Статья поступила в редакцию 21.06.12. Ред. рег. № 1364
The article has entered in publishing office 21.06.12. Ed. reg. No. 1364
УДК 621.311
ИССЛЕДОВАНИЕ ГИДРОДИНАМИЧЕСКОГО ЭФФЕКТА УСИЛЕНИЯ МОЩНОСТИ И ЕГО МАСШТАБНОЕ МОДЕЛИРОВАНИЕ
Г. В. Трещалов
Инженерно-исследовательская группа «ЭРГ» Ташкент, Узбекистан, 100098, Кара-Камыш-2/1-3-43 Тел./факс: (99871) 2790590, e-mail: erg@list.ru
Заключение совета рецензентов: 21.07.12 Заключение совета экспертов: 30.07.12 Принято к публикации: 04.08.12
В настоящей статье анализируется возможность масштабного моделирования гидродинамического эффекта, возникающего в безнапорном потоке жидкости при его ускорении и переходе режима потока через критическое состояние.
Ключевые слова: критерии гидродинамического подобия, число Рейнольдса, число Фруда, гидравлический прыжок, эффект эжекции, энергия, мощность, гидравлика, критическая глубина.
RESEARCH INTO THE HYDRODYNAMIC EFFECT OF BOSTING POWER AND ITS FULL-SCALE MODELLING
G.V. Treshchalov
Engineering and Research Group "ERG" Kara-Kamish-2/1-3-43, Tashkent, 100098, Uzbekistan Tel./fax: (99871) 2790590; e-mail: erg@list.ru
Referred: 21.07.12 Expertise: 30.07.12 Accepted: 04.08.12
This article analyses the possibility of full-scale modelling of the hydrodynamic effect that appears in free hydraulic flow as a result of its acceleration and transition through a critical state.
Keywords: criteria of hydrodynamic similarity, Froude number, Reynolds number, ejection effect, hydrodynamics, turbulent, critical, sub critical, super critical, hydraulic jump, depth, effect, feedback.
Introduction
The articles [1], [3] and [5] have analysed the tests of a free-flow hydraulic turbine of an original design and also have substantiated and analysed a special hydrodynamic effect that appears in a free-flow stream of liquid, which is believed to be a reason for the fairly high specific power output of the above device.
Subsequently, it has emerged that a peculiarity of the hydrodynamic effect is that a local artificial level difference is created thanks to the flow's acceleration and that a hydraulic turbine that works on this principle does not slow down - in contrast to traditional free-flow hydraulic turbines - the outflowing stream by taking
away its kinetic energy, but accelerates it by extracting the potential energy. The described hydrodynamic effect has been subsequently termed in some publications as "Treshchalov's effect" - after the author who was the first to analyse it as an independent physical phenomenon and to publish its theoretical substantiation
[4], [5].
In addition, mathematical patterns of this effect have been developed in [1], and characteristic energy diagrams have been plotted. It has been shown that the characteristic feature of the effect is that its energy diagram has a strongly pronounced maximum for all input and output parameters - the entry and exit speeds and the flow depth (Fig. 1).
Международный научный журнал «Альтернативная энергетика и экология» № 11 (115) 2012 © Научно-технический центр «TATA», 2012
Рис. 1. Зависимость энергии от трех параметров: разницы уровней, входной скорости и входной эффективной глубины
для значений 0,9; 1,2; 1,5 и 1,8 м Fig. 1. Energy's dependence on three parameters: the difference in levels h, the entry speed V1 and the effective entry depth H1
(0.9, 1.2, 1.5 and 1.8 m)
In addition, the conditions for appearance of the effect and its sustained manifestation in a flow of liquid have been tentatively defined and an assessment of the options for using it to generate energy free-flow through free-flow hydraulic turbines has been provided.
The findings of article [1] have tentatively shown that the appearance of the described hydrodynamic effect in scaled-down hydrodynamic models is hardly noticeable and cannot be identified easily.
In this article, we will examine the possibilities of the effect's manifestation during full scale modeling in compliance with the principles of hydrodynamic similarity and will prove the findings mathematically.
Theoretical analysis
Some of the technical solution options for the turbines that use the hydrodynamic effect under analysis are provided in articles [2-3], [6-7]. Fig. 2 shows one of the simplest and easy-to-see model options for this type of turbine.
The hydraulic turbine consists of two undershot water wheels linked with a feedback mechanism, which is a chain or belt drive in this instance. The feedback ensures that the second wheel rotates somewhat faster than the first one, which is what accelerates the outflowing stream of water.
