On the Influence of Inflow Model Selection for Time-Domain Tiltrotor Aeroelastic Analysis

Author(s):  
Ethan Corle ◽  
Matthew Floros ◽  
Sven Schmitz

The methods of using the viscous vortex particle method, dynamic inflow, and uniform inflow to conduct whirl-flutter stability analysis are evaluated on a four-bladed, soft-inplane tiltrotor model using the Rotorcraft Comprehensive Analysis System. For the first time, coupled transient simulations between comprehensive analysis and a vortex particle method inflow model are used to predict whirl-flutter stability. Resolution studies are performed for both spatial and temporal resolution in the transient solution. Stability in transient analysis is noted to be influenced by both. As the particle resolution is refined, a reduction in simulation time-step size must also be performed. An azimuthal time step size of 0.3 deg is used to consider a range of particle resolutions to understand the influence on whirl-flutter stability predictions. Comparisons are made between uniform inflow, dynamic inflow, and the vortex particle method with respect to prediction capabilities when compared to wing beam-bending frequency and damping experimental data. Challenges in assessing the most accurate inflow model are noted due to uncertainty in experimental data; however, a consistent trend of increasing damping with additional levels of fidelity in the inflow model is observed. Excellent correlation is observed between the dynamic inflow predictions and the vortex particle method predictions in which the wing is not part of the inflow model, indicating that the dynamic inflow model is adequate for capturing damping due to the induced velocity on the rotor disk. Additional damping is noted in the full vortex particle method model, with the wing included, which is attributed to either an interactional aerodynamic effect between the rotor and the wing or a more accurate representation of the unsteady loading on the wing due to induced velocities.

Author(s):  
Marius C. Banica ◽  
Peter Limacher ◽  
Heinz-Jürgen Feld

In large modern turbochargers, compressors often constitute the main source of noise, with a frequency spectrum typically dominated by tonal noise at the blade passing frequency (BPF) and its harmonics. In transonic operation, inflow BPF noise is mainly generated by rotor locked shock fronts. These and the resulting acoustic fields can be predicted numerically with reasonable accuracy. Outflow noise, while also dominated by BPF tones, is linked to more complex source mechanisms. Its modal structure and the relationships between sources and modal sound pressure levels (SPL) are less well understood. Perhaps this is linked to the intrinsically non-axisymmetric geometries, which results in the need for full stage simulations if high accuracy is of paramount importance. In order to shed some light on outflow noise generation, a transient simulation of a 360° model of a radial compressor stage, including a vaned diffuser and a volute, was carried out using state-of-the-art CFD. Additionally, experimental data was gathered at a multitude of data points downstream of the volute exit for post processing and modal analysis. The sources and the propagation were calculated directly. Optimized values for tempo-spatial acoustic wave resolution and buffer layer design were chosen, based on extensive studies on simplified models. Two grid refinement levels were used to check grid convergence and time step size independence of the results was ensured. Numerical and experimental data match within 1% for total pressure ratio, volume flow and exit total temperature for the studied operating point. Both show the same modal content at the 1st BPF and indicate the presence of the same single dominating mode. The numerical results underpredict overall sound power levels (PWL) at the 1st BPF by 6.6dB. This difference is expected to decrease with further grid refinement and improved accounting for numerical damping. At the 2nd BPF, the experimental data show a significant broadening of the modal content with homogeneous modal PWL distributions. The multitude of modes leads to the generation of complex interference patterns, which shows that single-point acoustic measurements are often inadequate for component noise qualification and should be substituted by modal techniques. The dominating dipole sound sources are found in narrow areas around the vane leading edges and the rotor blade trailing edges. Because of the non-axisymmetric geometry, vane dipole source strengths become a function of circumferential position. The unsteady shedding of vortices from the vane suction surfaces is identified as a further possible source mechanism. However, the contributions of structural vibrations and mode scattering due to small manufacturing imperfections remain unclear.


