Employing the Time-Domain Unsteady Discrete Adjoint Method for Shape Optimization of Three-Dimensional Multirow Turbomachinery Configurations

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Georgios Ntanakas ◽  
Marcus Meyer ◽  
Kyriakos C. Giannakoglou
Keyword(s):  
Time Domain ◽  
Adjoint Method ◽  
Transient Flow ◽  
Three Dimensional ◽  
Adjoint Equations ◽  
Objective Functions ◽  
Discrete Adjoint ◽  
Design Variables ◽  
Frequency Domain Methods ◽  
The Time Domain

In turbomachinery, the steady adjoint method has been successfully used for the computation of derivatives of various objective functions with respect to design variables in gradient-based optimization. However, the continuous advances in computing power and the accuracy limitations of the steady-state assumption lead toward the transition to unsteady computational fluid dynamics (CFD) computations in the industrial design process. Previous work on unsteady adjoint for turbomachinery applications almost exclusively rely upon frequency-domain methods, for both the flow and adjoint equations. In contrast, in this paper, the development the discrete adjoint to the unsteady Reynolds-averaged Navier–Stokes (URANS) solver for three-dimensional (3D) multirow applications, in the time-domain, is presented. The adjoint equations are derived along with the adjoint to the five-stage Runge–Kutta scheme. Communication between adjacent rows is achieved by the adjoint sliding interface method. An optimization workflow that uses unsteady flow and adjoint solvers is presented and tested in two cases, with objective functions accounting for the transient flow in a turbine vane and the periodic flow in a compressor three-row setup.

scholarly journals Unsteady discrete adjoint method formulated in the time - domain for shape optimization in turbomachinery

2018 ◽  
Author(s):  
Γεώργιος Ντανάκας
Keyword(s):  
Shape Optimization ◽  
Time Domain ◽  
Adjoint Method ◽  
Navier Stokes ◽  
Framework Programme ◽  
Discrete Adjoint ◽  
Seventh Framework Programme ◽  
Discrete Adjoint Method ◽  
Reynolds Averaged Navier Stokes ◽  
The Time Domain

