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All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Effect of Injector Geometry on Atomization of a Liquid-Liquid Double Swirl Coaxial Injector using Non-Invasive Laser, Optical and X-ray Techniques

The spray characteristics of a Liquid-Liquid Double Swirl Coaxial Injector were studied using noninvasive Optical, Laser, and X-ray diagnostics. A parametric study of injector exit geometry demonstrated that spray breakup time, breakup type and sheet stability could be controlled with exit geometry. Phase Doppler Particle Analysis characterized droplet statistics and non-dimensional droplet parameters over a range of inlet conditions and for various fluids allowing for a study on the role of specific fluid properties in atomization. Further, x-ray radiographs allowed for investigations of sheet thickness and breakup length to be quantified for different recess exits and inlet pressures. Finally Computed Tomography scans revealed that the spray cone was distinctively non-uniform and comprised of several pockets of increased mass flux.

Radke, C. R.↗
NASA NTRS2014

Effect of Injector Geometry on Atomization of a Liquid-Liquid Double Swirl Coaxial Injector Using Non-invasive Laser, Optical and X-ray Techniques

The spray characteristics of a liquid-liquid double swirl coaxial injector were studied using non-invasive optical, laser, and X-ray diagnostics. A parametric study of injector exit geometry demonstrated that spray breakup time, breakup type and sheet stability could be controlled with exit geometry. Phase Doppler interferometry was used to characterize droplet statistics and non-dimensional droplet parameters over a range of inlet conditions and for various fluids allowing for a study on the role of specific fluid properties in atomization. Further, X-ray radiography allowed for investigation of sheet thickness and breakup length to be quantified for different recess exit diameters and inlet pressures. Finally, computed tomography scans revealed that the spray cone was distinctively non-uniform and comprised of several pockets of increased mass flux.

Radke, C. R.↗
NASA NTRS2017

Effect of Air Swirler Configuration on Lean Direct Injector Flow Structure and Combustion Performance with a 7-Point Lean Direct Injector Array

Studies of various injector configurations in a 7-point Lean Direct Injector (LDI) array are reported for both non-reacting (cold) flow and for Jet-A/air reacting flows. For cold flow, central recirculation zone (CRZ) formation is investigated and for reacting flows, combustor operability and dynamics are of interest. 2D Particle Image Velocimetry (PIV) measurements are described for the cold flow experiments and flame chemiluminescence imaging and dynamic pressure results are discussed for the reacting flow cases. PIV results indicate that for this configuration the close spacing between swirler elements leads to strong interaction that affects whether a CRZ forms, and pilot recess and counter-swirl helps to isolate swirlers from one another. Dynamics results focus on features identified near 500-Hz.

aircraft combustors↗
DOE OSTI2014

Planar ultrananocrystalline diamond field emitter in accelerator radio frequency electron injector: Performance metrics

A case performance study of a planar field emission cathode (FEC) based on nitrogen-incorporated ultrananocrystalline diamond, (N)UNCD, was carried out in an RF 1.3 GHz electron gun. The FEC was a 100 nm (N)UNCD film grown on a 20 mm diameter stainless steel disk with a Mo buffer layer. At surface gradients 45–65 MV/m, peak currents of 1–80 mA (equivalent to 0.3–25 mA/cm{sup 2}) were achieved. Imaging with two YAG screens confirmed emission from the (N)UNCD surface with (1) the beam emittance of 1.5 mm × mrad/mm-rms and (2) longitudinal FWHM and rms widths of non-Gaussian energy spread of 0.7% and 11% at an electron energy of 2 MeV. Current stability was tested over the course of 36 × 10{sup 3} RF pulses (equivalent to 288 × 10{sup 6 }GHz oscillations)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Evaluation of accuracy and resolution of the electron beam profile scanner at the Fermilab Main Injector

The objective of this work is to assess the accuracy of measurements made by the Electron Beam Profile Scanner (EBPS), which captures the trajectory of an electron beam with and without a proton beam present. The proton beam induces deflection in the electron beam, which is influenced by proton charges.For high-resolution images, the probe beam needs to be of high intensity, small diameter, and small divergence, evaluated using a YAG screen and an optical transition radiation (OTR) screen. Additionally, the point spread function (PSF) will be calculated to characterize the optical system's properties using ZEMAX software. The capabilities of the Hamamatsu Charge-Injection Device (CID) camera and Kimball Physics electron gun (e-gun) will be considered for accuracy.

