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1. Salimdzhanov R. T., Lebedev O. V., Khakimzyanov R. R. Reliability growth of wheel cars. - Tashkent: TARI, 2007. - 338 p. (in Russian)
2. Malinowski V. S., Filjustin A. E., Bagramov M. G. Application of the theory of utility at distribution of requirements to reliability of a product between its elements on the basis of the account of their complexity.//Reliability and quality assurance. - 1988. -№ 11. - P. 7-11. (in Russian).
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Yangiev Asror,
Tashkent Institute of Irrigation and Melioration, Uzbekistan E-mail: yangiev_asror_63@mail.ru
Method of calculation of vortical spillways with tangential swirlers
Abstract: In vortical spillways the danger of cavitations of surfaces and elements of spillway structural elements contacting water decreases or excludes, also the velocity of water in the outlet decreases to admissible levels. In present the most simple and efficient solution is vortical shaft spillways with tangential twisting device, located at the end of the shaft. The article gives the calculation of discharge capacity for vortical spillways with various geometries of swirling device, the calculation of hydraulic resistance and change of specific energy of swirled flow on the whole waterway. Calculation results can assist on designing such spillways.
Keywords: Vortical spillway, swirled flow, cavitation, slacking, swirling intensity, resistance.
Introduction
During designing and construction of high pressure hydrosystems, there arises necessity to solve complex problems of creating deep-laid spillways, which can effectively work under pressure over 100 m. and water velocities, reaching 50.. .60 m/s. With mentioned values of determinant parameters it is necessary to: reliably defend flowing part of spillways from cavitational erosion; lower the dynamic loads on the structure elements; prevent the possibility of significant damage of tail-water supports and inadmissible bed washout.
As a rule, water passing hydrosystems which use positive effects of water flow swirling long since has attracted attention of specialists, especially for designing of high pressure hydrosystems. Spillways which use water swirling are known as vortical spillways.
In vortical spillways the danger of cavitations of surfaces and elements of spillway structural elements contacting water decreases or excludes. Effective slaking the flow energy in tunnel and suppression chamber allows to decrease water velocity in outlet from spillway route to admissible values, which in its part, simplifies the structure and its parts.
Most of the vortical spillway structures are not applied in practice for their complexity. In present the most simple and efficient solution is vortical shaft spillways with tangential twisting device, located at the end of the shaft [2; 3] (fig.1).
Research modeling
In the given work we research spillway operation, which is characterized with flow ofvarious structures, i. e. when at the same time flow is in swirled, non-pressure, and aerated axial flow conditions.
For deferent tunnel with axial flow we determined the Frud number and the Reynolds number:
$ O.T
_ gK'
So.t. — the average axial velocity in deferent tunnel; hn — non-pressure flow depth in deferent tunnel.
Re.^^", (2)
v
R0 T — hydraulic radius of flow in deferent tunnel. The Frud number can change within 1.98 ± 0.15, and the Reynolds number 0.7 x 10 4^5.4 x 10 5.
Fr =-
(1)
Main formulas for calculation
According to the results of model research we have got hydraulic estimates of such spillways.
Capacity of spillway is estimated with the formula [2]:
Q = fu*JlgH , (3)
where m, H — correspondingly deferent tunnel free area and head; ^ — discharge coefficient, estimated with following formula: 1
L.r , (4)
+i.r
where — summed coefficient of loss in supply tunnel; — loss coefficient of twisting device; ^„m, — summed coefficient of loss in deferent tunnel; E,V — loss coefficient considering residual twisting at the outlet of their deferent tunnel.
Coefficient is estimated with the following formula:
=
(5)
where n M — sum of loss coefficients on local resistances in supply tunnel;
wn — wetted section area of supply tunnel; X, inode ,dmde — accordingly coefficient of hydraulic friction, length and diameter of supply tunnel.
Coefficient is estimated with the following formula:
St. =2(So + S ^0 ( ' (6)
i=0 U i=0 u
where Ç0 and . - accordingly coefficients of loss for axial flow (0 = X ■ l) and additional losses, caused by twisting in deferent tunnel; A ^., d - accordingly site length and deferent tunnel diameter. Coefficient E,Y is estimated as ratio of specific kinetic energy of flow twisting at the tunnel outlet to velocity head calculated with average discharge velocity:
E = YUlL
(7)
As a initial approximation the value E,V can also be estimated by the following formula:
n2
*=1^ (8)
where, n - the value of integral p arameter at the end of deferent tunnel.
n is the ratio of tangential component of shearing strength tu to full strength near wall t or the ratio of peripheral velocity Vu to full velocity near wall V, which is practically the same ratio:
(9)
n = T = V..
t V
Not changing the locations of supply and deferent tunnels on the plan, due to tangential cuttings, the geometry of tangential swirler and therefore the parameter A [1] can be changed.
A = (10)
where R — radius of existing deferent tunnel;
R — the distance from tunnel axes to inlet section axes;
u '
mxx — the area of inlet section.
Calculation results
The value of initial integral parameter is accepted within no = 0.6...0.8 (the lower values of no are for lower heads) depending on the required extent of suppression of excess kinetic energy. The required value of no is provided by technical characteristics of twisting device. Knowing no we can get the value of geometric parameter of tangential swirler A from the graph
Fig.1. Schemes of vortical spillway deferent tunnels of Tupolang: 1 — shaft; 2 — tangential swirler; 3 — connecting element; 4 — suppression chamber; 5 — deferent tunnel
Fig. 2. Curve of ^ = f(A) for tangential swirler
Swirler with flat cut or elliptical cut is selected. It is noted that with the constant parameter A swirler with elliptical cut has larger discharge capacity than the one with flat cut. With known parameter A we can get hydraulic resistance of the swirler from figure 3.
