One-dimensional single rising bubble at low Reynolds numbers: solution of equation of motion by differential transformation method

2010 ◽  
Vol 7 (2) ◽  
pp. 256-265 ◽  
Author(s):  
M. Jalaal ◽  
S. Ghafoori ◽  
M. Motevalli ◽  
M. G. Nejad ◽  
D. D. Ganji
Keyword(s):  
Reynolds Numbers ◽  
Transformation Method ◽  
Equation Of Motion ◽  
Differential Transformation Method ◽  
Low Reynolds Numbers ◽  
One Dimensional ◽  
Differential Transformation ◽  
Rising Bubble ◽  
Low Reynolds

Experimental Measurement of the Magnus Force on a Rotating Sphere at Low Reynolds Numbers

1985 ◽  
Vol 107 (4) ◽  
pp. 484-488 ◽  
Author(s):  
Yutaka Tsuji ◽  
Yoshinobu Morikawa ◽  
Osamu Mizuno
Keyword(s):  
Angular Velocity ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Equation Of Motion ◽  
Inclined Plate ◽  
Magnus Force ◽  
Empirical Expression ◽  
Low Reynolds Numbers ◽  
Rotating Sphere ◽  
Low Reynolds

The Magnus force on a rotating sphere at low Reynolds numbers was obtained from trajectories of the sphere which impinged on an inclined plate and bounced. An empirical expression for the lift coefficient which is proportional to the angular velocity was deduced by comparing measurements of the range of flight with the solutions of the equation of motion.

Numerical Multistep Approach for Solving Fractional Partial Differential Equations

2017 ◽  
Vol 14 (03) ◽  
pp. 1750029 ◽  
Author(s):  
Mohammed Al-Smadi ◽  
Asad Freihat ◽  
Hammad Khalil ◽  
Shaher Momani ◽  
Rahmat Ali Khan
Keyword(s):  
Fractional Derivatives ◽  
Nonlinear Problems ◽  
Approximate Solutions ◽  
Transformation Method ◽  
Time Frame ◽  
Differential Transformation Method ◽  
Heat Equations ◽  
One Dimensional ◽  
Analytical Technique ◽  
Differential Transformation

In this paper, we proposed a novel analytical technique for one-dimensional fractional heat equations with time fractional derivatives subjected to the appropriate initial condition. This new analytical technique, namely multistep reduced differential transformation method (MRDTM), is a simple amendment of the reduced differential transformation method, in which it is treated as an algorithm in a sequence of small intervals, in order to hold out accurate approximate solutions over a longer time frame compared to the traditional RDTM. The fractional derivatives are described in the Caputo sense, while the behavior of solutions for different values of fractional order [Formula: see text] compared with exact solutions is shown graphically. The analysis is accompanied by four test examples to demonstrate that the proposed approach is reliable, fully compatible with the complexity of these equations, and can be strongly employed for many other nonlinear problems in fractional calculus.

Investigation on the effect of leading edge tubercles of sweptback wing at low reynolds number

2020 ◽  
Vol 21 (6) ◽  
pp. 621
Author(s):  
Veerapathiran Thangaraj Gopinathan ◽  
John Bruce Ralphin Rose ◽  
Mohanram Surya
Keyword(s):  
Leading Edge ◽  
Reynolds Numbers ◽  
Sweep Angle ◽  
Laminar Separation ◽  
Low Reynolds Numbers ◽  
Flow Energy ◽  
Airplane Wing ◽  
Low Reynolds ◽  
Naca 0015 ◽  
Wing Performance

Aerodynamic efficiency of an airplane wing can be improved either by increasing its lift generation tendency or by reducing the drag. Recently, Bio-inspired designs have been received greater attention for the geometric modifications of airplane wings. One of the bio-inspired designs contains sinusoidal Humpback Whale (HW) tubercles, i.e., protuberances exist at the wing leading edge (LE). The tubercles have excellent flow control characteristics at low Reynolds numbers. The present work describes about the effect of tubercles on swept back wing performance at various Angle of Attack (AoA). NACA 0015 and NACA 4415 airfoils are used for swept back wing design with sweep angle about 30°. The modified wings (HUMP 0015 A, HUMP 0015 B, HUMP 4415 A, HUMP 4415 B) are designed with two amplitude to wavelength ratios (η) of 0.1 & 0.24 for the performance analysis. It is a novel effort to analyze the tubercle vortices along the span that induce additional flow energy especially, behind the tubercles peak and trough region. Subsequently, Co-efficient of Lift (CL), Co-efficient of Drag (CD) and boundary layer pressure gradients also predicted for modified and baseline (smooth LE) models in the pre & post-stall regimes. It was observed that the tubercles increase the performance of swept back wings by the enhanced CL/CD ratio in the pre-stall AoA region. Interestingly, the flow separation region behind the centerline of tubercles and formation of Laminar Separation Bubbles (LSB) were asymmetric because of the sweep.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

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