Mwaniki, Matilda [IIT, Chicago; Fermilab]↗
DOE OSTI2021

Digital Twin Model for Advanced Manufacture of a Rotating Detonation Engine Injector

A digital twin material model (DTMM) of an additive manufacturing (AM) process was created to advance the state of the art in rotating detonation engine (RDE) injector design. Current RDE injectors are designed with large pressure drops, enabling a stable and repeatable combustion process. However, this comes at the cost of system efficiency. For the technology to transition to commercial fossil-based power generation, it is important to develop injectors with reduced flow losses. Low-loss injectors are difficult to design and manufacture with conventional manufacturing techniques. AM enables new design options, but the AM manufacturing process must be thoroughly understood to result in a robust design. A DTMM provides the necessary insight by defining the cause-effect relationships between process parameters, microstructure features, and properties. Therefore, a DTMM to support the design and manufacturing process was developed and applied to the design of a new additively manufactured low-loss injector. The injector combustion behavior was characterized through hot-fire tests, and mechanical performance was compared to the DTMM predictions. The two project goals were the successful development of the DTMM and the demonstration of an improved RDE injector design. The RDE injector design and DTMM developments occurred on parallel but dependent paths. The injector was designed to reduce pressure drop by increasing the cross-sectional flow area ratio between the injector air passages and the combustor annulus. This resulted in less structural material, raising the concern that thin members would be susceptible to high-cycle fatigue (HCF) under the periodic loading inherent to an RDE. It was most important for the DTMM to predict behavior in these features; therefore, the injector design concept guided the material thicknesses used in fatigue tests. The DTMM development started by manufacturing a series of coupons over the range of possible AM process variations. A design-of-experiment approach was used to select which process variable combinations gave the most efficient coverage relevant to the injector design space. The microstructure in each of these coupons was characterized, and then computational methods were used to create a numerical model of the correlation between process variables and microstructure. Next, a set of HCF samples were tested to calibrate existing models that map microstructure to HCF performance. Together, these two links formed the DTMM that calculates HCF behavior from AM process variables. Two injector prototypes were additively manufactured. The first injector design strategy aggressively pursued low-loss performance by substantially increasing the oxidizer flow area. The combination of manufacturing lead times and the fatigue testing schedule meant that the DTMM was not available when building this first prototype. Therefore, its process parameters were chosen based on a manual review of the available coupon data. This prototype was built successfully and evaluated in 58 combustion tests. Sustained detonation was achieved with remarkably reduced pressure loss, and some tests even displayed pressure loss characteristics similar to conventional gas turbine combustors. This achieved the project goal of improving RDE injector design. The second injector was manufactured according to the optimized parameters predicted by the DTMM. The flow area modifications of this injector were less aggressive than the first injector since demonstrating low pressure loss was not an objective of the second hot-fire test series. Rather, the test objective was to cause high cycle fatigue failure in the part due to periodic loading from the rotating detonation wave. The observed number of cycles to failure was to be compared to the number predicted by the DTMM and thereby assess the utility of the DTMM in component design. However, the required level of vibration was not obtained during combustion. Therefore, high cycle fatigue was not experienced in the hot-fire tests of the second injector. Fatigue data was obtained by further testing the second injector in a conventional HCF test apparatus. The injector demonstrated HCF strength above the DTMM prediction. In fact, it did not fail and testing was only discontinued due to reaching the end of the period of performance. This points to some success in the project’s primary goal of successfully developing and applying the DTMM to a component design. Implementing the DTMM recommendations for optimal processing parameters led to a part with acceptable properties. The DTMM was also shown to be an efficient correlator of data and to provide insight into the relationship between process settings, microstructure, and property performance. However, the failure of the DTMM prediction to match the experimental result of the injector fatigue test also points to the need to include significantly more data in the model development. In this project, coupons made with identical processing parameters exhibited drastically different properties from each other and from the injector part, which clearly influences the accuracy of a model that predicts performance based on parameters. Uncertainties in the build process must be quantified to develop more robust models. A denser and broader matrix of coupon process and geometry variations, several repeated builds of every point, more in-situ build process measurements, and direct observation of tensile and HCF sample microstructure (as opposed to separate microstructure specimens) are recommendations to improve future AM modeling efforts.

