Hydraulic Accumulator — validation & limitations

What it calculates

• Accumulator sizing by the polytropic gas law — bladder, piston and diaphragm types
• Isothermal and adiabatic gas law selection (Boyle's Law / polytropic n = 1.4 for nitrogen)
• Gas precharge pressure guidance: P₀ ≤ 0.9 × P₁ (common manufacturer guidance)
• Flow & pressure response with peak-flow supplement, line Reynolds number, Darcy friction factor and discharge-time estimate
• Energy storage analysis: stored energy (isothermal and adiabatic), peak discharge power, peak-power reduction fraction and annual CO₂ savings estimate
• PED 2014/68/EU category screen based on PV product (pressure × volume)
• Pressure cycle fatigue life estimation using Miner's rule and bladder-material lookup (engineering estimate — see disclaimer)

Standards this tool applies

• ISO 1219 — Size the accumulator shown in the circuit — nitrogen precharge, required gas volume, isothermal or adiabatic gas law, and PED 2014/68/EU category screen (gas-law sizing; EN 14359 not implemented).

Related standards — reference only, not implemented

• EN 14359reference only — Gas-law application sizing (EN 14359 itself is not implemented) — bladder/piston/diaphragm, isothermal and adiabatic gas laws, gas precharge check, PED 2014/68/EU category screen (simplified, from PS·V), energy storage analysis, and fatigue life estimate.

Validation evidence — independent reference cases (1)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• Gas-law sizing, gas temperature, energy and hot-day pressure

  Agrees

  Source: Polytropic law p·V^n = const (Esposito, Fluid Power with Applications, Ch. 10; hydraulic-component makers' sizing guides); ISO 2533 atmosphere; hand derivation

  Inputs: Bladder, P0 90 / P1 100 / P2 200 bar g, dV 4 L, T_amb 20 C, Tmax 50 C, P_sv 220 or 221 bar

  Quantity	Reference value	Tolerance
  V0 isothermal	8.924 L	1e-6 relative
  V0 adiabatic (n 1.4)	11.098 L	1e-6 relative
  T2 adiabatic	94.479 C	1e-6 relative
  Hot-day pressure P_hot	220.571 bar g	1e-6 relative

  tests/golden/REF-accumulator-sizing-gas-law.golden.test.ts

Limitations

Not checked by this tool

• Real-gas behaviour of the nitrogen charge at high pressure — Sizing uses the ideal gas law; at high pressure nitrogen deviates and more volume is needed — apply the accumulator maker's real-gas correction
• Heat transfer during the cycle (the real polytropic index) — One index n is used (1.0 or 1.4); for cycle times between seconds and minutes use the maker's sizing software or a measured n
• Shell strength and certification of the vessel — Use the maker's certified shell (EN 14359 / PED); the tool sizes volumes and screens the PED category only
• Safety-valve sizing (relief capacity) — Not sized; size the relief valve for the full pump flow and the fire / heat case (EN ISO 4126)
• Pressure surges in the connecting lines — The flow step is steady-state; check surge and pulsation at valve switching separately
• Mounting clamps and supports — Use the accumulator maker's clamp sets for the vessel weight and pulsation