On the laminar flow in a free jet of liquid at high Reynolds numbers

1968 ◽  
Vol 32 (2) ◽  
pp. 273-292 ◽  
Author(s):  
J. P. K. Tillett
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Applied Pressure ◽  
Reynolds Numbers ◽  
Momentum Balance ◽  
Free Jet ◽  
Contraction Ratio ◽  
Asymptotic Contraction ◽  
Classical Boundary ◽  
High Reynolds

This paper is concerned with the jet of liquid, open to the atmosphere, that emerges from a two-dimensional channel in which there is Poiseuille flow far upstream, the flow being driven by an applied pressure gradient. The problem is discussed with the aid of the method of matched asymptotic expansions; the small parameter involved is the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow there (for moderate distances downstream); the influence of this boundary layer on the flow in the core of the jet is then investigated. Higher-order boundary-layer effects, such as indeterminacy and eigensolutions, are also discussed. The first few terms are found of an asymptotic expansion for the equation of the free surface, and considerations of momentum balance are applied to find the asymptotic contraction ratio of the jet.

Non-uniqueness in wakes and boundary layers

1984 ◽  
Vol 391 (1800) ◽  
pp. 1-26 ◽  
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Near Wake ◽  
Algebraic Decay ◽  
Scale Separation ◽  
Boundary Layer Equations ◽  
Classical Boundary ◽  
Streamlined Flow ◽  
High Reynolds

In streamlined flow past a flat plate aligned with a uniform stream, it is shown that ( a ) the Goldstein near-wake and ( b ) the Blasius boundary layer are non-unique solutions locally for the classical boundary layer equations, whereas ( c ) the Rott-Hakkinen very-near-wake appears to be unique. In each of ( a ) and ( b ) an alternative solution exists, which has reversed flow and which apparently cannot be discounted on immediate grounds. So, depending mainly on how the alternatives for ( a ), ( b ) develop downstream, the symmetric flow at high Reynolds numbers could have two, four or more steady forms. Concerning non-streamlined flow, for example past a bluff obstacle, new similarity forms are described for the pressure-free viscous symmetric closure of a predominantly slender long wake beyond a large-scale separation. Features arising include non-uniqueness, singularities and algebraic behaviour, consistent with non-entraining shear layers with algebraic decay. Non-uniqueness also seems possible in reattachment onto a solid surface and for non-symmetric or pressure-controlled flows including the wake of a symmetric cascade.

Steady Laminar Axisymmetrical Nozzle Flow at Moderate Reynolds Numbers: Modeling and Experiment

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
X. Grandchamp ◽  
Y. Fujiso ◽  
B. Wu ◽  
A. Van Hirtum
Keyword(s):  
Boundary Layer ◽  
Nozzle Exit ◽  
Transverse Velocity ◽  
Reynolds Numbers ◽  
Universal Functions ◽  
Free Jet ◽  
Simple Boundary ◽  
Contraction Ratio ◽  
Moderate Reynolds Number ◽  
Friction Parameters

Flow through an axisymmetrical parameterized contraction nozzle of limited size with area contraction ratio 21.8 and total length 6 cm is studied for moderate Reynolds numbers 300 < Re < 20,200. The transverse flow profiles at the nozzle exit are characterized by hot film anemometry for two different spatial step sizes. The flow at the exit is laminar and uniform in its core. Boundary layer characteristics at the nozzle exit are estimated from the transverse velocity profiles. Flow throughout the nozzle is modeled by implementing Thwaites laminar axisymmetrical boundary layer solutions in an iterative algorithm for which both universal functions, describing the shape factor and skin friction parameters respectively, are altered by adding a constant. The value of the constants is determined by fitting the modified universal functions to tabulated values reported in Blevins (Blevins, R., 1992, Applied Fluid Dynamics Handbook. Krieger, Malabar, FL.). The model is validated on the measured data. Adding nonzero constants to the universal functions improves the prediction of boundary layer characteristics so that the range of Reynolds numbers for which the discrepancy with experimental findings is less than 4% is extended from Re > 3000 to Re > 1000. Therefore, the studied contraction nozzle is of use for applications requiring a small nozzle with known low turbulence flow at the exit such as moderate Reynolds number free jet studies or bio fluid mechanics (respiration, speech production,…) and the flow at the exit of the nozzle can be accurately described by a simple boundary layer algorithm for Re > 1000.