Η διδακτορική διατριβή πραγματεύεται τη μαθηματική διατύπωση, επίλυση, προγραμματισμό και πιστοποίηση της μη-μόνιμης διακριτής συζυγούς μεθόδου με διατύπωση στο πεδίο του χρόνου για τον υπολογισμό πρώτης τάξης παραγώγων αντικειμενικών συναρτήσεων ως προς τις μεταβλητές σχεδιασμού σε προβλήματα αεροδυναμικής και τη χρήση τους σε αλγορίθμους βελτιστοποίησης. Η μέθοδος εφαρμόζεται για την υπο περιορισμούς βελτιστοποίηση σχήματος τριδιάστατων, πολυβάθμιων διατάξεων στροβιλομηχανών σε μεταβατικές και περιοδικές ροές.Οι μη-μόνιμες συζυγείς εξισώσεις διατυπώνονται για αντικειμενική συνάρτηση που έχει τη μορφή ολοκληρώματος σε επιλεγμένο χρονικό διάστημα. Για την επίλυση των μη-μόνιμων εξισώσεων χρησιμοποιείται η τεχνική του διπλού χρονικού βήματος καθώς και ένα επαναληπτικό σχήμα, το οποίο είναι συζυγές της μεθόδου Runge-Kutta 5 βηµάτων, η οποία επιστρατεύεται για τη σύγκλιση των εξισώσεων ροής, και προκύπτει από διαφόριση "με το χέρι". Το σχήμα διατυπώνεται έτσι ώστε να διασφαλίσει σύγκλιση ίδιου ρυθμού με αυτόν του μη-μόνιμου Reynolds-Averaged Navier-Stokes επιλύτη.Για τον υπολογισμό επιλεγμένων διαφορικών όρων των συζυγών εξισώσεων χρησιμοποιείται η τεχνική της Αυτόματης Διαφόρισης (ΑΔ). Η χρήση της περιορίζεται σε προγραμματιστικές διαδικασίες "χαμηλού επιπέδου" και συνδυάζεται με τη διαφόριση "με το χέρι" με στόχο την υψηλή απόδοση του συζυγούς επιλύτη.Για τη σύζευξη διαδοχικών πτερυγώσεων χρησιμοποιείται η μέθοδος της διεπιφάνειας ολίσθησης στον συζυγή επιλύτη, αντικαθιστώντας τη μέθοδο της διεπιφάνειας ανάμιξης που εμφανίζεται στους μόνιμους υπολογισμούς. Ως αφετηρία λαμβάνεται η εφαρμογή της τεχνικής στο μη-μόνιμο επιλύτη ροής όπου τα πλέγματα διαδοχικών πτερυγώσεων έχουν επικάλυψη ενός κελιού μεταξύ τους. Για να διατηρηθεί η αντίστροφη ροή πληροφορίας στο συζυγή επιλύτη, η ΑΔ συνδυάζεται με προγραμματισμό "με το χέρι" για την υλοποίηση της μεθόδου.Ο επιλύτης χρησιμοποιεί χώρο σε SSD δίσκους αντί της μνήμης RAM για την αποθήκευση και την ανάκτηση των πεδίων ροής ανά χρονικό βήμα κατά την εκτέλεσή του. Έτσι, αποφεύγονται οι περιορισμοί της κατ' αναλογία μικρής σε χωρητικότητα μνήμης RAM χωρίς σημαντική χρονική επιβάρυνση. Η επιπλέον μείωση του χρόνου εκτέλεσης και του απαιτούμενου αποθηκευτικού χώρου πραγματοποιείται με την εφαρμογή της μεθόδου χρονικής αραίωσης.Οι παράγωγοι υπολογίζονται με τη συζυγή μέθοδο με στόχο τη χρήση τους σε κύκλο βελτιστοποίησης. Στην περίπτωση ύπαρξης περιορισμών ισότητας, η συνιστώσα της παραγώγου της αντικειμενικής συνάρτησης ως προς τις παραγώγους των περιορισμών υπολογίζεται και χρησιμοποιείται με τη μέθοδο της καθόδου κατά την προβεβλημένη παράγωγο για την ανανέωση των μεταβλητών σχεδιασμού και, άρα, της γεωμετρίας. Αν δεν υπάρχουν περιορισμοί, χρησιμοποιείται η μέθοδος της απότομης καθόδου.Το αναπτυχθέν λογισμικό εφαρμόζεται για τη βελτιστοποίηση σχήματος πτερυγίων τριδιάστατων, πολυβάθμιων διατάξεων στροβιλομηχανών για πρώτη φορά στη βιβλιογραφία. Οι περιπτώσεις εφαρμογής περιλαμβάνουν μία σταθερή πτερύγωση στροβίλου (μεταβατική ροή), μια βαθμίθα στροβίλου (περιοδική ροή) και μια διάταξη συμπιεστή 1,5 βαθμίδας (περιοδική ροή). Οι υπολογιζόμενες παράγωγοι μέσω της συζυγούς μεθόδου πιστοποιούνται συγκρίνοντας τις με τις παραγώγους που προκύπτουν από τη χρήση πεπερασμένων διαφορών και, στη συνέχεια, χρησιμοποιούνται σε σενάρια βελτιστοποίησης με και χωρίς περιορισμούς.Η διδακτορική διατριβή εκπονήθηκε στο πλαίσιο του ITN AboutFlow το οποίο χρηματοδοτήθηκε από το Seventh Framework Programme της Ευρωπαϊκής Ένωσης με τη Συμφωνία Επιχορήγησης Νο. 317006.

scholarly journals The time domain numerical method of three-dimensional conductors including radiation with lumped parameter circuit

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Souma Jinno ◽  
Shuji Kitora ◽  
Hiroshi Toki ◽  
Masayuki Abe
Keyword(s):  
Numerical Method ◽  
Time Domain ◽  
Maxwell Equations ◽  
Three Dimensional ◽  
New Formalism ◽  
Vector Potentials ◽  
Lumped Parameter ◽  
Radiation Theory ◽  
Stable Solutions ◽  
The Time Domain

AbstractWe formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions for transmission and radiation phenomena in conductors. We provide a formalism to connect the conductors to any passive lumped-parameter circuits. We show one example of numerical calculations, demonstrating that the new formalism provides stable solutions to the transmission and radiation phenomena.

scholarly journals Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Chen Xia ◽  
Chengzhi Qi ◽  
Xiaozhao Li
Keyword(s):  
Finite Element ◽  
Seismic Response ◽  
Time Domain ◽  
Seismic Waves ◽  
Three Dimensional ◽  
Seismic Loads ◽  
Element Analysis ◽  
Artificial Boundaries ◽  
The Time Domain ◽  
Transmitting Boundaries

Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation input method. The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil.

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

Numerical Simulation on Mooring Performance of LNG-FPSO System in Realistic Seas

2005 ◽  
Author(s):  
Yoshiyuki Inoue ◽  
Md. Kamruzzaman
Keyword(s):  
Time Domain ◽  
Oil And Gas ◽  
Three Dimensional ◽  
Time Domain Analysis ◽  
Analysis Tool ◽  
Motion Response ◽  
Non Linear ◽  
Floating System ◽  
Exciting Forces ◽  
The Time Domain

