Numerical Simulation of Unsteady Viscous Compressible Flows Applied to Blade Flutter Analysis

1991 ◽  
Author(s):  
L. D. Gunnar Sidén
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Flutter Analysis ◽  
Blade Flutter ◽  
Viscous Compressible Flow

A numerical method for simulating quasi three-dimensional unsteady viscous compressible flow is developed and applied to blade flutter analysis. The Reynolds-averaged Navier-Stokes equations are solved in a time accurate manner on a continuously deforming computational mesh. Turbulence is accounted for by the inclusion of a two-layer algebraic turbulence model. This method is compared with measurements and a full velocity potential solver for two different subsonic compressor cascades and a range of flow conditions. Both methods are found to predict unsteady attached flows reasonably well. However, the Navier-Stokes solver picks up the pressure fluctuations associated with the unsteady leading edge separation bubble. These types of fluctuations have large amplitudes and tend to dominate the cascade’s aerodynamic damping behavior.

On the Weis-Fogh mechanism of lift generation

1973 ◽  
Vol 60 (1) ◽  
pp. 1-17 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Stokes Equations ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Leading Edge ◽  
The Body ◽  
Navier Stokes ◽  
Encarsia Formosa ◽  
Concentrated Force ◽  
Stagnation Points ◽  
Wing Tips

Weis-Fogh (1973) proposed a new mechanism of lift generation of fundamental interest. Surprisingly, it could work even in inviscid two-dimensional motions starting from rest, when Kelvin's theorem states that the total circulation round a body must vanish, but does not exclude the possibility that if the body breaks into two pieces then there may be equal and opposite circulations round them, each suitable for generating the lift required in the pieces’ subsequent motions! The ‘fling’ of two insect wings of chord c (figure 1) turning with angular velocity Ω generates irrotational motions associated with the sucking of air into the opening gap which are calculated in § 2 as involving circulations −0·69Ωc2 and + 0.69Ωc2 around the wings when their trailing edges, which are stagnation points of those irrotational motions, break apart (position (f)). Viscous modifications to this irrotational flow pattern by shedding of vorticity at the boundary generate (§ 3) a leading-edge separation bubble, and tend to increase slightly the total bound vorticity. Its role in a three-dimensional picture of the Weis-Fogh mechanism of lift generation, involving formation of trailing vortices at the wing tips, and including the case of a hovering insect like Encarsia formosa moving those tips in circular paths, is investigated in § 4. The paper ends with the comment that the far flow field of such very small hovering insects should take the form of the exact solution (Landau 1944; Squire 1951) of the Navier-Stokes equations for the effect of a concentrated force (the weight mg of the animal) acting on a fluid of kinematic viscosity v and density p, whenever the ratio mg/pv2 is small enough for that jet-type induced motion to be stable.

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.

Simulation of the subsonic flow in a high-speed centrifugal compressor impeller by the pressure-based method

1998 ◽  
Vol 212 (4) ◽  
pp. 269-287 ◽  
Author(s):  
Y Wang ◽  
S Komori
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Navier Stokes Equations ◽  
Compressor Impeller ◽  
Collocated Grid

A pressure-based finite volume procedure developed previously for incompressible flows is extended to predict the three-dimensional compressible flow within a centrifugal impeller. In this procedure, the general curvilinear coordinate system is used and the collocated grid arrangement is adopted. Mass-averaging is used to close the instantaneous Navier-Stokes equations. The covariant velocity components are used as the main variables for the momentum equations, making the pressure-velocity coupling easier. The procedure is successfully applied to predict various compressible flows from subsonic to supersonic. With the aid of the k-ɛ turbulence model, the flow details within a centrifugal impeller are obtained using the present procedure. Predicted distributions of the meridional velocity and the static pressure are reasonable. Calculated radial velocities and flow angles are favourably compared with the measurements at the exit of the impeller.

