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Transonic Flutter


The Effect of Shock Waves Movement on Flutter and Self-Oscillations of an Elastic Aircraft in Transonic Flow

Tech Area / Field

  • SAT-AER/Aeronautics/Space, Aircraft and Surface Transportation

8 Project completed

Registration date

Completion date

Senior Project Manager
Visser H

Leading Institute
Central Aerodynamic Institute, Russia, Moscow reg., Zhukovsky


  • National Research Council Canada / Institute for Aerospace Research / Structures and Materials Performance Laboratory, Canada, ON, Ottawa

Project summary

The Project aim. The main purpose of this project is the investigation of the effect of changes in the location of a shock wave on flutter and limit cycle oscillations of an aerodynamic surface of an elastic aircraft in transonic flow. In the project, the creation of the methodology for researching not only flutter boundaries of an airplane, but also for calculation of parameters of both limit cycle oscillation, and flutter onset and evolution is proposed.

Current status. There are many linear and nonlinear stability dynamic response phenomena of a flying vehicle that need to be studied in an aeroelasticity analysis. The complexity of advanced aeroelastic problems from linear to nonlinear aeroelastic formulations may be briefly presented as follows:

  • Completely linear models. Example: classical aeroelasticity of an airplane.
  • Linearized models. Linearized dynamic equations provide linearized aeroelastic stability boundaries.
  • Completely nonlinear models – nonlinear physical system has to be considered in its entirety. Example: transonic flutter.

The traditional linear approach based on linear theory allows studying the majority of the flutter types and modes that can appear in practice. However some modern aircraft encounter phenomena known as a transonic flutter and limit cycle oscillations, which are types of dynamic instability where the aerodynamic forces are essentially nonlinear. Linear unsteady aerodynamics still have been proven as reliable in the subsonic and supersonic regimes where the flow is mostly attached and no shock-wave motion over lifting surfaces is present. The presence of shock waves may lead to significant changes of the flutter boundaries and limit cycle oscillations of an elastic airplane in transonic flow.

The project’ influence on progress in this area. The proposed methodology of research of flutter and limit cycle oscillations of an airplane will also allow rapid determination of acceleration levels and reliability of the limit cycle oscillations mode and amplitude at actual possible levels of disturbances. Recommendations obtained from the project results will be applied to the design of civil airplanes of various types. These recommendations will allow:

  • prevention of possible expensive changes of the airplane structure elements in the design stage related to the flying vehicle safety under requirements of flutter in flight at transonic Mach numbers;
  • reduction of the program and duration of the certification tests that enhance the economies of expenditures for the creation of an airplane by 0.05-0.08 %.

The participants’ expertise. Highly skilled experts in aeroelasticity, non-stationary aerodynamics, strength, flight dynamics and optimization of airplane structures are expected to take part in the Project. This gives them the opportunity to apply their knowledge and experience accumulated in military and other aircraft design to the development of advanced passenger and transport airliners. The leading scientific TsAGI experts taking part in the Project as the tasks leaders -are the Ph.D., the authors of numerous publications and papers in the international scientific conferences. The list of scientific publications is represented below.

Expected results and their application. The main result to be achieved will be recommendations to improve flight performance of airplanes and increasing air safety. In the Project the methods, algorithms and software of new aeroelasticity aspects will be developed to include transonic oscillation, connected with motions of shock waves on lifting surfaces. The theoretical research of strength and aeroelasticity of the considered structures of a baseline passenger regional airplane will be performed. As a whole it should allow the selection of the most useful approaches and to give recommendations on the application of the results obtained for several prospective directions.

Meeting the ISTC goals and objectives. Solving complicated tasks designated in this Project will provide alternative employment for more than 15 experts who more or less deals with weapons development and production. They will be engaged for three years with the research on improvement of civil aviation techniques. The work will be held in close cooperation with foreign Collaborator, and will promote integration of TsAGI scientists and engineers into the international scientific society through providing information on the Project during international conferences and workshops.

Scope of activities.

The whole scope of the proposed project is pided into four main tasks:

  1. Flutter and aeroservoelasticity analysis of the reference aircraft using linear approximations.
  2. Development of aeroelasticity analysis methods using Euler equations for computation of aerodynamic characteristics of transonic flow.
  3. Investigation of control system efficiency taking into account shock wave movements.
  4. Multidisciplinary analysis of loads, aeroelasticity, strength and fatigue characteristics of the reference aircraft in transonic flow.

Role of Foreign Collaborators.

Dr. David G. Zimcik, Group Leader of Aeroacoustics and Structural Dynamics, Structures and Materials Performance Laboratory (Institute for Aerospace Research, Canada) expressed his wish to become Collaborator of this Project.

The Collaborator has already taken an active part in the early stage of the project formation through the following:

  • Initiation of the project goal definition;
  • Discussion and coordination of the proposals to define the details of the statement of the problem to be investigated.

Technical approach and methodology.

On the base of the ARGON software developed by TsAGI and a methodology proposed in the Project a multidisciplinary analysis of strength, aeroelasticity and fatigue characteristics of the reference airplane in transonic flow will be carried out. The development of a methodology includes the following elements of research:

  • forming of mathematical models of motion of an elastic airplane with control surfaces in transonic flow;
  • calculation of flutter boundaries of an airplane considered as a linear system;
  • creation of a computational model for flutter taking into account nonlinearity caused by motion of shock waves on the lifting surface in transonic flow;
  • development of a computational method for determination of characteristics of flutter and limit cycle oscillations in the frequency domain;
  • creation of an algorithm for computation of unsteady aerodynamic coefficients using nonlinear Euler equations taking into account the viscosity of a flow;
  • research of non-linear transonic flutter in the time domain by the method of numerical integration.


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