Multi-hole cage
The multi-hole cage is designed for flow control. It consists of a hollow cylinder, in the wall of which a system of holes is drilled. The size of the throttling cross-section is controlled by exposing the field of these holes with the upper edge of the seat. A single stream of medium is fragmented into many local streams. The flow area is not one-piece and has no one boundary but is given by adding the cross-sections of the individual holes. Therefore, it is not possible to achieve such a smoothness of the curve and a certain ripple of the flow characteristic is evident here.
The multi-hole cage is ideal for handling high pressure. In addition, the seat can be shielded from the flow direction and does not need to be loaded. The direction of the medium flow towards the inside of the cage is important, where the individual partial currents meet and a considerable part of the kinetic energy is dissipated there, which would otherwise disrupt parts of the control system or body.
A multi-stage cage is required to reduce cavitation. If the pressure at a certain point during the flow through the cage falls below the value of the saturated vapor pressure of the liquid, corresponding to its temperature, cavitation occurs. The cavitation bubbles suddenly disappear when they reach a higher-pressure area with the liquid flow, and cavitation wear of the material is caused. For the formation of cavitation, it is decisive whether the liquid pressure falls below the critical value of cavitation pressure, which favorably corresponds to the saturated vapor pressure
$P_T$
lies in the range of minimum pressure and pressure behind the cage, when cavitation occurs, and cavitation wear can be expected after a certain time. If the minimum pressure is greater than the saturated vapor pressure, steam cavitation will not occur.
Fig. 1 - Cage
Fig. 2 - Developed view of the cage
Cage flow characteristic:
It is the dependence of the instantaneous free flow area in the throttle system of the regulating cage on the instantaneous position of the cage exposure. The basic types of flow characteristics are shown in Fig. 3.
-●-$M \mathrm{[-]}$
-●-$P \mathrm{[-]}$
-●-$E \mathrm{[-]}$
-●-$S \mathrm{[-]}$
In the case of control valves, cavitation cannot develop if the condition is met
$P_1$ | inlet absolute static pressure (max pressure 80MPa) | $\mathrm{Pa}$ |
$P_2$ | output absolute static pressure (min pressure 101325Pa) | $\mathrm{Pa}$ |
$P_T$ | saturated vapor pressure | $\mathrm{Pa}$ |
Valve speed:
$v_0$ | valve speed | $\mathrm{m/s}$ |
$Q_{max}$ | flow | $\mathrm{m^3/s}$ |
$D$ | valve diameter | $\mathrm{mm}$ |
The flow area:
$F$ | the flow area | $\mathrm{m^2}$ |
$Q_{max}$ | flow | $\mathrm{m^3/s}$ |
$D$ | valve diameter | $\mathrm{mm}$ |
$μ_i$ | output coefficient | $\mathrm{ }$ |
$P_1$ | inlet absolute static pressure (max pressure 80MPa) | $\mathrm{Pa}$ |
$P_2$ | output absolute static pressure (min pressure 101325Pa) | $\mathrm{Pa}$ |
$ρ$ | density | $\mathrm{kg/m^3}$ |
output coefficient:
- Sharp-edged hole
Fig. 4 - sharp-edged hole
- Beveled hole
Fig. 5 - beveled hole
- Rounded hole
Fig. 6 - rounded hole
Allowable maximum number of holes in one row:
$n_{max}$ | allowable maximum number of holes in one row | $\mathrm{ }$ |
$D_c$ | inner diameter of the cage | $\mathrm{mm}$ |
$d_i$ | diameter of the hole | $\mathrm{mm}$ |
Density:
Density $\rho\ \mathrm{[kg/m^3]}$ water depending on temperature and pressure
Pressure $\mathrm{[MPa]}$ | Temperature $\mathrm{[°C]}$ | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0° | 10° | 20° | 30° | 40° | 50° | 60° | 70° | 80° | 90° | 100° | |||
