<p>Accurate and reliable prediction of laminar-turbulent boundary layer transition at hypersonic velocities is important for the development of a variety of practical high-speed flight systems currently under development. Boundary layer transition can cause up to an order of magnitude increase in skin friction and heat flux on a flight vehicle, meaning that understanding boundary layer behavior is critical to the design of weight-efficient thermal protection systems. Despite the importance of the topic, significant gaps remain in the community's current understanding of boundary layer transition and control. </p> <p>One of the biggest areas of concern in the field of high-speed boundary layer transition is the effect of facility noise on wind tunnel measurements. Conventional hypersonic wind tunnels are contaminated by freestream fluctuations which can be as much as two orders of magnitude higher than free-flight atmospheric conditions. These disturbances are typically produced by turbulent boundary layers on the tunnel walls; they are acoustic in nature and consist of pressure waves which radiate into the test section. This facility noise plays a leading role in high-speed transition phenomena in conventional hypersonic tunnels.</p> <p><br></p> <p>The current work studies the effects of facility noise on hypersonic transition using both linear stability theory and direct numerical simulation. A model for the freestream disturbance environment of the von Karman Facility's Tunnel B based on experimental measurements of the disturbance spectra present in the tunnel is created and used to study a past experiment performed in the same wind tunnel using a sharp cone and hollow cylinder. The results show that while linear stability theory accurately captures the behavior of second-mode instability growth, it fails to predict the growth of low-frequency instabilities recorded in the experiments. The stability theory analysis also suggests that very fine scale variation in nose tip geometry can play an outsize role in the development of boundary layer instabilities significantly farther downstream.</p> <p><br></p> <p>The direct numerical simulation demonstrates that, using an artificial body forcing term to implement the constructed tunnel noise model, the experimental effects of facility noise can be adequately captured with a sufficiently dense computational grid. For the conical geometry used in the experiments, calculations of surface heat flux indicate good experimental agreement with in prediction of transition location, and total temperature spectra extracted from the flow compare favorably with the experimental data as well. Visualizations of the flowfield confirm the onset of turbulence as a result of the freestream forcing. The computations also suggest that nonlinear interactions may be present in the turbulent breakdown region, leading to the production of streamwise streaks along the cone's surface. Transition on the hollow cylinder was not achieved due to suspected resolution issues, so detailed physical comparison of the two cases was not possible.</p> <p><br></p> <p>Overall, the results of this work suggest that direct numerical simulation is a capable tool for studying the effects of facility noise on hypersonic transition for simple geometries, albeit one which can be difficult to practically realize considering the required computational cost. Computational results indicate that two phenomena may play a role in the development of boundary layer instabilities for a sharp cone --- the fine-scale shape of the tip, which may change the behavior of the entropy layer near the nose; and the interactions between low- and high-frequency waveforms, which seems to cause nonlinear breakdown in line with current experimental understanding.</p>

<p dir="ltr">Pressure transducer, infrared heat transfer, and schlieren imaging data for a flared cone and cone-cylinder-flare in Mach 6 quiet flow are presented. Flared cone pressure transducer results show second-mode RMS values comparable to that found in prior experimental work. Second-mode frequency is found to linearly increase with increasing freestream unit Reynolds number, and frequency varies little between sensors for a given freestream unit Reynolds number. Turbulent intermittency begins to increase at a freestream unit Reynolds number 2x10⁶/m greater than the unit Reynolds number corresponding to peak second-mode RMS. peak RMS. High-speed schlieren imaging on the downstream section of the flared cone shows the second-mode disturbance following trends in power which correlate with PCB RMS. Infrared heat transfer results contain the azimuthal heating streak pattern observed for the flared cone in prior research, but the hot-cold-hot streak pattern is not seen due to limited model length. Streak heating occurs downstream of second-mode peak RMS over the freestream unit Reynolds number range of 6.4x10⁶/m to 10.4x10⁶/m. The heat transfer of streaks is found to vary significantly from streak to streak, while mean streak heating variation with freestream unit Reynolds number is small.</p><p dir="ltr">PCB results of the cone-cylinder-flare show intermittent turbulence at a freestream unit Reynolds number of 16.0x10⁶/m. Examination of shear-layer and second-mode instabilities show significant increases in RMS moving downstream along the flare and with increasing freestream unit Reynolds number. High-speed schlieren imaging of the shear-layer reattachment region on the flare show the presence of the shear-layer and second-mode instabilities when the model is configured with a sharp nose tip. The instabilities are not present with a blunt 5 mm radius nose tip. Heat transfer is observed to increase along the downstream portion of the flare. The sharp nose tip configuration has higher heat transfer rates than the 5 mm radius nose tip configuration.</p>

