Numerical Validation of Characteristic and Linearized Unsteady Boundary Conditions for Non-Integer Blade Ratios in a Non-Linear Navier Stokes Solver

2005 ◽  
Author(s):  
Thomas Mokulys ◽  
Stephen C. Dewhurst ◽  
Reza S. Abhari
Keyword(s):  
Boundary Conditions ◽  
New Method ◽  
Navier Stokes ◽  
Conservative Approach ◽  
Single Row ◽  
Numerical Validation ◽  
Single Passage ◽  
Non Linear ◽  
Improved Stability ◽  
Similar Accuracy

Unsteady single passage methods for turbomachinery applications are becoming a more and more mature method in predicting unsteady blade-to-blade aerodynamics in a more efficient and accurate way compared to multipassage computations with scaled airfoil geometries. The outlined work presents results of a fourier-based method for phase-lagged boundary conditions using a usual conservative approach at the interfaceplane and compares it to a new characteristic treatment as well as a linearized single row approach. The new method provides results of similar accuracy with improved stability of the algorithm and faster convergence times.

The Influence of Compressor Blade Row Interaction Modeling on Performance Estimates From Time-Accurate, Multistage, Navier–Stokes Simulations

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Dale Van Zante ◽  
Jenping Chen ◽  
Michael Hathaway ◽  
Randall Chriss
Keyword(s):  
Boundary Conditions ◽  
High Speed ◽  
Axial Compressor ◽  
Time History ◽  
Navier Stokes ◽  
Strong Interactions ◽  
Phase Lag ◽  
Single Passage ◽  
Blade Row ◽  
Performance Estimates

The time-accurate, multistage, Navier–Stokes, turbomachinery solver TURBO was used to calculate the aeroperformance of a 2 1∕2 stage, highly loaded, high-speed, axial compressor. The goals of the research project were to demonstrate completion times for multistage, time-accurate simulations that are consistent with inclusion in the design process and to assess the influence of differing approaches to modeling the effects of blade row interactions on aeroperformance estimates. Three different simulation setups were used to model blade row interactions: (1) single-passage per blade row with phase lag boundaries, (2) multiple passages per blade row with phase lag boundaries, and (3) a periodic sector (1∕2 annulus sector). The simulations used identical inlet and exit boundary conditions and identical meshes. To add more blade passages to the domain, the single-passage meshes were copied and rotated. This removed any issues of differing mesh topology or mesh density from the following results. The 1∕2 annulus simulation utilizing periodic boundary conditions required an order of magnitude fewer iterations to converge when all three simulations were converged to the same level as assessed by monitoring changes in overall adiabatic efficiency. When using phase lag boundary conditions, the necessity to converge the time history information requires more iterations to obtain the same convergence level. In addition to convergence differences, the three simulations gave different overall performance estimates where the 1∕2 annulus case was 1.0 point lower in adiabatic efficiency than the single-passage phase lag case. The interaction between blade rows in the same frame of reference sets up spatial variations of properties in the circumferential direction, which are stationary in that reference frame. The phase lag boundary condition formulation will not capture this effect because the blade rows are not moving relative to each other. Thus, for simulations of more than two blade rows and strong interactions, a periodic simulation is necessary to estimate the correct aeroperformance.

scholarly journals THE NUMERICAL INVESTIGATION OF WAVE GENERATION BY LOW SPEED WINDS

2012 ◽  
Vol 1 (33) ◽  
pp. 57
Author(s):  
Ying-Po Liao ◽  
James M. Kaihatu
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Wave Generation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wave Growth ◽  
Developed Turbulence ◽  
Initial Stage ◽  
Non Linear ◽  
Coupled Boundary Conditions

In this study we investigate the process of wind-wave generation by using direct numerical simulation (DNS). Air and water domains are respectively solved by Navier-Stokes equations in 3D Cartesian coordinates in which air-water coupled boundary conditions are specified at interface. A shear wind on the top of the air domain is specified, and air and water domains are subsequently driven to fully-developed turbulence, allowing wave growth at interface. In this paper we improve the work published by Lin et al. (2008). Instead of simplified linear boundary conditions (BCs), we derive and impose the non-linear BCs for normal stress at interface, as well as non-linear curvature terms used to balance the discontinuity. The results show that at the linear (initial) stage, faster wave growth is seen with non-linear BCs than with linearized BCs. This is reversed during the exponential (developed) stage.

