Modified Time-Dependent Penetration Length and Inlet Pressure Field in Rectangular and Cylindrical Channel Flows Driven by Non-Mechanical Forces

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Martin Ndi Azese
Keyword(s):  
Velocity Profile ◽  
Governing Equation ◽  
Control Volume ◽  
Momentum Equation ◽  
Rate Of Change ◽  
Creeping Flow ◽  
Time Dependent ◽  
Penetration Length ◽  
Wide Range ◽  
Accurate Expression

In this paper, we derive the governing equation for the time dependent penetration length of a fluid column in rectangular and cylindrical channels under the action of nonmechanical forces like capillary or electro-osmotic force. For this purpose, first we obtain the velocity profile for unidirectional unsteady flow by satisfying momentum equation in differential form. Then, we relate the rate of change of penetration length with volume flux to obtain the governing equation of the penetration length. As the velocity profile is exact, the analysis is devoid of any mathematical error. As a result, the theoretical results are valid irrespective of the Reynolds number of the system as long as the flow inside the cylindrical or rectangular conduit is laminar. We then use the new expressions of velocity fields of respective conduits to derive a more accurate expression of the entrance pressure by using a hemispherical model for the control volume for finite aspect ratio. As these channels are very common, our governing equations for penetration length will have a wide range of applicability. These applications especially include creeping flow in micro fluidic domain for which we have a simplified version of the derived equation.

Application of a Simplified Velocity Profile to the Prediction of Pipe-Flow Heat Transfer

1968 ◽  
Vol 90 (2) ◽  
pp. 191-198 ◽  
Author(s):  
R. D. Haberstroh ◽  
L. V. Baldwin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Profile ◽  
Pipe Flow ◽  
Energy Equation ◽  
Momentum Equation ◽  
Turbulent Pipe Flow ◽  
Transfer Coefficients ◽  
Constant Property ◽  
Wide Range

The temperature profiles and heat-transfer coefficients are predicted for fully developed turbulent pipe flow with constant wall heat flux for a wide range of Prandtl and Reynolds numbers. The basis for integrating the energy equation comes from a continuously differentiable velocity profile which fits the physical boundary conditions and is a rigorous (though not necessarily unique) solution of the Reynolds equations. This velocity profile is the semiempirical relation proposed by S. I. Pai, reference [12]. The assumptions are those of steady, incompressible, constant-property, fully developed, turbulent flow of Newtonian fluids in smooth, circular pipes with constant heat flux at the wall. The ratio of the turbulent thermal diffusivity to the turbulent momentum diffusivity is taken to be unity. The thermal quantities are obtained by numerical integration of the energy equation, and they are presented as curves and tables. A compact formula for the Nusselt number is given for a wide range of Reynolds and Prandtl numbers. The results degenerate identically to the case of laminar flow. The heat-transfer calculation requires neither adjustable factors nor data-fitting beyond the empirical constants in the momentum equation; thus this analysis constitutes a heat-transfer prediction to be tested against heat-transfer data.

On the dynamics of wind-driven shelf currents

1981 ◽  
Vol 302 (1472) ◽  
pp. 617-634 ◽  
Keyword(s):  
Sea Level ◽  
Momentum Equation ◽  
Bottom Friction ◽  
Empirical Orthogonal Functions ◽  
Rate Of Change ◽  
Time Dependent ◽  
Momentum Balance ◽  
Orthogonal Functions ◽  
Northwest Africa ◽  
Coastal Sea

Measurements of currents, wind, and coastal sea level from off Oregon, northwest Africa and Peru are used to examine characteristics of the depth-integrated momentum balance at mid-shelf locations. Attention is focused on determining the nature of the balance, as a function of frequency, of time-dependent terms in the alongshore momentum equation. Decomposition of the estimated terms into empirical orthogonal functions, and regression of terms on the wind stress to obtain the wind-forced component, are methods used in an attempt to assess objectively the type of balance present. It is found, for Oregon, that there is a relatively large amount of variance in the depth-integrated cross-shelf velocity which is not balanced by other estimated terms. In addition, a substantial component of the flow is wind-forced, with bottom friction insignificant for periods less than 11 days. For northwest Africa, the motion is strongly wind-driven, with bottom friction playing an important role for periods greater than 6 days and with a quasi-steady response evident for periods longer than 10 days. For Peru, the motion is dominated by an inviscid, unforced balance which, for the 5- to 11-day frequency band, is primarily between the alongshore pressure gradient and the rate of change with time of the alongshore velocity.

