Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1991 ◽  
Vol 113 (4) ◽  
pp. 608-616 ◽  
Author(s):  
H. M. Jang ◽  
J. A. Ekaterinaris ◽  
M. F. Platzer ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp-type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler-387 and NACA-0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en method and the transitional region is modeled properly.

scholarly journals Essential Ingredients for the Computation of Steady and Unsteady Blade Boundary Layers

1990 ◽  
Author(s):  
H. M. Jang ◽  
M. F. Platzer ◽  
J. A. Ekaterinaris ◽  
T. Cebeci
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Transitional Region ◽  
Low Reynolds Numbers ◽  
Flow Equations ◽  
Low Reynolds

Two methods are described for calculating pressure distributions and boundary layers on blades subjected to low Reynolds numbers and ramp–type motion. The first is based on an interactive scheme in which the inviscid flow is computed by a panel method and the boundary layer flow by an inverse method that makes use of the Hilbert integral to couple the solutions of the inviscid and viscous flow equations. The second method is based on the solution of the compressible Navier–Stokes equations with an embedded grid technique that permits accurate calculation of boundary layer flows. Studies for the Eppler and NACA–0012 airfoils indicate that both methods can be used to calculate the behavior of unsteady blade boundary layers at low Reynolds numbers provided that the location of transition is computed with the en–method and the transitional region is modelled properly.

Aerodynamic Analysis of a Localized Flexible Airfoil at Low Reynolds Numbers

2012 ◽  
Vol 11 (4) ◽  
pp. 1300-1310 ◽  
Author(s):  
Wei Kang ◽  
Jia-Zhong Zhang ◽  
Pei-Hua Feng
Keyword(s):  
Stokes Equations ◽  
Reynolds Numbers ◽  
Aerodynamic Performance ◽  
The Self ◽  
Navier Stokes ◽  
Shallow Arch ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Excited Vibration ◽  
Low Reynolds

AbstractA localized flexible airfoil at low Reynolds numbers is modeled and the aerodynamic performance is analyzed numerically. With characteristic based split scheme, a fluid solver for two dimensional incompressible Navier-Stokes equations is developed under the ALE framework, coupled with the theory of shallow arch, which is approximated by Galerkin method. Further, the interactions between the unsteady flow and the shallow arch are studied in detail. In particular, the effect of the self-excited vibration of the structure on aerodynamic performance of the airfoil is investigated deeply at various angles of attack. The results show that the lift-to-drag ratio has been increased greatly compared with the rigid airfoil. Finally, the relationship between the self-excited vibration and the evolution of the flow is analyzed using FFT tools.

Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem

2019 ◽  
Vol 868 ◽  
pp. 141-175 ◽  
Author(s):  
Haithem Taha ◽  
Amir S. Rezaei
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
High Frequencies ◽  
Kutta Condition ◽  
Low Reynolds

The application of the Kutta condition to unsteady flows has been controversial over the years, with increased research activities over the 1970s and 1980s. This dissatisfaction with the Kutta condition has been recently rejuvenated with the increased interest in low-Reynolds-number, high-frequency bio-inspired flight. However, there is no convincing alternative to the Kutta condition, even though it is not mathematically derived. Realizing that the lift generation and vorticity production are essentially viscous processes, we provide a viscous extension of the classical theory of unsteady aerodynamics by relaxing the Kutta condition. We introduce a trailing-edge singularity term in the pressure distribution and determine its strength by using the triple-deck viscous boundary layer theory. Based on the extended theory, we develop (for the first time) a theoretical viscous (Reynolds-number-dependent) extension of the Theodorsen lift frequency response function. It is found that viscosity induces more phase lag to the Theodorsen function particularly at high frequencies and low Reynolds numbers. The obtained theoretical results are validated against numerical laminar simulations of Navier–Stokes equations over a sinusoidally pitching NACA 0012 at low Reynolds numbers and using Reynolds-averaged Navier–Stokes equations at relatively high Reynolds numbers. The physics behind the observed viscosity-induced lag is discussed in relation to wake viscous damping, circulation development and the Kutta condition. Also, the viscous contribution to the lift is shown to significantly decrease the virtual mass, particularly at high frequencies and Reynolds numbers.

scholarly journals CFD Analysis of airfoils with flaps for low Reynolds numbers

2019 ◽  
Vol 4 (4) ◽  
pp. 93-101
Author(s):  
William Denner Pires Fonseca ◽  
Max William Frasão Reis ◽  
Pedro Felipe Lavra Dias ◽  
Lourival Matos De Sousa Filho
Keyword(s):  
Stokes Equations ◽  
Mass Conservation ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Ansys Fluent ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Current Lines

This paper presents a numerical investigation of the aerodynamic flow through airfoils with and without flaps for low Reynolds numbers. A two-dimensional, permanent, viscous model is adopted in the problem. The mass conservation and Navier-Stokes equations are discretized using two numerical methods, the panels method and the finite volume method, using CFD (Computational Fluid Dynamics) XFLR5® and ANSYS Fluent™ softwares. Initially, the work aims to compare the results obtained in the numerical simulation for different mesh refining with the analytical model available in the literature. Afterwards, it was verified how the pressure fields, velocity, current lines, drag and carry coefficients for symmetrical and asymmetrical airfoils work. Then, which airfoil is the most aerodynamically efficient, and finally, which numerical method is more feasible for two-dimensional and incompressible aerodynamic simulations.

