scholarly journals Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Hadrien Montanelli ◽  
Marc Montagnac ◽  
François Gallard
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Stokes Equations ◽  
Single Point ◽  
Operating Conditions ◽  
Design Variables ◽  
Wide Range ◽  
The Cost ◽  
Multipoint Optimization ◽  
Utopia Point

This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier–Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

High-Fidelity Hydrodynamic Shape Optimization of a 3-D Hydrofoil

2015 ◽  
Vol 59 (04) ◽  
pp. 209-226
Author(s):  
Nitin Garg ◽  
Gaetan K.W. Kenway ◽  
Zhoujie Lyu ◽  
Joaquim R.R.A. Martins ◽  
Yin L. Young
Keyword(s):  
Shape Optimization ◽  
Incompressible Flows ◽  
Single Point ◽  
Operating Conditions ◽  
High Fidelity ◽  
Design Point ◽  
Optimal Geometry ◽  
Design Variables ◽  
Wide Range ◽  
Overall Efficiency

With recent advances in high-performance computing, computational fluid dynamics (CFD) modeling has become an integral part in the engineering analysis and even in the design process of marine vessels and propulsors. In aircraft wing design, CFD has been integrated with numerical optimization and adjoint methods to enable high fidelity aerodynamic shape optimization with respect to large numbers of design variables. There is a potential to use some of these techniques for maritime applications, but there are new challenges that need to be addressed to realize that potential. This work presents a solution to some of those challenges by developing a CFD-based hydrodynamic shape optimization tool that considers cavitation and a wide range of operating conditions. A previously developed three-dimensional compressible Reynold saveraged Navier-Stokes (RANS) solver is extended to solve for nearly incompressible flows, using a low-speed preconditioner. An efficient gradient-based optimizer and the adjoint method are used to carry out the optimization. The modified CFD solver is validated and verified for a tapered NACA 0009 hydrofoil. The need for a large number of design variables is demonstrated by comparing the optimized solution obtained using different number of shape design variables. The results showed that at least 200 design variables are needed to get a converged optimal solution for the hydrofoil considered. The need for a high-fidelity hydrodynamic optimization tool is also demonstrated by comparing RANS-based optimization with Euler-based optimization. The results show that at high lift coefficient (CL) values, the Euler-based optimization leads to a geometry that cannot meet the required lift at the same angle of attack as the original foil due to inability of the Euler solver to predict viscous effects. Single-point optimization studies are conducted for various target CL values and compared with the geometry and performance of the original NACA 0009 hydrofoil, as well as with the results from a multipoint optimization study. A total of 210 design variables are used in the optimization studies. The optimized foil is found to have a much lower negative suction peak, and hence delayed cavitation inception, in addition to higher efficiency, compared to the original foil at the design CL value. The results show significantly different optimal geometry for each CL, which means an active morphing capability was needed to achieve the best possible performance for all conditions. For the single-point optimization, using the highest CL as the design point, the optimized foil yielded the best performance at the design point, but the performance degraded at the off-design CL points compared to the multipoint design. In particular, the foil optimized for the highest CL showed inferior performance even compared to the original foil at the lowest CL condition. On the other hand, the multipoint optimized hydrofoil was found to perform better than the original NACA 0009 hydrofoil over the entire operation profile, where the overall efficiency weighted by the probability of operation at each CL, is improved by 14.4%. For the multipoint optimized foil, the geometry remains fixed throughout the operation profile and the overall efficiency was only 1.5% lower than the hypothetical actively morphed foil with the optimal geometry at each CL. The new methodology presented herein has the potential to improve the design of hydrodynamic lifting surfaces such as propulsors, hydrofoils, and hulls.

