1995 ASME Gas Turbine Award Paper: Development and Application of a Multistage Navier–Stokes Solver: Part I—Multistage Modeling Using Bodyforces and Deterministic Stresses

1998 ◽  
Vol 120 (2) ◽  
pp. 205-214 ◽  
Author(s):  
C. M. Rhie ◽  
A. J. Gleixner ◽  
D. A. Spear ◽  
C. J. Fischberg ◽  
R. M. Zacharias
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Design Procedure ◽  
Potential Interaction ◽  
Theoretical Development ◽  
Navier Stokes ◽  
Radial Profiles ◽  
Compressor Performance ◽  
High Level

A multistage compressor performance analysis method based on the three-dimensional Reynolds-averaged Navier-Stokes equations is presented in this paper. This method is an average passage approach where deterministic stresses are used to ensure continuous physical properties across interface planes. The average unsteady effects due to neighboring blades and/or vanes are approximated using deterministic stresses along with the application of bodyforces. Bodyforces are used to account for the “potential” interaction between closely coupled (staged) rows. Deterministic stresses account for the “average” wake blockage and mixing effects both axially and radially. The attempt here is to implement an approximate technique for incorporating periodic unsteady flow physics that provides for a robust multistage design procedure incorporating reasonable computational efficiency. The present paper gives the theoretical development of the stress/bodyforce models incorporated in the code, and demonstrates the usefulness of these models in practical compressor applications. Compressor performance prediction capability is then established through a rigorous code/model validation effort using the power of networked workstations. The numerical results are compared with experimental data in terms of one-dimensional performance parameters such as total pressure ratio and circumferentially averaged radial profiles deemed critical to compressor design. This methodology allows the designer to design from hub to tip with a high level of confidence in the procedure.

Development and Application of a Multistage Navier-Stokes Solver: Part I — Multistage Modeling Using Bodyforces and Deterministic Stresses

1995 ◽  
Author(s):  
Chae M. Rhie ◽  
Aaron J. Gleixner ◽  
David A. Spear ◽  
Craig J. Fischberg ◽  
Robert M. Zacharias
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Design Procedure ◽  
Potential Interaction ◽  
Theoretical Development ◽  
Navier Stokes ◽  
Interface Plane ◽  
Radial Profiles ◽  
Compressor Performance

A novel multistage compressor performance analysis method based on the three-dimensional Reynolds averaged Navier-Stokes equations is presented in this paper. This approach is a “continuous interface plane approach” where deterministic stresses are used to ensure continuous physical properties across interface planes. The average unsteady effects due to neighboring blades and/or vanes are approximated using deterministic stresses along with the application of bodyforces. Bodyforces are used to account for the “potential” interaction between closely coupled (staged) rows. Deterministic stresses account for the “average” wake blockage and mixing effects both axially and radially. The attempt here is to implement an approximate technique for incorporating periodic unsteady flow physics that provides for a robust multistage design procedure incorporating reasonable computational efficiency. The present paper gives the theoretical development of the stress/bodyforce models incorporated in the code, and demonstrates the usefulness of these models in practical compressor applications. Compressor performance prediction capability is then established through a rigorous code/model validation effort using the power of networked workstations. The numerical results are compared with experimental data in terms of one-dimensional performance parameters such as total pressure ratio and circumferentially averaged radial profiles deemed critical to compressor design. This methodology allows the designer to design from hub to tip with a high level of confidence in the procedure.

High Level Languages Implementation and Analysis of 3D Navier-Stokes Solvers

2011 ◽  
Vol 3 (3) ◽  
pp. 370-388
Author(s):  
Valerio Grazioso ◽  
Carlo Scalo ◽  
Giuseppe de Felice ◽  
Carlo Meola
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Flamelet Model ◽  
Advection Scheme ◽  
Variable Ordering ◽  
Pressure Variable ◽  
High Level

AbstractIn this work we introduce PRIN-3D (PRoto-code for Internal flows modeled by Navier-Stokes equations in 3-Dimensions), a new high level algebraic language (Matlab®) based code, by discussing some fundamental aspects regarding its basic solving kernel and by describing the design of an innovative advection scheme. The main focus was on designing a memory and computationally efficient code that, due to the typical conciseness of the Matlab coding language, could allow for fast and effective implementation of new models or algorithms. Innovative numerical methods are discussed in the paper. The pressure equation is derived with a quasi-segregation technique leading to an iterative scheme obtained within the framework of a global preconditioning procedure. Different levels of parallelization are obtainable by exploiting special pressure variable ordering patterns that lead to a block-structured Poisson-like matrix. Moreover, the new advection scheme has the potential of a controllable artificial diffusivity. Preliminary results are shown including a fully three-dimensional internal laminar flow evolving in a relatively complex geometry and a 3D methane-air flame simulated with the aid of libraries based on the Flamelet model.

