scholarly journals An Adjoint Optimization Prediction Method for Partially Cavitating Hydrofoils

2021 ◽  
Vol 9 (9) ◽  
pp. 976
Author(s):  
Dimitra Anevlavi ◽  
Kostas Belibassakis
Keyword(s):  
Prediction Method ◽  
Cavitation Number ◽  
Cavity Shape ◽  
Marine Propellers ◽  
Sheet Cavitation ◽  
Hydrokinetic Turbines ◽  
Design Variables ◽  
Gradient Based ◽  
Lifting Surfaces ◽  
Continuous Adjoint

Much work has been done over the past years to obtain a better understanding, predict and alleviate the effects of cavitation on the performance of lifting surfaces for hydrokinetic turbines and marine propellers. Lifting-surface sheet cavitation, when addressed as a free-streamline problem, can be predicted up to a desirable degree of accuracy using numerical methods under the assumptions of ideal flow. Typically, a potential solver is used in conjunction with geometric criteria to determine the cavity shape, while an iterative scheme ensures that all boundary conditions are satisfied. In this work, we propose a new prediction model for the case of partially cavitating hydrofoils in a steady flow that treats the free-streamline problem as an inverse problem. The objective function is based on the assumption that on the cavity boundary, the pressure remains constant and is evaluated at each optimization cycle using a source-vorticity BEM solver. The attached cavity is parametrized using B-splines, and the control points are included in the design variables along with the cavitation number. The sensitivities required for the gradient-based optimization are derived using the continuous adjoint method. The proposed numerical scheme is compared against other methods for the NACA 16-series hydrofoils and is found to predict well both the cavity shape and cavitation number for a given cavity length.

A Fast Method to Predict the Cavitation Volume on Two-Dimensional Sections

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Zhibo Zeng ◽  
Gert Kuiper
Keyword(s):  
Pressure Fluctuations ◽  
Prediction Method ◽  
Fast Method ◽  
Two Dimensional ◽  
Fast Calculation ◽  
Wake Field ◽  
Marine Propellers ◽  
Sheet Cavitation ◽  
Blade Section ◽  
Dimensional Section

The paper presents a simplified prediction method to estimate cavitation-induced pressure fluctuations by marine propellers in a nonuniform wake field. It is realized by a very fast calculation of the cavitation volume variation. The sheet cavitation volume is represented by the cavitation area in a two-dimensional section, which is the vapor area inside the cavity contour. The variation of the cavitation area on a two-dimensional blade section has been simplified to a relation in quasi-steady condition with only a limited number of nondimensional parameters. This results in a fast method to predict the cavitation area of a blade section passing a wake peak, using a precalculated database. Application of this method to the prediction of cavitation-induced pressure fluctuations shows to be effective. This makes optimization of propeller sections for minimum cavitation-induced pressure fluctuations feasible.

Application of a Boundary Element Method in the Prediction of Unsteady Blade Sheet and Developed Tip Vortex Cavitation on Marine Propellers

2004 ◽  
Vol 48 (01) ◽  
pp. 15-30
Author(s):  
Hanseong Lee ◽  
Spyros A. Kinnas
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Pressure Fluctuations ◽  
Ship Hull ◽  
Tip Vortex ◽  
Tip Vortex Cavitation ◽  
Marine Propellers ◽  
Sheet Cavitation ◽  
Numerical Predictions ◽  
Element Method

Most marine propellers operate in nonaxisymmetric inflows, and thus their blades are often subject to an unsteady flow field. In recent years, due to increasing demands for faster and larger displacement ships, the presence of blade sheet and tip vortex cavitation has become very common. Developed tip vortex cavitation, which often appears together with blade sheet cavitation, is known to be one of the main sources of propeller-induced pressure fluctuations on the ship hull. The prediction of developed tip vortex cavity as well as blade sheet cavity is thus quite important in the assessment of the propeller performance and the corresponding pressure fluctuations on the ship hull. A boundary element method is employed to model the fully unsteady blade sheet (partial or supercavitating) and developed tip vortex cavitation on propeller blades. The extent and size of the cavity is determined by satisfying both the dynamic and the kinematic boundary conditions on the cavity surface. The numerical behavior of the method is investigated for a two-dimensional tip vortex cavity, a three-dimensional hydrofoil, and a marine propeller subjected to nonaxisymmetric inflow. Comparisons of numerical predictions with experimental measurements are presented.

