Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fuel nozzle”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 325 records · Page 18

Aviation fuel property effects on altitude relight

The major objective of this experimental program was to investigate the effects of fuel property variation on altitude relight characteristics. Four fuels with widely varying volatility properties (JP-4, Jet A, a blend of Jet A and 2040 Solvent, and Diesel 2) were tested in a five-swirl-cup-sector combustor at inlet temperatures and flows representative of windmilling conditions of turbofan engines. The effects of fuel physical properties on atomization were eliminated by using four sets of pressure-atomizing nozzles designed to give the same spray Sauter mean diameter (50 + or - 10 micron) for each fuel at the same design fuel flow. A second series of tests was run with a set of air-blast nozzles. With comparable atomization levels, fuel volatility assumes only a secondary role for first-swirl-cup lightoff and complete blowout. Full propagation first-cup blowout were independent of fuel volatility and depended only on the combustor operating conditions.

Venkataramani, K.↗

Exploring the Effects of Varying Pre-Chamber Geometry in a Heavy-Duty Natural Gas Optical Engine under Dilution Conditions

Pre-chamber combustion is an advanced ignition strategy that has been shown to enhance spark ignition (SI) combustion stability in natural gas (NG) engines by providing distributed ignition sites from turbulent jets and enhancing main-chamber turbulence. Pre-chamber combustion has been proven especially advantageous compared to SI in ultra-lean and dilute operating conditions. This work involves experimental investigation of the effects of varying passive pre-chamber nozzle configuration on pre-chamber and main chamber combustion under simulated exhaust gas recirculation (EGR) dilution (0 and 20%) conditions in a heavy-duty, single-cylinder, optically accessible NG engine at stoichiometric fuel-air ratio. Pre-chamber nozzle configurations include four pre-chambers with constant nozzle area to pre-chamber volume ratio (A/V) with different nozzle sizes and orientations and one configuration with larger nozzles. The optical engine is operated in a skip-fire sequence consisting of 18 motored cycles followed by two consecutive fired cycles to elucidate the effect of combustion residuals (internal EGR) on combustion evolution. Pressure-based diagnostics are used to monitor pre-chamber and subsequent main chamber combustion, and optical diagnostics include high-speed OH* chemiluminescence to visualize the development of pre-chamber jets and the resulting ignition of the main chamber charge. Heat release analysis of the in-cylinder pressure data indicates that a faster pre-chamber pressure rise does not always translate into faster main-chamber combustion. The pre-chamber with the smallest nozzle diameter produced the highest pre-chamber pressure rise and fastest combustion under non-diluted conditions. However, dilution delays the main chamber ignition for smaller nozzles despite a comparable rise in pre-chamber pressure compared to configurations with larger nozzles. This effect is more pronounced for cycles with in-cylinder combustion residuals in addition to external dilution. Additionally, it was observed that pre-chambers with swirling nozzles have a faster pressure rise in the pre-chamber and main chamber under dilute conditions. Optical diagnostics suggest that the main reason for the delay between the pre-chamber pressure rise and main-chamber combustion lies in jet quenching and delayed re-ignition, which can even lead to misfire if jets emitted from small nozzles combined with dilution fail to re-ignite.

Dhotre, Akash [University Of Minnesota-Twin Cities↗

Loitering and range performance of turbojet-powered aircraft determined by off-design engine cycle analysis

The loitering and range performance of airplanes equipped with several different turbojet engines was analytically investigated by applying the results of off-design cycle analyses to specific airplane characteristics. The method of off-design cycle analysis is presented herein and is verified by a check with experimental data. For all engines considered, the loitering and the range fuel flows obtained with rated tail-pipe nozzle area, variable engine speed operations were within 2 or 3 percent of the optimum fuel flow obtainable with any method of engines operation. The optimum loitering altitude generally occurred between approximately 25,000 and 35,000 feet with corresponding optimum flight Mach numbers of 0.4 to 0.65. In general, the optimum range fuel flows occurred at 3000 to 5000 feet higher altitude and at approximately 0.15 higher flight Mach numbers than the optimum loitering fuel flow.

