## 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.

-●-$L \mathrm{[-]}$
-●-$M \mathrm{[-]}$
-●-$P \mathrm{[-]}$
-●-$E \mathrm{[-]}$
-●-$S \mathrm{[-]}$
$s\mathrm{[\%]}$
Fig. 3 - Overview of basic flow characteristics: L – linear, M – modified linear,P – parabolic, E – equal percentage, S – square root

In the case of control valves, cavitation cannot develop if the condition is met

$\cfrac{P_1-P_2}{0.6\cdot\left(P_1-P_T\right)}\le1$

where:
 $P_1$ 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:

$v_0$ $=\cfrac{4\cdot{10}^6\cdot Q_{max}}{π\cdot D^2}$

where:
 $v_0$ valve speed $\mathrm{m/s}$ $Q_{max}$ flow $\mathrm{m^3/s}$ $D$ valve diameter $\mathrm{mm}$

The flow area:

$F$ $=\cfrac{Q_{max}}{μ_i\sqrt{2\cfrac{P_1-P_2}{ρ}}}$

$\cfrac{4\cdot{10}^6\cdot F}{{π\cdot D^2}}\le0.5$

where:
 $F$ 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

$μ$ $=0.65$

$\cfrac{l}{d}$ $=1.65$

Fig. 4 - sharp-edged hole

- Beveled hole

$μ$ $=0.78$

$\cfrac{l}{d}$ $=1.65$

$\cfrac{z}{d}$ $=0.25$

Fig. 5 - beveled hole

- Rounded hole

$μ$ $=0.84$

$\cfrac{l}{d}$ $=1.65$

$\cfrac{r}{d}$ $=0.25$

Fig. 6 - rounded hole

Allowable maximum number of holes in one row:

$n_{max}$ $=\cfrac{π D_c}{\sqrt{\left(9d_i\right)^2-\left(3d_i\right)^2}}$

where:
 $n_{max}$ 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

saturated vapor pressure at a specific temperature:
The water temperature Saturated vapor pressure
$T$ $P_T$
$\mathrm{°C}$ $\mathrm{Pa}$
0611.3
101228.1
202338.8
304245.5
407381.4
5012344
6019932
7031176
8047373
9070117
100101320

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.