scholarly journals SCALE EFFECTS ON STABILITY AND WAVE REFLECTION REGARDING ARMOR UNITS

1986 ◽  
Vol 1 (20) ◽  
pp. 165 ◽  
Author(s):  
Atsuyuki Shimada ◽  
Toshimi Fujimoto ◽  
Syozo Saito ◽  
Tsutomu Sakakiyama ◽  
Hiromaru Hirakuchi
Keyword(s):  
Reynolds Number ◽  
Scale Effect ◽  
Critical Reynolds Number ◽  
Scale Effects ◽  
Minimum Weight ◽  
Small Scale ◽  
Large Wave ◽  
Wave Flume ◽  
Scale Test ◽  
The Stability

In the studies on stability of the armor units and reflection from those, there are some indications on scale effects which are included in the results of small scale experiments. In this study, the fact has been confirmed with large wave flume test, and estimated the critical Reynolds Number where was no scale effect. And by this result on the stability of urmor units, we can evaluated the results in small and middle scale test, and can correct the minimum weight of armor units. So we can design the breakwaters and seawalls rationaly and economicaliy. However, it has not been confirmed the critical Reynolds Number where the influence of scale effect on reflection became negligible.

scholarly journals LARGE VERIFICATION TESTS ON ROCK SLOPE STABILITY

1988 ◽  
Vol 1 (21) ◽  
pp. 157
Author(s):  
J.W. Van der Meer ◽  
K.W. Pilarczyk
Keyword(s):  
Large Scale ◽  
Scale Effects ◽  
Rock Slope Stability ◽  
Small Scale ◽  
Rock Slopes ◽  
Ripple Formation ◽  
Scale Test ◽  
Gravel Beaches ◽  
The Stability ◽  
Large Scale Tests

A number of large scale tests on stability of rock slopes and gravel beaches is described and compared with small scale test results. The following topics are treated: the stability of a rock armour layer, the profile formation of a berm breakwater, the profile formation of gravel beaches, including ripple formation, and reflection and overtopping on rock slopes. The general conclusion is that scale effects could not be found.

scholarly journals Non-normal origin of modal instabilities in rotating plane shear flows

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190550
Author(s):  
Sharath Jose ◽  
Rama Govindarajan
Keyword(s):  
Reynolds Number ◽  
Shear Flows ◽  
Critical Reynolds Number ◽  
Flow System ◽  
Neutral Line ◽  
Plane Couette Flow ◽  
Plane Shear ◽  
Perturbation Amplitude ◽  
Fundamental Reason ◽  
The Stability

Small variations introduced in shear flows are known to affect stability dramatically. Rotation of the flow system is one example, where the critical Reynolds number for exponential instabilities falls steeply with a small increase in rotation rate. We ask whether there is a fundamental reason for this sensitivity to rotation. We answer in the affirmative, showing that it is the non-normality of the stability operator in the absence of rotation which triggers this sensitivity. We treat the flow in the presence of rotation as a perturbation on the non-rotating case, and show that the rotating case is a special element of the pseudospectrum of the non-rotating case. Thus, while the non-rotating flow is always modally stable to streamwise-independent perturbations, rotating flows with the smallest rotation are unstable at zero streamwise wavenumber, with the spanwise wavenumbers close to that of disturbances with the highest transient growth in the non-rotating case. The instability critical rotation number scales inversely as the square of the Reynolds number, which we demonstrate is the same as the scaling obeyed by the minimum perturbation amplitude in non-rotating shear flow needed for the pseudospectrum to cross the neutral line. Plane Poiseuille flow and plane Couette flow are shown to behave similarly in this context.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Linear Spatial Stability of Developing Flow in a Parallel Plate Channel

1981 ◽  
Vol 48 (1) ◽  
pp. 192-194 ◽  
Author(s):  
S. C. Gupta ◽  
V. K. Garg
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Parallel Plate ◽  
Critical Reynolds Number ◽  
Two Dimensional ◽  
Spatial Stability ◽  
Percent Change ◽  
Developing Flow ◽  
The Stability ◽  
Plate Channel

It is found that even a 5 percent change in the velocity profile produces a 100 percent change in the critical Reynolds number for the stability of developing flow very close to the entrance of a two-dimensional channel.

