Akış kaynaklı titreşim için örnek problem: Ani genişleyen iki levha arasındaki akışın sayısal modellenmesi
Başlık çevirisi mevcut değil.
- Tez No: 39687
- Danışmanlar: PROF. DR. HALUK KARADOĞAN
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Enerji, Mechanical Engineering, Energy
- Anahtar Kelimeler: Ani genişleme, Enerji, Sayısal modelleme, Sınır koşulları, Titreşim, Viskozitesiz akış, Sudden expansion, Energy, Numerical modelling, Boundary conditions, Vibration, Inviscid flow
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
Özet yok.
Özet (Çeviri)
where thc dissipative ilux d, is giren as İV ^,i=^^{^fe,-%> (5.3) ^“(^,1-3Wno + 3Wo-W,,J| 6. T1MKSTKPPINGSCHKMES Semi-discretization ol* ecjuation (2.6) results in a systevn ol”first order ordinary differential equations with respect to time uhich is tvritten as 1%+^ = °(6-1) \\here ^-^(Oıj-Ûj(6-2) The operatör P is often called the residual of system (6.1). System (6J) is solved using explicit multistage schemes of Runge-Kutta type. CX)NC'LI:,S1ONS The codc usod con\:ergcs if thc viscosity eflbcts of thc llovv arc neyligable. Iha can V>c clearlv secn at thc 1wo dimcnsional llo\v in a no/zlc. This sludy shou's that Luler equalioııs and artifıcial viscosity arc insulfıcient lo sol ve the ilow het\\ een suddenly enlarge parallel tu o plates. Because of the rcal \ iscosity and the no-slip conditions this problem can only be handled with solying oi'Na\'ier-Stokes equations.Tlıree distinct type of conditions occur in the preseni analysis. These are the condition on solid, condition across coordinate cut and mflow/outflow conditions in the far field. 4.1. SOLID BODY BOHNDARY CONDITION On a solid body the pbvsica) condition of no-normal-floAV is imposed. 1'sing a body-iltted coordinate system (X.Y). the body coineiding with a coordinale üne is approximated by straighı Hnes in the fînite volume discrctization. Hence. tlıe no-nonnal-ilovv condition reduces to zero ilux velocity tbrough the faces oi the cells aligned with the body. 5. DISSIPATION llıe iînite N'olumediseretization (3.3) with central a\*eragmg is not dissipative which means that high irequency oscillations in the soîution. are nol damped. in order to avoid tlıese spurious oscillations dissipati\-e terrns ha\& lo be explicitly introdueed. If no artifıeial dissipative terrns are introduced in the scheme, the nıımerical soîution does not converge to a stead}' state. Having esecuted 2000 time steps these are stili wiggles in the pressure distribution. \\'ith dissipation, lıoue\'er, the soîution converges coraplelely to the steady stafe (1x10“7) and the pressure distribution is snıooth. 5.1. BLENDING OF FIRST AND THIRI) ORDER DISSIPATI\rE TERMS in order to preserve the consen'ation fonn of the scheme the artificial dissipali\e temıs are introduced by adding dissipati\re iluxes to the semi- discrete system (3.3). hJ^V*) + (V&*-°(5.1) \ Cllt l'sing a blend of second and fottrth diflerences, the dissipati\e operatör İ),} is dcfıned by D. = d,..-d. +d,. -d.,(5.2) '..t'*”..!I '.l'O1.“1..I J.v'where thc dissipative ilux d, is giren as İV ^,i=^^{^fe,-%> (5.3) ^”(^,1-3Wno + 3Wo-W,,J| 6. T1MKSTKPPINGSCHKMES Semi-discretization ol* ecjuation (2.6) results in a systevn ol“ first order ordinary differential equations with respect to time uhich is tvritten as 1%+^ = °(6-1) \\here ^-^(Oıj-Ûj(6-2) The operatör P is often called the residual of system (6.1). System (6J) is solved using explicit multistage schemes of Runge-Kutta type. CX)NC'LI:,S1ONS The codc usod con\:ergcs if thc viscosity eflbcts of thc llovv arc neyligable. Iha can V>c clearlv secn at thc 1wo dimcnsional llo\v in a no/zlc. This sludy shou's that Luler equalioııs and artifıcial viscosity arc insulfıcient lo sol ve the ilow het\\ een suddenly enlarge parallel tu o plates. Because of the rcal \ iscosity and the no-slip conditions this problem can only be handled with solying oi'Na\'ier-Stokes equations.Tlıree distinct type of conditions occur in the preseni analysis. These are the condition on solid, condition across coordinate cut and mflow/outflow conditions in the far field. 4.1. SOLID BODY BOHNDARY CONDITION On a solid body the pbvsica) condition of no-normal-floAV is imposed. 1'sing a body-iltted coordinate system (X.Y). the body coineiding with a coordinale üne is approximated by straighı Hnes in the fînite volume discrctization. Hence. tlıe no-nonnal-ilovv condition reduces to zero ilux velocity tbrough the faces oi the cells aligned with the body. 5. DISSIPATION llıe iînite N'olumediseretization (3.3) with central a\*eragmg is not dissipative which means that high irequency oscillations in the soîution. are nol damped. in order to avoid tlıese spurious oscillations dissipati\-e terrns ha\& lo be explicitly introdueed. If no artifıeial dissipative terrns are introduced in the scheme, the nıımerical soîution does not converge to a stead}' state. Having esecuted 2000 time steps these are stili wiggles in the pressure distribution. \\'ith dissipation, lıoue\'er, the soîution converges coraplelely to the steady stafe (1x10”7) and the pressure distribution is snıooth. 5.1. BLENDING OF FIRST AND THIRI) ORDER DISSIPATI\rE TERMS in order to preserve the consen'ation fonn of the scheme the artificial dissipali\e temıs are introduced by adding dissipati\re iluxes to the semi- discrete system (3.3). hJ^V*) + (V&*-°(5.1) \ Cllt l'sing a blend of second and fottrth diflerences, the dissipati\e operatör İ),} is dcfıned by D. = d,..-d. +d,. -d.,(5.2) '..t'*“..!I '.l'O1.”1..I J.v'where thc dissipative ilux d, is giren as İV ^,i=^^{^fe,-%> (5.3) ^“(^,1-3Wno + 3Wo-W,,J| 6. T1MKSTKPPINGSCHKMES Semi-discretization ol* ecjuation (2.6) results in a systevn ol”first order ordinary differential equations with respect to time uhich is tvritten as 1%+^ = °(6-1) \\here ^-^(Oıj-Ûj(6-2) The operatör P is often called the residual of system (6.1). System (6J) is solved using explicit multistage schemes of Runge-Kutta type. CX)NC'LI:,S1ONS The codc usod con\:ergcs if thc viscosity eflbcts of thc llovv arc neyligable. Iha can V>c clearlv secn at thc 1wo dimcnsional llo\v in a no/zlc. This sludy shou's that Luler equalioııs and artifıcial viscosity arc insulfıcient lo sol ve the ilow het\\ een suddenly enlarge parallel tu o plates. Because of the rcal \ iscosity and the no-slip conditions this problem can only be handled with solying oi'Na\'ier-Stokes equations.
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