The state of the art in computer simulations for transonic flowfields requiring solutions for the Navier-Stokes equations is assessed. It is noted that current simulations of transonic flowfields require comparisons with experimental results because the simulations are not free from discretization errors. Cases of turbulence are treated with weighted variables in a time-averaged scheme to yield Reynolds averaged Navier-Stokes equations. The turbulence is modeled in a first-order approach with a Reynolds stress tensor or a second-order approach where the tensor is obtained from the Navier-Stokes equations. The choice of coordinate systems and dependent variables for simulating the flow around airfoils is discussed, with particular attention to curvilinear coordinates. The determinations of boundary conditions is examined, along with numerical methods related to physical phenomena

Reynolds averaged Navier-Stokes computations of transonic flows The-state-of-the-art

Advantages to employing Green's function in describing unsteady three-dimensional transonic flows are explored. The development of the function for application to linear subsonic and supersonic unsteady aerodynamics is reviewed. It is shown that unique solutions are possible for external flows, with all functional expressions being defined in Prandtl-Glauert space. The development of methods of using the Green's function for transonic flows is traced, noting the necessity of including the effects of significant nonlinear terms. The steady-state problem is considered to demonstrate the shock-capturing ability of the method and the usefulness of the function in the incompressible, subsonic, transonic, and supersonic areas of potential unsteady three-dimensional flows around complex configurations. Computational time is asserted to be an order of magnitude less than with finite difference methods.

Nonlinear Green's function method for unsteady transonic flows

: This paper describes the application of non-asymptotic triple-deck theory of transonic shock-turbulent boundary layer interaction as a local modular element in the global calculation of supercritical airfoil flow fields. (Author)

Application of a Shock-Turbulent Boundary Layer Interaction Theory in Transonic Flow Field Analysis.

Alternative Methods for Modeling Unsteady Transonic Flows

It is my assignment to provide a background of the history and development of transonic aerodynamics as a preamble to the remainder of the papers in this book presenting critical reviews of recent advances and suggestions of prospective avenues for further progress. Such assignments are a sure sign of passing years, but I do have the advantage of getting an early start in transonic aerodynamics when I was assigned to the Flight Research Branch at NACA/Ames Aeronautical Laboratory upon arrival as a young engineer in mid-1943. This group, under the direction of Larry dousing, who was also a leading test pilot, was just beginning research to determine the causes of catastrophic accidents that were occurring when fighter planes were put into steep dives at high altitude, and hopefully to determine ways to cure or avoid the problems. In 1947, I transferred to the Theoretical Aerodynamics Branch under the direction^of Dr. Max A. Heaslet, and was soon at work trying to develop theories for dealing with transonic flows. During the following years, it fell my lot to provide summary papers on the state of transonic aerodynamics on a number of occasions. I will draw rather heavily on these papers, inasmuch as they were designed to be comprehensive summaries within imposed limits of length of the state of knowledge of transonic aerodynamics, with somewhat of a bias toward theory and its evaluation in wind-tunnel experiments. While this may seem a bit parochial, since corresponding research was also under way at a number of other places, the work at Ames was both at the forefront and in

Chapter I. Transonic Aerodynamics—History and Statement of the Problem

Integral equation methods are described. It is shown that the recent developments in these methods applied to two dimensional aerofoils give comparable results to the more advanced finite difference methods in shorter computing times.

Integral Equation Methods — a Reappraisal

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

D. Nixon

Author Tools

Chat about Author

Papers

Integral Equation Methods — a Reappraisal