Local Reynolds number

2019 ◽  
Author(s):  
Petr Pavlíček
Keyword(s):  
Reynolds Number ◽  
Local Reynolds Number

scholarly journals Theoretical Analysis of Brush Seals Leakage Using Local Computational Fluid Dynamics Estimated Permeability Laws

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Lilas Deville ◽  
Mihai Arghir
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Reynolds Number ◽  
Principal Direction ◽  
Experimental Results ◽  
Leakage Flow ◽  
Cfd Analysis ◽  
Brush Seal ◽  
Brush Seals ◽  
Local Reynolds Number

Brush seals are a mature technology that has generated extensive experimental and theoretical work. Theoretical models range from simple correlations with experimental results to advanced numerical approaches coupling the bristles deformation with the flow in the brush. The present work follows this latter path. The bristles of the brush are deformed by the pressure applied by the flow, by the interference with the rotor and with the back plate. The bristles are modeled as linear beams but a nonlinear numerical algorithm deals with the interferences. The brush with its deformed bristles is then considered as an anisotropic porous medium for the leakage flow. Taking into account, the variation of the permeability with the local geometric and flow conditions represents the originality of the present work. The permeability following the principal directions of the bristles is estimated from computational fluid dynamics (CFD) calculations. A representative number of bristles are selected for each principal direction and the CFD analysis domain is delimited by periodicity and symmetry boundary conditions. The parameters of the CFD analysis are the local Reynolds number and the local porosity estimated from the distance between the bristles. The variations of the permeability are thus deduced for each principal direction and for Reynolds numbers and porosities characteristic for brush seal. The leakage flow rates predicted by the present approach are compared with experimental results from the literature. The results depict also the variations of the pressures, of the local Reynolds number, of the permeability, and of the porosity through the entire brush seal.

Estimating amplitude ratios in boundary layer stability theory: a comparison between two approaches

2001 ◽  
Vol 439 ◽  
pp. 403-412 ◽  
Author(s):  
RAMA GOVINDARAJAN ◽  
R. NARASIMHA
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Small Difference ◽  
Detailed Comparison ◽  
The Other ◽  
Boundary Layer Stability ◽  
Mean Flow ◽  
Amplitude Ratios ◽  
The Stability ◽  
Local Reynolds Number

We first demonstrate that, if the contributions of higher-order mean flow are ignored, the parabolized stability equations (Bertolotti et al. 1992) and the ‘full’ non-parallel equation of Govindarajan & Narasimha (1995, hereafter GN95) are both equivalent to order R−1 in the local Reynolds number R to Gaster's (1974) equation for the stability of spatially developing boundary layers. It is therefore of some concern that a detailed comparison between Gaster (1974) and GN95 reveals a small difference in the computed amplitude ratios. Although this difference is not significant in practical terms in Blasius flow, it is traced here to the approximation, in Gaster's method, of neglecting the change in eigenfunction shape due to flow non-parallelism. This approximation is not justified in the critical and the wall layers, where the neglected term is respectively O(R−2/3) and O(R−1) compared to the largest term. The excellent agreement of GN95 with exact numerical simulations, on the other hand, suggests that the effect of change in eigenfunction is accurately taken into account in that paper.

scholarly journals Numerical simulation and circuit network modelling of flow distributions in 2-D array configurations

2018 ◽  
Vol 22 (5) ◽  
pp. 1987-1998 ◽  
Author(s):  
Jingyu Wang ◽  
Jian Yang ◽  
Long Li ◽  
Pei Qian ◽  
Qiuwang Wang
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Network Model ◽  
Voronoi Tessellation ◽  
Flow Distribution ◽  
Darcy Flow ◽  
Network Modelling ◽  
Flow Models ◽  
Line Array ◽  
Local Reynolds Number

Packing configuration is widely used in chemical industries such as chemical re-action and chromatograph where the flow distribution has a significant effect on the performance of heat and mass transfer. In the present paper, numerical simulation is carried out to investigate the fluid-flow in three 2-D array configurations including in-line array, staggered array and hexagonal array. Meanwhile, a simplified equivalent circuit network model based on the Voronoi tessellation is proposed to simulate the flow models. It is found that firstly, the local Reynolds number could be used as a criterion to determine the flow regime. Flow with maximum local Reynolds number less than 40 could be regarded as Darcy flow. Secondly, the flow pattern can be well represented by the network model in the range of Darcy flow with the determination method of hydraulic resistance pro-posed in the present paper.

Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field

1996 ◽  
Vol 309 ◽  
pp. 113-156 ◽  
Author(s):  
Lian-Ping Wang ◽  
Shiyi Chen ◽  
James G. Brasseur ◽  
John C. Wyngaard
Keyword(s):  
Reynolds Number ◽  
High Resolution ◽  
Probability Distribution ◽  
Similarity Theory ◽  
Turbulence Theory ◽  
Inertial Subrange ◽  
Velocity Increments ◽  
Decaying Turbulence ◽  
Log Normal ◽  
Local Reynolds Number

The fundamental hypotheses underlying Kolmogorov-Oboukhov (1962) turbulence theory (K62) are examined directly and quantitutivezy by using high-resolution numerical turbulence fields. With the use of massively parallel Connection Machine-5, we have performed direct Navier-Stokes simulations (DNS) at 5123 resolution with Taylor microscale Reynolds number up to 195. Three very different types of flow are considered: free-decaying turbulence, stationary turbulence forced at a few large scales, and a 2563 large-eddy simulation (LES) flow field. Both the forced DNS and LES flow fields show realistic inertial-subrange dynamics. The Kolmogorov constant for the k−5/3 energy spectrum obtained from the 5123 DNS flow is 1.68 ±.15. The probability distribution of the locally averaged disspation rate εr, over a length scale r is nearly log-normal in the inertial subrange, but significant departures are observed for high-order moments. The intermittency parameter p, appearing in Kolmogorov's third hypothesis for the variance of the logarithmic dissipation, is found to be in the range of 0.20 to 0.28. The scaling exponents over both εr, and r for the conditionally averaged velocity increments $\overline{\delta_ru|\epsilon_r}$ are quantified, and the direction of their variations conforms with the refined similarity theory. The dimensionless averaged velocity increments $(\overline{\delta_ru^n|\epsilon_r})/(\epsilon_rr)^{n/3}$ are found to depend on the local Reynolds number Reεr = ε1/3rr4/3/ν in a manner consistent with the refined similarity hypotheses. In the inertial subrange, the probability distribution of δru/(εrr)1/3 is found to be universal. Because the local Reynolds number of K62, Rεr = ε1/3rr4/3/ν, spans a finite range at a given scale r as compared to a single value for the local Reynolds number Rr = ε−1/3r4/3/ν in Kolmogorov's (1941a,b) original theory (K41), the inertial range in the K62 context can be better realized than that in K41 for a given turbulence field at moderate Taylor microscale (global) Reynolds number Rλ. Consequently universal constants in the second refined similarity hypothesis can be determined quite accurately, showing a faster-than-exponential growth of the constants with order n. Finally, some consideration is given to the use of pseudo-dissipation in the context of the K62 theory where it is found that the probability distribution of locally averaged pseudo-dissipation ε′r deviates more from a log-normal model than the full dissipation εr. The velocity increments conditioned on ε′r do not follow the refined similarity hypotheses to the same degree as those conditioned on εr.

P2433Local blood viscosity and local Reynolds number are associated with coronary plaque calcium and lipid

2019 ◽  
Vol 40 (Supplement_1) ◽  
Author(s):  
V Thondapu ◽  
E K W Poon ◽  
B Jiang ◽  
M Tacey ◽  
J Dijkstra ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Newtonian Fluid ◽  
Coronary Arteries ◽  
Blood Viscosity ◽  
Fluid Dynamic ◽  
Patient Specific ◽  
Plaque Composition ◽  
Cfd Simulations ◽  
Lower Odds ◽  
Local Reynolds Number

