Search Results (13)

This study proposes a design method based on adjoint shape optimization to enhance the heat transfer efficiency of shell-and-tube heat exchangers in oil and gas transportation systems. The primary focus of this work is the design optimization of shell-and-tube heat exchangers through geometric optimization. By simplifying the complex three-dimensional shell-and-tube heat exchanger into a pseudo-three-dimensional reduced-order model, two-dimensional adjoint shape optimization analyses were conducted under unidirectional symmetry about the x-axis and bidirectional symmetry in the x- and y-axes, respectively. The optimized two-dimensional models exhibited a significant increase in the average outlet temperature. Furthermore, the optimized two-dimensional shapes were extruded and reconstructed into three-dimensional models for validation. The results demonstrate that the average air outlet temperature of the three-dimensional models increased by 5.35 K and 3.07 K compared to the original design. Flow field analysis revealed that the heat transfer was improved, since the optimized pipeline layout enhances flow separation and turbulent mixing, leading to a more uniform temperature distribution. This study validates the effectiveness of the adjoint shape optimization method in improving the performance of shell-and-tube heat exchangers. Full article

To meet the stringent reliability requirements of rotor blades in turbomachines, greater effort should be devoted to improving both aerodynamic and structural performance in blade design. This paper introduces an aero-structural multi-disciplinary design optimization (MDO) method for compressor rotor blades using a discrete adjoint method and an equivalent stress model (ESM). The principles of the ESM are firstly introduced, and its accuracy in calculating equivalent stress is validated through comparison with a commercial program. Both the aerodynamic performance and the maximum equivalent stress (MES) are selected as optimization objectives. To modify the blade profile, the steepest descent optimization method is utilized, in which the necessary sensitivities of the cost function to the design parameters are calculated by solving the adjoint equations. Finally, the aero-structural MDO of a transonic compressor rotor, NASA Rotor 67, is conducted, and the Pareto solutions are obtained. The optimization results demonstrate that the adiabatic efficiency and the MES are competitive in improving multi-disciplinary performance. For most of the Pareto solutions, the MES can be considerably reduced with increased adiabatic efficiency. Full article

This paper presents a topology optimization (TopO) method for conjugate heat transfer (CHT), with turbulent flows. Topological changes are controlled by an artificial material distribution field (design variables), defined at the cells of a background grid and used to distinguish a fluid from a solid material. To effectively solve the CHT problem, it is crucial to impose exact boundary conditions at the computed fluid–solid interface (FSI); this is the purpose of introducing the cut-cell method. On the grid, including also cut cells, the incompressible Navier–Stokes equations, coupled with the Spalart–Allmaras turbulence model with wall functions, and the temperature equation are solved. The continuous adjoint method computes the derivatives of the objective function(s) and constraints with respect to the material distribution field, starting from the computation of derivatives with respect to the positions of nodes on the FSI and then applying the chain rule of differentiation. In this work, the continuous adjoint PDEs are discretized using schemes that are consistent with the primal discretization, and this will be referred to as the “Think Discrete–Do Continuous” (TDDC) adjoint. The accuracy of the gradient computed by the TDDC adjoint is verified and the proposed method is assessed in the optimization of two 2D cases, both in turbulent flow conditions. The performance of the TopO designs is investigated in terms of the number of required refinement steps per optimization cycle, the Reynolds number of the flow, and the maximum allowed power dissipation. To illustrate the benefits of the proposed method, the first case is also optimized using a density-based TopO that imposes Brinkman penalization terms in solid areas, and comparisons are made. Full article

This article presents single- and multi-disciplinary shape optimizations of a generic business jet wing at two transonic cruise flow conditions. The studies performed are based on two high-fidelity gradient-based optimization tools, assisted by the adjoint method (following both discrete and continuous approaches). Single discipline and coupled multi-disciplinary sensitivity derivatives computed from the two tools are compared and verified against finite differences. The importance of not making the frozen turbulence assumption in adjoint-based optimization is demonstrated. Then, a number of optimization runs, ranging from a pure aerodynamic with a rigid structure to an aerostructural one exploring the trade-offs between the involved disciplines, are presented and discussed. The middle-ground scenario of optimizing the wing with aerodynamic criteria and, then, performing an aerostructural trimming is also investigated. Full article

