The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1992 ◽  
Vol 114 (3) ◽  
pp. 528-537 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodology. The fully three-dimensional, compressible, Reynolds-averaged Navier–Stokes equations with k–ε turbulence modeling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

1991 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Unstructured Mesh ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Mean Value ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Transonic Compressor

This paper presents a numerical method for the simulation of flow in turbomachinery blade rows using a solution-adaptive mesh methodolgy. The fully three dimensional, compressible, Reynolds averaged Navier-Stokes equations with k-ε turbulence modelling (and low Reynolds number damping terms) are solved on an unstructured mesh formed from tetrahedral finite volumes. At stages in the solution, mesh refinement is carried out based on flagging cell faces with either a fractional variation of a chosen variable (like Mach number) greater than a given threshold or with a mean value of the chosen variable within a given range. Several solutions are presented, including that for the highly three-dimensional flow associated with the corner stall and secondary flow in a transonic compressor cascade, to demonstrate the potential of the new method.

IGV-Rotor Interaction Analysis in a Transonic Compressor Using the Navier-Stokes Equations

1996 ◽  
Author(s):  
Andrea Arnone ◽  
Roberto Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Guide Vane ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Inlet Guide Vane ◽  
Operating Characteristics ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Mass Flow Rates

A recently developed, time-accurate multigrid viscous solver has been extended to handle quasi-three-dimensional effects and applied to the first stage of a modern transonic compressor. Interest is focused on the inlet guide vane (IGV):rotor interaction where strong sources of unsteadiness are to be expected. Several calculations have been performed to predict the stage operating characteristics. Flow structures at various mass flow rates, from choke to near stall, are presented and discussed. Comparisons between unsteady and steady pitch-averaged results are also included in order to obtain indications about the capabilities of steady, multi-row analyses.

scholarly journals On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yat Tin Chow ◽  
Ali Pakzad
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Energy Dissipation Rate ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Additional Hypothesis ◽  
The Mean ◽  
Deterministic Force ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider the three-dimensional stochastically forced Navier–Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper bounds of the mean value of the time-averaged energy dissipation rate are derived directly from the equations for weak (martingale) solutions. This estimate is consistent with the Kolmogorov dissipation law. Moreover, an additional hypothesis of energy balance implies the zeroth law of turbulence in the absence of a deterministic force.</p>

IGV–Rotor Interaction Analysis in a Transonic Compressor Using the Navier–Stokes Equations

1998 ◽  
Vol 120 (1) ◽  
pp. 147-155 ◽  
Author(s):  
A. Arnone ◽  
R. Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Guide Vane ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Inlet Guide Vane ◽  
Operating Characteristics ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Mass Flow Rates

A recently developed, time-accurate multigrid viscous solver has been extended to handle quasi-three-dimensional effects and applied to the first stage of a modern transonic compressor. Interest is focused on the inlet guide vane (IGV)-rotor interaction where strong sources of unsteadiness are to be expected. Several calculations have been performed to predict the stage operating characteristics. Flow structures at various mass flow rates, from choke to near stall, are presented and discussed. Comparisons between unsteady and steady pitch-averaged results are also included in order to obtain indications about the capabilities of steady, multi-row analyses.

Development of a 3D Navier Stokes Solver for Application to all Types of Turbomachinery

1988 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Basic Algorithm ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Stage Of Development ◽  
Code Performance

This paper describes the current stage of development of a code aimed at solving the 3D Navier-Stokes equations in any type of turbomachinery geometry. The basic algorithm time marches the fully 3D unsteady equations of motion expressed in finite volume form with a two step explicit / one step implicit method. Full multigrid acceleration is used to reduce solution time and maintain code performance on fine meshes. Turbulence modelling is via mixing-length closure and the widely used Baldwin-Lomax model. The generality and robustness of the code is demonstrated by application to five different test cases, three axial and two radial configurations. Also included is a grid independence study which demonstrates near grid independent solutions for transonic compressor cascade flow (albeit with the actual result subject to transition modelling constraints). For two of the axial cases (transonic compressor in cascade, secondary flow in a high speed compressor) and one radial case (Eckardt high speed impellor) sufficient mesh is employed for the predictions to be essentially quantitative. The other two cases (radial inflow turbine with clearance and compressor stator with hub clearance) are really simulations rather than predictions, but are included as the flows are novel and provide much physical insight.