Turbulent Flow Simulation of a Runner for Francis Hydraulic Turbines Using Pseudo-Compressibility

1996 ◽  
Vol 118 (2) ◽  
pp. 285-291 ◽  
Author(s):  
Chuichi Arakawa ◽  
Yi Qian ◽  
Takashi Kubota
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Leading Edge ◽  
Design Tool ◽  
Design Flow ◽  
Navier Stokes ◽  
Small Computer ◽  
Strong Vortex

A three-dimensional Navier-Stokes code with pseudo-compressibility, an implicit formulation of finite difference, and a k – ε two-equation turbulence model has been developed for the Francis hydraulic runner. The viscous flow in the rotating field can be simulated well in the design flow operating condition as well as in the off-design conditions in which a strong vortex occurs due to the separation near the leading edge. Because the code employs an implicit algorithm and a wall function near the wall, it does not require a large CPU time. It can therefore be used on a small computer such as the desk-top workstation, and is available for use as a design tool. The same kind of algorithm that is used for compressible flows has been found to be appropriate for the simulation of complex incompressible flows in the field of turbomachinery.

Numerical Simulation of the Two-Dimensional Viscous Compressible Flow in Blade Cascades Using a Solution-Adaptive Unstructured Mesh

1990 ◽  
Vol 112 (3) ◽  
pp. 311-319 ◽  
Author(s):  
G. L. D. Side´n ◽  
W. N. Dawes ◽  
P. J. Albra˚ten
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Rapid Development ◽  
Automatic Generation ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Explicit Finite Element ◽  
Eddy Viscosity Model ◽  
Viscous Compressible Flow

An explicit finite element procedure has been coupled with an automatic generation procedure for mesh-adaptive steady-state simulations of two-dimensional viscous compressible flows in cascades. Turbulence is modeled by a two-layer algebraic eddy viscosity model. Results show good behavior in comparison with measurements and results of a conventional H-mesh viscous flow solver. Computed loss approaches measured loss as the mesh is refined. Currently, the unstructured solver suffers in efficiency terms because the automatic mesh generator tends to produce inefficient equilateral triangles in the regions of shock waves and boundary layers where stretched elements would be more appropriate. This means that, at least for the Navier–Stokes equations, the unstructured approach is not yet competitive with conventional structured techniques. Nevertheless, this will change once the key advantages of geometric flexibility and user-independent solutions force rapid development.

Numerical Analysis of Three-Dimensional Bjo¨rk–Shiley Valvular Flow in an Aorta

1997 ◽  
Vol 119 (1) ◽  
pp. 45-51 ◽  
Author(s):  
E.-B. Shim ◽  
K.-S. Chang
Keyword(s):  
Shear Stress ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Jet Flows ◽  
Computational Results ◽  
Navier Stokes Equations ◽  
Disk Valve

Laminar vortical flow around a fully opened Bjo¨rk–Shiley valve in an aorta is obtained by solving the three-dimensional incompressible Navier–Stokes equations. Used is a noniterative implicit finite-element Navier–Stokes code developed by the authors, which makes use of the well-known finite difference algorithm PISO. The code utilizes segregated formulation and efficient iterative matrix solvers such as PCGS and ICCG. Computational results show that the three-dimensional vortical flow is recirculating with large shear in the sinus region of the valve chamber. Passing through the valve, the flow is split into major upper and lower jet flows. The spiral vortices generated by the disk are advected in the wake and attenuated rapidly downstream by diffusion. It is shown also that the shear stress becomes maximum near the leading edge of the disk valve.

scholarly journals Closed-form solution for the edge vortex of a revolving plate

2017 ◽  
Vol 821 ◽  
pp. 200-218 ◽  
Author(s):  
Di Chen ◽  
Dmitry Kolomenskiy ◽  
Hao Liu
Keyword(s):  
Closed Form ◽  
Stokes Equations ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Leading Edge ◽  
Form Solution ◽  
Navier Stokes ◽  
Edge Vortex ◽  
Leading Edge Vortices

Flapping and revolving wings can produce attached leading-edge vortices when the angle of attack is large. In this work, a low-order model is proposed for the edge vortices that develop on a revolving plate at $90^{\circ }$ angle of attack, which is the simplest limiting case, yet shows remarkable similarity with the generally known leading-edge vortices. The problem is solved analytically, providing short closed-form expressions for the circulation and the position of the vortex. The good agreement with the numerical solution of the Navier–Stokes equations suggests that, for the conditions examined, the vorticity production at the sharp edge and its subsequent three-dimensional transport are the main effects that shape the edge vortex.

