Tank with constant pressurization and volume-dependent fluid level
Low-Pressure Blocks
The Variable Head Tank block represents a pressurized hydraulic reservoir, in which fluid is stored under a specified pressure. The pressurization remains constant regardless of volume change. The block accounts for the fluid level change caused by the volume variation, as well as for pressure loss in the connecting pipe that can be caused by a filter, fittings, or some other local resistance. The loss is specified with the pressure loss coefficient. The block computes the volume of fluid in the tank and exports it outside through the physical signal port V.
For reasons of computational robustness, the pressure loss in the connecting pipe is computed with the equations similar to that used in the Fixed Orifice block:
$$q=\sqrt{\frac{1}{K}}\cdot {A}_{p}\sqrt{\frac{2}{\rho}}\cdot \frac{{p}_{loss}}{{\left({p}_{loss}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$
$${p}_{cr}=K\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{d}\right)}^{2}$$
The Critical Reynolds number is set to 15.
The pressure at the tank inlet is computed with the following equations:
$$p={p}_{elev}-{p}_{loss}+{p}_{pr}$$
$${p}_{elev}=\rho \xb7g\xb7H$$
$${A}_{p}=\frac{\pi \xb7{d}^{2}}{4}$$
$$H=\{\begin{array}{ll}\frac{V}{A}\hfill & \text{forconstant-areatank}\hfill \\ f(V)\hfill & \text{fortable-specifiedtank}\hfill \end{array}$$
$$V={V}_{0}+q\xb7t$$
where
p | Pressure at the tank inlet |
p_{elev} | Pressure due to fluid level |
p_{loss} | Pressure loss in the connecting pipe |
p_{pr} | Pressurization |
ρ | Fluid density |
g | Acceleration of gravity |
H | Fluid level with respect to the bottom of the tank |
K | Pressure loss coefficient |
A_{p} | Connecting pipe area |
d | Connecting pipe diameter |
q | Flow rate |
p_{cr} | Minimum pressure for turbulent flow |
V | Instantaneous fluid volume |
V_{0} | Initial fluid volume |
A | Tank cross-sectional area |
t | Simulation time |
For a tank with a variable cross-sectional area, the relationship between fluid level and volume is specified with the table lookup
$$H=f(V)$$
You have a choice of two interpolation methods and two extrapolation methods.
Connection T is a hydraulic conserving port associated with the tank inlet. Connection V is a physical signal port. The flow rate is considered positive if fluid flows into the tank.
Warning If fluid level becomes so low that the tank inlet gets exposed, no warnings will be issued. The simulation will continue and pressure at the inlet will be set to the pressurization pressure. If this is not acceptable, MathWorks recommends that you employ the necessary control measures to guard against this situation in your models. |
The initial volume of fluid in the tank. This parameter must
be greater than zero. The default value is 20
l.
Gage pressure acting on the surface of the fluid in the tank. It can be created by a gas cushion, membrane, bladder, or piston, as in bootstrap reservoirs. This parameter must be greater than or equal to zero. The default value is 0, which corresponds to a tank connected to atmosphere.
Select one of the following block parameterization options:
Linear
— Provide
a value for the tank cross-sectional area. The level is assumed to
be linearly dependent on the fluid volume. This is the default method.
Table-specified
—
Provide tabulated data of fluid volumes and fluid levels. The level
is determined by one-dimensional table lookup. You have a choice of
two interpolation methods and two extrapolation methods.
The cross-sectional area of the tank. This parameter must be
greater than zero. The default value is 0.8
m^2.
This parameter is used if Level/Volume relationship is
set to Linear
.
Specify the vector of input values for fluid volume as a one-dimensional
array. The input values vector must be strictly increasing. The values
can be nonuniformly spaced. The minimum number of values depends on
the interpolation method: you must provide at least two values for
linear interpolation, at least three values for smooth interpolation.
The default values, in m^3, are [0 0.0028 0.0065 0.0114 0.0176
0.0252 0.0344 0.0436 0.0512 0.0574 0.0623 0.066 0.0688 0.0707 0.072
0.0727]
. This parameter is used if Level/Volume
relationship is set to Table-specified
.
Specify the vector of fluid levels as a one-dimensional array.
The fluid levels vector must be of the same size as the fluid volumes
vector. The default values, in meters, are [0 0.02 0.04 0.06
0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3]
.
This parameter is used if Level/Volume relationship is
set to Table-specified
.
The diameter of the connecting pipe. This parameter must be
greater than zero. The default value is 0.02
m.
The value of the pressure loss coefficient, to account for pressure
loss in the connecting pipe. This parameter must be greater than zero.
The default value is 1.2
.
Select one of the following interpolation methods for approximating the output value when the input value is between two consecutive grid points:
Linear
— Select
this option to get the best performance.
Smooth
— Select
this option to produce a continuous curve with continuous first-order
derivatives.
For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.
This parameter is used if Level/Volume relationship is
set to Table-specified
.
Select one of the following extrapolation methods for determining the output value when the input value is outside the range specified in the argument list:
Linear
— Select
this option to produce a curve with continuous first-order derivatives
in the extrapolation region and at the boundary with the interpolation
region.
Nearest
— Select
this option to produce an extrapolation that does not go above the
highest point in the data or below the lowest point in the data.
For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.
This parameter is used if Level/Volume relationship is
set to Table-specified
.
The block has the following ports:
T
Hydraulic conserving port associated with the tank inlet.
V
Physical signal port that outputs the volume of fluid in the tank.