A key component of research in the aerospace industry constitutes hypersonic flights (M>5) which includes the design of commercial high-speed aircrafts and development of rockets. Computational analysis becomes more important due to the difficulty in performing experiments and reliability of its results at these harsh operating conditions. There is an increasing demand from the industry for the accurate prediction of wall-shear and heat transfer with a low computational cost. Direct Numerical Simulations (DNS) create the standard for accuracy, but its practical usage is difficult and limited because of its high cost of computation. The usage of Reynold's Averaged Navier Stokes (RANS) simulations provide an affordable gateway for industry to capitalize its lower computational time for practical applications. However, the presence of existing RANS turbulence closure models and associated wall functions result in poor prediction of wall fluxes and inaccurate solutions in comparison with high fidelity DNS data. In recent years, machine learning emerged as a new approach for physical modeling. This thesis explores the potential of employing Machine Learning (ML) to improve the predictions of wall fluxes for hypersonic turbulent boundary layers. Fine-grid RANS simulations are used as training data to construct a suitable machine learning model to improve the solutions and predictions of wall quantities for coarser meshes. This strategy eliminates the usage of wall models and extends the range of applicability of grid sizes without a significant drop in accuracy of solutions. Random forest methodology coupled with a bagged aggregation algorithm helps in modeling a correction factor for the velocity gradient at the first grid points. The training data set for the ML model extracted from fine-grid RANS, includes neighbor cell information to address the memory effect of turbulence, and an optimal set of parameters to model the gradient correction factor. The successful demonstration of accurate predictions of wall-shear for coarse grids using this methodology, provides the confidence to build machine learning models to use DNS or high-fidelity modeling results as training data for reduced-order turbulence model development. This paves the way to integrate machine learning with RANS to produce accurate solutions with significantly lesser computational costs for hypersonic boundary layer problems.

<p>The first force and moment measurements were conducted in the BAM6QT. Three 7-degree half-angle sharp cones were tested, one with base radius of 4.5 in. and two with base radius of 3.5 in. made out of different materials. Models were tested at 0 and 2 degrees angle of attack. Models were tested over a range of burst pressures and Reynolds numbers. Models were fitted onto a strain gauge, 6 component, internal, moment balance. Multiple assemblies were tested that mounted the balance in the BAM6QT. High-speed schlieren video was used to monitor flow conditions and track the movement of the tunnel and model. Three entries were performed in the BAM6QT. The improvement in data quality with each new entry is shown and the startup and running loads from entry 3 are analyzed.</p> <p>Startup loads were measured and are of importance in determining the load range needed to operate in the BAM6QT. Large startup loads up to 40X the running load were identified. Tunnel movement was measured and was used to approximate the inertial loading during startup and the run. The inertial loading was not found to be the cause of the large startup loads. Schlieren video was used to qualitatively review the startup flow. It was found the large startup loads in axial force were plausibly from the high-pressure subsonic flow evacuating the nozzle. For normal force and pitching moment, the startup loads peak at a different time than axial force and appear to be from a shock-shock interaction nearby the model. Trends in startup load with changing model geometry, AoA, and burst pressure were put together to form an empirical estimation for startup loads sharp cones. </p> <p>Running loads were profiled and found to be trending with burst pressure and model geometry similarly to Newtonian flow theory predictions. However, due to the lack of a base pressure measurement, the results are uncorrected for sting effects and differ from Newtonian flow theory by a scalar. A 5.3 Hz oscillation in axial force was identified. The frequency of the oscillation is the same as the frequency of the quasi-steady flow periods caused by the reflection of the expansion fan in the driver tube. Normal force during the running load was found to be measuring positive loads when at 0 degrees angle of attack. Both the axial and normal force phenomena were unexpected and were investigated but both require further research. </p> <p><br></p> <p><br></p> <p><br></p> <p><br></p>