Drag Reduction and VIV Suppression Behaviour of LGS Technology Integral to Drilling Riser Buoyancy Units

2016 ◽  
Author(s):  
H. Marcollo ◽  
A. E. Potts ◽  
D. R. Johnstone ◽  
P. Pezet ◽  
P. Kurts
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Critical Reynolds Number ◽  
Hydrodynamic Performance ◽  
Small Scale ◽  
Practical Reasons ◽  
Cylindrical Shape ◽  
Reynolds Number Flow ◽  
Helical Strakes ◽  
Number Flow

Drilling risers are regularly deployed in deep water (over 1500 m) with large sections covered in buoyancy modules. The smooth cylindrical shape of these modules can result in significant vortex-induced vibration (VIV) response, causing an overall amplification of drag experienced by the riser. Operations can be suspended due to the total drag adversely affecting top and bottom angles. Although suppression technologies exist to reduce VIV (such as helical strakes or fairings), and therefore reduce VIV-induced amplification of drag, only fairings are able to be installed onto buoyancy modules for practical reasons, and fairings themselves have significant penalties related to installation, removal, and reliability. An innovative solution has been developed to address this gap; LGS (Longitudinally Grooved Suppression)1. Two model testing campaigns were undertaken; small scale (sub-critical Reynolds Number flow), and large scale (post-critical Reynolds Number flow) to test and confirm the performance benefits of LGS. The testing campaigns found substantial benefits measured in hydrodynamic performance that will be realized when LGS modules are deployed by operators for deepwater drilling operations.

The Stability of Water Flow Over Heated and Cooled Flat Plates

1968 ◽  
Vol 90 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Ahmed R. Wazzan ◽  
T. Okamura ◽  
A. M. O. Smith
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Stream Temperature ◽  
Heated Wall ◽  
Flat Plates ◽  
Critical Reynolds Numbers ◽  
The Stability ◽  
Sommerfeld Equation

The theory of two-dimensional instability of laminar flow of water over solid surfaces is extended to include the effects of heat transfer. The equation that governs the stability of these flows to Tollmien-Schlichting disturbances is the Orr-Sommerfeld equation “modified” to include the effect of viscosity variation with temperature. Numerical solutions to this equation at high Reynolds numbers are obtained using a new method of integration. The method makes use of the Gram-Schmidt orthogonalization technique to obtain linearly independent solutions upon numerically integrating the “modified Orr-Sommerfeld” equation using single precision arithmetic. The method leads to satisfactory answers for Reynolds numbers as high as Rδ* = 100,000. The analysis is applied to the case of flow over both heated and cooled flat plates. The results indicate that heating and cooling of the wall have a large influence on the stability of boundary-layer flow in water. At a free-stream temperature of 60 deg F and wall temperatures of 60, 90, 120, 135, 150, 200, and 300deg F, the critical Reynolds numbers Rδ* are 520, 7200, 15200, 15600, 14800, 10250, and 4600, respectively. At a free-stream temperature of 200F and wall temperature of 60 deg F (cooled case), the critical Reynolds number is 151. Therefore, it is evident that a heated wall has a stabilizing effect, whereas a cooled wall has a destabilizing effect. These stability calculations show that heating increases the critical Reynolds number to a maximum value (Rδ* max = 15,700 at a temperature of TW = 130 deg F) but that further heating decreases the critical Reynolds number. In order to determine the influence of the viscosity derivatives upon the results, the critical Reynolds number for the heated case of T∞ = 40 and TW = 130 deg F was determined using (a) the Orr-Sommerfeld equation and (b) the present governing equation. The resulting critical Reynolds numbers are Rδ* = 140,000 and 16,200, respectively. Therefore, it is concluded that the terms pertaining to the first and second derivatives of the viscosity have a considerable destabilizing influence.

The stability of the flow of an elastic-viscous liquid in a curves channel

1963 ◽  
Vol 274 (1358) ◽  
pp. 371-385 ◽  
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Viscous Liquid ◽  
Critical Reynolds Number ◽  
Curved Channel ◽  
Main Effect ◽  
The Stability

Consideration is given to the stability of the flow of an idealized elastico-viscous liquid in a narrow curved channel, the motion being due to a pressure gradient acting around the channel. It is shown that the main effect of the elasticity of the liquid is to lower the value of the critical Reynolds number at which instability occurs.