Haemorheological Effects on Thrombocyte Adhesion and Aggregation Found Under Controlled Flow Conditions

1979 ◽  
Author(s):  
P.D. Richardson
Keyword(s):  
Rate Of Change ◽  
Continuous Observation ◽  
Flow Conditions ◽  
Wide Range ◽  
Stream Migration ◽  
Local Shear ◽  
Videotape Recording ◽  
Controlled Flow ◽  
A Site

Thrombocyte adhesion and aggregation in a vessel or on a chamber wall can be measured most readily if the flow is controlled and steady, and continuous observation is used. Videotape recording is very helpful for subsequent quantification of the dynamics. The adhesion of each thrombocyte can occur for a finite time interval:this interval has been observed to have a wide range. Platelets which escape often leave open a site which attracts other platelets preferentially. The rate of change of adhesion density (platelets/mm2) is affected by the local shear rate and the shear history upstream. Aggregation is affected similarly, and also proceeds with some platelet turnover. The role of erythrocytes in facilitating cross-stream migration of thrombocytes (which can enhance the growth rate of large thrombi) appears due in part to convective flow fields induced by the motion of erythrocytes in a shear flow, which can be demonstrated theoretically and experimentally. Observations of the phenomenlogy of adhesion and aggregation under controlled flow conditions and comparison with fLu id-dynamically based theory allows representation in terras of a small number of parameters with prospects of prediction of behaviour over a wide range of haemodynamic conditions; biochemical changes lead to changes in values of the parameters, so that activating agents and inhibiting agents modify values in different directions.

Contributions of Time Dependent and Cyclic Crack Growth to the Crack Growth Behavior of Non Strain-Crystallizing Elastomers

2002 ◽  
Vol 75 (4) ◽  
pp. 643-656 ◽  
Author(s):  
J. J. C. Busfield ◽  
K. Tsunoda ◽  
C. K. L. Davies ◽  
A. G. Thomas
Keyword(s):  
Crack Growth ◽  
Growth Behavior ◽  
Time Dependent ◽  
Crack Growth Behavior ◽  
Wide Range ◽  
Dependent Component ◽  
Tearing Energy ◽  
Quasi Crystals ◽  
Crack Growth Rates ◽  
Time Dependent Crack Growth

Abstract Engineering components are observed to fail more rapidly under cyclic loading than under static loading. This reflects features of the underlying crack growth behavior. This behavior is characterized by the relation between the tearing energy, T, and the crack growth per cycle, dc/dn. The increment of crack growth during each cycle is shown here to result from the sum of time dependent and cyclic crack growth components. The time dependent component represents the crack growth behavior that would be present in a conventional constant T crack growth test. Under repeated stressing additional crack growth, termed the cyclic crack growth component, occurs. For a non-crystallizing elastomer, significant effects of frequency have been found on the cyclic crack growth behavior, reflecting the presence of this cyclic element of crack growth. The cyclic crack growth behavior over a wide range of frequencies was investigated for unfilled and swollen SBR materials. The time dependent crack growth component was calculated from constant T crack growth tests and the cyclic contribution derived from comparison with the observed cyclic growth. It is shown that decreasing the frequency or increasing the maximum tearing energy during a cycle results in the cyclic crack growth behavior being dominated by time dependent crack growth. Conversely at high frequency and at low tearing energy, cyclic crack growth is dominated by the cyclic crack growth component. A large effect of frequency on cyclic crack growth behavior was observed for highly swollen SBR. The cyclic crack growth behavior was dominated by the time dependent crack growth component over the entire range of tearing energy and/or crack growth rate. The origin of the cyclic component may be the formation/melting of quasi crystals at the crack tip, which is absent at fast crack growth rates in the unswollen SBR and is absent at all rates in the swollen SBR.

