Oscillatory Flow in a Cone-and-Plate Bioreactor

2004 ◽  
Vol 127 (4) ◽  
pp. 601-610 ◽  
Author(s):  
C. A. Chung ◽  
M. R. Tzou ◽  
R. W. Ho
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Secondary Flows ◽  
Shear Stresses ◽  
Centripetal Force ◽  
Plate Surface ◽  
Womersley Number ◽  
Small Parameters ◽  
Plate Geometry ◽  
Stationary Plate

Motivated by biometric applications, we analyze oscillatory flow in a cone-and-plate geometry. The cone is rotated in a simple harmonic way on a stationary plate. Based on assuming that the angle between the cone and plate is small, we describe the flow analytically by a perturbation method in terms of two small parameters, the Womersley number and the Reynolds number, which account for the influences of the local acceleration and centripetal force, respectively. Working equations for the shear stresses induced both by laminar primary and secondary flows on the plate surface are presented.

On the Prediction of Secondary Flows in a U-Bend

2001 ◽  
Author(s):  
B. Song ◽  
R. S. Amano
Keyword(s):  
Reynolds Number ◽  
Linear Model ◽  
Secondary Flows ◽  
Shear Stresses ◽  
Strain Rates ◽  
Interpolation Scheme ◽  
Streamline Curvature ◽  
Flow Development ◽  
Non Linear ◽  
Volume Difference

The secondary flows inside a sharp U-bend are numerically studied by using non-linear low Reynolds number (low-Re) k – ω model in which the cubic terms are included to represent the effects of extra strain-rates such as streamline curvature and three-dimensionality on both turbulence normal and turbulence shear stresses. The finite volume difference method incorporated with the higher-order bounded interpolation scheme has been employed in the present study. For the purpose of comparison, the predictions with the Launder-Sharma model (the linear low-Re k – ε model) are also given. The present results reveal that non-linear low-Re k – ω model and linear model produce the quite different secondary flow patterns. It is shown that the present non-linear model produces satisfactory predictions of the flow development inside the sharp U-bend comparing with linear Launder-Sharma model.

Secondary flow and turbulence in a cone-and-plate device

1984 ◽  
Vol 138 ◽  
pp. 379-404 ◽  
Author(s):  
H. P. Sdougos ◽  
S. R. Bussolari ◽  
C. F. Dewey
Keyword(s):  
Kinematic Viscosity ◽  
Stokes Equations ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Navier Stokes Equations ◽  
Rotating Cone ◽  
Film Heat Transfer ◽  
Hot Film ◽  
Stationary Plate

The flow between a shallow rotating cone and a stationary plate has been investigated using flow visualization, hot-film heat-transfer probes, and measurements of the torque required to rotate the cone against the retardation of the viscous fluid that fills the device. Theory appropriate to these experiments is also presented.An expansion of the Navier–Stokes equations is performed for small values of the single parameter $\tilde{R} = r^2\omega\alpha^2/12\nu $. (Here r is the local radius, ω the angular velocity of the cone, α([Lt ] 1) is the angle between the cone and plate, and v is the fluid kinematic viscosity.) The measurements at low rotational speeds describe a simple linear velocity profile as predicted for the laminar flow of a Newtonian fluid. At larger rotational speeds, strong secondary flows are observed. There is agreement between the laminar theory and the measured streamline angles and shear stresses for values of $\tilde{R} < 0.5$. Turbulence is observed for $\tilde{R} \gtrsim 4$.

scholarly journals Oscillatory Carreau flows in straight channels

2020 ◽  
Vol 7 (5) ◽  
pp. 191305
Author(s):  
S. Tabakova ◽  
N. Kutev ◽  
St. Radev
Keyword(s):  
Flow Velocity ◽  
Asymptotic Expansions ◽  
Oscillatory Flow ◽  
High Shear ◽  
Carreau Fluid ◽  
Womersley Number ◽  
Newtonian Flow ◽  
Numerical Examples ◽  
Small Parameters