20 FOSSIL-FUELED POWER PLANTS↗
NASA NTRS2010

Triaxial Swirl Injector Element for Liquid-Fueled Engines

A triaxial injector is a single bi-propellant injection element located at the center of the injector body. The injector element consists of three nested, hydraulic swirl injectors. A small portion of the total fuel is injected through the central hydraulic injector, all of the oxidizer is injected through the middle concentric hydraulic swirl injector, and the balance of the fuel is injected through an outer concentric injection system. The configuration has been shown to provide good flame stabilization and the desired fuel-rich wall boundary condition. The injector design is well suited for preburner applications. Preburner injectors operate at extreme oxygen-to-fuel mass ratios, either very rich or very lean. The goal of a preburner is to create a uniform drive gas for the turbomachinery, while carefully controlling the temperature so as not to stress or damage turbine blades. The triaxial injector concept permits the lean propellant to be sandwiched between two layers of the rich propellant, while the hydraulic atomization characteristics of the swirl injectors promote interpropellant mixing and, ultimately, good combustion efficiency. This innovation is suited to a wide range of liquid oxidizer and liquid fuels, including hydrogen, methane, and kerosene. Prototype testing with the triaxial swirl injector demonstrated excellent injector and combustion chamber thermal compatibility and good combustion performance, both at levels far superior to a pintle injector. Initial testing with the prototype injector demonstrated over 96-percent combustion efficiency. The design showed excellent high -frequency combustion stability characteristics with oxygen and kerosene propellants. Unlike the more conventional pintle injector, there is not a large bluff body that must be cooled. The absence of a protruding center body enhances the thermal durability of the triaxial swirl injector. The hydraulic atomization characteristics of the innovation allow the design to be rapidly scaled from small in-space applications [500-5,000 lbf (2.2 22.2 kN)] to large thrust engine applications [80,000 lbf (356 kN) and beyond]. The triaxial injector is also less sensitive to eccentricities, manufacturing tolerances, and gap width of many traditional coaxial and pintle injector designs. The triaxial-injector injection orifice configuration provides for high injection stiffness. The low parts count and relatively large injector design features are amenable to low-cost production.

Muss, Jeff↗
NASA NTRS1995

Cooperative Testing of Rocket Injectors That Use Gaseous Oxygen and Hydrogen

Gaseous oxygen and hydrogen propellants used in a special engine energy cycle called Full-Flow Staged Combustion are believed to significantly increase the lifetime of a rocket engine's pumps. The cycle can also reduce the operating temperatures of the engine. Improving the lifetime of the hardware reduces its overall maintenance and operations costs, and is critical to reducing costs for the joint NASA/industry Reusable Launch Vehicle (RLV). The work in this project will demonstrate the performance and lifetime of one-element and many-element combustors with gaseous O2/H2 injectors. This work supporting the RLV program is a cooperative venture of the NASA Lewis Research Center, the NASA Marshall Space Flight Center, Rocketdyne, and the Pennsylvania State University. Information about gas-gas rocket injector performance with O2/H2 is very limited. Because of this paucity of data, new testing is needed to improve the knowledge base for testing and designing new injectors for the RLV and to improve computer models that predict the combusting gas flows of new injector designs. Therefore, detailed observations and measurements of the combusting flow from many-element injectors in a rocket engine are being sought. These observations and measurements will be done with three different tools: schlieren photography, ultraviolet imaging, and Raman spectroscopy. The schlieren system will take photos of the density differences in combusting flow, the ultraviolet movies will determine the location of the hydroxyl (OH) radical in the combustion flow, and the Raman spectroscopic measurements will provide the combustion temperature and amount of water (H2O), hydrogen (H2), and oxygen (O2) in the combustor. Marshall is providing overall program management, design and computational fluid dynamics (CFD) analyses, as well as funding for the work at Penn State. An existing, windowed combustor and several injectors will be provided by Rocketdyne--two injectors for the initial screening tests and one with an optimized design based on the best design found in the screening tests. Lewis will provide a nozzle and several injectors for the screening test program. The configuration of the injectors will be based on a design chosen by all the participants, and their elements will be based on the coaxial and impinging flow. Lewis also will provide the instrumentation for the flow-field measurements: schlieren, ultraviolet imaging, and Raman spectroscopy. In addition, thermocouples will measure heat flow on the injector face. Other traditional measurements of rocket performance will be made as well: chamber pressure, mass flow of each propellant, purge flow, and the barrier cooling gas flow. Penn State will conduct single-element testing with the injector elements from both the Rocketdyne and the jointly designed injectors. A wide variety of traditional and nontraditional injector designs will be tested in this program. The results will be valuable in computational fluid dynamics code validation and overall rocket combustion efficiency measurements. Correlations between combustion efficiency, laser measurements of species, and ultraviolet and visible light photography will also be made. Thus far, several different single-element injectors have been tested at Penn State and Lewis. The experimental setup of a rocket engine with a viewing window is shown. The combusting flow is shown. The results are helping engineers design the many element injectors.

