Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T14:26:29.664Z Has data issue: false hasContentIssue false

11 - Actuator Disk

Published online by Cambridge University Press:  05 May 2013

Wayne Johnson
Wayne Johnson
Affiliation:
Aeromechanics Branch of NASA Ames Research Center
Get access

Summary

The analysis of the wake is considerably simplified if the rotor is modeled as an actuator disk, which is a circular surface of zero thickness that can support a pressure difference and thus accelerate the air through the disk. The actuator disk neglects the discreteness in the rotor and wake associated with a finite number of blades, and it distributes the vorticity throughout the wake volume. The actuator disk model is the basis for momentum theory (sections 3.1.1 and 5.1.1). The simplest version of vortex theory uses an actuator disk model, which produces a tractable mathematical problem, at least for axial flight (section 3.7). In contrast to hover, the mathematical problem in forward flight is still not trivial, because of the skewed cylindrical geometry (section 5.2). Some results from actuator disk models were presented in section 5.2.1.

The focus of this chapter is the unsteady aerodynamics of the rotor associated with the three-dimensional wake. In particular, the dynamic inflow model is developed. This is a finite-state model, relating a set of inflow variables and loading variables by differential equations. Such a model is required for aeroelastic stability calculations and real time simulation. Vortex theory uses the Biot-Savart law for the velocity induced by the wake vorticity. Potential theory solves the fluid dynamic equations for the velocity potential or acceleration potential.

Vortex Theory

For the actuator disk in axial flow, the wake is a right circular cylinder (Figure 11.1). With uniform loading, the bound circulation is constant over the span, and the trailed vorticity is concentrated in root and tip vortices.

