scholarly journals Derivation of the Adjoint Drift Flux Equations for Multiphase Flow

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 31 ◽  
Author(s):  
Shenan Grossberg ◽  
Daniel S. Jarman ◽  
Gavin R. Tabor
Keyword(s):  
Multiphase Flow ◽  
Objective Function ◽  
Settling Velocity ◽  
Flow Problem ◽  
Adjoint System ◽  
Drift Flux ◽  
Adjoint Approach ◽  
Continuous Adjoint ◽  
First Time ◽  
Mathematical Derivation

The continuous adjoint approach is a technique for calculating the sensitivity of a flow to changes in input parameters, most commonly changes of geometry. Here we present for the first time the mathematical derivation of the adjoint system for multiphase flow modeled by the commonly used drift flux equations, together with the adjoint boundary conditions necessary to solve a generic multiphase flow problem. The objective function is defined for such a system, and specific examples derived for commonly used settling velocity formulations such as the Takacs and Dahl models. We also discuss the use of these equations for a complete optimisation process.

Inverse Problem for Isentropic Mach-Number on Blade Wall in Aerodynamic Shape Design of Turbomachinery Cascades by Using Adjoint Method

2011 ◽  
Author(s):  
Haitao Li ◽  
Liming Song ◽  
Pengfei Zhang ◽  
Zhenping Feng
Keyword(s):  
Inverse Problem ◽  
Mach Number ◽  
Objective Function ◽  
Adjoint System ◽  
Boundary Integral ◽  
Adjoint Equations ◽  
Grid Node ◽  
Time Step ◽  
Flow Quantity ◽  
Continuous Adjoint

This paper presents an approach of the continuous adjoint system deduction based on the variation in grid node coordinates, in which the variation in the gradient of flow quantity is converted into the gradient of the variation in flow quantity and the gradient of the variation in grid node coordinates, which avoids the coordinate system transforming in the traditional derivation process of adjoint system and make the adjoint system much more sententious. By introducing the Jacobian matrix of viscous flux to the gradient of flow variables, the adjoint system for turbomachinery aerodynamic design optimization governed by compressible Navier-Stokes equations is derived in details. Given the general expression of objective functions consisted of both boundary integral and field integral, the adjoint equations and their boundary conditions are derived, and the final expression of the objective function gradient including only boundary integrals is formulated to reduce the CPU cost. Then the adjoint system is numerically solved by using the finite volume method with an explicit 5-step Runge-Kutta scheme and Riemann approximate solution of Roe’s scheme combined with multi-grid technique and local time step to accelerate the convergence procedure. Finally, the application of the method is illustrated through a turbine cascade inverse problem with an objective function of isentropic Mach number distribution on the blade wall.

scholarly journals Application of the Multiverse Optimization Method to Solve the Optimal Power Flow Problem in Direct Current Electrical Networks

2021 ◽  
Vol 13 (16) ◽  
pp. 8703
Author(s):  
Andrés Alfonso Rosales-Muñoz ◽  
Luis Fernando Grisales-Noreña ◽  
Jhon Montano ◽  
Oscar Danilo Montoya ◽  
Alberto-Jesus Perea-Moreno
Keyword(s):  
Objective Function ◽  
Successive Approximation ◽  
Direct Current ◽  
Optimization Algorithm ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Flow Problem ◽  
Distributed Generators ◽  
Optimal Power ◽  
Power Flow Problem

This paper addresses the optimal power flow problem in direct current (DC) networks employing a master–slave solution methodology that combines an optimization algorithm based on the multiverse theory (master stage) and the numerical method of successive approximation (slave stage). The master stage proposes power levels to be injected by each distributed generator in the DC network, and the slave stage evaluates the impact of each power configuration (proposed by the master stage) on the objective function and the set of constraints that compose the problem. In this study, the objective function is the reduction of electrical power losses associated with energy transmission. In addition, the constraints are the global power balance, nodal voltage limits, current limits, and a maximum level of penetration of distributed generators. In order to validate the robustness and repeatability of the solution, this study used four other optimization methods that have been reported in the specialized literature to solve the problem addressed here: ant lion optimization, particle swarm optimization, continuous genetic algorithm, and black hole optimization algorithm. All of them employed the method based on successive approximation to solve the load flow problem (slave stage). The 21- and 69-node test systems were used for this purpose, enabling the distributed generators to inject 20%, 40%, and 60% of the power provided by the slack node in a scenario without distributed generation. The results revealed that the multiverse optimizer offers the best solution quality and repeatability in networks of different sizes with several penetration levels of distributed power generation.