Efficient Gradient-Based Algorithms for the Construction of Pareto Fronts

2011 ◽  
Author(s):  
Sriram Shankaran ◽  
Brian Barr
Keyword(s):  
Pareto Front ◽  
Computational Cost ◽  
High Fidelity ◽  
Simulation Tools ◽  
Pareto Points ◽  
Uniform Spacing ◽  
Design Variables ◽  
Gradient Based ◽  
Pareto Fronts ◽  
Sampling Approach

The objective of this study is to develop and assess a gradient-based algorithm that efficiently traverses the Pareto front for multi-objective problems. We use high-fidelity, computationally intensive simulation tools (for eg: Computational Fluid Dynamics (CFD) and Finite Element (FE) structural analysis) for function and gradient evaluations. The use of evolutionary algorithms with these high-fidelity simulation tools results in prohibitive computational costs. Hence, in this study we use an alternate gradient-based approach. We first outline an algorithm that can be proven to recover Pareto fronts. The performance of this algorithm is then tested on three academic problems: a convex front with uniform spacing of Pareto points, a convex front with non-uniform spacing and a concave front. The algorithm is shown to be able to retrieve the Pareto front in all three cases hence overcoming a common deficiency in gradient-based methods that use the idea of scalarization. Then the algorithm is applied to a practical problem in concurrent design for aerodynamic and structural performance of an axial turbine blade. For this problem, with 5 design variables, and for 10 points to approximate the front, the computational cost of the gradient-based method was roughly the same as that of a method that builds the front from a sampling approach. However, as the sampling approach involves building a surrogate model to identify the Pareto front, there is the possibility that validation of this predicted front with CFD and FE analysis results in a different location of the “Pareto” points. This can be avoided with the gradient-based method. Additionally, as the number of design variables increases and/or the number of required points on the Pareto front is reduced, the computational cost favors the gradient-based approach.

Optimization of Magnetorheological Brake

2011 ◽  
Author(s):  
Snegdha Gupta ◽  
Harish Hirani
Keyword(s):  
Minimum Weight ◽  
Hybrid Genetic Algorithm ◽  
Brake System ◽  
Outer Diameter ◽  
Current Accounting ◽  
Hydraulic Brake ◽  
Rate Dependent ◽  
Design Variables ◽  
Braking Torque ◽  
Gradient Based

Quick response and rheological properties as a function of magnetic field are well known features of MR fluids which inspire their usage as brake materials. Controllable torque and minimum weight of brake system are the deciding functions based on which the viability of the MR brake against the conventional hydraulic brake system can be judged. The aim of this study is to optimize a multi-disk magneto-rheological brake system considering torque and weight as objective functions and geometric dimensions of conventional hydraulic brake as constraints. The electric current accounting magnetic saturation, MR gap, number of disk, thickness of disk, and outer diameter of disk have been considered as design variables. To model the behavior of MR Fluid, Bingham and Herschel Bulkley models have been compared. To implement these models in estimating the braking torque a modification in shear rate dependent component has been proposed. The overall design of MR brake has been optimized using a hybrid (Genetic algorithm plus gradient based) optimization scheme of MATLAB software.

