Analiza protoka helikopterskog rotora primjenom modela Mangler-Squire

master's thesis

• Title (english): Helicopter rotor inflow analysis with application of Mangler-Squire model
• Author: Filip Rožman
• Mentor: Milan Vrdoljak (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2018-01-25, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

Glavna tema ovog diplomskog zadatka je analiza modela protoka zraka kroz rotor koji su razvili K.W. Mangler i H. B. Squire 1950. godine. Pretpostavke na kojima počiva teorija modela vrijede samo pri određenim brzinama napredujućeg leta stoga se ovaj model ne može koristiti za analizu rotora u vertikalnom letu i lebdenju. Mangler i Squire pretpostavljaju dvije osnovne raspodjele opterećenja (tlaka) na disku rotora: tip 1 i tip 3. Opterećenje tipa 1 je eliptičnog oblika, a opterećenje tipa 3 opisuje raspodjelu tlaka koja teži k nuli na rubu i na sredini diska rotora. Budući da nijedno od osnovnih opterećenja nije realan slučaj protoka kroz helikopterski rotor, predložen je kombinirani model protoka kojeg sačinjavaju dva osnovna opterećenja u određenom omjeru. Analizom je pokazano da najbolje rezultate daje kombinirani model sa jednakim omjerom dvaju opterećenja. Budući da je model Mangler-Squire matematički zapisan pomoću Fourierovog reda, provedena je analiza utjecaja duljine (broja članova) Fourierovog reda na točnost rješenja. Analizom nije obuhvaćena cijela površina rotora pa nije bilo moguće sa najvećom sigurnošću odrediti minimalan broj članova Fourierovog reda za točno rješenje. Stoga je rezultat analize dodatno proširen zbog postojeće nesigurnosti. Analiza je pokazala da rješenje vrlo brzo konvergira ka konačnom rješenju. U literaturi se navodi prijedlog izmjene osnovne jednadžbe modela Mangler-Squire, no usporedba rješenja izmjenjenog i originalnog modela pokazala je nezamjetne razlike u dvama pristupima. Usporedba modela Mangler-Squire sa drugim modelima protoka i sa eksperimentalnim mjerenjima pokazala je da model Manglera i Squirea vrlo dobro opisuje protok na helikopterskom rotoru te da je kvalitetniji u odnosu na modele razmatrane u ovom radu. U ovom je radu provedena i implementacija modela Mangler-Squire u teoriju elementarnog kraka za analizu performansi helikoptera. Rezultati analize performansi uspoređivani su sa teorijom elementarnog kraka s implementiranim Dreesovim modelom protoka te sa mjerenjima u letu. Usporedba je pokazala da implementacija modela protoka po Mangleru i Squireu daje vrlo slične rezultate kao i implementacija Dreesovog modela.

Abstract (english)

The main issue dealt with in this thesis is the analysis of an induced velocity model for helicopter rotors. The model was developed in 1950 by K. W. Mangler and H. B. Squire. The model rests on approximations which are only valid at certain advance ratios of the rotor. Those approximations render the model invalid for practical use outside the subscribed flight conditions (e.g. in hover and axial flight). Mangler and Squire define two basic types of rotor disc loading: type 1 and type 3. Type 1 is an elyptically shaped loading, while type 3 is a loading that vanishes at the rim of the disc and near the center. Since none of these loading is a valid representation of a real-case scenario, a combined loading is proposed. This type of loading consists of both previously stated types of loading in a prescribed ratio. An investigation into the best practical ratio has yielded an equal distribution of types 1 and 3. The Mangler-Squire model is mathematically described with a Fourier series which can constitute an infinite number of terms. Thus, an analysis into the minimum required number of Fourier series terms for an accurate result was conducted. The analysis yielded a relatively quick convergence of the end-result. Due to the inability to analyze the entire surface of the rotor disc, an uncertainty factor was incorporated into the end result of the Fourier series investigation. A suggested correction of the main equation of the Mangler-Squire model opened an investigation into the effect of this correction. The investigation yielded practically no difference between the two forms. A comparison of several induced velocity models was presented alongside experimental measurements. The comparison showed that the Mangler-Squire model was superior to other, simpler models that were considered in this thesis. Also, the Mangler-Squire induced velocity model was implemented into the blade element theory and was compared against the Drees model and in-flight measurements of the helicopter. This showed that the Mangler-Squire model yields very good rotor performance analysis results (as does the Drees model) when incorporated into the blade element theory.

• Keywords: Mangler-Squire model protoka; analiza protoka; helikopterski rotor; teorija elementarnog kraka
• Keywords (english): Mangler-Squire model; induced velocity analysis; helicopter rotor; blade element theory
• Language: croatian
• URN:NBN: urn:nbn:hr:235:091901
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka strojarstva (magistar/magistra inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-05-22 21:17:42