Experimental Investigation of Subsonic Turbulent Flow Over Single and Double Backward Facing Steps

1962 ◽  
Vol 84 (3) ◽  
pp. 317-325 ◽  
Author(s):  
D. E. Abbott ◽  
S. J. Kline
Keyword(s):  
Experimental Investigation ◽  
Velocity Profile ◽  
Flow Pattern ◽  
Reynolds Numbers ◽  
Area Ratio ◽  
Single Step ◽  
Reattachment Length ◽  
Double Step ◽  
Wide Range ◽  
Geometric Variables

Results are presented for flow patterns over backward facing steps covering a wide range of geometric variables. Velocity profile measurements are given for both single and double steps. The stall region is shown to consist of a complex pattern involving three distinct regions. The double step contains an assymmetry for large expansions, but approaches the single-step configuration with symmetric stall regions for small values of area ratio. No effect on flow pattern or reattachment length is found for a wide range of Reynolds numbers and turbulence intensities, provided the flow is fully turbulent before the step.

Experimental Investigation of Turbine Stage Flow Field and Performance at Varying Cavity Purge Rates and Operating Speeds

2016 ◽  
Author(s):  
Johan Dahlqvist ◽  
Jens Fridh
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
High Speed ◽  
Control Volume ◽  
Spatial Average ◽  
Turbine Stage ◽  
Wide Range ◽  
Annulus Flow ◽  
Purge Flow ◽  
Secondary Air

The aspect of hub cavity purge has been investigated in a high-pressure axial low-reaction turbine stage. The cavity purge is an important part of the secondary air system, used to isolate the hot main annulus flow from cavities below the hub level. A full-scale cold-flow experimental rig featuring a rotating stage was used in the investigation, quantifying main annulus flow field impact with respect to purge flow rate as it was injected upstream of the rotor. Five operating speeds were investigated of which three with respect to purge flow, namely a high loading case, the peak efficiency, and a high speed case. At each of these operating speeds, the amount of purge flow was varied across a very wide range of ejection rates. Observing the effect of the purge rate on measurement plane averaged parameters, a minor outlet swirl decrease is seen with increasing purge flow for each of the operating speeds while the Mach number is constant. The prominent effect due to purge is seen in the efficiency, showing a similar linear sensitivity to purge for the investigated speeds. An attempt is made to predict the efficiency loss with control volume analysis and entropy production. While spatial average values of swirl and Mach number are essentially unaffected by purge injection, important spanwise variations are observed and highlighted. The secondary flow structure is strengthened in the hub region, leading to a generally increased over-turning and lowered flow velocity. Meanwhile, the added volume flow through the rotor leads to higher outlet flow velocities visible in the tip region, and an associated decreased turning. A radial efficiency distribution is utilized, showing increased impact with increasing rotor speed.

Motion of slender bodies in unsteady Stokes flow

2011 ◽  
Vol 688 ◽  
pp. 66-87 ◽  
Author(s):  
Efrath Barta
Keyword(s):  
Stokes Flow ◽  
Slenderness Ratio ◽  
Creeping Flow ◽  
Slender Body Theory ◽  
Wide Range ◽  
Unsteady Stokes Flow ◽  
Slender Bodies ◽  
Set Up ◽  
Micro Organisms ◽  
Parameter Values

