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Release and dispersion modeling of cryogenic under-expanded hydrogen jets
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 6 ) 1 e1 1
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Release and dispersion modeling of cryogenic under-expanded hydrogen jets A.G. Venetsanos a, S.G. Giannissi a,b,* a
Environmental Research Laboratory, National Centre for Scientific Research Demokritos, Aghia Paraskevi, Athens, 15341, Greece b School of Chemical Engineering, National Technical University of Athens, Heroon Polytechniou 9, 15780, Athens, Greece
article info
abstract
Article history:
In the present work performed within the framework of the SUSANA EC-project, we
Received 26 February 2016
address the release and dispersion modeling of hydrogen stored at cryogenic temperatures
Received in revised form
and high pressures. Due to the high storage pressures the resulting jets are under-
9 August 2016
expanded. Due to the low temperatures the choked conditions can be two-phase. For the
Accepted 10 August 2016
release modeling the homogeneous equilibrium model (HEM) was used combined with
Available online xxx
NIST equation of state for hydrogen. For the dispersion modeling the 3d CFD methodology was used combined with a) a notional nozzle approach to bridge the expansion to atmo-
Keywords:
spheric pressure region that exists near the nozzle, b) the ideal gas assumption for
Hydrogen release
hydrogen and air and c) the standard (buoyancy included) keε turbulence model. Predicted
Hydrogen dispersion
release choked mass fluxes are compared against 37 experiments from literature. Predicted
HEM model
steady state hydrogen concentrations along the jet axis are compared against five
ADREA-HF
dispersion experiments from literature as well as the Chen and Rodi correlation and the
Cryogenic jets
behavior of the proposed release and dispersion modeling approaches is assessed.
Under-expanded jets
© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction One of the options of storing hydrogen is at cryogenic temperatures and high pressures. By cryogenic temperatures here we refer to temperatures not very far from hydrogen's critical temperature (33.145 K). Depending on the particular storage conditions hydrogen can be in gaseous phase, liquid phase or supercritical phase. This storage method could be characterized as “cryo-compressed”. Safety analysis of any hydrogen storage method is important and necessary to ensure that risks after a potential
accidental leak are below the acceptable level. From the point of view of safety, the cryo-compressed storage has interesting physical features. In case of an accidental small break of containment or piping, choked conditions will develop at the break, due to the “high pressure” feature of this storage method and the resulting hydrogen jet will be underexpanded. On the other hand, due to the cryogenic temperatures involved, the choked conditions can result to be in the two-phase region. More specifically (assuming isentropic expansion from stagnation to the break location) in the misty region (vapor quality > 0.5), if stagnation entropy is higher than the entropy of the thermodynamic critical point of
* Corresponding author. Environmental Research Laboratory, National Centre for Scientific Research Demokritos, Aghia Paraskevi, Athens, 15341, Greece. E-mail addresses: [email protected] (A.G. Venetsanos), [email protected] (S.G. Giannissi). http://dx.doi.org/10.1016/j.ijhydene.2016.08.053 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Nomenclature
xi U
molecular diffusivity, m2/s nozzle diameter, m mass flux, kg/m2/s gravity acceleration in the i-direction, m/s2 enthalpy, J/kg mass fraction, dimensionless time, s turbulent Schmidt and Prandtl number, dimensionless entropy, J/kg/K temperature, saturation temperature, K i-component of velocity, m/s vapor quality (vapor mass fraction), dimensionless cartesian i-coordinate, m axial velocity, m/s
Greek dij l m; mt r
Kronecker delta thermal conductivity, W/m/K laminar and turbulent viscosity, kg/m/s density, kg/m3
d D G gi h q t Sct ; Prt s T; Ts ui x
Subscripts k substance k l liquid s surrounding conditions t throat v vapor 0 stagnation conditions 1 nozzle conditions 2 notional nozzle conditions
hydrogen or in the bubbly region (vapor quality < 0.5), if stagnation entropy is lower. An additional consequence of the cryogenic temperatures is the possible liquefaction of nitrogen and oxygen and solidification of the humidity of ambient air. All the above features make the modeling and experimentation of cryo-compressed hydrogen release and dispersion a difficult and complex task. One of the first works related to the cryo-compressed storage method was performed back in 1979 by NASA [1]. Experimental data were presented for the two-phase choked flow of three cryogenic fluidsdnitrogen, methane, and hydrogendin four convergingediverging nozzles. Oxygen data were reported earlier in [2]. In almost all the cases examined the throat conditions were two-phase. The cryogenic hydrogen critical flow tests were performed in an elliptical nozzle only with 2.934 mm throat diameter. Examined hydrogen stagnation conditions were in the range 0:82 < T0 =Tcr < 0:98 and 0:995 < P0 =Pcr < 4:54 corresponding to the sub-cooled liquid regime. In the same work, NASA performed simulations and proposed a modified Henry-Fauske release model which correlated all the choked-flow-rate data to within 10%. They found that neither the homogeneous equilibrium model (HEM), nor
the Henry-Fauske model predicted throat pressures well over the whole range of data. More specifically, above the thermodynamic critical temperature the HEM model was preferred for both flow rate and pressure ratio (choked pressure/stagnation pressure) simulations. The NASA release tests were much later successfully simulated by Travis et al. [3]. The authors proposed a homogeneous, non-equilibrium (HNE) two-phase critical flow model, which accounts for the possibility of the liquid phase to be in superheated conditions in the bubbly regime, while assumes equal velocities between liquid and vapor phase (mechanical equilibrium). The authors did not demonstrate the behavior of the HEM release model against the proposed HNE model. The first experiments with aim to study hydrogen dispersion under cryo-compressed storage conditions were performed by Veser et al. [4] at KIT (Karlsruhe Institute of Technology) and reported also Xiao et al. [5]. Steady state hydrogen concentrations along the jet axis were presented for two experiments: tests 3 and 4, which had nozzle diameter and stagnation conditions (2 mm, 8.25 bar, 80 K) and (1 mm, 32 bar, 80 K) respectively. Measured mass flow rate was 3.3 g/s. No measurements were performed at the release nozzle. Xiao et al. [5] successfully simulated the abovementioned tests 3 and 4. Simulated choked conditions were found in the gaseous regime far from saturation (choked temperatures nearly 60 K). Simulations of the dispersion were performed with a proposed non-Boussinesq integral model and showed good agreement with the measured concentrations along the jet axis. The authors applied the “notional nozzle approach” to bridge the highly compressible and computationally very expensive region that exists between the nozzle and a location further downstream, where the pressure has expanded to atmospheric. More specifically, they proposed a model based on conservation equations of mass, momentum and energy. A similar model has been proposed independently by Yu¨ceil and € ¨ gen [6]. An associated review on notional nozzle apM. Ottu proaches and their effects on dispersion can be found in reference [7]. The Veser et al. experiments were later successfully simulated by Houf et al. [8], using an integral dispersion model. Regarding the release modeling, the authors proposed the use of the two-phase sonic velocity model of Chung et al. [9]. It should be mentioned here that this model was not relevant to the particular data employed for validation, since: a) conditions at the nozzle were gaseous and far from saturation and b) the Chung et al. model was originally developed for bubbly flow (vapor quality < 0.5). Finally, Houf et al. employed the abovementioned notional nozzle approach of Xiao et al. in their dispersion simulations. The most recent experimental study on hydrogen release and dispersion from cryo-compressed storage conditions is the work of Friedrich et al. [10], performed at the HYKA site of KIT. A series of horizontal release tests were performed through 1 (for series 3000 and 4000) and 0.5 mm (for series 5000) diameter release nozzles, inside a confined but large enough compared to the jet region test chamber with initially quiescent atmosphere. Measured stagnation conditions were in the range 1:02 < T0 =Tcr < 1:96 and 0:54 < P0 =Pcr < 2:7, with most of them found in the supercritical and a few in the
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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gaseous phase. Although the main focus of the tests was the heat radiation after ignition, a limited number of dispersion experiments were also performed and the hydrogen concentrations were reported for selected tests along the jet axis. Release mass flow rates were measured during the tests but no information was provided for conditions at the release nozzle. The present work is a continuation of [11]. The target of the present work was to study the phenomena associated with cryo-compressed release and dispersion by simulating the abovementioned release and dispersion experiments, using the previously validated CFD code ADREA-HF [12,13] for dispersion and the GAJET code for release [14]. Since the GAJET code was originally developed for gaseous release from compressed gaseous storage, it was modified in the framework of this study to handle two-phase hydrogen conditions, using the NIST Equation of State [15] for normal hydrogen, which is based on explicit modeling of the Helmholtz free energy and which is considered as the current standard for hydrogen. Finally, the whole work was performed within the framework of the SUSANA EC-project [16], whose main targets are to develop an evaluation protocol, a guide to best practice for Computational Fluid Dynamics (CFD) codes/models used for hydrogen safety applications along with an associated database of high quality experimental data.
the present work the efficient Golden Search Algorithm was implemented and used. All physical properties required in the release simulations were calculated using the NIST EoS, which is continuous over liquid, vapor and supercritical regions. The HEM model in choked flow simulations is a simple and powerful tool. Various non-equilibrium models were proposed in the literature for cryo-compressed hydrogen releases, as mentioned in the introduction. The thermal equilibrium assumption may be violated in the bubbly twophase regime especially near the saturated liquid point, where the liquid phase can become superheated. The homogeneous flow assumption may be violated in the misty regime, where the vapor can be accelerated with respect to the droplets. The proposed non-equilibrium models were based on introducing a two-phase sound velocity at choked conditions. It should be noted here that the choking velocity for two phase flow is not necessarily equal to the sound velocity [17]. Furthermore, if a dispersion simulation is the final target then use of a non-equilibrium choked flow model should be combined with use of a dispersion model able to handle nonequilibrium effects.