The present paper studies the oscillatory flow of Carreau fluid in a channel at different Womersley and Carreau numbers. At high and low Womersley numbers, asymptotic expansions in small parameters, connected with the Womersley number, are developed. For the intermediate Womersley numbers, theoretical bounds for the velocity solution and its gradient, depending on the problem parameters, are proven and explicitly given. It is shown that the Carreau number changes the type of the flow velocity to be closer to the Newtonian velocity corresponding to low or high shear or to have a transitional character between both Newtonian velocities. Some numerical examples for the velocity at different Carreau and Womersley numbers are presented for illustration with respect to the similar Newtonian flow velocity.

Secondary Velocity Fields in the Conducting Airways of the Human Lung

2007 ◽  
Vol 129 (5) ◽  
pp. 722-732 ◽  
Author(s):  
Frank E. Fresconi ◽  
Ajay K. Prasad
Keyword(s):  
Secondary Flow ◽  
Oscillatory Flow ◽  
Flow Direction ◽  
Flow Fields ◽  
Velocity Fields ◽  
Secondary Flows ◽  
Womersley Number ◽  
Dean Number ◽  
Steady Streaming ◽  
Secondary Velocity

An understanding of flow and dispersion in the human respiratory airways is necessary to assess the toxicological impact of inhaled particulate matter as well as to optimize the design of inhalable pharmaceutical aerosols and their delivery systems. Secondary flows affect dispersion in the lung by mixing solute in the lumen cross section. The goal of this study is to measure and interpret these secondary velocity fields using in vitro lung models. Particle image velocimetry experiments were conducted in a three-generational, anatomically accurate model of the conducting region of the lung. Inspiration and expiration flows were examined under steady and oscillatory flow conditions. Results illustrate secondary flow fields as a function of flow direction, Reynolds number, axial location with respect to the bifurcation junction, generation, branch, phase in the oscillatory cycle, and Womersley number. Critical Dean number for the formation of secondary vortices in the airways, as well as the strength and development length of secondary flow, is characterized. The normalized secondary velocity magnitude was similar on inspiration and expiration and did not vary appreciably with generation or branch. Oscillatory flow fields were not significantly different from corresponding steady flow fields up to a Womersley number of 1 and no instabilities related to shear were detected on flow reversal. These observations were qualitatively interpreted with respect to the simple streaming, augmented dispersion, and steady streaming convective dispersion mechanisms.

scholarly journals Movement of a finite body in channel flow

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160164 ◽  
Author(s):  
Frank T. Smith ◽  
Edward R. Johnson
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Flow Instability ◽  
Flow Direction ◽  
Finite Size ◽  
The Body ◽  
Thin Body ◽  
Shear Stresses ◽  
Unsteady Interaction ◽  
High Reynolds

A body of finite size is moving freely inside, and interacting with, a channel flow. The description of this unsteady interaction for a comparatively dense thin body moving slowly relative to flow at medium-to-high Reynolds number shows that an inviscid core problem with vorticity determines much, but not all, of the dominant response. It is found that the lift induced on a body of length comparable to the channel width leads to differences in flow direction upstream and downstream on the body scale which are smoothed out axially over a longer viscous length scale; the latter directly affects the change in flow directions. The change is such that in any symmetric incident flow the ratio of slopes is found to be cos ⁡ ( π / 7 ) , i.e. approximately 0.900969, independently of Reynolds number, wall shear stresses and velocity profile. The two axial scales determine the evolution of the body and the flow, always yielding instability. This unusual evolution and linear or nonlinear instability mechanism arise outside the conventional range of flow instability and are influenced substantially by the lateral positioning, length and axial velocity of the body.

