Combustion Behavior of Solid-Fuel Ramjets

In this paper, large eddy simulations (LES) are employed to study the cold flow inside a Solid Fueled Ramjet (SFRJ) using a finite element method with a Discontinuous Galerkin bases in the open-source multi-physics software SU2. The fuel-gas boundary conditions and heat release due to mixing are modeled using novel LES formulations obtained using integration by parts over the discontinuous Galerkin bases. To capture scalar variance, the Smagorisnki and wall-adapted subgrid stress models are implemented and investigated in two-dimensions. Spectral Proper Orthogonal Decomposition is used to analyze CFD results and determine acoustic modes in the ramjet. Numerical and experimental results are compared by examining peak acoustic frequencies. Simulations performed with a 2D axisymmetric domain are compared to those with a full 3D domain/ The large eddy simulation (LES) of cold flow inside a Solid Fueled Ramjet (SFRJ) shows two dominant acoustic modes with Strouhal numbers St\equiv f/f_0=3.18, which appear to be insensitive to the cavity configuration. The first peak corresponds to a longitudinal mode associated with the chamber's fundamental oscillations, characterized by the length scale L_c. The second mode exhibits radial fluctuations in the mixing chamber and is associated with the maximum chamber radius of the ramjet as its scaling length. The intermediate frequency range shows mixed modes with both radial and axial fluctuations, highlighting the impact of a slanted aft wall on the acoustics. Three-dimensional cold flow simulations predict weak non-symmetric (azimuthal) modes. Integration by parts over the discontinuous Galerkin bases is used to obtain novel LES formulations for fuel-gas boundary conditions and heat release due to mixing, with the Smagorinsky and wall-adapted subgrid stress models for scalar variance implemented and investigated in two dimensions. The CFD results are analyzed using Spectral Proper Orthogonal Decomposition to determine acoustic modes in the ramjet, and the peak acoustic frequencies are compared with experimental results. Simulations are performed with both a 2D axisymmetric and full 3D domain, and comparisons are made between them. The hot-flow simulations reveal that the presence of the cavity leads to a significant increase in the mean chamber pressure, which is consistent with the experimental findings and suggests that the cavity improves the flame-holding in solid-fuel ramjets. Analysis of the ramjet's acoustic modes demonstrates that low-frequency modes emerge in the cavity cases, consistent with the experimental data. These low-frequency modes are associated with the breathing of the recirculation region at the nozzle throat through the use of SPOD analysis. The perturbations are localized in the throat region due to Mach number pressure scaling, and they do not appear to have any impact on pressure fluctuations or combustion in the chamber. Additionally, the cavity supports the decrease of high-wave number harmonics of the ramjet chamber acoustic mode, along with the emergence of low-frequency vortical modes. These fluctuations are the result of the nonlinear amplification of the fundamental mode, which is amplified by the thermo-acoustic coupling.

A research-scale solid-fuel ramjet test article has been developed to study the secondary combustion zone of solid fuel ramjets. Tests were performed at a constant core air mass flowrate of 0.77 kg/s with 0%, 15%, and 30% bypass ratios. The propulsive performance analysis results indicate that the 0% bypass case had the highest regression rate and fuel mass flowrate. The regression rate and fuel mass flowrate of fuel without carbon black was the lowest. The specific impulse with air mass flowrate included was highest for the 0% bypass case reaching 130 s and lowest for the 30% bypass case reaching 110 s. For specific impulse with air mass flowrate excluded, the 30% bypass case achieved 2,800 s while the 0% bypass case achieved 1,800 s. The characteristic velocity was greatest for 0% bypass reaching 1,025 m/s and lowest for 30% bypass reaching 900 m/s. The combustion efficiency was highest for the 15% bypass case with carbon black addition approaching 0.82. 50 kHz and 75 kHz CH* chemiluminescence imaging was performed. Analyzing thin slivers of the images over 40,001 frames with frequency-domain techniques showed that most of the high amplitude content occurred below 1-5kHz with small peaks near 20 kHz and 30 kHz. Dynamic mode decomposition (DMD) was performed on sets of 10,001 spatially-calibrated images and their corresponding uncalibrated, uncropped images. Most of the tests exhibited low-frequency axial pumping, transverse modes, and other mode shapes indicative of the secondary injection. The prominence of transverse and other jet-related modes over axial modes appeared to be related to increasing bypass ratio. High-frequency axial modes also appeared in a case thought to have high core-flow momentum that did not appear at these high frequencies for other cases. The DMD modes for 0% bypass were indiscernible due to high soot content. Most of the modes corresponding to the calibrated images also appeared in the uncalibrated images, however, with different mode amplitude rankings. PIV was performed at 5 kHz for one test at 15% bypass. The instantaneous vector fields for these tests displayed local velocities up to 600 m/s. The mean images showed velocities up to 250 m/s. The two-dimensional turbulent kinetic energies reached 200 m2/s2 in several regions throughout the flowfield. The turbulence intensity exceeded 0.20 near the bottom of the flowfield.

