Numerical Analysis of Three-Dimensional Unsteady Hot Streak Migration and Shock Interaction in a Turbine Stage

1996 ◽  
Vol 118 (2) ◽  
pp. 268-277 ◽  
Author(s):  
A. P. Saxer ◽  
H. M. Felici
Keyword(s):  
Shock Wave ◽  
Steady State ◽  
Rotor Blade ◽  
Three Dimensional ◽  
Steady State Solution ◽  
State Solution ◽  
Stagnation Temperature ◽  
Turbine Stage ◽  
Channel Configuration ◽  
Hot Streak

A three-dimensional unsteady flow computation has been performed for a transonic first turbine stage under the influence of streaks of hot gas exiting the combustion chamber. Realistic flow conditions are obtained by using an unequal stator-to-rotor pitch, a single-streak/multistator channel configuration, and periodic boundary conditions. The resulting unsteady shock wave system and the hot streak migration as well as the shock wave/streak interaction are presented and discussed. In addition, the time average of the periodic unsteady solution is analyzed and compared with a steady-state computation. The steady-state solution is analyzed and compared with a steady-state computation. The steady-state solution matches the time-averaged one in terms of the pressure field and the maximum stagnation temperature on the rotor blade surface. However, the rotor blade temperature patterns are different with a stronger radial secondary flow present in the time-averaged solution due to the retention of the circumferential streak variations at the stator/rotor interface.

scholarly journals Numerical Analysis of 3-D Unsteady Hot Streak Migration and Shock Interaction in a Turbine Stage

1994 ◽  
Author(s):  
André P. Saxer ◽  
Hélène M. Felicl
Keyword(s):  
Steady State ◽  
Rotor Blade ◽  
Pressure Field ◽  
Steady State Solution ◽  
Stagnation Temperature ◽  
Blade Surface ◽  
Turbine Stage ◽  
Flow Conditions ◽  
Hot Gas ◽  
Hot Streak

A 3-D unsteady flow computation has been performed for a transonic first turbine stage under the influence of streaks of hot gas exiting the combustion chamber. Realistic flow conditions are obtained by using a non-equal stator-to-rotor pitch, a single-streak/multi-stator channels configuration and periodic boundary conditions. The resulting unsteady shock waves system and the hot streaks migration as well as the shock wave/streak interaction are presented and discussed. In addition, the time-average of the periodic unsteady solution is analyzed and compared with a steady-state computation. The steady-state solution matches the time-averaged one in terms of the pressure field and the maximum stagnation temperature on the rotor blade surface. However, the rotor blade temperature patterns are different with a stronger radial secondary flow present in the time-averaged solution due to the retention of the circumferential streak variations at the stator/rotor interface.

Predictions of Three-Dimensional Steady and Unsteady Inviscid Transonic Stator/Rotor Interaction With Inlet Radial Temperature Nonuniformity

1994 ◽  
Vol 116 (3) ◽  
pp. 347-357 ◽  
Author(s):  
A. P. Saxer ◽  
M. B. Giles
Keyword(s):  
Steady State ◽  
Unsteady Flow ◽  
Static Pressure ◽  
Three Dimensional ◽  
Steady State Solution ◽  
State Solution ◽  
Stagnation Temperature ◽  
Radial Temperature ◽  
Numerical Predictions ◽  
First Case

Numerical predictions of three-dimensional inviscid, transonic steady and periodic unsteady flow within an axial turbine stage are analyzed in this paper. As a first case, the unsteady effects of the stator trailing edge shock wave impinging on the downstream rotor are presented. Local static pressure fluctuations up to 60 percent of the inlet stagnation pressure are observed on the rotor suction side. The second case is an analysis of the rotor-relative radial secondary flow produced by a spanwise parabolic nonuniform temperature profile at the stator inlet. The generation of local hot spots is observed on both sides of the rotor blade behind the passing shock waves. The magnitude of the unsteady stagnation temperature fluctuations is larger than the time-averaged rotor inlet disturbance. In both cases, steady, unsteady, and time-averaged solutions are presented and compared. From these studies, it is concluded that the steady-state solution in static pressure matches well with the time-averaged periodic unsteady flow field. However, for the stagnation temperature distribution only the trend of the time-averaged solution is modeled in the steady-state solution.

scholarly journals Predictions of 3-D Steady and Unsteady Inviscid Transonic Stator/Rotor Interaction With Inlet Radial Temperature Non-Uniformity