Choked flow simulations NASA tests
Release modeling Choked flow modeling We assume isentropic expansion between stagnation and nozzle. Under isentropic conditions, for known nozzle pressure P, the mass flux G is given by: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G ¼ r 2ðh0 hÞ
(1)
For single phase conditions density (r), enthalpy (h) and entropy (s) are functions of temperature and pressure. The unknown nozzle temperature can be found iteratively from the equation: sðT; PÞ ¼ s0 ðT0 ; P0 Þ, where subscript 0 denotes stagnation. For two phase conditions the Homogeneous Equilibrium Model (HEM) assumes thermal equilibrium between phases (same temperature and pressure) and homogeneous conditions (same velocity, i.e. hydrodynamic equilibrium). In this case fluid density, enthalpy and entropy are functions also of the vapor quality x. In the equations below subscripts (v, l) refer to saturated vapor and liquid phases respectively, while the saturation temperature TS is a function of pressure. r ¼ xrv ðTS ; PÞ þ ð1 xÞrl ðTS ; PÞ
(2)
h ¼ xhv ðTS ; PÞ þ ð1 xÞhl ðTS ; PÞ
(3)
s ¼ xsv ðTS ; PÞ þ ð1 xÞsl ðTS ; PÞ ¼ s0 ðT0 ; P0 Þ0x ¼
The stagnation conditions and measured data of the NASA cryogenic hydrogen critical flow experiments with an elliptical nozzle are shown in Table 1, adapted from Ref. [1]. All tests were simulated with the НЕМ choked flow model. As shown in Fig. 1, the overall agreement between predicted and measured choked mass fluxes is reasonably good and within the 10% error bands. In 20 out of the 22 tests the predicted mass flux was slightly overestimated. This is partly due to an
s0 sl sv sl
(4)
The choked (maximum) mass flow rate and associated nozzle conditions can be found either in single phase or in two phase conditions by iterating over the nozzle exit pressure. In
Table 1 e NASA data [1] for hydrogen critical flow experiments with an elliptical nozzle. Test
P0 (bar)
T0 (K)
G (kg/m2/s)
Pt/P0
1199 1200 1212 1210 1222 1216 1197 1198 1207 1213 1206 1219 1211 1217 1223 1215 1214 1221 1224 1218 1220 1201
29.3 34 43.1 47.1 58.2 58.9 12.9 21.9 28.8 35.6 36 37 42.2 42.1 42.5 16.7 22.3 22.1 28.1 28.5 29 29.4
27.8 27.2 28.7 28.7 28.1 28.6 30.7 29 30.3 29.5 29.5 30.6 29.1 30.3 29.8 32.3 31 32.2 31.3 32.3 31.3 32.2
17,000 18,700 20,900 22,100 25,000 25,100 8900 13,700 15,700 18,400 18,500 18,300 20,500 19,900 20,200 9000 12,700 11,900 15,000 14,300 15,200 14,200
0.143 0.113 0.104 0.098 0.074 0.075 0.364 0.232 0.220 0.139 0.185 0.154 0.110 0.128 0.119 0.448 0.276 0.298 0.231 0.260 0.225 0.252
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Fig. 2 e KIT-2012 experiments [10]: Predicted versus measured mass fluxes. The dashed lines represent the factor of 2 values.
Fig. 1 e NASA hydrogen critical flow experiments with an elliptical nozzle [1]: Predicted versus measured mass fluxes (above) and predicted versus measured throat to stagnation pressure ratio (below). Colors (red, green, blue) for T0 ≈ 28, 30, 32 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
assumed discharge coefficient of 1.0 in all simulations. The model underestimated the mass flux in the two tests with the lowest mass flux and one of these is shown to lie slightly out of the 10% error bands. The figure also shows predicted versus measured throat to stagnation pressure ratios. The comparison is not as good as with mass fluxes. The two points with the largest overestimation of pressure ratio correspond to the two points where the mass flux was underestimated. It should be mentioned that in all simulated cases predicted choked conditions were found to lie at the liquid saturation line.
KIT-2012 tests The HEM choked flow model with a discharge coefficient of 1.0 was applied to simulate all KIT-2012 experiments. Stagnation conditions and measured mass fluxes were reported in Ref. [10]. Measured mass fluxes are generally lower than in the NASA tests. Fig. 2 compares predicted and measured mass fluxes. Large deviations between predictions and experiments can be observed. In 12 out of the 15 tests mass fluxes were underestimated. The largest underestimation was 63% for tests 3001 and 3006, which had identical stagnation conditions in the vapor regime. Table 2 shows predicted choked
conditions for tests 3000, 3004 and 5000 for which dispersion simulations were performed (see next section). Predicted mass flux was overestimated by 20.6% for test 3004 and underestimated by 10.3% and 30.2% for tests 3000 and 5000 respectively. Fig. 3 presents, on a TS chart constructed using the implemented NIST-EoS for hydrogen, the reported stagnation conditions for KIT experiments 3001, 3000, 3004, 3006 and 5000 as well as the calculated nozzle expanded locations (after the assumed isentropic expansion). Stagnation conditions are in the supercritical state for tests 3000, 3004 and 5000 and gaseous state for test 3001 and 3006. Predicted choked conditions were found at the saturation lines except for test 5000, for which choked conditions are in the gaseous state. The HEM model behavior for stagnation entropy less than critical entropy is demonstrated in Fig. 4, for the conditions of KIT test 3004. As nozzle pressure decreases from stagnation the mass flux increases until the liquid saturation point is reached. The flow at the nozzle is in single phase. Since the gradient of the mass flux over pressure is not zero (condition for sonic velocity, see Ref. [3]) as the liquid saturation line is approached, the nozzle velocity at liquid saturation is lower than the sound speed of liquid. The HEM model is activated for lower nozzle pressures after crossing the liquid saturation line. The limit of the two phase sound velocity at x ¼ 0 predicted by the HEM model is shown to be lower than the sound speed of saturated liquid. This is a known feature of the HEM critical flow model, see Ref. [9]. Due to the thermal equilibrium assumption of the HEM model there is a discontinuity of the gradient of density over pressure (at constant entropy) at liquid saturation, which results in a discontinuity of the gradient of the mass flux. The resulting choked condition (maximum mass flux) is observed to occur at liquid saturation. Choked flow is under-expanded and can be considered as subsonic in this case. The HEM model behavior for test 3000 is shown in Fig. 5. Choking condition is found at the vapor saturation line in this case. As with test 3004 above sound velocity shows a discontinuity when crossing saturation (at x ¼ 1.0). Choked nozzle velocity is shown to lie between the sound speed of vapor and the limit of the two phase sound speed at x ¼ 1.0. Choked flow
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Table 2 e KIT experimental data and predicted choked conditions. Experiment
Prediction (choked conditions)
Test
P0 (bar)
T0 (K)
G (kg/m2/s)
T (K)
P (bar)
Density (kg/m3)
Vapor volume fraction
Velocity (m/s)
G (kg/m2/s)
3000 3004 5000
19 29 29.85
37 36 43.59
5793.2 10,211.4 10,542.4
32.85 32.28 33.16
12.42 11.42 12.50
22.37 45.48 19.03
1.0 0.0 1.0
232.43 270.98 386.75
5199.6 12,324.8 7358.2
50
50 45 40
45
35
30
25
5000
20 15
Temperature (K)
40
10
3000 3004
3001, 3006
35
5 bar
30
25
Sat liquid
Sat vapor
20 -2.5
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
22.5
Entropy (kJ/kg/K)
Fig. 3 e KIT-2012 experiments: Hydrogen TS chart showing stagnation conditions (filled squares) and predicted choked conditions (open squares).
is under-expanded and can be considered as subsonic in this case. For test 5000, the HEM model behavior is shown in Fig. 6. Choking condition occurs out of the two phase region in this case. At choking condition both the gradient of the mass flux curve equals to zero and the nozzle velocity equals the sound speed. Choked flow is under-expanded and sonic in this case.
It is not clear to the authors why the HEM choked flow model acceptably predicts the NASA tests, while gives such large discrepancies for the KIT tests. One reason could be the existence of non-homogeneous and non-equilibrium phenomena. Both tend to increase the mass flux compared to homogeneous equilibrium flow according to [18]. If these effects are more pronounced at low mass fluxes then this could
Fig. 4 e HEM model predictions for KIT test 3004. Mass flux (red) and nozzle velocity (green) versus pressure drop between stagnation and nozzle. Choked conditions predicted at liquid saturation line (vapor quality x ¼ 0). Choked nozzle velocity lies between the sound speeds (blue) of liquid and the limit of the two phase sound speed at x ¼ 0. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5 e HEM model predictions for KIT test 3000. Mass flux (red) and nozzle velocity (green) versus pressure drop between stagnation and nozzle. Choked conditions predicted at vapor saturation line (x ¼ 1.0). Choked nozzle velocity lies between the sound speeds (blue) of vapor and the limit of the two phase sound speed at x ¼ 1.0. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Fig. 7 e Under-expanded jet from the reservoir (level 0) through the nozzle (level 1). The gas is expanded to a notional location (level 2).
