BSU Bulletin. Mathematics, Informatics
Bibliographic description:
, , A METHOD FOR CALCULATING NON-STATIONARY FLOW OF AN ARBITRARY PROFILE // BSU Bulletin. Mathematics, Informatics. - 2019. №4. . - С. 65-72.
Title:
A METHOD FOR CALCULATING NON-STATIONARY FLOW OF AN ARBITRARY PROFILE
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Annotation:
The article deals with non-stationary continuous flow of an arbitrary profile fluctu- ating as a solid with small amplitude under some harmonic law by potential flow of incompressible liquid. We have used the Kutta-Zhukovsky postulate to eliminate the features of a kernel of Fredholm integral equation of the second kind with re- spect to the value of non-stationary speed at the point of profile trailing edge. The hydrodynamic meaning of the carried-out elimination of the features of a kernel lies in the fact that the decision is sought in the class of functions that ensure the continuity of pressure everywhere in the flow, including the sharp trailing edge. The critical streamline of a stationary flow necessary for calculating improper inte- grals is defined as a solution to the Cauchy problem. Replacing the integrals in the equations with finite sums, we obtain systems of N algebraic equations with respect to the sought quantities.
Keywords:
arbitrary profile; unsteady flow; ideal incompressible liquid; Fredholm integral equations of second kind.
List of references:
Prandtl L. Uber die Enstehung von Wirbeln in einer idealen Flussigkeit. Vortrage zur Hydro-und Aerodynamik. Berlin, 1924. Pp. 18–33.
Chaplygin S. A. O vliyanii ploskoparallelnogo potoka vozdukha na dvizhushchee v nem tsilindricheskoe krylo [About the Influence of Plane-Parallel Air Flow on the Cylindrical Wing Moving in It]. Trudy TsAGI. 1926. Vol. 19. 74 p.
Keldysh M. V, Lavrentyev M. A. K teorii koleblyushchegosya kryla [On the Theory of Oscillating Wing]. Tekhnicheskie zametki TsAGI. 1935. No. 45. Pp. 48–52.
Sedov L. I. K teorii neustanovivshikhsya dvizhenii vnutri zhidkosti [On the Theory of Unsteady Motions in Liquid]. Trudy TsAGI. 1935. Vol. 229. 40 p.
Sedov L. I. Teoriya ploskikh dvizhenii idealnoi zhidkosti [Theory of Planar Motions of an Ideal Fluid]. GTTI, 1939. 144 p.
Polyakov N. Ph. Teoriya nestatsionarnykh dvizhenii nesuschei poverkhnosti [Theory of Non-Stationary Motions of a Carrying Surface]. Leningrad, 1960. 84 p.
Gorelov D. N. Teoriya kryla v nestatsionarnom potoke [Wing Theory for Un- steady Flow]. Novosibirsk, 1975. 152 p.
Gorelov D. N., Kulyaev R. L. Nelineinaya zadacha o nestatsionarnom obte- kanii profilya neszhimaemoi zhidkostiyu [A Nonlinear Problem of Unsteady Flow of a Profile with an Ideal Liquid]. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza. 1971. No. 6. Pp. 38–47.
Golovkin V. A. Nelinaya zadacha o neustanovivshemsya obtekanii proizvol- nogo profilya so svobodno deformiruyuschimsya vikhrevym sledom [A Nonlinear Problem of Unsteady Flow of An Arbitrary Profile with a Freely Deformed Vortex Sheet]. TsAGI Science Journal. 1972. Vol. 3. No. 3. Pp. 1–11.
Pavlovets G. A. Metody rascheta obtekanya secheniya kryla idealnym nesz- himaemym potokom [Methods for Calculating the Flow of Wing Section with an Ideal Incompressible Flow]. Trudy TsAGI. 1971. Vol. 1344. 72 p.
Darmaev T. G., Dambaev Zh. O nestatsionarnom obtekanii proizvolnogo pro- filya [About the Unsteady Flow of an Arbitrary Profile]. Vestnik Buryatskogo gosu- darstvennogo universiteta. Matematika, informatika. 2013. No. 2. Pp. 60–69.
Darmaev T. G., Tsydypov B. D. Metod rascheta statsionarnogo obtekaniya proizvolnogo profilya [A Method for Calculating the Stationary Flow of an Arbitrary Profile]. Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, informatika. 2016. Vol. 3. Pp. 51–56.
