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Hybrid rocket motors have great development potential due to their outstanding thrust adjustment flexibility and long-term operation ability. However, nozzle erosion during the motor operation can cause an increase in the throat area of the nozzle, which leads to a decrease in combustion chamber pressure and nozzle efficiency. Therefore, a performance prediction model for hybrid rocket motors considering nozzle erosion has become a key technology that must be addressed when developing hybrid rocket motors. This study uses dynamic grid technology to simulate the regression of the combustion surface and nozzle erosion, which fits well with experimental values. The behavior of high-energy particles in the combustion chamber is simulated through a discrete phase model. Notably, distinctive behavior is observed in Al and Mg droplets, with Al droplets exhibiting incomplete vaporization in the combustion chamber while Mg droplets completely vaporize. A ground firing test using the Φ336 mm hybrid rocket motor lasting 200 s is conducted. The results show that the dynamic numerical simulation, accounting for nozzle erosion, substantially enhances performance prediction accuracy. The average deviation in motor thrust remains below 1.8%, and the combustion chamber pressure deviation stays under 2.6%, confirming the precision of the model. Ultimately, both simulation and experimental outcomes indicate a gradual decrease in specific impulse and characteristic velocity over the long-term operation, attributed to the gradual deviation of the oxygen-fuel ratio. This research provides valuable insights for guiding hybrid rocket motor design and optimizing design parameters to improve overall performance. This model can achieve long-duration and high-precision performance predictions for hybrid rocket motors. [ABSTRACT FROM AUTHOR]

This paper provides a valuable method to perform transient numerical simulations for hybrid rocket motors (HRMs). A two-dimensional transient numerical simulation model based on Butterworth filter and dynamic mesh is established. The Butterworth filter adopted in this project is a second-order low-pass filter. Then a firing test is arranged to prove the accuracy of the numerical simulation model of the HRMs. This rocket motor adopts 98% hydrogen peroxide (HP) and hydroxyl-terminated polybutadiene (HTPB) fuel containing aluminum as the propellants. The results demonstrate that the Butterworth filter can significantly improve the smoothness of the combustion surface compared with non-filter. And the combustion chamber pressure and thrust of simulation and test results are in good agreement. The average deviation of combustion chamber pressure between the simulation and test is 0.9%, and the average deviation of thrust between the simulation and test is 3.3%, which verifies the feasibility of the numerical simulation model for this HRM. Comparing the regression rate and filtered regression rate along with axial distance over time, it is indicated that the high-frequency oscillations are filtered by the Butterworth filter. In order to compare the port of simulation and test, the combustion chamber is scanned by computed tomography (CT) after the test. The results demonstrate that the simulation and test results are in good agreement, and the average deviation of simulation and test results is 4.5% mainly due to the end-burning of grain and nitrogen blowing. Then, the long-time simulations that adopted the Butterworth filter and non-filter were conducted. The results demonstrate that the use of the Butterworth filter can significantly smooth the combustion surface and the model has the ability to perform long-time simulations. This project can make the simulation for HRMs closer to the test results and provide a valuable guide for HRMs simulation. • A simulation model of hybrid rocket motor based on Butterworth filter is established. • The Butterworth filter is adopted to smooth the combustion surface. • A firing test of hybrid rocket motor with fuel containing aluminum is carried out. • Simulated combustion surface is compared with the computed tomography scan results. • A long-time simulation is conducted to validate model accuracy. [ABSTRACT FROM AUTHOR]

Machining distortion has been a long-term obstacle in the machining of aircraft monolithic parts. Furthermore, its stability has to be considered. The machining distortion stability represents the fluctuation degree of the machining distortion. This paper investigates the evolution of elastic energy induced by initial residual stress inside materials, revealing that this evolution directly affects machining distortion. In this paper, the concept of machining distortion stability and bending potential energy is defined. By analyzing bending potential energy releasing, this study proposes a novel method for improving machining distortion stability through optimization of material removal sequence. Numerical simulation and milling experiments are performed to verify and validate the model, respectively. The results indicate that the machining distortion stability is significantly improved when optimized material removal sequence is applied. By controlling the machining distortion stability, the final distortion can be further reduced via re-machining the machining datum at the beginning of the finishing stage. [ABSTRACT FROM AUTHOR]

