*3.6.2 NRGP measured results*

For measuring shear-thinning and thixotropic characteristics, fuel gel samples were subjected to hysteresis loop tests starting with increasing shear rate γ̇ from 1 to 100 s<sup>−</sup><sup>1</sup> (up curve) and then reducing back from 100 to 1 s<sup>−</sup><sup>1</sup> (down curve) while measuring the viscosity *μ*. In **Figure 14**, it can be seen that the shear-thinning behavior is significant: *μ* decreases almost two orders of magnitude in the presented shear rate range. At high shear rates γ̇ > 102 s<sup>−</sup><sup>1</sup> (not in the figure), the shear-thinning behavior diminishes due to the destruction of the gel structure and leads to a constant viscosity value *μ*∞, which is called upper Newtonian plateau and its value is near the viscosity of the Newtonian neat fluid fuel.

This result is in accordance with the requirements for the rocket engine propellant feeding system, for which the gel fluid passes through a pipe and finally is injected into the combustion chamber. The injectors are small in both length and cross-sectional area, and the fluid remains there for a very short time. The shear rates developed in the injectors due to the sudden decrease in the cross-sectional area are very large, and the shear-thinning effect is dominating.

**19**

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

The yield stress value of the gelled fuel can be measured by two main methods:

a.Shearing the fluid at a low and constant shear rate and measuring the shear stress as a function of time. In this method, the yield stress is defined as the

b.Measuring the shear stress vs. shear rate and extrapolating to zero shear rate (**Figure 15b**) using the Herschel-Bulkley equation, as detailed above

Here method (b) was used for measuring yield stress on the rotational rheometer, that is, by extending the flow curve at low shear rates and taking the shear stress y-axis intercept as the yield value. Using this method for an NRGP fuel sample is shown in **Figure 16**. In this example, the measured yield stress value is

The three aspects of the shear relevant rheological behaviors of a gel, that is, shear-thinning, upper Newtonian plateau, and yield stress, can be described by a constitutive equation, which is the Herschel-Bulkley extended (HBE) equation, Eq. (1), expressed here in terms of viscosity. This equation describes the dependence of

As mentioned above, **n** is the flow behavior index that varies from "0" for very shear thinning materials to "1" for Newtonian materials. A smaller value of **n** means a greater degree of shear thinning. An example using HBE method for assessing the

**<sup>n</sup>**−**<sup>1</sup>** + <sup>∞</sup> (7)

**0** ̇ + **K** ∙ ̇

maximal measured value as shown in **Figure 15a**.

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

*3.6.3 Yield stress measurement*

*Gelled fuel viscosity as a function of shear rate.*

**Figure 14.**

for Eq. (1).

the shear viscosity on the shear rate.

= \_\_

shear thinning behavior is shown in **Figure 17**.

16 Pa.

**Figure 13.** *AR 2000 rheometer and parallel plates [56].*

*Green Comparable Alternatives of Hydrazines-Based Monopropellant and Bipropellant Rocket… DOI: http://dx.doi.org/10.5772/intechopen.82676*

**Figure 14.** *Gelled fuel viscosity as a function of shear rate.*

#### *3.6.3 Yield stress measurement*

*Aerospace Engineering*

cal measurements.

*tube before centrifuge test.*

to 100 s<sup>−</sup><sup>1</sup>

**Figure 12.**

*3.6.2 NRGP measured results*

shear rate range. At high shear rates γ̇

near the viscosity of the Newtonian neat fluid fuel.

area are very large, and the shear-thinning effect is dominating.

for rotational rheometers are the parallel plates (see **Figure 13** right) and the cone and plate. The parallel plates configuration has been used here for gel characterization. A Peltier plate-type temperature regulation system inside the equipment ensures the prescribed controlled fluid temperatures during rheologi-

*Gel stability as a function of test duration time (left) and acceleration value (middle). On the right is a test* 

For measuring shear-thinning and thixotropic characteristics, fuel gel samples

from 1

(down curve) while

(not in the figure), the shear-thin-

were subjected to hysteresis loop tests starting with increasing shear rate γ̇

measuring the viscosity *μ*. In **Figure 14**, it can be seen that the shear-thinning behavior is significant: *μ* decreases almost two orders of magnitude in the presented

> > 102 s<sup>−</sup><sup>1</sup>

ning behavior diminishes due to the destruction of the gel structure and leads to a constant viscosity value *μ*∞, which is called upper Newtonian plateau and its value is

This result is in accordance with the requirements for the rocket engine propellant feeding system, for which the gel fluid passes through a pipe and finally is injected into the combustion chamber. The injectors are small in both length and cross-sectional area, and the fluid remains there for a very short time. The shear rates developed in the injectors due to the sudden decrease in the cross-sectional

(up curve) and then reducing back from 100 to 1 s<sup>−</sup><sup>1</sup>

**18**

**Figure 13.**

*AR 2000 rheometer and parallel plates [56].*

The yield stress value of the gelled fuel can be measured by two main methods:


Here method (b) was used for measuring yield stress on the rotational rheometer, that is, by extending the flow curve at low shear rates and taking the shear stress y-axis intercept as the yield value. Using this method for an NRGP fuel sample is shown in **Figure 16**. In this example, the measured yield stress value is 16 Pa.