Abstract Background Despite being a shear-thinning non-Newtonian fluid, most computational fluid dynamic (CFD) simulations assume blood to be a Newtonian fluid with constant viscosity. The use of more realistic assumptions may deepen mechanistic understanding of the relationship between blood flow disturbances and atherosclerosis, and improve the diagnostic accuracy of CFD simulations. Purpose To compare associations between plaque composition and local hemodynamics at a single time point using Newtonian versus non-Newtonian rheological models in patient-specific coronary arteries. To investigate whether viscosity-based local haemodynamic indices correlate with plaque composition. Methods Sixteen patient-specific coronary arteries containing non-culprit plaques were reconstructed from optical coherence tomography imaging. CFD simulations using Newtonian and non-Newtonian models were performed to calculate endothelial shear stress (ESS). Local blood viscosity (LBV) and local Reynolds number (ReL) were calculated from non-Newtonian simulation data. Each haemodynamic index was distributed into quintiles, mapped in 5-degree sectors, and compared to plaque composition using logistic regression. Results In total, 69120 sectors from 960 OCT frames were analysed. The lowest ESS quintiles were associated with underlying lipid (ESS<0.8Pa: odds ratio [OR] 1.26, p<0.001, 95% CI 1.15–1.38; ESS 0.8–1.1Pa: OR 1.71, p<0.001, 95% CI 1.58–1.85), while the highest quintile of ESS (>2.2Pa) had lower odds of underlying lipid (OR 0.89, p=0.015, 95% CI 0.82–0.98) compared to the median ESS quintile. However, in the non-Newtonian results, only the second lowest quintile of ESS (1.1–1.5Pa) was associated with lipid (OR 1.54, p<0.001, 95% CI 1.42–1.67). Low ReL was associated with lipid (ReL<28: OR 1.71, p<0.001, 95% CI 1.55–1.89; ReL 28–38: OR 1.47, p<0.001, 95% CI 1.35–1.58). Conversely, the highest quintile of ReL had decreased odds of lipid (ReL>68: OR 0.69, p<0.001, 95% CI 0.62–0.76) (FIGURE). In both the Newtonian and non-Newtonian results, lower ESS was associated with increased odds of underlying calcium. Whereas the lowest quintile of LBV had a lower odds of calcium (LBV<1.4: OR 0.60, p<0.001, 95% CI 0.52–0.71), the highest quintile had significantly higher odds of underlying calcium (LBV>1.5: OR 1.38, p<0.001, 95% CI 1.18–1.63) Conclusions Using the standard Newtonian assumption, low ESS is associated with underlying lipid. However, using a more realistic non-Newtonian rheological model, there is no strong or consistent relationship between ESS and underlying lipid, highlighting the importance of methodological assumptions and lingering questions in arterial CFD simulation. Non-Newtonian indices LBV and ReL are independently associated with calcium and lipid, respectively, suggesting possible mechanistic effects of local blood viscosity in atherosclerosis and implying their use as novel haemodynamic markers of atherosclerosis.

An experimental study of vortex shedding behind linearly tapered cylinders at low Reynolds number

1993 ◽  
Vol 246 ◽  
pp. 163-195 ◽  
Author(s):  
Paul S. Piccirillo ◽  
C. W. Van Atta
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Modulation Frequency ◽  
End Effects ◽  
Constant Frequency ◽  
Self Similar ◽  
Number Curve ◽  
Cell Shedding ◽  
Local Reynolds Number

Experiments were performed to study vortex shedding behind a linearly tapered cylinder. Four cylinders were used, with taper ratios varying from 50:1 to 100:1. The cylinders were each run at four different velocities, adjusted to cover the range of laminar vortex shedding for a non-tapered cylinder. The flow was confirmed to consist of discrete shedding cells, each with a constant frequency. For a centrespan Reynolds number greater than 100, the dimensionless mean cell length was found to be a constant. Individual cell size was found to be roughly self-similar. New shedding cells were created on the ends of the cylinders, or in regions adjacent to areas not shedding. Successful scalings were found for both the cell shedding frequencies and their differences, the modulation frequencies. The modulation frequencies were found to be constant along the cylinder span. The shedding frequency Strouhal number versus Reynolds number curve was found to have a slightly steeper slope than the Strouhal number curve for a non-tapered cylinder. Vortex shedding was found to begin at a local Reynolds number of about 60, regardless of any other factors. End effects were found to be of little importance.The vortex splits, which form the links between shedding cells, were found to be similar in some respects to those found by earlier investigators. Amplitude results suggested that the splits at different spanwise locations are temporally sequenced by an overall flow mechanism, a supposition confirmed by flow visualization. Wavelet analysis results showed that while the behaviour of the shedding frequencies in time was relatively unaffected by changing taper ratio, the behaviour of the modulation frequency in time was greatly affected. Comparisons with other experiments point out the universality of vortex splitting phenomena.

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