Numerical simulation based on the discrete phase model and dynamic mesh model can more accurately simulate the working process for hybrid rockets, including the motion and evaporation process of particles and regression process of the fuel grain. The dynamic numerical simulation of combustion and flow in hybrid rocket motors based on a discrete phase model is carried out. Aluminum and aluminum hydride are added to the internal flow field as discrete droplets. Then, a hybrid rocket is designed with 95 % hydrogen peroxide as oxidizer and 38 % aluminum hydride+20 % aluminum+42 % hydroxyl-terminated polybutadiene as the fuel and used to verify the model by firing test. A high degree of agreement between experiment and simulation findings is found. The average deviations for thrust and pressure are 3.6 % and 5.9 %, respectively. It offers the required backing for using the simulation method to investigate the flow and combustion process for the hybrid rockets. The results also demonstrate the transient characteristics of the inner flow field, including the separation and merging of vortexes in the pre-chamber. It is found that a peak of the regression rate appears at the front of the grain and moves backward. This is mainly because the vortex appears here and enhances its heat transfer. Through the discrete phase model, it is worth noting that the aluminum droplet content gradually decreases at the nozzle over time, which is consistent with the firing test. Further research on the impact of aluminum hydride content on the performance of the hybrid rockets has been carried out. The results show that the higher aluminum hydride content can lead to better performance for the hybrid rockets. The thrust, pressure, specific impulse, and characteristic velocity enhance with the increase of aluminum hydride content. An interesting discovery is that the average regression rate is maximum at 48 % aluminum hydride content. This research innovatively couples dynamic mesh and discrete phase models, which can help better understand the working process for hybrid rockets and provide important guidance for the selection of fuel formula. • A simulation model of hybrid rocket motors based on a discrete phase model is established. • The motion and evaporation of particles and regression of the fuel grain are simulated. • A test of hybrid rockets with fuel containing aluminum and aluminum hydride is carried out. • A high degree of agreement between experiment and simulation findings is found. • The impact of aluminum hydride content on the performance of the hybrid rockets is conducted. [ABSTRACT FROM AUTHOR]

The three-dimensional dynamic numerical simulation is rare in previous studies of hybrid rocket motors, therefore, a three-dimensional dynamic numerical model is established. A hybrid rocket motor is designed, which adopts 98 wt% hydrogen peroxide and polyethylene as the propellants. Then, a ground experiment is conducted to verify the model. The results show that the method of adopting dynamic mesh technology to simulate the three-dimensional regression of the combustion surface is feasible. The average errors of thrust and pressure in the simulation and experiment are 5.6% and 7.9%, respectively. Moreover, the inner surface of grain is scanned by computed tomography after the experiment. The average deviation of port diameter is 5% between the simulation and experiment, therefore, the accuracy of this model is acceptable. Then, the results also show that the thrust and pressure both gradually decrease with time in the simulation and experiment at 5-10 s. The main reason is the rapid reduction in the fuel mass flow rate. However, the pressure in simulation is stable but decreases with time in experiment at 10-25 s. The main reason is the expansion of the nozzle throat caused by the ablation. The results demonstrate that the numerical method can accurately predict motor performance. In addition, the flow field is approximately uniform along the circumference by the dynamic numerical method, which is difficult to obtain for the conventional steady-state and two-dimensional methods. It is the first time to realize the three-dimensional regression in hybrid rocket motors. Therefore, this method can be used to predict the three-dimensional regression of the complex shapes grain and also can guide the design of grain shape in hybrid rocket motors. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to characterize the regression rate behavior of hybrid rocket motor propellant combinations, using hydrogen peroxide (HP), gaseous oxygen (GOX), nitrous oxide (N 2 O) as the oxidizer and hydroxyl-terminated poly-butadiene (HTPB) as the based fuel. In order to complete this research by experiment and simulation, a hybrid rocket motor test system and a numerical simulation model are established. Series of hybrid rocket motor firing tests are conducted burning different propellant combinations, and several of those are used as references for numerical simulations. The numerical simulation model is developed by combining the Navies–Stokes equations with the turbulence model, one-step global reaction model, and solid–gas coupling model. The distribution of regression rate along the axis is determined by applying simulation mode to predict the combustion process and heat transfer inside the hybrid rocket motor. The time-space averaged regression rate has a good agreement between the numerical value and experimental data. The results indicate that the N 2 O/HTPB and GOX/HTPB propellant combinations have a higher regression rate, since the enhancement effect of latter is significant due to its higher flame temperature. Furthermore, the containing of aluminum (Al) and/or ammonium perchlorate(AP) in the grain does enhance the regression rate, mainly due to the more energy released inside the chamber and heat feedback to the grain surface by the aluminum combustion. [ABSTRACT FROM AUTHOR]

