Finite state induced flow models. II - Three-dimensional rotor disk

1995 ◽  
Vol 32 (2) ◽  
pp. 323-333 ◽  
Author(s):  
David A. Peters ◽  
Cheng Jian He
Keyword(s):  
Three Dimensional ◽  
Flow Models ◽  
Finite State ◽  
Rotor Disk ◽  
Induced Flow

Finite state induced flow models. I - Two-dimensional thin airfoil

1995 ◽  
Vol 32 (2) ◽  
pp. 313-322 ◽  
Author(s):  
David A. Peters ◽  
Swaminathan Karunamoorthy ◽  
Wen-Ming Cao
Keyword(s):  
Two Dimensional ◽  
Flow Models ◽  
Thin Airfoil ◽  
Finite State ◽  
Induced Flow

Coupling of a State-Space Inflow to Nonlinear Blade Equations and Extraction of Generalized Aerodynamic Force Mode Shapes

1993 ◽  
Vol 46 (11S) ◽  
pp. S295-S304 ◽  
Author(s):  
Donizeti de Andrade ◽  
David A. Peters
Keyword(s):  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flow Distribution ◽  
Mode Shapes ◽  
State Equations ◽  
Force Mode ◽  
Rotor Disk ◽  
Induced Flow ◽  
Wake Model

The aeroelastic stability of helicopter rotors in hovering flight has been investigated by a set of generalized dynamic wake equations and hybrid equations of motion for an elastic blade cantilevered in bending and having a torsional root spring to model pitch-link flexibility. The generalized dynamic wake model employed is based on an induced flow distribution expanded in a set of harmonic and radial shape functions, including undetermined time dependent coefficients as aerodynamic states. The flow is described by a system of first-order, ordinary differential equations in time, for which the pressure distribution at the rotor disk is expressed as a summation of the discrete loadings on each blade, accounting simultaneously for a finite number of blades and overall rotor effects. The present methodology leads to a standard eigenanalysis for the associated dynamics, for which the partitioned coefficient matrices depend on the numerical solution of the blade equilibrium and inflow steady-state equations. Numerical results for a two-bladed, stiff-inplane hingeless rotor with torsionally soft blades show the importance of unsteady, three-dimensional aerodynamics in predicting associated generalized aerodynamic force mode shapes.

scholarly journals A Numerical Study of a Rotor Induced Flow Based on a Finite-State Dynamic Wake Model.

2021 ◽  
Vol 22 (2) ◽  
pp. 307-324
Author(s):  
L. G. A. Ferreira ◽  
C. C. Pagani Júnior ◽  
E. M. Gennaro ◽  
C. De Marqui Junior
Keyword(s):  
Numerical Study ◽  
Mathematical Formulation ◽  
Problem Formulation ◽  
Flow Induced Vibration ◽  
Finite State ◽  
Practical Engineering ◽  
Rotor Disk ◽  
Induced Flow ◽  
Wake Model ◽  
Rotary Wings

A Helicopter rotor undergoes unsteady aerodynamic loads ruled by the aeroelastic coupling between the elastic blades and the dynamic wake induced by rotary wings. Modeling the dynamic interaction between the structural and aerodynamic fields is a key point to understand aeroelastic phenomena associated with rotor stability, flow induced vibration and noise generation, among others. In this study, we address the Generalized Dynamic Wake Model, which describes the inflow velocity field at the rotor disk as a superposition  of a finite number of induced flow states. It is a mature model that has been validated based on experimental data and numerically investigated from an eigenvalue problem formulation, whose eigenvalues and eigenvectors provide a deeper insight on the dynamic wake behavior. The paper extends the results presented in the literature to date in order to support physical interpretation of inflow states drawn from the finite-state wake model for flight conditions varying from hover to edgewise flight. The discussion of the wake model mathematical formulation is also oriented towards practical engineering applications to fill a gap in the literature.

scholarly journals Three-dimensional hydrostratigraphy and groundwater flow models in complex Quaternary deposits and weathered/fractured bedrock: evaluating increasing model complexity

2021 ◽  
Author(s):  
Susanne Charlotta Åberg ◽  
Annika Katarina Åberg ◽  
Kirsti Korkka-Niemi
Keyword(s):  
Groundwater Flow ◽  
Three Dimensional ◽  
Model Complexity ◽  
Quaternary Sediments ◽  
Fractured Bedrock ◽  
Flow Models ◽  
Flow Modelling ◽  
Crystalline Bedrock ◽  
Discharge Patterns ◽  
Geological Units