Accurate solution of the Orr–Sommerfeld stability equation

1971 ◽  
Vol 50 (4) ◽  
pp. 689-703 ◽  
Author(s):  
Steven A. Orszag
Keyword(s):  
Reynolds Number ◽  
Chebyshev Polynomials ◽  
Critical Reynolds Number ◽  
Great Accuracy ◽  
Accurate Solution ◽  
Plane Poiseuille Flow ◽  
Stability Equation ◽  
Orthogonal Functions ◽  
The Stability ◽  
Sommerfeld Equation

The Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm. It is shown that results of great accuracy are obtained very economically. The method is applied to the stability of plane Poiseuille flow; it is found that the critical Reynolds number is 5772·22. It is explained why expansions in Chebyshev polynomials are better suited to the solution of hydrodynamic stability problems than expansions in other, seemingly more relevant, sets of orthogonal functions.

Viscous Scaling Phenomena in Miniature Centrifugal Flow Cooling Fans: Theory, Experiments and Correlation

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Patrick A. Walsh ◽  
Edmond J. Walsh ◽  
Ronan Grimes
Keyword(s):  
Reynolds Number ◽  
Scale Effects ◽  
Pressure Coefficient ◽  
Pressure Rise ◽  
Chord Length ◽  
Flow Coefficient ◽  
Power Coefficient ◽  
Small Scale ◽  
Cooling Fans ◽  
Novel Theory

This paper analyzes the scale effects that occur in miniature centrifugal flow fans and investigates the possibility of optimizing blade geometry so that performance can be enhanced. Such fans are typically employed in small scale heat sinks such as those used for processor cooling applications or in portable electronics. The specific design parameter varied is the blade chord length, and the resulting fan performance is gauged by examining the flow rate, pressure rise, and power consumption characteristics. The former two are measured using a BS 848 fan characterization rig and the latter, by directly measuring the power consumed. These characteristics are studied for three sets of scaled fans with diameters of 15 mm, 24 mm, and 30 mm, and each set considers six individual blade chord lengths. A novel theory is put forward to explain the anticipated effect of changing this parameter, and the results are analyzed in terms of the relevant dimensionless parameters: Reynolds number, chord length to diameter of fan ratio, flow coefficient, pressure coefficient, and power coefficient. When these characteristic parameters are plotted against the Reynolds number, similar trends are observed as the chord length is varied in all sets of scaled fans. The results show that the flow coefficient for all the miniature fans degrade at low Re values, but the onset of this degradation was observed at higher Re values for longer blade chord designs. Conversely, it was found that the pressure coefficient is elevated at low Re, and the onset Re for this phenomenon correlates well with the drop off in flow coefficient. Finally, the trend in power coefficient data is similar to that for the flow coefficient. The derived theory is used to correlate this data for which all data points fall within 6% of the correlation. Overall, the findings reported herein provide a good understanding of how changing the blade chord length affects the performance of miniature centrifugal fans; hence, providing fan designers with guidelines to aid in developing optimum blade designs, which minimize adverse scaling phenomena.

Experimental Study on the Stability of the Flow Behind an Accelerating Circular Cylinder

2007 ◽  
Author(s):  
A. Inasawa ◽  
K. Toda ◽  
M. Asai
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Cylinder Wake ◽  
Global Instability ◽  
The Stability ◽  
Dimensional Instability ◽  
Wake Oscillation

Disturbance growth in the wake of a circular cylinder moving at a constant acceleration is examined experimentally. The cylinder is installed on a carriage moving in the still air. The results show that the critical Reynolds number for the onset of the global instability leading to a self-sustained wake oscillation increases with the magnitude of acceleration, while the Strouhal number of the growing disturbance at the critical Reynolds number is not strongly dependent on the magnitude of acceleration. It is also found that with increasing the acceleration, the Ka´rma´n vortex street remains two-dimensional even at the Reynolds numbers around 200 where the three-dimensional instability occurs to lead to the vortex dislocation in the case of cylinder moving at constant velocity or in the case of cylinder wake in the steady oncoming flow.

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