Fig. 6 e HEM model predictions for KIT test 5000. Mass flux (red) and nozzle velocity (green) versus pressure drop between stagnation and nozzle. Choked conditions predicted outside the two-phase region. Nozzle velocity equals the sound speed (blue) at choking condition. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
also explain the slight underestimation of mass flux observed in the two lowest mass flux NASA tests. On the other hand the underestimation of the mass flux for test 5000 is unexplained as in this case the isentropic expansion did not hit the saturation line. Another reason could be the transition from supercritical state to liquid or gaseous state during the isentropic expansion, which characterizes and differentiates the KIT tests from the NASA tests. The effect of this transition on the choked flow should be examined. Last explanation could be uncertainty in the experiments. This final argument though is very difficult to support given that repeatability tests were performed (test 5000 repeated 17 times, while test 3001 repeated 2 times, see Ref. [10]). Given the above, it is clear that the simulation of critical two-phase flow is an important open issue and not only for hydrogen. The KIT dispersion simulations presented in the next sections were performed with two sets of nozzle conditions as presented in Tables 2 and 3. In the second case we modified stagnation pressure such that the HEM model approximately reproduces the experimental mass flux. This approach implicitly assumes uncertainty in the experimental stagnation pressures and validity of the HEM model.
Notional nozzle modeling In under-expanded jets a highly compressible region exists downstream the nozzle where the pressure expands to atmospheric through a series of shocks. Accurate simulations in
this region are computationally very expensive, because they require use of non-ideal gas properties and high mesh resolution to capture the shocks. The notional nozzle approach (see Fig. 7) consists of replacing the true nozzle (level 1) with a notional nozzle of higher diameter further downstream (level 2), where the pressure has expanded to atmospheric. The main benefit of this approach is that dispersion simulations starting from the notional nozzle are computationally much faster, because the highly compressible and computationally very expensive region that exists immediately downstream the true nozzle is bypassed. Notional nozzle modeling consists of finding the diameter and flow conditions at level 2, knowing the conditions at level 1 from a previous choked flow simulation. Usually no entrainment of air is assumed between levels 1 and 2 and the notional diameter is derived from a mass balance between levels 1 and 2. Regarding the velocity at level 2, it was found in Ref. [7], where various notional nozzle approaches were examined, that when a momentum balance between level 1 and level 2 was applied (see equation below), the predicted concentrations were in better agreement with experimental. Actually, the effect of the momentum balance is to increase the velocity at level 2 compared to level 1. An increased velocity will lead to higher entrainment of air into the jet and therefore lower concentrations. In the present work we used the momentum balance below. U2 ¼ U1 þ
1 ðP1 P2 Þ G
(5)
Regarding the temperature at the notional nozzle, having in mind that we are dealing with cryogenic temperatures, it is not physical to assume it equal to ambient, as is done for example in the model of Birch [19]. An isentropic energy balance between levels 1 and 2 was used in Refs. [5] and [6]. Such a balance will produce temperature at level 2 lower than at level 1 and consequently higher density (possibly in the twophase region). In the present work we set the temperature at level 2 equal to that at level 1, similar to Ewan and Moodie [20],
Table 3 e Modified stagnation conditions for KIT experiments and predicted choked conditions. Modified stagnation conditions
Prediction (choked conditions)
Case
P0 (bar)
T0 (K)
T (K)
P (bar)
Density (kg/m3)
Vapor volume fraction
Velocity (m/s)
G (kg/m2/s)
3000 3004 5000
20 25.3 38.5
37 36 43.59
33.05 32.64 33.71
12.79 12.05 13.87
25.71 42.72 27.21
1.0 0.0 1.0
227.55 242.88 389.64
5850.4 10,376.8 10,602.7
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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implicitly assuming heating of the cold hydrogen between levels 1 and 2 from the ambient air and/or any shocks. Regarding required densities of hydrogen at level 2, these were evaluated with the NIST EoS, but as clearly shown in Fig. 8 the ideal gas assumption is acceptable.
CFD dispersion modeling Mathematical formulation The ADREA-HF code is a general transient three dimensional multi-component two-phase flow CFD solver. It solves the Cartesian conservation equations of mixture mass, momentum and enthalpy and the conservation equation for the total mass fraction of each component (see below in tensor notation). It assumes an ideal mixture, thermal equilibrium between phases and obtains phase distribution of components using Raoult's law. Mechanical non-equilibrium between phases can be handled using various slip models and additional terms (not included below) in the conservation equations. vr vrui þ ¼0 vt vxi
(6)
vrui vruj ui vP v vui vuj 2 vuk ðm þ mt Þ þ ¼ þ þ dij þ rgi vxi vxj vt vxj vxj vxi 3 vxk (7) N DP vrh v v vT X vq þ þ þ rdk hk k ruj h ¼ l vt vxj Dt vxj vxj k¼1 vxj v mt vh þ vxj Prt vxj
vrqk vruj qk v þ ¼ vxj vt vxj
!
(8)
m vqk rdk þ t Sct vxj
(9)
ADREA-HF can use a variety of RANS and LES turbulence models. In the present work turbulence was modeled using the standard keε model with buoyancy terms. Turbulent Prandtl and Schmidt numbers are set equal to 0.72. 1.4
Hydrogen density (kg/m3)
21 K
1.2
+10 % NIST EoS
1
31 K 0.8
41 K 0.6
0.4
100 K
0.2 0.2
0.4
0.6
0.8
1
1.2
1.4
Ideal EoS
Fig. 8 e Comparison between ideal gas and NIST hydrogen density at 1 atm pressure and low temperatures.
7
Regarding physical properties ADREA-HF uses by default ideal gas EoS for vapor phase and correlations for liquid phase from [21]. In the present simulations the mixture was assumed to be composed of dry air and hydrogen. For hydrogen ADREA-HF can use the NIST-EoS but also the third order equations of state of PengeRobinson and RedlicheKwongeMathiaseCopeman [22]. In the present dispersion work we made the ideal gas assumption for hydrogen, which is valid down to very low temperatures at ambient pressures as shown in Fig. 8.
Problem setup and numerical options All hydrogen releases considered were horizontal in the xdirection. The computational domain was 4.5 0.5 2 m in x, y, z directions respectively. Symmetry was assumed in the ydirection, consequently only half of the notional nozzle area was considered. The domain was discretized with a basic Cartesian grid with the following method. The half notional nozzle area was set to coincide with one computational cell x-face at coordinates (0.012, 0.0, 1.0). The x-size of the source cell was set to one notional diameter. Away from the source the grid cells expanded in the x, y, z directions with maximum expansion ratio of 1.12. The resulting grids consisted of approximately 170,000, 120,000, 280,000, 198,000 and 206,000 computational cells for KIT-2012 cases 3000, 3004 and 5000 and KIT-2011 cases 3 and 4 respectively. Grid sensitivity studies were performed with finer grids constructed either by reducing the maximum expansion ratio or by increasing the source discretization (two cells instead of one). The grid sensitivity studies showed that the basic grid gave practically grid independent results for the predicted hydrogen concentrations. For time integration of the conservation equations the 1st order fully implicit scheme was used, while for the convective terms the QUICK (3rd order) numerical scheme was used. A constant CFL number equal to 10 was imposed, in order to restrict the increase of time step. Smaller CFL numbers were tested and showed no impact on the results. West (upstream the nozzle) and bottom domain boundaries were set as wall boundaries and standard wall functions were used as velocity and turbulence boundary conditions. The other boundaries were set as open boundaries with constant pressure boundary condition. For temperature and hydrogen mass fraction on open boundaries the boundary condition was zero gradient if outflow occurs or Dirichlet (equal to the initial value) if inflow occurs, while a zero gradient was assumed on solid boundaries. At the source the previously calculated notional conditions (see Tables 4e6) were set as Dirichlet boundary conditions, assuming at the same time zero normal diffusion (inflow boundary condition). Finally, simulations were performed in transient mode until steady state conditions were reached. The steady state concentrations (v/v) along the jets axis were then compared against the experimental. Initial conditions were stagnant atmosphere (zero ambient velocity) at 288.15 K, 1 atm. Initial turbulence levels were set to small values (1.0 105).
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Table 4 e KIT-2011: Calculated notional nozzle conditions.
3 4
=
Test
Diameter (mm)
T (K)
Vapor volume fraction
Velocity (m/ s)
3.3 3.2
60.1 59.54
1.0 1.0
924.4 973.0
Table 5 e KIT-2012: Calculated notional nozzle conditions (original stagnation conditions). Test
Diameter (mm)
T (K)
Vapor volume fraction
Velocity (m/ s)
3000 3004 5000
3.9 6.7 2.1
32.85 32.28 33.16
1.0 1.0 1.0
451.7 355.4 542.8
Table 6 e KIT-2012: Calculated notional nozzle conditions (modified stagnation conditions). Test
Diameter (mm)
T (K)
Vapor volume fraction
Velocity (m/ s)
3000 3004 5000
4.2 6.2 2.6
33.05 32.64 33.71
1.0 1.0 1.0
428.8 349.2 510.9
Results and discussion KIT-2011 tests Predicted steady state hydrogen concentrations along the jet axis are compared against experimental data for tests 3 and 4 of Veser et al. [4,5] in Fig. 9 (left) and Fig. 10 (left). In the same Figures (right) the steady state predicted axial velocity along the jet axis is also presented. However, no experimental data are available for comparison. The solid lines correspond to the CFD solution while the dashed lines to the following Chen and Rodi [23] hyperbolic correlations, see also Molkov [24], q ¼ 5:4
pffiffiffiffiffiffiffiffiffiffiffiffi D r1 =rs x
12 U r D ¼ 6:2 1 U1 x rs
(10)
(11)
Note that for the CFD curves the x-axis is the distance from the notional nozzle, while for the experimental data and the correlation the distance from the real nozzle. The distance between true and notional nozzle is estimated to be around 30 nozzle diameters maximum, as reported in Ref. [5]. Since we are dealing with very small diameters this distance is small and was not taken into account in the figures. CFD predicted concentrations are generally found overestimated in both simulated cases with higher overestimation for test 3. Maximum relative error for this test occurs close to the source and is about 30%. Further away from the source the agreement with the experiments is generally much better. The observed overestimation might be due to an overestimated hydrogen mass flow rate calculation. The predicted mass flow rate and nozzle conditions for these tests were exactly as reported in Ref. [5], where it is mentioned that experimental mass flow rate could be less than the predicted 3.3 g/s. The overestimation could also be attributed to the turbulence model. Higher turbulent mixing could lead to mixture dilution and thus decrease of the predicted concentration. The Chen and Rodi correlation is shown to consistently overestimate both the CFD predictions and the experimental data as far as the concentration is concerned. From the safety point of view both the CFD dispersion predictions and the correlation are conservative for the two tests examined. Regarding the velocity profile the Chen and Rodi correlation underestimates the axial velocity close to the nozzle by maximum approximately 26%, while at further distances it computes axial velocity very close to the CFD prediction for both simulated cases.
