scholarly journals Characterization of the Behavior of Confined Laminar Round Jets

2012 ◽  
Author(s):  
D. Tyler Landfried ◽  
A. Jana ◽  
M. L. Kimber
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Expansion Ratio ◽  
Downstream Location ◽  
Practical Applications ◽  
Free Jet ◽  
Laminar Jet ◽  
Jet Behavior

Confined laminar fluid jets have many practical applications in industry. Several examples include expansions in pipes and flow of gas into a large plenum. While much consideration has been given experimentally to heat transfer and pressure gradients within the confinement, little attention has been paid to quantify the velocity profiles and transitions between various flow behaviours. Using a finite volume CFD code, OpenFOAM ®, the Navier-Stokes equations were solved for varying expansion ratio, 1/ε = renclosure/rj, and varying Reynolds numbers. In the present analysis, Reynolds number based on the inlet jet diameter is varied from 30 to 70, well within the accepted range for laminar jet behavior. The expansion ratio, 1/ε is varied from 20–200. Of primary focus in the current study are compact correlations for the jet centreline velocity as a function of jet Reynolds number, Rej and expansion ratio. Similar functional dependences for the “linear” decay region of the jet, and the location of the stagnation point on the enclosure wall, are also investigated. These are all important features of the global flow field for the confined jet. Results suggest that initially, the flow characteristics are identical to a free jet. At some downstream location, the presence of the enclosure is felt by the jet and deviations begin to be seen from free jet behavior. This transition region continues until at a sufficiently large downstream location, the flow becomes fully developed, internal Poiseuille flow. In this paper, we analyse these transition regions and offer explanations and practical correlations to successfully predict the important flow physics that occur between free jet behavior and Poiseuille flow. Key dimensionless parameters are identified, the magnitude of which can be used to classify the flow conditions.

Pressure, Frictional Resistance, and Flow Characteristics of the Partially Wetted Rotating Disk

1968 ◽  
Vol 90 (2) ◽  
pp. 395-404 ◽  
Author(s):  
H. N. Ketola ◽  
J. M. McGrew
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Flow Characteristics ◽  
Frictional Resistance ◽  
Rotating Disk ◽  
Practical Applications ◽  
Stationary Wall ◽  
Spacing Ratio ◽  
Analytical Expressions

A theory of the partially wetted rotating disk is described and experimental data presented which verify the application of this theory in practical applications. Four different flow regimes may be identified according to the value of the disk Reynolds number and the spacing ratio between the disk and stationary wall. The analytical expressions for prediction of the pressure gradient developed and the frictional resistance are uniquely determined by the disk Reynolds number, spacing ratio, and the degree of wetting of the disk.

scholarly journals Flow Characteristics of the Entrance Region with Roughness Effect within Rectangular Microchannels

Micromachines ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 30
Author(s):  
Haiwang Li ◽  
Yujia Li ◽  
Binghuan Huang ◽  
Tiantong Xu
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Stokes Equations ◽  
Critical Role ◽  
Flow Characteristics ◽  
Entrance Region ◽  
Working Fluid ◽  
Asymmetric Distribution ◽  
Rectangular Microchannels ◽  
Aspect Ratios

We conducted systematic numerical investigations of the flow characteristics within the entrance region of rectangular microchannels. The effects of the geometrical aspect ratio and roughness on entrance lengths were analyzed. The incompressible laminar Navier–Stokes equations were solved using finite volume method (FVM). In the simulation, hydraulic diameters ( D h ) ranging from 50 to 200 µm were studied, and aspect ratios of 1, 1.25, 1.5, 1.75, and 2 were considered as well. The working fluid was set as water, and the Reynolds number ranged from 0.5 to 100. The results showed a good agreement with the conducted experiment. Correlations are proposed to predict the entrance lengths of microchannels with respect to different aspect ratios. Compared with other correlations, these new correlations are more reliable because a more practical inlet condition was considered in our investigations. Instead of considering the influence of the width and height of the microchannels, in our investigation we proved that the critical role is played by the aspect ratio, representing the combination of the aforementioned parameters. Furthermore, the existence of rough elements obviously shortens the entrance region, and this effect became more pronounced with increasing relative roughness and Reynolds number. A similar effect could be seen by shortening the roughness spacing. An asymmetric distribution of rough elements decreased the entrance length compared with a symmetric distribution, which can be extrapolated to other irregularly distributed forms.