In this work, we propose a rapid optimization approach to examine its application potential for the design and performance prediction and optimization of a solid fuel ramjet (SFRJ) with a bluff body. For this, the shape of the bluff body is parameterized first using the non-uniform rational B-spline method. We then develop a model for predicting SFRJ performances by incorporating both levy motion-gradient descent and support vector regression methods. It is found that a faster prediction is achievable, while the average error is maintained to be less than 5%. We then develop a multi-objective optimization model by considering the full thrust and minimum total pressure loss (TPL). The optimization model is examined using the non-dominated sorting genetic algorithm. A cost parameter is also created to facilitate the tradeoffs between the thrust and TPL in the Pareto front, when different bluff-body design configurations are considered. The present results reveal that an increase in the cost parameter will elevate the turbulence intensity within the SFRJs while drawing the incoming air closer to the fuel surface, resulting in an increase in thrust and regression rate, but the TPL will also increase. When prioritizing the TPL reduction in the design stage, the optimized solution reduces TPL by 50%. Meanwhile, the net thrust is shown to be decreased by less than 3.5%. Furthermore, flow-field investigation reveals that the improved performance of the optimized SFRJ is due to more uniform flow velocity gradients around the bluff body and a reduced rear vortex, resulting in reduced momentum loss. Our proposed optimization approach's robustness has been further confirmed with consistent performances, as the ramjet inlet speed varies over a broad range. It shows that our approach has great potential to be applied for the SFRJ performance prediction and optimization, being operated under various conditions.

Effects of new solid propellant configurations on the combustion characteristics of a ramjet

Investigation of the effect of geometry of combustor on combustion characteristics of solid-fuel ramjet with swirl flow

This paper presents a numerical investigation of ignition and combustion stabilization of a novel design of a solid-fuel ramjet (SFRJ) motor with and without swirl flow. The proposed design includes two solid fuels, retaining the simple design of the classic SFRJ. Numerical simulations of unsteady, turbulent, reactive, and swirling flow coupled with solid-fuel pyrolysis have been performed using an in-house CFD solver. Experiments on SFRJ were conducted via a connected-pipe test facility to validate the developed code. Furthermore, the code was validated for chemical reactions, heat diffusion, and swirl flow by using benchmark test cases of shock-induced, semi-infinite plate, and dump combustor with swirl flow, respectively. Then, the proposed and classic designs were simulated for the same inflow conditions and configurations, and the results were analyzed and discussed. It is found that the mixing degree, reactant residence time, mass flux, ignition delay time, and regression rate improve when using the proposed design. Moreover, the proposed design reveals interesting observations of a new flame being created and merged with the main flame.

A study of solid ramjet fuel containing boron–magnesium mixtures

Low regression rate is the most critical issue for the development and application of hybrid rocket motors (HRMs). Paraffin-based fuels are potential candidates for HRMs due to their high regression rates but adding polymers to improve strength results in insufficient regression rates for HRMs applications. In this work, Computational Fluid Dynamics (CFD) modeling and analysis were used to investigate the mixing and combustion of gaseous fuels and oxidizers in HRMs for various fuel grains and injector combinations. In addition, the regression rate characteristics and combustion efficiency were evaluated using a ground test. The results showed that the swirling flow with both high mixing intensity and high velocity could be formed by using the swirl injector. The highest mixing degree attained for the star-swirl grain and swirl injector was 86%. The reported combustion efficiency calculated by the CFD model attained a maximum of 93% at the nozzle throat. In addition, a spatially averaged regression rate of 1.40 mm·s−1 was achieved for the star-swirl grain and swirl injector combination when the mass flux of N2O was 89.94 kg·m−2·s−1. This is around 191% higher than the case of non-swirling flow. However, there were obvious local regression rate differences between the root of the star and the slot. The regression rate increase was accompanied by a decrease in the combustion efficiency for the strong swirling flow condition due to the remarkable higher mass flow rate of gasified fuels. It was shown that the nano-sized aluminum was unfavorable for the combustion efficiency, especially under extreme fuel-rich conditions.

Small-scale in-situ burning (ISB) experiments with chemically confined crude oils on water

Hybrid Rocket Motor (HRM) has a critical weakness that impacts performance because of low regression rate. Due to this, extensive investigation has been done on the end-burning hybrid rocket (EBHR) to enhance the regression rate. Analytical studies were conducted on the EBHR to model the internal ballistic flow field in the combustion port at different initial configurations. The present investigation is focused on single port EBHR, paraffin wax doped with high entropy additives (HEA), and gas oxygen as the fuel and oxidiser, respectively. Three different HRM configurations will be investigated to compare the enhancement of regression rate: conventional HRM, EBHR, and EBHR with additives. The experimental work was conducted using FeCoNiAl(0.1-x)BxSi doped in paraffin wax for end-burning static firing. HEA contributes to an increase of 1.11% to the regression rate, 12.27% to the thrust, and 12.16% to the specific impulse of the HRM compared to pure paraffin wax fuel. EBHR has an overall lower performance than conventional HRM. The results show an increase of 44.32% and 52.75% in regression rate for fuel with 5% and 7% HEA concentrations, respectively, compared to the baseline of 3%. The mass of the fuel has the most impact on the regression rate, with an increase of 104.4% for 50% more fuel mass compared to the baseline. However, the HRM with the highest specific impulse is the one with a rise of 22.62% mass flux as compared to the baseline.

