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At least 19 records

Three-dimensional modeling of diesel engine intake flow, combustion and emissions-2

A three-dimensional computer code, KIVA, is being modified to include state-of-the-art submodels for diesel engine flow and combustion. Improved and/or new submodels which have already been implemented and previously reported are: wall heat transfer with unsteadiness and compressibility, laminar-turbulent characteristic time combustion with unburned HC and Zeldo'vich NO(x), and spray/wall impingement with rebounding and sliding drops. Progress on the implementation of improved spray drop drag and drop breakup models, the formulation and testing of a multistep kinetics ignition model, and preliminary soot modeling results are described. In addition, the use of a block structured version of KIVA to model the intake flow process is described. A grid generation scheme was developed for modeling realistic (complex) engine geometries, and computations were made of intake flow in the ports and combustion chamber of a two-intake-value engine. The research also involves the use of the code to assess the effects of subprocesses on diesel engine performance. The accuracy of the predictions is being tested by comparisons with engine experiments. To date, comparisons were made with measured engine cylinder pressure, temperature and heat flux data, and the model results are in good agreement with the experiments. Work is in progress that will allow validation of in-cylinder flow and soot formation predictions. An engine test facility is described that is being used to provide the needed validation data. Test results were obtained showing the effect of injection rate and split injections on engine performance and emissions.

Reitz, R. D.↗

Off-design analysis of a gas turbine powerplant augmented by steam injection using various fuels

Results are compared using coal derived low and intermediate heating valve fuel gases and a conventional distillate. The results indicate that steam injection provides substantial increases in both power and efficiency within the available compressor surge margin. The results also indicate that these performance gains are relatively insensitive as to the type of fuel. Also, in a cogeneration application, steam injection could provide some degree of flexibility by varying the split between power and process steam.

Stochl, R. J.↗

Liquid Methane/Oxygen Injector Study for Mars Ascent Engines

As a part of the advancing technology of the cryogenic propulsion system for the Mars exploration mission, this effort aims at evaluating propellant injection concepts for liquid methane/liquid oxygen (LOX) rocket engines. Split-triplet and unlike impinging injectors were selected for this study. A total of four injector configurations were tested under combustion conditions in a modular combustor test article (MCTA), equipped with optically accessible windows, at MSFC. A series of forty hot-fire tests, which covered a wide range of engine operating conditions with the chamber pressure ranging from 320 to 510 and the mixture ratio from 1.5 to 3.5, were conducted. The test matrix also included a variation in the combustion chamber length for the purpose of investigating its effects on the combustion performance and stability. Initial assessments of the test results showed that the injectors provided stable combustion and there were no injector face overheating problems under all operating conditions. The Raman scattering signal measurement method was successfully demonstrated for the hydrocarbon/oxygen reactive flow field. The near-injector face flow field was visually observed through the use of an infrared camera. Chamber wall temperature, high frequency chamber pressure, and average throat section heat flux were also recorded throughout the test series. Assessments of the injector performance are underway.

Trinh, Huu Phuoc↗

Three Dimensional Solution of Pneumatic Active Control of Forebody Vortex Asymmetry

Pneumatic active control of asymmetric vortical flows around a slender pointed forebody is investigated using the three dimensional solution for the compressible thin-layer Navier-Stokes equation. The computational applications cover the normal and tangential injection control of asymmetric flows around a 5 degree semi-apex angle cone at a 40 degree angle of attack, 1.4 freestream Mach number and 6 x 10(exp 6) freestream Reynolds number (based on the cone length). The effective tangential angle range of 67.5 approaches minus 67.5 degrees is used for both normal and tangential ports of injection. The effective axial length of injection is varied from 0.03 to 0.05. The computational solver uses the implicit, upwind, flux difference splitting finite volume scheme, and the grid consists of 161 x 55 x 65 points in the wrap around, normal and axial directions, respectively. The results show that tangential injection is more effective than normal injection.

