Effect of Nozzle Type on Combustion Characteristics of Ammonium Dinitramide-Based Energetic Propellant

Abstract

The present study explores the influence of diverse nozzle geometries on the combustion characteristics of ADN-based energetic propellants. The pressure contour maps reveal a rapid initial increase in the average pressure of ADN-based propellants across the three different nozzles. Subsequently, the pressure tapers off gradually as time elapses. Notably, during the crucial initial period of 0–5 μs, the straight nozzle exhibited the most significant pressure surge at 30.2%, substantially outperforming the divergent (6.67%) and combined nozzles (15.5%). The combustion product variation curves indicate that the contents of reactants ADN and CH₃OH underwent a steep decline, whereas the product N₂O displayed a biphasic behavior, initially rising and subsequently declining. In contrast, the CO₂ concentration remained on a steady ascent throughout the entire combustion process, which concluded within 10 μs. Our findings suggest that the straight nozzle facilitated the more expeditious generation of high-temperature and high-pressure combustion gases for ADN-based propellants, expediting reaction kinetics and enhancing combustion efficiency. This is attributed to the reduced intermittent interactions between the nozzle wall and shock waves, which are encountered in the divergent and combined nozzles. In conclusion, the superior combustion characteristics of ADN-based propellants in the straight nozzle, compared to the divergent and combined nozzles, underscore its potential in informing the design of advanced propulsion systems and guiding the development of innovative energetic propellants.

1. Introduction

In the realm of aerospace engineering, optimizing propulsion system performance is instrumental in enhancing the comprehensive functionality of aircraft [1,2,3,4,5]. Propellants, which act as the fundamental impetus for a multitude of carrier rockets and spacecraft, find ubiquitous use in a wide array of applications, from initiating rocket launches to executing orbital maneuvers for space stations and managing satellite attitude control. Notably, liquid propellants, including anhydrous hydrazine and ammonium perchlorate, distinguish themselves owing to their superior performance characteristics and propensity for advantageous chemical reactions. Consequently, they are often the favored selection for use in space attitude and orbit control thrusters. The potential health hazards associated with the acute toxicity of hydrazine-based propellants to both human health and the ecological sphere are of considerable concern and cannot be dismissed [6,7]. Thus, there is an increasing impetus within the aerospace industry to identify alternative liquid propellants that combine high-performance capabilities with environmentally benign and non-toxic characteristics. Ammonium dinitramide (ADN) stands out as a promising candidate in this pursuit. It is a highly water-soluble inorganic salt that not only boasts a high energy density but also exhibits superior combustion properties, while being environmentally friendly. These attributes have warranted a substantial focus on ADN as a potential successor to conventional hydrazine-based propellants in space propulsion technology [8,9,10]. The combination of ADN as an oxidizer with methanol (CH₃OH) dissolved in water has been recognized as a formulation strategy for ADN-based liquid propellants, which are regarded as a promising substitute for conventional hydrazine-based monopropellants [11,12,13]. A comprehensive investigation led by Zhang et al. has elucidated the energetic attributes of propellant mixtures with differing ADN concentrations. Their findings demonstrate that with the ascending proportion of ADN within the propellant matrix, there is a concomitant enhancement in the heat of explosion, burning rate, pressure exponent, as well as an increase in sensitivity to friction and impact [14]. Yao et al. utilized thermogravimetric analysis and Curie-point pyrolysis apparatus to study the evaporation and combustion processes of ADN-CH₃OH-H₂O solutions, further characterizing the gas-phase products using Fourier transform infrared spectroscopy [15]. Liyue Jing et al. employed a simplified chemical kinetic mechanism encompassing 18 species and 40 reactions to simulate the gas-phase reactions between ADN and methanol. Their results indicate that the decomposition of ADN and the oxidation of methanol in the combustion chamber do not occur synchronously [16].

