Engineering task and calculation objective
The TAVA module calculates the pressure history during the cool-down of hot storage tanks that are protected against inadmissible vacuum by vacuum breakers (vacuum relief valves). The classic scenario: after steam-out, the vessel is filled with hot saturated steam; as it cools – for example by cooling water sprayed on the shell or by heat losses to the surroundings – the steam condenses, the density of the vessel atmosphere increases and a vacuum forms inside the vessel. Without sufficient venting, even a small pressure difference can buckle a storage tank designed for internal pressure, because typical tanks can withstand only a few millibar externally.
The module balances the cool-down process transiently: from the temperatures of the vessel after steam-out, of the cooling water and of the surroundings, the heat capacities of vessel material, cooling water and air, the densities of the vessel atmosphere before and after cool-down, the cooling water mass flow and the heat losses to the surroundings, the pressure history inside the vessel is calculated step by step (with a user-defined maximum temperature step). Set against this is the amount of air the vacuum breaker admits from its response pressure onwards.
The result is the verification of whether the selected vacuum breaker keeps the vacuum above the permissible value throughout the entire cool-down – a safety-relevant design task, since vacuum collapse of tanks after steam cleaning is among the most frequent vessel failures of all.
Calculation workflow
- Define the initial state after steam-out: Recorded are vessel geometry and description, the temperature of the vessel after steam-out, the pressure in the vessel at this moment, the ambient pressure and the density of the steam-filled vessel atmosphere.
- Define the cooling conditions: Cooling water temperature and mass flow, ambient temperature, the heat losses of the vessel to the surroundings and the specific heat capacities of vessel material, cooling water and air determine how fast heat is removed from the system.
- Calculate the cool-down step by step: The cool-down is followed iteratively in temperature steps (limited by the maximum temperature step for the iteration): in each step, condensation of the steam, the density change of the vessel atmosphere and the resulting internal pressure are balanced; a correction factor allows adjustment to the real cool-down behavior.
- Include the vacuum breaker: As soon as the internal pressure falls below the response pressure of the vacuum breaker, ambient air flows in at its density and limits the further pressure drop. The module determines the resulting pressure history up to the cooled final state.
- Assess the result: The minimum internal pressure is compared with the permissible vacuum of the vessel. If the venting capacity is not sufficient, larger or additional vacuum breakers, a higher response pressure or a slower cool-down (e.g. a reduced cooling water flow) must be provided.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Volumen | V | m³ |
| Masse | mB | kg |
| Behältermaterials | cp,B | J/(kg·K) |
| Umgebung | QV | W |
| Massenstrom | mp,K | kg/s |
| Ausdämpfen | ta | °C |
| Eintrittstemperatur | tK | °C |
| Abkühlen | te | °C |
| Kühklwassers | cp,K | J/(kg·K) |
| heiß | ρ1 | kg/m³ |
| kalt | ρ2 | kg/m³ |
| Vakuumbrecher | N | – |
| Ventils | pA | Pa |
| heiß | p1 | Pa |
| Umgebungsdruck | pU | Pa |
| Luft | ρL | kg/m³ |
| Lufttemperatur | tU | °C |
| Abkühlverhalten | 0 < Fcool ≤ 1 Fcool | – |
| Temperaturschritt | ΔTmax | K (diff) |
| Vakuumbrechers | Vakuumbrechers | – |
| Luft | cp,L | J/(kg·K) |
| _KV-Wert | KV | m³/h |
| 1 | 1 | s |
| 2 | 2 | s |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Abkühlzeit | t | s |
| Vakuumbrecher | pu,o | Pa |
| Vakuumbrecher | pu,m | Pa |
| Wärme | hg | J |
| Kühlwassermenge | mK | kg |
| Unterdruck | Unterdruck | – |
| Unterdrucks | K | -- |
Calculation options
Vakuumbrechers
1 · 2 · 3 · 4 · 5 · 6 · 7 · 8
Vakuumbrechers
VL - Mit Liftfunktion und Auffangschale · V - Ohne Liftfunktion und Auffangschale
Frequently asked questions
Why is the cool-down after steam-out so critical in particular?
During steam-out, the vessel is practically completely filled with water vapor at about 100 °C. When this steam condenses during cool-down, its volume collapses by roughly a factor of 1000 – the pressure drop is therefore extremely fast, especially when cold water directly contacts the vessel wall or the vapor space (e.g. rain on the hot tank). Normal breather openings are often too small for this dynamic.
How much vacuum can a typical storage tank actually withstand?
Flat-bottom storage tanks built to tank codes are frequently designed only for vacuum in the order of a few millibar (typically 2.5 to 8.5 mbar, depending on design); pressure vessels tolerate considerably more, depending on their external pressure verification. The permissible vacuum must come from the vessel documentation or the stability verification (buckling under external pressure) – it is the decisive limit value for the TAVA assessment.
What role does the correction factor for the cool-down behavior play?
The real condensation and cool-down kinetics depend on details that are hard to model: wetting of the wall, stratification in the vapor space, inert gas fractions, rain or spray patterns. The correction factor makes it possible to set the calculation conservatively to the fastest possible cool-down or to adjust it to empirical values or measurements. For the safety verification, the most unfavorable (fastest) cool-down should always be assumed.
Does the calculation replace the vacuum breaker sizing per code?
It complements it: codes such as ISO 28300/API 2000 provide blanket venting rates for normal operation (in-breathing due to cooling, pump-out). The special case of the steam-filled vessel after steam-out is often not covered by them and requires the transient analysis performed here. The result then serves as the design basis for the required flow capacity of the vacuum breaker at the permissible vacuum.