AbstractGreater complexity in three-dimensional (3D) model structures yields more plausible groundwater recharge/discharge patterns, especially in groundwater/surface-water interactions. The construction of a 3D hydrostratigraphic model prior to flow modelling is beneficial when the hydraulic conductivity of geological units varies considerably. A workflow for 3D hydrostratigraphic modelling with Leapfrog Geo and flow modelling with MODFLOW-NWT was developed. It was used to evaluate how the modelling results for groundwater flow and recharge/discharge patterns differ when using simple or more complex hydrostratigraphic models. The workflow was applied to a study site consisting of complex Quaternary sediments underlain by fractured and weathered crystalline bedrock. Increasing the hydrostratigraphic detail appeared to improve the fit between the observed and simulated water table, and created more plausible groundwater flow patterns. Interlayered zones of low and high conductivity disperse the recharge/discharge patterns, increasing the vertical flow component. Groundwater flow was predominantly horizontal in models in which Quaternary sediments and bedrock were simplified as one layer per unit. It appears to be important to define the interlayered low-conductivity units, which can limit groundwater infiltration and also affect groundwater discharge patterns. Explicit modelling with Leapfrog Geo was found to be effective but time-consuming in the generation of scattered and thin-layered strata.

Finite‐State Induced‐Flow Model for Rotors in Hover and Forward Flight

1989 ◽  
Vol 34 (4) ◽  
pp. 5-17 ◽  
Author(s):  
David A. Peters ◽  
David Doug Boyd ◽  
Cheng Jian He
Keyword(s):  
Flow Model ◽  
Forward Flight ◽  
Finite State ◽  
Induced Flow

Technical Note: Finite State Induced Flow Model in Vortex Ring State

2000 ◽  
Vol 45 (4) ◽  
pp. 318-320 ◽  
Author(s):  
Chengjian He ◽  
C. S. Lee ◽  
Weibin Chen
Keyword(s):  
Vortex Ring ◽  
Flow Model ◽  
Technical Note ◽  
Finite State ◽  
Induced Flow ◽  
Vortex Ring State

scholarly journals Numerical and Experimental Analyses of Three- Dimensional Unsteady Flow around a Micro-Pillar Subjected to Rotational Vibration

Micromachines ◽  
2018 ◽  
Vol 9 (12) ◽  
pp. 668 ◽  
Author(s):  
Kanji Kaneko ◽  
Takayuki Osawa ◽  
Yukinori Kametani ◽  
Takeshi Hayakawa ◽  
Yosuke Hasegawa ◽  
...  
Keyword(s):  
Flow Field ◽  
Moving Boundary ◽  
Three Dimensional ◽  
Steady Streaming ◽  
Micro Piv ◽  
Piv Measurement ◽  
Image Velocimetry ◽  
Measurement Tools ◽  
Rotational Vibration ◽  
Induced Flow

The steady streaming (SS) phenomenon is gaining increased attention in the microfluidics community, because it can generate net mass flow from zero-mean vibration. We developed numerical simulation and experimental measurement tools to analyze this vibration-induced flow, which has been challenging due to its unsteady nature. The validity of these analysis methods is confirmed by comparing the three-dimensional (3D) flow field and the resulting particle trajectories induced around a cylindrical micro-pillar under circular vibration. In the numerical modeling, we directly solved the flow in the Lagrangian frame so that the substrate with a micro-pillar becomes stationary, and the results were converted to a stationary Eulerian frame to compare with the experimental results. The present approach enables us to avoid the introduction of a moving boundary or infinitesimal perturbation approximation. The flow field obtained by the micron-resolution particle image velocimetry (micro-PIV) measurement supported the three-dimensionality observed in the numerical results, which could be important for controlling the mass transport and manipulating particulate objects in microfluidic systems.

Analysis of separable Markov-modulated rate models for information-handling systems

1991 ◽  
Vol 23 (01) ◽  
pp. 105-139 ◽  
Author(s):  
Thomas E. Stern ◽  
Anwar I. Elwalid
Keyword(s):  
Solution Technique ◽  
Service Rate ◽  
Processing Unit ◽  
Equilibrium Equations ◽  
Flow Models ◽  
Separability Property ◽  
Finite State ◽  
Service Rates ◽  
Rate Processes ◽  
Markov Modulated

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP). In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.

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