scholarly journals Confined axisymmetric laminar jets with large expansion ratios

2002 ◽  
Vol 456 ◽  
pp. 319-352 ◽  
Author(s):  
A. REVUELTA ◽  
A. L. SÁNCHEZ ◽  
A. LIÑÁN
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Outer Region ◽  
Outer Wall ◽  
Relevant Parameter ◽  
Order Unity ◽  
Laminar Jet ◽  
Recirculating Flow ◽  
Large Expansion ◽  
Downstream Flow

This paper investigates the steady round laminar jet discharging into a coaxial duct when the jet Reynolds number, Rej, is large and the ratio of the jet radius to the duct radius, ε, is small. The analysis considers the distinguished double limit in which the Reynolds number Rea = Rejε for the final downstream flow is of order unity, when four different regions can be identified in the flow field. Near the entrance, the outer confinement exerts a negligible influence on the incoming jet, which develops as a slender unconfined jet with constant momentum flux. The jet entrains outer fluid, inducing a slow back flow motion of the surrounding fluid near the backstep. Further downstream, the jet grows to fill the duct, exchanging momentum with the surrounding recirculating flow in a slender region where the Reynolds number is still of the order of Rej. The streamsurface bounding the toroidal vortex eventually intersects the outer wall, in a non-slender transition zone to the final downstream region of parallel streamlines. In the region of jet development, and also in the main region of recirculating flow, the boundary-layer approximation can be used to describe the flow, while the full Navier–Stokes equations are needed to describe the outer region surrounding the jet and the final transition region, with Rea = Rejε entering as the relevant parameter to characterize the resulting non-slender flows.

Numerical Simulation of Flow in a Wavy Wall Microchannel Using Immersed Boundary Method

2020 ◽  
Vol 13 (2) ◽  
pp. 118-125
Author(s):  
Mithun Kanchan ◽  
Ranjith Maniyeri
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Immersed Boundary Method ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Immersed Boundary ◽  
Solid Boundary ◽  
Wavy Wall ◽  
Dirac Delta ◽  
Boundary Method

Background: Fluid flow in microchannels is restricted to low Reynolds number regimes and hence inducing chaotic mixing in such devices is a major challenge. Over the years, the Immersed Boundary Method (IBM) has proved its ability in handling complex fluid-structure interaction problems. Objectives: Inspired by recent patents in microchannel mixing devices, we study passive mixing effects by performing two-dimensional numerical simulations of wavy wall in channel flow using IBM. Methods: The continuity and Navier-Stokes equations governing the flow are solved by fractional step based finite volume method on a staggered Cartesian grid system. Fluid variables are described by Eulerian coordinates and solid boundary by Lagrangian coordinates. A four-point Dirac delta function is used to couple both the coordinate variables. A momentum forcing term is added to the governing equation in order to impose the no-slip boundary condition between the wavy wall and fluid interface. Results: Parametric study is carried out to analyze the fluid flow characteristics by varying amplitude and wavelength of wavy wall configurations for different Reynolds number. Conclusion: Configurations of wavy wall microchannels having a higher amplitude and lower wavelengths show optimum results for mixing applications.

Stationary perturbations of Couette–Poiseuille flow: the flow development in long cavities and channels

1995 ◽  
Vol 292 ◽  
pp. 153-182 ◽  
Author(s):  
Jennifer R. Stocker ◽  
Peter W. Duck
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Poiseuille Flow ◽  
Stokes Equations ◽  
Branching Processes ◽  
Reynolds Numbers ◽  
Streamwise Direction ◽  
End Effects ◽  
Driven Cavity ◽  
Streamwise Pressure Gradient

