On the Use of Direct and Inverse Numerical Flow Calculations for Supersonic Turbine Design

1994 ◽  
Author(s):  
F. Pommel
Keyword(s):  
Flow Field ◽  
Euler Equations ◽  
Velocity Component ◽  
Normal Velocity ◽  
Blade Design ◽  
Blade Profile ◽  
Flow Solver ◽  
Time Marching ◽  
Turbine Design ◽  
Marching Method

A procedure for blade design, using a time marching method to solve the Euler equations in the blade-to-blade plane is presented. This procedure uses an Office Nationale d’Etude et de Recherches Aeronautique flow solver. The classical slip conditions (no normal velocity component along the blade profile) has been replaced by another boundary conditions in such a way that the required pressure may be imposed directly. The orignal direct code was therefore transformed into an inverse solver. The unknows are calculated on the blade wall using the so-called compatibility relations. The blade geometry is then modified by resetting the wall parallel to the new flow field. The results obtained with this design process for a supersonic turbine blade of a space turbopump is presented.

Design Method for Subsonic and Transonic Cascade With Prescribed Mach Number Distribution

1992 ◽  
Vol 114 (3) ◽  
pp. 553-560 ◽  
Author(s):  
O. Le´onard ◽  
R. A. Van den Braembussche
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Pressure Distribution ◽  
Velocity Component ◽  
Design Method ◽  
Normal Velocity ◽  
Flow Solver ◽  
Number Distribution ◽  
Mach Number Distribution ◽  
Transonic Cascade

A iterative procedure for blade design, using a time marching procedure to solve the unsteady Euler equations in the blade-to-blade plane, is presented. A flow solver, which performs the analysis of the flow field for a given geometry, is transformed into a design method. This is done by replacing the classical slip condition (no normal velocity component) by other boundary conditions, in such a way that the required pressure or Mach number distribution may be imposed directly on the blade. The unknowns are calculated on the blade wall using the so-called compatibility relations. Since the blade shape is not compatible with the required pressure distribution, a nonzero velocity component normal to the blade wall evolves from the new flow calculation. The blade geometry is then modified by resetting the wall parallel to the new flow field, using a transpiration technique, and the procedure is repeated until the calculated pressure distribution has converged to the required one. Examples for both subsonic and transonic flows are presented and show a rapid convergence to the geometry required for the desired Mach number distribution. An important advantage of the present method is the possibility to use the same code for the design and the analysis of a blade.

Design Method for Subsonic and Transonic Cascade With Prescribed Mach Number Distribution

1991 ◽  
Author(s):  
O. Léonard ◽  
R. A. Van Den Braembussche
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Pressure Distribution ◽  
Velocity Component ◽  
Design Method ◽  
Normal Velocity ◽  
Flow Solver ◽  
Number Distribution ◽  
Mach Number Distribution ◽  
Transonic Cascade

An iterative procedure for blade design, using a Time Marching procedure to solve the unsteady Euler equations in the blade-to-blade plane is presented. A flow solver, which performs the analysis of the flow field for a given geometry, is transformed into a design method. This is done by replacing the classical slip condition (no normal velocity component) by other boundary conditions, in such a way that the required pressure or Mach number distribution may be imposed directly on the blade. The unknowns are calculated on the blade wall using the so-called compatibility relations. Since the blade shape is not compatible with the required pressure distribution, a non-zero velocity component normal to the blade wall evolves from the new flow calculation. The blade geometry is then modified by resetting the wall parallel to the new flow field, using a transpiration technique, and the procedure is repeated until the calculated pressure distribution has converged to the required one. Examples for both subsonic and transonic flows are presented and show a rapid convergence to the geometry required for the desired Mach number distribution. An important advantage of the present method is the possibility to use the same code for the design and the analysis of a blade.

Numerical Analysis of Internal Flow Field in an Impeller with the Time Marching Method

2011 ◽  
Vol 94-96 ◽  
pp. 1476-1480
Author(s):  
Cai Hua Wang
Keyword(s):  
Flow Field ◽  
High Speed ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Internal Flow ◽  
Centrifugal Impeller ◽  
Three Dimensional Flow ◽  
Vector Distribution ◽  
Time Marching ◽  
Marching Method

