Calculation of Transition in Adverse Pressure Gradient Flow by Conditioned Equations

1996 ◽  
Author(s):  
J. Steelant ◽  
E. Dick
Keyword(s):  
Pressure Gradient ◽  
Transport Equation ◽  
Stokes Equations ◽  
Growth Parameter ◽  
Gradient Flow ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations

Conditionally averaged Navier-Stokes equations are used to describe transitional flow in adverse pressure gradient combined with a transport equation for the intermittency factor γ. A transport equation developped in earlier work has been modified to eliminate the use of a distance along a streamline. An extension of the correlations is proposed to determine the spot growth parameter in adverse pressure gradient. This approach is verified against flows over a flat plate with an elliptical leading edge.

Conditioned Navier-Stokes and k–ϵ–γ Equations to Model Transition in Pressure Gradient Flow

1995 ◽  
Author(s):  
J. Steelant ◽  
E. Dick
Keyword(s):  
Pressure Gradient ◽  
Stokes Equations ◽  
Gradient Flow ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
Intermittency Factor ◽  
Conditional Averaging ◽  
Model Transition

Conditionally averaged Navier-Stokes equations are derived to describe transitional flow. The averages are taken during the fraction of time the flow is laminar or turbulent, respectively. Conditional averaging leads both for the laminar and turbulent parts to a set of equations for mass, momentum and energy. The conditioned equations differ from the original Navier-Stokes equations by the presence of source terms which are functions of the intermittency factor, γ. This factor is the extra unknown and is determined by a transport equation. The evolution of γ depends mainly on the turbulence level, pressure gradient and Reynolds-number. The turbulence is described by the classical k-ϵ model. The approach is verified against several test cases, with and without pressure gradients.

scholarly journals Effect of airfoil distance to water surface on static stall

2020 ◽  
Vol 14 (1) ◽  
pp. 6526-6537
Author(s):  
A. Yeganeh ◽  
Mohammad Hassan Djavareshkian ◽  
E. Esmaeil
Keyword(s):  
Pressure Gradient ◽  
Water Surface ◽  
Stokes Equations ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations

In this study, viscous, turbulent, and steady flow around an airfoil near the water surface has been simulated through a numerical method. In this simulation, Navier-Stokes equations have been solved using the finite volume method with a discretized second-order accuracy and PIMPLE algorithm. The Volume of Fraction (VOF) method has been employed to predict the free surface flow. A part of the simulation results has been validated through numerical and experimental data. Besides considering the style of flow separation in the angles of numerous attacks and airfoil static stall near the surface of the water. For this purpose, the airfoil simulation has been processed airfoil in the 68,000 Reynolds number, angle of attack of 2.5 to 11 degree and different distances from the water surface ( h/c = 0.5, 1,  ). In a larger angle of attacks, flow is initially separated from the leading edge of the surface, and then it attaches to the surface at a lower point. This reattachment leads to an increase in adverse pressure gradient and the formation of a larger separation in the downstream of the airfoil. The pressure gradient dramatically increases, and the flow gets separated from the upstream of the airfoil. Upon lowering distance from the surface, static stall takes place at a higher point and a lower angle of attack, respectively.

Exact Solution of the Navier-Stokes Equations for the Fully Developed, Pulsating Flow in a Rectangular Duct With a Constant Cross-Sectional Velocity1

2003 ◽  
Vol 125 (2) ◽  
pp. 382-385 ◽  
Author(s):  
S. Tsangaris ◽  
N. W. Vlachakis
Keyword(s):  
Pressure Gradient ◽  
Stokes Equations ◽  
Rectangular Cross Section ◽  
Gradient Flow ◽  
Pulsating Flow ◽  
Artificial Kidney ◽  
Navier Stokes ◽  
Rectangular Duct ◽  
Cross Sectional ◽  
Navier Stokes Equations

The Navier-Stokes equations have been solved in order to obtain an analytical solution of the fully developed laminar flow in a duct having a rectangular cross section with two opposite equally porous walls. We obtained solutions both for the case of steady flow as well as for the case of oscillating pressure gradient flow. The pulsating flow is obtained by the superposition of the steady and oscillating pressure gradient solutions. The solution has applications for blood flow in fiber membranes used for the artificial kidney.