The existence of magnetic fields in spiral galaxies is beyond doubt and is confirmed by both observational data and theoretical models. Their generation occurs due to the dynamo mechanism action associated with the properties of turbulence. Most studies consider magnetic fields at moderate distances to the center of the disk, since the dynamo number is small in the marginal regions, and the field growth should be suppressed. At the same time, the computational results demonstrate the possibility of magnetic field penetration into the marginal regions of galaxies. In addition to the action of the dynamo, magnetorotational instability (MRI) can serve as one of the mechanisms of the field occurrence. This research is devoted to the investigation of MRI impact on galactic magnetic field generation and solving the occurring eigenvalue problems. The problems are formulated assuming that the perturbations may possibly increase. In the present work, we consider the eigenvalue problem, picturing the main field characteristics in the case of MRI occurrence, where the eigenvalues are firmly connected with the average vertical scale of the galaxy, to find out whether MRI takes place in the outer regions of the galaxy. The eigenvalue problem cannot be solved exactly; thus, it is solved using the methods of the perturbation theory for self-adjoint operators, where the eigenvalues are found using the series with elements including parameters characterizing the properties of the interstellar medium. We obtain linear and, as this is not enough, quadratic approximations and compare them with the numerical results. It is shown that they give a proper precision. We have compared the approximation results with those from numerical calculations and they were relatively close for the biggest eigenvalue. Full article

Numerical optimization methods are widely used for designing turbomachinery components due to the cost and time savings they can provide. In the available literature, the shape optimization of radial compressors mainly focuses on improving the impeller alone. However, it is well-established knowledge that the volute plays a key role in the overall performance of the compressor. The aim of the present paper is to perform an adjoint-based optimization of a volute that is designed for the SRV2-O compressor. The CAD model was first created by using the parametrization of 33 design parameters. Then, a butterfly topology was applied to mesh the computational domain with a multi-block structured grid, and an elliptic smoothing procedure was used to improve the quality of the fluid grid. A steady-state RANS CFD solver with a Spalart-Allmaras turbulence model was used to solve the Navier–Stokes equations, and then the flow sensitivities were computed with an adjoint solver. The objective function consists of minimizing the loss coefficient of the volute. The optimization is performed to obtain an improved design with a 14% loss reduction. A detailed flow and design analysis is carried out to highlight the loss reduction mechanisms, followed by the optimizer. Finally, the compressor map of the full stage is compared between the baseline and the optimized volute from the CFD simulations using a mixing plane interface. This research demonstrates the successful use of a gradient-based optimization technique to improve the volute of a radial compressor and opens the door towards simultaneously optimizing the wheel and the volute. Full article

The demand in solving complex turbulent fluid flows has been growing rapidly in the automotive industry for the last decade as engineers strive to design better vehicles to improve drag coefficients, noise levels and drivability. This paper presents the implementation of an arbitrary hybrid turbulence modeling (AHTM) approach in OpenFOAM for the efficient simulation of common automotive aerodynamics with unsteady turbulent separated flows such as the Kelvin–Helmholtz effect, which can also be used as an efficient part of aerodynamic design optimization (ADO) tools. This AHTM approach is based on the concept of Very Large Eddy Simulation (VLES), which can arbitrarily combine RANS, URANS, LES and DNS turbulence models in a single flow field depending on the local mesh refinement. As a result, the design engineer can take advantage of this unique and highly flexible approach to tailor his grid according to his design and resolution requirements in different areas of the flow field over the car body without sacrificing accuracy and efficiency at the same time. This paper presents the details of the implementation and careful validation of the AHTM method using the standard benchmark case of the Ahmed body, in comparison with some other existing models, such as RANS, URANS, DES and LES, which shows VLES to be the most accurate among the five examined. Furthermore, the results of this study demonstrate that the AHTM approach has the flexibility, efficiency and accuracy to be integrated with ADO tools for engineering design in the automotive industry. The approach can also be used for the detailed study of highly complex turbulent phenomena such as the Kelvin–Helmholtz instability commonly found in automotive aerodynamics. Currently, the AHTM implementation is being integrated with the DAFoam for gradient-based multi-point ADO using an efficient adjoint solver based on a Sparse Nonlinear optimizer (SNOPT). Full article

This paper presents an adjoint-based shape optimization framework and its demonstration in a conjugate heat transfer problem in a turbine blading. The gradient of the objective function is computed based on the continuous adjoint method, which also includes the adjoint to the turbulence model. Differences in the gradient resulting from making the frozen turbulence assumption are discussed. The developed software was used to optimize both the blade shape of the internally cooled linear C3X turbine blade and the position of cooling channels aiming at (a) minimum total pressure drop of the hot gas flow and (b) minimum highest temperature within the blade. A two-step optimization procedure was used. A free-form parameterization tool, based on volumetric NURBS, controls the blade airfoil contour, while the cooling channels are free to move following changes in the coordinates of their centers. Geometric and flow constraints are included in the performed optimizations, keeping the cooling channels away from the airfoil sides and retaining the turbine inlet capacity and flow turning. Full article