Fully Parametric High-Fidelity CFD Model for the Design Optimisation of the Cyclic Stagger Pattern of a Set of Fan Outlet Guide Vanes

2009 ◽  
Author(s):  
Andrea Milli ◽  
Olivier Bron
Keyword(s):  
Complex Geometry ◽  
Single Point ◽  
Sensitivity Study ◽  
Operating Conditions ◽  
High Fidelity ◽  
Cfd Model ◽  
Design Optimisation ◽  
Guide Vanes ◽  
High Loss ◽  
Design Variables

The present paper deals with the redesign of cyclic variation of a set of fan outlet guide vanes by means of high-fidelity full-annulus CFD. The necessity for the aerodynamic redesign originated from a change to the original project requirement, when the customer requested an increase in specific thrust above the original engine specification. The main objectives of this paper are: 1) make use of 3D CFD simulations to accurately model the flow field and identify high-loss regions; 2) elaborate an effective optimisation strategy using engineering judgement in order to define realistic objectives, constraints and design variables; 3) emphasise the importance of parametric geometry modelling and meshing for automatic design optimisation of complex turbomachinery configurations; 4) illustrate that the combination of advanced optimisation algorithms and aerodynamic expertise can lead to successful optimisations of complex turbomachinery components within practical time and costs constrains. The current design optimisation exercise was carried out using an in-house set of software tools to mesh, resolve, analyse and optimise turbomachinery components by means of Reynolds-averaged Navier-Stokes simulations. The original configuration was analysed using the 3D CFD model and thereafter assessed against experimental data and flow visualisations. The main objective of this phase was to acquire a deep insight of the aerodynamics and the loss mechanisms. This was important to appropriately limit the design scope and to drive the optimisation in the desirable direction with a limited number of design variables. A mesh sensitivity study was performed in order to minimise computational costs. Partially converged CFD solutions with restart and response surface models were used to speed up the optimisation loop. Finally, the single-point optimised circumferential stagger pattern was manually adjusted to increase the robustness of the design at other flight operating conditions. Overall, the optimisation resulted in a major loss reduction and increased operating range. Most important, it provided the project with an alternative and improved design within the time schedule requested and demonstrated that CFD tools can be used effectively not only for the analysis but also to provide new design solutions as a matter of routine even for very complex geometry configurations.

Effects of Cycle Operating Conditions on Combustor Performance

1997 ◽  
Vol 119 (1) ◽  
pp. 45-49 ◽  
Author(s):  
N. T. Davis ◽  
V. G. McDonell ◽  
G. S. Samuelsen
Keyword(s):  
Cost Function ◽  
Duty Cycle ◽  
Load Condition ◽  
Combustion Efficiency ◽  
Operating Conditions ◽  
Nox Emissions ◽  
Variable Geometry ◽  
Oxides Of Nitrogen ◽  
Mixing Processes ◽  
The Cost

To mitigate the environmental impact of next-generation gas turbine combustors, the emission performance at each condition throughout the load duty cycle must be optimized. Achieving this with a single combustor geometry may not be possible. Rather, the mixing processes and airflow splits must likely be modified as a function of load in order to (1) abate the emission of oxides of nitrogen, (2) maintain combustion efficiency, and (3) preclude lean blow-out over the entire duty cycle. The present study employs a model combustor to evaluate combustor performance as a function of load and explore the application of variable geometry to optimize performance at each condition. A parametric variation of flow splits is conducted at each load condition by independently adjusting the primary jet area and swirler choke area. The resultant impact on combustor performance is measured and quantified in terms of a cost function. The cost function is defined to increase with improving combustor performance (e.g., improving combustion efficiency and/or declining NOx emissions). Cycle operating conditions are found to alter the response mappings of efficiency and NOx. As a result, the optimal configuration of the combustor changes as the load is varied over the duty cycle. The results provide guidance on the application of active control.

