Perspective: Numerical Simulations of Wakes and Blade-Vortex Interaction

1994 ◽  
Vol 116 (1) ◽  
pp. 5-21 ◽  
Author(s):  
Dean T. Mook ◽  
Bonian Dong
Keyword(s):  
Incompressible Flows ◽  
Lower Surface ◽  
The Body ◽  
Spatial Density ◽  
Inviscid Fluid ◽  
Time Step ◽  
Trailing Edge ◽  
Blade Vortex Interaction ◽  
Attached Flow ◽  
Viscous Core

A method for simulating incompressible flows past airfoils and their wakes is described. Vorticity panels are used to represent the body, and vortex blobs (vortex points with their singularities removed) are used to represent the wake. The procedure can be applied to the simulation of completely attached flow past an oscillating airfoil. The rate at which vorticity is shed from the trailing edge of the airfoil into the wake is determined by simultaneously requiring the pressure along the upper and lower surface streamlines to approach the same value at the trailing edge and the circulation around both the airfoil and its wake to remain constant. The motion of the airfoil is discretized, and a vortex is shed from the trailing edge at each time step. The vortices are convected at the local velocity of fluid particles, a procedure that renders the pressure continuous in an inviscid fluid. When the vortices in the wake begin to separate they are split into more vortices, and when they begin to collect they are combined. The numerical simulation reveals that the wake, which is originally smooth, eventually coils, or wraps, around itself, primarily under the influence of the velocity it induces on itself, and forms regions of relatively concentrated vorticity. Although discrete vortices are used to represent the wake, the spatial density of the vortices is so high that the computed velocity profiles across a typical region of concentrated vorticity are quite smooth. Although the computed wake evolves in an entirely inviscid model of the flowfield, these profiles appear to have a viscous core. The computed spacing between the regions of concentrated vorticity in the wake and the circulations around them are in good agreement with the experimental results. As an application, a simulation of the interaction between vorticity in the oncoming stream and a stationary airfoil is also discussed.

Unsteady Rotor Dynamics in Cascade

1993 ◽  
Vol 115 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Y. T. Lee ◽  
T. W. Bein ◽  
J. Feng ◽  
C. L. Merkle
Keyword(s):  
Analytic Solution ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Vortex Motion ◽  
Potential Effect ◽  
Time Step ◽  
Trailing Edge ◽  
Turbine Stator ◽  
Blade Row ◽  
Constant Source

A time-accurate potential-flow calculation method has been developed for unsteady incompressible flows through two-dimensional multi-blade-row linear cascades. The method represents the boundary surfaces by distributing piecewise linear-vortex and constant-source singularities on discrete panels. A local coordinate is assigned to each independently moving object. Blade-shed vorticity is traced at each time step. The unsteady Kutta condition applied is nonlinear and requires zero blade trailing-edge loading at each time. Its influence on the solutions depends on the blade trailing-edge shapes. Steady biplane and cascade solutions are presented and compared to exact solutions and experimental data. Unsteady solutions are validated with the Wagner function for an airfoil moving impulsively from rest and the Theodorsen function for an oscillating airfoil. The shed vortex motion and its interaction with blades are calculated and compared to an analytic solution. For a multi-blade-row cascade, the potential effect between blade rows is predicted using steady and quasi-unsteady calculations. The accuracy of the predictions is demonstrated using experimental results for a one-stage turbine stator-rotor.

scholarly journals Unsteady Rotor Dynamics in Cascade

1991 ◽  
Author(s):  
Yu-Tai Lee ◽  
Thomas W. Bein ◽  
Jin Zhang Feng ◽  
Charles L. Merkle
Keyword(s):  
Analytic Solution ◽  
Incompressible Flows ◽  
Piecewise Linear ◽  
Vortex Motion ◽  
Potential Effect ◽  
Time Step ◽  
Trailing Edge ◽  
Turbine Stator ◽  
Blade Row ◽  
Constant Source

