Concurrent Blade Aerodynamic-Aero-elastic Design Optimization Using Adjoint Method

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
L. He ◽  
D. X. Wang
Keyword(s):  
Unsteady Flow ◽  
Solution Method ◽  
Stokes Equations ◽  
Adjoint System ◽  
Elastic Stability ◽  
Adjoint Equations ◽  
Navier Stokes ◽  
Simple Extension ◽  
Mean Flow ◽  
Elastic Design

Increasing aerothermal and aero-elastic performance requirements and constraints are closely linked in modern blading designs. There is thus a need for more concurrent interaction between the disciplines at earlier stages of a design process. Presented in this paper are the development, validation, and demonstration of the adjoint approach to concurrent blading aerodynamic and aero-elastic design optimizations. A nonlinear harmonic phase solution method is adopted to solve the unsteady Reynolds-averaged Navier–Stokes equations. The flow field response in terms of both the mean aerothermal performance and aero-elastic stability to a geometrical perturbation can be obtained by three “steadylike” flow solutions at three distinctive temporal phases. This unsteady flow solution method is computationally very efficient and provides a convenient and consistent base for formulating the corresponding adjoint equations. The adjoint system for the unsteady flow solver is solved effectively by a relatively simple extension of the method and techniques previously developed for a steady flow adjoint solver. As a result, the sensitivities of both the steady (time-mean) flow loss and the aerodynamic damping/forcing to detailed blade geometry changes can be very efficiently obtained by solving equivalently three steadylike adjoint equations. Several case studies are presented to illustrate the validity and effectiveness of this new concurrent approach.

Concurrent Aerodynamic-Aeromechanic Design Optimization for Turbomachinery Blades Using Adjoint Method

2009 ◽  
Author(s):  
D. X. Wang ◽  
L. He
Keyword(s):  
Unsteady Flow ◽  
Adjoint Method ◽  
Solution Method ◽  
Stokes Equations ◽  
Adjoint Equations ◽  
Navier Stokes ◽  
Simple Extension ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Flow Loss

Presented in this paper is the development and application of the adjoint method to efficient concurrent blading aerodynamic and aeromechanic design optimizations. A nonlinear harmonic phase solution method is adopted to solve the unsteady Reynolds Averaged Navier-Stokes equations for blading aerodynamic and aeromechanic performance evaluations. This unsteady flow solution method has a high computational efficiency and provides a concise and convenient basis for formulating the corresponding adjoint equations. The adjoint equations for the unsteady flow system are solved effectively by a relatively simple extension of the methods and techniques previously developed for a steady flow adjoint solver. As a result, the sensitivities of both the steady (time-mean) flow loss and the aerodynamic damping/forcing to detailed blade geometry changes can be very efficiently obtained by solving equivalently 3 steady adjoint equations. Two case studies are provided to illustrate the appropriate implementation and the effectiveness of these methodologies.

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.

A 3D Unsteady Flow Analysis in a Doubly Constricted Tube

2000 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
T. Yamaguchi ◽  
H. Liu ◽  
R. Himeno
Keyword(s):  
Pressure Drop ◽  
Unsteady Flow ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
In Series ◽  
3D Unsteady Flow

Abstract Unsteady flow dynamics in a doubly constricted vessel is analyzed by using a time accurate Finite Volume solution of three dimensional incompressible Navier-Stokes equations. Computational experiments are carried out for various values of Reynolds number in order to assess the criticality of multiple mild constrictions in series and also to bring out the subtle 3D features like vortex formation. Studies reveal that pressure drop across a series of mild constrictions can get physiologically critical. Further this pressure drop is found to be sensitive to the spacing between the constrictions and also to the oscillatory nature of the inflow profile.

scholarly journals Modeling the 3-d flow around a cylinder using the SAS hybrid model

2014 ◽  
Vol 16 (5) ◽  
pp. 901-918 ◽  
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Numerical Code ◽  
Navier Stokes ◽  
Computational Domain ◽  
Mean Flow ◽  
Unstable Flow ◽  
Vortex Size

<div> <p>Three-dimensional calculations were performed to simulate the flow around a cylindrical vegetation element using the Scale Adaptive Simulation (SAS) model; commonly, this is the first step of the modeling of the flow through multiple vegetation elements. SAS solves the Reynolds Averaged Navier-Stokes equations in stable flow regions, while in regions with unstable flow it goes unsteady producing a resolved turbulent spectrum after reducing eddy viscosity according to the locally resolved vortex size represented by the von Karman length scale. A finite volume numerical code was used for the spatial discretisation of the rectangular computational domain with stream-wise, cross-flow and vertical dimensions equal to 30D, 11D and 1D, respectively, which was resolved with unstructured grids. Calculations were compared with experiments and Large Eddy Simulations (LES). Predicted overall flow parameters and mean flow velocities exhibited a very satisfactory agreement with experiments and LES, while the agreement of predicted turbulent stresses was satisfactory. Calculations showed that SAS is an efficient and relatively fast turbulence modeling approach, especially in relevant practical problems, in which the very high accuracy that can be achieved by LES at the expense of large computational times is not required.</p> </div> <p>&nbsp;</p>

scholarly journals Asymptotically based self-similarity solution of the Navier–Stokes equations for a porous tube with a non-circular cross-section

