Reynolds Number Effect Investigation of Shock Wave on Supercritical Airfoil

2014 ◽  
Vol 548-549 ◽  
pp. 520-524
Author(s):  
Xin Xu ◽  
Da Wei Liu ◽  
De Hua Chen ◽  
Yuan Jing Wang
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Boundary Layer Separation ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Supercritical Airfoil ◽  
Reynolds Number Effects ◽  
Shock Location

The supercritical airfoil has been widely applied to large airplanes for sake of high aerodynamic efficiency. But at transonic speeds, the shock wave on upper surface of supercritical airfoil may induce boundary layer separation, which would change the aerodynamic characteristics. The shock characteristics such as location and intensity are sensitive to Reynolds number. In order to predict aerodynamic characteristics of supercritical airfoil exactly, the Reynolds number effects of shock wave must be investigated.The transonic flows over a typical supercritical airfoil CH were numerically simulated with two-dimensional Navier-Stokes equations, and the numerical method was validated with test results in ETW(European Transonic Windtunnel). The computation attack angles of CH airfoil varied from 0oto 8o, Mach numbers varied from 0.74 to 0.82 while Reynolds numbers varied from 3×106 to 50×106 per airfoil chord. It is obvious that shock location moves afterward and shock intensity strengthens as Reynolds number increasing. The similar curves of shock location and intensity is linear with logarithm of Reynolds number, so that the shock location and intensity at flight condition could be extrapolated from low Reynolds number.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

1989 ◽  
Author(s):  
Kazuomi Yamamoto ◽  
Yoshimichi Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

Finite-Reynolds-Number Effects in Steady, Three-Dimensional Airway Reopening

2006 ◽  
Vol 128 (4) ◽  
pp. 573-578 ◽  
Author(s):  
Andrew L. Hazel ◽  
Matthias Heil
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Elastic Tube ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Airway Reopening ◽  
Reynolds Number Effects ◽  
Steady Propagation

Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, Re∕Ca, a material parameter. Fluid inertia has a significant effect on the system’s behavior, even at relatively small values of Re∕Ca. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.

Impulsively started flow separation in wavy-walled tubes

1998 ◽  
Vol 359 ◽  
pp. 1-22 ◽  
Author(s):  
FEDERICO DOMENICHINI ◽  
GIANNI PEDRIZZETTI
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Asymptotic Model ◽  
Navier Stokes Equations ◽  
Boundary Layer Problem

The axisymmetric boundary-layer separation of an incompressible impulsively started flow in a wavy-walled tube is analysed at moderate to high values of the Reynolds number. The investigation is carried out by numerical integration of either the Navier–Stokes equations or Prandtl's asymptotic formulation of the boundary-layer problem. The presence of an adverse pressure gradient induces reverse flow at the tube wall independently of the Reynolds number; its occurrence can be predicted by a timescale analysis. Following that, the viscous calculations show different dynamics depending on the Reynolds number. As the Reynolds number increases, the boundary layer has in a well-defined internal structure where longitudinal lengthscales become comparable with the viscous one. Thus the boundary-layer scaling fails locally, with a minimum of pressure inside the boundary layer itself. The formation of the primary recirculation is well captured by the asymptotic model which, however, is not able to describe the roll-up of the vortex structure inside the recirculating region. This inadequacy appears well before the flow evolves to the characteristic terminal singularity usually assumed as foreshadowing the vortex shedding phenomenon. The outcomes are compared with the existing results of analogous problems giving an overall agreement but improving, in some cases, the physical picture.

Influencing Factors Analysis of the Shock-Induced Separation for Supercritical Airfoil

2013 ◽  
Vol 444-445 ◽  
pp. 221-226
Author(s):  
Xin Xu ◽  
Da Wei Liu ◽  
De Hua Chen ◽  
Yuan Jing Wang
Keyword(s):  
Mach Number ◽  
Influencing Factors ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Supercritical Airfoil ◽  
Factors Analysis ◽  
Mach Numbers

The shock-induced separation easily occurred on the upper surface of supercritical airfoil at transonic speeds, which would change the aerodynamic characteristics. The problem of the shock-induced separation was not solved completely for the complicated phenomena and flow mechanism. In this paper, the influencing factors of shock-induced separation for supercritical airfoil CH was analyzed at transonic speeds. The Navier-Stokes equations were solved, in order to investigate influence of different attack angles, Mach numbers and Reynolds numbers. The computation attack angles of CH airfoil varied from 0oto 7o, Reynolds numbers varied from 5×106to 50×106per airfoil chord while Mach number varied from 0.74 to 0.82. It was shown that the shock-induced separation was affected by attack angles, Mach numbers and Reynolds numbers, but the influence tendency and areas were quite different. The shock wave location and intensity were affected by the three factors, and the boundary layer thickness was mainly affected by Reynolds number, while the separation structure was mainly determined by the attack angle and Mach number.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channels