<p>There is growing interest in the use of nanosecond surface dielectric barrier discharge (ns-SDBD) actuators for high-speed (supersonic/hypersonic) flow control. A plasma discharge is created using a nanosecond-duration pulse of several kilovolts, and leads to a rapid heat release and a complex three-dimensional flow field. Past work has been limited to qualitative visualizations such as schlieren imaging, and detailed measurements of the induced flow are required to develop a mechanistic model of the actuator performance. </p><p><br></p><p></p><p>Background-Oriented Schlieren (BOS) is a quantitative variant of schlieren imaging and measures density gradients in a flow field by tracking the apparent distortion of a target dot pattern. The distortion is estimated by cross-correlation, and the density gradients can be integrated spatially to obtain the density field. Owing to the simple setup and ease of use, BOS has been applied widely, and is becoming the preferred density measurement technique. However, there are several unaddressed limitations with potential for improvement, especially for application to complex flow fields such as those induced by plasma actuators. </p><p></p><p>This thesis presents a series of developments aimed at improving the various aspects of the BOS measurement chain to provide an overall improvement in the accuracy, precision, spatial resolution and dynamic range. A brief summary of the contributions are: </p><p>1) a synthetic image generation methodology to perform error and uncertainty analysis for PIV/BOS experiments, </p><p>2) an uncertainty quantification methodology to report local, instantaneous, a-posteriori uncertainty bounds on the density field, by propagating displacement uncertainties through the measurement chain,</p><p>3) an improved displacement uncertainty estimation method using a meta-uncertainty framework whereby uncertainties estimated by different methods are combined based on the sensitivities to image perturbations, </p><p>4) the development of a Weighted Least Squares-based density integration methodology to reduce the sensitivity of the density estimation procedure to measurement noise.</p><p>5) a tracking-based processing algorithm to improve the accuracy, precision and spatial resolution of the measurements, </p><p>6) a theoretical model of the measurement process to demonstrate the effect of density gradients on the position uncertainty, and an uncertainty quantification methodology for tracking-based BOS,</p><p>Then the improvements to BOS are applied to perform a detailed characterization of the flow induced by a filamentary surface plasma discharge to develop a reduced-order model for the length and time scales of the induced flow. The measurements show that the induced flow consists of a hot gas kernel filled with vorticity in a vortex ring that expands and cools over time. A reduced-order model is developed to describe the induced flow and applying the model to the experimental data reveals that the vortex ring's properties govern the time scale associated with the kernel dynamics. The model predictions for the actuator-induced flow length and time scales can guide the choice of filament spacing and pulse frequencies for practical multi-pulse ns-SDBD configurations.</p>

<p dir="ltr">This thesis concentrates on the improvement of the quality of shock-dominated flows in supersonic inlets by controlling shock wave / boundary layer interactions (SWBLIs). SWBLI flow control has been a major issue relevant to scramjet-associated endeavors for many years. The ultimate goal of this study is to numerically investigate SWBLI flow control through the application of steady-state thermal sources --- which were defined to replicate the Joule heating effect produced by Quasi-DC electric discharges --- and compare the results with data obtained from previous experiments.</p><p dir="ltr">Numerical solutions were obtained using both a three-dimensional, unsteady Reynolds-averaged Navier-Stokes (RANS) solver with a Spalart-Allmaras (SA) Detached Eddy Simulation (DES) turbulence modeling method and also a simple three-dimensional, compressible RANS solver with a SA turbulence model. Computations employed an ideal gas thermodynamic model. The numerical code is Stanford University Unstructured (SU2), an open-source, unstructured grid, computational fluid dynamics code. The SU2 code was modified to include volumetric thermal source terms to represent the Joule heating effect of electric current flowing through the gas. The computational domain, source term configuration, and flow conditions were defined in accordance with experiments carried out at the University of Notre Dame. Mach 2 flow enters the three-dimensional test domain with a stagnation pressure of 1.7 bar. The test domain is contained by four isothermal side walls maintained at room temperature, as well as an inlet and outlet. A shock wave (SW) generator, a symmetric 10 degree wedge, is positioned on the upper surface of the test domain. The overall length of the test sections is 910 mm and inlet length of the computational domain is increased prior to the location of shock wave generator in order to allow for adequate boundary layer growth. Volumetric heating source terms were positioned on the lower surface of the test domain in the reflected SW region.