Dual Point Redesign of Axial Turbines Using a Viscous Inverse Design Method

2009 ◽  
Author(s):  
Benedikt Roidl ◽  
Wahid Ghaly
Keyword(s):  
Inverse Method ◽  
Stokes Equations ◽  
Design Method ◽  
Single Point ◽  
Accurate Solution ◽  
Inverse Design ◽  
Suction Surface ◽  
Pressure Distributions ◽  
Wide Range ◽  
Inverse Design Method

A new dual-point inverse blade design method was developed and applied to the redesign of a highly loaded transonic vane, the VKI-LS89, and the first 2.5 stages of a low speed subsonic turbine, the E/TU-4 4-stage turbine that is built and tested at the university of Hannover, Germany. In this inverse method, the blade walls move with a virtual velocity distribution derived from the difference between the current and the target pressure distributions on the blade surfaces at both operating points. This new inverse method is fully consistent with the viscous flow assumption and is implemented into the time accurate solution of the Reynolds-Averaged Navier-Stokes equations. An algebraic Baldwin-Lomax turbulence model is used for turbulence closure. The mixing plane approach is used to couple the stator and rotor regions. The dual-point inverse design method is then used to explore the effect of different choices of the pressure distributions on the suction surface of one or more rotor/stator on the blade/stage performance. The results show that single point inverse design resulted in a local performance improvement whereas the dual point design method allowed for improving the performance of both VKI-LS89 vane and E/TU-4 2.5 stage turbines over a wide range of operation.

Unsteady Flow Structure and Global Variables in a Centrifugal Pump

2006 ◽  
Vol 128 (5) ◽  
pp. 937-946 ◽  
Author(s):  
José González ◽  
Carlos Santolaria
Keyword(s):  
Unsteady Flow ◽  
Centrifugal Pump ◽  
Flow Structure ◽  
Flow Model ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Operating Conditions ◽  
Local Flow ◽  
Global Variables ◽  
Wide Range

A relationship between the global variables and the dynamic flow structure numerically obtained for a low specific speed centrifugal pump is presented in this paper. A previously developed unsteady flow model is used to correlate the dynamic field with the flow characteristics inside the impeller and volute of a single-stage commercial pump. Actually, the viscous incompressible Navier-Stokes equations are solved within a 3D unsteady flow model. A sliding mesh technique is applied to take into account the impeller-volute interaction. After the numerical model has been successfully compared with the experimental data for the unsteady pressure fluctuations pattern in the volute shroud, a new step is proposed in order to correlate the observed effects with the flow structure inside the pump. In particular, the torque as a function of the relative position of the impeller blades is related to the blades loading, and the secondary flow in the volute is related to the different pressure patterns numerically obtained. Local flow analysis and qualitative study of the helicity in different volute sections is performed. The main goal of the study presented is the successful correlation of local and global parameters for the flow in a centrifugal pump. The pressure forces seem to be the main driven mechanism to establish the flow features both in the impeller and volute, for a wide range of operating conditions.

scholarly journals Numerical and Experimental Investigation of Formability in Incremental Sheet Forming of Particle Reinforced Metal Matrix Composite Sheets

2021 ◽  
Author(s):  
Shakir Gatea ◽  
Thana Abdel Salam Tawfiq ◽  
Hengan Ou
Keyword(s):  
Metal Matrix ◽  
Room Temperature ◽  
Single Point ◽  
Weight Ratio ◽  
High Strength ◽  
Operating Conditions ◽  
Particle Composite ◽  
Heat Treated ◽  
Wide Range ◽  
Sic Particle

Abstract Metal matrix composites (MMCs) have a high strength-to-weight ratio, high stiffness, and good damage resistance under a wide range of operating conditions, making them a viable alternative to traditional materials in a variety of technical applications. Because of their high strength, composite materials are hard to deform to a significant depth at room temperature. As a result, additional treatments are required to enhance the composite's room ductility prior to deformation. In this investigation, as-received 6092Al/SiCp composite sheets (T6-condition) are heat treated to O-condition annealing to enhance its ductility in order to assess the influence of single point incremental forming (SPIF) parameters on the formability and fracture behavior of the Al/SiC particle composite sheets at room temperature. Then the annealed sheets are heat treated to T6-condition to enhance the strength and achieve properties equivalent to as-received sheets properties. The results demonstrate that the Al/SiC particle composite sheets with T6 treatment could not be deformed to the specified depth at room temperature due to low room ductility and that further treatment, such as O-condition annealing, is required to enhance the room ductility. When annealed Al/SiCp composite sheets are heat treated to T6, the sheets exhibit properties comparable to the as-received sheets. Al/SiC particle composite sheets with low SPIF parameters may have greater formability and fracture depth with low strain hardening curve.