In order to estimate the value ¿,ome the deferent tunnel is divided into n sites, and for each of them the average value & is esti-
mated. The estimation starts with finding the integral parameter of twisting n.
Attenuation of twisting along tunnel is established by estimating the values of integral parameter of twisting n for corresponding cross sections, located from the initial section £ o = 4d at the distance £ = £
'd
Fig. 3. Coefficient of hydraulic resistance of tangential swirler with flat cut vs. parameter A curve £ 3 Y = f^): 1 — with vortical water gate; 2 — with tangential swirler with air intake from shaft
Fig.4. The change of integral parameter П along circular section 1, 2, 3 — А=0.6, 0.925, 1.245 correspondingly; 4 — generalized curve for tunnel with vortical water gate; 5 — generalized curve for tangential swirler with air intake from shaft
Fig. 5. Coefficient 0 vs. parameter П curve
Fig. 6. Thechanges along tunnel with average values on section and discharge of full specific energy of twisted flow e , kinetic energy of axial component velocity em, kinetic energy of circular component velocity eu, on wall x0, rated to head of 1 m.,
for various values of parameter A
The change of integral parameter n along tunnel with circular section is shown in fig. 4. From the graph fy = f (n;) we find [4] (fig. 5). ' ' '
The character of changes along tunnel with average values on section and discharge of full specific energy of twisted flow e, kinetic energy of axial component velocity em, kinetic energy of circular component velocity on wall xo, rated to head of 1 m., for various values of parameter A are shown in fig. 6.
The values of energy and pressure are estimated with the following formulas:
- E — E — E P
m •• x =_—_. (11)
-; e = -
-; e = -
PSH,X PgHx PgH„ PgH„ The value of potential energy of flow is estimated as follows:
ep = e - (em + eu). (12)
Hydraulic resistance of twisted flow in cylindrical tunnel is way larger than the resistance of axial flow. It is related to the change of flow structure, in particular to the increase of velocity and velocity gradient near tunnel surface and correspondingly to the increase of surface friction and internal friction, caused by the increase of turbulent pulsation intensity.
The loss of energy in twisted flow can be introduced as the sum of energy losses in axial flow AEC and energy losses, caused by flow twisting AE [2]:
AE = AE + AE . (13)
OC 3 y '
It is known that energy loss on tunnel site with axial flow is:
V 2e
AE = X^-, (14)
2g 4R
V!
where X — hydraulic friction coefficient, —^ — velocity head, es-
2g Q
timated from averaged discharge velocity for simplicity, V = —
I Cf ® ( w — tunnel cross section area),--relative length of tunnel,
where the energy loss occurs.
Additional energy losses, caused by twisting can be introduced
similarly:
V1!
AE = £ , 3 2g 4R
where £ - the coefficient of hydraulic friction from flow twisting.
I
If we consider — = 1 and for sameness denote X with , we get the following:
V2
AE = (^ +£)-*. (16)
2£
(15)
The formula (10) can be presented as:
AE = (1 + t ).
2g L
(17)
The quantity^ /£oc in [2] is denoted with 9 and characterizes the ratio of hydraulic friction coefficient to twisting and axial flow.
Then:
32
AE = ^(1 + 9). (18)
2g
The calculation of hydraulic resistance of twisted flow in cylindrical tunnel is carried out as follows.
The initial twisting of flow n is determined from known characteristics of twisting device (no = 0.6.. .0.8).
The value of specific flow energy in initial section Eo is established from known characteristics of twisting device, i. e. from the
graph: e = f (-) (fig. 6).
a
Then the tunnel is divided into sites, on which the energy losses are found with consideration of twisting suppression along tunnel from site to site, starting from the initial section. The initial section is the section, located at distance = 4 from the twisting device.
Twisting suppression is established by determining the values of integral twisting parameter n for corresponding cross sections of tunnel, located at distance £ = from initial section from I
graph n = f (-) (see fig. 4). a
The value of 9i is estimated by the average value of ni for the given site from the graph^ = f (n) (see fig. 5).
The value of loss coefficients for the axial flow is established with the consideration of the actual roughness of tunnel walls from known formulas.
The values , f. and are determined, the sum of energy losses of twisted flow AE. on the given site and consecutively along tunnel, and also the sum of energy losses EAE. are calculated using formula (17)
Specific flow energy at the end of site EKi is equal to:
= E0 -XAE . " (19)
The calculation starts from the initial site and consecutively conducted along tunnel. As a result the change of full specific energy of twisted flow along the whole tunnel is determined.
Conclusion
Vortical spillways are reliable from the point ofview of noncavi-tational work and effective energy slaking. We received the values for swirled flow hydraulic resistance coefficient on the whole waterway in air intake conditions. From the above given consistency we can carry out calculation of discharge capacity of vertical spillway with various geometrical shapes of twisting device, calculation of hydraulic resistance and change of full specific energy of twisted flow along the whole tunnel.
References:
1. 2.
3.
4.
Hydraulic calculations of water spillway hydrotechnical structures. Reference book. - Moscow: Energoatomizdat, 1988. - P. 624. Jivotovski B. A. The hydraulics of twisted flow and its use in hydrotechnical construction: Dissertation... Doctor of technical sciences. - Moscow: VNII VODGEO, 1986. - P. 325.
Report of NIR NIS MGMI. Development of rational designs for individual elements of shaft water spillway fo Tupolang hydrosystem. - Moscow, 1986. - P. 117.
Yangiev A. A. Evaluation of energy suppression capability of the elements of deferent route of high pressure vortical water spillways. Abstract. Dissertation. candidate of technical sciences. - MGMI, 1991. - P. 19.