The LNG-FPSO concept is receiving much attention in recent years, due to its active usage to exploit oil and gas resources. The FPSO offloads LNG to an LNG carrier that is located close to the FPSO, and during this transfer process two large vessels are in close proximity to each other for daylong periods of time. Due to the presence of neighboring vessel, the motion response of both the vessels will be affected significantly. Hydrodynamic interactions related to wave effects may result in unfavorable responses or the risk of collisions in a multi-body floating system. Not only the motion behavior but also the second order drift forces are influenced by the neighboring structures due to interactions of the waves among the structures. A study is made on the time domain analysis to assess the behavior and the operational capability of the FPSO system moored in the sea having an LNG carrier alongside under environmental conditions such as waves, wind and currents. This paper presents an analysis tool to predict the dynamic motion response and non-linear connecting and mooring forces on a parallel-connected LNG-FPSO system due to non-linear exciting forces of wave, wind and current. Simulation for the mooring performance is also investigated. The three-dimensional source-sink technique has been applied to obtain the radiation forces and the transfer function of wave exciting forces on floating multi-bodies. The hydrodynamic interaction effect between the FPSO and the LNG carrier is included to calculate the hydrodynamic forces. For the simulation of a random sea and also for the generation of time depended wind velocity, a fully probabilistic simulation technique has been applied. Wind and current loads are estimated according to OCIMF. The effects of variations in wave, wind and current loads and direction on the slowly varying oscillations of the LNG and FPSO are also investigated in this paper. Finally, some conclusions are drawn based on the numerical results obtained from the present time domain simulations.

The aerodynamic optimisation of a low-Reynolds paper plane with adjoint method

2020 ◽  
pp. 1-15
Author(s):  
Y. Zhang ◽  
X. Zhang ◽  
G. Chen
Keyword(s):  
Adjoint Method ◽  
Low Cost ◽  
Aerodynamic Performance ◽  
Discrete Adjoint ◽  
Design Variables ◽  
Limited Variation ◽  
Aerial Vehicle ◽  
Paper Plane ◽  
Drag Ratio ◽  
Lift To Drag Ratio

ABSTRACT The aerodynamic performance of a deployable and low-cost unmanned aerial vehicle (UAV) is investigated and improved in present work. The parameters of configuration, such as airfoil and winglet, are determined via an optimising process based on a discrete adjoint method. The optimised target is locked on an increasing lift-to-drag ratio with a limited variation of pitching moments. The separation that will lead to a stall is delayed after optimisation. Up to 128 design variables are used by the optimised solver to give enough flexibility of the geometrical transformation. As much as 20% enhancement of lift-to-drag ratio is gained at the cruise angle-of-attack, that is, a significant improvement in the lift-to-drag ratio adhering to the preferred configuration is obtained with increasing lift and decreasing drag coefficients, essentially entailing an improved aerodynamic performance.

scholarly journals Scattering of gravity waves by a periodically structured ridge of finite extent

2019 ◽  
Vol 871 ◽  
pp. 350-376 ◽  
Author(s):  
Agnès Maurel ◽  
Kim Pham ◽  
Jean-Jacques Marigo
Keyword(s):  
Gravity Waves ◽  
Time Domain ◽  
Water Waves ◽  
Classical Result ◽  
Water Channel ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
Homogenized Model ◽  
The Time Domain ◽  
Finite Extent

We study the propagation of water waves over a ridge structured at the subwavelength scale using homogenization techniques able to account for its finite extent. The calculations are conducted in the time domain considering the full three-dimensional problem to capture the effects of the evanescent field in the water channel over the structured ridge and at its boundaries. This provides an effective two-dimensional wave equation which is a classical result but also non-intuitive transmission conditions between the region of the ridge and the surrounding regions of constant immersion depth. Numerical results provide evidence that the scattering properties of a structured ridge can be strongly influenced by the evanescent fields, a fact which is accurately captured by the homogenized model.

Dip moveout in the Radon domain

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 278-288
Author(s):  
Chengshu Wang
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Fourier Method ◽  
Real Data ◽  
Processing Technique ◽  
The Common ◽  
The Time Domain

I consider a new dip‐moveout (DMO) processing technique in the Radon domain called Radon DMO. The Radon DMO operator directly maps data from the NMO-corrected time domain to the DMO wavefield in the Radon domain. The method is built upon a process that transforms a single NMO-corrected trace into multiple traces spread along hyperbolas in the Radon domain. These hyperbolas are a linear Radon map of the DMO ellipses in the time domain. In this paper, I introduce the amplitude‐preserving Radon DMO and compare some examples of Radon DMO and Fourier DMO for both synthetic and real data. I also show the better frequency preservation properties of the Radon DMO method. Three‐dimensional data are often irregularly sampled with respect to fold, azimuth, and offset. Population deficiencies are exaggerated in the common‐offset domain. Radon DMO does not require that input traces belong to one common‐offset bin as does the Fourier method. Input traces can be organized from multiple offset bins grouping to perform Radon DMO, which is well used in 3-D surveys. Some synthetic and real data examples show these properties.

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