Centrifugal compressors are power machineries used widely. Fully understanding of the complex three-dimensional flow field is very important to design higher pressure ratio, higher efficiency centrifugal compressor. In this paper, time marching method is adopted to solve the three-dimensional viscous N-S equations under the relative coordinate system. The internal flow field of the “full controllable vortex” high speed centrifugal impeller is analyzed and the medial velocity vector distribution and the development of the velocity of each section in the impeller are showed. From the figures, it can be seen that the “wake” phenomenon, such as Ecckart described, caused by the curvature, Coriolis force and the boundary layer is exist

scholarly journals A Blended Continuation Method for Solving Steady Inviscid Flow

2018 ◽  
Vol 36 (1) ◽  
pp. 57-65
Author(s):  
Lei Qiao ◽  
Junqiang Bai ◽  
Yasong Qiu ◽  
Jun Hua ◽  
Jiakuan Xu
Keyword(s):  
Flow Field ◽  
Steady Flow ◽  
Flow Problem ◽  
Continuation Method ◽  
Inviscid Flow ◽  
Laplacian Operator ◽  
Uniform Field ◽  
Aerodynamic Design ◽  
Time Marching ◽  
Marching Method

Steady flow field solving is wieldly used in aircraft aerodynamic design, efficiency of steady flow field solving has great influnence on efficiency of aircraft aerodynamic design. A continuation method that blended Laplacian operator and pseudo time marching method for solving steady inviscid flow problem is proposed. In steady flow problem, the field is usually initialized as an uniform field before starting iteration. This resulted in the fact that the initial residual in only nonzero on wall boundary. Based on this feature, Laplacian operator is introduced to accelarate convergence at the starting stage of nonlinear solving. At the ending stage of nonlinear solving, the blended continuation term is biased to pseduo time marching method to avoid over dissipation graduately. To establish a complete continuation method, the starting, evolution and termination method are also described. At last, the proposed continuation method is implemented in a finite element solver, and tested aginst GAMM channel and NACA0012 foil subsonic and transonic cases. Numerical test results confirmed that the blended continuation method could get an efficency improvement about 1/3 to 1/4 comparing with stand alone Laplacian continuation and much more better than pure pseudo time marching method.

A numerical study of the wave-induced solute transport above a rippled bed

1995 ◽  
Vol 299 ◽  
pp. 267-288 ◽  
Author(s):  
K. T. Shum
Keyword(s):  
Flow Field ◽  
Solute Transport ◽  
Concentration Profile ◽  
Vortical Flow ◽  
Sediment Surface ◽  
Normal Velocity ◽  
Advective Transport ◽  
Fluid Particles ◽  
Wave Induced ◽  
Rippled Bed

The role of wave-induced separated flow in solute transport above a rippled bed is studied from numerical solutions to the two-dimensional Navier–Strokes equations and the advection-diffusion equation. A horizontal ambient flow that varies sinusoidally in time is imposed far above the bed, and a constant concentration difference between the upper and lower boundaries of computation is assumed. The computed flow field is the sum of an oscillatory rectilinear flow and a vortical flow which is periodic both in time and in the horizontal. Poincaré sections of this flow suggest chaotic mixing. Vertical lines of fluid particles above the crest and above the trough deform into whorls and tendrils, respectively, in just one wave period. Horizontal lines near the bottom deform into Smale horseshoe patterns. The combination of high shear and vortex-induced normal velocity close to the sediment surface results in large net displacements of fluid particles in a period. The resulting advective transport normal to the bed can be higher than molecular diffusion from well within the viscous boundary layer up to a few ripple heights above the bed. When this flow field is applied to the transport equation of a passive scalar, two distinct features – regular temporal oscillations in concentration and a linear time-averaged vertical concentration profile – are found immediately above the bed. These features have also been observed previously in field measurements on oxygen concentration. Advective transport is shown to be dominant even in the region where the time-averaged concentration profile is linear, a region where vertical solute transport has often been estimated using diffusion-type models in many field studies.

Calculation of the Quasi Three-Dimensional Flow in a Turbomachine Blade Row

1977 ◽  
Vol 99 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Jean-Pierre Veuillot
Keyword(s):  
Finite Difference ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Through Flow ◽  
Blade Row ◽  
Time Marching ◽  
Space Discretization ◽  
Finite Volume Approach ◽  
Marching Method ◽  
Finite Difference Techniques

The equations of the through flow are obtained by an asymptotic theory valid when the blade pitch is small. An iterative method determines the meridian stream function, the circulation, and the density. The various equations are discretized in an orthogonal mesh and solved by classical finite difference techniques. The calculation of the steady transonic blade-to-blade flow is achieved by a time marching method using the MacCormack scheme. The space discretization is obtained either by a finite difference approach or by a finite volume approach. Numerical applications are presented.

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