scholarly journals Transonic Turbomachinery Calculations Using a Hybrid Structured-Unstructured Grid Method

1994 ◽  
Author(s):  
Scott M. Richardson
Keyword(s):  
Unstructured Grid ◽  
Unstructured Mesh ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Grid Method ◽  
Navier Stokes ◽  
Flow Equations ◽  
Transonic Compressor ◽  
Flow Features ◽  
Grid Points

A method is presented for solving the two-dimensional Navier-Stokes equations on a solution-adaptive grid of both structured and unstructured meshes. Flow near airfoil surfaces is modeled using an implicit finite difference algorithm on a structured O-type mesh. The flow equations in the blade passages are written in a cell-vertex finite volume formulation and are solved on an unstructured mesh using a Runge-Kutta explicit algorithm. Both the structured and unstructured grid also include solution dependent adaptation to allow resolution of flow features with a minimum of grid points. The structured mesh divides to locally add grid lines, while the unstructured mesh allows the addition or removal of individual cells. An overlapping interface region is used to conservatively communicate flow variable information between the two grids. The quasi-three-dimensional effects of streamtube contraction and radius change are included to allow calculation of modern turbomachine designs. A study is included to determine the effect on cacade parameters of inclusion of viscous terms in the solution of the flow equations in the unstructured domain. Quasi-three-dimensional computations of flow through a transonic compressor and turbine cascade are compared with experimental data.

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 3D Flow Structures and Operating Characteristic of an Industrial Fluid Coupling

1995 ◽  
Author(s):  
H. Huitenga ◽  
T. Formanski ◽  
N. K. Mitra ◽  
M. Fiebig
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Laminar And Turbulent Flow ◽  
Fluid Coupling ◽  
Complex Flow Structure ◽  
Insight Into

A liquid circulating between an input rotor and an output rotor transmits power in a fluid coupling. Insight into the flow field is required to influence the transmission behaviour. Parameter studies of model geometries of fluid couplings were presented previously. Laminar and turbulent flow fields and characteristic curves of an actual industrial fluid coupling have been computed from the numerical solution of the three-dimensional, nonsteady Navier-Stokes equations on a body fitted rotating coordinate system. Results show the complex flow structure and vortices that determine the transported angular momentum. Comparison with measured torque suggests that the turbulence modeling by standard k-ϵ model may be inadequate at large slip.

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.

A Computational Study of Tip Desensitization in Axial Flow Turbines: Part 1 — Baseline Turbine Computations and Comparisons With Measurement

2004 ◽  
Author(s):  
James A. Tallman
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Computational Study ◽  
Three Dimensional ◽  
Axial Flow ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Penn State ◽  
High Pressure Stage

This study used Computational Fluid Dynamics (CFD) to investigate modified turbine blade tip shapes as a means of reducing the leakage flow and vortex. The subject of this study was the single-stage experimental turbine facility at Penn State University, with scaled three-dimensional geometry representative of a modern high-pressure stage. To validate the numerical procedure, the rotor flowfield was first computed with no modification to the tip, and the results compared with measurements of the flowfield. The flow was then predicted for a variety of different tip shapes: first with coarse grids for screening purposes and then with more refined grids for final verification of preferred tip geometries. Part 1 of this two-part paper focuses on the turbine case description, numerical procedure, baseline flat-tip computations, and comparison of the baseline results with measurement. A Runge-Kutta time-marching CFD solver (ADPAC) was used to solve the Reynolds-Averaged Navier-Stokes equations. Two-equation turbulence modeling with low Reynolds number adjustments was used for closure. The baseline rotor flowfield was computed twice: with a moderately sized mesh (720,000 nodes) and also with a much more refined mesh (7.2 million nodes). Both solutions showed good agreement with previously taken measurements of the rotor flowfield, including five-hole probe measurements of the velocity and total pressure inside the passage, as well as pressure measurements on the blade and casing surfaces.

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