scholarly journals Power-to-Syngas: A Parareal Optimal Control Approach

2021 ◽  
Vol 9 ◽  
Author(s):  
Andrea Maggi ◽  
Dominik Garmatter ◽  
Sebastian Sager ◽  
Martin Stoll ◽  
Kai Sundmacher
Keyword(s):  
Optimal Control ◽  
Water Gas Shift ◽  
Control Approach ◽  
Renewable Power ◽  
Reverse Water Gas Shift ◽  
Time Modeling ◽  
Continuous Adjoint Method ◽  
Continuous Adjoint ◽  
Water Gas ◽  
First Time

A chemical plant layout for the production of syngas from renewable power, H2O and biogas, is presented to ensure a steady productivity of syngas with a constant H2-to-CO ratio under time-dependent electricity provision. An electrolyzer supplies H2 to the reverse water-gas shift reactor. The system compensates for a drop in electricity supply by gradually operating a tri-reforming reactor, fed with pure O2 directly from the electrolyzer or from an intermediate generic buffering device. After the introduction of modeling assumptions and governing equations, suitable reactor parameters are identified. Finally, two optimal control problems are investigated, where computationally expensive model evaluations are lifted viaparareal and necessary objective derivatives are calculated via the continuous adjoint method. For the first time, modeling, simulation, and optimal control are applied to a combination of the reverse water-gas shift and tri-reforming reactor, exploring a promising pathway in the conversion of renewable power into chemicals.

scholarly journals Optimized lattice-based metamaterials for elastostatic cloaking

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210418
Author(s):  
E. D. Sanders ◽  
M. A. Aguiló ◽  
G. H. Paulino
Keyword(s):  
Objective Function ◽  
Uniaxial Tension ◽  
Weighted Least Squares ◽  
Elliptical Hole ◽  
Adjoint System ◽  
System Optimization ◽  
Small Region ◽  
Shear Loading ◽  
Stiffness Properties ◽  
Stiffness Characteristics

An optimization-based approach is proposed to design elastostatic cloaking devices in two-dimensional (2D) lattices. Given an elastic lattice with a defect, i.e. a circular or elliptical hole, a small region (cloak) around the hole is designed to hide the effect of the hole on the elastostatic response of the lattice. Inspired by the direct lattice transformation approach to elastostatic cloaking in 2D lattices, the lattice nodal positions in the design region are obtained using a coordinate transformation of the reference (undisturbed) lattice nodes. Subsequently, additional connectivity (i.e. a ground structure) is defined in the design region and the stiffness properties of these elements are optimized to mimic the global stiffness characteristics of the reference lattice. A weighted least-squares objective function is proposed, where the weights have a physical interpretation—they are the design-dependent coefficients of the design lattice stiffness matrix. The formulation leads to a convex objective function that does not require a solution to an additional adjoint system. Optimization-based cloaks are designed considering uniaxial tension in multiple directions and are shown to exhibit approximate elastostatic cloaking, not only when subjected to the boundary conditions they were designed for but also for uniaxial tension in directions not used in design and for shear loading.

