scholarly journals Second-order supercavitating hydrofoil theory

1962 ◽  
Vol 13 (3) ◽  
pp. 321-332 ◽  
Author(s):  
C. F. Chen
Keyword(s):  
Exact Solutions ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Lift Coefficient ◽  
Integral Form ◽  
Order Theory ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Lift And Drag

The second-order problem of Helmholtz flow past lifting hydrofoils and symmetric struts has been formulated and solved. The solution involves elementary operations on the known solutions of the first-order problem. The second-order lift and drag coefficients are given in integral form. Results obtained for a flat plate at incidence and a symmetric wedge agree with the exact solutions up to the second order. In terms of quantitative improvements, the present second-order theory predicts a lift coefficient for a flat plate at 45° incidence with an error of 8%, and a drag coefficient for a symmetric wedge of 50° included angle with an error of 5%; the corresponding angles at which the linear theory would predict force coefficients incurring the same errors are 5° and 15° respectively.

A feasible theory for analysis

1994 ◽  
Vol 59 (3) ◽  
pp. 1001-1011 ◽  
Author(s):  
Fernando Ferreira
Keyword(s):  
Polynomial Time ◽  
Order Theory ◽  
Second Order ◽  
First Order ◽  
Weak König’S Lemma ◽  
König’S Lemma ◽  
Computable Functions

AbstractWe construct a weak second-order theory of arithmetic which includes Weak König's Lemma (WKL) for trees defined by bounded formulae. The provably total functions (with -graphs) of this theory are the polynomial time computable functions. It is shown that the first-order strength of this version of WKL is exactly that of the scheme of collection for bounded formulae.

scholarly journals A Partial Lagrangian Approach to Mathematical Models of Epidemiology

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
I. Naeem ◽  
F. M. Mahomed
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
First Integrals ◽  
Order Equation ◽  
Second Order ◽  
Lagrangian Approach ◽  
Hiv Model ◽  
First Order ◽  
Partial Lagrangian

This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

First and Second Order Wave-Current Interactions for Floating Bodies

2012 ◽  
Author(s):  
Charles Monroy ◽  
Yann Giorgiutti ◽  
Xiao-Bo Chen
Keyword(s):  
Field Method ◽  
Boundary Integral ◽  
Second Order ◽  
Boundary Integral Method ◽  
Diffraction Radiation ◽  
Floating Bodies ◽  
Order Problem ◽  
First Order ◽  
Wave Drift Damping ◽  
Order Quantities

The influence of current in sea-keeping problems is felt not only for first order quantities such as wave run-ups in front of the structure, but also mainly for second order quantities. In particular, the wave drift damping (which is expressed as the derivative of drift force with respect to the current) is of special interest for mooring systems. The interaction effects of a double-body steady flow on wave diffraction-radiation is studied through a decomposition of the time-harmonic potential into linear and interaction components. A boundary integral method is used to solve the first order problem. Ultimately, a far-field method is proposed to get access to second order drift forces.

Analysis of Vortex-Induced Vibration of Riser using Spalart-Almaras Model

2014 ◽  
Vol 69 (7) ◽  
Author(s):  
Jaswar Koto ◽  
Abdul Khair Junaidi
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Vortex Shedding ◽  
Lift Coefficient ◽  
Offshore Structures ◽  
The Other ◽  
Main Concern ◽  
Vortex Induced Vibration ◽  
Simulation Results ◽  
Lift And Drag

