CN203404014U - Low-head hydraulic and pneumatic conversion device - Google Patents

Abstract

The utility model relates to a low-head hydraulic and pneumatic conversion device. The device comprises: an ascending tube which is arranged on the high water level side of a mill weir and connected with a baffling tube, the baffling tube is connected with a descending tube which is arranged on the low water level side of the mill weir, a ventilation point is arranged on the descending tube and connected with a suction tube of an air turbine, and the air turbine is connected with a power generator. The maximum system output efficiency is used as the design start and various constraints are set, so that two optimized most basic parameters of a siphon hydraulic and pneumatic conversion device (hydraulic air pump) are calculated: the height of the ventilation point and the cross section of a siphon. Compared with the traditional siphon hydraulic and pneumatic conversion device, the device is simpler and more practical. The result of the suggested hydraulic and pneumatic conversion efficiency calculation method is closer to the actual measurement value, so that the practical application of the hydraulic air pump is theoretically promoted. The theoretical study shows that, the efficiency of the hydraulic and pneumatic conversion device can be up to 86%.

Description

A kind of low water head liquid gas energy conversion equipment

Technical field

The utility model relates to a kind of low water head liquid gas energy conversion equipment, is a kind of device of transformation of energy, is that a kind of flow energy by low water head is converted to the device that gas can generate electricity or draw water.

Background technique

Water can be current unique renewable energy sources that can large-scale commercial applications exploitation in the world.Hydroelectric resources technical expectation that can exploitation amount in the whole world is 15000TWh/, but only about half of, i.e. 6000-9000TWh/, and being considered at present can not economic development.The head that main cause is these hydroelectric resources is low, and power is little.Although utilize water turbine water can be able to be changed into electric energy, system system efficiency often can only reach 40% left and right, and it is uneconomical that the high investment cost of device specific power usually makes to build hydroelectric power plant, thereby be not also utilized to so far generating.Waterpower air pump is the system that a kind of high efficiency, low cost utilizes micro-head generating.This system is a kind ofly can utilize the low water head that comprises ocean wave energy, or the renewable energy sources new technology of utmost point low water head generating.Waterpower air pump relies on syphon tube liquid gas energy transfer principle under certain condition, can convert water to gas energy, then can utilize air turbine that gas can be converted to mechanical energy generating or draw water.

Different from traditional water turbine power station, air turbine can be arranged the place being arranged on away from river course, the river rising Flood Control Problem that can avoid flood to cause, and factory building construction investment is few; And because only have syphon tube in water, there is no moving element, maintenance cost is low.In addition, compare with water turbine, the air turbine rotating speed of same power is usually several times of water turbine, even tens times.On the other hand, the turbine volume of the air turbine that waterpower air pump uses is very little, and for given power stage, the cost of less High Rotation Speed machine transmitted power is lower.The most important thing is at head, to only have the place of 0.5-2m, the waterpower air pump efficiency based on siphon can reach 70% left and right, and the efficiency of air turbine can reach more than 85%.In other words, can convert low water head water to gas energy, then utilize total efficiency that air turbine produces mechanical energy more than 60%, and the efficiency of the conventional water turbine of corresponding low water head is between 60%-70%, both efficiency are very approaching.For these reasons, waterpower air pump system should have business market prospect widely.

In order to predict efficiency and the power of waterpower air pump system, French and Widden derive and obtain the analytic solutions of a waterpower air pump efficiency.In the process of analyzing, what they supposed syphon tube section can guarantee that along Cheng Bianhua the flow velocity of current is constants.Under steady flow condition, because hydraulic pressure in pipe can increase along with the decline of position height, thereby cause the compression of section bubble volume, under the negligible condition of water body compressibility, in order to meet flow rate of water flow along the constant assumed condition of journey, conduit section must reduce along with the minimizing of elevation.Should say, their method is very helpful at the aspect of performance of understanding waterpower air pump, but also may lead to misunderstanding, and people is thought design of siphon pipes is become can obtain higher efficiency like this.Howey and Pullen have carried out preliminary test to such siphonic system, have checked the difference of theoretical prediction and efficiency by inputoutput test, and result shows to use efficiency and the power of model prediction of French and Widden higher.

Summary of the invention

In order to overcome the problem of prior art, the utility model proposes a kind of low water head liquid gas energy conversion equipment.Described device is a kind of waterpower air pump of optimal design.

The purpose of this utility model is achieved in that a kind of low water head liquid gas energy conversion equipment, described device comprises: the ascending tube that is arranged on mill weir high water level one side, described ascending tube is connected with baffle pipe, described baffle pipe is connected with the down tube of mill weir low water level one side, ventilation point is set on described down tube, the sucking pipe that connects air turbine is set on described ventilation point, and described air turbine is connected with generator, and the position of described ventilation point on down tube is:

$z_A=z_C+H+\frac{p_C-p_A}{\mathrm{\ρg}}-[L_A+{\left(\frac{n}{1-{\mathrm{\α}}_A}\right)}^2+(L_C-1){\left(\frac{n}{1-{\mathrm{\α}}_C}\right)}^2]\frac{{V_1}^2}{2g}$

Described siphonal sectional area is:

A ₁＝A＝Q/V ₁

In formula: z _athe position elevation of-ventilation point, z _cthe position elevation of-down tube outlet, H-acting head, p _athe pressure of-ventilation point, p _cthe pressure of-water outlet, L _a-ventilation point local head loss coefficient, α _athe voids at-ventilation point place, a n-ventilation point upstream and downstream pipeline area ratio, when syphon tube basal area is along Cheng Xiangtong n=1, L _c-water outlet local head loss coefficient, V ₁-ascending tube flow velocity, α _cthe voids of-water outlet, g-gravity accleration, the density of ρ-water, A ₁the syphon tube sectional area of-ventilation point, A-down tube sectional area, Q-flow.