Type
Chapter
Information
Rotorcraft Aeromechanics , pp. 414 - 441
Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amer, K.B. “Theory of Helicopter Damping in Pitch or Roll and a Comparison with Flight Measurements.” NACA TN 2136, October 1950.Google Scholar
Arnold, U.T.P., Keller, J.D., Curtiss, H.C. Jr., and Reichert, G. “The Effect of Inflow Models on the Predicted Response of Helicopters.” Journal of the American Helicopter Society, 43:1 (January 1998).CrossRefGoogle Scholar
Bagai, A., Leishman, J.G., and Park, J. “Aerodynamic Analysis of a Helicopter in Steady Maneuvering Flight Using a Free-Vortex Rotor Wake Model.” Journal of the American Helicopter Society, 44:2 (April 1999).CrossRefGoogle Scholar
Banerjee, D., Crews, S.T., Hohenemser, K.H., and Yin, S.K. “Identification of State Variables and Dynamic Inflow from Rotor Model Dynamic Tests.” Journal of the American Helicopter Society, 22:2 (April 1977).Google Scholar
Carpenter, P.J., and Fridovich, B. “Effect of a Rapid Blade-Pitch Increase on the Thrust and Induced-Velocity Response of a Full-ScaleHelicopter Rotor.” NACATN 3044, November 1953.Google Scholar
Castles, W. Jr., “Approximate Solution for Streamlines About a Lifting Rotor Having Uniform Loading and Operating in Hovering or Low-Speed Vertical-Ascent Flight Conditions.” NACA TN 3921, February 1957.Google Scholar
Chaimovich, M., Rosen, A., Rand, O., Mansur, M.H., and Tischler, M.B. “Investigation of the Flight Mechanics Simulation of a Hovering Helicopter.” American Helicopter Society 48th Annual Forum, Washington, DC, June 1992.Google Scholar
Coleman, R.P., Feingold, A.M., and Stempin, C.W. “Evaluation of the Induced-Velocity Field of an Idealized Helicopter Rotor.” NACA ARR L5E10, June 1945.Google Scholar
Crews, S.T., Hohenemser, K.H., and Ormiston, R.A. “An Unsteady Wake Model for a Hingeless Rotor.” Journal of Aircraft, 10:12 (December 1973).CrossRefGoogle Scholar
Curtiss, H.C. Jr., and Shupe, N.K. “A Stability and Control Theory for Hingeless Rotors.” American Helicopter Society 27th Annual National V/STOL Forum, Washington, DC, May 1971.Google Scholar
Drees, J.M. “A Theory of Airflow Through Rotors and Its Application to Some Helicopter Problems.” Journal of the Helicopter Association of Great Britain, 3:2 (July-August-September 1949).Google Scholar
Fletcher, J.W. “Identification of Linear Models of the UH-60 in Hover and Forward Flight.” Twenty-First European Rotorcraft Forum, Saint Petersburg, Russia, September 1995.Google Scholar
Gaonkar, G.H., and Peters, D.A. “Effectiveness of Current Dynamic-Inflow Models in Hover and Forward Flight.” Journal of the American Helicopter Society, 31:2 (April 1986).CrossRefGoogle Scholar
Gaonkar, G.H., and Peters, D.A. “Review of Dynamic Inflow Modeling for Rotorcraft Flight Dynamics.” Vertica, 12:3 (1988).Google Scholar
Harding, J.W., and Bass, S.M. “Validation of a Flight Simulation Model of the AH-64 Apache Attack Helicopter Against Flight Test Data.” American Helicopter Society 46th Annual Forum, Washington, DC, May 1990.Google Scholar
Hohenemser, K.H., and Crews, S.T. “Model Tests on Unsteady Rotor Wake Tests.” Journal of Aircraft, 10:1 (January 1973).CrossRefGoogle Scholar
Joglekar, M., and Loewy, R. “An Actuator-Disc Analysis of Helicopter Wake Geometry and the Corresponding Blade Response.” USAAVLABS TR 69-66, December 1970.CrossRefGoogle Scholar
Keller, J.D. “An Investigation of Helicopter Dynamic Coupling Using an Analytical Model.” Journal of the American Helicopter Society, 41:4 (October 1996).CrossRefGoogle Scholar
Keller, J.D., and Curtiss, H.C. Jr., “A Critical Examination of the Methods to Improve the Off-Axis Response Prediction of Helicopters.” American Helicopter Society 54th Annual Forum, Washington, DC, May 1998.Google Scholar
Kinner, W. “Die Kreisförmige Tragfläche auf Potentialtheoretischer Grundlage.” Ingenieur-Archiv, 8:1, 1937. (“Theory of the Circular Wing,” R.T.P. Translation No. 2345, issued by the Ministry of Aircraft Production.)CrossRefGoogle Scholar
Kramer, P., Gimonet, B., and von Grunhagen, W. “A Systematic Approach to Nonlinear Rotorcraft Model Identification.” Aerospace Science and Technology, 6:8 (December 2002).CrossRefGoogle Scholar
Kuczynski, W.A., and Sissingh, G.J. “Characteristics of Hingeless Rotors with Hub Moment Feedback Controls Including Experimental Rotor Frequency Response.” NASA CR 114427, January 1972.Google Scholar
Mangler, K.W. “Calculation of the Induced Velocity Field of a Rotor.” RAE Report No. Aero 2247, February 1948a.Google Scholar
Mangler, K.W. “Fourier Coefficients for Downwash at a Helicopter Rotor.” RAE Tech Note Aero. 1958, May 1948b.Google Scholar
Mangler, K.W., and Squire, H.B. “The Induced Velocity Field of a Rotor.” ARC R&M 2642, May 1950.Google Scholar
Mansur, M.H., and Tischler, M.B. “An Empirical Correction for Improving Off-Axes Response in Flight Mechanics Helicopter Models.” Journal of the American Helicopter Society, 43:2 (April 1998).CrossRefGoogle Scholar
Miller, R.H. “Unsteady Air Loads on Helicopter Rotor Blades.” Journal of the Royal Aeronautical Society, 68:640 (April 1964).CrossRefGoogle Scholar
Munk, M.M. “Some Tables of the Factor of Apparent Additional Mass.” NACA TN 197, July 1924.Google Scholar
Ormiston, R.A., and Peters, D.A. “Hingeless Helicopter rotor Response with Nonuniform Inflow and Elastic Blade Bending.” Journal of Aircraft, 9:10 (October 1972).CrossRefGoogle Scholar
Peters, D.A. “Hingeless Rotor Frequency Response with Unsteady Inflow.” American Helicopter Society Specialists' Meeting on Rotor Dynamics, Moffett Field, CA, February 1974. (NASA SP-352, February 1974).Google Scholar
Peters, D.A., and He, C.J. “Finite State Induced Flow Models – Part II: Three-Dimensional Rotor Disk.” Journal of Aircraft, 32:2 (March-April 1995).Google Scholar
Pitt, D.M. “Rotor Dynamic Inflow Derivatives and Time Constants from Various Inflow Models.” USATSARCOM TR 81-2, December 1980.Google Scholar
Pitt, D.M., and Peters, D.A. “Theoretical Prediction of Dynamic-Inflow Derivatives.” Vertica, 5:1 (1981).Google Scholar
Rebont, J., Soulez-Lariviere, J., and Valensi, J. “Response of Rotor Lift to an Increase in Collective Pitch in the Case of Descending Flight, the Regime of the Rotor Being Near Autorotation.” NASA TT F-18, April 1960a (original paper September 1958).Google Scholar
Rebont, J., Valensi, J., and Soulez-Lariviere, J. “Wind-Tunnel Study of the Response in Lift of a Rotor to an Increase in Collective Pitch in the Case of Vertical Flight Near the Autorotative Regime.” NASA TT F-17, April 1960b (original paper September 1958).Google Scholar
Rebont, J., Valensi, J., and Soulez-Lariviere, J. “Response of a Helicopter Rotor to an Increase in Collective Pitch for the Case of Vertical Flight.” NASA TT F-55, January 1961 (original paper May-June 1959).Google Scholar
Schulein, G.J., Tischler, M.B., Mansur, M.H., and Rosen, A. “Validation of Cross-Coupling Modeling Improvements for UH-60 Flight Mechanics Simulations.” Journal of the American Helicopter Society, 47:3 (July 2002).CrossRefGoogle Scholar
Shupe, N.K. “A Study of theDynamic Motions of HingelessRotor Helicopters.” USAECOM TR ECOM-3323, August 1970.Google Scholar
Sissingh, G.J. “The Effect of Induced Velocity Variation on Helicopter Rotor Damping in Pitch or Roll.” ARC CP 101, November 1951.Google Scholar
Takahashi, M.D. “A Flight-Dynamic Helicopter Mathematical Model with a Single Flap-Lag-Torsion Main Rotor.” NASA TM 102267, February 1990.Google Scholar
Tuckerman, L.B. “Inertia Factors of Ellipsoids for Use in Airship Design.” NACA Report 210, 1925.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Actuator Disk
  • Wayne Johnson
  • Book: Rotorcraft Aeromechanics
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139235655.012
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Actuator Disk
  • Wayne Johnson
  • Book: Rotorcraft Aeromechanics
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139235655.012
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Actuator Disk
  • Wayne Johnson
  • Book: Rotorcraft Aeromechanics
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139235655.012
Available formats
×