A ‘stick-slip’ problem related to the motion of a free jet at low Reynolds numbers

1970 ◽  
Vol 67 (2) ◽  
pp. 477-489 ◽  
Author(s):  
S. Richardson
Keyword(s):  
Numerical Technique ◽  
Constant Width ◽  
Reynolds Numbers ◽  
Dimensional Case ◽  
Momentum Balance ◽  
Two Dimensional ◽  
Stick Slip ◽  
Axisymmetric Case ◽  
Contraction Ratio ◽  
High Reynolds

A problem in fluid mechanics which has received some attention recently concerns the emergence of an incompressible Newtonian fluid jet from a uniform tube into an inviscid atmosphere. Both the axisymmetric case of a circular tube and the two-dimensional case of flow from between parallel planes are of interest. When the jet falls vertically under gravity, the motion far downstream is dominated by gravity and the expansion procedures of Clarke (3), and Kaye and Vale (10) give details of the flow in this region. When the flow near the exit is at a high Reynolds number, it is reasonable to expect the flow appropriate to that in an infinite tube to prevail right up to the exit (except, perhaps, near the point of discontinuity of the boundary conditions). With this assumption, Duda and Vrentas(5) use a numerical technique to solve for the flow in the axisymmetric jet beyond the exit, both with and without gravity acting in the axial direction. In the absence of gravity, the jet can be expected to attain a constant width some distance downstream, and at high Reynolds numbers the above assumption is sufficient to allow a mass and momentum balance to determine the contraction ratio of the jet as for the axisymmetric case, and for the two-dimensional case (see Harmon (8)). By treating the dynamics of the jet as those of a boundary layer growing on the free surface, Goren and Wronski (6) and Tillett (18) are able to examine the flow in greater detail.

Effects of Reynolds Number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor Cascade

2000 ◽  
Author(s):  
Heinz-Adolf Schreiber ◽  
Wolfgang Steinert ◽  
Bernhard Küsters
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
High Reynolds Numbers ◽  
High Turbulence ◽  
High Reynolds

An experimental and analytical study has been performed on the effect of Reynolds number and free-stream turbulence on boundary layer transition location on the suction surface of a controlled diffusion airfoil (CDA). The experiments were conducted in a rectilinear cascade facility at Reynolds numbers between 0.7 and 3.0×106 and turbulence intensities from about 0.7 to 4%. An oil streak technique and liquid crystal coatings were used to visualize the boundary layer state. For small turbulence levels and all Reynolds numbers tested the accelerated front portion of the blade is laminar and transition occurs within a laminar separation bubble shortly after the maximum velocity near 35–40% of chord. For high turbulence levels (Tu > 3%) and high Reynolds numbers transition propagates upstream into the accelerated front portion of the CDA blade. For those conditions, the sensitivity to surface roughness increases considerably and at Tu = 4% bypass transition is observed near 7–10% of chord. Experimental results are compared to theoretical predictions using the transition model which is implemented in the MISES code of Youngren and Drela. Overall the results indicate that early bypass transition at high turbulence levels must alter the profile velocity distribution for compressor blades that are designed and optimized for high Reynolds numbers.

Airfoil Trailing Edge Noise Reduction Using a Boundary-Layer Bump

2019 ◽  
Vol 105 (5) ◽  
pp. 814-826 ◽  
Author(s):  
Yuejun Shi ◽  
Seongkyu Lee
Keyword(s):  
Boundary Layer ◽  
Noise Reduction ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Numerical Approach ◽  
Trailing Edge ◽  
Velocity Deficit ◽  
Trailing Edge Noise ◽  
Field Noise ◽  
High Reynolds

This paper presents a new idea of reducing airfoil trailing edge noise using a small bump in the turbulent boundary layer. First, we develop and validate a new computational approach to predict airfoil trailing edge noise using steady RANS CFD, an empirical wall pressure spectrum model, and Howe's diff raction theory. This numerical approach enables fast and accurate predictions of trailing edge noise, which is used to study the noise reduction from the bump for various airfoil geometries and flow conditions at high Reynolds numbers. Three types of bumps, the suction-side bump, pressure-side bump, and both-side bumps, are studied. The results show that all types of bumps are able to reduce far-field noise up to 10 dB compared to clean airfoils, but their impacts are diff erent in terms of the eff ective frequency range. Also, bumps with four diff erent heights are compared with each other to investigate the eff ect of the height of bumps on noise reduction. It is demonstrated that a bump causes velocity deficit within the boundary layer near the wall. This velocity deficit results in reduced turbulence kinetic energy near the wall, which is responsible for trailing edge noise reduction. Overall, this paper demonstrates the potential of a boundary-layer bump in trailing edge noise reduction and sheds light on the physical mechanism of noise reduction with boundary-layer bumps.

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

Experiments on the Flow Around a Sphere at High Reynolds Numbers

1969 ◽  
Vol 36 (3) ◽  
pp. 598-607 ◽  
Author(s):  
T. Maxworthy
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Distribution ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Recirculation Region ◽  
Layer Separation ◽  
High Reynolds Numbers ◽  
High Reynolds

Flow around a sphere for Reynolds numbers between 2 × 105 and 6 × 104 has been observed by measuring the pressure distribution around a circle of longitude under a variety of conditions. These include the effects of laminar and turbulent boundary layer separation, tunnel blockage, various boundary layer trip arrangements and inserting an object to disrupt the unsteady, recirculation region behind the sphere.

Sign in / Sign up

Export Citation Format

Share Document