The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

https://ntrs.nasa.gov/api/citations/20010018414/downloads/20010018414.pdf

Reduced-order modeling: new approaches for computational physics

Review of state of the art in smart rotor control research for wind turbines

Structures, Structural Dynamics and Materials Conference

A new method for constructing reduced-order models (ROM) of unsteady small-disturbance e ows is presented. The reduced-order models are constructed using basis vectors determined from the proper orthogonal decomposition (POD) of an ensemble of small-disturbance frequency-domain solutions. Each of the individual frequencydomain solutions is computed using an efe cient time-linearized e ow solver. We show that reduced-order models can be constructed using just a handful of POD basis vectors, producing low-order but highly accurate models of the unsteady e ow over a wide range of frequencies. We apply the POD/ROM technique to compute the unsteady aerodynamic and aeroelastic behavior of an isolated transonic airfoil and to a two-dimensional cascade of airfoils.

/pdf/proper-orthogonal-decomposition-technique-for-transonic-1qcwd6gv8a.pdf

Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows

The application and assessment is described of CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code for flutter prediction. The CAP-TSD program was developed for aeroelastic analysis of complete aircraft configurations and was previously applied to the calculation of steady and unsteady pressures. Flutter calculations are presented for two thin, swept-and-tapered wing planforms with well defined modal properties. The calculations are for Mach numbers from low subsonic to low supersonic values, including the transonic range, and are compared with subsonic linear theory and experimental flutter data. The CAP-TSD flutter results are generally in good agreement with the experimental values and are in good agreement with subsonic linear theory when wing thickness is neglected.

/pdf/wing-flutter-calculations-with-the-cap-tsd-unsteady-x0t1fhxl3j.pdf

Wing-flutter calculations with the CAP-TSD unsteady transonic small-disturbance program

An experimental effort was implemented in aeroelasticity called the Benchmark Models Program. The primary purpose of this program is to provide the necessary data to evaluate computational fluid dynamic codes for aeroelastic analysis. It also focuses on increasing the understanding of the physics of unsteady flows and providing data for empirical design. An overview is given of this program and some results obtained in the initial tests are highlighted. The tests that were completed include measurement of unsteady pressures during flutter of rigid wing with a NACA 0012 airfoil section and dynamic response measurements of a flexible rectangular wing with a thick circular arc airfoil undergoing shock boundary layer oscillations.

/pdf/the-benchmark-aeroelastic-models-program-description-and-4zv1bo1g97.pdf

The benchmark aeroelastic models program: Description and highlights of initial results

Wind tunnel technique for measuring frequency response of flexible airplane to vertical sinusoidal gusts

A Wind-Tunnel Technique for Measuring Frequency-Response Functions for Gust Load Analyses

A new, fast, and economical automated procedure for implementing the traditional V-g method of flutter solution is described. The procedure requires as input the generalized aerodynamic forces for a range of reduced frequencies obtained from an aerodynamic program. These aerodynamic forces are interpolated with respect to reduced frequency using a newly developed, partially tabulated cubic spline that is both fast in execution and economical in storage. The flutter solution is then obtained using an eigenvalue routine that has been developed to take advantage of the parametric nature of the V-g type of solution. Furthermore, the routine takes care of the fundamental and troublesome problem of properly sorting the output eigenvalues. By solving the root-sorting problem, the interpolation for flutter crossings and automatic plotting are accomplished efficiently. The computational techniques used in this new program are described and some sample results are given.

Robert M. Bennett

Papers

Wing-flutter calculations with the CAP-TSD unsteady transonic small-disturbance program

The benchmark aeroelastic models program: Description and highlights of initial results

A Wind-Tunnel Technique for Measuring Frequency-Response Functions for Gust Load Analyses

An Automated Procedure for Computing Flutter Eigenvalues

Wind-Tunnel Technique for Determining Stability Derivatives from Cable-Mounted Models