Koutz, Stanley L↗

Durability Study of a High-Pressure Common Rail Fuel Injection System Using Lubricity Additive-Dosed Gasoline-Like Fuel—Improved Endurance with Upgraded Hardware

Gasoline compression ignition (GCI) is a promising combustion technology that can help the commercial transportation sector achieve operational flexibility and meet upcoming criteria pollutant regulations. However, high-pressure fuel injection systems (>1000 bar) are needed to enable GCI and fully realize its benefits compared to conventional diesel combustion. This work is a continuation of previous durability studies that identified three key technical risks after running gasoline-like fuel through a heavy-duty, common rail injection system: (i) cavitation damage to the inlet check valve of the high-pressure pump, (ii) loss of injector fueling capacity, (iii) cavitation erosion of the injector nozzle holes. Upgraded hardware solutions were tested on a consistent 400- to 800-hour NATO durability cycle with the same gasoline-like fuel as previous studies. The upgraded pump showed no signs of abnormal wear or cavitation damage to the inlet check valve. In contrast to previous studies, there were no signs of pump performance degradation observed after 400 hours of testing. Material selection and design upgrades were also made to the injector which, only showed a 6.5% loss in fueling capacity after 800 hours of durability testing compared to 49.3% previously. Finally, geometric nozzle hole features such as higher inlet radius of curvature and higher K-factor were found to correlate with reduced cavitation erosion. However, mitigation of eccentric radial needle motion (i.e., wobble) is likely needed to further suppress cavitation. In general, the results from this study indicate there are viable hardware-based solutions for improving the endurance of high-pressure systems when running with gasoline-like fuel.

33 ADVANCED PROPULSION SYSTEMS↗

Effect of propulsion system characteristics on ascent performance of dual-fueled single-stage earth-to-orbit transports

The results of a parametric study of ascent performance are presented for a vertical take off, horizontal landing, single stage earth-to-orbit transport vehicle. Two dual fueled concepts, series burn and parallel burn, were investigated, both of which utilized dual position rocket nozzles. The analysis was made by systematically varying a set of propulsion similarity parameters, initial thrust-weight ratio, the proportion of the thrust due to dual position nozzle engines, expansion ratios of the rocket nozzle, and the relative split between the two fuels, hydrogen and hydrocarbon. The data are presented as a series of curves of mass ratio plotted against each of the similarity parameters for various combinations of the other similarity parameters.

Rehder, J. J.↗

Evaluation of innovative rocket engines for single-stage earth-to-orbit vehicles

Computer models of rocket engines and single-stage-to-orbit vehicles that were developed by the authors at DFVLR and NASA have been combined. The resulting code consists of engine mass, performance, trajectory and vehicle sizing models. The engine mass model includes equations for each subsystem and describes their dependences on various propulsion parameters. The engine performance model consists of multidimensional sets of theoretical propulsion properties and a complete thermodynamic analysis of the engine cycle. The vehicle analyses include an optimized trajectory analysis, mass estimation, and vehicle sizing. A vertical-takeoff, horizontal-landing, single-stage, winged, manned, fully reusable vehicle with a payload capability of 13.6 Mg (30,000 lb) to low earth orbit was selected. Hydrogen, methane, propane, and dual-fuel engines were studied with staged-combustion, gas-generator, dual bell, and the dual-expander cycles. Mixture ratio, chamber pressure, nozzle exit pressure liftoff acceleration, and dual fuel propulsive parameters were optimized.

Manski, Detlef↗

Micro-channel cooling of integrated combustor nozzle of a segmented annular combustion system

A segmented annular combustion system includes integrated combustor nozzles, each of which has a fuel injection panel disposed radially between an inner liner segment and an outer liner segment. The fuel injection panel includes an aft end portion, a first side wall, a second side wall, premixing channels defined between the first side wall and the side wall, and injection outlets defined along at least one of the first side wall and the second side wall. The aft end portion defines a turbine nozzle portion. An interior portion between the first side wall and the second side wall includes walls that extend between the first and second side walls, thereby partitioning the interior portion into discrete air cavities. The liner segments may be cooled by micro-channel cooling passages, which may be fluidly coupled to a collection trough.