The beneficial effect that the utility model produces is: device described in the utility model is design starting point to the maximum with system delivery efficiency, set each constraint conditio, with this, release the basic parameter of two optimizations of syphon tube liquid-gas transfer device (waterpower air pump): height and the siphonal sectional area of ventilation point.Compare with traditional syphon tube liquid-gas transfer device, device described in the utility model is simpler, practical.The liquid gas shift efficiency calculation method proposing is more approaching with actual measurement, has promoted theoretically the practical application of waterpower air pump.Theoretical research shows, according to the efficiency maximum of liquid-gas transfer device described in the utility model, can reach 86%.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the utility model is described in further detail.

Fig. 1 is the structural representation of device described in embodiment one of the present utility model;

Fig. 2 is z described in embodiment two of the present utility model _aowith α _arelation curve with H;

Fig. 3 is z described in embodiment three of the present utility model _aowith α _awith H relation curve.

Embodiment

Embodiment one:

The present embodiment is a kind of low water head liquid gas energy conversion equipment, as shown in Figure 1.Device described in the present embodiment comprises: the ascending tube 1 that is arranged on mill weir 2 high water level one sides, described ascending tube is connected with baffle pipe 3, described baffle pipe is connected with the down tube 6 of mill weir low water level one side, ventilation point 4 is set on described down tube, the sucking pipe that connects air turbine 5 is set on described ventilation point, described air turbine is connected with generator, and the position of described ventilation point on down tube is:

$z_A=z_C+H+\frac{p_C-p_A}{\mathrm{\ρg}}-[L_A+{\left(\frac{n}{1-{\mathrm{\α}}_A}\right)}^2+(L_C-1){\left(\frac{n}{1-{\mathrm{\α}}_C}\right)}^2]\frac{{V_1}^2}{2g}$

Described siphonal sectional area is:

A ₁＝A＝Q/V ₁

In formula: z _athe position elevation of-ventilation point, z _cthe position elevation of-down tube outlet, H-acting head (water-heads of mill weir both sides), p _athe pressure of-ventilation point, p _cthe pressure of-water outlet, L _a-ventilation point local head loss coefficient, α _athe voids at-ventilation point place, n-ventilation point upstream and downstream pipeline area compares n=A ₁/ A, when syphon tube basal area is along Cheng Xiangtong n=1, L _c-water outlet local head loss coefficient, V ₁-ascending tube flow velocity, α _cthe voids of-water outlet, g-gravity accleration, the density of ρ-water, A ₁the syphon tube sectional area of-ventilation point, A-down tube sectional area, Q-flow.

Ascending tube described in the present embodiment, baffle pipe and down tube form complete syphon tube, use line pipe, baffle pipe and these nouns of down tube, just, in order to narrate conveniently, there is no other particular meanings.Syphon tube described in the present embodiment is drawn to from the high one end 9 of mill weir water level one end 7 that mill weir water level is low by water, and whole siphonal water pipe diameter is consistent, and the diameter dimension of three sections of pipes is identical.Reference level 8 is base level faces that position elevation calculates, such as sea level.

When current flow in syphon tube, can in syphon tube, produce negative pressure, therefore, the present embodiment arranges ventilation point at the connection part of syphon tube baffle pipe and down tube.In Fig. 1, with the A of letter capitalization, represent the position of ventilation point, the A that expresses syphon tube sectional area here in the A of capitalization and each embodiment of the utility model is not a concept, in the footnote that the capitalization A here and the capitalization C of water outlet occur, represent position, for example: α _arepresent that ventilation point voids is A point voids; And α _cthe voids that represents water outlet, i.e. C point voids.

The air sucking at ventilation point must be appropriate, too much just may make syphon tube cutout, mechanical efficiency is low at least.Described turbo machine can be axial flow air turbine, can be also radial inflow air turbine.Air turbine described in the present embodiment is different from steam turbine and is also different from gas turbine.These two kinds of turbo machines are by concentrating the dynamic air-flow ejecting to promote.Air turbine described in the present embodiment is the power being produced by the air stream sucking.Therefore, the air turbine described in the present embodiment and steam turbine and gas turbine have obvious difference in shape.The blade of the inlet end of steam turbine and gas turbine is less, and outlet side blade is larger.And air turbine described in the present embodiment is just in time contrary, the blade of inlet end is larger, and the blade of outlet side is less.

Embodiment two:

The present embodiment is the improvement of implementing embodiment one, is that embodiment one is about the refinement of air turbine.Air turbine described in the present embodiment is a kind of in axial flow turbine or radial-inward turbine.

Radial-inward turbine described in the present embodiment is for traditional radial outward flow turbine.In traditional radial outward flow turbine, air mobile is first along the axial flow at turbine center, then on turbine face, turns, and with centrifugal form, from the center of turbine along turbine radially, from turbine edge, flows out.This type of flow is because the air stream with kinetic energy is to become diffusion from concentrating in traditional turbo machine.And in air turbine described in the present embodiment with the air-flow direction of kinetic energy be have disperse to become concentrated.Its air flowing on turbine face is just contrary: be to enter turbine by turbine edge, turn after focusing on turbine center, along turbine central axis, move, therefore, be called radial-inward turbine.