2017 ◽  
Vol 826 ◽  
pp. 396-420 ◽  
Author(s):  
M. Bouyges ◽  
F. Chedevergne ◽  
G. Casalis ◽  
J. Majdalani
Keyword(s):  
Cross Section ◽  
Similarity Solution ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Internal Flow ◽  
Navier Stokes ◽  
Solid Rocket Motor ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Radial Deviation

This work introduces a similarity solution to the problem of a viscous, incompressible and rotational fluid in a right-cylindrical chamber with uniformly porous walls and a non-circular cross-section. The attendant idealization may be used to model the non-reactive internal flow field of a solid rocket motor with a star-shaped grain configuration. By mapping the radial domain to a circular pipe flow, the Navier–Stokes equations are converted to a fourth-order differential equation that is reminiscent of Berman’s classic expression. Then assuming a small radial deviation from a fixed chamber radius, asymptotic expansions of the three-component velocity and pressure fields are systematically pursued to the second order in the radial deviation amplitude. This enables us to derive a set of ordinary differential relations that can be readily solved for the mean flow variables. In the process of characterizing the ensuing flow motion, the axial, radial and tangential velocities are compared and shown to agree favourably with the simulation results of a finite-volume Navier–Stokes solver at different cross-flow Reynolds numbers, deviation amplitudes and circular wavenumbers.

Analytical and Semi-empirical Models of Tornadoes and Downbursts

2021 ◽  
Author(s):  
Djordje Romanic ◽  
Horia Hangan
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Empirical Models ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Simplifying Assumptions ◽  
The Individual ◽  
Semi Empirical

Analytical and semi-empirical models are inexpensive to run and can complement experimental and numerical simulations for risk analysis-related applications. Some models are developed by employing simplifying assumptions in the Navier-Stokes equations and searching for exact, but many times inviscid solutions occasionally complemented by boundary layer equations to take surface effects into account. Other use simple superposition of generic, canonical flows for which the individual solutions are known. These solutions are then ensembled together by empirical or semi-empirical fitting procedures. Few models address turbulent or fluctuating flow fields, and all models have a series of constants that are fitted against experiments or numerical simulations. This chapter presents the main models used to provide primarily mean flow solutions for tornadoes and downbursts. The models are organized based on the adopted solution techniques, with an emphasis on their assumptions and validity.

Low-Frequency Fluctuations In The Flow Over Confined Cylinder In A Narrow Rectangular Duct At Re = 3 750

2017 ◽  
Vol 12 (1) ◽  
pp. 43-49
Author(s):  
Egor Palkin ◽  
Rustam Mullyadzhanov
Keyword(s):  
Stokes Equations ◽  
Low Frequency ◽  
Horseshoe Vortex ◽  
Navier Stokes ◽  
Infinite Cylinder ◽  
Rectangular Duct ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Frequency Modulations ◽  
Bounding Surfaces

Flows between two closely spaced bounding surfaces are frequently appear in engineering applications and natural flows. In current paper the flow over a cylinder in a narrow rectangular duct was investigated by numerical computations of Navier-Stokes equations using Large eddy simulations (LES) at ReD = 3 750 based on cylinder diameter and the bulk velocity at inflow boundary. The influence of the bounding walls was demonstrated by comparing mean flow streamlines with the flow over an infinite cylinder at close Reynolds numbers. A comparison between the time-averaged velocity field in front and past the cylinder with experimental from the literature data showed good agreement although the characteristic horseshoe vortex structures are highly sensitive to Reynolds number and turbulence level at inflow boundary. Most energetic modes in recirculating region were revealed by spectral analysis. These low-frequency modulations were characterized by the pair of dominating vortices which are expected to have high influence on the heat transfer in near wake of the cylinder.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

scholarly journals Unsteady flow around a two-dimensional section of a vertical axis turbine for tidal stream energy conversion

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
Hyun Ju Jung ◽  
Ju Hyun Lee ◽  
Shin Hyung Rliee ◽  
Museok Song ◽  
Beom-Soo Hyun
Keyword(s):  
Unsteady Flow ◽  
Energy Conversion ◽  
Stokes Equations ◽  
Vertical Axis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Tidal Stream ◽  
Tidal Stream Energy ◽  
Vertical Axis Turbine

ABSTRACTThe two-dimensional unsteady flow around a vertical axis turbine for tidal stream energy' conversion was investigated using a computational fluid dynamics tool solving the Reynolds-Averaged Navier-Stokes equations. The geometry' of the turbine blade section was NACA653-01S airfoil. The computational analysis was done at several different angles of attack and the results were compared with the corresponding experimental data for validation and calibration. Simulations were then carried out for the two-dimensional cross section of a vertical axis turbine. The simulation results demonstrated the usefulness of the method for the typical unsteady flows around vertical axis turbines. The optimum turbine efficiency was achieved for carefully selected combinations of the number of blades and tip speed ratios.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

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