33 ADVANCED PROPULSION SYSTEMS↗

Cooling of integrated combustor nozzle of segmented annular combustion system

A segmented annular combustion system includes integrated combustor nozzles, each of which has a fuel injection panel disposed radially between an inner liner segment and an outer liner segment. The fuel injection panel includes an aft end portion, a first side wall, a second side wall, premixing channels defined between the first side wall and the side wall, and injection outlets defined along at least one of the first side wall and the second side wall. The aft end portion defines a turbine nozzle portion. An interior portion between the first side wall and the second side wall includes walls that extend between the first and second side walls, thereby partitioning the interior portion into discrete air cavities. The air cavities and the liner segments may be cooled by impingement inserts or panels.

42 ENGINEERING↗

Design and Fabrication of Oxygen/RP-2 Multi-Element Oxidizer-Rich Staged Combustion Thrust Chamber Injectors

As part of the Combustion Stability Tool Development project funded by the Air Force Space and Missile Systems Center, the NASA Marshall Space Flight Center was contracted to assemble and hot-fire test a multi-element integrated test article demonstrating combustion characteristics of an oxygen/hydrocarbon propellant oxidizer-rich staged-combustion engine thrust chamber. Such a test article simulates flow through the main injectors of oxygen/kerosene oxidizer-rich staged combustion engines such as the Russian RD-180 or NK-33 engines, or future U.S.-built engine systems such as the Aerojet-Rocketdyne AR-1 engine or the Hydrocarbon Boost program demonstration engine. On the current project, several configurations of new main injectors were considered for the thrust chamber assembly of the integrated test article. All the injector elements were of the gas-centered swirl coaxial type, similar to those used on the Russian oxidizer-rich staged-combustion rocket engines. In such elements, oxidizer-rich combustion products from the preburner/turbine exhaust flow through a straight tube, and fuel exiting from the combustion chamber and nozzle regenerative cooling circuits is injected near the exit of the oxidizer tube through tangentially oriented orifices that impart a swirl motion such that the fuel flows along the wall of the oxidizer tube in a thin film. In some elements there is an orifice at the inlet to the oxidizer tube, and in some elements there is a sleeve or "shield" inside the oxidizer tube where the fuel enters. In the current project, several variations of element geometries were created, including element size (i.e., number of elements or pattern density), the distance from the exit of the sleeve to the injector face, the width of the gap between the oxidizer tube inner wall and the outer wall of the sleeve, and excluding the sleeve entirely. This paper discusses the design rationale for each of these element variations, including hydraulic, structural, thermal, combustion performance, and combustion stability considerations. This paper also discusses the fabrication and assembly of the injector components, including the injector body/interpropellant plate, the additive manufactured GRCop-84 faceplate, and the pieces that make up the injector elements including the oxidizer tube, an inlet to the oxidizer tube, and a facenut that includes the fuel tangential inlets and forms the initial recessed volume where oxidizer and fuel first interact. Hot-fire test results of these main injector designs in an integrated test article that includes an oxidizer-rich preburner are described in companion papers at this JANNAF meeting.

Garcia, C. P.↗

Effects of confinement on partially premixed flames

Partially premixed combustion is an intermediate regime between the limiting cases of premixed and nonpremixed combustion. Although combustion problems are generally approached from one of these two limiting cases, there are many practical situations where flames cannot be considered as purely premixed or nonpremixed, and thus the partially premixed approach must be used. In partially premixed combustion, mechanisms from the premixed and nonpremixed regimes can coexist, and as a result some interesting new phenomena can arise. One such phenomenon is the flame stabilization in laminar mixing layers by triple flames. One of the first observations of triple flames was made by Phillips (1965), who investigated a triple flame propagating in a methane mixing layer. Kioni et al. (1993) also examined triple flames both experimentally and numerically. There have also been numerous analytical studies on the shape and propagation of triple flames under various assumptions by Dold (1989), Dold et al. (1991), and Hartley and Dold (1991). In terms of modeling, Muller et al. (1994) have combined the flamelet formulations for premixed and nonpremixed combustion in order to treat lifted diffusion flames. One common feature in the analytical and numerical studies mentioned above is the assumption of zero heat release, which is necessary to make the problem tractable. The effect of heat release on triple flames was investigated by Ruetsch et al. (1995), where for the unconfined case, flame speeds larger than their premixed counterparts were found. One of the most important practical situations in which these conditions arise is in lifted turbulent jet diffusion flames. At a critical velocity the burning zone of a fuel jet lifts off from the nozzle, moves to increasing distances as the jet velocity increases, and finally blows off. The mechanisms that control these phenomena, i.e. that determine the stability of these flames, are still not understood. In addition to regions where diffusion flame stabilization takes place, partially premixed conditions also exist during the ignition process in nonpremixed systems. Numerical simulations by Reveillon et al. (1994) of the ignition process in a weakly stirred mixture of fuel and oxidizer show that triple flames propagate along lines of stoichiometric mixture fraction throughout the fluid. In addition, Peters (1994) notes that NO(x) emissions are likely to be large in such transient cases, and therefore an understanding of triple flames can provide information concerning pollutant formation. This study extends the work previously done and examines the effects of lateral confinement on partially premixed flames. Once again, we study both the flame structure and propagation.