Source record↗
NASA NTRS2013

Swirl Coaxial Injector Testing with LOX/RP-J

Testing was conducted at NASA fs Marshall Space Flight Center (MSFC) in the fall of 2012 to evaluate the operation and performance of liquid oxygen (LOX) and kerosene (RP ]1) in an existing swirl coaxial injector. While selected Russian engines use variations of swirl coaxial injectors, component level performance data has not been readily available, and all previously documented component testing at MSFC with LOX/RP ]1 had been performed using a variety of impinging injector designs. Impinging injectors have been adequate for specific LOX/RP ]1 engine applications, yet swirl coaxial injectors offer easier fabrication efforts, providing cost and schedule savings for hardware development. Swirl coaxial elements also offer more flexibility for design changes. Furthermore, testing with LOX and liquid methane propellants at MSFC showed that a swirl coaxial injector offered improved performance compared to an impinging injector. So, technical interest was generated to see if similar performance gains could be achieved with LOX/RP ]1 using a swirl coaxial injector. Results would allow such injectors to be considered for future engine concepts that require LOX/RP ]1 propellants. Existing injector and chamber hardware was used in the test assemblies. The injector had been tested in previous programs at MSFC using LOX/methane and LOX/hydrogen propellants. Minor modifications were made to the injector to accommodate the required LOX/RP ]1 flows. Mainstage tests were performed over a range of chamber pressures and mixture ratios. Additional testing included detonated gbombs h for stability data. Test results suggested characteristic velocity, C*, efficiencies for the injector were 95 ]97%. The injector also appeared dynamically stable with quick recovery from the pressure perturbations generated in the bomb tests.

Greene, Sandra Elam↗
NASA NTRS2016

Predictive Evaluations of Oxygen-Rich Hydrocarbon Combustion Gas-Centered Swirl Coaxial Injectors using a Flamelet-Based 3-D CFD Simulation Approach

NASA Marshall Space Flight Center (MSFC) has embarked upon a joint project with the Air Force to improve the state-of-the-art of space application combustion device design and operational understanding. One goal of the project is to design, build and hot-fire test a 40,000 pound-thrust Oxygen/Rocket Propellant-2 (RP-2) Oxygen-Rich staged engine at MSFC. The overall project goals afford the opportunity to test multiple different injector designs and experimentally evaluate the any effect on the engine performance and combustion dynamics. To maximize the available test resources and benefits, pre-test, combusting flow, Computational Fluid Dynamics (CFD) analysis was performed on the individual injectors to guide the design. The results of the CFD analysis were used to design the injectors for specific, targeted fluid dynamic features and the analysis results also provided some predictive input for acoustic and thermal analysis of the main Thrust Chamber Assembly (TCA). MSFC has developed and demonstrated the ability to utilize a computationally efficient, flamelet-based combustion model to guide the pre-test design of single-element Gas Centered Swirl Coaxial (GCSC) injectors. Previous, Oxygen/RP-2 simulation models utilizing the Loci-STREAM flow solver, were validated using single injector test data from the EC-1 Air Force test facility. The simulation effort herein is an extension of the validated, CFD driven, single-injector design approach applied to single injectors which will be part of a larger engine array. Time-accurate, Three-Dimensional, CFD simulations were performed for five different classes of injector geometries. Simulations were performed to guide the design of the injector to achieve a variety of intended performance goals. For example, two GCSC injectors were designed to achieve stable hydrodynamic behavior of the propellant circuits while providing the largest thermal margin possible within the design envelope. While another injector was designed to purposefully create a hydrodynamic instability in the fuel supply circuit as predicted by the CFD analysis. Future multi-injector analysis and testing will indicate what if any changes occur in the predicted behavior for the single-element injector when the same injector geometry is placed in a multi-element array.

