scholarly journals Application of a Navier-Stokes Analysis to Transonic Cascade Flow Fields

1982 ◽  
Author(s):  
S. J. Shamroth ◽  
H. McDonald ◽  
W. R. Briley
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Controlled Diffusion ◽  
Cascade Flow ◽  
Model Predictions ◽  
Flow Through ◽  
Transonic Cascade

A numerical solution procedure for the ensemble-averaged compressible time-dependent Navier-Stokes equations is applied to the transonic cascade flow field. The equations are solved by the consistently split linearized block implicit (LBI) method of Briley and McDonald. Boundary conditions are set so as to specify upstream total pressure and downstream static pressure. Turbulence is modeled by a mixing length model. Predictions are made for flow through a Jose Sanz controlled diffusion cascade and the method yields converged solutions within a relatively small number of time steps (≈ 150). Although to date comparisons with data have not been made, the results show the expected cascade flow field features.

Prediction of Cascade Flow Fields Using the Averaged Navier-Stokes Equations

1984 ◽  
Vol 106 (2) ◽  
pp. 383-390 ◽  
Author(s):  
S. J. Shamroth ◽  
H. McDonald ◽  
W. R. Briley
Keyword(s):  
Transonic Flow ◽  
Static Pressure ◽  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Cascade Flow ◽  
Model Predictions ◽  
Flow Through

A numerical solution procedure for the ensemble-averaged, compressible, time-dependent Navier-Stokes equations is applied to predict the flow about a cascade of airfoils operating in the transonic flow regime. The equations are solved by the consistently split, linearized block implicit (LBI) method of Briley and McDonald. Boundary conditions are set so as to specify upstream total pressure and downstream static pressure. Turbulence is modeled by a mixing length model. Predictions are made for flow through a compressor cascade configuration. The method yields converged solutions within a relatively small number of time steps ( ≈ 150), which give good comparisons with experimental data.

Calculations of Two and Three-Dimensional Transonic Cascade Flow Fields Using the Navier-Stokes Equations

1986 ◽  
Vol 108 (1) ◽  
pp. 93-102 ◽  
Author(s):  
B. C. Weinberg ◽  
R.-J. Yang ◽  
H. McDonald ◽  
S. J. Shamroth
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Solid Surfaces ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Cascade Calculation ◽  
Transonic Cascade ◽  
Good Agreement

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and no-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive ‘O’-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (∼ 80–150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.

Navier–Stokes Solution for Steady Two-Dimensional Transonic Cascade Flows

1988 ◽  
Vol 110 (3) ◽  
pp. 339-346 ◽  
Author(s):  
O. K. Kwon
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Transonic Turbine ◽  
Transonic Cascade

A robust, time-marching Navier–Stokes solution procedure based on the explicit hopscotch method is presented for solution of steady, two-dimensional, transonic turbine cascade flows. The method is applied to the strong conservation form of the unsteady Navier–Stokes equations written in arbitrary curvilinear coordinates. Cascade flow solutions are obtained on an orthogonal, body-conforming “O” grid with the standard k–ε turbulence model. Computed results are presented and compared with experimental data.

scholarly journals Transonic Cascade Flow Prediction Using the Navier-Stokes Equations

1991 ◽  
Author(s):  
A. Arnone ◽  
S. S. Stecco
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Good Reliability ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Numerical Predictions ◽  
Cascade Flow ◽  
Flow Prediction ◽  
Transonic Cascade ◽  
Comparison With Experiments

This paper presents results which summarize the work carried out during the last three years to improve the efficiency and accuracy of numerical predictions in turbomachinery flow calculations. A new kind of non-periodic C-type grid is presented and a Runge-Kutta scheme with accelerating strategies is used as a flow solver. The code capability is presented by testing four different blades at different exit Mach numbers in transonic regimes. Comparison with experiments shows the very good reliability of the numerical prediction. In particular the loss coefficient seems to be correctly predicted by using the well-known Baldwin-Lomax turbulence model.

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

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