A time-accurate potential-flow calculation method has been developed for unsteady incompressible flows through two-dimensional multi-blade-row linear cascades. The method represents the boundary surfaces by distributing piecewise linear-vortex and constant-source singularities on discrete panels. A local coordinate is assigned to each independently moving object. Blade-shed vorticity is traced at each time step. The unsteady Kutta condition applied is nonlinear and requires zero blade trailing-edge loading at each time. Its influence on the solutions depends on the blade trailing-edge shapes. Steady biplane and cascade solutions are presented and compared to exact solutions and experimental data. Unsteady solutions are validated with the Wagner function for an airfoil moving impulsively from rest and the Theodorsen function for an oscillating airfoil. The shed vortex motion and its interaction with blades are calculated and compared to an analytic solution. For multi-blade-row cascade, the potential effect between blade rows is predicted using steady and quasi unsteady calculations. The accuracy of the predictions is demonstrated using experimental results for a one-stage turbine stator-rotor.

Incipient Separation Near Corners

2018 ◽  
Author(s):  
Anatoly I. Ruban
Keyword(s):  
Corner Point ◽  
Analytic Form ◽  
The Body ◽  
Recirculation Region ◽  
Body Contour ◽  
Concave Corner ◽  
Attached Flow ◽  
Surface Deflection ◽  
Interaction Problem ◽  
Incipient Separation

Chapter 4 analyses the transition from an attached flow to a flow with local recirculation region near a corner point of a body contour. It considers both subsonic and supersonic flow regimes, and shows that the flow near a corner can be studied in the framework of the triple-deck theory. It assumes that the body surface deflection angle is small, and formulates the linearized viscous-inviscid interaction problem. Its solution is found in an analytic form. It also presents the results of the numerical solution of the full nonlinear problem. It shows how, and when, the separation region forms in the boundary layer. In conclusion, it suggests that in the subsonic flow past a concave corner, the solution is not unique.

scholarly journals An Unstructured Finite Volume Method for Incompressible Flows With Complex Immersed Boundaries

2009 ◽  
Author(s):  
Lin Sun ◽  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Incompressible Flows ◽  
Simple Algorithm ◽  
Flow Region ◽  
Solid Material ◽  
The Body ◽  
Immersed Boundary ◽  
Material Points ◽  
Volume Method

A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Optimal Self-Propulsion of a Deformable Prolate Spheroid

1983 ◽  
Vol 27 (02) ◽  
pp. 121-130
Author(s):  
T. Miloh
Keyword(s):  
Kinetic Energy ◽  
Surface Deformation ◽  
Deformable Body ◽  
Large Degree ◽  
Prolate Spheroid ◽  
The Body ◽  
Deformation Pattern ◽  
Inviscid Fluid ◽  
Periodic Surface ◽  
Deformation Velocity

The problem of self-propulsion of an elongated deformable body moving in an infinite medium of inviscid fluid is considered in some detail. A prolate spheroid is chosen as a model shape, and a particular deformation pattern which maximizes the Froude efficiency is sought. The Froude efficiency in this context is defined by the ratio of the kinetic energy of the body to the total kinetic energy of the system comprising the body and the fluid. It is demonstrated that a body can propel itself from rest in a persistent manner even for a periodic surface deformation with zero mean which preserves both the volume and the location of its centroid. Under these constraints the induced forward velocity of the body is of 0(ε2) where ε is the amplitude of the deformation velocity. It is also demonstrated that for a persistent self-propulsion to exist the body should develop a large degree of skewness, resulting from the interaction between the two deformation components—one with fore-and-aft symmetry and one without. It is also essential that the symmetric and asymmetric deformation components should be out of phase.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

2021 ◽  
pp. 2150012
Author(s):  
G. Rigatos
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Nonlinear Optimal Control ◽  
The Body ◽  
Algebraic Riccati Equation ◽  
Control Input ◽  
Time Step ◽  
Control Approach ◽  
Vtol Aircraft ◽  
Optimal Control Approach

