Engineering topics

Bratanow, T.

Publications and source records attributed to Bratanow, T..

12 records

NASA NTRS1979

Unsteady flow and dynamic response analyses for helicopter rotor blades

Research is presented on helicopter rotor blade vibration and on two and three dimensional analyses of unsteady incompressible viscous flow past oscillating helicopter rotor blades. A summary is presented of the two international research collaborations which resulted from the NASA project: the collaboration under the auspices of NATO between the University of Wisconsin-Milwaukee, University of Brussels, Belgium and the Aerodynamics Research Establishment in Goettingen, West Germany, and the collaboration under the auspices of the National Science Foundation between UWM and the University of Hamburg and the Ship Research Establishment in Hamburg, West Germany. A summary is given of the benefits from the NASA project to UWM, the College of Engineering and Applied Science, and the participants on the project.

Bratanow, T.↗

NASA NTRS1978

Computational flow development for unsteady viscous flows: Foundation of the numerical method

A procedure is presented for effective consideration of viscous effects in computational development of high Reynolds number flows. The procedure is based on the interpretation of the Navier-Stokes equations as vorticity transport equations. The physics of the flow was represented in a form suitable for numerical analysis. Lighthill's concept for flow development for computational purposes was adapted. The vorticity transport equations were cast in a form convenient for computation. A statement for these equations was written using the method of weighted residuals and applying the Galerkin criterion. An integral representation of the induced velocity was applied on the basis of the Biot-Savart law. Distribution of new vorticity, produced at wing surfaces over small computational time intervals, was assumed to be confined to a thin region around the wing surfaces.

Bratanow, T.↗

NASA NTRS1975

A rigorous solution of the Navier-Stokes equations for unsteady viscous flow at high Reynolds numbers around oscillating airfoils

A method based on the Navier-Stokes equations was developed for analyzing the unsteady incompressible viscous flow around oscillating airfoils at high Reynolds numbers. The Navier-Stokes equations have been integrated in their classical Helmholtz vorticity transport equation form, and the instantaneous velocity field at each time step was determined by the solution of Poisson's equation. A refined finite element was utilized to allow for a conformable solution of the stream function and its first space derivatives at the element interfaces. A corresponding set of accurate boundary conditions was applied; thus obtaining a rigorous solution for the velocity field. The details of the computational procedure and examples of computed results describing the unsteady flow characteristics around the airfoil are presented.

Bratanow, T.↗

NASA NTRS1974

Sensitivity analysis of torsional vibration characteristics of helicopter rotor blades. Part 1: Structural dynamics analysis

A theoretical investigation of structural vibration characteristics of rotor blades was carried out. Coupled equations of motion for flapwise bending and torsion were formulated for rotor blades with noncollinear elastic and mass axes. The finite element method was applied for a detailed representation of blade structural properties. Coupled structural mass and stiffness coefficients were evaluated. The range of validity of a set of coupled equations of motion linearized with respect to eccentricity between elastic and mass axes was investigated. The sensitivity of blade vibration characteristics to torsion were evaluated by varying blade geometric properties, boundary conditions, and eccentricities between mass and elastic axes.

Bratanow, T.↗

NASA NTRS1974

Sensitivity analysis of torsional vibration characteristics of helicopter rotor blades. Part 2: Aerodynamics and sensitivity analysis

A theoretical investigation of dynamic response characteristics of rotor blades was carried out with special emphasis on torsional degrees-of-freedom. Coupled equations of motion for flapwise bending and torsion were formulated at varying azimuth positions for rotor blades with noncollinear aerodynamic, elastic and mass axes. Both structural and aerodynamic mass, damping and stiffness coefficients were included. The variations of a sample blade at different flight conditions were investigated from these equations. The obtained numerical results were illustrated. The sensitivity of overall blade vibration characteristics to torsional oscillations was also investigated from the equations of motion for the sample blade. The illustrated results show the importance of torsional degrees-of-freedom in rotor blade analysis. Various possibilities of improving the overall response by tuning blade geometric, structural and aerodynamic characteristics are discussed.