2021 ◽  
Vol 11 (7) ◽  
pp. 3149
Author(s):  
Wenguo Zhu ◽  
Marco Morandini ◽  
Shu Li

A panel/vortex particle hybrid method is coupled with a computational structure dynamics code to predict helicopter rotor loads. The rotor blade surfaces and near wakes are modeled by the panel method, while the far wake is modeled by resorting to the vortex particles method. A fast summation method is introduced to accelerate the evolution of particle–particle-induced velocity and its derivative as well as panel–particle interactions. The developed vortex particle method code is coupled with the multibody code MBDyn to predict the rotor airloads. Numerical validations are carried, out and the results are compared with the experiments and simulation results in the literature.


2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.


Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.


2021 ◽  
Author(s):  
Seyhan Emre Gorucu ◽  
Vijay Shrivastava ◽  
Long X. Nghiem

Abstract An existing equation-of-state compositional simulator is extended to include proppant transport. The simulator determines the final location of the proppant after fracture closure, which allows the computation of the permeability along the hydraulic fracture. The simulation then continues until the end of the production. During hydraulic fracturing, proppant is injected in the reservoir along with water and additives like polymers. Hydraulic fracture gets created due to change in stress caused by the high injection pressure. Once the fracture opens, the bulk slurry moves along the hydraulic fracture. Proppant moves at a different speed than the bulk slurry and sinks down by gravity. While the proppant flows along the fracture, some of the slurry leaks off into the matrix. As the fracture closes after injection stops, the proppant becomes immobile. The immobilized proppant prevents the fracture from closing and thus keeps the permeability of the fracture high. All the above phenomena are modelled effectively in this new implementation. Coupled geomechanics simulation is used to model opening and closure of the fracture following geomechanics criteria. Proppant retardation, gravitational settling and fluid leak-off are modeled with the appropriate equations. The propped fracture permeability is a function of the concentration of immobilized proppant. The developed proppant simulation feature is computationally stable and efficient. The time step size during the settling adapts to the settling velocity of the proppants. It is found that the final location of the proppants is highly dependent on its volumetric concentration and slurry viscosity due to retardation and settling effects. As the location and the concentration of the proppants determine the final fracture permeability, the additional feature is expected to correctly identify the stimulated region. In this paper, the theory and the model formulation are presented along with a few key examples. The simulation can be used to design and optimize the amount of proppant and additives, injection timing, pressure, and well parameters required for successful hydraulic fracturing.