Adjoint-based aerodynamic drag minimisation with trim penalty

2021 ◽  
pp. 1-25
Author(s):  
S. Shitrit
Keyword(s):  
Drag Reduction ◽  
Aerodynamic Drag ◽  
Lift Coefficient ◽  
Free Form ◽  
Shape Optimisation ◽  
Control Points ◽  
Aerodynamic Shape ◽  
Design Variables ◽  
Gradient Based ◽  
Mesh Warping

Abstract The aerodynamic performance of conventional aircraft configurations are mainly affected by the wing and horizontal tail. Drag reduction by shape optimisation of the wing, while taking into account the aircraft trimmed constraint, has more benefit than focusing solely on the wing. So in order to evaluate this approach, the following study presents results of a single and multipoint aerodynamic shape optimisation of the wing-body-tail configuration, defined by the Aerodynamic Design Discussion Group (ADODG). Most of the aerodynamic shape optimisation problems published in the last years are focused mainly on the wing as the main driver for performance improvement, with no trim constraint and/or excess drag obtained from the fuselage, fins or other parts. This work partially fills this gap by an investigation of RANS-based aerodynamic optimisation for transonic trimmed flight. Mesh warping and geometry parametrisation is accomplished by fitting the multi-block structured grid to a B-spline volumes and performing the mesh movement by using surface control points embedded within the free-form deformation (FFD) volumes. A gradient-based optimisation algorithm is used with an adjoint method in order to compute the derivatives of the objective and constraint functions with respect to the design variables. In this work the aerodynamic shape optimisation of the CRM wing-body-tail configuration is investigated, including a trim constraint that is satisfied by rotating the horizontal tail. The shape optimisation is driven by 432 design variables that envelope the wing surface, and 120 shape variables for the tail, as well as the angle of attack and tail rotation angles. The constraints are the lift coefficient, wing’s thickness controlled by 1,000 control points, and the wing’s volume. For the untrimmed configuration the drag coefficient is reduced by 5.76%. Optimising the wing with a trim condition by tail rotation results in shock-free design with a considerably improved drag, even better than the untrimmed-optimised case. The second optimisation problem studied is a single and multi-point lift constraint drag minimisation of a gliding configuration wing in transonic viscous flow. The shock is eliminated, reducing the drag of the untrimmed configuration by more than 60%, using 192 design variables. Further robustness is achieved through a multi-point optimisation with more than 45% drag reduction.

A Nonlinear Method for Predicting Unsteady Sheet Cavitation on Marine Propellers

1983 ◽  
Vol 27 (01) ◽  
pp. 56-74
Author(s):  
Frederick Stern ◽  
William S. Vorus
Keyword(s):  
Complete Solution ◽  
Near Field ◽  
Fluid Velocity ◽  
Far Field ◽  
Static Potential ◽  
Nonlinear Method ◽  
Slender Body Theory ◽  
Marine Propellers ◽  
Sheet Cavitation ◽  
Dynamic Potential

A method is presented which provides a basis for predicting the nonlinear dynamic behavior of unsteady propeller sheet cavitation. The method separates the fluid velocity potential boundary-value problem into two parts, static and dynamic, which are solved sequentially in a forward time stepping procedure. The static potential problem is for the cavity fixed instantaneously relative to the propeller and the propeller translating through the nonuniform wake field. This problem can be solved by standard methods. The dynamic potential represents the instantaneous reaction of the cavity to the static potential field and thus predicts the cavity's deformation and motion relative to the blade. A solution is obtained for the dynamic potential by using the concepts of slender-body theory to define near-and far-field potentials which are matched to form the complete solution. In the far field, the cavity is represented by a three-dimensional spanwise line distribution of sources. In the near field, the cavity is approximated at each cross section as a semi-ellipse with unknown axes a(t), b(t), and position l(t) along the chord of the foil section. Conditions are derived that determine (a, b, l) by minimizing the square error in satisfying the dynamic boundary condition. These conditions yield the equations of motion of the cavity in the form of three coupled nonlinear second-order ordinary differential equations with time as the independent variable. The theory is presented for the general foil and not specifically for propellers. However, the method incorporates features in its formulation which facilitate its application to marine propellers. The method is demonstrated by using the steady noncavitating potential for the two-dimensional half-body as an approximation to the static potential. Both fixed and unsteady cavities are calculated. The unsteady cavities are calculated by varying the hydrostatic pressure in the half-body pressure field sinusoidally.