The nozzle plays a crucial role as the conduit for the propellant’s combustion reactions, significantly influencing the flow characteristics of the produced combustion byproducts. Its unique structural attributes exert a direct influence on the temperature and pressure profiles of these products, thereby exerting a profound effect on the stability and efficiency of the propellant’s combustion process. The Beijing Institute of Control Engineering conducted thermal test firings of an ADN-based liquid propellant space engine within a vacuum chamber. The research demonstrated that during stable operation, the pressure and temperature within the combustion chamber reached 0.48 MPa and 1170 K, respectively, with the engine producing a thrust of 1.306 N and a specific impulse of 220 s [5]. Itouyama and colleagues employed continuous laser heating to analyze the effects of carbon additive dispersion on the flammability of ADN-based ionic liquid propellants [17,18]. Hou and colleagues have investigated the effects of different microwave powers on the expansion, microexplosion, and combustion characteristics of ADN-based liquid propellant droplets, and they have reported on the intrinsic mechanisms of microwave-assisted droplet ignition [10]. Korobeinichev and his team utilized molecular beam mass spectrometry and thermocouple measurements to study the ADN flame structure under various pressures, discovering that at a pressure of 0.3 MPa, the flame primarily consists of a cool flame region near the combustion surface, whereas at an increased pressure of 0.6 MPa, a high-temperature luminous flame region is observed [19]. Cheng and co-workers have systematically explored the control of ignition and combustion processes of ADN-based liquid propellants using microwave technology [8]. However, as of now, the effects of different nozzle types on the combustion characteristics of ADN-based energetic propellants and their underlying physical mechanisms remain unclear and demand further in-depth investigation.

This paper employs numerical simulations to investigate the influence of three distinct nozzle types on the combustion characteristics of ADN-based energetic propellants. By examining the temporal evolution of adiabatic temperature, pressure, and combustion reaction components for ADN-based energetic propellants in a straight nozzle, a divergent nozzle, and a combined nozzle, the mechanisms by which different nozzle types affect the combustion process of ADN-based energetic propellants are elucidated. These findings are anticipated to provide theoretical support for the optimization and performance enhancement of propulsion systems.

2. Methods

2.1. Model Establishment

The simplified models of the straight nozzle, divergent nozzle, and combined nozzle utilized in this study are depicted in Figure 1. The specific dimensional details of these three nozzles are presented in

Table 1. Specific dimension parameters of different nozzle types.

Parameters	a	b	b1	b2	θ
Value	0.2 mm	10 mm	5 mm	5 mm	5°

. The ADN-based propellant is fully loaded into a combustion chamber with dimensions of 200 × 200 μm. The size of combustion chamber is consistent with the pit in the literature [20]. The remaining portion of the nozzles is filled with nitrogen, and the expansion angle in the nozzle expansion section is 5° for all three configurations.

As an open-source computational fluid dynamics software, OpenFOAM has been widely used in the calculation of reaction flows [21,22,23]. The two-dimensional calculation of combustion conditions in this paper employs the compressible multi-component reaction flow solver detonationFoam (based on OpenFOAM V6) in which finite-rate chemistry model is adopted [24]. The solver utilizes adaptive mesh refinement (AMR) and load balancing, significantly improving computational efficiency. During the calculation process, the model does not consider body forces and external heat sources, thus satisfying the equations of mass conservation, momentum conservation, species conservation, and energy conservation, as shown in Equations (1)–(4) [4]. In the model, the mixture is considered as the ideal gas. The thermodynamic properties of each species are evaluated with JANAF model [25]. To ensure the calculation accuracy of shock waves, the flux format adopts the second-order accurate central discrete Kurganov scheme [16].

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_i\right)}{\partial x_i}}=0$$

(1)

$${\displaystyle \frac{\partial \left(\rho u_j\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_i{u}_j\right)}{\partial x_i}}=-{\displaystyle \frac{\partial p}{\partial x_j}}+{\displaystyle \frac{\partial {\tau }_{ij}}{\partial x_i}}$$

(2)

$${\displaystyle \frac{\partial \left(\rho Y_k\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho \right(u_i+V_{k,i}\left)Y_k\right)}{\partial x_i}}={\dot{\omega }}_k k=\mathrm{1,2}\dots N$$

(3)

$${\displaystyle \frac{\partial \left(\rho E\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_{i}E\right)}{\partial x_i}}={\dot{\omega }}_T-{\displaystyle \frac{\partial q_i}{\partial x_i}}+{\displaystyle \frac{\partial \left({\sigma }_{ij}{u}_i\right)}{\partial x_j}}$$

(4)

In above equations, ${\tau }_{ij}$ is the viscous stress tensor; $V_{k,i}$ stands for the i-th component of the diffusion velocity k of species; Y_k is mass fraction of species k, ${\dot{\omega }}_k$ is reaction rate of species k; ${\dot{\omega }}_T$ is heat release rate of the combustion process, $q_i$ is heat flux, which includes the thermal diffusion term caused by the temperature gradient and the thermal diffusion term caused by the diffusion of species with different specific enthalpies; and ${\sigma }_{ij}$ stands for deviatoric stress tensor. In this paper, the simplified chemical reaction mechanism for ADN-based propellant contains 18 components and 39 elementary reactions, as shown in

Table 2. Simplified reaction mechanism of ADN-based propellant (18 species, 39 elementary reactions).