Vortex-induced vibration is natural phenomena where an object is exposed to moving fluid caused vibration of the object. Vortex-induced vibration occurred due to vortex shedding behind the object. One of the offshore structures that experience this vortex-induced vibration is riser. The riser experience vortex-induced vibration due to vortex shedding caused by external load which is sea current. The effect of this vortex shedding to the riser is fatigue damage. Vortex-induced vibration of riser becomes the main concern in oil and gas industry since there will be a lots of money to be invested for the installation and maintenance of the riser. The previous studies of this vortex-induced vibration have been conducted by experimental method and Computational Fluid Dynamics (CFD) method in order to predict the vortex shedding behaviour behind the riser body for the determination of way to improve the riser design. This thesis represented the analysis of vortex induced vibration of rigid riser in two-dimensional. The analysis is conducted using Computational Fluid Dynamic (CFD) simulations at Reynolds number at 40, 200, 1000, and 1500. The simulations were performed using Spalart-Allmaras turbulent model to solve the transport equation of turbulent viscosity. The simulations results at Reynolds number 40 and 200 is compared with the other studies for the validation of the simulation, then further simulations were conducted at Reynolds number of 1000 and 1500. The coefficient of lift and drag were obtained from the simulations. The comparison of lift and drag coefficient between the simulation results in this study and experiment results from the other studies showed good agreement. Besides that, the in-line vibration and cross-flow vibration at different Reynolds number were also investigated. The drag coefficient obtained from the simulation results remain unchanged as the Reynolds number increased from 200 to 1500. The lift coefficient obtained from the simulations increased as the Reynolds number increased from 40 to 1500.

Drag and lift measurements of solid sports balls in still air

2017 ◽  
Vol 232 (3) ◽  
pp. 255-263 ◽  
Author(s):  
Jeff R Kensrud ◽  
Lloyd V Smith
Keyword(s):  
Surface Roughness ◽  
Wind Tunnel ◽  
Drag Coefficient ◽  
Rough Surface ◽  
Lift Coefficient ◽  
Laboratory Setting ◽  
Air Drag ◽  
High Speeds ◽  
Drag And Lift ◽  
Lift And Drag

The following article considers lift and drag measurements of solid sports balls propelled through still air in a laboratory setting. The balls traveled at speeds ranging from 26 to 134 m/s with spin rates up to 3900 r/min. Light gates measured the speed and location of the balls at two locations from which lift and drag values were determined. Ball roughness varied from polished to rough surface protrusions, that is, seams as high as 1.5 mm. Lift and drag were observed to depend on speed, spin rate, surface roughness, and seam orientation. A drag crisis was observed on smooth balls as well as non-rotating seamed balls with seam heights less than 0.9 mm. The drag coefficient of approximately 0.42 was nearly constant with speed for spinning seamed balls with seam height greater than 0.9 mm. The still air drag coefficient of smooth balls was comparable to wind tunnel drag at low speeds ( Re < 2 × 105) and higher than wind tunnel results at high speeds ( Re > 2 × 105). The lift and drag coefficients of spinning balls increased with increasing spin rate. The lift coefficient of baseballs was not sensitive to ball orientation or seam height.

Second-Order Diffraction Forces on an Array of Vertical Cylinders in Bichromatic Bidirectional Waves

1995 ◽  
Vol 117 (1) ◽  
pp. 12-18 ◽  
Author(s):  
J. H. Vazquez ◽  
A. N. Williams
Keyword(s):  
Cross Section ◽  
Finite Depth ◽  
Hydrodynamic Forces ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Wave Directionality ◽  
Vertical Cylinders ◽  
Green Function Approach

A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.

Effects of surface flow visualisation on aerodynamic loads at low Reynolds number

2015 ◽  
Vol 119 (1215) ◽  
pp. 663-672
Author(s):  
L. W. Traub ◽  
R. Waghela ◽  
E. M. Botero
Keyword(s):  
Drag Coefficient ◽  
Lift Coefficient ◽  
Time History ◽  
Surface Flow ◽  
Flow Visualisation ◽  
Distribution Method ◽  
History Of ◽  
Low Reynolds ◽  
Lift And Drag ◽  
Lift And Drag Coefficient

AbstractIn this article, the effect of on-surface flow visualisation (SVF) techniques on measured loads over an airfoil are explored. Titanium dioxide based mixture effects on the lift and drag coefficient are experimentally quantified at low Reynolds numbers by recording the time history as the patterns evolve and freeze. With statistical comparison based on Student’s t-distribution method, it was determined that the effect on the drag coefficient was minimal but the lift coefficient was slightly attenuated. Additionally, it was observed that at high angles-of-attack the temporal history of the flow as the wind tunnel ramps up may alter the steady-state flow field in the presence of a SFV mixture.