1993 ◽  
Author(s):  
André P. Saxer ◽  
Michael B. Giles
Keyword(s):  
Steady State ◽  
Unsteady Flow ◽  
Static Pressure ◽  
Suction Side ◽  
Steady State Solution ◽  
State Solution ◽  
Stagnation Temperature ◽  
Radial Temperature ◽  
Numerical Predictions ◽  
First Case

Numerical predictions of 3-D inviscid, transonic steady and periodic unsteady flow within an axial turbine stage are analyzed in this paper. As a first case, the unsteady effects of the stator trailing edge shock wave impinging on the downstream rotor are presented. Local static pressure fluctuations up to 60% of the inlet stagnation pressure are observed on the rotor suction side. The second case is an analysis of the rotor-relative radial secondary flow produced by a spanwise parabolic non-uniform temperature profile at the stator inlet. The generation of local hot spots is observed on both sides of the rotor blade behind the passing shock waves. The magnitude of the unsteady stagnation temperature fluctuations is larger than the time-averaged rotor inlet disturbance. In both cases, steady, unsteady and time-averaged solutions are presented and compared. From these studies, it is concluded that the steady-state solution in static pressure matches well with the time-averaged periodic unsteady flow field. However, for the stagnation temperature distribution only the trend of the time-averaged solution is modeled in the steady-state solution.

Unsteady Analysis of Inlet Hot Streaks Clocking Effects in a 1-1/2 Turbine Stage

2020 ◽  
Author(s):  
Yejia Jin ◽  
Hongwei Ma ◽  
Xinghang Yu
Keyword(s):  
Rotor Blade ◽  
Three Dimensional ◽  
Decomposition Analysis ◽  
Turbine Stage ◽  
Second Stage ◽  
Stator Vane ◽  
Flow Features ◽  
Higher Temperature ◽  
Hot Streak ◽  
Proper Orthogonal

Abstract Migration of inlet hot streaks and the clocking effects are investigated by three-dimensional unsteady numerical simulations in a 1-1/2 turbine stage. Two hot streak circumferential positions with respect to first-stage stator, passage centered and vane centered, are simulated. Results indicate that hot streaks tend to accumulate on rotor blade pressure side and move towards shroud, causing hot spots on these parts. Separation of hot and cold fluid is observed in rotor, thus influence of hot streaks spreads to second-stage stator. Hot streaks are broken into fragments by rotor blade wakes and rotor-stator interactions in second-stage stator. Impinging hot streaks on first-stage stator passages results in separation of hot and cold lats longer in rotor, but area-averaged temperature at rotor outlet is relatively lower. Hot streaks keep a higher temperature through rotor, yet area-averaged temperature has a quicker drop in second-stage stator. Impinging hot streaks on first-stage stator vanes brings a more uniform temperature distribution at rotor and turbine outlet while a higher area-averaged temperature at the same time. Hot streaks adhere to the first-stage stator vane surfaces and move towards hub due to tip leakage, causing extra heating to these parts compared with passage centered hot streaks. Rortex, as a new way to identify vortexes in fluid, is employed to understand how vortexes contribute to migration and dissipation of hot streaks. Also, Proper Orthogonal Decomposition analysis is applied to identify flow features that impact migration and dissipation of hot streaks, and a few connections between the flow features and POD modes are made.

Bifurcation Analysis in an n-Dimensional Diffusive Competitive Lotka–Volterra System with Time Delay

2015 ◽  
Vol 25 (06) ◽  
pp. 1550089
Author(s):  
Xiaoyuan Chang ◽  
Junjie Wei
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Three Dimensional ◽  
Steady State Solution ◽  
State Solution ◽  
Diffusion System ◽  
Asymptotic Expressions ◽  
The Stability ◽  
System With Time Delay

In this paper, we investigate the stability and Hopf bifurcation of an n-dimensional competitive Lotka–Volterra diffusion system with time delay and homogeneous Dirichlet boundary condition. We first show that there exists a positive nonconstant steady state solution satisfying the given asymptotic expressions and establish the stability of the positive nonconstant steady state solution. Regarding the time delay as a bifurcation parameter, we explore the system that undergoes a Hopf bifurcation near the positive nonconstant steady state solution and derive a calculation method for determining the direction of the Hopf bifurcation. Finally, we cite the stability of a three-dimensional competitive Lotka–Volterra diffusion system with time delay to illustrate our conclusions.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

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