Ruetsch, G. R.↗

Investigation of soot and carbon formation in small gas turbine combustors

An investigation of hardware configurations which attempt to minimize carbon and soot-production without sacrificing performance in small gas turbine combustors was conducted. Four fuel injectors, employing either airblast atomization, pressure atomization, or fuel vaporization techniques were combined with nozzle air swirlers and injector sheaths. Eight configurations were screened at sea-level takeoff and idle test conditions. Selected configurations were focused upon in an attempt to quantify the influence of combustor pressure, inlet temperature, primary zone operation, and combustor loading on soot and carbon formation. Cycle tests were also performed. It was found that smoke emission levels depended on the combustor fluid mechanics, the atomization quality of the injector and the fuel hydrogen content.

Rosfjord, T. J.↗

Parabolized Navier-Stokes analysis of ducted turbulent mixing problems with finite-rate chemistry

A hybrid implicit/explicit approach for analyzing 2D ducted turbulent mixing problems with finite-rate chemistry is presented. The approach combines a fully-implicit parabolic mixing algorithm, an explicit viscous-characteristic based shock-capturing algorithm, and linearized implicit chemical kinetic algorithm. The resultant model provides spatial marching solutions of the parabolized Navier-Stokes (PNS) equations for supersonic combustion and viscous nozzle flowfields. Specialized procedures are incorporated to deal with the near wall sublayer and with small central pockets of subsonic flow. A parabolic option is available which can be utilized in the direct or inverse mode for design applications. The ability of the model to treat shock waves and wave/mixing layer interactions is assessed via comparisons of predictions with those of well established explicit shock-capturing Euler (SCIPPY) and PNS (SCIPVIS) models. Applications to a variety of supersonic combustion flowfield problems involving tangential or moderately inclined fuel injection, and, to a viscous nozzle flow problem, are presented. This paper serves to exhibit overall capabilities of the model developed and no comparisons with supersonic combustion data are presented. Such comparisons serve mainly to validate the modeling of the turbulence and turbulence/chemical interactions and will be the subject of a future paper.

Sinha, N.↗

Conceptual Design of a Z-Pinch Fusion Propulsion System

This slide presentation reviews a project that aims to develop a conceptual design for a Z-pinch thruster, that could be applied to develop advanced thruster designs which promise high thrust/high specific impulse propulsion. Overviews shows the concept of the design, which use annular nozzles with deuterium-tritium (D-T) fuel and a Lithium mixture as a cathode, Charts show the engine performance as a function of linear mass, nozzle performance (i.e., plasma segment trajectories), and mission analysis for possible Mars and Jupiter missions using this concept for propulsion. Slides show views of the concepts for the vehicle configuration, thrust coil configuration, the power management system, the structural analysis of the magnetic nozzle, the thermal management system, and the avionics suite,

Adams, Robert↗

Experimental measurements of the Space Shuttle main engine fuel and oxygen turbopump vibration characteristics

The vibration characteristics of the SSME (Space Shuttle main engine) are dealt with. The Space Shuttle engine consists of a main rocket nozzle and attached to it are high pressure fuel and oxygen pumps. Various vibration problems have been encountered with both the hydrogen and oxygen pumps. The vibration spectrum of the hydrogen and oxygen pumps has been analyzed by various techniques using synchronous tracking filters and FFT analyzers. The experimental data has been correlated to theoretical predictions of resonance frequencies.