2014 ◽  
Author(s):  
Γεώργιος Παπαδάκης

Σκοπός της διδακτορικής διατριβής ήταν η ανάπτυξη μιας νέας υβριδικής μεθο-δολογίας CFD για την επίλυση εξωτερικών αεροδυναμικών ροών. Η ιδέα πίσω απότην εργασία ήταν η ανάγκη για προσομοιώσεις σύνθετων προβλημάτων στα οποία κυ-ριαρχούν ισχυρές δομές στροβιλότητας και που υπάρχουν σώματα τα οποία κινούνταιανεξάρτητα μεταξύ τους. Για το λόγο αυτό αναπτύχθηκαν δύο υπολογιστικά εργαλείατα οποία συνενώθηκαν σε ένα υβριδικό επιλυτή. Πιο συγκεκριμένα:Ο Eulerian CFD επιλυτής (MaPFlow): Αναπτύχθηκε ένας συμπιεστός URANS επι-λυτής που λύνει πάνω σε μή δομημένα πλέγματα. Ο συγκεκριμένος επιλυτής είναιεφοδιασμένος με προσταθεροποιητή για χαμηλούς αριθμούς Mach για την προσομοί-ωση ασυμπίεστων ροών. Η μοντελοποίηση της τύρβης γίνεται είτε με το μοντέλομίας εξίσωσης του Spalart-Almaras είτε με το μοντέλο δύο εξισώσεων k-! SST τουMenter. Ακόμη, ο επιλυτής μπορεί να χειριστεί κινούμενα ή παραμορφώσιμα πλέγματαενώ έχει παραλληλοποιηθεί με τη χρήση του πρωτοκόλλου MPI.O Lagrangian επιλυτής: Διατυπώθηκε και αναπτύχθηκε ένας συμπιεστός Lagrangianεπιλυτής που χρησιμοποιεί στοιχεία στροβιλότητας. Η συγκεκριμένη διατύπωση χρη-σιμοποιεί στοιχεία ρευστού που μεταφέρουν μάζα, μεταβολή του όγκου, στροβι-λότητα, ενέργεια και όγκο για να μπορεί να διαχειριστεί συμπιεστές ροές. Για ναμειωθεί το υπολογιστικό κόστος του επιλυτή χρησιμοποιήθηκε η μέθοδος ParticleMesh (PM) η οποία παραλληλοποιήθηκε χρησιμοποιώντας τον αλγόριθμο του James-Lackner.Σύυζευξη των δύο επιλυτών σε ένα υπολογιστικό εργαλειό (HoPFlow): Υλοποιήθηκεισχυρή σύζευξη των Eulerian και Lagrangian επιλυτών σε μία υβριδική μεθοδολογία.Η σύζευξη έγινε με τέτοιο τρόπο ώστε να διασφαλίζει συνέχεια και συνέπεια τηςλύσης ανάμεσα στους δύο επιλυτές.Τα αποτελέσματα που παρουσιάζονται στην παρούσα εργασία έχουν σκοπό τηνπιστοποίηση των εργαλείων που υλοποιήθηκαν. Αρχικά, παρουσιάζονται αποτελέ-σματα που αφορούν την πιστοποίηση του Εulerian URANS επιλυτή. Η πιστοποίησηπεριλαμβάνει συγκρίσεις με πειραματικά αλλά και υπολογιστικά δεδομένα σε διάφο-ρες διδιάστατες και τριδιάστατες ροές. Στη συνέχεια, ακολουθεί η πιστοποίηση τουυβριδικού επιλυτή όπου γίνεται σύγκριση με τα αντίστοιχα Eulerian αποτελέσματααλλά και με πειραματικά δεδομένα.Οι περιπτώσεις πιστοποίησης που εξετάστηκαν περιλαμβάνουν διδιάστατες ροέςγύρω από σταθερές και κινούμενες αεροτομές σε πληθώρα αριθμών Reynolds καιMach. Οι τρισδιάστατες περιπτώσεις που παρουσιάζονται αφορούν ροές γύρω απόσταθερά και περιστρεφόμενα πτερύγια (Δρομείς Ανεμογεννητριών και Ελικοπτέρου).Η χρήση των υπολογιστικών εργαλείων σε πληθώρα περιπτώσεων έδειξαν ότι καιο Εulerian CFD επιλυτής (MaPFlow) όπως και ο υβριδικός επιλυτής (HoPFlow)παράγουν ικανοποιητικά αποτελέσματα. Συγκεκριμένα, ο υβριδικός επιλυτής έχει λι-γότερη διάχυση από τον Eulerian και για αυτό στις περιπτώσεις όπου κυριαρχούνισχυροί στρόβιλοι (όπως ο δρομέας ελικοπτέρου σε αιώρηση) τα αποτελέσματα πουπαράγονται είναι καλύτερα. Θα πρέπει να τονιστεί ότι οι περισσότερες περιπτώσειςπου εξετάστηκαν, είναι απλούστερες από αυτές για τις οποίες αναπτύχθηκε η υβρι-δική μέθοδος. Παρόλα αυτά, η επιλογή τους έγινε με σκοπό την πιστοποίηση τηςκαινούργιας μεθόδου που προηγείται της χρήσης της σε πιο σύνθετες ροές.


Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1652
Author(s):  
Dong-Sin Shih ◽  
Gour-Tsyh Yeh

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.


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