This paper attempts to research and predict the effect of the convention aluminum particle additives on the performance of the HTPB/98HP hybrid rocket motor with the numerical approach. The aluminum particle is injected to the flow field in form of droplet from the grain surface, and then simulated by the discrete phase model. A CFD code has been developed to solve the coupling mass, momentum and energy equations of gas and solid at the grain surface, as well as the initial parameters of the aluminum droplet. A good agreement exists between the calculated regression rate from numerical model and the experimental data, indicating that the accuracy of applying numerical approach to predict the characteristics of aluminum metallized HRM is acceptable. Series of static numerical simulation have been conducted to determine the effect of aluminum particle property on the combustion and specific impulse performance of the HRM. The regression rate increases with the weight fraction of convention aluminum particle, but shows no distinguished correlation with the particle diameter. The characteristic velocity and vacuum specific impulse display a strong dependence on the particle diameter. The results illustrate that the proposed numerical approach is potentially an effective tool for predicting and investigating the enhancement of the regression rate and performance of the HRM with the addition of aluminum particle. [ABSTRACT FROM AUTHOR]

The accurate determination of the gas in place in shale reservoirs is a basic but challenging issue for shale gas evaluation. Conventional canister gas desorption tests on retrieved core samples and subsequent data analyses (via linear or polynomial regression)—originally developed for coalbed methane, where gases are mainly stored in the adsorbed phase—is unadvisable for shale gas, which is stored as an appreciable amount of free gas in shale reservoirs. In the present study, a mathematical model that simultaneously takes into account gas expansion, adsorption/desorption, and the gas flow in shale is proposed to simulate gas release from a core sample retrieved from the Lower Silurian Longmaxi Formation of the Fuling shale gas field, Sichuan Basin. The results indicate that, compared with the value of 2.11 m3/t rock estimated with the traditional United States Bureau of Mines (USBM) method, the total gas in place within the studied Longmaxi Shale estimated with our mathematical model under reservoir pressure conditions is up to 5.88 m3/t rock, which is more consistent with the result from the new volumetric approach based on Ambrose et al. According to our mathematical model, the content of free gas is 4.11 m3/t rock at true "time zero", which accounts for 69.9% of the total gas. On the other hand, the lost gas portion is determined to be up to 4.88 m3/t rock (~85% of the total gas). These results suggest that the majority of the free shale gas is actually trapped within the pore space of the shale formation. [ABSTRACT FROM AUTHOR]

Machining distortion is a recurring problem in the machining of monolithic aircraft parts. This paper aims to study the machining distortion minimization of monolithic aircraft parts. Firstly, the energy principle of machining distortion was analyzed. Then, a rapid prediction model of the final part distortion for beam parts was proposed based on the equivalent stress, and the initial bending strain energy contained in the final part was used to characterize the bending distortion risk of the final part. Numerical simulation and milling experiments verified the effectiveness of the proposed prediction model. The relative error between the experimental and calculated results does not exceed 26.5%. Finally, the influence of initial residual stress fluctuation, part geometry and the part location on part distortion was analyzed from the energy point of view. The obtained results indicated that the expected final part distortion can be minimized by adjusting these three factors. [ABSTRACT FROM AUTHOR]

This paper is aimed to analyze heat transfer in injector plate of hydrogen peroxide hybrid rocket motor by two-dimensional axisymmetric numerical simulations and full-scale firing tests. Long-time working, which is an advantage of hybrid rocket motor over conventional solid rocket motor, puts forward new challenges for thermal protection. Thermal environments of full-scale hybrid rocket motors designed for long-time firing tests are studied through steady-state coupled numerical simulations of flow field and heat transfer in chamber head. The motor adopts 98% hydrogen peroxide (98HP) oxidizer and hydroxyl-terminated poly-butadiene (HTPB) based fuel as the propellants. Simulation results reveal that flowing liquid 98HP in head oxidizer chamber could cool the injector plate of the motor. The cooling of 98HP is similar to the regenerative cooling in liquid rocket engines. However, the temperature of the 98HP in periphery portion of the head oxidizer chamber is higher than its boiling point. In order to prevent the liquid 98HP from unexpected decomposition, a thermal protection method for chamber head utilizing silica-phenolics annular insulating board is proposed. The simulation results show that the annular insulating board could effectively decrease the temperature of the 98HP in head oxidizer chamber. Besides, the thermal protection method for long-time working hydrogen peroxide hybrid rocket motor is verified through full-scale firing tests. The ablation of the insulating board in oxygen-rich environment is also analyzed. [ABSTRACT FROM AUTHOR]

