• 대한기계학회논문집A
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• 제27권11호
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• pp.1824-1830
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• 2003

The vibrational system of this study is consisted of a rotating cantilever pipe conveying fluid and the tip mass. The equation of motion is derived by using the Lagrange equation. The influences of the rotating angular velocity and the velocity of fluid flow in a cantilever pipe have been studied on the dynamic characteristics of a rotating cantilever pipe by the numerical method. The effects of a tip mass on the dynamic response of a cantilever pipe are also studied. The tip-amplitude and maximum tip-deflection of each direction are directly proportional to the tip mass of the cantilever pipe in steady state. It identifies that the influence of the fluid velocity and the rotating angular velocity of the cantilever pipe give much variation the bending tip-displacement of steady state and the bending tip-displacement of non-steady state, respectively. The influence of the rotating angular velocity gives much the deflection of axial direction.

• 대한기계학회논문집B
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• 제29권4호
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• pp.495-503
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• 2005

Experiments were conducted in a low speed stationary annular cascade to investigate local heat transfer characteristics on the tip and shroud and the effect of inlet Reynolds number on the tip and shroud heat transfer. Detailed mass transfer coefficients on the blade tip and the shroud were obtained using a naphthalene sublimation technique. The turbine test section has a single stage composed of sixteen guide vanes and blades. The chord length and the height of the tested blade are 150 mm and about 125 mm, respectively. The blade has flat tip geometry and the mean tip clearance is about $2.5{\%}$of the blade chord. The inlet flow Reynolds number based on chord length and incoming flow velocity is changed from $1.0{\times}10^{5}\;to\;2.3{\times}10^{5}.$ to investigate the effect of Reynolds number. Flow reattachment after the recirculation near the pressure side edge dominates the heat transfer on the tip surface. Shroud surface has very intricate heat/mass transfer distributions due to complex flow patterns such as acceleration, relaminarization, transition to turbulent flow and tip leakage vortex. Heat/mass transfer coefficient on the blade tip is about 1.7 times as high as that on the shroud or blade surface. Overall averaged heat/mass transfer coefficients on the tip and shroud are proportional to $Re_{c}^{0.65}\;and\;Re_{c}^{0.71},$ respectively.

• 대한기계학회논문집B
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• 제30권11호
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• pp.1074-1083
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• 2006

In the present study, the effect of blade rotation on blade heat transfer is investigated by comparing with the heat transfer results for the stationary blade. The experiments are conducted in a low speed annular cascade with a single stage turbine and the turbine stage is composed of sixteen guide vanes and blades. The chord length and the height of the tested blade are 150 mm and about 125 mm, respectively. The blade has a flat tip and the mean tip clearance is 2.5% of the blade chord. A naphthalene sublimation method is used to measure detailed mass transfer coefficient on the blade. For the experiments, the inlet Reynolds number is $Re_c=1.5{\times}10^5$, which results in the blade rotation speed of 255.8 rpm. Blade rotation induces a relative motion between the blade and the shroud as well as a periodic variation of incoming flow. Therefore, different heat/mass transfer patterns are observed on the rotating blade, especially near the tip and on the tip. The relative motion reduces the tip leakage flow through the tip gap, which results in the reduction of the tip heat transfer. However, the effect of the tip leakage flow on the blade surface is increased because the tip leakage vortex is formed closer to the surface than the stationary case. The overall heat/mass transfer on the shroud is not affected much by the blade rotation.

• 대한기계학회논문집B
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• 제31권4호
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• pp.349-356
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• 2007

The present study investigated local heat/mass transfer characteristics on the tip of the rotating turbine blade with various incoming flow incidence angles. The experiments are conducted in a low speed annular cascade with a single stage turbine. The blade has a flat tip with a mean tip clearance of 2.5% of the blade chord. The incoming flow Reynolds number is $1.5{\times}10^5$ at design condition. To examine the effect of off-design condition, the experiments with various incidence angles ranging between $-15^{\circ}$ and $+7{\circ}$ were conducted. A naphthalene sublimation method is used to measure detailed mass transfer coefficient on the blade. The results indicated that the incidence angle strongly affects the behavior of tip leakage flow around the blade tip and consequently plays an important role in determining heat transfer characteristics on the tip. For negative incidence angles, the heat/mass transfer in the upstream region on the tip decreases by up to 20%. On the contrary, for positive incidence angles, much higher heat transfer coefficients are observed even with small increase of incidence angle.

