Measurement and Observation of Jet Thrust for Water Flow Through Micro-Orifice

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Akiomi Ushida ◽  
Tomiichi Hasegawa ◽  
Takehiro Hoshina ◽  
Shouta Kudou ◽  
Hiroshige Uchiyama ◽  
...  
Keyword(s):  
Elastic Stress ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Biological Applications ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
Orifice Flow ◽  
Flow Through ◽  
The Many

Owing to the many potential industrial and biological applications of microfluid mechanics, it has recently become an attractive research topic. However, researchers have mainly concentrated on microchannel flows and studies investigating micro-orifice flows are rare cases. In the present study, the results from experiments conducted on flows through micro-orifices with diameters of 100 μm, 50 μm, and 25 μm are presented. In these experiments, the thrust and diameter of observed outflow jets are measured. The resultant thrust and diameter of the jets for the 100 μm orifice flow agree with the numerical predictions obtained via the Navier–Stokes equations. Conversely, for an orifice with a diameter of 50 μm or less, it is found that the thrust is lower than that predicted and the existence of jet swell becomes apparent. With the estimated elastic stress proportional to squared mean velocity, a change in the elasticity of the water as it flows through a micro-orifice is strongly suggested.

Numerical Study of the Pulsating Flow at the Tongue Region of a Centrifugal Pump for Several Flow Rates

2008 ◽  
Author(s):  
Rau´l Barrio ◽  
Jorge Parrondo ◽  
Eduardo Blanco ◽  
Joaqui´n Ferna´ndez
Keyword(s):  
Unsteady Flow ◽  
Centrifugal Pump ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
Partial Load ◽  
Flow Through

A numerical study is presented on the unsteady flow at the tongue region of a single suction volute-type centrifugal pump with a specific speed of 0.46. The flow through the pump, available at laboratory, was simulated by means of a commercial CFD software that solved the Reynolds averaged Navier-Stokes equations for three-dimensional unsteady flow (3D-URANS). A sensitivity analysis of the numerical model was carried out and the numerical predictions were compared with previous experimental results of both global and unsteady variables. Once validated, the model was used to study the flow pulsations associated to the interaction between the impeller blades and the volute tongue as a function of the flow rate, from partial load to overload. The study allowed relating the passage of the impeller blades with the tangential and radial velocity pulsations at some reference positions and with the pressure pulsations at the tongue region.

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

Some numerical experiments on developing laminar flow in circular-sectioned bends

1985 ◽  
Vol 154 ◽  
pp. 357-375 ◽  
Author(s):  
J. A. C. Humphrey ◽  
H. Iacovides ◽  
B. E. Launder
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Numerical Predictions

The paper reports numerical solutions to a semi-elliptic truncation of the Navier–Stokes equations for the case of developing laminar flow in circular-sectioned bends over a range of Dean numbers. The ratios of bend radius to pipe radius are 7:1 and 20:1, corresponding with the configurations examined experimentally by Talbot and his co-workers in recent years. The semi-elliptic treatment facilitates a much finer grid than has been possible in earlier studies. Numerical accuracy has been further improved by assuming radial equilibrium over a thin sublayer immediately adjacent to the wall and by re-formulating the boundary conditions at the pipe centre.Streamwise velocity profiles at Dean numbers of 183 and 565 are in excellent agreement with laser-Doppler measurements by Agrawal, Talbot & Gong (1978). Good, albeit less complete, accord is found with the secondary velocities, though the differences that exist may be mainly due to the difficulty of making these measurements. The paper provides new information on the behaviour of the streamwise shear stress around the inner line of symmetry. Upstream of the point of minimum shear stress, our numerical predictions display a progressive shift towards the result of Stewartson, Cebici & Chang (1980) as the Dean number is successively raised. Downstream of the minimum, however, in contrast with the monotonic approach to an asymptotic level reported by Stewartson, the numerical solutions display a damped oscillatory behaviour reminiscent of those from Hawthorne's (1951) inviscid-flow calculations. The amplitude of the oscillation grows as the Dean number is raised.