Bratanow, T.↗

NASA NTRS1974

Numerical calculations of velocity and pressure distribution around oscillating airfoils

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Bratanow, T.↗

NASA NTRS1974

Analysis of three-dimensional unsteady flow around oscillating wings

A method based on the Navier-Stokes equations was developed for determining analytically the three-dimensional unsteady flow patterns around oscillating wings. The Helmholz vorticity transport equations were discretized in three-dimensional finite element form from a variational formulation and integrated numerically. At each time step of the numerical integration the velocity field was calculated from the representation of the three-dimensional wing by a system of optimized distribution of vortices in space. During the numerical integration of the vorticity transport equations the time-dependent boundary conditions on the wing were specified as external constraint conditions. Examples of obtained results describing the three-dimensional unsteady flow around a wing were presented.

Bratanow, T.↗

NASA NTRS1974

Nonlinearities in analyses of unsteady flow around oscillating wings

An analysis of nonlinearities involved in unsteady subsonic viscous flow around wings at high Reynolds numbers is presented. The finite element method was applied for the numerical integration of the vorticity transport equations. Physical and numerical aspects of the nonlinearities are discussed. Magnification of nonlinearities in the convection terms near wing surfaces due to changing geometry at leading and trailing edges of the wing chord is determined. As a bubble is generated near the leading edge, the timewise variation of vorticity and pressure distributions over the surface is shown. The different procedures for the integration of the vorticity transport equations in three dimensions along spanwise, chordwise, and normal directions are discussed.

Bratanow, T.↗

NASA NTRS1973

Finite element analysis and computer graphics visualization of flow around pitching and plunging airfoils

A general computational method for analyzing unsteady flow around pitching and plunging airfoils was developed. The finite element method was applied in developing an efficient numerical procedure for the solution of equations describing the flow around airfoils. The numerical results were employed in conjunction with computer graphics techniques to produce visualization of the flow. The investigation involved mathematical model studies of flow in two phases: (1) analysis of a potential flow formulation and (2) analysis of an incompressible, unsteady, viscous flow from Navier-Stokes equations.

Bratanow, T.↗

NASA NTRS1973

Sensitivity of rotor blade vibration characteristics to torsional oscillations.

A theoretical investigation of dynamic response characteristics of helicopter rotor blades in forward flight was carried out with special emphasis on the torsional degrees-of-freedom. The finite element method was applied in the formulation of the coupled equations of motion for flapwise bending and torsion for blades with non-collinear elastic, mass and aerodynamic axes. The sensitivity of blade vibration characteristics with respect to structural, geometric and aerodynamic properties as well as flight conditions was evaluated. Numerical results for sample blades were plotted to show the variation of the coupling between bending and torsional components of the response.

Bratanow, T.↗

NASA NTRS1973

Finite element analysis of unsteady incompressible flow around an oscillating obstacle of arbitrary shape.

An analytical procedure based on Navier-Stokes equations was developed for representing unsteady flow patterns around oscillating obstacles. A variational formulation of the Helmholtz vorticity equation was discretized in finite element form and integrated numerically. At each step of the numerical integration the velocity field around the obstacle was determined from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints at each time step of the numerical integration. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Bratanow, T.↗

NASA NTRS1973

Computational considerations in application of the finite element method for analysis of unsteady flow around airfoils.

Difficulties related to the application of the finite element method for numerical solution of the Navier-Stokes equation are discussed. The unsteady flow around a stationary and oscillating NACA 0012 airfoil was analyzed. In an effort to establish the range of applicability of the developed numerical method, the accuracy and stability problems in representing unsteady flow patterns and determining pressure distribution around the airfoil were investigated. Error involved in determining the velocity field and in the numerical integration of the discretized equations were analyzed in terms of geometry of the finite element gridwork, boundary conditions for stationary and oscillating airfoils, angles of attack and flow conditions.

Bratanow, T.↗