scholarly journals Numerical Analysis of the Aerodynamic Characteristics of NACA-4312 Airfoil

2020 ◽  
Vol 01 (02) ◽  
pp. 29-36
Author(s):  
Md Rhyhanul Islam Pranto ◽  
Mohammad Ilias Inam
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Lift Coefficient ◽  
Turbulence Models ◽  
Aerodynamic Characteristics ◽  
Numerical Results ◽  
Ansys Fluent ◽  
Coefficient Increase ◽  
Lift And Drag ◽  
Lift And Drag Coefficient

The aim of the work is to investigate the aerodynamic characteristics such as lift coefficient, drag coefficient, pressure distribution over a surface of an airfoil of NACA-4312. A commercial software ANSYS Fluent was used for these numerical simulations to calculate the aerodynamic characteristics of 2-D NACA-4312 airfoil at different angles of attack (α) at fixed Reynolds number (Re), equal to 5×10^5 . These simulations were solved using two different turbulence models, one was the Standard k-ε model with enhanced wall treatment and other was the SST k-ω model. Numerical results demonstrate that both models can produce similar results with little deviations. It was observed that both lift and drag coefficient increase at higher angles of attack, however lift coefficient starts to reduce at α =13° which is known as stalling condition. Numerical results also show that flow separations start at rare edge when the angle of attack is higher than 13° due to the reduction of lift coefficient.

scholarly journals Analysis on Flow Field Characteristics of Airfoil in Pitching Motion

2021 ◽  
Vol 2076 (1) ◽  
pp. 012069
Author(s):  
Rui Yin ◽  
Jing Huang ◽  
Zhi-Yuan He
Keyword(s):  
Flow Field ◽  
Drag Coefficient ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Decisive Role ◽  
Aerodynamic Characteristics ◽  
Pitching Motion ◽  
Maximum Value ◽  
Flow Field Characteristics ◽  
Lift And Drag

Abstract Based on CFD, the flow field characteristics of NACA4412 airfoil are analyzed under pitching motion, and its aerodynamic characteristics are interpreted. The results show that streamline changes on the upper surface of the airfoil play a decisive role in the aerodynamic characteristics. The interaction between the vortex leads to fluctuations in the lift and drag coefficients. Under a big angle of attack, the secondary trailing vortex on the upper surface of the airfoil adheres to the trailing edge of the airfoil, resulting in an increased drag coefficient. Under a small angle of attack, the secondary trailing vortex can break away from the airfoil. The lift coefficient reaches the maximum value of 2.961 before the airfoil is turned upside down, and the drag coefficient reaches the maximum value of 1.515 after the airfoil is turned upside down, but the corresponding angles of attack of the two are equal.

An Experimental Study of Deviations from the Linear Transfer Function

1974 ◽  
Vol 32 ◽  
pp. 400-401
Author(s):  
William A. Voter ◽  
Harold P. Erickson
Keyword(s):  
Experimental Study ◽  
Image Formation ◽  
Order Theory ◽  
Second Order ◽  
Diffraction Spot ◽  
Order Effects ◽  
First Order ◽  
First Order Theory ◽  
Second Order Effects ◽  
The Fourier Transform

In a previous experimental study of image formation using a thin (20 nm) negatively stained catalase crystal, it was found that a linear or first order theory of image formation would explain almost entirely the changes in the Fourier transform of the image as a function of defocus. In this case it was concluded that the image is a valid picture of the object density. For thicker, higher contrast objects the first order theory may not be valid. Second order effects could generate false diffraction spots which would lead to spurious and artifactual image details. These second order effects would appear as deviations of the diffraction spot amplitudes from the first order theory. Small deviations were in fact noted in the study of the thin crystals, but there was insufficient data for a quantitative analysis.

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