**3.4 Calculation of the sedimentation threshold acceleration of a particle through the NRGP gelled fuel**

Rearranging Eq. (4) and replacing the gravitational acceleration *g* with the applicable acceleration *a* in order to solve it, and substituting the height to shelf life ratio for velocity, obtains Eq. (5).

$$\mathfrak{a} = \frac{\mathbf{3} \,\sigma\_{\mathbf{y}}}{\mathbf{Y} \cdot \mathbf{d} \,(\rho\_{\mathbf{p}} - \rho\_{\mathbf{l}})} \tag{5}$$

**17**

*Green Comparable Alternatives of Hydrazines-Based Monopropellant and Bipropellant Rocket…*

**2**

This, with a gel viscosity measured in experiments of *μg* = 100 *Pa* <sup>∙</sup> *<sup>s</sup>*. However, the viscosity derived from the Herschel-Bulkley rheological model coefficients in the

In 10 s under acceleration of 2400 *g*, the resultant sedimentation distance is

sedimentation. Therefore, it is important to remember that the extremely high

to the actually high yield stress of the fuel, while in reality any considerable accelerations are applied on the fuel for very short periods only, such as experienced by

For a fuel with similar viscosity, but without a yield stress (not being the case

It can be seen that the sedimentation distance of a particle is proportional to its squared diameter, gravity, and particle density and inversely proportional to the viscosity of the gel. Thus, it is possible to reduce the sediment distance by the following ways: reducing particle diameter, reducing particle density, and increasing

Based on Technion experience, it can be stated that after storage of a couple of years, there is no degradation in terms of phase separation, sedimentation, agglomeration, ignition delays, etc. For quantitative evaluation of these behaviors, both real-time and accelerated tests are relevant. These were obtained by centrifuge tests

To simulate the mechanical environmental loads during a typical rocket launch, which might cause concern regarding gel separation in the tank and propellant feed system, centrifuge tests have been conducted. Example of result obtained for a gelled fuel with a suspended particle with a diameter of 250 μm is depicted in **Figure 12**, which shows the gel stability as a function of operating time or degree of acceleration. In this experiment, a gelled fuel sample within a test tube was tested in a centrifuge for assessing the influence of two different conditions: firstly, applying constant acceleration (40 g) while varying the time duration (**Figure 12** left) on the test and secondly, applying constant duration time (2 minutes) while varying the magnitude of the acceleration (**Figure 12** middle). After each centrifuge test, the separated liquid due to the acceleration has been sought in order to be compared with the initial mass to quantify the

It is important to note that from a visual examination of all samples, no particle

For characterization of the rheological behavior of the gelled fuels, a TA Instruments AR 2000 rotational rheometer [56] operated in controlled rate mode is being used. The rotational rheometer imposes strain to the liquid and measures the resulting stress for shear rates up to 1000 1/s. Most common test geometries

m, namely one-thirtieth of a micron sedimentation. In 10 years (10 ×

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ **<sup>18</sup>** <sup>∙</sup> **<sup>100</sup>** *Pa* <sup>∙</sup> *<sup>s</sup>*

∙ (**2400** ∙ **9.81**)*m*/ *s*

s), this represents sedimentation of 1 m, namely full

**2**

, was assumed here just in order to compare

, in 10 years the sedimentation

= **3.5** ∙ **10**<sup>−</sup>**<sup>9</sup>***m*/*s* (6)

∙ (**2** ∙ **10**<sup>−</sup>**<sup>6</sup>***m*)

*DOI: http://dx.doi.org/10.5772/intechopen.82676*

= **<sup>650</sup>**

following paragraph would be taken into account here.

*kg* \_\_\_ *m***<sup>3</sup>**

v = (**<sup>p</sup>** – **l**) **d<sup>2</sup>***<sup>a</sup>* \_\_\_\_\_\_\_\_\_ **<sup>18</sup>**

3600 × 24 × 365 = 3.15 × 108

would merely be 4 mm.

the viscosity of the gel.

stability of the investigated gel.

**3.6 NRGP fuel rheological characterization**

sedimentation was observed.

*3.6.1 Measuring system*

acceleration value, in the order of km/s2

here), for gravitational acceleration of 9.81 m/s2

for assessing the stability of the gel in accelerations.

3.5 × 10<sup>−</sup><sup>8</sup>

space launch.

Using Eq. (5) for a particle with diameter **d** = 2 μm and density of **ρp** = 1.45 g/ cc, immersed in a gel with density **ρl** = 0.8 g/cc and with a **σy** of 10 Pa (a conservative order of magnitude representative of the 16 Pa measured in the paragraph below), while assuming a worst case of a **Ycrit** = 1, the solid particle will start to move when the acceleration reaches a threshold value of *a* = 23,077 m/s2 or *a* **= 2352** *g*.