Richardson, Brian R.↗
NASA NTRS1998

Burner Emissions Associated with Lobed and Non-Lobed Fuel Injectors

The present experimental study examines NO(sub x), and CO emissions associated with three alternative fuel-injector geometries. These injectors mix fuel and air and strain their interfaces to differing extents and thus create different local equivalence ratios within flow regions upstream of flame ignition and stabilization. Two of the devices studied are lobed fuel injectors, in which molecular mixing of reactants is associated with streamwise vorticity generation, while the third one is a non-lobed fuel injector. Results show that rapid mixing allowed both lobed injector geometries to produce very lean premixed flame structures, with a lower achievable turn-down or fuel/air mass flux ratio than for the analogous non-lobed injector, which largely, produced distinct diffusion flames. All three injectors exhibited some level of sooting near walls and in the far-field region, with the non-lobed injector sooting to the greatest extent. At low fuel flow rates, in which the lobed injectors created locally very lean premixed conditions, there resulted lower NO(sub x) emissions as compared with non-lobed injector emissions. Yet at higher fuel-air mass flux ratios, NO(sub x) emissions from the lobed injectors were actually higher than for the nonlobed injector, likely due to reduced sooting and hence reduced radiative heat losses associated with enhanced mixing. For both lobed injector geometries examined here, CO emissions became high for low values of the fuel/air mass flux ratio, again consistent with locally premixed combustion behavior, despite the fact that fuel was injected separately from air directly into the burner test section. The present study demonstrates that, for fuel-air mixing enhancement devices, control of the local equivalence ratio is critical in order to optimize burner emissions.

Mitchell, M. G.↗
NASA NTRSDate not supplied

Three Dimensional Instantaneous Spray Measurements of Additively Manufactured Candidate Injector Schemes at Varying Pressure Drops

Additively manufactured (AM) injectors have the potential to improve upon the combustion performance achieved using traditionally manufactured (TM) injectors. Traditionally manufactured injector combustion performance decreases greatly in off-design conditions. Additively manufactured injectors hold the potential to sustain high combustion performance over a broader range of operating conditions than currently seen in TM injectors. Additively manufactured injectors promise to offer higher resistances to instability and achieve better overall propellant mixing and atomization for all types of combustion devices. This study expands upon previous studies that used 2-D imaging techniques to characterize the injector spray pattern of candidate AM injector elements. In this study, 3-D instantaneous measurements of the injector spray pattern are taken, allowing for deeper insight into the liquid spray breakup, an inherently 3-D phenomena. Stereo imaging is used for three dimensional analysis, which utilizes two cameras at different angles to reconstruct a three dimensional reconstruction. With this information, AM injectors can be designed to improve propellant mixing and atomization and reduce breakup length. As part of this work, a high-pressure, cold flow experimental spray facility was modified to measure each injector’s spray characteristics in terms of 𝑅𝑒 𝐿 and 𝑊𝑒 𝑔 . This facility is operated to capture instantaneous stereo photographic images, mass flow rates, and injector element thrust for pressure drop across the injector face ranging from 100 to 200 psig at a stiffness ratio of 1.0.