1	NH4N(NO2)2<=>NH3 + N2O+	2	NH3 + HNO3<=>N2O + 2H2O
3	N2O + NO<=>NO2 + N2	4	N2O + H<=>N2 + OH
5	N2O + O<=>2NO	6	NO2 + H<=>NO + OH
7	N2O(+M)<=>N2 + O(+M)	8	NO + O + M<=>NO2 + M
9	O + H2<=>H + OH	10	H2 + OH<=>H2O + H
11	O + H2O<=>2OH	12	H2 + M<=>2H + M
13	O + H + M<=>OH + M	14	H + OH + M<=>H2O + M
15	HCO + M<=>H + CO + M	16	HCO + H<=>CO + H2
17	HCO + O<=>CO + OH	18	HCO + OH<=>CO + H2O
19	2HCO<=>H2 + 2CO	20	H + HCO(+M)<=>CH2O(+M)
21	H2 + CO(+M)<=>CH2O(+M)	22	CH2O + H<=>HCO + H2
23	CH2O + O<=>HCO + OH	24	CH2O + OH<=>HCO + H2O
25	CH2OH + M<=>CH2O + H + M	26	CH2OH + H<=>CH2O + H2
27	CH2OH + H<=>CH2O + H2	28	CH2OH + O<=>CH2O + OH
29	CH2OH + OH<=>CH2O + H2O	30	CH2OH + HCO<=>CH3OH + CO
31	CH2OH + HCO<=>2CH2O	32	2CH2OH<=>CH3OH + CH2O
33	H + CH2OH(+M)<=>CH3OH(+M)	34	CH3OH + H<=>CH2OH + H2
35	CH3OH + O<=>CH2OH + OH	36	CH3OH + OH<=>CH2OH + H2O
37	CH3OH + HCO<=>CH2OH + CH	38	CO + O(+M) = CO2(+M)
39	CO + OH = CO2 + H

.

2.2. Parameter Setting

The ADN-based propellant employed in the present investigation is designed as a mixture with three components: 63%ADN, 11% methanol (CH₃OH), and 26% water (H₂O). The percentage mentioned here refers to the mass fraction. The propellant in the combustion chamber and the nitrogen in the nozzle are both treated as ideal gases. The initial pressure of the propellant is 10 atm and the initial temperature is 2930 K. The vaporization state at high temperature and high pressure is consistent with the state after the propellant absorbs instantaneous energy such as laser or microwave. The initial pressure of the nitrogen is 1 atm, and the initial temperature is 293 K. Considering the geometric symmetry, the upper half is selected for mesh generation and numerical calculation. Throughout the overall computation process, symmetry boundary conditions are applied at the axis of symmetry, zero-gradient boundary conditions are used at the exit, and the remaining boundaries are set as no-slip walls. In the straight nozzle, a grid of 2000 × 20 (including the combustion chamber) is employed. In the divergent nozzle, the grid settings for the combustion chamber and the divergent section are 40 × 40 and 1960 × 40, respectively. In the combined nozzle, the grid settings for the straight section (including the combustion chamber) and the divergent section are 1000 × 40 and 1000 × 40, respectively. The criteria for AMR are set based on the magnitude of the density gradient. When the magnitude of the density gradient exceeds the predefined lower threshold of 2000, the grid will be adaptively refined. The horizontal grid resolution with 5 μm offers finer flow fields distribution compared to 10 μm in literature [26]. Additionally, the mesh can be encrypted according to the density gradient with the AMR method, further ensuring the capture of flow field characteristics. Structured grids are used in the straight sections, and due to the small divergence angle, the grids in the divergent sections are also very close to being structured.

3. Results

3.1. The Evolution of Temperature, Pressure, and Mass Fraction Distribution Clouds of ADN-Based Propellants in Different Types of Nozzles

Figure 2 presents the distribution contour maps of ignition temperature (T), pressure (p), ADN (NH₄N(NO₂)₂) mass fraction (y_ADN), and nitrogen oxide (N₂O) mass fraction (y_N2O) for ADN-based propellants in different types of nozzles at various time intervals. As depicted in Figure 2a for the straight nozzle, at t = 1 μs, a distinct shock wave propagating from left to right can be observed at the position x = 1 mm within the straight nozzle from the pressure contour map. On the temperature contour map, a clear interface known as a “contact discontinuity” is visible between the wall and the shock wave. Due to the viscous effects at the nozzle wall, the “contact discontinuity” exhibits a pronounced curvature, leading to a decoupling of the shock wave from the reaction front during the deflagration heat release process of ADN. This decoupling prevents synchronous propagation, and as time progresses, the gap between the shock wave and the reaction front gradually increases. Simultaneously, under the action of high temperature and pressure, the ADN-based propellant rapidly undergoes a chemical reaction (t = 1 μs). The y_ADN contour map transitions from the initial deep red (t = 0 μs) to blue (t = 5 μs), and then to deep blue (t = 10 μs), illustrating the continuous consumption of ADN. After t = 10 μs, ADN is almost completely reacted. Concurrently, the content of the intermediate product N₂O increases initially and then decreases. Before t = 5 μs, the rapid reaction of ADN leads to an increase in N₂O content, which accumulates near the wall surface. With the evolution of time, N₂O begins to decompose, creating an uneven distribution on the y_N2O mass fraction contour map, with higher y_N2O content at the working fluid-air interface and lower content near the wall surface. Throughout the reaction process, ADN is located to the left of the contact discontinuity and moves to the right under the combined effects of pressure and concentration gradients.

