An Efficient Unsteady Adjoint Optimization System for Multistage Turbomachinery

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Can Ma ◽  
Xinrong Su ◽  
Xin Yuan
Keyword(s):  
Unsteady Flow ◽  
Harmonic Balance Method ◽  
Adjoint Equations ◽  
Aerodynamic Optimization ◽  
Flow Equations ◽  
Optimization System ◽  
Unsteady Aerodynamic ◽  
Flow Features ◽  
The Cost ◽  
Unsteady Adjoint

Unsteady blade row interactions play an important role in the performance of multistage turbomachinery. However, most aerodynamic optimizations of multistage turbomachinery are based on mixing-plane steady flow simulations. To take into account the unsteady flow features in the optimization cycle, this paper develops an adjoint-based unsteady aerodynamic optimization system for multistage turbomachinery. To the authors' best knowledge, this is the first work in the literature conducting the unsteady adjoint aerodynamic optimization of multistage turbomachinery. The unsteady flow equations and the discrete adjoint equations are solved using a finite volume code, with the harmonic balance method adopted to reduce the cost of unsteady simulations. The system is applied to the unsteady aerodynamic optimization of a 1.5-stage compressor. Results show the efficiency and capability of the proposed framework for the unsteady aerodynamic optimization of multistage turbomachinery.

Adjoint-Based Unsteady Aerodynamic Optimization of a Transonic Turbine Stage

2016 ◽  
Author(s):  
Can Ma ◽  
Xinrong Su ◽  
Xin Yuan
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Harmonic Balance Method ◽  
Adjoint Equations ◽  
Turbine Stage ◽  
Aerodynamic Optimization ◽  
Optimization System ◽  
Unsteady Aerodynamic ◽  
Blade Row ◽  
Transonic Turbine

Unsteady blade row interactions considerably affect the performance of turbomachinery consisting of multiple blade rows. However, most aerodynamic optimizations of turbomachinery are based on mixing-plane steady flow simulations which cannot account for the unsteady effects of blade row interactions. In this work, the rotor of a two-dimensional transonic turbine stage is optimized using an in-house unsteady aerodynamic optimization system that allows for a more accurate modeling of the unsteady flow features occurring in multi-row turbomachinery configurations. The gradients of the objective function and constraint to the design variables are efficiently calculated with the discrete adjoint method. In the developed adjoint-based unsteady aerodynamic optimization system, the unsteady Reynolds-Averaged Navier-Stokes equations are solved using the harmonic balance method with an in-house code. The adjoint equations are derived by hand from the discrete form of the unsteady flow equations. The present results demonstrate the efficiency and capability of the unsteady aerodynamic optimization system for turbomachinery with multiple blade rows.

Discrete Adjoint Solution of Unsteady Turbulent Flow in Compressor

2015 ◽  
Author(s):  
Can Ma ◽  
Xinrong Su ◽  
Xin Yuan
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Flow Simulation ◽  
Adjoint Equations ◽  
Navier Stokes ◽  
Aerodynamic Optimization ◽  
Flow Equations ◽  
Discrete Adjoint ◽  
Continuous Adjoint ◽  
Unsteady Flow Simulation

Unsteady blade row interactions play an important role in the performance of the compressor stages. However, due to the large cost of the unsteady flow simulation, most aerodynamic optimizations of the compressor are based on the steady flow simulation. This paper adopts the time spectral method to reduce the cost of the unsteady flow simulation and a discrete adjoint solver based on the unsteady flow solver has been developed. The unsteady flow equations and the adjoint equations are solved using an in-house code. The in-house code is based on the finite volume method and solves the URANS (Unsteady Reynolds Averaged Navier-Stokes) equations on the multi-block structured mesh. For spatial discretization the 3rd order WENO (Weighted Essentially Nonoscillatory) upwind scheme is used for reconstruction and the convective flux is computed with Roe’s approximate Riemann solver. The widely used one-equation Spalart-Allmaras turbulence model is adopted for the flow simulation. For the adjoint solution, the constant-eddy viscosity assumption is adopted and only the main flow adjoint equations are solved. The adjoint equations are formed in a discrete manner, which leads to more accurate discrete objective function sensitivity than the continuous adjoint method. The present work serves as an essential part of the system for efficient unsteady aerodynamic optimization of turbomachinery.

Three-Dimensional Non-Reflecting Boundary Condition for Linearized Flow Solvers

2010 ◽  
Author(s):  
Paul J. Petrie-Repar
Keyword(s):  
Boundary Condition ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Far Field ◽  
Two Dimensional ◽  
Flow Equations ◽  
Flow Simulations ◽  
Unsteady Aerodynamic ◽  
2D And 3D

A three-dimensional (3D) non-reflecting boundary condition for linearized flow solvers is presented. The unsteady aerodynamic modes at the inlet and outlet (far-field) are numerically determined by solving an eigen problem for the semi-discretized flow equations on a two-dimensional mesh. Unlike previous methods the shape of the far-field can be general and the non-uniformity of the steady flow across the far-field is considered. The calculated unsteady modes are used to decompose the unsteady flow at the far-field into modes. The direction of each mode is determined, and incoming modes are prescribed and outgoing modes are extrapolated. The results of 2D and 3D inviscid linearised flow simulations using the new boundary condition are presented.

Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I: Mathematical Derivation of Adjoint Lattice Boltzmann Equations

2014 ◽  
Vol 6 (5) ◽  
pp. 570-589 ◽  
Author(s):  
Mohamad Hamed Hekmat ◽  
Masoud Mirzaei
Keyword(s):  
Cost Function ◽  
Lattice Boltzmann ◽  
Optimization Problems ◽  
General Procedure ◽  
Main Idea ◽  
Distribution Functions ◽  
Adjoint Equations ◽  
Aerodynamic Optimization ◽  
Discrete Adjoint ◽  
The Cost

AbstractThe significance of flow optimization utilizing the lattice Boltzmann (LB) method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques. These unique characteristics of the LB method form the main idea of its application to optimization problems. In this research, for the first time, both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost. The proposed approach could be performed similarly for any optimization problem with the corresponding cost function and design variables vector. Moreover, this approach was not limited to flow fields and could be employed for steady as well as unsteady flows. Initially, the continuous and discrete adjoint LB equations and the cost function gradient vector were derived mathematically in detail using the continuous and discrete LB equations in space and time, respectively. Meanwhile, new adjoint concepts in lattice space were introduced. Finally, the analytical evaluation of the adjoint distribution functions and the cost function gradients was carried out.

On the Application of a Harmonic Balance Method With a Volume Source Cooling Model to the Simulation of a Film-Cooled Turbine Stage

2016 ◽  
Author(s):  
Kai Becker ◽  
Graham Ashcroft ◽  
Anton Weber ◽  
Stefan Rochhausen ◽  
Jose Rodriguez ◽  
...  
Keyword(s):  
Unsteady Flow ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Source Model ◽  
Volume Source ◽  
Computational Overhead ◽  
Flow And Heat Transfer ◽  
Nonlinear Solver ◽  
The Cost ◽  
Cooling Model

The application of Reduced Order Models (ROMs) in the simulation of complex, time-dependent flows in turbomachines provides a means to significantly reduce the cost, both in terms of preprocessing and computational overhead, of numerical simulations. In this work the development and combination of two ROMs for the simulation of the unsteady, time-periodic flow and heat transfer in a film-cooled turbine are presented. For the simulation of the unsteady flow an alternating frequency/time domain Harmonic Balance (HB) method is applied. To allow the efficient preprocessing and simulation of film-cooled blades a second, volume source based, ROM is incorporated into the underlying nonlinear solver of the HB method. Through the application of the volume source model the time consuming and error prone resolution and specification of individual cooling holes is no longer necessary. To validate the newly implemented volume source model a number of simple academic test cases are presented and analyzed in detail. Following the basic validation of the cooling model the approach is combined with the HB method to simulate the unsteady flow in the first one and half stages of a high-pressure turbine.

QUACC, a novel method for predicting unsteady flows — including propellers and store release

2001 ◽  
Vol 105 (1050) ◽  
pp. 427-434
Author(s):  
D. L. Hunt ◽  
M. Childs ◽  
M. Maina
Keyword(s):  
Analytic Function ◽  
Unsteady Flow ◽  
Unsteady Flows ◽  
Accurate Solution ◽  
Test Case ◽  
Moving Surface ◽  
Flow Equations ◽  
Novel Method ◽  
The Cost

AbstractAerospace designers are increasingly interested in predicting unsteady flowfields such as those associated with store release, rotating propellers etc. However, the cost of performing fully unsteady calculations is usually prohibitively expensive. In order to address this problem for unsteady flows driven by a moving surface, a novel method is presented which calculates the time derivates as an analytic function of the instantaneous flowfield. This allows an accurate solution of the unsteady flow equations to be calculated using a quasi-unsteady approach. The validity of this approach is demonstrated for a store release and a propeller test case. Possible extensions to this method for more complex unsteady flows are presented.

scholarly journals Stochastic Expansion Planning of Various Energy Storage Technologies in Active Power Distribution Networks

2021 ◽  
Vol 13 (10) ◽  
pp. 5752
Author(s):  
Reza Sabzehgar ◽  
Diba Zia Amirhosseini ◽  
Saeed D. Manshadi ◽  
Poria Fajri
Keyword(s):  
Energy Storage ◽  
Power Distribution ◽  
Power Flow ◽  
Lithium Ion ◽  
Distribution Networks ◽  
Renewable Energy Resources ◽  
Flow Equations ◽  
Second Order Cone ◽  
Li Ion ◽  
The Cost