</p><p dir="ltr">Experimental results show that the thermal sources create a new shock train within the duct and do not initiate significant additional pressure losses. What remains to be explored is the overall characterization of the 3D flow features and dynamics of the thermally induced SW and the effect of gas heating on total pressure losses in the test section.</p><p dir="ltr">Numerical solutions validate what is observed experimentally, and offer the ability to gather more temporally and spatially-resolved measurements to better understand and characterize shock-dominated flow control in a supersonic inlet or duct. Although thermally driven SWBLI flow control requires additional research, this study alleviates the dependency on experimentally driven data and adds insight into the nature of the complex unsteady, three-dimensional flowfield.</p>

<p dir="ltr">Laser absorption spectroscopy (LAS) is a widely used technique to acquire path-integrated measurements of gas properties such as temperature and mole fraction. Although extremely useful, the application of LAS to study heterogeneous combustion environments can be challenging. For example, beam steering can be one such challenge that arises during measurements in heterogeneous combustion environments such as metallized propellant flames or measurements at high-pressure conditions. The ability to only obtain path integrated measurements has been a major challenge of conventional LAS techniques, especially in characterizing combustion environments with a non-uniform thermo-chemical distribution along the line of sight (LOS). Additionally, simultaneous measurements of multiple species using LAS with narrow-bandwidth lasers often necessitates employing multiple light sources. Aerospace applications, such as characterizing hypersonic flows may require ultrashort time resolution to study fast-evolving chemistry. Similarly, atmospheric entry most often requires measurements of atoms and molecules that absorb at wavelengths ranging from ultraviolet to mid-infrared. The availability of appropriate light sources for such measurements has been limited. In the past, several researchers have come up with diagnostic techniques to overcome the above-mentioned challenges to a certain extent. Most often, these solutions have been need-based while compromising on other diagnostic capabilities. Therefore, LAS diagnostics capable of acquiring broadband measurements with ultrafast time resolution and the ability to acquire measurements at wavelengths in ultraviolet through mid-infrared is required to study advanced combustion systems and for the development of advanced aerospace systems for future space missions. Ultrafast laser absorption spectroscopy is one such technique that provides broadband measurements, enabling simultaneous multi-species and high-pressure measurements. The light source utilized for ULAS provides the ultrafast time resolution necessary for resolving fast-occurring chemistry and more importantly the ability to acquire measurements at a wide range of wavelengths ranging from ultraviolet to far-infrared. The development and application of ULAS for characterizing propellant flames and hypersonic flows under non-equilibrium conditions by overcoming the above-mentioned challenges is presented here. </p><p>This work describes the development of a single-shot ultrafast laser absorption spectroscopy (ULAS) diagnostic for simultaneous measurements of temperature and concentrations of CO, NO, and H₂O in flames and aluminized fireballs of HMX (C₄H₈N₈O₈). Ultrashort (55 fs) pulses from a Ti:Sapphire oscillator emitting near 800 nm were amplified and converted into the mid-infrared through optical parametric amplification (OPA) at a repetition rate of 5 kHz. Ultimately, pulses with a spectral bandwidth of ≈600 cm^-1 centered near 4.9 µm were utilized in combination with a mid-infrared spectrograph to measure absorbance spectra of CO, NO, and H₂O across a 30 nm bandwidth with a spectral resolution of 0.3 nm. The gas temperature and species concentrations were determined by least-squares fitting simulated absorbance spectra to measured absorbance spectra. Measurements of temperature, CO, NO, and H₂O were acquired in an HMX flame burning in air at atmospheric pressure and the measurements agree well with previously published results. Measurements were also acquired in fireballs of HMX with and without 16.7 wt% H-5 micro-aluminum. Time histories of temperature and column densities are reported with a 1-σ precision of 0.4% for temperature and 0.3% (CO), 0.6% (NO), and 0.5% (H₂O), and 95% confidence intervals (C.I.) of 2.5% for temperature and 2.5% (CO), 11% (NO), and 7% (H₂O), thereby demonstrating the ability of ULAS to provide high-fidelity, multi-parameter measurements in harsh combustion environments. The results indicate that the addition of the micron-aluminum increases the fireball peak temperature by ≈100 K and leads to larger concentrations of CO. The addition of aluminum also increases the duration fireballs remain at elevated temperatures above 2000 K.