1. Gamma-ray attenuation for characterization of future space launcher fuels
Alain CARAPELLE et al., Centre Spatial de Liège - Université de Liège
IEEE Transactions On Nuclear Science, Volume: 53, Issue: 4, Part 1, On page(s):
Abstract
European Space Agency is studying the use of cryogenic solid-liquid mixture (Slush) of hydrogen as fuel for launcher. This work demonstrates the feasibility of gamma-ray attenuation to measure Slush density. An automated densitometer is built.
1. Introduction
In the frame of the European Space Agency (ESA) activities, previous study [1] shows that replacing liquid hydrogen by cryogenic solid-liquid mixture (Slush mixture) of hydrogen for the launcher's fuel can reduce its mass up to 26 %. An important parameter of this Slush mixture is the solid fraction. It can be obtained by measuring the density of the mixture. The mixture's density must remain in specified range to avoid mechanical problems: mainly pipe and pump obstruction. This work shows the density measurement of cryogenic Slush mixture by the attenuation of g rays. Densimeters using g rays attenuation are well know and have been adapted to special applications [2] but none of them have been used to measure cryogenic Slush mixture. The aim of this work is to demonstrate the ability of cryogenic density measurement of Slush mixture and to build an automatic densimeter. A similar study has been done by in the US during the 90's but results have not been fully published for confidentiality reasons.
2. Physical principle
The density measurement is based on the well-known Lambert law:
I=I0.e-μM.r.x
With the classical geometry described in Fig. 1:
Fig. 1. Measurement principle
Where I0 and I are incoming and outgoing g rays flux, r the density of the sample, x the length of the sample and μM the mass absorption coefficient. In our case, the units used were g/cm3 for r, cm for w and cm2/g for mM.The density is then given by:
As I and I0 are found by pulse counting, and for high count rates the statistical error on I and I0 are respectively (I)1/2 and (I0)1/2. If we neglect the error on μM parameter, we can use the propagation error formula [3] to obtain the relative error on density:
+ Relative error on x
It is interesting to evaluate the influence of different parameters on the error (Fig. 2 & 3).
Fig. 6 Automated densimeter design
The following picture show the automated densimeter
Fig. 2. Influence of Slush density, measurement time and source activity on statistical error
According to Fig. 2 the error can be reduced by increasing source activity and/or measurement time. The source activity is limited by legal limitation and the measurement time is limited by experimental set-up (Slush lifetime in production facility, Slush transfer time into pipes...).
According to Fig. 3 the relative error on density decreases as μM parameter decreases (values for μM can be obtained by using XCOM software from the NIST [4]). But for very small value of μM parameter, the relative error on density increases rapidly as μM parameter decreases. Practically, it is a good idea to have μM as small as possible but to keep it greater than 0.1 cm2/g. For a given sample of a given density, μM only varies with the energy of g rays. Fig. 4 shows the evolution of μM parameter as a function of the energy of g rays in the case of hydrogen [4].
In case of utilization of this densimeter for measurement inside a space launcher's tank, we must ensure that the attenuation due to the tank's walls will not affect the measurement. This set-up is used to carry out measurements with and without additional walls. Here are the results with two Stainless steel 316 (2-mm wide) walls.
Liquid nitrogen density measurement without additional walls: (785±39) kg/m3
Liquid nitrogen density measurement with additional walls: (837±42) kg/m3
Liquid nitrogen theoretical density: 808 kg/m3
As one can see, the effect of additional wall is only a slight increase of error on measurement. This increase can be explained by the fact that the presence of walls reduce the I0 flux and hence increase the error on measurement
To better understand the trade-off between, in one hand, source activity and measurement time and, in the other hand, measurement accuracy, practical calculation is made based on Ariane V geometry. We assume that Slush Hydrogen is used in Etage Principal Cryotechnique (EPC) H155 of Ariane V [6] launcher. EPC diameter is 5.4 m and its Aluminum wall thickness is 1.3 mm. The following pictures illustrate this case.
Fig. 3. Influence of absorption parameter μM on statistical error
Fig.4. μM parameter as a function of g rays energy in the case of hydrogen
If we want small value for μM but greater than 0.1 cm2/g, we see that we must use g rays with energy between 0.1 and 1 MeV. We chose to use 137Cs as g ray source because it has one main g emission at 662 keV.
3. Experimental results
Here are the results of measured density for different liquids at room and cryogenic temperature. For safety reasons Nitrogen and Neon are used instead of Hydrogen. μM parameter for liquid Nitrogen and 137Cs as g ray source is equal to cm2/g [4]. Fig. 5 shows the result of density measurement on Nitrogen & Neon Slush melting down measured using the set-up detailed in Fig. 6.
Material
Density measured (.103 kg/m3)
Tabulated density (.103 kg/m3)
Difference (%) (with account to absolute error)
Temperature range
H2O2 (17%)
(1.180±0,059)
1.090
2.84
Room
Acetone
(0.909±0,045)
0.792
9.09
Chloroform
(1.51±0,0755)
1.489
Liquid Nitrogen at triple point
(811±41)
808
Cryogenic
Liquid Neon at triple point
(1210.7±35)
1207.3
If we use a 0.5 MBq 137Cs source, a 10 minutes density measurement on a 50 % Slush will be affected by a 14.2 % error. With a 50 GBq source a 1 second measurement time on the same Slush will be affected by a 1.2 % error. Between these two extreme cases, a trade off must be found according to required measurement accuracy and constraints (allowed measurement time and legal limitations due to radioactive source). Hence, depending on the accuracy requirement on measurement, this non-destructive method could be used.
5. References
[1] SDP FESTIP phase 1 Heat Management final presentation, ESA April 1997
[2] S.-A. Tujgum, J. Frieling, G.A. Johansen, Nucl. Instr. And Meth. B 197 (2002) 301
[3] European co-operation for Accreditation, Expression of the Uncertainty of Measurement in Calibration, , Publication Reference EA-4/02 (1999)
[4] M.J. Berger and J.H. Hubbell , NBSIR 87¯3597, XCOM: Photon Cross Sections on a Personal Computer, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA (1987).
[5] Patent n° EP (2002)
[6]
Fig. 5 Density measurement on Nitrogen & Neon Slush melting down