The structure of two-dimensional separation

1990 ◽  
Vol 220 ◽  
pp. 397-411 ◽  
Author(s):  
Laura L. Pauley ◽  
Parviz Moin ◽  
William C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Shedding Frequency

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier–Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady’ separation experiments of Gaster (1966). It was found that his ‘bursting’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separated shear layer.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

Numerical Simulation of Clocking Effect on Wake Transportation and Interaction in a 1.5-Stage Axial Turbine

2010 ◽  
Author(s):  
Wei Li ◽  
Hua Ouyang ◽  
Zhao-hui Du
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Maximum Efficiency ◽  
Suction Surface ◽  
Navier Stokes Equations ◽  
Pressure Surface ◽  
Turbine Efficiency ◽  
Small Influence

To give insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has a very small influence on the turbine efficiency in this investigation. The efficiency difference between the maximum and minimum configuration is nearly 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passed through the mid-channel in the 2nd stator.

Boundary layer leading-edge receptivity to sound at incidence angles

2001 ◽  
Vol 444 ◽  
pp. 383-407 ◽  
Author(s):  
ERCAN ERTURK ◽  
THOMAS C. CORKE
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Incidence Angle ◽  
Leading Edge ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Sound Waves ◽  
Nose Radius ◽  
Navier Stokes Equations

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier–Stokes equations in vorticity/streamfunction form in parabolic coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) in which the solution for the basic flow and linearized perturbation flow are solved separately. We primarily investigated the effect of frequency and angle of incidence (−180° [les ] α2 [les ] 180°) of the acoustic waves on the leading-edge receptivity. The results at α2 = 0° were found to be in quantitative agreement with those of Haddad & Corke (1998), and substantiated the Strouhal number scaling based on the nose radius. The results with sound waves at angles of incidence agreed qualitatively with the analysis of Hammerton & Kerschen (1996). These included a maximum receptivity at α2 = 90°, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than α2 = 0° and α2 = 180°.

Investigation of G4-73 Centrifugal Fan Airfoil Stall Characteristics

2011 ◽  
Vol 383-390 ◽  
pp. 4221-4226
Author(s):  
Song Ling Wang ◽  
Zhe Liu ◽  
Lei Zhang
Keyword(s):  
Stokes Equations ◽  
Incidence Angle ◽  
Leading Edge ◽  
Suction Side ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Reliable Operation ◽  
Safe Operation ◽  
Navier Stokes Equations ◽  
Strong Vortex

It’s of great significance for safe and reliable operation of fan to research on the stall characteristics of the airfoil. The 2D non-compressible Reynolds-Averaged Navier-Stokes equations was built to simulate the flow around the airfoil of G4-73No.8D centrifugal fan, a detailed numerical simulation under different angles has been carried out which based on the Realizable turbulence model with Fluent. The numerical results show that the smaller of the flow rate, the bigger incidence angle is, when the incidence angle is bigger than the critical incidence angle, the suction side stall appears. According simulation the airfoil stall appears when the incidence angle is -28°, with the increasing of the negative incidence angle, the separation point gradually moves to the leading edge. There is a strong vortex which locates at suction side =0.5,the alternating stress on the blade which caused by vortex will make the blade fatigue. If the incidence angle is less than -20°,there is no flow separation, therefore, to ensure the safe operation of the fan, the incidence angle should be less than -20°.

Laminar incompressible flow past a semi-infinite flat plate

1967 ◽  
Vol 27 (4) ◽  
pp. 691-704 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Flat Plate ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Local Similarity ◽  
Approximate Methods ◽  
Navier Stokes Equations ◽  
Flow Past

Laminar incompressible flow past a semi-infinite flat plate is examined by using the method of series truncation (or local similarity) on the full Navier-Stokes equations. The first and second truncations are calculated at points on the plate away from the leading edge, while only the first truncation is calculated at the leading edge. The solutions are compared with the results from other approximate methods.

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