Comparison of modelling approaches for CFD simulations of high pressure H2 releases E. Papanikolaou, D. Baraldi Joint Research Centre - Institute for Energy and Transport daniele.baraldi@jrc.nl http://www.jrc.ec.europa.eu http://iet.jrc.ec.europa.eu

Outline Notional nozzle concept Notional nozzle approaches investigated Experimental description Simulations set up Results Conclusions Ongoing work

Notional nozzle concept The jet flow of a high pressure unintended release is complex: a supersonic region in the near field and a subsonic region downstream. Numerical modelling of the near field is quite demanding Need for reasonable computer run-times, for engineering applications Replacement of the actual release nozzle by a notional, occupying an area with the same flow rate as the actual one Does not necessarily exist in a physical sense Assumptions made: atmospheric pressure uniform velocity profile Under-expanded jet release Level 1: “reservoir” conditions Level 2: real orifice Level 3: notional nozzle location

Notional nozzle approaches investigated Birch et al. (1984) Conservation of mass, isentropic change, ideal gas, temperature at notional nozzle equal to atmospheric Birch et al. (1987) Conservation of mass, conservation of momentum, isentropic change, ideal gas, temperature at notional nozzle equal to atmospheric Ewan and Moodie (1986) Conservation of mass, isentropic change, ideal gas, temperature at notional nozzle equal to the one at the actual release nozzle Schefer et al. (2007) Conservation of mass, conservation of momentum, isentropic change, real gas (Abel-Noble equation of state), temperature at notional nozzle equal to atmospheric Notional nozzle approaches that take into account the conservation of energy have been also proposed such as Yücel & Ötügen (2002), Molkov et al. (2009) and Xiao et al. (2011)

Experimental description High momentum horizontal (free-surface) H2 experiments in the HYKA test facility of the Institute for Nuclear and Energy Technologies of FZK Selected experiment for investigation: H2 release from 1 mm diameter at stagnation pressure of 98.1 bar and stagnation temperature of 14.5 ºC H2 concentration and flow velocity were measured on the jet symmetry axis at 1.5 m and 2.25 m from the release

Simulations set up: conditions at the actual and notional nozzle Pressure (kPa) Density (kg/m3) Temperature (K) Sonic Velocity (m/s) Ideal gas* 5165 5.25 239 1178 Real gas* (Abel-Noble) 4932 4.89 235 1216 Table 1: Conditions at the release (actual nozzle) Approach Diameter (10-3 m) Area (10-5 m2) Density (kg/m3) Temperature (K) Velocity (m/s) Birch (1984)* 7.14 4.00 0.085 288 1293 Birch (1987)* 5.78 2.62 1972 Ewan&Moodie* 6.81 3.64 0.103 239 1178 Schefer 5.86 2.69 2029 Table 2: Conditions at the notional nozzle * A discharge coefficient equal to 0.91 was used to match the calculated mass flow rate to the experimental

Simulations set up: dispersion calculations ANSYS-CFX version 12.1 4 notional nozzle approaches “real” pipe with diameter equal to the experimental (D=1mm) and length equal to 10D to evaluate the level of accuracy with a coarse mesh (shock region not resolved) Equations of mass, momentum and energy (total enthalpy) conservation 4 commonly used turbulence models: standard k-, SST, RNG k- and baseline k- (BSL) All simulations run as transient cases for 5 s High resolution scheme for discretization of advection terms 2nd Order Backward Euler for discretization of transient terms Ideal gas law for the notional nozzle cases, Redlich Kwong equation for the “real” pipe cases Inlet with boundary conditions for velocity and temperature from the notional nozzle approaches or a given mass flowrate (equal to the experimental) for the “real” pipe cases. All simulations had a common incoming level of turbulence (intensity of 5%) assigned to the inlet