Research shows, in the waterpower air pump system described in the present embodiment, uses radial inflow air turbine than the better effects if of using axial flow air turbine, and efficiency is higher.

Embodiment three:

The present embodiment is the design method of low water head liquid gas energy conversion equipment described in above-described embodiment, and the step of described method is as follows:

Calculate the step of mean velocity in section of voids, pressure and the ascending tube current of ventilation point: for take maximize water can be converted to gas can efficiency eta be according to the voids, pressure and the flow velocity that calculate ventilation point, according to maximum efficiency formula:

$\max \left\{\mathrm{\η}(p_A,V_1,{\mathrm{\α}}_A)\right\}=\max \left\{\frac{k}{k-1}\frac{p_A}{\mathrm{ng}{\mathrm{\ρ}}_{w}H}({\left(\frac{p_a}{p_A}\right)}^{(k-1)/k}-1){\mathrm{\α}}_A(\frac{n}{1-{\mathrm{\α}}_A}-\frac{V_r}{V_1})\right\}$

The constraint conditio that maximizes η is:

$H=K\frac{{V_1}^2}{2g}+B---\left[1\right]$

$K=L_A+n^2(\frac{L_C}{{(1-{\mathrm{\α}}_C)}^2}+\frac{L_{\mathrm{AC}}}{{(1-{\mathrm{\α}}_A)}^2})---\left[2\right]$

$B=\frac{c_1}{\mathrm{\ρg}}[\frac{1}{V_r+c_2}\ln \frac{(c_2+V_r{\mathrm{\α}}_A)(1-{\mathrm{\α}}_C)}{(1-{\mathrm{\α}}_A)(c_2+V_r{\mathrm{\α}}_C)}-\frac{1}{c_2}\ln \frac{(c_2+V_r{\mathrm{\α}}_A){\mathrm{\α}}_C}{(c_2+V_r{\mathrm{\α}}_C){\mathrm{\α}}_A}-\frac{1}{c_2+V_r{\mathrm{\α}}_A}+\frac{1}{c_2+V_r{\mathrm{\α}}_C}]---\left[3\right]$

${\mathrm{\α}}_C=\frac{-(c_1+c_2{p}_C)+\sqrt{{(c_1+c_2{p}_C)}^2+4c_1{V}_r{p}_C}}{2V_r{p}_C}---\left[4\right]$

$c_1=p_A{\mathrm{\α}}_A(n\frac{V_1}{(1-{\mathrm{\α}}_A)}-V_r)---\left[5\right]$

c ₂＝nV ₁-V _r [6]

0＜α _A＜0.3?[7]

p _A＞p _v [8]

In formula: α _athe voids at-ventilation point place, p _athe pressure at-ventilation point place, V ₁-ascending tube flow velocity, p _vthe vaporization pressure of-local liquid, is known quantity, and H-acting head is known quantity, L _a-ventilation point local head loss coefficient, is known quantity, L _c-water outlet local head loss coefficient, is known quantity, L _aC-ventilation point, to the pipeline head loss coefficient between water outlet, is known quantity, p _a-local atmospheric pressure, is known quantity, ρ _a-air density, is known quantity, and k-gas adiabatic exponent is known quantity, and g-gravity accleration is known quantity, V _rthe speed difference of-current and air-flow, is known quantity, and a n-ventilation point upstream and downstream pipeline area ratio, when syphon tube section area is along Cheng Xiangtong n=1, p _cthe pressure of-water outlet is got p in process of calculation analysis _c=p _afor known quantity, use two layers of optimization to calculate the voids α of ventilation point A _a, pressure p _a, ascending tube current mean velocity in section V ₁;

Calculate the step of ventilation point height: for passing through formula:

$z_A=z_C+H+\frac{p_C-p_A}{\mathrm{\ρg}}-[L_A+{\left(\frac{n}{1-{\mathrm{\α}}_A}\right)}^2+(L_C-1){\left(\frac{n}{1-{\mathrm{\α}}_C}\right)}^2]\frac{{V_1}^2}{2g}$

Calculate the position height of ventilation point in syphon tube down tube;

Calculate the step of syphon tube sectional area: for passing through formula:

A ₁＝A＝Q/V ₁

Calculate siphonal sectional area.

The basic ideas of the present embodiment are by studying the optimum efficiency of conventional syphon tube liquid gas shift (waterpower air pump), obtain the optimised form of liquid-gas transfer device.Conventional siphonic system refers to the syphon tube system that caliber is constant along journey, and as shown in Figure 1, wherein in down tube gas-liquid mixture, the mean velocity in section of current is variablees, rather than constant.

For the ease of analyzing, suppose: mobile in syphon tube is steady flow; Gas is temperature-resistant in flow process; The compressibility of water body can be ignored.Analyze the mathematical model of using:

1, the relation of voids and hydraulic pressure and flow velocity:

When representing voids with α, i.e. the ratio of the volume of air and control volume volume in control volume shown in Fig. 1, the averag density of control volume gas-liquid mixture is

ρ _e＝αρ _a+ρ(1-α)≈ρ(1-α) (1)

In formula: ρ _ethe averag density of=gas-liquid mixture, kg/m ³; ρ _a=gas density, kg/m ³; The density of ρ=water, kg/m ³.The test of Wallis (1969) shows, when α > 0.3, bubble causes siphon flow disruption with regard to Hui Bian great, so maintain two mobile necessary conditions of normal gas-liquid, is α < 0.3.