1990 ◽  
Vol 112 (4) ◽  
pp. 723-731 ◽  
Author(s):  
K. Yamamoto ◽  
Y. Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and the unsteady static pressure field predict a closed-loop mechanism, in which the pressure disturbance that is generated by the oscillation of boundary layer separation propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier–Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the antiphase oscillation.

scholarly journals A Numerical Investigation of Co-flow Jet Effects on Airfoil Aerodynamic Characteristics

2021 ◽  
Author(s):  
Shima Yazdani ◽  
Erfan Salimipour ◽  
Ayoob Salimipour
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Active Flow Control ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Momentum Coefficient

Abstract The present paper numerically investigates the performance of a Co-Flow Jet (CFJ) on the static and dynamic stall control of the NACA 0024 airfoil at Reynolds number 1.5 × 105. The two-dimensional Reynolds-averaged Navier-Stokes equations are solved using the SST k-ω turbulence model. The results show that the lift coefficients at the low angles of attack (up to α = 15̊) are significantly increased at Cµ = 0.06, however for the higher momentum coefficients, it is not seen an improvement in the aerodynamic characteristics. Also, the dynamic stall for a range of α between 0̊ and 20̊ at the mentioned Reynolds number and with the reduced frequency of 0.15 for two CFJ cases with Cµ = 0.05 and 0.07 are investigated. For the case with Cµ = 0.07, the lift coefficient curve did not present a noticeable stall feature compared to Cµ = 0.05. The effect of this active flow control by increasing the Reynolds numbers from 0.5 × 105 to 3 × 105 is also investigated. At all studied Reynolds numbers, the lift coefficient enhances as the momentum coefficient increases where its best performance is obtained at the angle of attack α = 15̊.

Numerical Estimation of Aerodynamic Characteristics of Footbridge Deck

2014 ◽  
Vol 617 ◽  
pp. 291-295
Author(s):  
Robert Šoltýs ◽  
Michal Tomko
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Boundary Layer Separation ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Computational Fluid Dynamics Cfd ◽  
Simulation Parameters

For estimation of aerodynamic characteristics of cable-stayed footbridge deck a computational fluid dynamics (CFD) has been used. An incompressible fluid flow with Navier-Stokes equations has been applied. An adequate numerical model has been created to obtain accurate values of aerodynamic characteristics. Preliminary determination of simulation parameters have been estimated using laminar fluid flow model. Subsequently, Smagorinsky large-eddy simulation (LES) turbulent model has been applied with different simulation parameters to obtain converged values. The boundary layer separation regions and downwind vortex shedding has been observed.

Finite Reynolds number effects in the propagation of an air finger into a liquid-filled flexible-walled channel

2000 ◽  
Vol 424 ◽  
pp. 21-44 ◽  
Author(s):  
MATTHIAS HEIL
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Deformation Pattern ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Airway Reopening ◽  
Reynolds Number Effects ◽  
Wall Deformation ◽  
Pulmonary Airway

This paper investigates finite Reynolds number effects in the problem of the propagation of an air finger into a liquid-filled flexible-walled two-dimensional channel. The study is motivated by the physiological problem of pulmonary airway reopening. A fully consistent model of the fluid–structure interaction is formulated and solved numerically using coupled finite element discretizations of the free-surface Navier–Stokes equations and the Lagrangian wall equations. It is shown that for parameter values which are representative of the conditions in the lung and in typical laboratory experiments, fluid inertia plays a surprisingly important role: even for relatively modest ratios of Reynolds and capillary numbers (Re/Ca ≈ 5–10), the pressure required to drive the air finger at a given speed increases significantly compared to the zero Reynolds number case. Fluid inertia leads to significant changes in the velocity and pressure fields near the bubble tip and is responsible for a noticeable change in the wall deformation pattern ahead of the bubble. For some parameter variations (such as variations in the wall tension), finite Reynolds number effects are shown to lead to qualitative changes in the system's behaviour. Finally, the implications of the result for pulmonary airway reopening are discussed.

Numerical Simulation of a Low Reynolds Number Airfoil

2013 ◽  
Vol 390 ◽  
pp. 141-146
Author(s):  
Yu Fu Wang ◽  
Guo Quan Tao ◽  
Ze Hai Wang ◽  
Zhe Wu
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Lift Coefficient ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Low Reynolds ◽  
Low Reynolds Number Airfoil

In this paper, a low Reynolds number airfoil (S1223) is the objective of the study. The Navier-Stokes equations were established to simulate the complex flow around a low Reynolds number airfoil, in which the turbulence model was used. The complex flow around the airfoil was simulated at 2x105 Reynolds number and its aerodynamic characteristics were analyzed. The relationship among lift coefficient, drag coefficient and angle of attack was studied.

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