Drift-Flux Modeling of Multiphase Flow in Wellbores

2003 ◽  
Author(s):  
H. Shi ◽  
J.A. Holmes ◽  
L.J. Durlofsky ◽  
K. Aziz ◽  
L.R. Diaz ◽  
...  
Keyword(s):  
Multiphase Flow ◽  
Drift Flux

A Hybrid Adjoint Network Model for Thermoacoustic Optimization

2021 ◽  
Author(s):  
Fellcitas Schäfer ◽  
Luca Magri ◽  
Wolfgang Polifke
Keyword(s):  
Network Model ◽  
Hybrid Approach ◽  
Adjoint System ◽  
Scattering Matrix ◽  
Adjoint Equations ◽  
Jump Conditions ◽  
Discrete Adjoint ◽  
Direct Scattering ◽  
Annular Combustor ◽  
Continuous Adjoint

Abstract A method is proposed that allows the computation of the continuous adjoint of a thermoacoustic network model based on the discretized direct equations. This hybrid approach exploits the self-adjoint character of the duct element, which allows all jump conditions to be derived from the direct scattering matrix. In this way, the need to derive the adjoint equations for every element of the network model is eliminated. This methodology combines the advantages of the discrete and continuous adjoint, as the accuracy of the continuous adjoint is achieved whilst maintaining the flexibility of the discrete adjoint. It is demonstrated how the obtained adjoint system may be utilized to optimize a thermoacoustic configuration by determining the optimal damper setting for an annular combustor.

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.

scholarly journals A Hydraulic Model for Multiphase Flow Based on the Drift Flux Model in Managed Pressure Drilling

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3930 ◽  
Author(s):  
Fang ◽  
Meng ◽  
Wei ◽  
Xu ◽  
Li
Keyword(s):  
Multiphase Flow ◽  
Oil And Gas ◽  
Splitting Method ◽  
Field Application ◽  
Effective Control ◽  
Two Phase ◽  
Drift Flux Model ◽  
Drift Flux ◽  
Managed Pressure Drilling ◽  
Flux Model

Managed pressure drilling (MPD) is a drilling technique used to address the narrow density window under complex geological environments. It has widespread applications in the exploration and exploitation of oil and gas, both onshore and offshore. In this study, to achieve effective control of the downhole pressure to ensure safety, a gas–liquid two-phase flow model based on the drift flux model is developed to describe the characteristics of transient multiphase flow in the wellbore. The advection upwind splitting method (AUSM) numerical scheme is used to assist with calculation and analysis, and the monotonic upwind scheme for conservation laws (MUSCLs) technique with second-order precision is adopted in combination with the Van Leer slope limiter to improve precision. Relevant data sourced from prior literature are used to validate the suggested model, the results of which reveal an excellent statistical consistency. Further, the influences of various parameters in a field application, including backpressure, density, and mass flow, are analyzed. Over the course of later-stage drilling, a combination of wellhead backpressure and displacement is recommended to exercise control.

Study and Verification of Continuous Adjoint System for Aerodynamic Optimization in Turbomachinery Cascades

2013 ◽  
Author(s):  
Pengfei Zhang ◽  
Haitao Li ◽  
Zhenping Feng
Keyword(s):  
Adjoint Method ◽  
Adjoint System ◽  
Inviscid Flow ◽  
Laminar Flows ◽  
Aerodynamic Optimization ◽  
Adjoint Systems ◽  
Inverse Designs ◽  
Turbine Design ◽  
2D And 3D ◽  
Continuous Adjoint

This paper is a further study of the authors’ previous work on the continuous adjoint method based on the variation in grid node coordinates and Jacobi Matrices of the flow fluxes. This method simplifies the derivation and expression of the adjoint system, and reduces the computation cost. In this paper, the differences between the presented and the traditional methods are analyzed in details by comparing the derivation processes and the adjoint systems. In order to demonstrate the reliability and accuracy of the adjoint system deduced by the authors, the presented method is applied to different optimal problems, which include two inverse designs and two shape optimizations in both 2D and 3D cascades. The inverse designs are implemented by giving the isentropic Mach number distributions along the blade wall for 2D inviscid flow and 3D laminar flow. The shape optimizations are implemented with the objective function of the entropy generation in flow passage for 2D and 3D laminar flows. In the 3D optimal case, this method is validated by supersonic turbine design case with and without mass flow rate constraint. The numerical results testify the accuracy of this adjoint method, which includes only the boundary integrals, and furthermore, the universality and portability of this adjoint system for inverse designs and shape optimizations are demonstrated.

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