Ryabchenko V. P., Saryan V. E. K raschetu aerodinamicheskikh kharakteristik reshetok profilei proizvolnoi formy [On Calculation of Aerodynamic Characteristics of the Lattices of Arbitrarily-Shaped Profiles]. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza. 1972. No. 2. Pp.105–112.
Ryabchenko V. P. Nestatsionarnye aerodynamicheskie kharakteristiki reshe- tok proizvolnykh profilei, vibriruyushikh v potentsialnom potoke neszhimaemoi zhid- kosti [Non-Stationary Aerodynamic Characteristics of Lattices of Arbitrary Profiles Vibrating in a Potential Flow of Incompressible Liquid]. Izvestiya AN SSSR. Mek- hanika zhidkosti i gaza. 1974. No. 1. Pp. 15–20.
Chaplygin S. A. O vliyanii ploskoparallelnogo potoka vozdukha na dvizhushchee v nem tsilindricheskoe krylo [About the Influence of Plane-Parallel Air Flow on the Cylindrical Wing Moving in It]. Trudy TsAGI. 1926. Vol. 19. 74 p.
Keldysh M. V, Lavrentyev M. A. K teorii koleblyushchegosya kryla [On the Theory of Oscillating Wing]. Tekhnicheskie zametki TsAGI. 1935. No. 45. Pp. 48–52.
Sedov L. I. K teorii neustanovivshikhsya dvizhenii vnutri zhidkosti [On the Theory of Unsteady Motions in Liquid]. Trudy TsAGI. 1935. Vol. 229. 40 p.
Sedov L. I. Teoriya ploskikh dvizhenii idealnoi zhidkosti [Theory of Planar Motions of an Ideal Fluid]. GTTI, 1939. 144 p.
Polyakov N. Ph. Teoriya nestatsionarnykh dvizhenii nesuschei poverkhnosti [Theory of Non-Stationary Motions of a Carrying Surface]. Leningrad, 1960. 84 p.
Gorelov D. N. Teoriya kryla v nestatsionarnom potoke [Wing Theory for Un- steady Flow]. Novosibirsk, 1975. 152 p.
Gorelov D. N., Kulyaev R. L. Nelineinaya zadacha o nestatsionarnom obte- kanii profilya neszhimaemoi zhidkostiyu [A Nonlinear Problem of Unsteady Flow of a Profile with an Ideal Liquid]. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza. 1971. No. 6. Pp. 38–47.
Golovkin V. A. Nelinaya zadacha o neustanovivshemsya obtekanii proizvol- nogo profilya so svobodno deformiruyuschimsya vikhrevym sledom [A Nonlinear Problem of Unsteady Flow of An Arbitrary Profile with a Freely Deformed Vortex Sheet]. TsAGI Science Journal. 1972. Vol. 3. No. 3. Pp. 1–11.
Pavlovets G. A. Metody rascheta obtekanya secheniya kryla idealnym nesz- himaemym potokom [Methods for Calculating the Flow of Wing Section with an Ideal Incompressible Flow]. Trudy TsAGI. 1971. Vol. 1344. 72 p.
Darmaev T. G., Dambaev Zh. O nestatsionarnom obtekanii proizvolnogo pro- filya [About the Unsteady Flow of an Arbitrary Profile]. Vestnik Buryatskogo gosu- darstvennogo universiteta. Matematika, informatika. 2013. No. 2. Pp. 60–69.
Darmaev T. G., Tsydypov B. D. Metod rascheta statsionarnogo obtekaniya proizvolnogo profilya [A Method for Calculating the Stationary Flow of an Arbitrary Profile]. Vestnik Buryatskogo gosudarstvennogo universiteta. Matematika, informatika. 2016. Vol. 3. Pp. 51–56.
Ryabchenko V. P., Saryan V. E. K raschetu aerodinamicheskikh kharakteristik reshetok profilei proizvolnoi formy [On Calculation of Aerodynamic Characteristics of the Lattices of Arbitrarily-Shaped Profiles]. Izvestiya AN SSSR. Mekhanika zhidkosti i gaza. 1972. No. 2. Pp.105–112.
Ryabchenko V. P. Nestatsionarnye aerodynamicheskie kharakteristiki reshe- tok proizvolnykh profilei, vibriruyushikh v potentsialnom potoke neszhimaemoi zhid- kosti [Non-Stationary Aerodynamic Characteristics of Lattices of Arbitrary Profiles Vibrating in a Potential Flow of Incompressible Liquid]. Izvestiya AN SSSR. Mek- hanika zhidkosti i gaza. 1974. No. 1. Pp. 15–20.
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