</p><p dir="ltr">Next, the application of ULAS for dual-zone temperature and multi-species (CO, NO, H₂O, CO₂, HCl, and HF) measurements in solid-propellant flames is presented. ULAS measurements were acquired at three different central wavelengths (5.121 µm, 4.18 µm, and 3.044 µm) for simultaneous measurements of temperature and: 1) CO, NO, and H₂O, 2) CO₂ and HCl, and 3) HF and H₂O. Absorption measurements with a spectral resolution of 0.35 nm and bandwidth of 7 cm^-1, 18 cm^-1, and 35 cm^-1, respectively were acquired. In some cases, a dual-zone absorption spectroscopy model was implemented to accurately determine the gas temperature in the hot flame core and cold flame boundary layer via broadband absorption measurements of CO₂, thereby overcoming the impact of line-of-sight non-uniformities. Results illustrate that the hot-zone temperature of CO₂ agrees well with the equilibrium flame temperature and single-zone thermometry of CO, the latter of which is insensitive to the cold boundary layer due to the corresponding oxidation of CO to CO₂.</p><p dir="ltr">The initial development and implementation of an ultraviolet and broadband ultrafast-laser-absorption-imaging (UV-ULAI) diagnostic for one dimensional (1D) imaging of temperature and CN via its <i>B</i>²Σ⁺←<i>X</i>²Σ⁺absorption bands near 385 nm. The diagnostic was demonstrated by acquiring single-shot measurements of 1D temperature and CN profiles in HMX flames at a repetition rate of 25 Hz. Ultrashort pulses (55 fs) at 800 nm were generated using a Ti:Sapphire oscillator and then amplification and wavelength conversion to the ultraviolet was carried out utilizing an optical parametric amplifier and frequency doubling crystals. The broadband pulses were spectrally resolved using a 1200 l/mm grating and imaged on an EMCCD camera to obtain CN absorbance spectra with a resolution of ≈0.065 nm and a bandwidth of ≈4 nm (i.e. 260 cm^-1). Simulated absorbance spectra of CN were fit to the measured absorbance spectra using non-linear curve fitting to determine the gas properties. The spatial evolution of gas temperature and CN concentration near the burning surface of an HMX flame was measured with a spatial resolution of ≈10 µm. 1D profiles of temperature and CN concentration were obtained with a 1-σ spatial precision of 49.3 K and 4 ppm. This work demonstrates the ability of UV-ULAI to acquire high-precision, spatially resolved absorption measurements with unprecedented temporal and spatial resolution. Further, this work lays the foundation for ultraviolet imaging of numerous atomic and molecular species with ultrafast time resolution.</p><p dir="ltr">Ultraviolet ULAS was applied to characterize the temporal evolution of non-Boltzmann CN (<i>X</i>²Σ⁺) formed behind strong shock waves in N₂-CH₄ mixtures at conditions relevant to entry into Titan's atmosphere. An ultrafast (femtosecond) light source was utilized to produce 55 fs pulses near 385 nm at a repetition rate of 5 kHz and a spectrometer with a 2400 lines/mm grating was utilized to spectrally resolve the pulses after passing through the Purdue High-Pressure Shock Tube. This enabled broadband single-shot absorption measurements of CN to be acquired with a spectral resolution and bandwidth of ≈0.02 nm and ≈6 nm (≈402 cm^-1 at these wavelengths), respectively. A line-by-line absorption spectroscopy model for the <i>B</i>²Σ⁺←<i>X</i>²Σ⁺ system of CN was developed and utilized to determine six internal temperatures (two vibrational temperatures, four rotational) of CN from the (0,0), (1,1), (2,2) and (3,3) absorption bands. Measurements were acquired behind reflected shock waves in 5.65% CH₄ and 94.35% N₂ with an initial pressure of 1.56 mbar and incident shock speed of ≈2.1 km/s. For this test condition, the chemically and vibrationally frozen temperature of the mixture behind the reflected shock was 5000 K and the pressure was 0.6 atm. The high repeatability of the shock-tube experiments (0.3% variation in shock speed across tests) enabled multi-shock time histories of CN mole fraction and six internal temperatures to be acquired with a single-shot time resolution of less than 1 ns. The measurements revealed that CN <i>X</i>²Σ⁺ is non-Boltzmann rotationally and vibrationally for greater than 200 µs, thereby strongly suggesting that chemical reactions are responsible for the non-Boltzmann population distributions. </p><p><br></p>

