Methodology for Calculating Automatic Gate Valves with a Hydraulic Damper
Abstract Generated abstract
This paper presents a calculation procedure for automatic starting gate valves with a hydraulic damper used in mine drainage pump installations, where the discharge pipeline must be closed during pump start-up to reduce motor starting torque. Using a worked example for a specified pump, pipeline, piston travel, oil density, and viscosity, the method determines pipeline filling time, valve opening speed, damper cylinder diameter, oil flow through the throttle, throttle opening size, and valve closing time, relying on experimentally obtained resistance coefficients for throttling openings. The example yields an opening time of 125 seconds, a valve opening speed of about 1.8 mm/s, a damper cylinder diameter of 300 mm, a throttle opening diameter of about 1.33 cm, and a closing time of about 430 seconds, with parameters adjustable through throttle size, oil viscosity, and decompression valve setting.
Full Text
Method for Calculating Automatic Gate Valves with a Hydraulic Damper
B. M. Titov
(Presented by the scientific seminar of the Department of Mining Mechanics)
The discharge pipeline of powerful mine-drainage installations must be shut off during pump start-up in order to reduce the starting torque of the electric motor. To automate this process, starting gate valves with spring-oil (Fig. 1) and water dampers [1] have been proposed. Below, using a specific example, a method is given for calculating these gate valves, using the resistance coefficients of throttling openings (Fig. 2) obtained experimentally by I. N. Kichin [2].
Given: pump delivery
\[ Q_n = 300 \ \text{m}^3/\text{h}, \]
pump head
\[ H_n = 300 \ \text{m water column}, \]
pipeline diameter
\[ D_{\text{sh}} = 200 \ \text{mm}, \]
pipeline length
\[ l = 330 \ \text{m}, \]
piston travel before the start of opening of the gate valve
\[ h = 20 \ \text{mm}, \]
specific weight of the oil
\[ \gamma = 0.915 \ \text{g}/\text{cm}^3, \]
oil viscosity
\[ \nu = 1.0 \ \text{St}. \]
It is required to determine: the time and speed of opening of the gate valve, the diameter of the damper cylinder, the size of the throttling opening, and the time of closing of the gate valve.
Fig. 1. Automatic starting gate valve with a spring-oil damper.
1—pump discharge branch pipe; 2—piston-gate valve; 3—elastic seal; 4—decompression channel; 5—throttling opening; 6—check valve of the discharge pipeline; 7—spring; 8—decompression valve; 9—gland; 10—plug for filling oil; 11—gate-valve piston position indicator.
Solution
- Volume of the discharge pipeline.
\[ V=\frac{\pi D_m^2}{4}L=\frac{3{,}14\cdot 0{,}2^2}{4}\cdot 330=10{,}4\ \text{m}^3. \]
- The time for opening the gate valve, required to fill the discharge pipeline with water, at a pump capacity of \(300\ \text{m}^3/\text{h}\),
\[ t=3600\frac{V}{Q_{\text{n}}}=3600\frac{10{,}4}{300}=125\ \text{sec}. \]
In the figure: \(\ell/d_{\text{n}}=\dfrac{0{,}20}{\pi\sqrt{\gamma}}\), \(\Delta p=K\dfrac{v_{\text{av}}^2}{2g}\gamma\).
Fig. 2. Dependence of the resistance coefficient on the dimensions of the throttle device.
- Stroke of the gate-valve piston
\[ s=D_m+h=200+20=220\ \text{mm}. \]
- Opening speed of the gate valve
\[ w=\frac{s}{t}=\frac{220}{125}=1{,}8\ \text{mm/sec}. \]
- Diameter of the damper cylinder; in order to reduce the pressure drop, it is taken as one and a half times the diameter of the gate-valve piston:
\[ D_{\text{c}}=1{,}5D_m=1{,}5\cdot 200=300\ \text{mm}. \]
- Volume of oil in the damper cylinder
\[ V_{\text{c}}=\frac{\pi D_{\text{c}}^2}{4}s=\frac{3{,}14\cdot 0{,}3^2}{4}\,0{,}22=0{,}0156\ \text{m}^3. \]
- Oil flow through the throttle opening
\[ Q=\frac{V_{\text{c}}10^6}{t}=\frac{0{,}0156\cdot 10^6}{125}=125\ \text{cm}^3/\text{sec}. \]
- Length of the initial section of the laminar flow:
\[ l_{\mathrm{n}}=\frac{0.2\,Q}{\pi \nu}=\frac{0.2\cdot 125}{3.14\cdot 1.0}=8.0\ \mathrm{cm}. \]
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For design reasons we take the thickness of the damper piston to be \(60\ \mathrm{mm}\), \(l=5.0\ \mathrm{cm}\), and from the ratio \(l/l_{\mathrm{n}}=0.625\) we find (Fig. 2) \(k=3.6\).
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Pressure drop in the throttle cylinder:
\[ \Delta p=H_{\mathrm{n}}\left(\frac{D_{\mathrm{m}}}{D_{\mathrm{n}}}\right)^2 =30\left(\frac{200}{300}\right)^2 =13.4\ \mathrm{kg/cm^2}. \]
- Mean velocity of the oil outflow through the throttle opening [2]:
\[ v_{\mathrm{cp}}=\sqrt{\frac{2g\Delta p}{k\gamma}} =\sqrt{\frac{2\cdot 980\cdot 13.4}{3.6\cdot 0.915}} =90\ \mathrm{cm/sec}. \]
- Area and diameter of the throttle opening:
\[ F=\frac{Q}{v_{\mathrm{cp}}}=\frac{125}{90}=1.39\ \mathrm{cm^2}; \]
\[ d=\sqrt{\frac{4F}{\pi}} =\sqrt{\frac{4\cdot 1.39}{3.14}} =1.33\ \mathrm{cm}. \]
- The pressure drop during closing of the gate valve is determined by the weight of the piston-valve and by the force of the return spring. Let \(\Delta p'=1\ \mathrm{kg/cm^2}\); then
\[ v'_{\mathrm{cp}}=\sqrt{\frac{2g\Delta p'}{k\gamma}} =\sqrt{\frac{2\cdot 980\cdot 1.0}{3.6\cdot 0.915}} =26\ \mathrm{cm/sec}. \]
- Oil flow rate through the throttle opening:
\[ Q'=\frac{\pi d^2}{4}\,v'_{\mathrm{cp}} =\frac{3.14\cdot 1.33^2}{4}\cdot 26 =36\ \mathrm{cm^3/sec}. \]
- Closing time of the gate valve:
\[ t'=\frac{v_{\mathrm{n}}}{Q'}=\frac{15600}{36}=430\ \mathrm{sec}. \]
If the results obtained do not meet the specified requirements, then \(t\), \(D_{\mathrm{n}}\), \(e\), and \(\nu\) are changed accordingly and the calculation is repeated. Under operating conditions the opening speed of the gate valve can be regulated by changing the diameter of the throttle opening and the viscosity of the oil, and the closing speed by setting the decompression valve on the piston of the damper cylinder.
The calculation of an automatic starting gate valve with a water damper [1] is carried out in an analogous manner.
References
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B. M. Glotov, “Automatic Starting Gate Valve and Hydraulic Shock Absorber.” Design and Construction of Mining Enterprises, No. 2, Ugletekhizdat, 1956.
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I. N. Kichin, “Determination of Hydraulic-Loss Coefficients for Throttle Resistances in Hydroautomation Systems.” Automation and Remote Control, Vol. 18, Issue 1, Publishing House of the Academy of Sciences of the USSR, 1957.