Design and Experimental Study on the Surge Performance Improvement by the Effects of Bleed Slot Casing of a Centrifugal Compressor

2014 ◽  
Author(s):  
Hong Won Kim ◽  
Jae Hoon Chung ◽  
Hyo Seong Lee ◽  
Min Ouk Choi
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Design Parameters ◽  
Navier Stokes Equations ◽  
Operating Range ◽  
Surge Margin ◽  
Commercial Code

The primary design goal of a compressor is focused on improving efficiency. Secondary objective is to widen the compressor’s operating range. This paper presents a numerical and experimental investigation of the influence of the bleed slot to enlarge operating range for the 1.2MW class centrifugal compressor installed in a turbocharger. The main design parameters of the bleed slot casing are upstream slot position, inlet pipe slope, downstream slot position and width. The DOE (design of experiment) method was carried out to optimize the casing design. Numerical analyses were done by the commercial code ANSYS-CFX based on the three dimensional Reynolds-averaged Navier-Stokes equations. From the analysis, as the downstream slot position and width are smaller and upstream position is located away from impeller inlet, efficiency and pressure ratio are increased. Experimental works were done with and without the bleed slot casing. The simulation results were in good agreement with the test data. In case without the bleed slot casing, the surge margin value came out to be only 11.8% but with the optimized bleed slot design, the surge margin reached 23%. Therefore, the surge margin increase of 11.2% was achieved.

Vorticity Dynamics in Axial Compressor Flow Diagnosis and Design

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Yantao Yang ◽  
Hong Wu ◽  
Qiushi Li ◽  
Sheng Zhou ◽  
Jiezhi Wu
Keyword(s):  
Pressure Ratio ◽  
Axial Compressor ◽  
Design Procedure ◽  
Abel Equation ◽  
Navier Stokes ◽  
Design Stage ◽  
Analysis And Design ◽  
Compressor Performance ◽  
Performance Check ◽  
Integrated Performance

It is well recognized that vorticity and vortical structures appear inevitably in viscous compressor flows and have strong influence on the compressor performance. However, conventional analysis and design procedure cannot pinpoint the quantitative contribution of each individual vortical structure to the integrated performance of a compressor, such as the stagnation-pressure ratio and efficiency. We fill this gap by using the so-called derivative-moment transformation, which has been successfully applied to external aerodynamics. We show that the compressor performance is mainly controlled by the radial distribution of azimuthal vorticity, of which an optimization in the through-flow design stage leads to a simple Abel equation of the second kind. The satisfaction of the equation yields desired circulation distribution that optimizes the blade geometry. The advantage of this new procedure is demonstrated by numerical examples, including the posterior performance check by 3D Navier–Stokes simulation.

Study of Supersonic Flowfield With Secondary Injection

2004 ◽  
Author(s):  
D. Sun ◽  
R. S. Amano
Keyword(s):  
Total Pressure ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Weighted Essentially Nonoscillatory ◽  
Secondary Injection ◽  
Total Pressure Ratio

Two and three-dimensional steady flowfields generated by transverse secondary injection into a supersonic flow, was simulated by solving the Favre-averaged Navier-Stokes equations using the weighted essentially nonoscillatory (WENO) schemes. Both the two-dimensional and three-dimensional results are given. Some parameters affecting the penetration height and separation length of the interactive flowfield, including the total pressure ratio of the jet to the freestream, the boundary layer thickness, slot width, the Mach number of the freestream and injection, the jet angle, and the shape of the injection orifice in the 3D flowfield, were calculated in more detail.

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.

Investigation of Vortex Structures for Supersonic Jet Interaction Flowfield

2015 ◽  
Vol 798 ◽  
pp. 546-550 ◽  
Author(s):  
Asel Beketaeva ◽  
Amr H. Abdalla ◽  
Yekaterina Moisseyeva
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Supersonic Jet ◽  
Three Dimensional ◽  
Horseshoe Vortex ◽  
Bow Shock ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Trailing Vortices ◽  
Barrel Shock

The three-dimensional supersonic turbulent flow in presence of symmetric transverse injection of round jet is simulated numerically. The simulation is based on the Favre-averaged Navier-Stokes equations coupled with Wilcox’s turbulence model. The numerical solution is performed using ENO scheme and is validated with the experimental data that include the pressure distribution on the wall in front of the jet in the plane symmetry. The numerical simulation is used to investigate in detail the flow physics for a range of the pressure ratio . The well-known primary shock formations are observed (a barrel shock, a bow shock, and the system of λ-shock waves), and the vortices are identified (horseshoe vortex, an upper vortex, two trailing vortices formed in the separation region and aft of the bow shock wave, two trailing vortices that merge together into one single rotational motion). During the experiment the presence of the new vortices near the wall behind the jet for the pressure ratio is revealed.