This work aims to minimize the cost of installing renewable energy resources (photovoltaic systems) as well as energy storage systems (batteries), in addition to the cost of operation over a period of 20 years, which will include the cost of operating the power grid and the charging and discharging of the batteries. To this end, we propose a long-term planning optimization and expansion framework for a smart distribution network. A second order cone programming (SOCP) algorithm is utilized in this work to model the power flow equations. The minimization is computed in accordance to the years (y), seasons (s), days of the week (d), time of the day (t), and different scenarios based on the usage of energy and its production (c). An IEEE 33-bus balanced distribution test bench is utilized to evaluate the performance, effectiveness, and reliability of the proposed optimization and forecasting model. The numerical studies are conducted on two of the highest performing batteries in the current market, i.e., Lithium-ion (Li-ion) and redox flow batteries (RFBs). In addition, the pros and cons of distributed Li-ion batteries are compared with centralized RFBs. The results are presented to showcase the economic profits of utilizing these battery technologies.

Assessment of Unsteady Flows in Turbines

1992 ◽  
Vol 114 (1) ◽  
pp. 79-90 ◽  
Author(s):  
O. P. Sharma ◽  
G. F. Pickett ◽  
R. H. Ni
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Experimental Investigations ◽  
Flow Parameters ◽  
Research Activities ◽  
Flow Features ◽  
Computational Fluid Dynamics Cfd ◽  
Turbine Design ◽  
The Impact

The impacts of unsteady flow research activities on flow simulation methods used in the turbine design process are assessed. Results from experimental investigations that identify the impact of periodic unsteadiness on the time-averaged flows in turbines and results from numerical simulations obtained by using three-dimensional unsteady Computational Fluid Dynamics (CFD) codes indicate that some of the unsteady flow features can be fairly accurately predicted. Flow parameters that can be modeled with existing steady CFD codes are distinguished from those that require unsteady codes.

scholarly journals The drag-adjoint field of a circular cylinder wake at Reynolds numbers 20, 100 and 500

2013 ◽  
Vol 730 ◽  
pp. 145-161 ◽  
Author(s):  
Qiqi Wang ◽  
Jun-Hui Gao
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Unsteady Flow ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Adjoint Equations ◽  
Cylinder Wake ◽  
Near Wake ◽  
Navier Stokes Equation ◽  
D 20

AbstractThis paper analyses the adjoint solution of the Navier–Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, ${\mathit{Re}}_{D} = 20, 100$ and $500$. The quantity of interest in the adjoint formulation is the drag on the cylinder. We use classical fluid mechanics approaches to analyse the adjoint solution, which is a vector field similar to a flow field. Production and dissipation of kinetic energy of the adjoint field is discussed. We also derive the evolution of circulation of the adjoint field along a closed material contour. These analytical results are used to explain three numerical solutions of the adjoint equations presented in this paper. The adjoint solution at ${\mathit{Re}}_{D} = 20$, a viscous steady state flow, exhibits a downstream suction and an upstream jet, the opposite of the expected behaviour of a flow field. The adjoint solution at ${\mathit{Re}}_{D} = 100$, a periodic two-dimensional unsteady flow, exhibits periodic, bean-shaped circulation in the near-wake region. The adjoint solution at ${\mathit{Re}}_{D} = 500$, a turbulent three-dimensional unsteady flow, has complex dynamics created by the shear layer in the near wake. The magnitude of the adjoint solution increases exponentially at the rate of the first Lyapunov exponent. These numerical results correlate well with the theoretical analysis presented in this paper.

On the Use of the Automatic Differentiation for Developing a Linear Harmonic Solver

2018 ◽  
Author(s):  
Wei Zhang ◽  
Dingxi Wang ◽  
Xiuquan Huang ◽  
Tianxiao Yang ◽  
Hong Yan ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Automatic Differentiation ◽  
Harmonic Balance Method ◽  
Source Codes ◽  
Reverse Mode ◽  
Frequency Domain Methods ◽  
The Cost ◽  
Time Periodic ◽  
Small Disturbances

The linear and nonlinear harmonic methods are efficient frequency domain methods for analyzing time periodic unsteady flow fields. They have been widely used in both academia and industry. But the cost and complexity of developing a linear harmonic solver has been limiting its wider applications. On the other hand, the automatic differentiation (AD) has long been used in the CFD community with a focus on generating adjoint codes in a reverse mode. All those AD tools can do a much better job in generating linearized codes in a tangent mode, but so far very little, if any, attention is paid to using AD for developing linear harmonic solvers. The linear harmonic method, in comparison with the harmonic balance method, has its own advantages. For example, it can capture small disturbances very effectively, and avoids aliasing errors which can lead to solution instability since each wave component is solved for separately. This paper presents the effort of using an AD tool to generate major source codes for the development of a linear harmonic solver for analyzing time periodic unsteady flows. It includes the procedures and advice of using AD for such a purpose. A case study is also presented to validate the developed linear harmonic solver.

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