scholarly journals Navier-Stokes Analysis of Unsteady Transonic Flows Through Gas Turbine Cascades With and Without Coolant Ejection

1997 ◽  
Author(s):  
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto
Keyword(s):  
Gas Turbine ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Implicit Time ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Turbine Cascades ◽  
Annular Cascade

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

Comparison of Semi-Empirical Correlations and a Navier-Stokes Method for the Overall Performance Assessment of Turbine Cascades

2003 ◽  
Vol 125 (2) ◽  
pp. 308-314 ◽  
Author(s):  
C. Cravero ◽  
A. Satta
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Angle ◽  
Aerodynamic Performances ◽  
Outlet Flow ◽  
Time Marching ◽  
Overall Performance ◽  
Turbine Cascades ◽  
Semi Empirical

Turbomachinery flows can nowadays be investigated using several numerical techniques to solve the full set of Navier-Stokes equations; nevertheless the accuracy in the computation of losses is still a challenging topic. The paper describes a time-marching method developed by the authors for the integration of the Reynolds averaged Navier-Stokes equations in turbomachinery cascades. The attention is focused on turbine sections and the computed aerodynamic performances (outlet flow angle, profile loss, etc.,) are compared to experimental data and/or correlations. The need for this kind of CFD analysis tools is stressed for the substitution of standard correlations when a new blade is designed.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

scholarly journals Fluid-kinetic modelling for respiratory aerosols with variable size and temperature

2020 ◽  
Vol 67 ◽  
pp. 100-119 ◽  
Author(s):  
Laurent Boudin ◽  
Céline Grandmont ◽  
Bérénice Grec ◽  
Sébastien Martin ◽  
Amina Mecherbet ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Kinetic Modelling ◽  
Type Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aerosol Dynamics ◽  
Convection Diffusion Equation ◽  
Time Marching ◽  
Branched Structure ◽  
The Impact

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.

Perturbation Procedures for Nonlinear Viscous Flows

1983 ◽  
Vol 50 (2) ◽  
pp. 265-269
Author(s):  
D. Nixon
Keyword(s):  
Perturbation Theory ◽  
Shock Waves ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Two Dimensions ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations

The perturbation theory for transonic flow is further developed for solutions of the Navier-Stokes equations in two dimensions or for experimental results. The strained coordinate technique is used to treat changes in location of any shock waves or large gradients.

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