Inverse Design of and Experimental Measurements in a Double-Passage Transonic Turbine Cascade Model

2005 ◽  
Vol 127 (3) ◽  
pp. 619-626 ◽  
Author(s):  
G. M. Laskowski ◽  
A. Vicharelli ◽  
G. Medic ◽  
C. J. Elkins ◽  
J. K. Eaton ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Design Procedure ◽  
Cascade Model ◽  
Inverse Design ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Flow Conditions ◽  
Navier Stokes Equations ◽  
Attached Flow ◽  
Transonic Turbine

A new transonic turbine cascade model that accurately produces infinite cascade flow conditions with minimal compressor requirements is presented. An inverse design procedure using the Favre-averaged Navier-Stokes equations and k‐ε turbulence model based on the method of steepest descent was applied to a geometry consisting of a single turbine blade in a passage. For a fixed blade geometry, the passage walls were designed such that the surface isentropic Mach number (SIMN) distribution on the blade in the passage matched the SIMN distribution on the blade in an infinite cascade, while maintaining attached flow along both passage walls. An experimental rig was built that produces realistic flow conditions, and also provides the extensive optical access needed to obtain detailed particle image velocimetry measurements around the blade. Excellent agreement was achieved between computational fluid dynamics (CFD) of the infinite cascade SIMN, CFD of the designed double passage SIMN, and the measured SIMN.

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 Viscous Flow Computations in Turbomachine Cascades

1990 ◽  
Author(s):  
P.-A. Chevrin ◽  
C. Vuillez
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Different Types ◽  
Time Marching ◽  
Transonic Turbine

Accurate prediction of the flow in turbomachinery requires numerical solution of the Navier-Stokes equations. A two-dimensional Navier-Stokes solver developed at ONERA for the calculation of the flow in turbine and compressor cascades was adapted at SNECMA to run on different types of grid. The solver uses an explicit, time-marching, finite-volume technique, with a multigrid acceleration scheme. A multi-domain approach is used to handle difficulties due to the geometry of the flow. An H-C grid was used in the calculations. Two turbulence models, based on the mixing length approach, were used. The flow in a transonic compressor cascade, a subsonic and a transonic turbine cascade were computed. Comparison with experiments is presented.

The evolution of piston-driven pipe flow: thermal transpiration

2006 ◽  
Vol 463 (2079) ◽  
pp. 675-696
Author(s):  
A.M.J Davis
Keyword(s):  
Pipe Flow ◽  
State Transition ◽  
Stokes Equations ◽  
Solvability Condition ◽  
Navier Stokes ◽  
Entry And Exit ◽  
Flow Conditions ◽  
Additional Result ◽  
Navier Stokes Equations ◽  
Thermal Transpiration

The steady-state transition from and to the uniform entry and exit flow profiles is well described, at large aspect ratio, in terms of the stream function by the pipe eigenfunctions. But these latter are unsuited to oscillatory motion or the time evolution of the symmetric piston-driven pipe flow, for which an appropriate solution has a combination of a Fourier series along the finite pipe and a Fourier–Bessel series in the transverse direction. A non-uniqueness requires the identification of a solvability condition and care is needed in demonstrating its satisfaction. An additional result is that the solution must be constructed to satisfy the normal flow conditions identically. Application is made to thermal transpiration, recently explained by the revised Navier–Stokes equations and boundary conditions.

3D Viscous Inverse Design of Vaned Diffuser to Suppress Flow Unsteadiness in a Centrifugal Compressor

2005 ◽  
Author(s):  
Victor I. Mileshin ◽  
Igor A. Brailko ◽  
Andrew N. Startsev ◽  
Igor K. Orekhov
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Pressure Ratio ◽  
Design Procedure ◽  
Inverse Design ◽  
Navier Stokes ◽  
Low Velocity ◽  
Vaned Diffuser ◽  
Pressure Surface

Present paper is devoted to numerical investigation of unsteadiness caused by impeller-diffuser interaction in a 8:1 total pressure ratio centrifugal compressor. The compressor designed by CIAM [7], and manufactured and tested by Customer gave satisfactory performances even under the first test. Further development requires new insights and advanced numerical tools. In this context, this paper presents Navier-Stokes computations of 3D viscous unsteady flow field within the impeller-diffuser configuration. Steady and unsteady computations indicated spacious zone of low velocity / reverse flow on pressure surface of the diffuser vane. To suppress this reverse flow, new vaned diffuser has been tailored through application of 3D inverse design procedure for Navier-Stokes equations [8]. Subsequent steady and unsteady N-S calculations performed for compressor with the new diffuser demonstrated depression of reverse flow within diffuser and different unsteady loading of the diffuser vane.