This paper is aimed to analyse the combustion characteristics of hybrid rocket motor with multi-section swirl injection by simulating the combustion flow field. Numerical combustion flow field and combustion performance parameters are obtained through three-dimensional numerical simulations based on a steady numerical model proposed in this paper. The hybrid rocket motor adopts 98% hydrogen peroxide and polyethylene as the propellants. Multiple injection sections are set along the axis of the solid fuel grain, and the oxidizer enters the combustion chamber by means of tangential injection via the injector ports in the injection sections. Simulation results indicate that the combustion flow field structure of the hybrid rocket motor could be improved by multi-section swirl injection method. The transformation of the combustion flow field can greatly increase the fuel regression rate and the combustion efficiency. The average fuel regression rate of the motor with multi-section swirl injection is improved by 8.37 times compared with that of the motor with conventional head-end irrotational injection. The combustion efficiency is increased to 95.73%. Besides, the simulation results also indicate that (1) the additional injection sections can increase the fuel regression rate and the combustion efficiency; (2) the upstream offset of the injection sections reduces the combustion efficiency; and (3) the fuel regression rate and the combustion efficiency decrease with the reduction of the number of injector ports in each injection section. [ABSTRACT FROM AUTHOR]

Chemical ablation and mechanical erosion of hybrid rocket nozzles can cause loss of nozzle thermal protection material, resulting thrust reduction. In this paper, the chemical ablation and mechanical erosion mechanisms of nozzle thermal protection materials are studied through numerical simulation. For chemical ablation, a coupled thermal-mechanical-chemical model is established, considering three mechanisms: wall regression caused by non-homogeneous chemical reactions at the wall, convective heat transfer and fluid-structure interaction. For mechanical erosion, a Fluent DPM model and an Abaqus DEM model are established, which are investigated from the perspectives of empirical formula and solid mechanics mechanisms respectively, and validated against each other. The comprehensive effect of chemical ablation and mechanical erosion on the morphology of the nozzle is considered. The results show that both chemical ablation and mechanical erosion dominate the wall regression rate at the downstream of the converging section and upstream of the throat while the other location is only dominate by chemical ablation. After 5s of operation, thrust of rocket engine decreases by 5.8%. The Abaqus DEM model presented by this paper breaks the limitations of the empirical formulae due to the introduction of the material constitutive model and the failure criterion. • A coupled thermal-mechanical-chemical model is established. • Mechanical erosion is studied from perspective of empirical formula and the solid mechanics mechanism. • Comprehensive effect of chemical ablation and mechanical erosion on nozzle inner wall morphology is studied. [ABSTRACT FROM AUTHOR]

The objective of this effort is to study the combustion performance of a hybrid rocket motor with the help of 3D steady-state numerical simulation, which applies 90% hydrogen peroxide as the oxidizer and hydroxyl-terminated polybutadiene as the fuel. A method of secondary oxidizer injection in post-chamber is introduced to investigate the flow field characteristics and combustion efficiency. The secondary injection medium is the mixed gas coming from liquid hydrogen peroxide catalytic decomposition. The secondary injectors are uniformly set along the circumferential direction of the post-chamber. The simulation results obtained by above model are verified by experimental data. Three influencing parameters are considered: secondary injection diameter, secondary injection angle and secondary injection numbers. Simulation results reveals that this design could improve the combustion efficiency with respect to the same motor without secondary injection. Besides, the secondary injection almost has no effect on the regression rate and fuel sueface temperature distribution. It is also presented that the oxidizer is injected by 8 secondary injectors with a diameter of 7–8 mm in the direction of 120°in post-chamber is identified as the optimized secondary injection pattern, through which combustion efficiency, specific impulse efficiency as well as utilization of propellants are all improved obviously. [ABSTRACT FROM AUTHOR]