<p dir="ltr">Soot is a byproduct formed during incomplete combustion of hydrocarbon fuels. Atmospheric soot from aircraft emissions increases local air temperatures, drives cloud formation, and decreases albedo on snow and ice: three factors that promote global warming. It is also potentially harmful to humans and has been associated with negative effects on heart and lung health. Operationally, soot formation indicates an inefficiency in combustion and can cause deterioration in aircraft engines. Modeling soot formation in complex flow fields is difficult and has been largely unsuccessful. In-situ soot measurements at relevant conditions can inform the design and operation of aircraft engines with reduced soot emissions. Laser-induced incandescence (LII) is a diagnostic that allows for non-intrusive measurements of soot volume fraction and primarily particle size in combustion environments. It involves laser-heating soot particles to temperatures at which they incandescence and measuring the radiated signal. The strong absorption capabilities and high sublimation temperature of soot make this diagnostic highly selective against the detection of other species. A coupled set of differential equations can be used to model the change in temperature and mass of a soot particle over time. Methods for modeling the fundamental processes in LII were reviewed in this work and comparisons were made between several different models.</p><p dir="ltr">International Sooting Flame target conditions were used to form a laminar diffusion flame in a Yale burner with a range of soot levels. Soot volume fraction measurements were conducted and compared with other experimental values to validate the accuracy of the experimental setup and techniques used. A calibration was performed using a laser extinction measurement from a previous study. Results showed an overall increase in soot volume fraction with increasing percentages of ethylene, as well as a transition in the peak location. Time-resolved LII was conducted at 10 MHz to determine the primary particle size of soot particles. Larger primary particles were observed with increasing height for flames with higher ethylene content. Changes in the soot formation and surface growth rates are suspected factors in the observed trends in the data. </p><p dir="ltr">The overall objective of this study was to validate an experimental setup for Laser-Induced Incandescence using a laminar diffusion flame. LII measurements were successfully demonstrated using the same diagnostic setup in a liquid-fueled swirl-stabilized flame at aircraft engine-relevant conditions. This study sets the groundwork for further investigation into aircraft soot generation using LII. </p>

<div>Since as early as the 1920s, dinitrogen tetroxide (N2O4) has been regarded as a promising oxidizer in rocket propulsion systems. In more recent times, its predecessor, mixed oxides of nitrogen (MON), remains a top contender among oxidizers, due to its unique characteristics such as low freezing temperature and compatibility with common spacecraft materials. Today, these N2O4-based oxidizers are the preferred choice in many upper stages, launch escape systems, reaction control systems, liquid apogee engines, and in-space primary propulsion systems. N2O4-based oxidizers are a key factor in rocket propulsion, and thoroughly understanding their history, development, characteristics, synthesis, and composition analysis are crucial for space exploration today and into the future.<br><br></div><div>To fully understand and predict the physical properties of a MON sample, it is important to measure and quantify its chemical composition. The recommended method for MON composition analysis, as prescribed by the Department of Defense’s Defense Specification (MIL-SPEC) document on N2O4, involves the oxidation of NO and dinitrogen trioxide (N2O3) in the MON sample to determine their amounts. An equation unofficially called the “MIL-SPEC equation” is then used to determine the amount of NO needed to mix with N2O4 to synthesize that particular MON sample. However, no explanation is given as to how the equation was derived, or its significance.<br><br></div><div>This thesis aims to collect and organize key information on the synthesis, handling, and composition analysis of MON propellant. First, the history of development of N2O4-based oxidizers was researched, and current and future uses of N2O4 and MON propellants were identified. Then a method for synthesis and composition analysis was devised and tested. Water contamination was expected of skewing the results, so the process of water contamination was examined analytically. Then a detailed derivation of the MIL-SPEC equation was conducted, to fully understand its mechanics. An attempt was then made to reverse-engineer an unexplained numerical value in the equation, labeled by the author as the “solubility factor”. Several derivations were provided with varying degrees of complexity, producing alternative solubility factors of varying accuracies. Finally, experimental data was applied to these derived, hypothetical solubility factors and the MIL-SPEC solubility factor, with the intent of determining whether improvements could be made to the MON composition determination process.<br><br></div><div>The results suggest that the MIL-SPEC equation is sufficient for providing a relatively accurate measurement of the composition of a MON sample, while also being easy to implement, both in taking the necessary measurements and in conducting the numerical calculation. However, some minor adjustments to the equation could produce consistently more accurate composition measurements without adding any more difficulty or complication.</div>