With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow by focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 ${}^{\circ }$ of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin–Helmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic forcing is tackled by means of a variational formulation, adjoint methods, penalization schemes, and an orthogonalization algorithm. Dealing with the transient growth of spanwise-periodic perturbations, and inspired by the need of physically-realizable disturbances, we finally provide a procedure attaining a kinetic-energy maximal gain on the order of ${10}^6$ , with respect to the power introduced by the external forcing. Full article

The LS89 high pressure axial turbine vane was originally designed and optimized for a downstream isentropic Mach number of 0.9. This profile has been widely used for computational fluid dynamics (CFD) validation in the open literature but very few attempts have been made to improve the already optimized design. This paper presents a sound methodology to design and optimize the LS89 using computer-aided design (CAD) at design conditions. The novelty of the study resides in the parametrization of design space, which is done at the CAD level, and the detailed analysis of the aerodynamic performance of the optimized design. Higher level constraints are imposed on the shape, such as the trailing edge thickness, the axial chord length, and G2 geometric continuity between the suction side and pressure side at the leading edge. The gradients used for the optimization are obtained by applying algorithmic differentiation to the CAD kernel and grid generator and the discrete adjoint method to the CFD solver. A reduction of almost 12% entropy generation is achieved, which is equivalent to a 16% total pressure loss reduction. The entropy generation is reduced while keeping the exit flow angle as a flow constraint, which is enforced via the penalty formulation. The resulting unconstrained optimization problem is solved by the L-BFGS-B algorithm. The flow is governed by the Reynolds-averaged Navier-Stokes equations and the one-equation transport Spalart-Allmaras turbulence model. The optimal profile is compared and benchmarked against the baseline case. Full article

Wind energy rotor blades are highly complex structures, both combining a large aerodynamic efficiency and a robust structure for lifetimes up to 25 years and more. Current research deals with smart rotor blades, improved for turbulent wind fields, less maintenance and low wind sites. In this work, an optimization tool for rotor blades using bend-twist-coupling is developed and tested. The adjoint approach allows computation of gradients based on the flow field at comparably low cost. A suitable projection method from the large design space of one gradient per numerical grid cell to a suitable design space for rotor blades is derived. The adjoint solver in OpenFOAM is extended for external flow. As novelty, we included rotation via the multiple reference frame method, both for the flow and the adjoint field. This optimization tool is tested for the NREL Phase VI turbine, optimizing the thrust by twisting of various outer parts between 20–50% of the blade length. Full article

The adjoint approach in gradient-based optimization combined with computational fluid dynamics is commonly applied in various engineering fields. In this work, the gradients are used for the design of a two-dimensional airfoil shape, where the aim is a change in lift and drag coefficient, respectively, to a given target value. The optimizations use the unconstrained quasi-Newton method with an approximation of the Hessian. The flow field is computed with a finite-volume solver where the continuous adjoint approach is implemented. A common assumption in this approach is the use of the same turbulent viscosity in the adjoint diffusion term as for the primal flow field. The effect of this so-called “frozen turbulence” assumption is compared to the results using adjoints to the Spalart–Allmaras turbulence model. The comparison is done at a Reynolds number of $Re=2\times {10}^6$ for two different airfoils at different angles of attack. Full article

We investigate the use of optimal coordinated control techniques in large eddy simulations of wind farm boundary layer interaction with the aim of increasing the total energy extraction in wind farms. The individual wind turbines are considered as flow actuators, and their energy extraction is dynamically regulated in time, so as to optimally influence the flow field. We extend earlier work on wind farm optimal control in the fully-developed regime (Goit and Meyers 2015, J. Fluid Mech. 768, 5–50) to a ‘finite’ wind farm case, in which entrance effects play an important role. For the optimal control, a receding horizon framework is employed in which turbine thrust coefficients are optimized in time and per turbine. Optimization is performed with a conjugate gradient method, where gradients of the cost functional are obtained using adjoint large eddy simulations. Overall, the energy extraction is increased 7% by the optimal control. This increase in energy extraction is related to faster wake recovery throughout the farm. For the first row of turbines, the optimal control increases turbulence levels and Reynolds stresses in the wake, leading to better wake mixing and an inflow velocity for the second row that is significantly higher than in the uncontrolled case. For downstream rows, the optimal control mainly enhances the sideways mean transport of momentum. This is different from earlier observations by Goit and Meyers (2015) in the fully-developed regime, where mainly vertical transport was enhanced. Full article