Unsteady transonic nozzle flow of dense gases

1996 ◽  
Vol 310 ◽  
pp. 113-137 ◽  
Author(s):  
A. Kluwick ◽  
St. Scheichl
Keyword(s):  
Stokes Equations ◽  
Classical Equation ◽  
Transition Process ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Supersonic Expansion ◽  
Navier Stokes Equations ◽  
Specific Heats ◽  
Dense Gases ◽  
Theoretical Considerations

Vapours of retrograde fluids, i.e. media with large values of the specific heats, may have the remarkable property that sonic conditions are reached three times rather than once during isentropic expansion or compression. As a result, the acceleration of such a fluid through a converging-diverging Laval nozzle under steady flow conditions may lead to the occurrence of an expansion shock discontinuity. Theoretical considerations then suggest that nozzles with two throats should be designed to achieve a full shock-free subsonic-supersonic expansion.In this study the unsteady flow of a dense, retrograde gas through slender nozzles (with one and two throats) is considered. The combination of the Navier-Stokes equations supplemented with a non-classical equation of state for the fluid yields a generalized wave equation, with its validity restricted to flow conditions near the critical value M = 1. This equation is used to study the transition process which sets in if a steady subsonic solution is perturbed by lowering the pressure at the end of the nozzle.

Advanced Transonic Fan Design Procedure Based on a Navier–Stokes Method

1994 ◽  
Vol 116 (2) ◽  
pp. 291-297 ◽  
Author(s):  
C. M. Rhie ◽  
R. M. Zacharias ◽  
D. E. Hobbs ◽  
K. P. Sarathy ◽  
B. P. Biederman ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Design Method ◽  
Three Dimensional ◽  
Design Procedure ◽  
Cost Savings ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Validation Data ◽  
Navier Stokes Equations

A fan performance analysis method based upon three-dimensional steady Navier–Stokes equations is presented in this paper. Its accuracy is established through extensive code validation effort. Validation data comparisons ranging from a two-dimensional compressor cascade to three-dimensional fans are shown in this paper to highlight the accuracy and reliability of the code. The overall fan design procedure using this code is then presented. Typical results of this design process are shown for a current engine fan design. This new design method introduces a major improvement over the conventional design methods based on inviscid flow and boundary layer concepts. Using the Navier–Stokes design method, fan designers can confidently refine their designs prior to rig testing. This results in reduced rig testing and cost savings as the bulk of the iteration between design and experimental verification is transferred to an iteration between design and computational verification.

scholarly journals Adaptive Unstructured 2D Navier-Stokes Solutions on Mixed Quadrilateral/Triangular Meshes

1993 ◽  
Author(s):  
Stuart D. Connell ◽  
D. Graham Holmes ◽  
Mark E. Braaten
Keyword(s):  
Stokes Equations ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Quadrilateral Elements ◽  
Time Marching ◽  
Transonic Turbine ◽  
The One ◽  
Marching Scheme

This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on an unstructured mixed grid of triangles and quadrilaterals. The solution procedure uses an explicit Runge-Kutta finite volume time marching scheme with an adaptive blend of second and fourth order smoothing. The governing equations are solved in a 2D, axisymmetric or quasi-3D form. In viscous regions quadrilateral elements are used to facilitate the one dimensional refinement required for the efficient resolution of boundary layers and wakes. The effect of turbulence is incorporated through using either a Baldwin-Lomax or k-ε turbulence model. Solutions are presented for several examples that illustrate the capability of the algorithm to predict viscous phenomena accurately. The examples are a transonic turbine, a nozzle and a combustor diffuser.

Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids

2005 ◽  
Vol 219 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Y Mei ◽  
A Guha
Keyword(s):  
Numerical Simulation ◽  
Finite Volume ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Flow Through

Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model ( k-ɛ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.

scholarly journals Large eddy simulations in 2030 and beyond

2014 ◽  
Vol 372 (2022) ◽  
pp. 20130320 ◽  
Author(s):  
U Piomelli
Keyword(s):  
Stokes Equations ◽  
Academic Community ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Academic Environment ◽  
Flow Conditions ◽  
Local Flow ◽  
Navier Stokes Equations ◽  
The Past ◽  
Large Eddy

Since its introduction, in the early 1970s, large eddy simulations (LES) have advanced considerably, and their application is transitioning from the academic environment to industry. Several landmark developments can be identified over the past 40 years, such as the wall-resolved simulations of wall-bounded flows, the development of advanced models for the unresolved scales that adapt to the local flow conditions and the hybridization of LES with the solution of the Reynolds-averaged Navier–Stokes equations. Thanks to these advancements, LES is now in widespread use in the academic community and is an option available in most commercial flow-solvers. This paper will try to predict what algorithmic and modelling advancements are needed to make it even more robust and inexpensive, and which areas show the most promise.

Computational Analysis of Conjugate Heat Transfer in Gaseous Microchannels

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Giulio Croce ◽  
Olga Rovenskaya ◽  
Paola D'Agaro
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mach Number ◽  
Heat Sink ◽  
Conjugate Heat Transfer ◽  
Stokes Equations ◽  
Heat Transfer Analysis ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Navier Stokes Equations

A fully conjugate heat transfer analysis of gaseous flow in short microchannels is presented. Navier–Stokes equations, coupled with Maxwell and Smoluchowski slip and temperature jump boundary conditions, are used for numerical analysis. Results are presented in terms of Nusselt number, heat sink thermal resistance, and resulting wall temperature as well as Mach number profiles for different flow conditions. The comparative importance of wall conduction, rarefaction, and compressibility are discussed. It was found that compressibility plays a major role. Although a significant penalization in the Nusselt number, due to conjugate heat transfer effect, is observed even for a small value of solid conductivity, the performances in terms of heat sink efficiency are essentially a function only of the Mach number.

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