AbstractThe flow regime in the vicinity of oscillatory slender bodies, either an isolated one or a row of many bodies, immersed in viscous fluid (i.e. under creeping flow conditions) is studied. Applying the slender-body theory by distributing proper singularities on the bodies’ major axes yields reasonably accurate and easily computed solutions. The effect of the oscillations is revealed by comparisons with known Stokes flow solutions and is found to be most significant for motion along the normal direction. Streamline patterns associated with motion of a single body are characterized by formation and evolution of eddies. The motion of adjacent bodies results, with a reduction or an increase of the drag force exerted by each body depending on the direction of motion and the specific geometrical set-up. This dependence is demonstrated by parametric results for frequency of oscillations, number of bodies, their slenderness ratio and the spacing between them. Our method, being valid for a wide range of parameter values and for densely packed arrays of rods, enables simulation of realistic flapping of bristled wings of some tiny insects and of locomotion of flagella and ciliated micro-organisms, and might serve as an efficient tool in the design of minuscule vehicles. Its potency is demonstrated by a solution for the flapping of thrips.

Performing Fourier Transform on a Velocity Profile From Atmospheric Turbulence Studies

2021 ◽  
Author(s):  
Richard Adansi ◽  
Jose Terrazas ◽  
Arturo Rodriguez ◽  
V. M. Krushnarao Kotteda ◽  
Vinod Kumar ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Velocity Profile ◽  
Size Distribution ◽  
Atmospheric Turbulence ◽  
Situational Awareness ◽  
Control Volume ◽  
The United States ◽  
Vertical Distance ◽  
Large Eddy ◽  
Computational Fluid Dynamics Cfd

Abstract Atmospheric Turbulence poses a challenge to land-based observatories operated by the United States Air Force (USAF) tasked with space situational awareness. By developing new methods for quantifying Turbulence, we intend to provide increased USAF capability in this domain. Current models for quantifying atmospheric Turbulence include Kolmogorov and Non-Kolmogorov methods. Through the nature of Fourier Transform, sinusoidal function, it is possible to determine the frequency at which velocities occur in a specified vertical distance and eventually determine eddy size in a control volume. First, an ANSYS Computational Fluid Dynamics (CFD) model will be created to simulate atmospheric Turbulence in a defined control volume. The simulation will include a one-dimensional flow over a flat plate. The data we acquired from the simulation were used to derive an equation relating the velocity to the vertical distance (velocity profile). We will perform a regression analysis to fit data from Large-Eddy Simulations (LES) and apply Fourier transformation from a time domain to a frequency domain. The objective is to use Fourier transform analysis to determine eddy size distribution and turbulent cascade dissipation in a control volume by analyzing the frequency of velocities. By calculating such eddy size distribution, we may quantify Turbulence in said control volume and compare results with the traditional Kolmogorov method.

Effects of Buoyancy on Laminar Flow in Curved Elliptic Ducts

1992 ◽  
Vol 114 (4) ◽  
pp. 936-943 ◽  
Author(s):  
Z. F. Dong ◽  
M. A. Ebadian
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Published Data ◽  
Circular Duct ◽  
Uniform Wall Temperature ◽  
Wide Range

This paper numerically investigates the effects of buoyancy on fully developed laminar flow in a curved duct with an elliptic cross section. The flow of Newtonian fluids is assumed steady in terms of Boussinesq approximation. The curved elliptic duct is subjected to thermal boundary conditions of axially uniform heat flux and peripherally uniform wall temperature. The numerically generated boundary-fitted coordinate system is applied to discretize the solution domain of the elliptic duct, and the Navier-Stokes equations and the energy equation, including the curvature ratio, are solved by use of the control volume-based finite difference method. The solution covers a wide range of curvature ratios, and Dean and Grashof numbers. The results presented are displayed graphically and in tabular form to illustrate the buoyancy effect. It is further shown that buoyancy acts to increase both the Nusselt number and the friction factor and changes the distribution of the velocity and the temperature. The results for the curved circular duct with and without buoyancy are compared with the data available in the open literature for all cases. Also compared with the published data are the results of laminar flow in a curved elliptic duct, and very good agreement is obtained.

Sign in / Sign up

Export Citation Format

Share Document