Performance Evaluation of an Internal Flow Navier-Stokes Solver for Compressible Viscous Flow Simulations

2002 ◽  
Author(s):  
H. Tug˘rul Tınaztepe ◽  
Ahmet S¸. U¨c¸er ◽  
I˙. Sinan Akamandor
Keyword(s):  
Flow Field ◽  
Separation Bubble ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Internal Flow ◽  
Leading Edge ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Local Scaling ◽  
Characteristic Boundary

A three-dimensional compressible full Navier-Stokes solver is developed for the analysis of the flow field inside turbomachinary cascades. The solver uses an explicit second order accurate (cell-vertex) finite volume Lax-Wendroff scheme over hexahedral cells. The viscous and heat conduction terms are discretized in conservative form at the cell center. Second and fourth order numerical smoothing terms are added with local scaling factors. Eddy viscosity is calculated by the Baldwin-Lomax model and is adapted to the pointered cell based algorithm. Turbulent viscosity is blended by inverse distance square weighting functions near corners. Characteristic boundary conditions are used. A computational analysis has been carried out to present the capability of the solver in capturing secondary velocity patterns, flow angles and total pressure loss distributions inside a linear high turning turbine cascade. A controlled diffusion compressor cascade at high incidence has been analyzed. Main features of the flow field in this compressor cascade were resolved (secondary and end wall flows and leading edge laminar separation bubble) as in the experimental data. The main aim of the work is to demonstrate the performance of the code in capturing the details of the complicated flow fields using grids that can be regarded as coarse.

On the Numerical Solution of Two-Dimensional, Laminar Compressible Flows With Imbedded Shock Waves

1972 ◽  
Vol 94 (4) ◽  
pp. 765-769 ◽  
Author(s):  
W. D. Goodrich ◽  
J. P. Lamb ◽  
J. J. Bertin
Keyword(s):  
Shock Waves ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Leading Edge ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Numerical Experimentation ◽  
Explicit Finite Difference

The complete, time-dependent Navier-Stokes equations are expressed in conservation form and solved by employing an explicit finite difference numerical technique which incorporates artificial viscosity terms of the form first suggested by Rusanov for numerical stability in the vicinity of shock waves. Surface boundary conditions are developed in a consistent and unique manner through the use of a physically oriented extrapolation procedure. From numerical experimentation an extended range for the explicit stability parameter is established. Also employed is an additional convergence parameter which relates incremental spatial steps. Convergence of the transient solution to a steady state flow was obtained after 400 to 500 time steps. Sample solutions are presented for supersonic flow of air over the leading edge of a slightly blunted flat plate, past a backward facing step, and in the near wake of a blunt trailing edge. Free-stream Mach numbers from 2 to 10 are included in the sample computations.

Numerical Investigations of Transonic Cavity Flow Control Using Steady and Pulsed Fluidic Injection

2005 ◽  
Author(s):  
K. Das ◽  
A. Hamed ◽  
D. Basu
Keyword(s):  
Kinetic Energy ◽  
Sound Pressure Level ◽  
Sound Pressure ◽  
Stokes Equations ◽  
Numerical Study ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Pressure Level ◽  
Navier Stokes ◽  
Detached Eddy Simulation

A numerical study is conducted to investigate steady and pulsed fluidic actuation in transonic flow over an open cavity. Numerical results are obtained for the unsteady three-dimensional flow with three different steady mass injection rates and one pulsed injection upstream of the cavity. The simulations are carried out using the full 3-D Navier Stokes equations with the two-equation k-ε based Detached Eddy Simulation (DES) model to calculate the flow and acoustic fields. Computational results are presented for unsteady pressure fluctuations, vorticity contours and kinetic energy profiles at different injection ratios. The sound pressure level (SPL) and the kinetic energy spectra highlight the effectiveness of actuation in tone attenuation at peak frequencies. The computed sound pressure level (SPL) spectra with and without injection are compared with available experimental data and LES predictions.

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