Modeling of Unsteady Transitional Boundary Layers

1992 ◽  
Vol 114 (3) ◽  
pp. 580-589 ◽  
Author(s):  
J. S. Addison ◽  
H. P. Hodson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Reynolds Numbers ◽  
Considerable Proportion ◽  
Blade Surface ◽  
Hot Wire ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Hot Film ◽  
Profile Loss

In turbomachinery, a considerable proportion of the blade surface area can be covered by transitional boundary layers. This means that accurate prediction of the profile loss and boundary layer behavior in general depends on the accurate modeling of the transitional boundary layers, especially at low Reynolds numbers. This paper presents a model for determining the intermittency resulting from the unsteady transition caused by the passage of wakes over a blade surface. The model is founded on work by Emmons (1951) who showed that the intermittency could be calculated from a knowledge of the behavior of randomly formed turbulent spots. The model Is used to calculate the development of the boundary layer on the rotor of a low Reynolds number single-stage turbine. The predictions are compared with experimental results obtained using surface-mounted hot-film anemometers and hot-wire traverses of the rotor midspan boundary layer at two different rotor-stator gaps. The validity and limitations of the model are discussed.

scholarly journals Modelling of Unsteady Transitional Boundary Layers

1991 ◽  
Author(s):  
J. S. Addison ◽  
H. P. Hodson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Reynolds Numbers ◽  
Considerable Proportion ◽  
Blade Surface ◽  
Hot Wire ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Hot Film ◽  
Profile Loss

In turbomachinery, a considerable proportion of the blade surface area can be covered by transitional boundary layers. This means that accurate prediction of the profile loss and boundary layer behaviour in general depends on the accurate modelling of the transitional boundary layers, especially at low Reynolds numbers. This paper presents a model for determining the intermittency resulting from the unsteady transition caused by the passage of wakes over a blade surface. The model is founded on work by Emmons (1951) who showed that the intermittency could be calculated from a knowledge of the behaviour of randomly formed turbulent spots. The model is used to calculate the development of the boundary layer on the rotor of a low Reynolds number single-stage turbine. The predictions are compared with experimental results obtained using surface-mounted hot-film anemometers and hot-wire traverses of the rotor mid-span boundary layer at two different rotor-stator gaps. The validity and limitations of the model are discussed.

Suppression of vortex shedding behind a circular cylinder by another control cylinder at low Reynolds numbers

2007 ◽  
Vol 573 ◽  
pp. 171-190 ◽  
Author(s):  
A. DIPANKAR ◽  
T. K. SENGUPTA ◽  
S. B. TALLA
Keyword(s):  
Vortex Shedding ◽  
Physical Mechanism ◽  
Grid Method ◽  
Reynolds Numbers ◽  
Accurate Solution ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Control Cylinder

Vortex shedding behind a cylinder can be controlled by placing another small cylinder behind it, at low Reynolds numbers. This has been demonstrated experimentally by Strykowski & Sreenivasan (J. Fluid Mech. vol. 218, 1990, p. 74). These authors also provided preliminary numerical results, modelling the control cylinder by the innovative application of boundary conditions on some selective nodes. There are no other computational and theoretical studies that have explored the physical mechanism. In the present work, using an over-set grid method, we report and verify numerically the experimental results for flow past a pair of cylinders. Apart from providing an accurate solution of the Navier–Stokes equation, we also employ an energy-based receptivity analysis method to discuss some aspects of the physical mechanism behind vortex shedding and its control. These results are compared with the flow picture developed using a dynamical system approach based on the proper orthogonal decomposition (POD) technique.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

The influence of the flow separation bubble and transition location on the profile drag of three 4-digit NACA aerofoil profiles

2021 ◽  
pp. 0309524X2110550
Author(s):  
Moutaz Elgammi ◽  
Tonio Sant ◽  
Atiyah Abdulmajid Ateeah
Keyword(s):  
Wind Tunnel ◽  
Flow Separation ◽  
Separation Bubble ◽  
Reynolds Numbers ◽  
Force Balance ◽  
Navier Stokes ◽  
Separation Mechanism ◽  
Numerical Work ◽  
Low Reynolds Numbers ◽  
Low Reynolds

Modeling of the flow over aerofoil profiles at low Reynolds numbers is difficult due to the complex physics associated with the laminar flow separation mechanism. Two major problems arise in the estimation of profile drag: (1) the drag force at low Reynolds numbers is extremely small to be measured in a wind tunnel by force balance techniques, (2) the profile drag is usually calculated by pressure integration, hence the skin friction component of drag is excluded. In the present work, three different 4-digit NACA aerofoils are investigated. Measurements are conducted in an open-ended subsonic wind tunnel, while numerical work is performed by time Reynolds-averaged Navier Stokes (RANS) coupled with the laminar-kinetic-energy ( K-kl-w) turbulence model. The influence of the flow separation bubbles and transition locations on the profile drag is discussed and addressed. This paper gives important insights into importance of measurements at low Reynolds numbers for better aerodynamic loads predictions.

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