When gas is considered as to perfect gas, equation of state of gas can be expressed as

In formula: the pressure of p=fluid, Pa; m ³; The quality of m=gas, kg; R=universal gas constant; The kelvin temperature of T=gas, ℃.

For steady flow, the throughput of two section air of down tube AC section is

Q _a＝αA(V-V _r)＝α _AA(V _A-V _r) (3)

In formula: Q _a=throughput, m ³/ s; The mean velocity of V=section current, m/s; A=cross-sectional area, m ²; V _rthe speed difference of=current and air-flow, m/s; Subscript A=ventilation point A Outlet Section, i.e. AC section admission section.

The volume of gas in unit time

the function relation that can be obtained voids and hydraulic pressure by formula (2) is

pαA(V-V _r)＝p _Aα _AA(V _A-V _r) (4)

The equation of continuity of down tube current can be described as

VA(1-α)＝V _AA(1-α _A)＝V ₁A ₁ (5)

In formula: V ₁and A ₁mean velocity and the area of=ascending tube (ventilation point A upstream line).

From formula (5), can obtain

$V_A=\frac{V_1{A}_1}{A(1-{\mathrm{\&alpha;}}_A)}=n\frac{V_1}{(1-{\mathrm{\&alpha;}}_A)}---\left(6\right)$

$V=\frac{V_1{A}_1}{A(1-\mathrm{\&alpha;})}=n\frac{V_1}{(1-\mathrm{\&alpha;})}---\left(7\right)$

In formula:

for constant, when siphonic system caliber is constant along journey, n=1.

Wushu (6) and formula (7) substitution formula (4)

$p=\frac{p_A{\mathrm{\&alpha;}}_A(n\frac{V_1}{(1-{\mathrm{\&alpha;}}_A)}-V_r)}{\mathrm{\&alpha;}(n\frac{V_1}{(1-\mathrm{\&alpha;})}-V_r)}---\left(8\right)$

Arrange

$p=\frac{c_1(1-\mathrm{\&alpha;})}{\mathrm{\&alpha;}(c_2+V_r\mathrm{\&alpha;})}---\left(9\right)$

In formula: $c_1=p_A{\mathrm{\&alpha;}}_A(n\frac{V_1}{(1-{\mathrm{\&alpha;}}_A)}-V_r),$ c ₂＝nV ₁-V _r。

Formula (9) can be rewritten as

V _rα ²p+(c ₁+c ₂p)α-c ₁＝0

Solve

$\mathrm{\&alpha;}=\frac{-(c_1+c_{2}p)+\sqrt{{(c_1+c_{2}p)}^2+4c_1{V}_{r}p}}{2V_{r}p}---\left(10\right)$

For AC section, p _a, α _a, V ₁be import boundary conditions, can think known quantity.

The research of French and Widden (2001) shows, V _rchange very littlely, can think constant, V _r≈ 0.25m/s.Like this, to formula (9) differential, can obtain

$\mathrm{dp}=-c_1\{\frac{1}{\mathrm{\&alpha;}(c_2+V_r\mathrm{\&alpha;})}+\frac{(1-\mathrm{\&alpha;})(c_2+2V_r\mathrm{\&alpha;})}{{\left[\mathrm{\&alpha;}(c_2+V_r\mathrm{\&alpha;})\right]}^2}\}\mathrm{d\&alpha;}---\left(11\right)$

2, breather line momentum equation:

The pipeline section frictional loss of Fig. 1 Liquid Flow and gravity item are relatively very little, can concentrate reduction in the loss item of upstream and downstream.When reverse as a reference with flow direction, the momentum equation of control volume can be described as

$\mathrm{pA}-(\mathrm{pA}+A\frac{\mathrm{dp}}{\mathrm{dz}}\mathrm{\&delta;z})-g{\mathrm{\&rho;}}_e\mathrm{A\&delta;z}={\mathrm{\&rho;}}_e\mathrm{AV}\frac{\mathrm{dV}}{\mathrm{dz}}\mathrm{\&delta;z}---\left(12\right)$

In formula: A=pipeline area, m ².The above formula equal sign left side: first is the water pressure that acts on control volume bottom, and second is the water pressure that acts on control volume top, and the 3rd is the gravity acting on control volume.Equal sign the right is the change amount of water body momentum.

Wushu (1) substitution formula (12) can obtain

$-\mathrm{dp}-\frac{\mathrm{\&alpha;}}{1-\mathrm{\&alpha;}}\mathrm{dp}-\mathrm{\&rho;gdz}=\mathrm{\&rho;VdV}---\left(13\right)$

Wushu (11) substitution (13)

$-\frac{\mathrm{dp}}{\mathrm{\&rho;g}}+\frac{c_1}{\mathrm{\&rho;g}}\{\frac{1}{(c_2+V_r\mathrm{\&alpha;})(1-\mathrm{\&alpha;})}+\frac{(c_2+2V_r\mathrm{\&alpha;})}{\mathrm{\&alpha;}{(c_2+V_r\mathrm{\&alpha;})}^2}\}\mathrm{d\&alpha;}-\mathrm{dz}=\frac{\mathrm{VdV}}{g}---\left(14\right)$