Compressor Blade Optimization Using a Continuous Adjoint Formulation

2006 ◽  
Author(s):  
Dimitiros I. Papadimitriou ◽  
Kyriakos C. Giannakoglou
Keyword(s):  
Stokes Equations ◽  
Compressor Blade ◽  
Navier Stokes ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Adjoint Formulation ◽  
Design Variables ◽  
Gradient Computation ◽  
Geometrical Constraints ◽  
Continuous Adjoint

In this paper, a constrained optimization algorithm is formulated and utilized to improve the aerodynamic performance of a 3D peripheral compressor blade cascade. The cascade efficiency is measured in terms of entropy generation along the developed flowfield, which defines the field objective functional to be minimized. Its gradient with respect to the design variables, which are the coordinates of the Non-Uniform Rational B-Spline (NURBS) control points defining the blade, is computed through a continuous adjoint formulation of the Navier-Stokes equations based on the aforementioned functional. The steepest descent algorithm is used to locate the optimal set of design variables, i.e. the optimal blade shape. In addition to the well-known advantages of the adjoint method, the current formulation has even less CPU cost for the gradient computation as it leads to gradient expression which is free of field variations in geometrical quantities (such as derivatives of interior grid node coordinates with respect to the design variables); the computation of the latter would be costly since it requires remeshing anew the computational domain for each bifurcated design variable. The geometrical constraints, which depend solely on the blade parameterization, are handled by a quadratic penalty method by introducing additional Lagrange multipliers.

S2 Surface Quasi-3D Aerodynamic Design Using the Continuous Adjoint Method for Multi-Stage Turbine

2014 ◽  
Author(s):  
Lei Chen ◽  
Jiang Chen
Keyword(s):  
Objective Function ◽  
Adjoint Method ◽  
Adjoint Equations ◽  
Design System ◽  
Shape Design ◽  
Aerodynamic Design ◽  
Aerodynamic Shape ◽  
Multi Stage ◽  
Gradient Based ◽  
Continuous Adjoint

The adjoint method eliminates the dependence of the gradient of the objective function with respect to design variables on the flow field making the obtainment of the gradient both accurate and fast. For this reason, the adjoint method has become the focus of attention in recent years. This paper develops a continuous adjoint formulation for through-flow aerodynamic shape design in a multi-stage gas turbine environment based on a S2 surface quasi-3D problem governed by the Euler equations with source terms. Given the general expression of the objective function calculated via a boundary integral, the adjoint equations and their boundary conditions are derived in detail by introducing adjoint variable vectors. As a result, the final expression of the objective function gradient only includes the terms pertinent to those physical shape variations that are calculated by metric variations. The adjoint system is solved numerically by a finite-difference method with explicit Euler time-marching scheme and a Jameson spatial scheme which employs first and third order dissipative flux. Integrating the blade stagger angles and passage perturbation parameterization with the simple steepest decent method, a gradient-based aerodynamic shape design system is constructed. Finally, the application of the adjoint method is validated through a 5-stage turbine blade and passage optimization with an objective function of entropy generation. The result demonstrates that the gradient-based system can be used for turbine aerodynamic design.

Numerical Simulation and Analysis for Influence of Wall Effect on Cavity Shape

2013 ◽  
Vol 385-386 ◽  
pp. 400-403
Author(s):  
Fu Yuan Li ◽  
Yu Wen Zhang ◽  
Xi Zhao Du
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
Empirical Formula ◽  
Diameter Ratio ◽  
Cavitation Number ◽  
Wall Effect ◽  
Water Tunnel ◽  
Cavity Shape ◽  
Model Size ◽  
The Impact

In the experiment of cavitation, the same water tunnel with different model size will get cavity shape that is different from the result of the empirical formula under the same cavitation number. In this article, we studied the impact of wall effect on natural cavity shape and the resistance of cavitator. We get the cavity shape and resistance of cavitator under different diameter ratio. We also get the law how cavity shape and resistance of cavitator change with the diameter ratio. The results provide a reference for experiment in water tunnel and the simulation model.

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