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

scholarly journals Smartphone Monitoring of Gait and Balance During Irregular Surface Walking and Obstacle Crossing

2020 ◽  
Vol 2 ◽  
Author(s):  
Janeesata Kuntapun ◽  
Patima Silsupadol ◽  
Teerawat Kamnardsiri ◽  
Vipul Lugade
Keyword(s):  
Older Adults ◽  
Intraclass Correlation ◽  
Step Length ◽  
Living Environment ◽  
The Body ◽  
Irregular Surface ◽  
Time Step ◽  
Free Living ◽  
Obstacle Crossing ◽  
Gait Adaptation

As gait adaptation is vital for successful locomotion, the development of field-based tools to quantify gait in challenging real-world environments are crucial. The aims of this study were to assess the reliability and validity of a smartphone-based gait and balance assessment while walking on unobstructed and obstructed terrains using two phone placements. Furthermore, age-related differences in smartphone-derived gait strategies when navigating different walking conditions and environments were evaluated. By providing a method for evaluating gait in the simulated free-living environment, results of this study can elucidate the strategies young and older adults utilize to navigate obstructed and unobstructed walking paths. A total of 24 young and older adults ambulated indoors and outdoors under three conditions: level walking, irregular surface walking, and obstacle crossing. Android smartphones placed on the body and in a bag computed spatiotemporal gait (i.e., velocity, step time, step length, and cadence) and balance (i.e., center of mass (COM) displacement), with motion capture and video used to validate parameters in the laboratory and free-living environments, respectively. Reliability was evaluated using the intraclass correlation coefficient and validity was evaluated using Pearson's correlation and Bland-Altman analysis. A three-way ANOVA was used to assess outcome measures across group, condition, and environment. Results showed that smartphones were reliable and valid for measuring gait across all conditions, phone placements, and environments (ICC2,1: 0.606–0.965; Pearson's r: 0.72–1.00). Although body and bag placement demonstrated similar results for spatiotemporal parameters, accurate vertical COM displacement could only be obtained from the body placement. Older adults demonstrated a longer step time and lower cadence only during obstacle crossing, when compared to young adults. Furthermore, environmental differences in walking strategy were observed only during irregular surface walking. In particular, participants utilized a faster gait speed and a longer step length in the free-living environment, compared to the laboratory environment. In conclusion, smartphones demonstrate the potential for remote patient monitoring and home health care. Along with being easy-to-use, inexpensive, and portable, smartphones can accurately evaluate gait during both unobstructed and obstructed walking, indoors and outdoors.

Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 727-750 ◽  
Author(s):  
Gareth P. Williams
Keyword(s):  
Poisson Equation ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Wave Flow ◽  
Trigonometric Interpolation ◽  
Time Step ◽  
Navier Stokes Equations ◽  
The Poisson Equation

A method of numerically integrating the Navier-Stokes equations for certain three-dimensional incompressible flows is described. The technique is presented through application to the particular problem of describing thermal convection in a rotating annulus. The equations, in cylindrical polar co-ordinate form, are integrated with respect to time by a marching process, together with the solving of a Poisson equation for the pressure. A suitable form of the finite difference equations gives a computationally-stable long-term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow.Trigonometric interpolation techniques provide accurate (discretely exact) solutions to the Poisson equation. By using an auxiliary algorithm for rapid evaluation of trigonometric transforms, the proportion of computation needed to solve the Poisson equation can be reduced to less than 25% of the total time needed to’ advance one time step. Computing on a UNIVAC 1108 machine, the flow can be advanced one time-step in 2 sec for a 14 × 14 × 14 grid upward to 96 sec for a 60 × 34 × 34 grid.As an example of the method, some features of a solution for steady wave flow in annulus convection are presented. The resemblance of this flow to the classical Eady wave is noted.

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