Formula (14) integration is obtained

$-\frac{1}{\mathrm{\&rho;g}}\underset{p_C}{\overset{p_A}{\&Integral;}}\mathrm{dp}+\frac{c_1}{\mathrm{\&rho;g}}\underset{{\mathrm{\&alpha;}}_C}{\overset{{\mathrm{\&alpha;}}_A}{\&Integral;}}\{\frac{1}{(c_2+V_r\mathrm{\&alpha;})(1-\mathrm{\&alpha;})}+\frac{(c_2+2V_r\mathrm{\&alpha;})}{\mathrm{\&alpha;}{(c_2+V_r\mathrm{\&alpha;})}^2}\}\mathrm{d\&alpha;}-\underset{z_C}{\overset{z_A}{\&Integral;}}\mathrm{dz}=\frac{1}{g}\underset{V_C}{\overset{V_A}{\&Integral;}}\mathrm{VdV}---\left(15\right)$

Can obtain

$-\frac{p_A-p_C}{\mathrm{\&rho;g}}+B-(z_A-z_C)=\frac{V_A^2-V_C^2}{2g}---\left(16\right)$

In formula:

$B=\frac{c_1}{\mathrm{\&rho;g}}\underset{{\mathrm{\&alpha;}}_C}{\overset{{\mathrm{\&alpha;}}_A}{\&Integral;}}\{\frac{1}{(c_2+V_r\mathrm{\&alpha;})(1-\mathrm{\&alpha;})}+\frac{(c_2+2V_r\mathrm{\&alpha;})}{\mathrm{\&alpha;}{(c_2+V_r\mathrm{\&alpha;})}^2}\}\mathrm{d\&alpha;}=$

$=\frac{c_1}{\mathrm{\&rho;g}}{[\frac{1}{V_r+c_2}\ln \frac{c_2+V_r\mathrm{\&alpha;}}{1-\mathrm{\&alpha;}}-\frac{1}{c_2}\ln \frac{c_2+V_r\mathrm{\&alpha;}}{\mathrm{\&alpha;}}-\frac{1}{c_2+V_r\mathrm{\&alpha;}}]}_{{\mathrm{\&alpha;}}_C}^{{\mathrm{\&alpha;}}_A}$

Arrange

$B=\frac{c_1}{\mathrm{\&rho;g}}[\frac{1}{V_r+c_2}\ln \frac{(c_2+V_r{\mathrm{\&alpha;}}_A)(1-{\mathrm{\&alpha;}}_C)}{(1-{\mathrm{\&alpha;}}_A)(c_2+V_r{\mathrm{\&alpha;}}_C)}-\frac{1}{c_2}\ln \frac{(c_2+V_r{\mathrm{\&alpha;}}_A){\mathrm{\&alpha;}}_C}{(c_2+V_r{\mathrm{\&alpha;}}_C){\mathrm{\&alpha;}}_A}-\frac{1}{c_2+V_r{\mathrm{\&alpha;}}_A}+\frac{1}{c_2+V_r{\mathrm{\&alpha;}}_C}]---\left(17\right)$

With French and Widden (2001) similarly, B is the head that the buoyancy due to bubble produces, and is called buoyancy head.

By formula (10), can be obtained

${\mathrm{\&alpha;}}_C=\frac{-(c_1+c_2{p}_C)+\sqrt{{(c_1+c_2{p}_C)}^2+4c_1{V}_r{p}_C}}{2V_r{p}_C}---\left(18\right)$

Formula (16) can be rewritten as

$(\frac{p_A}{\mathrm{\&rho;g}}+z_A+\frac{V_A^2}{2g})-(\frac{p_C}{\mathrm{\&rho;g}}+z_C+\frac{V_C^2}{2g})=B---\left(19\right)$

Above formula is exactly the momentum equation of ventilation syphon tube current.

When considering the loss of head of AC segment pipe, formula (19) can be rewritten as

$(\frac{p_A}{\mathrm{\&rho;g}}+z_A+\frac{V_A^2}{2g})-(\frac{p_C}{\mathrm{\&rho;g}}+z_C+\frac{V_C^2}{2g})=B+L_{\mathrm{AC}}\frac{V_A^2}{2g}---\left(20\right)$

In formula: L _aCthe loss of head coefficient of=AC section, local head loss's coefficient and friction factor of head loss.

3, siphonic system momentum equation:

In Fig. 1, syphon mouth does not have air in ventilation point A admission section pipeline section, according to bernoulli equation, can obtain

$\frac{p_a}{\mathrm{\&rho;g}}+z_1=\frac{p_A}{\mathrm{\&rho;g}}+z_A+\frac{V_A^2}{2g}+L_A\frac{{V_1}^2}{2g}---\left(21\right)$

In formula: p _a=water surface atmospheric pressure, Pa; z ₁=weir upper pool elevation, m; L _a=syphon mouth is to a loss of head coefficient for ventilation point A Outlet Section pipeline section, comprises local head loss's coefficient of micro-section of import local head loss coefficient, friction factor of head loss and ventilation point A.

C to the bernoulli equation of syphon tube outlet pipe section current is

$\frac{p_C}{\mathrm{\&rho;g}}+z_C+\frac{V_C^2}{2g}=\frac{p_a}{\mathrm{\&rho;g}}+z_2+L_C\frac{V_C^2}{2g}---\left(22\right)$

In formula: z ₂=weir the level of tail water, m; L _c=C, to the loss of head coefficient of syphon tube outlet pipe section, comprises outlet part and friction factor of head loss.

