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| 2. |
- Kung, C. S., et al.
(författare)
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Energy interpretation of hydraulic transients in pipelines
- 1993
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Ingår i: Journal of Hydraulic Research. - 0022-1686 .- 1814-2079. ; 31:6
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Tidskriftsartikel (refereegranskat)abstract
- The energy concept sheds light upon the hydraulic system that comprises the throttled surge tank, the tunnel and the penstock. The mathematical manipulation of the governing differential equations of water hammer yields an energy (power) equation in point form. By integration with respect to pipe distance, this relation is extended first to an individual pipe, then to the surge-tank system with branching connection. The system energy (power) equation states the relationship between the total (internal plus kinetic) energy, the convective energy, the work done on the system and the energy dissipation. A case study identifies the conversion between the internal and kinetic energy, and quantifies the behaviour and magnitudes of related energy components of the system.
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| 3. |
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| 4. |
- Yang, James, et al.
(författare)
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Large-amplitude oscillations in closed surge chamber
- 1992
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Ingår i: Journal of Hydraulic Research. - 0022-1686 .- 1814-2079. ; 30:3
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Tidskriftsartikel (refereegranskat)abstract
- The governing equations for surge oscillations in a closed surge chamber yield a second-order nonlinear differential equation for constant power. The surge stability is investigated by the direct method of Liapunov, which introduces the Liapunov function from the energy consideration. The nonlinear terms arising from large surges are included. The resulting stability criterion is demonstrated on a phase plane. For the equilibrium point of practical interest, the stability diagram specifies domains of asymptotic stability as a function of the safety factor of the surge-chamber. The diagram indicates that large-amplitude surges necessitate larger chamber size than that laid down by Svee for damping and the surge stability deteriorates with downward oscillations. By postulating sinusoidal surge motion, the critical chamber area is equal to the product of the critical area in case of small oscillations (Svee's formula) and a factor greater than 1.0. The factor is a function of surge amplitude and air cushion parameters for given turbine head. Stability criteria for open surge tanks can be obtained as special cases of those for closed ones.
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| 5. |
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| 6. |
- Yang, James, et al.
(författare)
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Stability of air-cushion surge tanks with throttling
- 1992
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Ingår i: Journal of Hydraulic Research. - 0022-1686 .- 1814-2079. ; 30:6
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Tidskriftsartikel (refereegranskat)abstract
- The throttling orifice is introduced into air-cushion surge chambers to improve stability. The presence of the orifice adds another nonlinear term to the dynamic system, and its effect becomes predominant for oscillations with large displacements. By means of linearization, the type of singularities in the phase plane and their stability criteria in case of small oscillations are identified. The nonlinear analysis by direct numerical integration indicates that the system manifests itself as Hopf bifurcation with the surge-chamber size as its controlling factor. The bifurcation point corresponds to Svee's stability criterion. Before bifurcation, an unstable limit cycle may occur around the equilibrium state of practical interest, and it defines the domain of asymptotic stability. After bifurcation, two limit cycles may occur. Because of the existence of the stable one, the chamber size can be smaller than that specified by the Svee criterion. The orifice has stabilizing effect on surge motions.
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