Probability Density Functions of Vorticities in Turbulent Channels with Effects of Blowing and Suction

2016 ◽  
Vol 17 (2) ◽  
pp. 127-135
Author(s):  
Can Liu ◽  
Xi Chen
Keyword(s):  
New York ◽  
Probability Density ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Generalized Hyperbolic Distribution ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Channel Flows ◽  
Probability Density Function Pdf

AbstractThis paper presents direct numerical simulation (DNS) result of the Navier–Stokes equations for turbulent channel flows with blowing and suction effects. The friction Reynolds number is ${\rm{R}}{{\rm{e}}_\tau} = 394$ and a range of blowing and suction conditions is covered with different perturbation strengths, i. e. $A = 0.05, $ 0.1, 0.2. While the mean velocity profile has been severely altered, the probability density function (PDF) for (spanwise) vorticity – depending on wall distance $({y^ +})$ and blowing/suction strength (A) – satisfies the generalized hyperbolic distribution (GHD) of Birnir [The Kolmogorov-Obukhov statistical theory of turbulence, J. Nonlinear Sci. (2013a), doi: 10.1007/s00332-012-9164–z; The Kolmogorov-Obukhov theory of turbulence, Springer, New York, 2013b] in the bulk of the flow. The latter leads to accurate descriptions of all PDFs (at ${y^ +} = 40, $ 200, 390 and $A = 0.05, $ 0.2, for instance) with only four parameters. The result indicates that GHD is a general tool to quantify PDF for turbulent flows under various wall surface conditions.

Effect of a Time-Dependent Stenosis on Flow Through a Tube

1968 ◽  
Vol 90 (2) ◽  
pp. 248-254 ◽  
Author(s):  
D. F. Young
Keyword(s):  
Stokes Equations ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Arterial System ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Dependent Growth ◽  
Abnormal Tissue

A common occurrence in the arterial system is the narrowing of arteries due to the development of atherosclerotic plaques or other types of abnormal tissue development. As these growths project into the lumen of the artery, the flow is disturbed and there develops a potential coupling between the growth and the blood flow through the artery. A discussion of the various possible consequences of this interaction is given. It is noted that very small growths leading to mild stenotic obstructions, although not altering the gross flow characteristics significantly, may be important in triggering biological mechanisms such as intimal cell proliferation or changes in vessel caliber. An analysis of the effect of an axially symmetric, time-dependent growth into the lumen of a tube of constant cross section through which a Newtonian fluid is steadily flowing is presented. This analysis is based on a simplified model in which the convective acceleration terms in the Navier-Stokes equations are neglected. Effect of growth on pressure distribution and wall shearing stress is given and possible biological implications are discussed.

Effect of the turbulence models on Rushton turbine generated flow in a stirred vessel

2011 ◽  
Vol 1 (4) ◽  
Author(s):  
Wajdi Chtourou ◽  
Meriem Ammar ◽  
Zied Driss ◽  
Mohamed Abid
Keyword(s):  
Dissipation Rate ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stirred Vessel ◽  
Rushton Turbine ◽  
Numerical Predictions ◽  
Volume Method

AbstractIn this paper, we performed a comparison of four turbulence models using for numerical simulation of the hydrodynamic structure generated by a Rushton turbine in a cylindrical tank. The finite volume method was employed to solve the Navier-Stokes equations governing the transport of momentum. In this study four closure models tested were: k-ɛ standard, k-ɛ RNG, k-ɛ Realizable and RSM (Reynolds Stress Model). MRF (Multi Reference Frame) technique was used with FLUENT software package. The present work aimed to provide improved predictions of turbulent flow in a stirred vessel and in particular to assess the ability to predict the dissipation rate of turbulent kinetic energy (e) that constitutes a most stringent test of prediction capability due to the small scales at which dissipation takes place. The amplitude of local and overall dissipation rate is shown to be strongly dependent on the choice of turbulence model. The numerical predictions were compared with literature results for comparable configurations and with experimental data obtained using Particle Image Velocimetry (PIV). A very good agreement was found with regards to turbulence.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

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