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The broadband aerodynamic noise can be studied, assuming isotropic flow, turbulence and decay. Proudman’s approach allows practical calculations of noise based on CFD solutions of RANS or URANS equations at the stage of post processing and analysis of the solution. Another aspect is the broadband acoustic spectrum and the distribution of acoustic power over a range of frequencies. The acoustic energy spectrum distribution in isotropic turbulence is non monotonic and has a maximum at a certain value of Strouhal number. In the present work the value of acoustic power peak frequency is determined using a prescribed form of acoustic energy spectrum distribution presented in papers by S. Sarkar and M. Y. Hussaini and by G. M. Lilley. CFD modelling of the flow around isolated helicopter fuselage model was considered using the HMB CFD code and the RANS equations.

Two mathematical models are used in this work to estimate the acoustics of a hovering main rotor. The first model is based on the Ffowcs Williams-Howkings equations using the formulation of Farassat. An analytical approach is followed for this model, to determine the thickness and load noise contributions of the rotor blade in hover. The second approach allows using URANS and RANS CFD solutions and based on numerical solution of the Ffowcs Williams-Howkings equations. The employed test cases correspond to a model rotor available at the KNRTUKAI aerodynamics laboratory. The laboratory is equipped with a system of acoustic measurements, and comparisons between predictions and measurements are to be attempted as part of this work.

This contribution is devoted to investigation of multiwave Volume Free Electron Laser (VFEL) by methods of mathematical modelling. Special emphasis is placed on consideration of three‐wave VFEL. Mathematical modelling carried out confirmed some preliminary physical estimates. Computer code VOLC for simulation of different schemes of two‐ and three‐wave VFEL is described. Key words: free electron laser, quasi‐Cherenkov instability, simulation, nonlinear integro‐differential system. First Published Online: 14 Oct 2010

Analysis of nonstationary stage of quasi‐Cherenkov instability of electron beam in the case of two‐wave distributed feedback is carried out. Mathematical models and numerical methods of nonstationary quasi‐Cherenkov electron beam instability are proposed. Results of numerical experiments are proposed. Bifurcations of nonstationary solution are discussed. Straipsnyje analizuojama nestacionariosios fazes kvazi‐Cherenkovo elektronu spinduliuotes nestabilumas esant dvieju bangu saveikai su grižtamo ryšio pernešimu. Pasiūlyti šios elektronu spinduliuotes nestacionariosios fazes atveju matematiniai ir skaitiniai sprendimo metodai. Pateikti skaitinio eksperimento rezultatai. Aptartos nestacionariojo sprendinio bifurkacijos. First Published Online: 14 Oct 2010

Nonlinear stage of quasi‐Cherenkov instability of electron beam under conditions of two‐ and three‐dimensional distributed feedback is simulated. The scheme of distributed feedback with two strong coupled waves is considered. Mathematical model of quasi‐Cherenkov electron beam instability is proposed. Numerical method to solve the nonlinear integro‐differential system, describing such instability, is worked out. Results of numerical experiments are discussed. Kvazi-Cerenkovo elektroninio spindulio nestabilumo modeliavimas periodinėse struktūrose Santrauka Modeliuojama elektronų spindulio kvazi‐Cherenkovo nestabilumo netiesinė fazė su dvimačio ir trimačio paskirstytojo grįžtamojo ryšio sąlyga. Nagrinėjama schema su grįžtamuoju ryšiu su dviem susietomis stipriomis bangomis. Pateiktas kvazi‐Cherenkovo elektroninio spindulio nestabilumo matematinis modelis. Pasiūlytas veiksmingas skaitinis algoritmas, skirtas netiesinėms integro‐diferencialinėms lygčių sistemoms su tokio tipo nestabilumu, spręsti. Apžvelgti skaitinio eksperimento rezultai. First Published Online: 14 Oct 2010