Heat Transfer Enhancement in a Rectangular (AR = 3:1) Channel With V-Shaped Dimples

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
C. Neil Jordan ◽  
Lesley M. Wright
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Liquid Crystal ◽  
Pressure Drop ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Secondary Flows ◽  
Transfer Enhancement ◽  
Reduced Pressure

An alternative to ribs for internal heat transfer enhancement of gas turbine airfoils is dimpled depressions. Relative to ribs, dimples incur a reduced pressure drop, which can increase the overall thermal performance of the channel. This experimental investigation measures detailed Nusselt number ratio distributions obtained from an array of V-shaped dimples (δ/D = 0.30). Although the V-shaped dimple array is derived from a traditional hemispherical dimple array, the V-shaped dimples are arranged in an in-line pattern. The resulting spacing of the V-shaped dimples is 3.2D in both the streamwise and spanwise directions. A single wide wall of a rectangular channel (AR = 3:1) is lined with V-shaped dimples. The channel Reynolds number ranges from 10,000–40,000. Detailed Nusselt number ratios are obtained using both a transient liquid crystal technique and a newly developed transient temperature sensitive paint (TSP) technique. Therefore, the TSP technique is not only validated against a baseline geometry (smooth channel), but it is also validated against a more established technique. Measurements indicate that the proposed V-shaped dimple design is a promising alternative to traditional ribs or hemispherical dimples. At lower Reynolds numbers, the V-shaped dimples display heat transfer and friction behavior similar to traditional dimples. However, as the Reynolds number increases to 30,000 and 40,000, secondary flows developed in the V-shaped concavities further enhance the heat transfer from the dimpled surface (similar to angled and V-shaped rib induced secondary flows). This additional enhancement is obtained with only a marginal increase in the pressure drop. Therefore, as the Reynolds number within the channel increases, the thermal performance also increases. While this trend has been confirmed with both the transient TSP and liquid crystal techniques, TSP is shown to have limited capabilities when acquiring highly resolved detailed heat transfer coefficient distributions.

Heat Transfer and Flowfield Measurements in the Leading Edge Region of a Stator Vane Endwall

1999 ◽  
Vol 121 (3) ◽  
pp. 558-568 ◽  
Author(s):  
M. B. Kang ◽  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Edge Region ◽  
Leading Edge Vortex ◽  
Stator Vane ◽  
Edge Vortex ◽  
The Mean

The leading edge region of a first-stage stator vane experiences high heat transfer rates, especially near the endwall, making it very important to get a better understanding of the formation of the leading edge vortex. In order to improve numerical predictions of the complex endwall flow, benchmark quality experimental data are required. To this purpose, this study documents the endwall heat transfer and static pressure coefficient distribution of a modern stator vane for two different exit Reynolds numbers (Reex = 6 × 105 and 1.2 × 106). In addition, laser-Doppler velocimeter measurements of all three components of the mean and fluctuating velocities are presented for a plane in the leading edge region. Results indicate that the endwall heat transfer, pressure distribution, and flowfield characteristics change with Reynolds number. The endwall pressure distributions show that lower pressure coefficients occur at higher Reynolds numbers due to secondary flows. The stronger secondary flows cause enhanced heat transfer near the trailing edge of the vane at the higher Reynolds number. On the other hand, the mean velocity, turbulent kinetic energy, and vorticity results indicate that leading edge vortex is stronger and more turbulent at the lower Reynolds number. The Reynolds number also has an effect on the location of the separation point, which moves closer to the stator vane at lower Reynolds numbers.

Quantitative Analysis of Reynolds and Navier–Stokes Based Modeling Approaches for Isothermal Newtonian Elastohydrodynamic Lubrication

2021 ◽  
Vol 143 (12) ◽  
Author(s):  
Leoluca Scurria ◽  
Tommaso Tamarozzi ◽  
Oleg Voronkov ◽  
Dieter Fauconnier
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Thickness Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Lubricant Film ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Low Viscosity ◽  
Fluid Film Thickness

Abstract When simulating elastohydrodynamic lubrication, two main approaches are usually followed to predict the pressure and fluid film thickness distribution throughout the contact. The conventional approach relies on the Reynolds equation to describe the thin lubricant film, which is coupled to a Boussinesq description of the linear elastic deformation of the solids. A more accurate, yet a time-consuming method is the use of computational fluid dynamics in which the Navier–Stokes equations describe the flow of the thin lubricant film, coupled to a finite element solver for the description of the local contact deformation. This investigation aims at assessing both methods for different lubrication conditions in different elastohydrodynamic lubrication (EHL) regimes and quantify their differences to understand advantages and limitations of both methods. This investigation shows how the results from both approaches deviate for three scenarios: (1) inertial contributions (Re &gt; 1), i.e., thick films, high speed, and low viscosity; (2) high shear stresses leading to secondary flows; and (3) large deformations of the solids leading to inaccuracies of the Boussinesq equation.