Gunter, E. J.↗

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Supersonic Turbine Bladed Disks

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. Assessing the blade structural integrity is a complex task requiring an initial characterization of whether resonance is possible and then performing a forced response analysis if that condition is met. The standard technique for forced response analysis in rocket engine turbines is to decompose a computational fluid dynamics (CFD).generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies using cyclically symmetric structural dynamic models. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non ]harmonic excitation sources that become present in complex flows. This complex content can only be captured by a CFD flow field encompassing at least an entire revolution. A substantial development effort to create a series of software programs to enable application of the 360 degree forcing function in a frequency response analysis on cyclic symmetric models has been completed (to be described in a future paper), but the question still remains whether the frequency response analysis itself is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, of bladed-disks undergoing this complex flow environment have been performed. The first is of a bladed disk with each blade modeled by simple beam elements and the disk modeled with plates (using the finite element code MSC/NASTRAN). The focus of this model is to be representative of response of realistic bladed disks, and so the dimensions are roughly equivalent to the new J2X rocket engine 1st stage fuel pump turbine. The simplicity of the model allows the CFD load to be able to be readily applied, along with analytical and experimental variations in both the temporal and spatial fourier components of the excitation. In addition, this model is a first step in identifying response differences between transient and frequency forced response analysis techniques. The second phase assesses this difference for a much more realistic solid model of a bladed-disk in order to evaluate the effect of the spatial variation in loading on blade dominated modes. Neither research on the accuracy of the frequency response method when used in this context or a comprehensive study of the effect of test-observed variation on blade forced response have been found in the literature, so this research is a new contribution to practical structural dynamic analysis of gas turbines. The primary excitation of the upstream nozzles interacts with the blades on fuel pump of the J2X causes the 5th Nodal diameter modes to be excited, as explained by Tyler and Sofrin1, so a modal analysis was first performed on the beam/plate model and the 5ND bladed-disk mode at 40167 hz was identified and chosen to be the one excited at resonance (see figure 1). The first forced response analysis with this model focuses on identifying differences between frequency and transient response analyses. A hypothesis going into the analysis was that perhaps the frequency response was enforcing a temporal periodicity that did not really exist, and so therefore it would overestimate the response. As high dynamic response was a considerable source of stress in the J2X, examining this concept could potentially be beneficial for the program.

Brown, Andrew M.↗

Pretest Simulations of a Supersonic Mixing and Combustion Validation Experiment to Assess Sensitivities

The reliance on CFD simulations to develop, design, and optimize scramjet systems (or components) has become commonplace. This reliance inevitably hinges on the ability of the computational analyst to quantify the level of confidence in their computational results. Unfortunately, nearly all the measured data available for this assessment comes from antiquated experimental datasets, or from tests that focused on the extraction of scramjet system (or component) performance. The objective of a CFD validation experiment is to quantify the predictive accuracy of one or more of the CFD physics submodels, implying that other uncertainties related to replicating the facility flow environment (e.g., knowledge of boundary conditions) must be minimized to the extent possible. This inevitably places stringent requirements on the quality and quantity of measurements taken to accurately specify inflow, outflow, and surface conditions for the CFD simulations; in addition to the measurements taken for the validation of physics submodels. This places additional demands on the experimental process above and beyond those for test article performance assessment. A recent high speed code credibility workshop series sponsored by AFRL identified a gap in existing validation data for fundamental assessments of turbulent mixing and combustion CFD closure models at scramjet engine relevant conditions. To address this gap, engineers at AFRL have designed a coaxial jet flame configuration that will be tested at two facilities (Research Cell 19 at the Air Force Research Lab, and at Purdue University). The effort described here documents pretest simulations of this validation experiment with the goal of fleshing out the extent of the facility flowpath that must be included to adequately reproduce the facility test section flow environment. The findings indicate that the flow around the support structure for the fuel injection centerbody upstream of the facility nozzle generates disturbances that persist throughout the nozzle expansion process; corrupting the azimuthal symmetry that was desired in the fuel/air mixing region of the test section. Simulations without this support structure maintained a high degree of azimuthal symmetry up until the fuel injection plane. However, even in this scenario the azimuthal symmetry was not maintained once the centerbody boundary layer transitioned to a wake flow downstream of the fuel injection plane.

