Discharge Models

Most of incident and hazards associated with escaping hydrogen such as fire, explosion, and even formation of a flammable vapour cloud usually involve the escape of liquid or gaseous hydrogen from the containment owing to failure followed vaporization and dispersion. In particular, a large quantity of liquid hydrogen and/or vapour may be released by failure of the tank, line or valve.

For hydrogen gas at low pressure, the flow through an orifice is governed initially by the equation of isentropic (constant entropy) flow, by solving the conservation of energy and mass equation. When the ratio of upstream pressure is lower than so-called critical pressure, the mass flow through the orifice is given by [183]:


2 gMw g

Vro 0

Vro 0


Stagnation pressure upstream (N/m2)


Ratio specific heat for H2 (=1.42)


Downstream stagnation pressure


Discharge coefficient (=0.86, GH2.

(=101325 N/m2)

generated by PHAST)


Molecular weight (=2.016)


Aperture area (m2)


Universal gas constant (=8310


Acceleration of gravitation (=9.80




Upstream stagnation temperature (K)

The velocity of the gas is given by r Po u = 2 C

In most situation, the pressure outside the throat of the orifice is atmospheric, so that for upstream pressures greater than about 2 bar absolute, the flow will be critical, or supersonic. For these conditions, the mass flow is given by:

Uthroat = V gRTt throat

To calculate the rate of release given the size of the aperture using thermodynamic and physical properties of escaping liquid hydrogen (LH2) we can use the Bernoulli equation [17]:

Q Release rate (kg/s) C Discharge coefficient (=0.6, LH2, generated by PHAST) Pi Vapor pressure of LH2 (N/m2)

h Height of liquid tank (m) Pa Ambient pressure (=101325

The fluid release may be gas, liquid, or a two-phase mixture, depending on certain conditions. For example, if the release is from a container holding liquid under pressure, it will normally be liquid if the aperture is below the liquid level, and vapour or vapour-liquid mixture if it is above the liquid level. For given pressure difference, the mass rate of release is usually much greater for a liquid or vapour-liquid mixture than for a gas.

Two-phase flows are classified as either reactive or non-reactive [2]. The reactive case is typical of emergency relief of exothermic chemical reactions, while the non-reactive case involves the flashing of liquids as they are discharged from containment. Two special considerations are required. If the liquid is sub-cooled, the discharge flow will choke at its saturation vapor pressure at ambient temperature. If the liquid is stored under its own vapor pressure, a more detailed analysis is required. Both of these situations are accounted for by the following expression:



is two-phase mass discharge rate (kg/s)


is area of the discharge (m2)


is sub-cooled mass flux (kg/m2s)


is equilibrium mass flux (kg/m2s)


is a non-equilibrium parameter (-)

Mass flux for the sub-cooled and equilibrium is given by

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