Rotation numbers

2021 ◽  
pp. 5-36
Author(s):  
Ana Rodrigues
Keyword(s):  
1994 ◽  
Vol 116 (1) ◽  
pp. 133-140 ◽  
Author(s):  
S. Mochizuki ◽  
J. Takamura ◽  
S. Yamawaki ◽  
Wen-Jei Yang

Heat transfer characteristics of a three-pass serpentine flow passage with rotation are experimentally studied. The walls of the square flow passage are plated with thin stainless-steel foils through which electrical current is applied to generate heat. The local heat transfer performance on the four side walls of the three straight flow passages and two turning elbows are determined for both stationary and rotating cases. The throughflow Reynolds, Rayleigh (centrifugal type), and rotation numbers are varied. It is revealed that three-dimensional flow structures cause the heat transfer rate at the bends to be substantially higher than at the straight flow passages. This mechanism is revealed by means of a flow visualization experiment for a nonrotating case. Along the first straight flow passage, the heat transfer rate is increased on the trailing surface but is reduced on the leading surface, due to the action of secondary streams induced by the Coriolis force. At low Reynolds numbers, the local heat transfer performance is primarily a function of buoyancy force. In the higher Reynolds number range, however, the circumferentially averaged Nusselt number is only a weak function of the Rayleigh and rotation numbers.


2007 ◽  
Vol 27 (5) ◽  
pp. 1509-1524 ◽  
Author(s):  
FRITZ COLONIUS ◽  
ROBERTA FABBRI ◽  
RUSSELL JOHNSON

AbstractAverages of functionals along trajectories are studied by evaluating the averages along chains. This yields results for the possible limits and, in particular, for ergodic limits. Applications to Lyapunov exponents and to concepts of rotation numbers of linear Hamiltonian flows and of general linear flows are given.


Author(s):  
Shang-Feng Yang ◽  
Je-Chin Han ◽  
Salam Azad ◽  
Ching-Pang Lee

This paper experimentally investigates the effect of rotation on heat transfer in typical turbine blade serpentine coolant passage with ribbed walls at low Mach numbers. To achieve the low Mach number (around 0.01) condition, pressurized Freon R-134a vapor is utilized as the working fluid. The flow in the first passage is radial outward, after the 180 deg tip turn the flow is radial inward to the second passage, and after the 180 deg hub turn the flow is radial outward to the third passage. The effects of rotation on the heat transfer coefficients were investigated at rotation numbers up to 0.6 and Reynolds numbers from 30,000 to 70,000. Heat transfer coefficients were measured using the thermocouples-copper-plate-heater regional average method. Heat transfer results are obtained over a wide range of Reynolds numbers and rotation numbers. An increase in heat transfer rates due to rotation is observed in radially outward passes; a reduction in heat transfer rate is observed in the radially inward pass. Regional heat transfer coefficients are correlated with Reynolds numbers for nonrotation and with rotation numbers for rotating condition, respectively. The results can be useful for understanding real rotor blade coolant passage heat transfer under low Mach number, medium–high Reynolds number, and high rotation number conditions.


Author(s):  
I-Lun Chen ◽  
Izzet Sahin ◽  
Lesley M. Wright ◽  
Je-Chin Han ◽  
Robert Krewinkel

Abstract The thermal performance of two V-type rib configurations is measured in a rotating, two-pass cooling channel. Modeling modern, high pressure, turbine blades, the cross-section of the cooling channel varies from the first pass to the second pass. The coolant travels radially outward in the rectangular first pass with an aspect ratio of 4:1. Near the tip region, the coolant turns 180°, and travels radially inward in a 2:1 rectangular channel. The serpentine passage is positioned such that both the first and second passes are oriented 90° to the direction of rotation. The leading and trailing surfaces of both the first and second pass of the channel are roughened with V-type rib turbulators. The thermal performance of two V-type configurations is measured in this two-pass channel. The first V-shaped configuration is similar to a traditional V-shaped turbulator with a narrow gap at the apex of the V. The configuration is modified by off-setting one leg of the V to create a staggered discrete, V-shaped configuration. The ribs are oriented 45° relative to the streamwise coolant direction. In both passes, the rib spacing is P/e = 10 and the rib height – to – channel height is e/H = 0.16. The heat transfer enhancement and frictional losses are measured for both rib configurations with varying Reynolds and rotation numbers. The Reynolds number varies from 10,000 to 45,000 in the AR = 4:1 first pass; this corresponds to 16,000 to 73,500 in the AR = 2:1 second pass. Considering the effect of rotation, the rotational speed of the channel varies from 0–400 rpm with maximum rotation numbers of 0.39 and 0.16 in the first and second passes, respectively. The heat transfer enhancement on both the leading and trailing surfaces of the first pass of the 45° V-shaped channel is slightly reduced with rotation. In the second pass, the heat transfer increases on the leading surface while it decreases on the trailing surface. The 45° staggered, discrete V-shaped ribs provide increased heat transfer and thermal performance compared to the traditional V-shaped and standard, 45° angled rib turbulators.


Author(s):  
Suddhasattwa Das ◽  
Yoshitaka Saiki ◽  
Evelyn Sander ◽  
James A. Yorke
Keyword(s):  

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Shyy Woei Chang ◽  
Tong-Miin. Liou ◽  
Wei-Chun Chen

Detailed heat transfer distributions over two opposite leading and trailing walls roughened by hemispherical protrusions were measured from a rotating rectangular channel at rotation number up to 0.6 to examine the effects of Reynolds (Re), rotation (Ro), and buoyancy (Bu) numbers on local and area-averaged Nusselt numbers (Nu and Nu¯) using the infrared thermography. A set of selected heat transfer data illustrates the Coriolis and rotating buoyancy effects on the detailed Nu distributions and the area-averaged heat transfer performances of the rotating channel. The Nu¯ for the developed flow region on the leading and trailing walls are parametrically analyzed to devise the empirical heat transfer correlations that permit the evaluation of the interdependent and individual Re, Ro, and Bu effect on Nu¯.


2007 ◽  
Vol 131 (1) ◽  
pp. 49-71 ◽  
Author(s):  
Isabelle Liousse
Keyword(s):  

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