The three aspects of the shear relevant rheological behaviors of a gel, that is, shear-thinning, upper Newtonian plateau, and yield stress, can be described by a constitutive equation, which is the Herschel-Bulkley extended (HBE) equation, Eq. (1), expressed here in terms of viscosity. This equation describes the dependence of the shear viscosity on the shear rate.

$$
\mu\_{\parallel} = \frac{\mathbf{r}\_0}{\dot{\mathbf{y}}} + \mathbf{K} \cdot \dot{\mathbf{y}}^{\mathbf{n}-1} + \mu\_{\text{oo}} \tag{7}
$$

As mentioned above, **n** is the flow behavior index that varies from "0" for very shear thinning materials to "1" for Newtonian materials. A smaller value of **n** means a greater degree of shear thinning. An example using HBE method for assessing the shear thinning behavior is shown in **Figure 17**.

**Figure 15.**

*Common methods for measuring yield stress [56]. (a) Shearing a fluid at a low and constant shear rate and measuring the shear stress as a function of time and (b) extending the shear stress vs. shear rate curve at low shear rates.*

**Figure 16.** *Yield test for an NRGP fuel.*

#### *3.6.4 Temperature effect*

The gel fuel temperature has an effect on its rheological properties (shear thinning, yield stress, thixotropic behavior). In general, the yield stress of the gel decreases with increasing temperature since the cohesion forces between the gel molecules are decreasing and their mobility is increasing, thereby the resistance of the gel to deformation is reduced as the temperature increases. Shear thinning and thixotropic behaviors are becoming less prominent at higher temperatures.

An example of measurement made for an NRGP fuel gel sample at three different temperatures, −10, +40, and +70°C is shown in **Figure 18**, which shows that the influence of the temperature on the viscosity values is more prominent at lower shear rates and the shear thinning behavior becomes less prominent as the temperature increases.

**21**

**Figure 18.**

**Figure 17.**

the temperature effect is very small.

pitting) were not observed either.

**3.7 Concluding remarks for bipropellant**

*Gelled fuel viscosity as a function of shear rate at −10, 40, and 70°C.*

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

It is important to note that for an expected operational range of −10 to +40°C,

Visual inspection of a sample that has been exposed to a temperature of 80°C revealed no phase separation or sedimentation at all. Other changes (color, bubbles,

Recently, it has been recognized that "the development of a bipropellant gel propellant system, which is ideally both green and hypergolic, is an important area

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

*Curve fitting using Herschel-Bulkley extended model.*

*Green Comparable Alternatives of Hydrazines-Based Monopropellant and Bipropellant Rocket… DOI: http://dx.doi.org/10.5772/intechopen.82676*

**Figure 17.** *Curve fitting using Herschel-Bulkley extended model.*

#### **Figure 18.**

*Aerospace Engineering*

**Figure 15.**

*shear rates.*

**20**

*3.6.4 Temperature effect*

*Yield test for an NRGP fuel.*

**Figure 16.**

temperatures.

ture increases.

The gel fuel temperature has an effect on its rheological properties (shear thinning, yield stress, thixotropic behavior). In general, the yield stress of the gel decreases with increasing temperature since the cohesion forces between the gel molecules are decreasing and their mobility is increasing, thereby the resistance of the gel to deformation is reduced as the temperature increases. Shear thinning and thixotropic behaviors are becoming less prominent at higher

*Common methods for measuring yield stress [56]. (a) Shearing a fluid at a low and constant shear rate and measuring the shear stress as a function of time and (b) extending the shear stress vs. shear rate curve at low* 

An example of measurement made for an NRGP fuel gel sample at three different temperatures, −10, +40, and +70°C is shown in **Figure 18**, which shows that the influence of the temperature on the viscosity values is more prominent at lower shear rates and the shear thinning behavior becomes less prominent as the tempera*Gelled fuel viscosity as a function of shear rate at −10, 40, and 70°C.*

It is important to note that for an expected operational range of −10 to +40°C, the temperature effect is very small.

Visual inspection of a sample that has been exposed to a temperature of 80°C revealed no phase separation or sedimentation at all. Other changes (color, bubbles, pitting) were not observed either.

#### **3.7 Concluding remarks for bipropellant**

Recently, it has been recognized that "the development of a bipropellant gel propellant system, which is ideally both green and hypergolic, is an important area of research" [57]. In general, the NewRocket concept seems to be such that can provide replacements for hydrazines in many types of applications, most notably as "green" replacement to the veteran bipropellants MMH and N2O4.

The results of the firing tests of the proof-of-concept and development model systems demonstrate the capability to operate this technology in both pulses and steady modes and in various thrust levels. This bipropellant technology offers a promising alternative to the presently employed hydrazine-based systems, through the fact that the fuel and oxidizer show very robust hypergolicity and short ignition delay times, as well as characteristic velocity efficiency (*ηC*\*) exceeding 98%.