By formula (21) and formula (22), can be obtained

$(\frac{p_A}{\mathrm{\&rho;g}}+z_A+\frac{V_A^2}{2g})-(\frac{p_C}{\mathrm{\&rho;g}}+z_C+\frac{V_C^2}{2g})=H-(L_A\frac{{V_1}^2}{2g}+L_C\frac{V_C^2}{2g})---\left(23\right)$

In formula: H=z ₁-z ₂for acting head, i.e. the water-head of weir upstream and downstream, m.

Wushu (20) substitution formula (23) can obtain siphonic system momentum equation

$H=(L_A\frac{{V_1}^2}{2g}+L_C\frac{V_C^2}{2g}+L_{\mathrm{AC}}\frac{{V_A}^2}{2g})+B---\left(24\right)$

By formula (7), can be obtained

$V_C=n\frac{V_1}{(1-{\mathrm{\&alpha;}}_C)}---\left(25\right)$

Wushu (6) and formula (25) substitution formula (24) can obtain

$H=K\frac{{V_1}^2}{2g}+B---\left(26\right)$

In formula:

$K=L_A+n^2(\frac{L_C}{{(1-{\mathrm{\&alpha;}}_C)}^2}+\frac{L_{\mathrm{AC}}}{{(1-{\mathrm{\&alpha;}}_A)}^2})---\left(27\right)$

First, formula (26) the right is total loss of head that water flow produces, second buoyancy head that B is bubble.So formula (26) shows acting head H, drives head, equal the algebraic sum of the total loss of head of syphon tube and buoyancy head.Increase Throughput and can increase buoyancy phase, but can reduce water velocity V ₁.In addition, reduce siphonal resistance coefficient K and can increase flow rate of water flow.While there is no gas in pipeline, buoyancy head B=0, formula (27) is reduced to the Bernoulli energy equation of current, and therefore, the size of B has reflected that water can convert the size of gas energy to.In other words, formula (20) described water can be gentle can be each other function relation.

By formula (23), can be obtained

$z_A=z_C+H+\frac{p_C-p_A}{\mathrm{\&rho;g}}-[L_A+{\left(\frac{n}{1-{\mathrm{\&alpha;}}_A}\right)}^2+(L_C-1){\left(\frac{n}{1-{\mathrm{\&alpha;}}_C}\right)}^2]\frac{{V_1}^2}{2g}---\left(28\right)$

4, the input power of air turbine and efficiency:

The working procedure of gas in air turbine, due to gas and extraneous heat exchange seldom, can be similar to and regard adiabatic process as.The unit mass flow power E that can obtain air turbine consumption according to law of conservation of energy is:

$E=\frac{k}{k-1}\frac{p_2}{{\mathrm{\&rho;}}_{a2}}({\left(\frac{p_1}{p_2}\right)}^{(k-1)/k}-1)+g(z_1-z_2)+\frac{C_1^2-C_2^2}{2}---\left(29\right)$

In formula: k=gas adiabatic exponent, general desirable k=1.4; P=pressure, Pa; C=gas mean velocity, m/s; Z=elevation, m; Subscript 1 and 2 represents respectively the inlet/outlet section of air turbine.

In the ordinary course of things, have

$\frac{k}{k-1}\frac{p_2}{{\mathrm{\&rho;}}_{a2}}({\left(\frac{p_1}{p_2}\right)}^{(k-1)/k}-1)>>g(z_1-z_2)+\frac{C_1^2-C_2^2}{2}$

So E can be expressed as

$E=\frac{k}{k-1}\frac{p_2}{{\mathrm{\&rho;}}_{a2}}({\left(\frac{p_1}{p_2}\right)}^{(k-1)/k}-1)---\left(30\right)$

When not considering that air turbine is to the loss due to duct friction between siphonic system, p ₁≈ p _a(atmospheric pressure) and p ₂=p _a, like this, the input power of air turbine is

$P={\mathrm{\&rho;}}_{a2}{Q}_{a}E=\frac{k}{k-1}{p}_A({\left(\frac{p_a}{p_A}\right)}^{(k-1)/k}-1)Q_a---\left(31\right)$

In formula: the input power of P=air turbine, W; Q _a=enter the throughput of syphon tube ventilation point A.

By formula (3), can be obtained

$Q_a={\mathrm{\&alpha;}}_A{A}_A(V_A-V_r)={\mathrm{\&alpha;}}_A{A}_A(\frac{n}{1-{\mathrm{\&alpha;}}_A}{V}_1-V_r)$

So

$P=\frac{k}{k-1}{p}_A({\left(\frac{p_a}{p_A}\right)}^{(k-1)/k}-1){\mathrm{\&alpha;}}_A{A}_A(\frac{n}{1-{\mathrm{\&alpha;}}_A}{V}_1-V_r)---\left(32\right)$

Because the power of current is

P _w＝gρ _wHQ _w＝gρ _wHA ₁V ₁ (33)

So water can be converted to the efficiency of gas energy

$\mathrm{\&eta;}=\frac{P}{P_w}=\frac{k}{k-1}\frac{p_A}{\mathrm{ng}{\mathrm{\&rho;}}_{w}H}({\left(\frac{p_a}{p_A}\right)}^{(k-1)k}-1){\mathrm{\&alpha;}}_A(\frac{n}{1-{\mathrm{\&alpha;}}_A}-\frac{V_r}{V_1})---\left(34\right)$

5, the optimal design of waterpower air pump:

Waterpower air pump optimal design target is the efficiency eta maximum that water can be converted to gas energy,