The Influence of Compressor Blade Row Interaction Modeling on Performance Estimates From Time-Accurate, Multi-Stage, Navier-Stokes Simulations

2005 ◽  
Author(s):  
Dale Van Zante ◽  
Jenping Chen ◽  
Michael Hathaway ◽  
Randall Chriss
Keyword(s):  
Boundary Conditions ◽  
High Speed ◽  
Time History ◽  
Navier Stokes ◽  
Strong Interactions ◽  
Phase Lag ◽  
Single Passage ◽  
Multi Stage ◽  
Blade Row ◽  
Performance Estimates

The time-accurate, multi-stage, Navier-Stokes, turbomachinery solver TURBO was used to calculate the aero performance of a 2 1/2 stage, highly-loaded, high-speed, axial compressor. The goals of the research project were to demonstrate completion times for multi-stage, time-accurate simulations that are consistent with inclusion in the design process, and to assess the influence of differing approaches to modeling the effects of blade row interactions on aero performance estimates. Three different simulation setups were used to model blade row interactions: 1.) single passage per blade row with phase lag boundaries, 2.) multiple passages per blade row with phase lag boundaries, and 3.) a periodic sector (1/2 annulus sector). The simulations used identical inlet and exit boundary conditions and identical meshes. To add more blade passages to the domain, the single passage meshes were copied and rotated. This removed any issues of differing mesh topology or mesh density from the following results. The 1/2 annulus simulation utilizing periodic boundary conditions required an order of magnitude less iterations to converge when all three simulations were converged to the same level as assessed by monitoring changes in overall adiabatic efficiency. When using phase lag boundary conditions the need to converge the time history information necessitates more iterations to obtain the same convergence level. In addition to convergence differences, the three simulations gave different overall performance estimates where the 1/2 annulus case was 1.0 point lower in adiabatic efficiency than the single passage phase lag case. The interaction between blade rows in the same frame of reference set up spatial variations of properties in the circumferential direction which are stationary in that reference frame. The phase lag boundary condition formulation will not capture this effect because the blade rows are not moving relative to each other. Thus for simulations of more than two blade rows and strong interactions, a periodic simulation is necessary to estimate the correct aero performance.

LOCAL APPROXIMATIONS : A NEW WAY OF DEALING WITH IRREGULAR WAVES

1986 ◽  
Vol 1 (20) ◽  
pp. 48 ◽  
Author(s):  
Peter Nielsen
Keyword(s):  
Spectral Method ◽  
Spectral Methods ◽  
Computational Effort ◽  
New Method ◽  
Irregular Waves ◽  
Wave Analysis ◽  
Linear Waves ◽  
Local Approximations ◽  
Non Linear ◽  
Similar Accuracy

The concept of local approximations via locally defined frequencies is introduced as a tool for dealing with irregular, non linear waves. Practical testing has been performed on the problem of estimating surface elevations from measured bottom pressures. In these tests the new method even in its simplest form proves more accurate than the linear spectral method. With respect to computational effort the new method requires orders of magnitude less than spectral methods, or wave by wave analysis of similar accuracy.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

New Method of Fault Knowledge Acquisition of Electronic Equipment

2014 ◽  
Vol 496-500 ◽  
pp. 931-934
Author(s):  
Zhi Cheng Huo ◽  
Qi Shun Sun ◽  
Feng Jun Qi ◽  
Guo Bao Ding
Keyword(s):  
Knowledge Acquisition ◽  
Electronic Equipment ◽  
New Method ◽  
Topological Information ◽  
Amplifier Circuit ◽  
C Language ◽  
Transistor Amplifier ◽  
Analog System ◽  
Non Linear ◽  
Electric Equipment

For the problems like discreteness, tolerance, non-linear of the parts, acquiring the fault knowledge of analog system in electric equipment is hard. This method realized the process of KA automatization through the combination of PSPICE software and C language and taking command lines as combining site. Using the batch file, the programs will form some topological information and parameter information about the fault states of a circuit system each time. The result of a experiment about an Basic Transistor Amplifier circuit proves its feasibility.

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