We consider stationary perturbations to Couette–Poiseuille flows. These may be considered to be related to far downstream/upstream entry/end effects in flow inside long cavities and channels. Three distinct classes of basic flow are considered, all of which are exact solutions of the Navier–Stokes equations. We first study the problem in the case of Poiseuille flow, and are able to explain a previous discrepancy between fully numerical results, and asymptotic theory valid for large Reynolds numbers, R. The second case, which may be derived from a combination of an imposed streamwise pressure gradient and sliding of the upper channel wall, is for the particular situation where the flow on the lower surface is on the verge of reversing direction. The third case is relevant to the flow inside a long driven cavity (with closed ends, no imposed streamwise pressure gradient and no net mass flux). The flow is driven exclusively by a sliding top wall and mass conservation demands that the flow is no longer unidirectional.For low Reynolds numbers, the stationary eigenvalues in all cases considered are complex (and hence are not monotonic in the streamwise direction). Indeed as R → 0 the eigenvalues become completely independent of the base profile. As the Reynolds number is increased, the eigenvalues generally undergo a number of branching processes switching between being complex and real (and vice versa) in nature, and at large Reynolds numbers fall broadly into three distinct categories, namely O(1), O(R−1/7) and O(1/R). In this limit the eigenvalues may be either complex or real (tending to monotonic eigensolutions in the streamwise direction).Of particular interest are certain of the O(1) eigensolutions for the ‘driven-cavity’ problem, in the high-Reynolds-number limit; these turn out to be highly oscillatory (WKB-type) over much of the cavity section.In all three cases, we use a combination of numerical and asymptotic techniques, and a thorough comparison between results thus obtained is made.

Fluid Flow Characteristics Around a Pair of Diamond-Shaped Cylinders in Side-by-Side and Tandem Arrangements

2011 ◽  
Author(s):  
Shuichi Torii ◽  
Noritugu Ueda ◽  
Zijie Lin
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Time History ◽  
Flow Patterns ◽  
Separation Distance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Gap Spacing

The present study deals with unsteady laminar fluid flow phenomena around a pair of diamond-shaped cylinders in free stream. Emphasis is placed on the effects of the Reynolds number, Re, and the ratio of cylinder separation distance to length of diamond-shaped cylinder, s/d, on the flow patterns in side-by-side and tandem arrangements. The Navier-Stokes equations are discretized using finite difference method to determine the time history of velocity vector in the flow field. The Reynolds numbers, Re, is ranged from 30 to 300 and gap spacing, s/d, is varied from 0.0 to 2.5 for side-by-side and 0.0 to 5.0 for tandem, respectively. The results are compared with the experimental results with the aid of flow visualization method. The study discloses that (i) the generations of Karman vortex streets behind the diamond-shaped cylinders are intensified with an increase in the Reynolds number, (ii) the categorized flow patterns in the wake region of the diamond-shaped islands are affected by s/d, and (iii) the vortex shedding frequency in the wake of diamond-shaped cylinders depends on both the gap spacing and the formation of the vortices.

Vortex Formation for Different Geometry of Cavities Using High Reynolds Number

2014 ◽  
Vol 699 ◽  
pp. 416-421
Author(s):  
Mohd Noor Asril Saadun ◽  
Muhammad Zulhakim Sharudin ◽  
Nor Azwadi Che Sidik ◽  
Mohd Hafidzal Mohd Hanafi
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Contaminant Removal ◽  
Navier Stokes Equations ◽  
High Reynolds

A preliminary study of Computational Fluid Dynamics (CFD) on the effect of high Reynolds numbers in the cavity has been carried out. Two dimensional model analysis of the flow characteristics were conducted using the numerical solution of Navier-Stokes equations based on the finite difference method. The flow characteristics in the cavity and the driven flow were modeled via turbulence equation modelling. This paper focuses on the effects of different high Reynolds number on the flow pattern of contaminant removal in the cavity. Different types of geometry and aspect ratio of the geometry were used as the parameters of the cavity in this study. Based on visualization of flows between each model with the different parameters used, the results of a comparison analysis focusing on the behavior of the flow were reported.