• 대한기계학회논문집B
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• 제29권4호
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• pp.485-494
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• 2005

For the extensive investigation of local heat/mass transfer on the near-tip surface of turbine blade, experiments were conducted in a low speed stationary annular cascade. The turbine test section has a single stage composed of sixteen guide vanes and blades. The chord length and the height of the tested blade are 150 mm and about 125 mm, respectively. The blade has flat tip geometry and the mean tip clearance is about $2.5{\%}$ of the blade chord. Detailed mass transfer coefficient on the blade near-tip surface was obtained using a naphthalene sublimation technique. The inlet flow Reynolds number based on chord length and incoming flow velocity is changed from $1.0{\times}10^{5}\;to\;2.3{\times}10^{5}.$ Extremely complex heat transfer characteristics are observed on the blade surface due, to complicated flow patterns, such as flow acceleration, laminarization, transition, separation bubble and tip leakage flow. Especially, the suction side surface of the blade has higher heat/mass transfer coefficients and more complex distribution than the pressure side surface, which is related to the leakage flow. For all the tested Reynolds numbers, the heat/mass transfer characteristics on the turbine blade are the similar. The overall averaged $Sh_{c}$ values are proportional to $Re_{c}^{0.5}$ on the stagnation region and the laminar flow region such as the pressure side surface. However, since the flow is fully turbulent in the near-tip region, the heat/mass transfer coefficients are proportional to $Re_{c}^{0.8}.$

• 대한기계학회논문집B
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• 제30권5호
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• pp.446-456
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• 2006

The effect of relative position of the stationary turbine blade for the fixed vane has been investigated on blade tip and shroud heat transfer. The local mass transfer coefficients were measured on the tip and shroud fur the blade fixed at six different positions within a pitch. A low speed stationary annular cascade with a single turbine stage was used. The chord length of the tested blade is 150 mm and the mean tip clearance of the blade having flat tip is 2.5% of the blade chord. A naphthalene sublimation technique was used for the detailed mass transfer measurements on the tip and the shroud. The inlet flow Reynolds number based on chord length and incoming flow velocity is fixed to $1.5{\times}10^5$. The results show that the incoming flow condition and heat transfer characteristics significantly change when the relative position of the blade changes. On the tip, the size of high heat/mass transfer region along the pressure side varies in the axial direction and the difference of heat transfer coefficient is up to 40% in the upstream region of the tip because the position of flow reattachment changes. On shroud, the effect of tip leakage vortex on the shroud as well as tip gap entering flow changes as the blade position changes. Thus, significantly different heat transfer patterns are observed with various blade positions and the periodic variation of heat transfer is expected with the blade rotation.

• 한국소음진동공학회논문집
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• 제14권11호
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• pp.1115-1122
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• 2004

The paper discussed the effect of a tip mass on the stability of pipes on elastic foundations. Governing equations of motion are derived by extended Hamilton's principle, and the numerical scheme using finite element method is applied to obtain the discretized equations. With or without internal damping, the critical flow velocities of the pipes are investigated according to the variation of elastic foundation parameters and tip mass ratios. Also. the relationship between the eigenvalue branches and the corresponding flutter modes of the cantilevered pipes with a tip mass on the elastic foundations is fully investigated.

• 한국소음진동공학회논문집
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• 제20권11호
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• pp.1058-1063
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• 2010

The vibration analysis of a rotating cantilever beam with tip mass was studied by using DTM(differential transformation method). DTM is one of the numerical methods, for finding series solutions by transforming differential equations to algebraic ones similar with Laplace transform. The advantages of the DTM are that it is easy to understand and is effective in finding numerical solutions. Applying DTM, the natural frequencies of a rotating cantilever beam were obtained taking into consideration the effects of tip mass. Also, convergence study of DTM was performed to decide the number of terms used in eigenvalue problems. Numerical results obtained by DTM show good agreement with those by other methods. As a result, it is expected that DTM can be a useful method in vibration analysis such as that of a rotating cantilever beam with tip mass.

• 한국소음진동공학회논문집
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• 제19권6호
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• pp.569-574
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• 2009

The paper presents the influences of the external damping and the tip mass on dynamic stability of a vertical cantilevered pipe conveying fluid. In general, real pipe systems may have some valves and attached mechanical parts, which can be regarded as attached lumped masses and support-dampers. The support-dampers can be assumed as viscous dampers. The equations of motion are derived by energy expressions using extended Hamilton's principle, and some numerical results using Galerkin's method are presented. Critical flow velocities and stability maps of the pipe with external dampers and tip mass are obtained for various tip mass ratios, external damping coefficients and positions of the viscous dampers.

• 한국정밀공학회지
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• 제22권10호
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• pp.150-157
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• 2005

The vibration system in this study is consisted of a rotating cantilever pipe conveying fluid and a tip mass. The equation of motion is derived by using the Lagrange's equation. The influences of the rotating angular velocity and the velocity of fluid flow on the natural frequencies of a cantilever pipe have been studied by the numerical method. The effects of a tip mass on the natural frequencies of a rotating cantilever pipe are also studied. The influences of a tip mass, the velocity of fluid, the angular velocity of a cantilever pipe and the coupling of these factors on the natural frequency of a cantilever pipe are analytically clarified. The natural frequencies of a cantilever pipe conveying fluid are proportional to the angular velocity of the pipe in both axial direction and lateral direction.