KIT-2012 tests CFD predicted steady state hydrogen concentrations along the jet axis are compared against experimental data for tests 3000, 3004 and 5000 of Friedrich et al. [10] and the Chen and Rodi correlation in Figs. 11e13 below. In the same Figures (right) the steady state predicted axial velocity along the jet axis is also presented and compared against the Chen and Rodi
Fig. 9 e Steady state predicted versus measured hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis. Chen and Rodi correlation is also shown. Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Fig. 10 e Steady state predicted versus measured hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis. Chen and Rodi correlation is also shown.
correlation. Few points along the jet axis were considered for monitoring the velocity. As with the KIT-2011 tests, the x-axis for the CFD curves is the distance from the notional nozzle, while in the experimental data and the correlation the distance from the real nozzle. Due to the large discrepancy found between predicted and observed mass fluxes (see release section above), two different predictive approaches are shown in the figures depending on release conditions used: a) using the experimental mass flux and b) using the mass flux predicted with HEM model for the given experimental stagnation conditions. The second case is what would happen in case of a simulated accident scenario, without any previous knowledge of real release rates. In the first case the HEM predicted mass flux was set to match the experimental by modifying the stagnation conditions. Fig. 11 shows axial concentrations (left) and velocities (with the 10.3% lower mass flux approach) (right) for test 3000. The two predictive approaches differ very slightly, with the 10.3% lower mass flux resulting in lower concentrations as expected. When compared with experimental data CFD predicted concentrations are overestimated near the source by approximately 30% maximum. Away from the source underestimation occurs which is reduced with increasing distance. The CFD model behavior can be considered satisfactory in this case. The Chen and Rodi correlation on the other hand overestimates both the CFD solution and the experimental data as far as the concentration is concerned. As
far as the axial velocity is concerned the Chen and Rodi correlation underestimates the CFD solution by a maximum 32% close to the nozzle. In test 3004 (see Fig. 12) the two predictive approaches differ again slightly, with the 20.6% higher mass flux resulting in higher concentrations as expected. When compared with experimental data, the CFD predicted concentrations are generally underestimated by 30% maximum resulting in a non-conservative model behavior. The Chen and Rodi correlation as before overestimates the CFD solution but gives reasonably good agreement with the experimental data as far as the concentration is concerned. Regarding the velocity profile (with the 20.6% higher mass flux approach) the Chen and Rodi correlation tends to underestimate the CFD velocity by a maximum 18% close to the nozzle. Further downwind the nozzle the Chen and Rodi correlation and the CFD predictions are in good agreement. For test series 5000 (see Fig. 13) the two predictive approaches show much larger deviation, due to the higher difference in mass flux (30.2%), with again higher mass flux resulting in higher concentrations. Compared against the experiments, the CFD predictions performed using the experimental mass flux generally overestimate concentrations. This could be due to small misalignment of jet direction from horizontal during the tests, since the nozzle diameter in this case was 0.5 mm. On the other hand the CFD prediction with the predictive approach b) shows that the concentrations are
Fig. 11 e Steady state predicted versus measured hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis for case 3000. Chen and Rodi correlation is also shown. Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Fig. 12 e Predicted versus measured steady state hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis for case 3004. Chen and Rodi correlation is also shown.
Fig. 13 e Predicted versus measured steady state hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis for case 5000. Chen and Rodi correlation is also shown.
in reasonable agreement with the experiment. The Chen and Rodi correlation in this case overestimates both the CFD solution and the experimental data for concentration, while it underestimates the CFD axial velocity (by a maximum 18%) similar to the other simulated tests. From the above it can be concluded that CFD predictions of axial concentrations for the KIT-2012 dispersion experiments 3000, 3004 and 5000 have a non-consistent trend when compared to experimental data, in contrast to the KIT-2011 experiments simulations. In all cases examined the Chen and Rodi correlation was found to overestimate the CFD solution and the experimental data except for test 3004, for which the agreement with the data was reasonably good.
Conclusions Release and dispersion of cryogenic compressed hydrogen jets has been investigated using the HEM critical flow model combined with hydrogen properties from NIST EoS, implemented in the GAJET release code and the CFD dispersion code ADREA-HF using ideal gas assumption, a notional nozzle approach and the standard (buoyancy included) keε turbulence model. Simulations were compared against the release
data of NASA [1] and KIT-2012 [10] and the dispersion data of KIT-2011 [4,5] and KIT-2012 [10]. For the release, predicted mass fluxes were found slightly overestimated (10%) compared to the data of NASA. Higher deviations from experiment were observed regarding the predicted throat to stagnation pressures. For the data of KIT2012 the predicted versus observed mass flux behavior was found inconsistent. In 12 out of the 15 tests performed predicted mass fluxes were underestimated compared to experiments, with 63% and 37% maximum underestimation and overestimation respectively. This behavior suggests that the HEM model may not be conservative for hydrogen release simulations. The CFD dispersion simulations showed generally consistent and acceptable agreement with the data of KIT-2011 regarding axial hydrogen concentrations, with trend to give conservative results. On the other hand the results obtained for the data of KIT-2012 at lower stagnation temperatures (down to 36 K) did not exhibit a specific trend. For test 3000 predicted axial concentrations were found in reasonable agreement with experiment. For test 3004 predicted concentrations were found consistently underestimated even when the 20.6% higher than experimental mass flux predicted by the HEM model was used in the simulations. For test 5000, when
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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simulations were performed with the release mass flow rate predicted by HEM model using the experimental stagnation conditions, predicted axial concentrations were found in reasonable agreement with experimental. When the simulations were performed with the experimental flow rate (30.2% higher), predicted concentrations were found to be overestimated. The Chen and Rodi correlation for axial decay of hydrogen concentration was found generally conservative when compared against the selected data. It was also shown that this correlation systematically overestimates the CFD predictions. On the contrary, the Chen and Rodi correlation for decay of axial flow velocity underestimates the CFD predictions, especially, at distances close to the nozzle. In view of the above inconsistent results both for release and dispersion, it is suggested to further investigate the issue of cryogenic hydrogen release and dispersion both experimentally and theoretically. Future experimental work should include compressed and non-compressed hydrogen storage at as much as possible controlled ambient conditions (preferably indoors). Future theoretical work should be focused on examining the effects of non-homogeneous and/or nonequilibrium phenomena, turbulence modeling, as well as air oxygenenitrogen liquefaction and humidity solidification, due to the cryogenic temperatures involved.
Acknowledgements The research leading to these results was financially supported by the SUSANA project, which has received funding from the European Union's Seventh Framework Programme (FP7/2007e2013) for the Fuel Cells and Hydrogen Joint Technology Initiative under grant agreement n FCH-JU-325386.
references
[1] Simoneau R, Hendricks R. Two-phase choked flow of cryogenic fluids in convergingediverging nozzles. NASA Tech. Rep. Pap. 1484. 1979. [2] Hendricks RF, Simoneau RC, Barrows RJ. Two-phase choked flow of subcooled oxygen and nitrogen. NASA Tech. Rep. Pap. TN-8169. 1976. [3] Travis J, Koch D, Breitung W. A homogeneous nonequilibrium two-phase critical flow model. Int J Hydrogen Energy 2012;37(22):17373e9. [4] Veser A, Kuznetsov M, Fast G, Friedrich A, Kotchourko N, Stern G, et al. The structure and flame propagation regimes in turbulent hydrogen jets. Int J Hydrogen Energy 2011;36(3):2351e9.