In comparison to the straight nozzle, when the nozzle shape is altered to a divergent nozzle, as shown in Figure 2b, the pressure at the same position decreases at the same moment due to the change in nozzle shape. This results in a slower propagation speed of the shock wave and a reduced diffusion rate of the various substance components. The change in the mass fraction of ADN in the divergent nozzle is essentially consistent with that in the straight nozzle, with complete reaction of ADN at t = 10 μs, indicating that the change in nozzle shape has a minimal effect on the decomposition of ADN. However, at t = 10 μs, there is no significant accumulation of y_N2O, and a considerable amount remains, primarily because the divergent nozzle has more ambient temperature stationary nitrogen than the straight nozzle, which effectively dilutes and cools the various substance components within the nozzle. The reduced gas velocity in the divergent section accelerates the decrease in temperature and pressure, leading to a slower consumption rate of the intermediate products, resulting in a higher residual content of y_N2O at the same moment. The behavior of ADN within the combined nozzle is largely consistent with that observed in the straight nozzle (Figure 2c). This is due to the fact that substances such as ADN have moved to the position x = 3 mm within the 10 μs time frame, which corresponds to the straight section of the combined nozzle. As a result, the influence of the rear expansion section of the combined nozzle on the parameter distribution (such as temperature and composition) of ADN can be disregarded. As the shock wave propagates into the expansion section of the combined nozzle, the velocity of the material movement decreases, resembling the scenario observed in the divergent nozzle.

3.2. Temporal Evolution of ADN-Based Propellant Pressure and Temperature in Various Nozzle Types

The combustion reaction rate of the propellant is closely related to the pressure and temperature within the nozzle. Figure 3 illustrates the curves of average pressure and adiabatic temperature over time for ADN-based propellants in three different types of nozzles. As shown in Figure 3a, the average pressure of the ADN-based propellant in the three nozzles exhibits an overall trend of rapid initial increase followed by a slower growth rate. Specifically, within the 0–5 μs interval, the average pressure in the straight nozzle increases from 1.19 atm to 1.55 atm; in the divergent nozzle, it rises from 1.05 atm to 1.12 atm; and in the combined nozzle, it increases from 1.10 atm to 1.27 atm. It is evident that the pressure growth rate of the ADN-based propellant in the straight nozzle (30.2%) is significantly greater than that in the divergent nozzle (6.67%) and the combined nozzle (15.5%), indicating that the combustion reaction rate of the ADN-based propellant is faster in the straight nozzle. After 8 μs, the pressure growth trends in all three types of nozzles slow down and essentially stabilize after 10 μs, which is indicative of the ADN-based propellant’s combustion reaction coming to a close. Figure 3b presents the curves of adiabatic temperature over time for the ADN-based propellant in different nozzles. Overall, the changes in adiabatic temperature within the three nozzles follow a similar trend to that of pressure over time. In the 0–5 μs interval, the adiabatic temperatures in the straight nozzle, divergent nozzle, and combined nozzle increase from 347 K to 693 K, 303 K to 396 K, and 319 K to 485 K, respectively, corresponding to increases of 99.7%, 30.7%, and 52%. As time progresses, the slopes of the curves gradually flatten out, attributable to the decrease in the content of reactants during the propellant combustion process.

