Tank Transient Theory

An infinite tank is equivalent to an Assigned Pressure junction defined with a stagnation pressure. The solution for a finite tank is more complex, and is discussed below.

Adiabatic Finite Tank

For a finite tank a fixed volume is known, along with an initial stagnation pressure and temperature/enthalpy. The known values can be used to calculate initial values for the density, enthalpy, and energy.

(1)

(2)

(3)

The total mass and energy in the tank is calculated at the current time step, and the mass flow rate and energy flow rate out of the tank is assumed to be constant between the old and current time step. This assumption is reasonable when the time step is reasonably small, and the parameters in the tank are changing relatively slowly. With the known tank mass and the constant tank volume the density can be calculated for the current time step using Equation 2. The pressure and temperature are related to the total energy using Equations 1 and 3 as shown above. We can iterate on the pressure and temperature to solve these equations.. After each iteration the new pressure and temperature are used to recalculate the density, which is checked against the density calculated previously from Equation 2 to confirm when the iteration is complete.

Once the pressure and temperature have been calculated for the current time step, the new pressure and temperature can be used to calculate how the mass flow rate and energy flow rate will change for the future time step t + 1.

Isothermal Finite Tank

The isothermal tank solution will proceed similar to the adiabatic finite tank solution outlined above. However, in this case the temperature is fixed as well as the volume.

The mass at the current time step can be calculated assuming the mass flow rate from the previous time step remained constant. The mass and volume can then be used to calculate the density at the current time step, which can be used to iterate on the enthalpy state equation which is represented by Equation 1 above.

Once the pressure has been calculated for the current time step, the new pressure and temperature can be used to calculate how the mass flow rate and energy flow rate will change for the future time step t + 1.

Known Heat and Volume vs Time

The Known Heat and Volume vs. Time option allows the user to specify the tank volume over time plus an external rate of heat added to (or removed from) the tank. A similar process to the Adiabatic Finite Tank solution is used, where the external heat rate is used along with the mass flow into and out of the tank to determine the new pressure, temperature, and enthalpy inside the tank. The known tank volume is also coupled into the solution to iterate on tank mass and gas density as the tank volume changes.

Sonic Choking Transient Theory

An outlet tank junction can experience endpoint choking during the steady state, or can become choked during the transient due to transient events in the system. If sonic choking occurs at the tank junction a different solution method must be enacted. See Transient Sonic Choking for more information.