$\max \left\{\mathrm{\&eta;}(p_A,V_1,{\mathrm{\&alpha;}}_A)\right\}=\max \left\{\frac{k}{k-1}\frac{p_A}{\mathrm{ng}{\mathrm{\&rho;}}_{w}H}({\left(\frac{p_a}{p_A}\right)}^{(k-1)/k}-1){\mathrm{\&alpha;}}_A(\frac{n}{1-{\mathrm{\&alpha;}}_A}-\frac{V_r}{V_1})\right\}---\left(35\right)$

Constraint conditio

$H=K\frac{{V_1}^2}{2g}+B---\left(36\right)$

$K=L_A+n^2(\frac{L_C}{{(1-{\mathrm{\&alpha;}}_C)}^2}+\frac{L_{\mathrm{AC}}}{{(1-{\mathrm{\&alpha;}}_A)}^2})---\left(37\right)$

$B=\frac{c_1}{\mathrm{\&rho;g}}[\frac{1}{V_r+c_2}\ln \frac{(c_2+V_r{\mathrm{\&alpha;}}_A)(1-{\mathrm{\&alpha;}}_C)}{(1-{\mathrm{\&alpha;}}_A)(c_2+V_r{\mathrm{\&alpha;}}_C)}-\frac{1}{c_2}\ln \frac{(c_2+V_r{\mathrm{\&alpha;}}_A){\mathrm{\&alpha;}}_C}{(c_2+V_r{\mathrm{\&alpha;}}_C){\mathrm{\&alpha;}}_A}-\frac{1}{c_2+V_r{\mathrm{\&alpha;}}_A}+\frac{1}{c_2+V_r{\mathrm{\&alpha;}}_C}]---\left(38\right)$

${\mathrm{\&alpha;}}_C=\frac{-(c_1+c_2{p}_C)+\sqrt{{(c_1+c_2{p}_C)}^2+4c_1{V}_r{p}_C}}{2V_r{p}_C}---\left(39\right)$

$c_1=p_A{\mathrm{\&alpha;}}_A(n\frac{V_1}{(1-{\mathrm{\&alpha;}}_A)}-V_r)---\left(40\right)$

c ₂＝nV ₁-V _r (41)

0＜α _A＜0.3?(42)

p _A＞p _v (43)

In formula: p _vthe vaporization pressure of=local liquid, Pa.In the process of optimal design, controlled variable or design parameter are: the voids α of down tube section A _a, pressure p _a, ascending tube current mean velocity in section V ₁.Known quantity is: acting head H, pipeline head loss coefficient L _a, L _c, L _aC, local atmospheric pressure p _a, air density ρ _a, gas adiabatic exponent k, gravity acceleration g, the speed difference V of current and air-flow _r, some A upstream and downstream pipeline area compares n.Desirable p in process of calculation analysis _c=p _afor known quantity.When syphon tube basal area is along journey phase while, n=1.

Observation type (36)-Shi (41), at given α _aand p _acondition under, buoyancy head B and α in formula (38) and formula (39) _cbe controlled variable V ₁function, and formula (37) in K be α _cfunction, so only have a unknown quantity V in formula (36) ₁, can solve V by numerical value iterative computation ₁.

Once determine the controlled variable α that makes maximizing efficiency _a, p _a, V ₁optimum value, by formula (28), can be determined the position elevation z of siphonic system suction port _a, and by A ₁=A=Q/V ₁determine siphonal sectional area, thereby determine the optimum design of siphonic system.

Obviously, waterpower air pump Optimized model belongs to nonlinear programming problem, has a variety of modes, such as: Bao Weier (Powell) algorithm with utilize the variation quantity algorithm etc. of difference coefficient, can adopt the method for numerical calculation to obtain its optimal solution.

In the process of design, desirable atmospheric pressure p generally _a=100000Pa, air density ρ _a=1.2kg/m ³, gas adiabatic exponent k=1.4, gravity acceleration g=9.8m/s ², the speed difference V of current and air-flow _r=0.25m/s.As shown in Figure 1, when hypothesis syphon tube inlet/outlet respectively arranges a butterfly valve, ascending tube local resistance item is comprised of import, a butterfly valve and two elbows, desirable L _a=1.3; Down tube resistance to flow output coefficient L _c=1; If L _aC=0.3.

Optimum efficiency η when Fig. 2 and Fig. 3 show respectively under these conditions given acting head H value _oand z _aowith α _aone-to-one relationship.Observe Fig. 2 and Fig. 3, at 0 < α _ain the interval of < 0.3, can draw following conclusion:

(1), when H≤1.5m, there is a α _avalue and z _aomake the efficiency of waterpower air pump maximum.Maximal efficiency excursion is 70%≤η _max≤ 86%, and acting head H is large, η _maxgreatly.

(2) when H > 1.7m, optimum efficiency η _oalong with voids α _aincrease and monotone increasing.In other words, adopt in this case larger α _acan improve the efficiency of waterpower air pump.

(3) when H>=2.0m, for given α _avalue, along with the increase of acting head H, optimum efficiency η _oto significantly reduce.

By above analysis, can draw following conclusion:

(1), when H≤1.5m, the maximal efficiency excursion of waterpower air pump is 70%≤η _max≤ 86%, and acting head H is large, η _maxgreatly.

(2) when H > 1.7m, optimum efficiency η _oalong with voids α _aincrease and monotone increasing.

(3) when H>=2.0m, for given α _avalue, along with the increase of acting head H, optimum efficiency η _oto significantly reduce.