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[5] Xiao J, Travis JR, Breitung W. Hydrogen release from a high pressure gaseous hydrogen reservoir in case of a small leak. Int J Hydrogen Energy 2011;36(3):2545e54. € ¨ gen M. Scaling parameters for underexpanded [6] Yu¨ceil K, Ottu supersonic jets. Phys Fluids 2002;14(12):4206e15. [7] Papanikolaou E, Baraldi D, Kuznetsov M, Venetsanos AG. Evaluation of notional nozzle approaches for CFD simulations of free-shear under-expanded hydrogen jets. Int J Hydrogen Energy 2012;37(23):18563e74. [8] Houf WG, Winters WS. Simulation of high-pressure liquid hydrogen releases. Int J Hydrogen Energy Jun. 2013;38(19):8092e9. [9] Chung M-S, Park S-B, Lee H-K. Sound speed criterion for twophase critical flow. J Sound Vib 2004;276(1-2):13e26. [10] Friedrich A, Breitung W, Stern G, Veser A, Kuznetsov M, Fast G, et al. Ignition and heat radiation of cryogenic hydrogen jets. Int. J. Hydrogen Energy Nov. 2012;37(22):17589e98. [11] Giannissi SG, Venetsanos AG, Markatos N. Modelling of cryogenic hydrogen jets. In: 6th Int. Conference on hydrogen safety; Oct. 19e21/2015. Yokohama, Japan. [12] Venetsanos AG, Papanikolaou E, Bartzis JG. The ADREA-HF CFD code for consequence assessment of hydrogen applications. Int J Hydrogen Energy Apr. 2010;35(8):3908e18. [13] Giannissi SG, Hoyes JR, Chernyavskiy B, Hooker P, Hall J, Venetsanos AG, et al. CFD benchmark on hydrogen release and dispersion in a ventilated enclosure: passive ventilation and the role of an external wind. Int J Hydrogen Energy 2015;40(19):6465e77. [14] Venetsanos AG, Huld T, Adams P, Bartzis JG. Source, dispersion and combustion modeling of an accidental release of hydrogen in an urban environment. J Hazard Mater 2003;A105(1-3):1e25. [15] Leachman JW, Jacobsen RT, Penoncello SG, Lemmon EW. Fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen. J Phys Chem Ref Data 2009;38(3):721e48. [16] SUSANA project webpage, http://www.support-cfd.eu. [17] Johnson RW. The handbook of fluid dynamics. CRC Press LLC and Springer-Verlag GmbH & Co. KG; 1998. [18] Perry RH, Green DW. Perry 's chemical engineers’ handbook. McGraw-Hill; 1999. p. 2582. [19] Birch AD, Hughes DJ, Swaffield F. Velocity decay of high pressure jets. Combust Sci Technol 1987;52(1-3):161e71. [20] Ewan BCR, Moodie K. Structure and velocity measurements in underexpanded jets. Combust Sci Technol 1986;45(5e6):275e88. [21] Poling BE, Prausnitz JM, O'Connell JP. The properties of gases and liquids. 5th ed. McGraw-Hill; 2004. [22] Nasrifar K. Comparative study of eleven equations of state in predicting the thermodynamic properties of hydrogen. Int J Hydrogen Energy 2010;35(8):3802e11. [23] Chen CJ, Rodi W. Vertical turbulent buoyant jets: a review of experimental data. HMT-4. Pergamon; 1980. [24] Molkov V. Fundamentals of hydrogen safety engineering I. free book at, bookboon.com; 2012.
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Release and dispersion modeling of cryogenic under-expanded hydrogen jets A.G. Venetsanos a, S.G. Giannissi a,b,* a
Environmental Research Laboratory, National Centre for Scientific Research Demokritos, Aghia Paraskevi, Athens, 15341, Greece b School of Chemical Engineering, National Technical University of Athens, Heroon Polytechniou 9, 15780, Athens, Greece
article info
abstract
Article history:
In the present work performed within the framework of the SUSANA EC-project, we
Received 26 February 2016
address the release and dispersion modeling of hydrogen stored at cryogenic temperatures
Received in revised form
and high pressures. Due to the high storage pressures the resulting jets are under-
9 August 2016
expanded. Due to the low temperatures the choked conditions can be two-phase. For the
Accepted 10 August 2016
release modeling the homogeneous equilibrium model (HEM) was used combined with
Available online xxx
NIST equation of state for hydrogen. For the dispersion modeling the 3d CFD methodology was used combined with a) a notional nozzle approach to bridge the expansion to atmo-
Keywords:
spheric pressure region that exists near the nozzle, b) the ideal gas assumption for
Hydrogen release
hydrogen and air and c) the standard (buoyancy included) keε turbulence model. Predicted
Hydrogen dispersion
release choked mass fluxes are compared against 37 experiments from literature. Predicted
HEM model
steady state hydrogen concentrations along the jet axis are compared against five
ADREA-HF
dispersion experiments from literature as well as the Chen and Rodi correlation and the
Cryogenic jets
behavior of the proposed release and dispersion modeling approaches is assessed.
Under-expanded jets
© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction One of the options of storing hydrogen is at cryogenic temperatures and high pressures. By cryogenic temperatures here we refer to temperatures not very far from hydrogen's critical temperature (33.145 K). Depending on the particular storage conditions hydrogen can be in gaseous phase, liquid phase or supercritical phase. This storage method could be characterized as “cryo-compressed”. Safety analysis of any hydrogen storage method is important and necessary to ensure that risks after a potential
accidental leak are below the acceptable level. From the point of view of safety, the cryo-compressed storage has interesting physical features. In case of an accidental small break of containment or piping, choked conditions will develop at the break, due to the “high pressure” feature of this storage method and the resulting hydrogen jet will be underexpanded. On the other hand, due to the cryogenic temperatures involved, the choked conditions can result to be in the two-phase region. More specifically (assuming isentropic expansion from stagnation to the break location) in the misty region (vapor quality > 0.5), if stagnation entropy is higher than the entropy of the thermodynamic critical point of
* Corresponding author. Environmental Research Laboratory, National Centre for Scientific Research Demokritos, Aghia Paraskevi, Athens, 15341, Greece. E-mail addresses: [email protected] (A.G. Venetsanos), [email protected] (S.G. Giannissi). http://dx.doi.org/10.1016/j.ijhydene.2016.08.053 0360-3199/© 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Nomenclature
xi U
molecular diffusivity, m2/s nozzle diameter, m mass flux, kg/m2/s gravity acceleration in the i-direction, m/s2 enthalpy, J/kg mass fraction, dimensionless time, s turbulent Schmidt and Prandtl number, dimensionless entropy, J/kg/K temperature, saturation temperature, K i-component of velocity, m/s vapor quality (vapor mass fraction), dimensionless cartesian i-coordinate, m axial velocity, m/s
Greek dij l m; mt r
Kronecker delta thermal conductivity, W/m/K laminar and turbulent viscosity, kg/m/s density, kg/m3
d D G gi h q t Sct ; Prt s T; Ts ui x
Subscripts k substance k l liquid s surrounding conditions t throat v vapor 0 stagnation conditions 1 nozzle conditions 2 notional nozzle conditions
hydrogen or in the bubbly region (vapor quality < 0.5), if stagnation entropy is lower. An additional consequence of the cryogenic temperatures is the possible liquefaction of nitrogen and oxygen and solidification of the humidity of ambient air. All the above features make the modeling and experimentation of cryo-compressed hydrogen release and dispersion a difficult and complex task. One of the first works related to the cryo-compressed storage method was performed back in 1979 by NASA [1]. Experimental data were presented for the two-phase choked flow of three cryogenic fluidsdnitrogen, methane, and hydrogendin four convergingediverging nozzles. Oxygen data were reported earlier in [2]. In almost all the cases examined the throat conditions were two-phase. The cryogenic hydrogen critical flow tests were performed in an elliptical nozzle only with 2.934 mm throat diameter. Examined hydrogen stagnation conditions were in the range 0:82 < T0 =Tcr < 0:98 and 0:995 < P0 =Pcr < 4:54 corresponding to the sub-cooled liquid regime. In the same work, NASA performed simulations and proposed a modified Henry-Fauske release model which correlated all the choked-flow-rate data to within 10%. They found that neither the homogeneous equilibrium model (HEM), nor
the Henry-Fauske model predicted throat pressures well over the whole range of data. More specifically, above the thermodynamic critical temperature the HEM model was preferred for both flow rate and pressure ratio (choked pressure/stagnation pressure) simulations. The NASA release tests were much later successfully simulated by Travis et al. [3]. The authors proposed a homogeneous, non-equilibrium (HNE) two-phase critical flow model, which accounts for the possibility of the liquid phase to be in superheated conditions in the bubbly regime, while assumes equal velocities between liquid and vapor phase (mechanical equilibrium). The authors did not demonstrate the behavior of the HEM release model against the proposed HNE model. The first experiments with aim to study hydrogen dispersion under cryo-compressed storage conditions were performed by Veser et al. [4] at KIT (Karlsruhe Institute of Technology) and reported also Xiao et al. [5]. Steady state hydrogen concentrations along the jet axis were presented for two experiments: tests 3 and 4, which had nozzle diameter and stagnation conditions (2 mm, 8.25 bar, 80 K) and (1 mm, 32 bar, 80 K) respectively. Measured mass flow rate was 3.3 g/s. No measurements were performed at the release nozzle. Xiao et al. [5] successfully simulated the abovementioned tests 3 and 4. Simulated choked conditions were found in the gaseous regime far from saturation (choked temperatures nearly 60 K). Simulations of the dispersion were performed with a proposed non-Boussinesq integral model and showed good agreement with the measured concentrations along the jet axis. The authors applied the “notional nozzle approach” to bridge the highly compressible and computationally very expensive region that exists between the nozzle and a location further downstream, where the pressure has expanded to atmospheric. More specifically, they proposed a model based on conservation equations of mass, momentum and energy. A similar model has been proposed independently by Yu¨ceil and € ¨ gen [6]. An associated review on notional nozzle apM. Ottu proaches and their effects on dispersion can be found in reference [7]. The Veser et al. experiments were later successfully simulated by Houf et al. [8], using an integral dispersion model. Regarding the release modeling, the authors proposed the use of the two-phase sonic velocity model of Chung et al. [9]. It should be mentioned here that this model was not relevant to the particular data employed for validation, since: a) conditions at the nozzle were gaseous and far from saturation and b) the Chung et al. model was originally developed for bubbly flow (vapor quality < 0.5). Finally, Houf et al. employed the abovementioned notional nozzle approach of Xiao et al. in their dispersion simulations. The most recent experimental study on hydrogen release and dispersion from cryo-compressed storage conditions is the work of Friedrich et al. [10], performed at the HYKA site of KIT. A series of horizontal release tests were performed through 1 (for series 3000 and 4000) and 0.5 mm (for series 5000) diameter release nozzles, inside a confined but large enough compared to the jet region test chamber with initially quiescent atmosphere. Measured stagnation conditions were in the range 1:02 < T0 =Tcr < 1:96 and 0:54 < P0 =Pcr < 2:7, with most of them found in the supercritical and a few in the
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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gaseous phase. Although the main focus of the tests was the heat radiation after ignition, a limited number of dispersion experiments were also performed and the hydrogen concentrations were reported for selected tests along the jet axis. Release mass flow rates were measured during the tests but no information was provided for conditions at the release nozzle. The present work is a continuation of [11]. The target of the present work was to study the phenomena associated with cryo-compressed release and dispersion by simulating the abovementioned release and dispersion experiments, using the previously validated CFD code ADREA-HF [12,13] for dispersion and the GAJET code for release [14]. Since the GAJET code was originally developed for gaseous release from compressed gaseous storage, it was modified in the framework of this study to handle two-phase hydrogen conditions, using the NIST Equation of State [15] for normal hydrogen, which is based on explicit modeling of the Helmholtz free energy and which is considered as the current standard for hydrogen. Finally, the whole work was performed within the framework of the SUSANA EC-project [16], whose main targets are to develop an evaluation protocol, a guide to best practice for Computational Fluid Dynamics (CFD) codes/models used for hydrogen safety applications along with an associated database of high quality experimental data.