Analysis of Fluid Flow Under a Grinding Wheel

1991 ◽  
Vol 113 (2) ◽  
pp. 190-197 ◽  
Author(s):  
M. R. Schumack ◽  
Jin-Bok Chung ◽  
W. W. Schultz ◽  
E. Kannatey-Asibu
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Lubrication Theory ◽  
Grinding Wheel ◽  
Perturbation Scheme ◽  
Moderate Reynolds Number ◽  
Reynolds Number Flows ◽  
Good Agreement

Fluid flow under a grinding wheel is modeled using a perturbation scheme. In this initial effort to understand the flow characteristics, we concentrate on the case of a smooth wheel with slight clearance between the wheel and workpiece. The solution at lowest order is that given by standard lubrication theory. Higher-order terms correct for inertial and two-dimensional effects. Experimental and analytical pressure profiles are compared to test the validity of the model. Lubrication theory provides good agreement with low Reynolds number flows; the perturbation scheme provides reasonable agreement with moderate Reynolds number flows but fails at high Reynolds numbers. Results from experiments demonstrate that the ignored upstream and downstream conditions significantly affect the flow characteristics, implying that only a model based on the fully two- (or three-) dimensional Navier-Stokes equations will accurately predict the flow. We make one comparison between an experiment with a grinding wheel and the model incorporating a one-dimensional sinusoidal roughness term. For this case, lubrication theory surprisingly provides good agreement with experiment.

The dimension of attractors underlying periodic turbulent Poiseuille flow

1992 ◽  
Vol 242 ◽  
pp. 1-29 ◽  
Author(s):  
Laurence Keefe ◽  
Parviz Moin ◽  
John Kim
Keyword(s):  
Reynolds Number ◽  
Lower Bound ◽  
Poiseuille Flow ◽  
Stokes Equations ◽  
Coarse Grained ◽  
Turbulent Shear ◽  
Global Dynamics ◽  
Computational Domain ◽  
Turbulent Shear Flow ◽  
Attractor Dimension

Using a coarse grained (16 × 33 × 8) numerical simulation, a lower bound on the Lyapunov dimension, Dλ, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 has been calculated to be approximately 352. These results were obtained on a spatial domain with streamwise and spanwise periods of 1.6π, and correspond to a wall-unit Reynolds number of 80. Comparison of Lyapunov exponent spectra from this and a higher-resolution (16 × 33 × 16) simulation on the same domain shows these spectra to have a universal shape when properly scaled. Using these scaling properties, and a partial exponent spectrum from a still higher-resolution (32 × 33 × 32) simulation, we argue that the actual dimension of the attractor underlying motion on the given computational domain is approximately 780. The medium resolution calculation establishes this dimension as a strong lower bound on this computational domain, while the partial exponent spectrum calculated at highest resolution provides some evidence that the attractor dimension in fully resolved turbulence is unlikely to be substantially larger. These calculations suggest that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier–Stokes equations in such flows. However, the magnitude of the dimension measured invalidates any notion that the global dynamics of such turbulence can be attributed to the interaction of a few degrees of freedom. Dynamical systems theory has provided the first measurement of the complexity of fully developed turbulence; the answer has been found to be dauntingly high.

Computational Studies of Turbulent Flow in an Isothermal Suddenly Enlarged Combustion Chamber

2004 ◽  
Author(s):  
D. P. Mishra ◽  
T. Vishak
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Combustion Chamber ◽  
Shear Layer ◽  
Turbulence Intensity ◽  
Stokes Equations ◽  
Isothermal Condition ◽  
Expansion Ratio ◽  
Computational Studies ◽  
Reattachment Length

The present work is concerned with computational studies of turbulent flow under isothermal condition in a suddenly enlarged combustion chamber using time averaged Navier-Stokes equations with an eddy-viscosity turbulence closure model. Results were compared well with that of experimental data available in open literature. The effect of inlet turbulence intensity is found to be the dominant parameter determining the flow field. However this effect is found to be decreasing with the increase in the expansion ratio. The increase of turbulence level decreases the reattachment length due to the energy supply to the separating shear layer, which is a major factor determining the reattachment length. It has been found out that for same expansion ratio, the reattachment length attains a minimum value for low turbulence Reynolds number, increases with increase in Reynolds number, and attains a maximum limit. Both the turbulent kinetic energy and the turbulent dissipation rate are found to be maximum in the shear layer and also keep increasing with the increase in turbulence intensity.

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