Embodiment four:

The present embodiment is embodiment three improvement, that embodiment three is about the refinement of " calculating the voids of ventilation point, the pressure of ventilation point and the step of ascending tube flow velocity ", the present embodiment calculates voids, pressure and ascending tube flow velocity and uses two layers of loop optimization numeration, and described numeration comprises following sub-step:

1) input initial data, and make efficiency eta _o=0; For maximal efficiency;

2) first layer circulation starts: make controlled variable α _a=α _{a, i}=α _{a, 1}for initial value, wherein subscript i is cyclic variable;

3) second layer circulation starts: make controlled variable p _a=p _{a, j}=p _{a, 1}for the first value of establishing, wherein subscript j is cyclic variable;

4) solve controlled variable V ₁, numerical value iterative computation V ₁program be:

1. make V ₁=V ₁₀;

2. by formula

$c_1=p_A{\mathrm{\&alpha;}}_A(n\frac{V_1}{(1-{\mathrm{\&alpha;}}_A)}-V_r)$ And formula

c ₂＝nV ₁-V _r

Calculate respectively c ₁and c ₂, then by formula

${\mathrm{\&alpha;}}_C=\frac{-(c_1+c_2{p}_C)+\sqrt{{(c_1+c_2{p}_C)}^2+4c_1{V}_r{p}_C}}{2V_r{p}_C}$

Calculate α _c;

3. by formula

${\mathrm{\&alpha;}}_C=\frac{-(c_1+c_2{p}_C)+\sqrt{{(c_1+c_2{p}_C)}^2+4c_1{V}_r{p}_C}}{2V_r{p}_C}$

And formula

$B=\frac{c_1}{\mathrm{\&rho;g}}[\frac{1}{V_r+c_2}\ln \frac{(c_2+V_r{\mathrm{\&alpha;}}_A)(1-{\mathrm{\&alpha;}}_C)}{(1-{\mathrm{\&alpha;}}_A)(c_2+V_r{\mathrm{\&alpha;}}_C)}-\frac{1}{c_2}\ln \frac{(c_2+V_r{\mathrm{\&alpha;}}_A){\mathrm{\&alpha;}}_C}{(c_2+V_r{\mathrm{\&alpha;}}_C){\mathrm{\&alpha;}}_A}-\frac{1}{c_2+V_r{\mathrm{\&alpha;}}_A}+\frac{1}{c_2+V_r{\mathrm{\&alpha;}}_C}]$

Calculate respectively B and K; If H < is B, jump out the second circulation, turn step 7); Otherwise, by formula

$H=K\frac{{V_1}^2}{2g}+B$

Solve unknown quantity V ₁;

4. judgement | V ₁-V ₁₀|≤10 ^-3if set up, V ₁be exactly given α _{a, i}and p _{a, j}solution under condition, then turns next step; Otherwise, get V ₁₀=0.5 (V ₁+ V ₁₀), repeat to walk 2.-4.;

5) calculate respectively elevation z _aand efficiency eta=η (p _{a, j}, V _{1, i, j}, α _{a, i}), if η > is η _o, make: η _o=η, p _ao=p _{a, j}, α _ao=α _{a, i}, V _o=V ₁, z _ao=z _a;

6) continue second layer circulation: make j=j+1 and p _{a, j}=p _{a, j-1}-δ, wherein δ > 0 is fractional increments.If cyclic variable j is less than the CLV ceiling limit value of predetermining, turn step 4); Otherwise, turn next step;

7) continue first layer circulation: make i=i+1, and α _{a, i}=α _{a, i-1}+ ε, wherein ε > 0 is fractional increments.If cyclic variable i is less than the CLV ceiling limit value of predetermining, or α _{a, i}≤ 0.3, turn step 4); Otherwise, turn next step;

8) output optimal solution: η _o=η, p _ao=p _{a, j}, α _ao=α _{a, i}, V _o=V ₁, z _ao=z _a.Calculate and finish;

Wherein: subscript o represents optimum value optimal.As: η _orepresent the optimum value of η etc.

Finally it should be noted that, below only unrestricted in order to the technical solution of the utility model to be described, although the utility model is had been described in detail with reference to preferred arrangement scheme, those of ordinary skill in the art is to be understood that, can be to the technical solution of the utility model (such as the priority of siphonal form, computational process, the formula using etc.) modify or be equal to replacement, and not departing from the spirit and scope of technical solutions of the utility model.

Claims (2)

1. a low water head liquid gas energy conversion equipment, described device comprises: the ascending tube that is arranged on mill weir high water level one side, described ascending tube is connected with baffle pipe, described baffle pipe is connected with the down tube of mill weir low water level one side, ventilation point is set on described down tube, the sucking pipe that connects air turbine is set on described ventilation point, described air turbine is connected with generator, it is characterized in that, the position of described ventilation point on down tube is:

Siphonal sectional area is:

A ₁=A=Q/V ₁

In formula: z _athe position elevation of-ventilation point, z _cthe position elevation of-down tube outlet, H-acting head, p _athe pressure of-ventilation point, p _cthe pressure of-water outlet, L _a-ventilation point local head loss coefficient, α _athe voids at-ventilation point place, n-ventilation point upstream and downstream pipeline area ratio, when syphon tube basal area is along Cheng Xiangtong n=1, L _c-water outlet local head loss coefficient, V ₁-ascending tube flow velocity, α _cthe voids of-water outlet, g-gravity accleration, A ₁the syphon tube sectional area of-ventilation point, A-down tube sectional area, Q-flow.

2. device according to claim 1, is characterized in that, described air turbine is a kind of in axial flow turbine or radial-inward turbine.

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