the present work the efficient Golden Search Algorithm was implemented and used. All physical properties required in the release simulations were calculated using the NIST EoS, which is continuous over liquid, vapor and supercritical regions. The HEM model in choked flow simulations is a simple and powerful tool. Various non-equilibrium models were proposed in the literature for cryo-compressed hydrogen releases, as mentioned in the introduction. The thermal equilibrium assumption may be violated in the bubbly twophase regime especially near the saturated liquid point, where the liquid phase can become superheated. The homogeneous flow assumption may be violated in the misty regime, where the vapor can be accelerated with respect to the droplets. The proposed non-equilibrium models were based on introducing a two-phase sound velocity at choked conditions. It should be noted here that the choking velocity for two phase flow is not necessarily equal to the sound velocity [17]. Furthermore, if a dispersion simulation is the final target then use of a non-equilibrium choked flow model should be combined with use of a dispersion model able to handle nonequilibrium effects.
Choked flow simulations NASA tests
Release modeling Choked flow modeling We assume isentropic expansion between stagnation and nozzle. Under isentropic conditions, for known nozzle pressure P, the mass flux G is given by: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G ¼ r 2ðh0 hÞ
(1)
For single phase conditions density (r), enthalpy (h) and entropy (s) are functions of temperature and pressure. The unknown nozzle temperature can be found iteratively from the equation: sðT; PÞ ¼ s0 ðT0 ; P0 Þ, where subscript 0 denotes stagnation. For two phase conditions the Homogeneous Equilibrium Model (HEM) assumes thermal equilibrium between phases (same temperature and pressure) and homogeneous conditions (same velocity, i.e. hydrodynamic equilibrium). In this case fluid density, enthalpy and entropy are functions also of the vapor quality x. In the equations below subscripts (v, l) refer to saturated vapor and liquid phases respectively, while the saturation temperature TS is a function of pressure. r ¼ xrv ðTS ; PÞ þ ð1 xÞrl ðTS ; PÞ
(2)
h ¼ xhv ðTS ; PÞ þ ð1 xÞhl ðTS ; PÞ
(3)
s ¼ xsv ðTS ; PÞ þ ð1 xÞsl ðTS ; PÞ ¼ s0 ðT0 ; P0 Þ0x ¼
The stagnation conditions and measured data of the NASA cryogenic hydrogen critical flow experiments with an elliptical nozzle are shown in Table 1, adapted from Ref. [1]. All tests were simulated with the НЕМ choked flow model. As shown in Fig. 1, the overall agreement between predicted and measured choked mass fluxes is reasonably good and within the 10% error bands. In 20 out of the 22 tests the predicted mass flux was slightly overestimated. This is partly due to an
s0 sl sv sl
(4)
The choked (maximum) mass flow rate and associated nozzle conditions can be found either in single phase or in two phase conditions by iterating over the nozzle exit pressure. In
Table 1 e NASA data [1] for hydrogen critical flow experiments with an elliptical nozzle. Test
P0 (bar)
T0 (K)
G (kg/m2/s)
Pt/P0
1199 1200 1212 1210 1222 1216 1197 1198 1207 1213 1206 1219 1211 1217 1223 1215 1214 1221 1224 1218 1220 1201
29.3 34 43.1 47.1 58.2 58.9 12.9 21.9 28.8 35.6 36 37 42.2 42.1 42.5 16.7 22.3 22.1 28.1 28.5 29 29.4
27.8 27.2 28.7 28.7 28.1 28.6 30.7 29 30.3 29.5 29.5 30.6 29.1 30.3 29.8 32.3 31 32.2 31.3 32.3 31.3 32.2
17,000 18,700 20,900 22,100 25,000 25,100 8900 13,700 15,700 18,400 18,500 18,300 20,500 19,900 20,200 9000 12,700 11,900 15,000 14,300 15,200 14,200
0.143 0.113 0.104 0.098 0.074 0.075 0.364 0.232 0.220 0.139 0.185 0.154 0.110 0.128 0.119 0.448 0.276 0.298 0.231 0.260 0.225 0.252
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Fig. 2 e KIT-2012 experiments [10]: Predicted versus measured mass fluxes. The dashed lines represent the factor of 2 values.
Fig. 1 e NASA hydrogen critical flow experiments with an elliptical nozzle [1]: Predicted versus measured mass fluxes (above) and predicted versus measured throat to stagnation pressure ratio (below). Colors (red, green, blue) for T0 ≈ 28, 30, 32 K. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
assumed discharge coefficient of 1.0 in all simulations. The model underestimated the mass flux in the two tests with the lowest mass flux and one of these is shown to lie slightly out of the 10% error bands. The figure also shows predicted versus measured throat to stagnation pressure ratios. The comparison is not as good as with mass fluxes. The two points with the largest overestimation of pressure ratio correspond to the two points where the mass flux was underestimated. It should be mentioned that in all simulated cases predicted choked conditions were found to lie at the liquid saturation line.
KIT-2012 tests The HEM choked flow model with a discharge coefficient of 1.0 was applied to simulate all KIT-2012 experiments. Stagnation conditions and measured mass fluxes were reported in Ref. [10]. Measured mass fluxes are generally lower than in the NASA tests. Fig. 2 compares predicted and measured mass fluxes. Large deviations between predictions and experiments can be observed. In 12 out of the 15 tests mass fluxes were underestimated. The largest underestimation was 63% for tests 3001 and 3006, which had identical stagnation conditions in the vapor regime. Table 2 shows predicted choked
conditions for tests 3000, 3004 and 5000 for which dispersion simulations were performed (see next section). Predicted mass flux was overestimated by 20.6% for test 3004 and underestimated by 10.3% and 30.2% for tests 3000 and 5000 respectively. Fig. 3 presents, on a TS chart constructed using the implemented NIST-EoS for hydrogen, the reported stagnation conditions for KIT experiments 3001, 3000, 3004, 3006 and 5000 as well as the calculated nozzle expanded locations (after the assumed isentropic expansion). Stagnation conditions are in the supercritical state for tests 3000, 3004 and 5000 and gaseous state for test 3001 and 3006. Predicted choked conditions were found at the saturation lines except for test 5000, for which choked conditions are in the gaseous state. The HEM model behavior for stagnation entropy less than critical entropy is demonstrated in Fig. 4, for the conditions of KIT test 3004. As nozzle pressure decreases from stagnation the mass flux increases until the liquid saturation point is reached. The flow at the nozzle is in single phase. Since the gradient of the mass flux over pressure is not zero (condition for sonic velocity, see Ref. [3]) as the liquid saturation line is approached, the nozzle velocity at liquid saturation is lower than the sound speed of liquid. The HEM model is activated for lower nozzle pressures after crossing the liquid saturation line. The limit of the two phase sound velocity at x ¼ 0 predicted by the HEM model is shown to be lower than the sound speed of saturated liquid. This is a known feature of the HEM critical flow model, see Ref. [9]. Due to the thermal equilibrium assumption of the HEM model there is a discontinuity of the gradient of density over pressure (at constant entropy) at liquid saturation, which results in a discontinuity of the gradient of the mass flux. The resulting choked condition (maximum mass flux) is observed to occur at liquid saturation. Choked flow is under-expanded and can be considered as subsonic in this case. The HEM model behavior for test 3000 is shown in Fig. 5. Choking condition is found at the vapor saturation line in this case. As with test 3004 above sound velocity shows a discontinuity when crossing saturation (at x ¼ 1.0). Choked nozzle velocity is shown to lie between the sound speed of vapor and the limit of the two phase sound speed at x ¼ 1.0. Choked flow
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Table 2 e KIT experimental data and predicted choked conditions. Experiment
Prediction (choked conditions)
Test
P0 (bar)
T0 (K)
G (kg/m2/s)
T (K)
P (bar)
Density (kg/m3)
Vapor volume fraction
Velocity (m/s)
G (kg/m2/s)
3000 3004 5000
19 29 29.85
37 36 43.59
5793.2 10,211.4 10,542.4
32.85 32.28 33.16
12.42 11.42 12.50
22.37 45.48 19.03
1.0 0.0 1.0
232.43 270.98 386.75
5199.6 12,324.8 7358.2
50
50 45 40
45
35
30
25
5000
20 15
Temperature (K)
40
10
3000 3004
3001, 3006
35
5 bar
30
25
Sat liquid
Sat vapor
20 -2.5
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
22.5
Entropy (kJ/kg/K)
Fig. 3 e KIT-2012 experiments: Hydrogen TS chart showing stagnation conditions (filled squares) and predicted choked conditions (open squares).
is under-expanded and can be considered as subsonic in this case. For test 5000, the HEM model behavior is shown in Fig. 6. Choking condition occurs out of the two phase region in this case. At choking condition both the gradient of the mass flux curve equals to zero and the nozzle velocity equals the sound speed. Choked flow is under-expanded and sonic in this case.