Computational Study of Gas Turbine Blade Cooling Channel

2010 ◽  
Author(s):  
R. S. Amano ◽  
Krishna Guntur ◽  
Jose Martinez Lucci
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Gas Turbine ◽  
Turbulence Models ◽  
Flow Patterns ◽  
Higher Order ◽  
Secondary Flows ◽  
Complex Flow ◽  
Cooling Performance ◽  
Cooling Channels

It has been a common practice to use cooling passages in gas turbine blade in order to keep the blade temperatures within the operating range. Insufficiently cooled blades are subject to oxidation, to cause creep rupture, and even to cause melting of the material. To design better cooling passages, better understanding of the flow patterns within the complicated flow channels is essential. The interactions between secondary flows and separation lead to very complex flow patterns. To accurately simulate these flows and heat transfer, both refined turbulence models and higher-order numerical schemes are indispensable for turbine designers to improve the cooling performance. Power output and the efficiency of turbine are completely related to gas firing temperature from chamber. The increment of gas firing temperature is limited by the blade material properties. Advancements in the cooling technology resulted in high firing temperatures with acceptable material temperatures. To better design the cooling channels and to improve the heat transfer, many researchers are studying the flow patterns inside the cooling channels both experimentally and computationally. In this paper, the authors present the performance of three turbulence models using TEACH software code in comparison with the experimental values. To test the performance, a square duct with rectangular ribs oriented at 90° and 45° degree and placed at regular intervals. The channel also has bleed holes. The normalized Nusselt number obtained from simulation are validated with that of experiment. The Reynolds number is set at 10,000 for both the simulation and experiment. The interactions between secondary flows and separation lead to very complex flow patterns. To accurately simulate these flows and heat transfer, both refined turbulence models and higher-order numerical schemes are indispensable for turbine designers to improve the cooling performance. The three-dimensional turbulent flows and heat transfer are numerically studied by using several different turbulence models, such as non-linear low-Reynolds number k-omega and Reynolds Stress (RSM) models. In k-omega model the cubic terms are included to represent the effects of extra strain-rates such as streamline curvature and three-dimensionality on both turbulence normal and shear stresses. The finite volume difference method incorporated with the higher-order bounded interpolation scheme has been employed in the present study. The outcome of this study will help determine the best suitable turbulence model for future studies.

The development of asymmetry and period doubling for oscillatory flow in baffled channels

1996 ◽  
Vol 328 ◽  
pp. 19-48 ◽  
Author(s):  
E. P. L. Roberts ◽  
M. R. Mackley
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Period Doubling ◽  
Progressive Increase ◽  
Newtonian Flow ◽  
Chaotic Flow ◽  
Spatially Periodic ◽  
Dimensional Simulation ◽  
Time Periodic

We report experimental and numerical observations on the way initially symmetric and time-periodic fluid oscillations in baffled channels develop in complexity. Experiments are carried out in a spatially periodic baffled channel with a sinusoidal oscillatory flow. At modest Reynolds number the observed vortex structure is symmetric and time periodic. At higher values the flow progressively becomes three-dimensional, asymmetric and aperiodic. A two-dimensional simulation of incompressible Newtonian flow is able to follow the flow pattern at modest oscillatory Reynolds number. At higher values we report the development of both asymmetry and a period-doubling cascade leading to a chaotic flow regime. A bifurcation diagram is constructed that can describe the progressive increase in complexity of the flow.

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