CFD↗

Pretest Simulations of a Supersonic Mixing and Combustion Validation Experiment to Assess Sensitivities

The reliance on CFD simulations to develop, design, and optimize scramjet systems (or components) has become commonplace. This reliance inevitably hinges on the ability of the computational analyst to quantify the level of confidence in their computational results. Unfortunately, nearly all the measured data available for this assessment comes from antiquated experimental datasets, or from tests that focused on the extraction of scramjet system (or component) performance. The objective of a CFD validation experiment is to quantify the predictive accuracy of one or more of the CFD physics submodels, implying that other uncertainties related to replicating the facility flow environment (e.g., knowledge of boundary conditions) must be minimized to the extent possible. This inevitably places stringent requirements on the quality and quantity of measurements taken to accurately specify inflow, outflow, and surface conditions for the CFD simulations; in addition to the measurements taken for the validation of physics submodels. This places additional demands on the experimental process above and beyond those for test article performance assessment. A recent high speed code credibility workshop series sponsored by AFRL identified a gap in existing validation data for fundamental assessments of turbulent mixing and combustion CFD closure models at scramjet engine relevant conditions. To address this gap, engineers at AFRL have designed a coaxial jet flame configuration that will be tested at two facilities (Research Cell 19 at the Air Force Research Lab, and at Purdue University). The effort described here documents pretest simulations of this validation experiment with the goal of fleshing out the extent of the facility flowpath that must be included to adequately reproduce the facility test section flow environment. The findings indicate that the flow around the support structure for the fuel injection centerbody upstream of the facility nozzle generates disturbances that persist throughout the nozzle expansion process; corrupting the azimuthal symmetry that was desired in the fuel/air mixing region of the test section. Simulations without this support structure maintained a high degree of azimuthal symmetry up until the fuel injection plane. However, even in this scenario the azimuthal symmetry was not maintained once the centerbody boundary layer transitioned to a wake flow downstream of the fuel injection plane.

CFD↗

Ignition and combustion characteristics of metallized propellants, phase 2

Experimental and analytical investigations focusing on aluminum/hydrocarbon gel droplet secondary atomization and its effects on gel-fueled rocket engine performance are being conducted. A single laser sheet sizing/velocimetry diagnostic technique, which should eliminate sizing bias in the data collection process, has been designed and constructed to overcome limitations of the two-color forward-scatter technique used in previous work. Calibration of this system is in progress and the data acquisition/validation code is being written. Narrow-band measurements of radiant emission, discussed in previous reports, will be used to determine if aluminum ignition has occurred in a gel droplet. A one-dimensional model of a gel-fueled rocket combustion chamber, described in earlier reports, has been exercised in conjunction with a two-dimensional, two-phase nozzle code to predict the performance of an aluminum/hydrocarbon fueled engine. Estimated secondary atomization effects on propellant burnout distance, condensed particle radiation losses to the chamber walls, and nozzle two phase flow losses are also investigated. Calculations indicate that only modest secondary atomization is required to significantly reduce propellant burnout distances, aluminum oxide residual size, and radiation heat losses. Radiation losses equal to approximately 2-13 percent of the energy released during combustion were estimated, depending on secondary atomization intensity. A two-dimensional, two-phase nozzle code was employed to estimate radiation and nozzle two phase flow effects on overall engine performance. Radiation losses yielded a one percent decrease in engine Isp. Results also indicate that secondary atomization may have less effect on two-phase losses than it does on propellant burnout distance and no effect if oxide particle coagulation and shear induced droplet breakup govern oxide particle size. Engine Isp was found to decrease from 337.4 to 293.7 seconds as gel aluminum mass loading was varied from 0-70 wt percent. Engine Isp efficiencies, accounting for radiation and two phase flow effects, on the order of 0.946 were calculated for a 60 wt percent gel, assuming a fragmentation ratio of five.

Mueller, D. C.↗