of separation. For a tube of fixed geometry, periodic unsteadiness causes flow separation to occur at lower Reynolds numbers and upstream of a corresponding steady-state situation. The point of separation moves progressively downstream, however, towards its steady-state location, as the frequency of oscillation increases. These results are discussed as consequences of the nonlinear steady streaming phenomenon described in an earlier paper.

Flow in Locally Constricted Tubes at Low Reynolds Numbers

1970 ◽  
Vol 37 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Jen-Shih Lee ◽  
Yuan-Cheng Fung
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Shear Stress ◽  
Cylindrical Tube ◽  
Reynolds Numbers ◽  
Velocity Measurements ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Circular Cylindrical Tube ◽  
Velocity Pressure

With an objective to understand arteriosclerosis, the blood flow in a circular cylindrical tube with a local constriction is analyzed. Numerical results are presented for the streamlines and the distributions of velocity, pressure, vorticity, and shear stress in the Reynolds number range 0–25. These results have applications to other fluid-mechanical problems such as gauges for velocity measurements, etc.

Experimental Study of the Unsteady Aerodynamics in a Linear Cascade With Low Reynolds Number Low Pressure Turbine Blades

1997 ◽  
Author(s):  
Christopher G. Murawski ◽  
Rolf Sondergaard ◽  
Richard B. Rivir ◽  
Kambiz Vafai ◽  
Terrence W. Simon ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulence Intensity ◽  
Turbine Blades ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
Freestream Turbulence ◽  
Suction Surface ◽  
Linear Cascade ◽  
Low Pressure Turbine ◽  
Flow Reynolds Number

Low pressure turbines in aircraft experience large changes in flow Reynolds number as the gas turbine engine operates from takeoff to high altitude cruise. Low pressure turbine blades are also subject to regions of strong acceleration and diffusion. These changes in Reynolds number, strong acceleration, as well as elevated levels of turbulence can result in unsteady separation and transition zones on the surface of the blade. An experimental study was conducted in a two-dimensional linear cascade, focusing on the suction surface of a low pressure turbine blade. The intent was to assess the effects of changes in Reynolds number, and freestream turbulence intensity. Flow Reynolds numbers, based on exit velocity and suction surface length, have been varied from 50,000 to 300,000. The freestream turbulence intensity was varied from 1.1 to 8.1 percent. Separation was observed at all test Reynolds numbers. Increasing the flow Reynolds number, without changing freestream turbulence, resulted in a slightly rearward movement of the onset of separation and shrinkage of the separation zone. Increasing the freestream turbulence intensity, without changing Reynolds number resulted in a shrinkage of the separation region on the suction surface. Increasing both flow Reynolds numbers and freestream turbulence intensity compounded these effects such that at a Reynolds number of 300,000 and a freestream turbulence intensity of 8.1%, the separation zone was almost nonexistent. The influences on the blade’s wake from altering freestream turbulence and Reynolds number are also documented. The width of the wake and velocity defect rise with a decrease in either turbulence level or chord Reynolds number. Numerical simulations were performed in support of experimental results. The numerical results compare well qualitatively with the low freestream turbulence experimental cases.

Various Flow Regimes and Permeabilities for Packed-Spheres Porous Media

2015 ◽  
Vol 364 ◽  
pp. 1-8
Author(s):  
Özer Bağcı ◽  
Nihad Dukhan ◽  
Mustafa Özdemir
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Flow Regimes ◽  
Initial Step ◽  
Reynolds Numbers ◽  
Flow In Porous Media ◽  
Uniform Size ◽  
Naturally Occurring ◽  
Flow Reynolds Number ◽  
Engineered Systems