0.1 | 999.8 | 999.7 | 998.2 | 995.6 | 992.2 | 988.1 | 983.2 | 977.8 | 971.8 | 965.3 | - | ||
0.25 | 999.9 | 999.8 | 998.3 | 995.7 | 992.3 | 988.1 | 983.3 | 977.8 | 971.9 | 965.3 | 958.4 | ||
0.5 | 1000 | 999.9 | 998.4 | 995.8 | 992.4 | 988.2 | 983.4 | 978 | 972 | 965.5 | 958.5 | ||
1 | 1000.3 | 1000.1 | 998.6 | 996 | 992.7 | 988.4 | 983.6 | 978.2 | 972.2 | 965.7 | 958.8 | ||
1.5 | 1000.6 | 1000.4 | 998.8 | 996.3 | 992.9 | 988.6 | 983.9 | 978.4 | 972.4 | 966 | 959 | ||
2 | 1000.8 | 1000.6 | 999.1 | 996.5 | 993 | 988.8 | 984.1 | 978.6 | 972.7 | 966.2 | 959.2 | ||
2.5 | 1001.1 | 1000.8 | 999.3 | 996.7 | 993.3 | 989.1 | 984.3 | 978.9 | 972.9 | 966.4 | 959.5 | ||
3 | 1001.3 | 1001 | 999.5 | 996.9 | 993.4 | 989.2 | 984.5 | 979.1 | 973.1 | 966.6 | 959.7 | ||
3.5 | 1001.6 | 1001.3 | 999.8 | 997.2 | 993.7 | 989.5 | 984.6 | 979.2 | 973.3 | 966.8 | 960 | ||
4 | 1001.8 | 1001.6 | 1000 | 997.4 | 993.9 | 989.7 | 984.9 | 979.5 | 973.5 | 967.1 | 960.2 | ||
4.5 | 1002.1 | 1001.8 | 1000.2 | 997.6 | 994.1 | 989.9 | 985.1 | 979.7 | 973.8 | 967.3 | 960.4 | ||
5 | 1002.3 | 1002 | 1000.4 | 997.8 | 994.3 | 990.2 | 985.3 | 979.9 | 974 | 967.6 | 960.6 | ||
6 | 1002.8 | 1002.5 | 1000.9 | 998.3 | 994.8 | 990.6 | 985.8 | 980.4 | 974.5 | 968 | 961.1 | ||
7 | 1003.3 | 1003 | 1001.3 | 998.7 | 995.2 | 991 | 989.2 | 980.8 | 974.9 | 968.4 | 961.5 | ||
8 | 1003.8 | 1003.4 | 1001.8 | 999.1 | 995.6 | 991.5 | 986.6 | 981.3 | 975.3 | 968.9 | 962 | ||
9 | 1004.3 | 1003.9 | 1002.2 | 999.6 | 996.1 | 991.9 | 987.1 | 981.6 | 975.7 | 969.4 | 962.5 | ||
10 | 1004.8 | 1004.4 | 1002.7 | 1000 | 996.5 | 992.3 | 987.5 | 982.1 | 976.2 | 969.7 | 962.9 | ||
12.5 | 1006 | 1005.5 | 1003.8 | 1001.1 | 997.6 | 993.3 | 988.5 | 983.2 | 977.2 | 970.9 | 964 | ||
15 | 1007.3 | 1006.7 | 1004.9 | 1002.2 | 998.6 | 994.4 | 989.6 | 984.3 | 978.4 | 972 | 965.2 | ||
17.5 | 1008.5 | 1007.9 | 1006 | 1003.2 | 999.7 | 995.5 | 990.7 | 985.3 | 979.4 | 973.1 | 966.3 | ||
20 | 1009.7 | 1009 | 1007.2 | 1004.3 | 1000.8 | 996.5 | 991.7 | 986.4 | 980.5 | 974.2 | 967.4 | ||
25 | 1012.1 | 1011.3 | 1009.3 | 1006.5 | 1002.8 | 998.6 | 993.7 | 988.4 | 982.6 | 976.4 | 969.7 | ||
30 | 1014.5 | 1013.6 | 1011.4 | 1008.6 | 1004.9 | 1000.7 | 995.8 | 990.5 | 984.7 | 978.5 | 971.8 | ||
35 | 1016.9 | 1015.7 | 1013.6 | 1010.6 | 1007 | 1002.7 | 997.9 | 992.6 | 986.8 | 980.6 | 974 | ||
40 | 1019.3 | 1018 | 1015.7 | 1012.8 | 1009 | 1004.7 | 999.9 | 994.6 | 988.8 | 982.7 | 976.1 | ||
45 | 1021.6 | 1020.2 | 1017.8 | 1014.7 | 1011 | 1006.8 | 1001.9 | 996.6 | 990.9 | 984.7 | 978.2 | ||
50 | 1023.9 | 1022.3 | 1019.9 | 1016.8 | 1013 | 1008.7 | 1003.8 | 998.6 | 992.9 | 986.8 | 980.3 | ||
60 | 1028.3 | 1026.6 | 1024.1 | 1020.8 | 1017 | 1012.6 | 1007.8 | 1002.5 | 996.8 | 990.8 | 984.3 | ||
70 | 1032.7 | 1030.7 | 1028.1 | 1024.7 | 1020.8 | 1016.4 | 1011.5 | 1006.3 | 1000.7 | 994.6 | 988.3 | ||
80 | 1037 | 1034.9 | 1032 | 1028.5 | 1024.6 | 1020.2 | 1015.3 | 1010.1 | 1004.4 | 998.5 | 992.3 |
The water temperature | Saturated vapor pressure |
---|---|
$T$ | $P_T$ |
$\mathrm{°C}$ | $\mathrm{Pa}$ |
0 | 611.3 |
10 | 1228.1 |
20 | 2338.8 |
30 | 4245.5 |
40 | 7381.4 |
50 | 12344 |
60 | 19932 |
70 | 31176 |
80 | 47373 |
90 | 70117 |
100 | 101320 |
Recommendation:
- The individual screens must be apart min.
$5d$
.
- The individual outlets located on one screen must be spaced apart min.
$3d$
.
- The individual outlet openings between the screens must not overlap.
Literature:
- Prof. Ing. Jaromír Noskievič, DrSc a kolektiv: Kavitace v hydraulických strojích a zařízení.
- R. Mareš: Tabulky termodynamických vlastností vody a vodní páry.
- V. Kolář, S. Vinopal: Hydraulika průmyslových armatur. SNTL 1964.