modelSurgeTank

Information

Surge Tank Model

The surge shaft/tank is modeled as a vertical open pipe with constant diameter together with a manifold connecting the conduit, surge volume, and penstock. Four different surge tank configurations are available:

1. Simple surge tank - Basic vertical open pipe

   

2. Air cushion surge tank - Includes compressed air chamber

   

3. Sharp orifice surge tank - With orifice restriction

   

4. Throttle valve surge tank - With restricted throat section

   

Mass and Momentum Balances

All surge tank types are modeled using mass and momentum balance equations:

$$ \frac{\mathrm{d}m}{\mathrm{d}t} = \dot{m}_\mathrm{s,in} = \rho \dot{V} $$

$$ \frac{\mathrm{d}(mv)}{\mathrm{d}t} = \dot{m}_\mathrm{i}v_\mathrm{i} + F_\mathrm{p} + F_\mathrm{g} + F_\mathrm{f} $$

Water Mass and Geometry

The water mass in the surge tank is: $$ m = \rho V = \rho lA = \rho A\frac{h}{\cos\theta} $$ where ρ is water density, V is volume, h and l are height and length of water column, and A = πD²/4 is the cross-sectional area.

Water velocities: $$ v = \frac{\dot{V}}{A}, \quad v_\mathrm{i} = \frac{\dot{V}}{A} $$

Force Terms

Pressure force: $$ F_\mathrm{p} = A(p_\mathrm{i} - p^\mathrm{atm}) $$ where p_i is inlet pressure and p^atm is atmospheric pressure.

Gravity force: $$ F_\mathrm{g} = m g \cos\theta $$ where θ = arccos(H/L) is the slope angle.

Friction force: $$ F_\mathrm{f} = -\frac{1}{8}lf_\mathrm{D}\pi\rho Dv|v| $$ calculated using the Darcy friction factor f_D,s.

Manifold Connection

The manifold preserves mass in steady-state: $$ \dot{V}_\mathrm{i} = \dot{V}_\mathrm{p} + \dot{V} $$ The manifold pressure is equal for all three connections. This is implemented via ContactNode connectors.

Creek Intake

The surge tank has a creek inlet connector that can be attached to a VolumeFlowSource to model lateral inflow (e.g., a creek or groundwater seepage) entering the surge tank. The connector is always present; when left unconnected, the flow is zero by Modelica's default flow-variable semantics and has no effect on the model. The parameter H_creek specifies the height of the intake above the surge tank base (default: equal to H). The boolean useCreekIntake controls the visibility of H_creek in the parameter dialog.

The connector pressure is set hydrostatically from the water surface down to the intake elevation, so it correctly follows the actual water level h in the tank:

$$ p_\mathrm{creek} = p_\mathrm{t} + \rho g (h - H_\mathrm{creek}) $$

The creek connector participates in the overconstrained elevation graph via Connections.branch(creek.elevation, o.elevation), ensuring that its elevation is consistent with the rest of the waterway: $$ z_\mathrm{creek} = z_\mathrm{o} + H_\mathrm{creek} $$

The creek inflow is included in the mass balance:

$$ \frac{\mathrm{d}m}{\mathrm{d}t} = \rho \dot{V} + \dot{m}_\mathrm{creek} $$

Parameters and Initialization

Required geometry parameters: length L, height H, diameter D, roughness p_ε, and atmospheric pressure p^atm. Initialize with flow rate V̇₀ and water height h₀. Option for steady-state initialization is available.

Parameters

Connectors

Components