A Critical Review Of The Drag Force On A Sphere In The Transition Flow Regime

2005 ◽  
Author(s):  
C. L. Bailey
Keyword(s):  
Flow Regime ◽  
Drag Force ◽  
Critical Review ◽  
Transition Flow ◽  
Transition Flow Regime

scholarly journals A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models

2015 ◽  
Vol 7 (2) ◽  
pp. 245-266 ◽  
Author(s):  
Songze Chen ◽  
Kun Xu ◽  
Qingdong Cai
Keyword(s):  
Kinetic Model ◽  
Flow Regime ◽  
Free Parameter ◽  
Numerical Solutions ◽  
Test Cases ◽  
Transition Flow ◽  
New Model ◽  
Transition Flow Regime ◽  
Generalized Kinetic Model ◽  
S Model

AbstractThe Ellipsoidal Statistical model (ES-model) and the Shakhov model (Smodel) were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heat flux. With the introduction of a new parameter to combine the ES-model and S-model, a generalized kinetic model can be developed. This new model can give the correct Navier-Stokes equations in the continuum flow regime. Through the adjustment of the new parameter, it provides abundant dynamic effect beyond the ES-model and S-model. Changing the free parameter, the physical performance of the new model has been tested numerically. The unified gas kinetic scheme (UGKS) is employed for the study of the new model. In transition flow regime, many physical problems, i.e., the shock structure and micro-flows, have been studied using the generalized model. With a careful choice of the free parameter, good results can be achieved for most test cases. Due to the property of the Boltzmann collision integral, the new parameter in the generalized kinetic model cannot be fully determined. It depends on the specific problem. Generally speaking, the Smodel predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model, while ES-model performs better in the cases where the flow is mostly driven by temperature gradient, such as a channel flow with large boundary temperature variation at high Knudsen number.

Fibrous Filter Efficiency and Pressure Drop in the Viscous-Inertial Transition Flow Regime

2012 ◽  
Vol 46 (2) ◽  
pp. 138-147 ◽  
Author(s):  
J. A. Hubbard ◽  
J. E. Brockmann ◽  
J. Dellinger ◽  
D. A. Lucero ◽  
A. L. Sanchez ◽  
...  
Keyword(s):  
Pressure Drop ◽  
Flow Regime ◽  
Transition Flow ◽  
Fibrous Filter ◽  
Filter Efficiency ◽  
Transition Flow Regime

Experimental Study and Computational Fluid Dynamics Modeling of Pulp Suspensions Flow in a Pipe

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Carla Cotas ◽  
Bruno Branco ◽  
Dariusz Asendrych ◽  
Fernando Garcia ◽  
Pedro Faia ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Pressure Drop ◽  
Flow Regime ◽  
Turbulent Regime ◽  
Cfd Model ◽  
Dynamics Modeling ◽  
Transition Flow ◽  
Pulp Suspensions ◽  
Transition Flow Regime

Eucalyptus and Pine suspensions flow in a pipe was studied experimentally and numerically. Pressure drop was measured for different mean inlet flow velocities. Electrical impedance tomography (EIT), was used to evaluate the prevailing flow regime. Fibers concentration distribution in the pipe cross section and plug evolution were inferred from EIT tomographic images. A modified low-Reynolds-number k–ε turbulence model was applied to simulate the flow of pulp suspensions. The accuracy of the computational fluid dynamics (CFD) predictions was significantly reduced when data in plug regime was simulated. The CFD model applied was initially developed to simulate the flow of Eucalyptus and Pine suspensions in fully turbulent flow regime. Using this model to simulate data in the plug regime leads to an excessive attenuation of turbulence which leads to lower values of pressure drop than the experimental ones. For transition flow regime, the CFD model could be applied successfully to simulate the flow data, similar to what happens for the turbulent regime.

On the drag of a flat plate at zero incidence in almost-free-molecule flow

1959 ◽  
Vol 5 (3) ◽  
pp. 481-490 ◽  
Author(s):  
V. C. Liu
Keyword(s):  
Flat Plate ◽  
Skin Friction ◽  
Flow Regime ◽  
Rarefied Gas ◽  
Approximate Theory ◽  
Free Molecule ◽  
Transition Flow ◽  
Rigid Spheres ◽  
Governing Parameter ◽  
Transition Flow Regime

A physical theory is proposed for the skin friction on a flat plate at zero incidence in the transition flow regime, i.e. in the flow of a moderately rarefied gas. The ratio of the molecular mean free path to the characteristic size of the plate is assumed of order unity or larger. A general formula for the perturbation to the well-known friction of the free-molecule theory is given. This perturbation is attributed to the intermolecular collisions which are neglected on the basis of the free-molecule hypothesis. The expected rate of collisions are calculated for rigid spheres, using the classical kinetic theory.Although this is intended as an approximate theory, the theoretical results check surprisingly well with the limited experimental data that are available. The present theory shows that the ratio of the Reynolds number to the Mach number squared is the governing parameter for determining the intermolecular collision effect on skin friction in the transition flow regime.

Static Performance of Smooth Liquid Annular Seals in the Transition and Turbulent Regimes

2021 ◽  
Author(s):  
Dara W. Childs ◽  
Joshua Bullock
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Operating Conditions ◽  
Radial Clearance ◽  
Turbulent Regime ◽  
Swirl Ratio ◽  
Transition Flow ◽  
Transition Flow Regime ◽  
San Andres ◽  
Annular Seals

Abstract Static test results are presented for smooth annular seals with a length-to-diameter ratio of 0.50, radius R = 51.00 mm, at the nominal radial clearance Cr = 0.2032 mm. Tests were conducted for angular shaft speeds; ω = 2, 4, 6, 8 krpm, axial pressure drops; ΔP = 2.1, 4.13, 6.21, 8.27 bars, and eccentricity ratios ϵ0 = e0/Cr = 0.00, 0.27, 0.53, 0.8 where e0 is the static eccentricity. Three pre-swirl inserts were used to target zero, medium, and high (0., 0.4, and 0.8) pre-swirl ratios for a set of pre-determined operating conditions with ISO VG 2 oil at 46.1°C. Pitot tubes measured the circumferential velocity at separate upstream and downstream seal locations and were used to calculate pre-swirl ratio, PSR = vinlet/Rω, and outlet-swirl ratio, OSR = voutlet/Rω. For all tested pre-swirl inserts, PSR tended to converge to 0.4∼0.5 as ω increased. PSR and OSR were poorly correlated. Volumetric leakage rate Q ˙ versus pressure differential ΔP was measured. The measured vector Reynolds number Re, combining the axial and circumferential Reynolds numbers ranged from ∼1000 to ∼3500. Based on Zirkelback and San Andrés 1996 publication, almost all of the flow regime is predicted to lie in the transition regime, with fewer points in the turbulent regime. Generally, the seals’ static centering properties were obtained by applying a static load Fs and measuring the resulting displacement vector e0. At many low-speed, low-ΔP test conditions, the seal would not remain in the desired centered or near-centered position and had to be forced into place with a centering force Fs. The authors believe that the observed de-centering effects resulted from test operations in the transition flow regime where the friction factor λ does not drop with increasing ΔP and increasing Re. A positive centering Lomakin effect requires that λ drop with increasing axial Reynolds number. The seals had positive centering effects over a large portion of the predicted transition flow regime, supporting the view that the shift from transition-to-turbulent flow regularly occurred at lower Re values than the Re = 3000 boundary used by Zirkleback and San Andrés.

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