It is not clear to the authors why the HEM choked flow model acceptably predicts the NASA tests, while gives such large discrepancies for the KIT tests. One reason could be the existence of non-homogeneous and non-equilibrium phenomena. Both tend to increase the mass flux compared to homogeneous equilibrium flow according to [18]. If these effects are more pronounced at low mass fluxes then this could
Fig. 4 e HEM model predictions for KIT test 3004. Mass flux (red) and nozzle velocity (green) versus pressure drop between stagnation and nozzle. Choked conditions predicted at liquid saturation line (vapor quality x ¼ 0). Choked nozzle velocity lies between the sound speeds (blue) of liquid and the limit of the two phase sound speed at x ¼ 0. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 5 e HEM model predictions for KIT test 3000. Mass flux (red) and nozzle velocity (green) versus pressure drop between stagnation and nozzle. Choked conditions predicted at vapor saturation line (x ¼ 1.0). Choked nozzle velocity lies between the sound speeds (blue) of vapor and the limit of the two phase sound speed at x ¼ 1.0. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7 e Under-expanded jet from the reservoir (level 0) through the nozzle (level 1). The gas is expanded to a notional location (level 2).
Fig. 6 e HEM model predictions for KIT test 5000. Mass flux (red) and nozzle velocity (green) versus pressure drop between stagnation and nozzle. Choked conditions predicted outside the two-phase region. Nozzle velocity equals the sound speed (blue) at choking condition. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
also explain the slight underestimation of mass flux observed in the two lowest mass flux NASA tests. On the other hand the underestimation of the mass flux for test 5000 is unexplained as in this case the isentropic expansion did not hit the saturation line. Another reason could be the transition from supercritical state to liquid or gaseous state during the isentropic expansion, which characterizes and differentiates the KIT tests from the NASA tests. The effect of this transition on the choked flow should be examined. Last explanation could be uncertainty in the experiments. This final argument though is very difficult to support given that repeatability tests were performed (test 5000 repeated 17 times, while test 3001 repeated 2 times, see Ref. [10]). Given the above, it is clear that the simulation of critical two-phase flow is an important open issue and not only for hydrogen. The KIT dispersion simulations presented in the next sections were performed with two sets of nozzle conditions as presented in Tables 2 and 3. In the second case we modified stagnation pressure such that the HEM model approximately reproduces the experimental mass flux. This approach implicitly assumes uncertainty in the experimental stagnation pressures and validity of the HEM model.
Notional nozzle modeling In under-expanded jets a highly compressible region exists downstream the nozzle where the pressure expands to atmospheric through a series of shocks. Accurate simulations in
this region are computationally very expensive, because they require use of non-ideal gas properties and high mesh resolution to capture the shocks. The notional nozzle approach (see Fig. 7) consists of replacing the true nozzle (level 1) with a notional nozzle of higher diameter further downstream (level 2), where the pressure has expanded to atmospheric. The main benefit of this approach is that dispersion simulations starting from the notional nozzle are computationally much faster, because the highly compressible and computationally very expensive region that exists immediately downstream the true nozzle is bypassed. Notional nozzle modeling consists of finding the diameter and flow conditions at level 2, knowing the conditions at level 1 from a previous choked flow simulation. Usually no entrainment of air is assumed between levels 1 and 2 and the notional diameter is derived from a mass balance between levels 1 and 2. Regarding the velocity at level 2, it was found in Ref. [7], where various notional nozzle approaches were examined, that when a momentum balance between level 1 and level 2 was applied (see equation below), the predicted concentrations were in better agreement with experimental. Actually, the effect of the momentum balance is to increase the velocity at level 2 compared to level 1. An increased velocity will lead to higher entrainment of air into the jet and therefore lower concentrations. In the present work we used the momentum balance below. U2 ¼ U1 þ
1 ðP1 P2 Þ G
(5)
Regarding the temperature at the notional nozzle, having in mind that we are dealing with cryogenic temperatures, it is not physical to assume it equal to ambient, as is done for example in the model of Birch [19]. An isentropic energy balance between levels 1 and 2 was used in Refs. [5] and [6]. Such a balance will produce temperature at level 2 lower than at level 1 and consequently higher density (possibly in the twophase region). In the present work we set the temperature at level 2 equal to that at level 1, similar to Ewan and Moodie [20],
Table 3 e Modified stagnation conditions for KIT experiments and predicted choked conditions. Modified stagnation conditions
Prediction (choked conditions)
Case
P0 (bar)
T0 (K)
T (K)
P (bar)
Density (kg/m3)
Vapor volume fraction
Velocity (m/s)
G (kg/m2/s)
3000 3004 5000
20 25.3 38.5
37 36 43.59
33.05 32.64 33.71
12.79 12.05 13.87
25.71 42.72 27.21
1.0 0.0 1.0
227.55 242.88 389.64
5850.4 10,376.8 10,602.7
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implicitly assuming heating of the cold hydrogen between levels 1 and 2 from the ambient air and/or any shocks. Regarding required densities of hydrogen at level 2, these were evaluated with the NIST EoS, but as clearly shown in Fig. 8 the ideal gas assumption is acceptable.
CFD dispersion modeling Mathematical formulation The ADREA-HF code is a general transient three dimensional multi-component two-phase flow CFD solver. It solves the Cartesian conservation equations of mixture mass, momentum and enthalpy and the conservation equation for the total mass fraction of each component (see below in tensor notation). It assumes an ideal mixture, thermal equilibrium between phases and obtains phase distribution of components using Raoult's law. Mechanical non-equilibrium between phases can be handled using various slip models and additional terms (not included below) in the conservation equations. vr vrui þ ¼0 vt vxi
(6)
vrui vruj ui vP v vui vuj 2 vuk ðm þ mt Þ þ ¼ þ þ dij þ rgi vxi vxj vt vxj vxj vxi 3 vxk (7) N DP vrh v v vT X vq þ þ þ rdk hk k ruj h ¼ l vt vxj Dt vxj vxj k¼1 vxj v mt vh þ vxj Prt vxj
vrqk vruj qk v þ ¼ vxj vt vxj
!
(8)
m vqk rdk þ t Sct vxj
(9)
ADREA-HF can use a variety of RANS and LES turbulence models. In the present work turbulence was modeled using the standard keε model with buoyancy terms. Turbulent Prandtl and Schmidt numbers are set equal to 0.72. 1.4
Hydrogen density (kg/m3)
21 K
1.2
+10 % NIST EoS
1
31 K 0.8
41 K 0.6
0.4
100 K
0.2 0.2
0.4
0.6
0.8
1
1.2
1.4
Ideal EoS
Fig. 8 e Comparison between ideal gas and NIST hydrogen density at 1 atm pressure and low temperatures.
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Regarding physical properties ADREA-HF uses by default ideal gas EoS for vapor phase and correlations for liquid phase from [21]. In the present simulations the mixture was assumed to be composed of dry air and hydrogen. For hydrogen ADREA-HF can use the NIST-EoS but also the third order equations of state of PengeRobinson and RedlicheKwongeMathiaseCopeman [22]. In the present dispersion work we made the ideal gas assumption for hydrogen, which is valid down to very low temperatures at ambient pressures as shown in Fig. 8.
Problem setup and numerical options All hydrogen releases considered were horizontal in the xdirection. The computational domain was 4.5 0.5 2 m in x, y, z directions respectively. Symmetry was assumed in the ydirection, consequently only half of the notional nozzle area was considered. The domain was discretized with a basic Cartesian grid with the following method. The half notional nozzle area was set to coincide with one computational cell x-face at coordinates (0.012, 0.0, 1.0). The x-size of the source cell was set to one notional diameter. Away from the source the grid cells expanded in the x, y, z directions with maximum expansion ratio of 1.12. The resulting grids consisted of approximately 170,000, 120,000, 280,000, 198,000 and 206,000 computational cells for KIT-2012 cases 3000, 3004 and 5000 and KIT-2011 cases 3 and 4 respectively. Grid sensitivity studies were performed with finer grids constructed either by reducing the maximum expansion ratio or by increasing the source discretization (two cells instead of one). The grid sensitivity studies showed that the basic grid gave practically grid independent results for the predicted hydrogen concentrations. For time integration of the conservation equations the 1st order fully implicit scheme was used, while for the convective terms the QUICK (3rd order) numerical scheme was used. A constant CFL number equal to 10 was imposed, in order to restrict the increase of time step. Smaller CFL numbers were tested and showed no impact on the results. West (upstream the nozzle) and bottom domain boundaries were set as wall boundaries and standard wall functions were used as velocity and turbulence boundary conditions. The other boundaries were set as open boundaries with constant pressure boundary condition. For temperature and hydrogen mass fraction on open boundaries the boundary condition was zero gradient if outflow occurs or Dirichlet (equal to the initial value) if inflow occurs, while a zero gradient was assumed on solid boundaries. At the source the previously calculated notional conditions (see Tables 4e6) were set as Dirichlet boundary conditions, assuming at the same time zero normal diffusion (inflow boundary condition). Finally, simulations were performed in transient mode until steady state conditions were reached. The steady state concentrations (v/v) along the jets axis were then compared against the experimental. Initial conditions were stagnant atmosphere (zero ambient velocity) at 288.15 K, 1 atm. Initial turbulence levels were set to small values (1.0 105).
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Table 4 e KIT-2011: Calculated notional nozzle conditions.