Flow in porous media occurs in many naturally-occurring and engineered systems. One of the key properties for understanding the fluid flow and pressure drop in porous media is permeability, which is varies widely among researchers. The current work presents systematic experimental data for packed spheres of uniform size (3 mm) having a porosity of 36.6% subjected to water flow. The experiments covered a sufficiently broad range of flow Reynolds number such that all flow regimes are encountered: pre-Darcy, Darcy, Forchheimer and Turbulent. The pre-Darcy regime is very scarce or non-present in the literature. As a necessary initial step, flow regimes were identified and different permeabilities exhibited by the porous medium in each flow regime were calculated. The length scales in defining the Reynolds number included the diameter of the sphere and the square root of the various permeabilities in order to study the transitional Reynolds numbers among the flow regimes. It is shown that the permeability in the Darcy regime is most appropriate and produces results consistent with accepted understanding in the literature of porous media.

Pair-sphere trajectories in finite-Reynolds-number shear flow

2008 ◽  
Vol 596 ◽  
pp. 413-435 ◽  
Author(s):  
PANDURANG M. KULKARNI ◽  
JEFFREY F. MORRIS
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Rigid Spheres ◽  
Newtonian Dynamics ◽  
Flow Reynolds Number ◽  
Boltzmann Method ◽  
Neutrally Buoyant

The pair trajectories of neutrally buoyant rigid spheres immersed in finite-inertia simple-shear flow are described. The trajectories are obtained using the lattice-Boltzmann method to solve the fluid motion, with Newtonian dynamics describing the sphere motions. The inertia is characterized by the shear-flow Reynolds number ${\it Re} \,{=}\,\rho\dot{\gamma}a^2/\mu$, where μ and ρ are the viscosity and density of the fluid respectively, $\dot{\gamma}$ is the shear rate and a is the radius of the larger of the pair of spheres in the case of unequal sizes; the majority of results presented are for pairs of equal radii. Reynolds numbers of 0 ≤ Re ≤ 1 are considered with a focus on inertia at Re = O(0.1). At finite inertia, the topology of the pair trajectories is altered from that predicted at Re = 0, as closed trajectories found in Stokes flow vanish and two new forms of trajectories are observed. These include spiralling and reversing trajectories in addition to largely undisturbed open trajectories. For Re = O(0.1), the limits of the various regions in pair space yielding open, reversing and spiralling trajectories are roughly defined.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

scholarly journals Turbulence model performance for ventilation components pressure losses

2021 ◽  
Author(s):  
Karsten Tawackolian ◽  
Martin Kriegel
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Pressure Loss ◽  
Low Reynolds Number ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Test Case ◽  
Pressure Losses ◽  
Loss Coefficients ◽  
Near Wall

AbstractThis study looks to find a suitable turbulence model for calculating pressure losses of ventilation components. In building ventilation, the most relevant Reynolds number range is between 3×104 and 6×105, depending on the duct dimensions and airflow rates. Pressure loss coefficients can increase considerably for some components at Reynolds numbers below 2×105. An initial survey of popular turbulence models was conducted for a selected test case of a bend with such a strong Reynolds number dependence. Most of the turbulence models failed in reproducing this dependence and predicted curve progressions that were too flat and only applicable for higher Reynolds numbers. Viscous effects near walls played an important role in the present simulations. In turbulence modelling, near-wall damping functions are used to account for this influence. A model that implements near-wall modelling is the lag elliptic blending k-ε model. This model gave reasonable predictions for pressure loss coefficients at lower Reynolds numbers. Another example is the low Reynolds number k-ε turbulence model of Wilcox (LRN). The modification uses damping functions and was initially developed for simulating profiles such as aircraft wings. It has not been widely used for internal flows such as air duct flows. Based on selected reference cases, the three closure coefficients of the LRN model were adapted in this work to simulate ventilation components. Improved predictions were obtained with new coefficients (LRNM model). This underlined that low Reynolds number effects are relevant in ventilation ductworks and give first insights for suitable turbulence models for this application. Both the lag elliptic blending model and the modified LRNM model predicted the pressure losses relatively well for the test case where the other tested models failed.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

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