Numerical Investigation on Shock-Induced Separation Structure of Supercritical Airfoil

2013 ◽  
Vol 756-759 ◽  
pp. 4502-4505 ◽  
Author(s):  
Xin Xu ◽  
Da Wei Liu ◽  
De Hua Chen ◽  
Yuan Jing Wang
Keyword(s):  
Stokes Equations ◽  
Separation Bubble ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Supercritical Airfoil ◽  
Coefficient Distribution

The supercritical airfoil has been widely applied to large airplanes for sake of high aerodynamic efficiency. But at transonic speeds, the complicated shock-induced separation on the upper surface of supercritical airfoil will change the aerodynamic characteristics. The transonic flows over a typical supercritical airfoil CH were numerically investigated in this paper, in order to analyses different shock-induced separation structure. The two-dimensional Navier-Stokes equations were solved with structure grids by utilizing the S-A turbulence model. The computation attack angles of CH airfoil varied from 0oto 4o, Mach numbers varied from 0.74 to 0.82 while Reynolds numbers varied from 3×106to 50×106per airfoil chord. It is shown that with the attack angle increases, the separation bubble occurred on the upper surface first, then the trailing-edge separation occurred, the trailing-edge would separate totally at last. The different separation structure would result in different pressure coefficient distribution and boundary layer thickness.

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.

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.

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.

Computation of Velocity Profiles and Pressure Coefficients for a Laminar Flow of Air Over Staggered Array of Tubes

2005 ◽  
Author(s):  
Ramin Rahmani ◽  
Ahad Ramezanpour ◽  
Iraj Mirzaee ◽  
Hassan Shirvani
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Tube Bundle ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tube Arrays ◽  
Volume Method

In this study a two dimensional, steady state and incompressible laminar flow for staggered tube arrays in crossflow is investigated numerically. A finite-volume method is used to discretize and solve the governing Navier-Stokes equations for the geometries expressed by a boundary-fitted coordinate system. Solutions for Reynolds numbers of 100, 300, and 500 are obtained for a tube bundle with 10 longitudinal rows. Local velocity profiles on top of each tube and corresponding pressure coefficient are presented at nominal pitch-to-diameter ratios of 1.33, 1.60, and 2.00 for ES, ET, and RS arrangements. Differences in location of separation points are compared for three different arrangements. The predicted results on flow field for pressure coefficient showed a good agreement with available experimental measurements.

A numerical study of laminar separation bubbles using the Navier-Stokes equations

1971 ◽  
Vol 47 (4) ◽  
pp. 713-736 ◽  
Author(s):  
W. Roger Briley
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Reynolds Numbers ◽  
Boundary Layer Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Separation ◽  
Boundary Layer Equations

The flow in a two-dimensional laminar separation bubble is analyzed by means of finite-difference solutions to the Navier-Stokes equations for incompressible flow. The study was motivated by the need to analyze high-Reynolds-number flow fields having viscous regions in which the boundary-layer assumptions are questionable. The approach adopted in the present study is to analyze the flow in the immediate vicinity of the separation bubble using the Navier-Stokes equations. It is assumed that the resulting solutions can then be patched to the remainder of the flow field, which is analyzed using boundary-layer theory and inviscid-flow analysis. Some of the difficulties associated with patching the numerical solutions to the remainder of the flow field are discussed, and a suggestion for treating boundary conditions is made which would permit a separation bubble to be computed from the Navier-Stokes equations using boundary conditions from inviscid and boundary-layer solutions without accounting for interaction between individual flow regions. Numerical solutions are presented for separation bubbles having Reynolds numbers (based on momentum thickness) of the order of 50. In these numerical solutions, separation was found to occur without any evidence of the singular behaviour at separation found in solutions to the boundary-layer equations. The numerical solutions indicate that predictions of separation by boundary-layer theory are not reliable for this range of Reynolds number. The accuracy and validity of the numerical solutions are briefly examined. Included in this examination are comparisons between the Howarth solution of the boundary-layer equations for a linearly retarded freestream velocity and the corresponding numerical solutions of the Navier-Stokes equations for various Reynolds numbers.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

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