scholarly journals Design Optimization of a Transonic-Fan Rotor Using Numerical Computations of the Full Compressible Navier-Stokes Equations and Simplex Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
M. A. Aziz ◽  
Farouk M. Owis ◽  
M. M. Abdelrahman
Keyword(s):  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Simplex Algorithm ◽  
Navier Stokes ◽  
Numerical Computations ◽  
Navier Stokes Equations ◽  
Pressure Losses ◽  
Optimization Parameters ◽  
Transonic Fan

The design of a transonic-fan rotor is optimized using numerical computations of the full three-dimensional Navier-Stokes equations. The CFDRC-ACE multiphysics module, which is a pressure-based solver, is used for the numerical simulation. The code is coupled with simplex optimization algorithm. The optimization process is started from a suitable design point obtained using low fidelity analytical methods that is based on experimental correlations for the pressure losses and blade deviation angle. The fan blade shape is defined by its stacking line and airfoil shape which are considered the optimization parameters. The stacking line is defined by lean, sweep, and skews, while blade airfoil shape is modified considering the thickness and camber distributions. The optimization has been performed to maximize the rotor total pressure ratio while keeping the rotor efficiency and surge margin above certain required values. The results obtained are verified with the experimental data of Rotor 67. In addition, the results of the optimized fan indicate that the optimum design is found to be leaned in the direction of rotation and has a forward sweep from the hub to mean section and backward sweep to the tip. The pressure ratio increases from 1.427 to 1.627 at the design speed and mass flow rate.

CFD Analysis of a Centrifugal Compressor Impeller and Volute

1999 ◽  
Author(s):  
Harri Pitkänen ◽  
Hannu Esa ◽  
Petri Sallinen ◽  
Jaakko Larjola
Keyword(s):  
Centrifugal Compressor ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Prediction Method ◽  
Navier Stokes ◽  
Recovery Coefficient ◽  
Compressor Impeller ◽  
Compressor Performance ◽  
Pressure Recovery Coefficient

In this study, centrifugal compressor performance was predicted using CFD. Three-dimensional time-averaged impeller and volute simulations were performed using a Navier–Stokes code. The presented performance prediction method has been divided into three phases. Firstly, the impeller was calculated with a vaneless diffuser. That gives inlet boundary conditions for the volute analysis and the pressure ratio at the diffuser exit. Next, the volute analysis was performed and a static pressure recovery coefficient obtained. Finally, that result was combined with the pressure ratio prediction from the impeller analysis, and the overall compressor performance thus obtained.

scholarly journals Детально-сравнительный анализ взаимодействия сверхзвукового потока с поперечной газовой струей при больших параметрах нерасчетности

2019 ◽  
Vol 89 (10) ◽  
pp. 1513
Author(s):  
А.О. Бекетаева ◽  
P. Bruel ◽  
А.Ж. Найманова
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Mach Disk ◽  
Navier Stokes ◽  
Third Order ◽  
Navier Stokes Equations ◽  
The Third ◽  
Eno Scheme

The interaction of the spatial supersonic turbulent gas flow with a sound jet injected perpendicularly was widely studied both numerically and experimentally. However, there are only a few studies of the detail analysis of the formation and distribution of vortex structures from moderate till high pressure ratio (the ratio of pressure in the jet to pressure in the main flow).The aim of this paper is the study and identify the system of the vortex forming behind the injected sound jet in a transverse supersonic flow from the point of view of the mixing efficiency. For that the three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The presence of well known vortex structures are shown: two oppositely rotating vortices in front of the jet; horseshoe vortex; two pairs of the vortex in the mixing zone of the jet and the main flow, where one of them is located in the wake behind the jet and other in the lateral line of the jet. Also, the pressure ratio parameters are determined at which the additional pairs of vortices appear. Where, the first of them is formed on the edge of the Mach disk as a result of the interaction of the decelerated jet flow behind the Mach disk with the high-speed ascending flow behind the barrel. And, the second is due to the interaction of the ascending jet flow with the main gas flow. As a result of comparative analysis the criterion of the pressure ratio parameters are found under which a clear picture of additional horn vortices is observed near the wall in the region behind the jet. The graph of the dependence of the angle of inclination of the bow shock wave on the parameter of pressure ratio is obtained. Satisfactory agreement of the pressure distribution on the wall in front of the jet in the symmetry plane with experimental data is established.

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