scholarly journals Analytical Models for Optimal Design of a Trapezoidal Composite Channel Cross-Section

2021 ◽  
Vol 31 (1) ◽  
pp. 118-138
Author(s):  
Somayyeh Pourbakhshian ◽  
Majid Pouraminian
Keyword(s):  
Optimal Design ◽  
Cost Function ◽  
Objective Function ◽  
Cross Section ◽  
Analytical Models ◽  
Channel Cross Section ◽  
Roughness Coefficient ◽  
Composite Channel ◽  
Design Variables ◽  
The Cost

Abstract In this paper, several analytical models are presented for the optimal design of a trapezoidal composite channel cross-section. The objective function is the cost function per unit length of the channel, which includes the excavation and lining costs. To define the system, design variables including channel depth, channel width, side slopes, freeboard, and roughness coefficients were used. The constraints include Manning’s equation, flow velocity, Froude number, and water surface width. The Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was used to solve the optimization problem. The results are presented in three parts; in the first part, the optimal values of the design variables and the objective function are presented in different discharges. In the second part, the relationship between cost and design variables in different discharges is presented in the form of conceptual and analytical models and mathematical functions. Finally, in the third part, the changes in the design variables and cost function are presented as a graph based on the discharge variations. Results indicate that the cost increases with increasing water depth, left side slope, equivalent roughness coefficient, and freeboard.

scholarly journals Proliferation of non-linear excitations in the piecewise-linear perceptron

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Antonio Sclocchi ◽  
Pierfrancesco Urbani
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Hard Spheres ◽  
Piecewise Linear ◽  
Power Laws ◽  
Universality Class ◽  
Local Minima ◽  
Convex Optimization Problem ◽  
Non Linear ◽  
The Cost

We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and displaying a set of pseudogaps, singularities and non-linear excitations whose properties appear to be in the same universality class of jammed packings of hard spheres. The piecewise linear perceptron problem appears as an evolution of the purely linear perceptron optimization problem that has been recently investigated in [1]. Its cost function contains two non-analytic points where the derivative has a jump. Correspondingly, in the non-convex/glassy phase, these two points give rise to four pseudogaps in the force distribution and this induces four power laws in the gap distribution as well. In addition one can define an extended notion of isostaticity and show that local minima appear again to be isostatic in this phase. We believe that our results generalize naturally to more complex cases with a proliferation of non-linear excitations as the number of non-analytic points in the cost function is increased.

Effects of Cycle Operating Conditions on Combustor Performance

1995 ◽  
Author(s):  
N. T. Davis ◽  
V. G. McDonell ◽  
G. S. Samuelsen
Keyword(s):  
Cost Function ◽  
Duty Cycle ◽  
Load Condition ◽  
Combustion Efficiency ◽  
Operating Conditions ◽  
Nox Emissions ◽  
Variable Geometry ◽  
Oxides Of Nitrogen ◽  
Mixing Processes ◽  
The Cost

To mitigate the environmental impact of next generation gas turbine combustors, the emission performance at each condition throughout the load duty cycle must be optimized. Achieving this with a single combustor geometry may not be possible. Rather, the mixing processes and air flow splits must likely be modified as a function of load in order to (1) abate the emission of oxides of nitrogen, (2) maintain combustion efficiency, and (3) preclude lean blow out over the entire duty cycle. The present study employs a model combustor to evaluate combustor performance as a function of load and explore the application of variable geometry to optimize performance at each condition. A parametric variation of flow splits is conducted at each load condition by independently adjusting the primary jet area and swirler choke area. The resultant impact on combustor performance is measured and quantified in terms of a cost function. The cost function is defined to increase with improving combustor performance (e.g., improving combustion efficiency and/or declining NOx emissions). Cycle operating conditions are found to alter the response mappings of efficiency and NOx. As a result, the optimal configuration of the combustor changes as the load is varied over the duty cycle. The results provide guidance on the application of active control.

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