📚 Course ContentsChapter 4 Tank test methodology

4. Tank test methodology

The tank test is the reference measurement for airbag inflator output. An inflator is fired inside a sealed, rigid pressure vessel, and the resulting pressure rise is recorded as a function of time. From that single curve, engineers derive the mass flow rate, total gas yield, and burn duration that anchor every downstream CAE model. Because the tank test is comparatively cheap, repeatable, and traceable, it is the de facto ground truth against which simulation results are judged. This section covers how the pressure–time curve is measured, how the vessel is sized for a given inflator class, and which correction factors must be applied before the data can be used for model validation.

Measurement Principle and Instrumentation

The physical basis is straightforward: gas generated by the inflator is confined in a fixed volume, so the pressure rise is proportional to the mass of gas released and its temperature. The vessel is a thick-walled steel or aluminum cylinder, typically rated well above the expected peak pressure, with a burst disc or relief port as a safety backstop. A piezoelectric or strain-gauge pressure transducer is mounted flush with the inner wall to avoid acoustic cavity effects. Sampling rates of 50–100 kHz are common because the initial pressure rise can be extremely steep; undersampling smears the peak and biases the derived mass flow.

A typical acquisition setup records three channels: vessel pressure, a trigger signal from the firing circuit, and ambient temperature. The trigger defines t = 0. The pressure trace is then integrated using the ideal-gas relation to obtain the effective gas mass:

m(t) = (P(t) - P0) * V / (R * T_tank)

where:
  P(t)    = instantaneous absolute pressure [Pa]
  P0      = initial absolute pressure [Pa]
  V       = vessel free volume [m^3]
  R       = specific gas constant of the combustion products [J/(kg*K)]
  T_tank  = mean gas temperature in the vessel [K]

Differentiating m(t) gives the mass flow rate, which is the quantity most CAE solvers actually consume. Note that T_tank is not the adiabatic flame temperature; it is the mixed temperature of the gas after it has expanded into the vessel, and it changes during the event. This is the first place where a correction factor becomes necessary.

Tank Sizing

Vessel volume is selected so that the peak pressure stays within the transducer's linear range and below the vessel's design limit, while the pressure rise remains large enough to resolve above noise. A practical rule is to target a peak gauge pressure between 20 % and 60 % of the transducer's full-scale rating. For a driver-side inflator with roughly 60–100 g of gas generant, a 60 L tank is a common choice; passenger-side inflators with larger gas output typically use 100–280 L vessels.

The sizing calculation starts from an estimate of total gas moles. If the propellant mass is m_prop and the specific gas yield is n_g (moles per gram), the expected peak pressure at the initial temperature is:

P_peak = P0 + (n_g * m_prop * R * T0) / V

Example (illustrative, not measured data):
  m_prop = 80 g, n_g = 0.025 mol/g, T0 = 298 K
  n_total = 2.0 mol
  V = 0.060 m^3, R = 8.314 J/(mol*K)
  P_peak = 101325 + (2.0 * 8.314 * 298) / 0.060
         = 101325 + 82,600 = 183,925 Pa (about 0.83 bar gauge)

If that gauge pressure is too low for good resolution, the tank is too large; if it approaches the transducer limit, the tank is too small. In practice, the free volume must also account for the inflator body, mounting fixture, and any internal baffles, which can reduce effective volume by 2–5 %.

Always measure the free volume by gas expansion (a known quantity of helium or nitrogen) rather than trusting the nominal cylinder volume. Manufacturing tolerances and internal hardware can shift the effective volume enough to introduce a several-percent error in the derived mass flow.

Correction Factors

Raw pressure data cannot be used directly for CAE validation without correcting for three effects: heat loss to the vessel walls, gas non-ideality at high pressure, and the temperature drop as the gas expands. Each correction is applied in sequence.

Heat loss correction. The vessel walls act as a heat sink. A first-order correction uses a heat-transfer coefficient h and the wetted area A to estimate the energy lost: Q_loss = h * A * (T_gas - T_wall). For short-duration events (< 100 ms), this correction is typically 3–8 % of the total energy. For longer events, it can exceed 15 %.
Non-ideality correction. At peak pressures above roughly 10 bar, the ideal-gas law overpredicts the gas mass. A compressibility factor Z from a real-gas equation of state (e.g., Peng–Robinson) is applied: m = (P - P0) * V / (Z * R * T). For typical inflator gases at 5–15 bar, Z ranges from 0.96 to 0.99.
Temperature correction. The gas temperature at the moment of measurement is not the initial temperature. A common approach is to assume adiabatic mixing and solve iteratively for T(t) using the measured pressure and the known vessel volume. This is the most sensitive correction and the largest source of uncertainty.

The corrected mass flow curve is what gets compared against the CAE-predicted mass flow. If the correction is omitted, the simulation will appear to overpredict the inflator output, leading to an incorrect conclusion about model accuracy.

Practical Workflow and Verification

A complete tank test campaign for one inflator variant typically involves five to ten shots at a controlled temperature (e.g., 23 °C ± 2 °C) to establish repeatability. The coefficient of variation of the peak pressure should be under 2 %; if it is higher, check the firing circuit, the transducer mounting torque, and the vessel temperature uniformity. The corrected mass flow curves from all shots are averaged, and the average curve is used as the CAE input.

Verification of the correction factors themselves is done by firing a known reference inflator (one with a certified gas yield) and confirming that the corrected mass matches the certificate within 3 %. If it does not, the heat-loss coefficient or the free volume is wrong. A common failure symptom is a corrected mass that is consistently 5–10 % low across all shots; this usually points to an overestimated heat-loss coefficient or an underestimated free volume.

Do not apply correction factors from one tank to another without re-validating. Heat-transfer characteristics depend on vessel geometry, wall material, and surface finish. A correction set developed for a 60 L steel tank will not transfer directly to a 280 L aluminum tank.

Data Reduction Example

Suppose a 60 L tank records a peak gauge pressure of 1.85 bar at 23 °C, with a time to peak of 42 ms. The uncorrected mass using the ideal-gas law and an assumed gas constant of 280 J/(kg·K) is approximately 0.138 kg. Applying a heat-loss correction of 6 % and a compressibility factor of 0.98 gives a corrected mass of about 0.132 kg. The mass flow rate at peak is then obtained by differentiating the corrected curve; for this example, the peak flow is roughly 4.2 kg/s. These values are illustrative and would need to be replaced by actual measured data in a real validation exercise.

The corrected mass flow curve is the deliverable that feeds the CAE inflator model. Every correction step must be documented alongside the raw data so that a reviewer can reproduce the reduction. When the CAE-predicted pressure–time curve is compared against the tank test, the comparison should be made on the corrected curve, not the raw trace. A mismatch of more than 5 % in peak mass flow or more than 3 ms in time-to-peak is typically treated as a model discrepancy requiring investigation, whether in the inflator model, the tank boundary conditions, or the correction factors themselves.