3 4
=
Test
Diameter (mm)
T (K)
Vapor volume fraction
Velocity (m/ s)
3.3 3.2
60.1 59.54
1.0 1.0
924.4 973.0
Table 5 e KIT-2012: Calculated notional nozzle conditions (original stagnation conditions). Test
Diameter (mm)
T (K)
Vapor volume fraction
Velocity (m/ s)
3000 3004 5000
3.9 6.7 2.1
32.85 32.28 33.16
1.0 1.0 1.0
451.7 355.4 542.8
Table 6 e KIT-2012: Calculated notional nozzle conditions (modified stagnation conditions). Test
Diameter (mm)
T (K)
Vapor volume fraction
Velocity (m/ s)
3000 3004 5000
4.2 6.2 2.6
33.05 32.64 33.71
1.0 1.0 1.0
428.8 349.2 510.9
Results and discussion KIT-2011 tests Predicted steady state hydrogen concentrations along the jet axis are compared against experimental data for tests 3 and 4 of Veser et al. [4,5] in Fig. 9 (left) and Fig. 10 (left). In the same Figures (right) the steady state predicted axial velocity along the jet axis is also presented. However, no experimental data are available for comparison. The solid lines correspond to the CFD solution while the dashed lines to the following Chen and Rodi [23] hyperbolic correlations, see also Molkov [24], q ¼ 5:4
pffiffiffiffiffiffiffiffiffiffiffiffi D r1 =rs x
12 U r D ¼ 6:2 1 U1 x rs
(10)
(11)
Note that for the CFD curves the x-axis is the distance from the notional nozzle, while for the experimental data and the correlation the distance from the real nozzle. The distance between true and notional nozzle is estimated to be around 30 nozzle diameters maximum, as reported in Ref. [5]. Since we are dealing with very small diameters this distance is small and was not taken into account in the figures. CFD predicted concentrations are generally found overestimated in both simulated cases with higher overestimation for test 3. Maximum relative error for this test occurs close to the source and is about 30%. Further away from the source the agreement with the experiments is generally much better. The observed overestimation might be due to an overestimated hydrogen mass flow rate calculation. The predicted mass flow rate and nozzle conditions for these tests were exactly as reported in Ref. [5], where it is mentioned that experimental mass flow rate could be less than the predicted 3.3 g/s. The overestimation could also be attributed to the turbulence model. Higher turbulent mixing could lead to mixture dilution and thus decrease of the predicted concentration. The Chen and Rodi correlation is shown to consistently overestimate both the CFD predictions and the experimental data as far as the concentration is concerned. From the safety point of view both the CFD dispersion predictions and the correlation are conservative for the two tests examined. Regarding the velocity profile the Chen and Rodi correlation underestimates the axial velocity close to the nozzle by maximum approximately 26%, while at further distances it computes axial velocity very close to the CFD prediction for both simulated cases.
KIT-2012 tests CFD predicted steady state hydrogen concentrations along the jet axis are compared against experimental data for tests 3000, 3004 and 5000 of Friedrich et al. [10] and the Chen and Rodi correlation in Figs. 11e13 below. In the same Figures (right) the steady state predicted axial velocity along the jet axis is also presented and compared against the Chen and Rodi
Fig. 9 e Steady state predicted versus measured hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis. Chen and Rodi correlation is also shown. Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Fig. 10 e Steady state predicted versus measured hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis. Chen and Rodi correlation is also shown.
correlation. Few points along the jet axis were considered for monitoring the velocity. As with the KIT-2011 tests, the x-axis for the CFD curves is the distance from the notional nozzle, while in the experimental data and the correlation the distance from the real nozzle. Due to the large discrepancy found between predicted and observed mass fluxes (see release section above), two different predictive approaches are shown in the figures depending on release conditions used: a) using the experimental mass flux and b) using the mass flux predicted with HEM model for the given experimental stagnation conditions. The second case is what would happen in case of a simulated accident scenario, without any previous knowledge of real release rates. In the first case the HEM predicted mass flux was set to match the experimental by modifying the stagnation conditions. Fig. 11 shows axial concentrations (left) and velocities (with the 10.3% lower mass flux approach) (right) for test 3000. The two predictive approaches differ very slightly, with the 10.3% lower mass flux resulting in lower concentrations as expected. When compared with experimental data CFD predicted concentrations are overestimated near the source by approximately 30% maximum. Away from the source underestimation occurs which is reduced with increasing distance. The CFD model behavior can be considered satisfactory in this case. The Chen and Rodi correlation on the other hand overestimates both the CFD solution and the experimental data as far as the concentration is concerned. As
far as the axial velocity is concerned the Chen and Rodi correlation underestimates the CFD solution by a maximum 32% close to the nozzle. In test 3004 (see Fig. 12) the two predictive approaches differ again slightly, with the 20.6% higher mass flux resulting in higher concentrations as expected. When compared with experimental data, the CFD predicted concentrations are generally underestimated by 30% maximum resulting in a non-conservative model behavior. The Chen and Rodi correlation as before overestimates the CFD solution but gives reasonably good agreement with the experimental data as far as the concentration is concerned. Regarding the velocity profile (with the 20.6% higher mass flux approach) the Chen and Rodi correlation tends to underestimate the CFD velocity by a maximum 18% close to the nozzle. Further downwind the nozzle the Chen and Rodi correlation and the CFD predictions are in good agreement. For test series 5000 (see Fig. 13) the two predictive approaches show much larger deviation, due to the higher difference in mass flux (30.2%), with again higher mass flux resulting in higher concentrations. Compared against the experiments, the CFD predictions performed using the experimental mass flux generally overestimate concentrations. This could be due to small misalignment of jet direction from horizontal during the tests, since the nozzle diameter in this case was 0.5 mm. On the other hand the CFD prediction with the predictive approach b) shows that the concentrations are
Fig. 11 e Steady state predicted versus measured hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis for case 3000. Chen and Rodi correlation is also shown. Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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Fig. 12 e Predicted versus measured steady state hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis for case 3004. Chen and Rodi correlation is also shown.
Fig. 13 e Predicted versus measured steady state hydrogen concentration (left) and steady state predicted axial velocity (right) along the jet axis for case 5000. Chen and Rodi correlation is also shown.
in reasonable agreement with the experiment. The Chen and Rodi correlation in this case overestimates both the CFD solution and the experimental data for concentration, while it underestimates the CFD axial velocity (by a maximum 18%) similar to the other simulated tests. From the above it can be concluded that CFD predictions of axial concentrations for the KIT-2012 dispersion experiments 3000, 3004 and 5000 have a non-consistent trend when compared to experimental data, in contrast to the KIT-2011 experiments simulations. In all cases examined the Chen and Rodi correlation was found to overestimate the CFD solution and the experimental data except for test 3004, for which the agreement with the data was reasonably good.
Conclusions Release and dispersion of cryogenic compressed hydrogen jets has been investigated using the HEM critical flow model combined with hydrogen properties from NIST EoS, implemented in the GAJET release code and the CFD dispersion code ADREA-HF using ideal gas assumption, a notional nozzle approach and the standard (buoyancy included) keε turbulence model. Simulations were compared against the release
data of NASA [1] and KIT-2012 [10] and the dispersion data of KIT-2011 [4,5] and KIT-2012 [10]. For the release, predicted mass fluxes were found slightly overestimated (10%) compared to the data of NASA. Higher deviations from experiment were observed regarding the predicted throat to stagnation pressures. For the data of KIT2012 the predicted versus observed mass flux behavior was found inconsistent. In 12 out of the 15 tests performed predicted mass fluxes were underestimated compared to experiments, with 63% and 37% maximum underestimation and overestimation respectively. This behavior suggests that the HEM model may not be conservative for hydrogen release simulations. The CFD dispersion simulations showed generally consistent and acceptable agreement with the data of KIT-2011 regarding axial hydrogen concentrations, with trend to give conservative results. On the other hand the results obtained for the data of KIT-2012 at lower stagnation temperatures (down to 36 K) did not exhibit a specific trend. For test 3000 predicted axial concentrations were found in reasonable agreement with experiment. For test 3004 predicted concentrations were found consistently underestimated even when the 20.6% higher than experimental mass flux predicted by the HEM model was used in the simulations. For test 5000, when
Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053
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simulations were performed with the release mass flow rate predicted by HEM model using the experimental stagnation conditions, predicted axial concentrations were found in reasonable agreement with experimental. When the simulations were performed with the experimental flow rate (30.2% higher), predicted concentrations were found to be overestimated. The Chen and Rodi correlation for axial decay of hydrogen concentration was found generally conservative when compared against the selected data. It was also shown that this correlation systematically overestimates the CFD predictions. On the contrary, the Chen and Rodi correlation for decay of axial flow velocity underestimates the CFD predictions, especially, at distances close to the nozzle. In view of the above inconsistent results both for release and dispersion, it is suggested to further investigate the issue of cryogenic hydrogen release and dispersion both experimentally and theoretically. Future experimental work should include compressed and non-compressed hydrogen storage at as much as possible controlled ambient conditions (preferably indoors). Future theoretical work should be focused on examining the effects of non-homogeneous and/or nonequilibrium phenomena, turbulence modeling, as well as air oxygenenitrogen liquefaction and humidity solidification, due to the cryogenic temperatures involved.
Acknowledgements The research leading to these results was financially supported by the SUSANA project, which has received funding from the European Union's Seventh Framework Programme (FP7/2007e2013) for the Fuel Cells and Hydrogen Joint Technology Initiative under grant agreement n FCH-JU-325386.
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Please cite this article in press as: Venetsanos AG, Giannissi SG, Release and dispersion modeling of cryogenic under-expanded hydrogen jets, International Journal of Hydrogen Energy (2016), http://dx.doi.org/10.1016/j.ijhydene.2016.08.053