Sensitivity Analysis and Computations of the Time Relaxation Model

2015 ◽  
Vol 7 (1) ◽  
pp. 89-115 ◽  
Author(s):  
Monika Neda ◽  
Fran Pahlevani ◽  
Jiajia Waters
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Study ◽  
Fluid Model ◽  
Equation Method ◽  
Test Case ◽  
Numerical Comparison ◽  
Relaxation Model ◽  
Sensitivity Equation ◽  
Time Relaxation ◽  
Sensitivity Equation Method

AbstractThis paper presents a numerical study of the sensitivity of a fluid model known as time relaxation model with respect to variations of the time relaxation coefficientχ. The sensitivity analysis of this model is utilized by the sensitivity equation method and uses the finite element method along with Crank Nicolson method in the fully discretization of the partial differential equations. We present a test case in support of the sensitivity convergence and also provide a numerical comparison between two different strategies of computing the sensitivity, sensitivity equation method and forward finite differences.

Three-Dimensional Optimization of Turbomachinery Bladings Using Sensitivity Analysis

2003 ◽  
Author(s):  
S. Ka¨mmerer ◽  
J. F. Mayer ◽  
M. Paffrath ◽  
U. Wever ◽  
A. R. Jung
Keyword(s):  
Three Dimensional ◽  
Flow Simulation ◽  
Equation Method ◽  
Physical Parameters ◽  
Test Case ◽  
Analytical Sensitivity ◽  
Optimization Strategy ◽  
Sensitivity Equation ◽  
Design Variables ◽  
Sensitivity Equation Method

This paper presents an approach to optimize the geometry of turbomachinery blades utilizing an automated optimization loop. Optimization examples of turbomachinery blade geometries with selected objective functions and a set of design variables are introduced. The presented optimization examples are performed for a 1.5-stage turbine test case. The blade geometries are fully parameterized, enabling three-dimensional changes to the blade shape during the optimization. Therefore various non-physical and physical parameters such as stacking line or stagger angle can be selected as design variables. Three-dimensional steady-state numerical flow simulations and a sensitivity equation method are part of the optimization process. The design sensitivities used within the optimization are obtained by numerically solving the analytical sensitivity equations. This optimization scheme uses the same numerical method for the flow simulation and for the computation of the sensitivity equation. A Navier-Stokes flow solver, which has especially been designed for turbomachinery applications was used for the implementation of the sensitivity equation method. The focus of this paper is on the application of the described optimization strategy to turbomachinery flows. The presented optimization examples are used to demonstrate and to discuss the capabilities of this approach.

Analytical sensitivity map of head observations on heterogeneous hydraulic parameters via the sensitivity equation method

2020 ◽  
Vol 591 ◽  
pp. 125282
Author(s):  
Yuanyuan Zha ◽  
Liangsheng Shi ◽  
Yue Liang ◽  
Chak-Hau Michael Tso ◽  
Wenzhi Zeng ◽  
...  
Keyword(s):  
Equation Method ◽  
Hydraulic Parameters ◽  
Analytical Sensitivity ◽  
Sensitivity Equation ◽  
Sensitivity Equation Method ◽  
Sensitivity Map

An unsteady Sensitivity Equation Method for Fast Evaluation of FSI Nearby Configurations

2007 ◽  
Author(s):  
Stephane Etienne ◽  
Alexander Hay ◽  
Jean-Francois Cori ◽  
Dominique Pelletier ◽  
Andre Garon
Keyword(s):  
Equation Method ◽  
Sensitivity Equation ◽  
Fast Evaluation ◽  
Sensitivity Equation Method

The sensitivity equation method in fluid mechanics

2008 ◽  
Vol 17 (1-2) ◽  
pp. 31-61 ◽  
Author(s):  
Dominique Pelletier ◽  
Alexander Hay ◽  
Stéphane Etienne ◽  
Jeff Borggaard
Keyword(s):  
Fluid Mechanics ◽  
Equation Method ◽  
Sensitivity Equation ◽  
Sensitivity Equation Method
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