Figure 4 presents the curves of pressure and temperature distribution along the central axis of different types of nozzles. In the case of the straight nozzle (Figure 4a,b), the high-temperature, high-pressure gas generated by the combustion of ADN-based propellant rapidly expands to form a strong shock wave. As the shock wave propagates to the right, it heats and compresses the downstream gas within the nozzle, transferring momentum and causing the shock wave’s intensity to gradually weaken over time, with the peak pressure continuously decreasing. Compared to the straight nozzle, the divergent nozzle, due to the presence of divergent angle, has an increased cross-sectional area, resulting in lower gas pressure, temperature and propagation speed at the same moment, as shown in Figure 4c,d. For the combined nozzle, the changes in pressure and temperature along the central axis are almost identical to those in the straight nozzle, as depicted in Figure 4e,f. At 10 μs, an evident “bump” phenomenon occurs at 5 mm within the nozzle, which is attributed to the disturbance caused by the change in nozzle shape. The sudden expansion of the cross-section leads to deceleration and congestion of the subsonic flow behind the shock wave, further increasing the pressure at the upstream interface and creating a sudden rise in temperature and pressure. The diffusion speed of the ADN-based propellant in the high-temperature region is slower compared to the propagation speed of the shock wave. Specifically, at 10 μs, the shock wave has propagated to 6.7 mm in the nozzle, while the high-temperature region only extends to 2.8 mm, significantly lagging behind the shock wave’s position, which is consistent with the changes observed in the previous contour maps. The high-temperature region at the initial section of the nozzle (<0.5 mm) remains relatively constant, while due to the combined effects of diffusion and the gas expansion doing work on the surroundings, the temperature in the high-temperature region at the nozzle’s rear (>0.5 mm) shows a continuous decreasing trend. It is evident that the change in nozzle shape has a significant impact on the pressure and temperature generated by the combustion of ADN-based propellant, as well as the combustion characteristics.

3.3. Temporal Evolution of Mass Fraction for ADN-Based Propellant Components

To elucidate the impact of different nozzle types on the mass fraction changes of reactants and products in the ADN combustion characteristics, Figure 5 depicts the variation curves of the main substance mass fractions over time during the combustion process of ADN-based propellants. Overall, the decrease in the content of reactants ADN and CH₃OH, the emergence of new substances such as N₂O, CO, CO₂, and OH, and the increase in their content indicate that ADN-based propellants undergo combustion reactions within all three types of nozzles. These findings are in agreement with the results reported by Yao et al. [27]. As shown in Figure 5a,b, ADN and CH₃OH, as reactants in ADN-based propellants, exhibit exponential decreases in their mass fractions from t = 0 in different nozzles, indicating the rapid combustion reaction rate of ADN-based propellants. Concurrently, N₂O, an important intermediate product of ADN decomposition (as shown in Figure 5c), shows a two-stage trend in its mass fraction in the three nozzles. In the first stage (0–2.5 μs), N₂O starts to appear and its mass fraction increases rapidly as ADN reacts. In the second stage (>2.5 μs), the content of N₂O begins to decrease, primarily due to its continued participation in the reaction as both a product and a reactant as the combustion reaction progresses. The intermediate product OH from the oxidation decomposition of CH₃OH (Figure 5d) exhibits a trend similar to that of N₂O. Notably, the content of the fully oxidized product CO₂ maintains a continuous increasing trend throughout the overall combustion process, while the incomplete oxidation product CO initially rises rapidly within 1 μs and then decreases slowly. It is worth noting that the time at which N₂O’s content starts to decrease in the divergent nozzle is delayed compared to the straight nozzle (>5 μs), which is due to the decrease in temperature and pressure caused by the nozzle expansion effect, resulting in a reduced combustion rate between ADN and CH₃OH. The mass fraction of the reactants ADN and CH₃OH almost decreased to zero within 6 μs, indicating that the combustion reaction of the ADN-based propellant was complete. The variation in the average mass fraction of components over time in the combined nozzle (ADN, CH₃OH, CO₂, N₂O, OH, CO) is similar to that in the straight nozzle.

4. Conclusions

The study primarily investigates the influence of different nozzle types on the combustion characteristics of ADN-based propellants. Our findings are anticipated to provide theoretical support for the optimization and performance enhancement of propulsion systems. Through the comparison of different nozzle types, the main conclusions were as follows:

• Compared to divergent nozzles and combined nozzles, the ADN-based propellant can generate higher temperatures and pressures within a straight nozzle, which is beneficial for the thruster to achieve greater thrust.
• The combustion of ADN-based propellants is an extremely rapid chemical reaction, with the entire combustion duration being within 10 μs. The mass fractions of reactants ADN and CH3OH in the ADN-based propellant decrease exponentially, while the mass fraction of the product CO2 continuously increases throughout the combustion process.
• Due to the “intermittent contact” between the nozzle wall and shock waves in the divergent and combined nozzles, the ADN-based propellant can produce high-temperature and high-pressure combustion gases more rapidly in the straight nozzle. This accelerates the combustion reaction rate of the reactants and improves the combustion efficiency of the propellant, demonstrating superior combustion characteristics.