Explanation for Fig. 2: H1, H2 - the depth (potential head) of the inflowing and outflowing streams
respectively; V,2/2g , V22/2g - the velocity head of the inflowing and outflowing streams respectively; AE - the difference between the energy density of the inflowing and outflowing streams.
The device works based on the following principle: The working parts of the inflowing stream (left wheel) extract part of the kinetic energy from the stream and transmit it - with the help of the positive feedback (chain, belt) - to the working parts of the outflowing stream (right wheel), which give the outflowing stream additional acceleration.
Because the amount of water entering the device is equal to the amount of outflowing water, and the speed of the outflowing stream is higher than that of the inflowing stream, then the sectional area of the outflowing stream will be less than that of the inflowing stream. Therefore, its depth H2 will be less than the depth of the inflowing stream H1. The difference between the reach levels of the inflowing and outflowing streams that appears because of this releases potential energy, which is what the turbine generates as net energy.
Fig. 2 also shows the balance of energy at the entry and exit from the turbine. The figure shows that the potential head (depth) of the outflowing stream H2 decreases in relation to the inflowing - H1, whereas the velocity head (kinetic energy) V//2 g at the exit increases considerably in relation to the inflowing stream.
Рис. 2. Один из вариантов турбины и баланс энергии входного и выходного потоков Fig. 2. One of the variant of the device and energy balance at the exit from the device
International Scientific Journal for Alternative Energy and Ecology № 11 (115) 2012
© Scientific Technical Centre «TATA», 2012
Г.В. Трещалов. Исследование гидродинамического эффекта усиления мощности и его масштабное моделирование
The mathematical analysis made in [1] showed that after device the velocity and depth of outflowing stream are equal to the critical and a hydraulic jump appears on the exit of the device as a result of ejection effect [8]. In the hydraulic jump zone, there appears a shortage of the total specific energy of the flow (AE') in relation to the initial flow mode and the flow mode that sets in after the hydraulic jump.
It is precisely this part of the flow's energy that is taken by the turbine, and Fig. 2 shows that it is much greater than (several times as much) the full kinetic energy of the inflowing stream (V?¡2g). The scale of specific energies on Fig. 2 is shown in relation to the inflowing stream with the depth H1 = 1 m and the velocity V1 = 1 m/s. The figure clearly shows that after exit from the turbine the velocity head of the outflowing stream is exactly half the potential head - the depth of outflowing stream, which corresponds to the critical state of the outflowing stream.
The formula of flow's specific energy during appearance of this hydrodynamic effect has been developed in [1] on the basis of the basic laws of hydrodynamics - Bernoulli's equation (the law of conservation of energy) and the flow continuity equation (the law of conservation of mass) - which can be used for preliminary calculations of the energy characteristics of the turbines that work on this principle.
For convenience, we will show this formula here by converting the specific energy into the full energy extracted by the turbine from a flow of water per second for a prismatic channel with the width L.
E = PL ^HVg + H V- - f#HV)V j , (1)
where L is the effective width of the turbine across the flow; H is the effective depth of inflowing stream; V is the velocity of the inflowing stream; p is the density of fluid (water).
Let us analyse the power characteristics of turbines that use this effect. Calculate the power output of the turbine in watts according to the formula (1) for different rates of velocity and the effective depth of the input stream per one meter across the flow (Table 1).
From Table 1 it can be seen that the output flow speed of the stream equals 1.8 m/s and the depth equals 0.3 m, the state of the incoming flow is critical, as can be easily seen by inserting the data into the critical depth of flow formula [1], [4], [8]. As seen from the table, the additional output of turbine in this mode goes to zero. The table also shows that increasing the effective depth of the downstream turbine capacity increases in a nonlinear manner and has an extreme point.
The criteria of hydrodynamic similarity are used during modeling of hydraulic phenomena, of which the main ones are the Reynolds number and the Froude number, which should be the same for both the real object and the model.
Таблица 1
Мощность турбины (в ваттах) в зависимости от глубины и скорости входного потока
Table 1
Turbine output power (in watts), depending on the depth and speed of the input stream
Flow velocity (m/s) Depth (m)
0.3 0.6 0.9 1.2 1.5 1.8
0.3 144 672 1619 2998 4820 7090
0.6 167 930 2400 4624 7629 11436
0.9 128 934 2637 5329 9064 13883
1.2 66 779 2494 5357 9460 14864
1.5 14 542 2098 4897 9068 14703
1.8 0 291 1563 4108 8102 13670
However, as is shown in [8, p.476], it is impossible to achieve a complete hydrodynamic similarity between the model and the actual object because the similarity coefficients turn out to be different when b
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