A small-scale motor and test stand were designed and developed with specific emphasis on characterizing swirl flow injection angles. The motor is designed for simple integration and setup, such that both the forward-end enclosure and end cap can be easily removed for rapid integration of components during testing. While examining injectors and their potential it is thought ideal to obtain the highest regression rates and overall motor performance. The oxidizer and fuel are nitrous oxide and hydroxyl-terminated polybutadiene, respectively, due to previous experience and simplicity. The injector designs, selected for the same reasons, are designed such that they vary only in the swirl angle with tested Swirl Flow numbers of S= 0, 0.18, 0.39, 0.6 and 1.15. The system was limited in oxidizer mass flow rate so additional tests are required at higher mass fluxes for a reasonable fit for the regression rate exponent. Key results include an increase in 60 degree swirl flow injector regression rate as high as 1.63 times the regression rates of zero degree swirl flow injectors for similar oxidizer mass flux conditions. The results also show a nearly uniform regression rate along the grain length for the highest swirl flow number injector tests. A sensitivity analysis demonstrates that oxidizer mass flux and swirl flow number are the leading variables in the regression rate of this hybrid rocket motor. This is evidence that an alternate definition of oxidizer mass flux should be investigated to augment the fundamental hybrid rocket motor regression rate equation when using swirl flow injection.

Expandable Graphite, a Novel Regression Rate Enhancer in the Solid Fuel Ramjet

In this paper, the effect of sudden expansion ratio of solid fuel ramjet (SFRJ) combustor is numerically investigated with swirl flow. A computational fluid dynamics (CFD) code is written in FORTRAN to simulate the combustion and flow patterns in the combustion chamber. The connected-pipe facility is used to perform the experiment with swirl, and high-density Polyethylene (HDPE) is used as the solid fuel. The investigation is performed with different sudden expansion ratios, in which the port and inlet diameters are independently varied. The results indicated that the self-sustained combustion of the SFRJ occurs around the reattachment point at first, and then the heat released in reattachment point is used to achieve the self-sustained combustion in the redevelopment zone. The average regression rate is proportional to the sudden expansion ratio for the cases with a fixed port diameter, which is mainly dominated by the enhancement of heat transfer in backward-facing step. However, the average regression rate is inversely proportional to the sudden expansion ratio for the cases with fixed inlet diameter, which is influenced by the heat transfer mechanism of developed turbulent flow in the redevelopment zone.

The Combustion characteristic with respect to initial port diameter variation in hybrid rocket motor is investigated using single port cylindrical grain. Experimental studies are performed with GOX and GN2O as oxidizers, and HDPE as fuel. Four initial port diameters of 10 mm, 15 mm, 20 mm and 25 mm were tested to see the effect of initial diameter on the burning rate where the regression rate behaved differently depending on the type of oxidizer. With GOX as oxidizer, the regression rates for the four port diameters are laid closely to each other so that they can be represented by a single empirical correlation i.e., as if the effect of initial port diameter can be negligible on the burning rate. At the contrary with GN2O, the regression rates are hardly represented by a single empirical correlation, and a large scatter of O/F ratio is observed with different initial diameters implying that the effect of initial port diameter can be important on the burning rate. While the behavior of regression rate on the variation of initial port diameter appeared differently depending on the type of oxidizer, the burning rate of fuel at a given oxidizer mass flow rate is decreased with increasing initial port diameter due to the decrease of heat flux from the flame to the solid fuel surface for both the oxidizer. A simple relation between thrust at the nozzle throat and initial geometry characteristic which is composed of oxidizer mass flow rate, initial port diameter and fuel grain length is proposed for the design method of hybrid rocket motor.

The simplest regression rate formula, which depends solely on oxidizer mass flux, originates from Marxman’s theory introduced in the 1960s. This commonly adopted model is still widely used, even though it cannot adequately represent the important effect of thermochemical properties associated to a given specific fuel. In this study, the space–time-averaged regression rate formula taking into account the mass transfer number is reevaluated to highlight its relative sensitivity with respect to the commonly used simple formula even if has been known to be a weak function on the regression rate. Polymers (High Density Polyethylene, Polymethylmethacrylate, and Polypropylene) are considered as fuel where theoretical mass flux exponent of 0.75 from the classical theory of Marxman is investigated when applied to the empirical regression rate. Besides, the effect of chamber pressure and use of motor oxidizer to fuel ratio on sensitivity have been quantified and experimentally analyzed. It is shown that Marxman’s theory is a very robust model and that its local regression rate theory extends well to the space–time-averaged experimental results for fuel lean cases. Finally, results of this study were consistent with the finding of Karabeyoglu et al., which showed that an oxidizer to fuel ratio correction is merely required for system operating under fuel lean condition.