Simulations set up: dispersion calculations Computational domain: 15 m × 10 m × 10 m Minimum and maximum timestep was 10-8 s and 10-3 s for the notional nozzle cases and 10-8 s and 10-4 for the “real” pipe cases Unstructured mesh: 250.000 nodes for notional nozzle cases and 135.000 nodes for “real” pipe cases Solution domain for all cases

Results: H2 concentration at 1.5 m and 2.25 m from the release MEV: Mean Experimental Value STD: Standard Deviation 30% - 50% over or under prediction of MEV Comparison between approaches In general, Birch 1987, Schefer and “real” pipe cases perform better Comparison between turbulence models General tendency for higher predictions with k- , followed by RNG k- , BSL and lastly SST

Results: Flow velocity at 1.5 m and 2.25 m from the release Comparison between approaches Majority of predictions lie within the 30% over/under prediction of MEV Highest values predicted by approaches with highest release velocity (Schefer, Birch 1987) Comparison between turbulence models General tendency for higher predictions with k- , followed by either RNG k-  or BSL and lastly SST

Results: Contour plots of H2 concentration – Birch 1984 & Birch 1987 Case: Birch84 – BSL H2 mass in flammable cloud: 0.957 g Flammable volume: 0.189 m3 Case: Birch87 – BSL H2 mass in flammable cloud: 0.549 g Flammable volume: 0.112 m3 Case: Birch84 – k- H2 mass in flammable cloud: 1.51 g Flammable volume: 0.308 m3 Case: Birch87 – k- H2 mass in flammable cloud: 0.73 g Flammable volume: 0.149 m3 0.5 m Case: Birch84 – RNG H2 mass in flammable cloud: 0.919 g Flammable volume: 0.182 m3 Case: Birch87 – RNG H2 mass in flammable cloud: 0.494 g Flammable volume: 0.100 m3 Case: Birch84 – SST H2 mass in flammable cloud: 0.803 g Flammable volume: 0.159 m3 Case: Birch87 – SST H2 mass in flammable cloud: 0.438 g Flammable volume: 0.088 m3

Results: Contour plots of H2 concentration – Schefer and Ewan Case: Schefer – BSL H2 mass in flammable cloud: 0.542 g Flammable volume: 0.11 m3 Case: Ewan – BSL H2 mass in flammable cloud: 1.083 g Flammable volume: 0.21 m3 Case: Schefer – k- H2 mass in flammable cloud: 0.787 g Flammable volume: 0.16 m3 Case: Ewan – k-e H2 mass in flammable cloud: 1.698 g Flammable volume: 0.34 m3 Case: Schefer – RNG H2 mass in flammable cloud: 0.513 g Flammable volume: 0.105 m3 Case: Ewan – RNG H2 mass in flammable cloud: 1.174 g Flammable volume: 0.23 m3 Case: Schefer – SST H2 mass in flammable cloud: 0.443 g Flammable volume: 0.089 m3 Case: Ewan – SST H2 mass in flammable cloud: 0.937 g Flammable volume: 0.18 m3

Conclusions The conclusions are relevant to the selected experiment, the available data and the simulations’ set up. To make general comments, more experimental conditions should be investigated Birch 1987 and Schefer approaches produce more accurate results for the H2 concentration Including the conservation of momentum in the approach increases the accuracy of the results The coarse mesh of the “real” pipe cases produced accurate enough results for both H2 concentration and flow velocities on the symmetry axis Further investigation is necessary on both axial and radial distances from the release

Ongoing work Assessment of approaches with: different initial conditions (stagnation properties, release diameter) both axial and radial experimental measurements of H2 concentration and flow velocity Effect of: Grid resolution. Grid independence for notional nozzle approaches. Turbulence intensity at the source (5%, 10%). Discretization schemes

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Results: Contour plots of H2 concentration – Schefer and “real” pipe H2 mass in flammable cloud: 0.542 g Case: Schefer – BSL Flammable volume: 0.11 m3 Case: “real” pipe – BSL H2 mass in flammable cloud: 0.575 g Flammable volume: 0.115 m3