Murphy Mitchell↗
DOE OSTI2024

CEBAF Injector for K Long Beam Conditions

The Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab concurrently operates four experimental Halls with distinct bunch charge specifications and repetition rates. Numerous critical beam parameters within CEBAF are configured in the injector, some remaining unchanged throughout the accelerator. Consequently, the injector plays a crucial role in determining final beam characteristics, including bunch structure, beam sizes, bunch lengths, energy spread, and beam transmission. The Jefferson Lab KL experiment is scheduled to take place at CEBAF in Hall D, featuring a much lower bunch repetition rate of 7.80 MHz or 15.59 MHz, below the nominal values of 249.5 MHz or 499 MHz. Although the proposed average current of 5 ?A or 10 ?A is low compared to the maximum CEBAF cur- rent of approximately 180 ?A, the corresponding bunch charge is unusually high for CEBAF injector operation. This study focuses on the behavior of low-repetition-rate, high-bunch- charge (0.32 to 0.64 pC) beams in the CEBAF injector. We investigated the evolution and transmission of low-charge beams to space-charge dominated high-charge beams in the front end of the CEBAF injector for two configurations: the pre-existing CEBAF Phase 1 injector upgrade, operated at 130 kV, and the existing CEBAF Phase 2 injector upgrade, operated at 140 kV, 180 kV, and to be operated at 200 kV. The electron beam through the CEBAF injector is characterized using beam dynamics simulations and comparisons with the available measurements performed at 130 kV. Multi-objective genetic optimizations of the CEBAF injector were performed to determine the operating magnetic elements and RF settings for the evolution and transmission of low, moderate, and high charge beams in the CEBAF injector at 180 kV and 200 kV DC gun voltages. Subsequently, simulations at the same voltages were conducted to obtain the beam characteristics at the front end of the CEBAF injector. The laser spot size and laser pulse length at the cathode were varied to observe their effects on beam transmission in the injector at different voltages (130 kV, 180 kV, and 200 kV). Experimental studies at 130 kV, 140 kV, and 180 kV validate the simulations. Beam study measurements are carried out using EPICS tools, while optimizations and simulations are facilitated by General Particle Tracer. Based on the findings, optimal parameters for the upcoming Jefferson Lab KL experiment are proposed, utilizing a lower repetition rate and higher bunch charge

Pokharel, Sunil↗
DOE OSTI2017

High-Resolution X-Ray and Neutron Computed Tomography of an Engine Combustion Network Spray G Gasoline Injector

Given the importance of the fuel-injection process on the combustion and emissions performance of gasoline direct injected engines, there has been significant recent interest in understanding the fluid dynamics within the injector, particularly around the needle and through the nozzles. Furthermore, the pressure losses and transients that occur in the flow passages above the needle are also of interest. Simulations of these injectors typically use the nominal design geometry, which does not always match the production geometry. Computed tomography (CT) using x-ray and neutron sources can be used to obtain the real geometry from production injectors, but there are trade-offs in using these techniques. X-ray CT provides high resolution, but cannot penetrate through the thicker parts of the injector. Neutron CT has excellent penetrating power but lower resolution. Here, we present results from a joint effort to characterize a gasoline direct injector representative of the Spray G injector as defined by the Engine Combustion Network. High-resolution (1.2 to 3 µm) x-ray CT measurements from the Advanced Photon Source at Argonne National Laboratory were combined with moderate-resolution (40 µm) neutron CT measurements from the High Flux Isotope Reactor at Oak Ridge National Laboratory to generate a complete internal geometry for the injector. This effort combined the strengths of both facilities’ capabilities, with extremely fine spatially resolved features in the nozzles and injector tips and fine resolution of internal features of the needle along the length of injector. Analysis of the resulting surface model of the internal fluid flow volumes of the injector reveals how the internal cross-sectional area and nozzle hole geometry differs slightly from the design dimensions. A simplified numerical simulation of the internal flow shows how deviations from the design geometry can alter the flow inside the sac and holes. Our results of this study will provide computational modelers with very accurate solid and surface models for use in computational fluid dynamics studies and experimentalists with increased insight into the operating characteristics of their injectors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1975

Characteristics of response factors of coaxial gaseous rocket injectors

The results of an experimental investigation undertaken to determine the frequency dependence of the response factors of various gaseous propellant rocket injectors subject to axial instabilities are presented. The injector response factors were determined, using the modified impedance-tube technique, under cold-flow conditions simulating those observed in unstable rocket motors. The tested injectors included a gaseous-fuel injector element, a gaseous-oxidizer injector element and a coaxial injector with both fuel and oxidizer elements. Emphasis was given to the determination of the dependence of the injector response factor upon the open-area ratio of the injector, the length of the injector orifice, and the pressure drop across the injector orifices. The measured data are shown to be in reasonable agreement with the corresponding injector response factor data predicted by the Feiler and Heidmann model.

Janardan, B. A.↗