Kandil, Osama A.↗

Operating characteristics of 120-millimeter-bore ball bearings at 3 million DN

A parametric study was performed with split inner-race 120-mm-bore angular-contact ball bearings at a speed of 25,000 rpm (3 million DN) at initial contact angles of 20 deg and 24 deg. Provisions were made for outer- and inner-race cooling and for injection of lubricant into the bearing through a number of radial holes in the split inner-race of the bearing. Oil flow and coolant rate to the bearing was controlled and varied for a total up to approximately 3.2 gal/min. Bearing temperature was found to decrease as the total lubricant flow to the bearing increased. However, at intermediate flow rates temperature began to increase with increasing flow. Power consumption increased with increasing flow rate. Bearing operating temperature, differences in temperatures between the inner and outer races, and bearing power consumption can be tuned to any desirable operating requirement. Cage speed increased by not more than 2 percent with increasing oil flow to the inner race.

Zaretsky, E. V.↗

Magnetic field drift shell splitting - Cause of unusual dayside particle pitch angle distributions during storms and substorms

This paper presents a magnetic field drift shell-splitting model for the unusual butterfly and head-and-shoulder energetic (E greater than 25 keV) particle pitch angle distributions (PADs) which appear deep within the dayside magnetosphere during the course of storms and substorms. Drift shell splitting separates the high and low pitch angle particles in nightside injections as they move to the dayside magnetosphere, so that the higher pitch angle particles move radially away from earth. Consequently, butterfly PADs with a surplus of low pitch angle particles form on the inner edge of the injection, but head-and-shoulder PADs with a surplus of high pitch angle particles form on the outer edge. A similar process removes high pitch angle particles from the inner dayside magnetosphere during storms, leaving the remaining lower pitch angle particles to form butterfly PADs on the inner edge of the ring current. A detailed case and statistical study of Charge Composition Explorer/Medium-energy Particle Analyzer observations, as well as a review of previous work, shows most examples of unusual PADs to be consistent with the model.

Sibeck, D. G.↗

Design and Testing of Non-Toxic RCS Thrusters for Second Generation Reusable Launch Vehicle

The current NASA Space Shuttle auxiliary propulsion system utilizes nitrogen tetroxide (NTO) and monomethylhydrazine (MMH), hypergolic propellants. This use of these propellants has resulted in high levels of maintenance and precautions that contribute to costly launch operations. By employing alternate propellant combinations, those less toxic to humans, the hazards and time required between missions can be significantly reduced. Use of alternate propellants can thereby increase the efficiency and lower the cost in launch operations. In support of NASA's Space Launch Initiative (SLI), TRW proposed a three-phase project structured to significantly increase the technology readiness of a high-performance reaction control subsystem (RCS) thruster using non-toxic propellant for an operationally efficient and reusable auxiliary propulsion system (APS). The project enables the development of an integrated primary/vernier thruster capable of providing dual-thrust levels of both 1000-lbf class thrust and 25-lbf thrust. The intent of the project is to reduce the risk associated with the development of an improved RCS flight design that meets the primary NASA objectives of improved safety and reliability while reducing systems operations and maintenance costs. TRW proposed two non-toxic auxiliary propulsion engine designs, one using liquid oxygen and liquid hydrogen and the other using liquid oxygen and liquid ethanol, as candidates to meet the goals of reliability and affordability at the RCS level. Both of these propellant combinations offer the advantage of a safe environment for maintenance, while at the same time providing adequate to excellent performance for a conventional liquid propulsion systems. The key enabling technology incorporated in both TRW thrusters is the coaxial liquid on liquid pintle injector. This paper will concentrate on only the design and testing of one of the thrusters, the liquid oxygen (LOX) and liquid hydrogen (LH2) thruster. The LOX/LH2 thruster design includes a LOX-centered pintle injector, consisting of two rows of slots that create a radial spoke spray pattern in the combustion chamber. The main fuel injector creates a continuous sheet of LH2 originating upstream of the LOX pintle injector. The two propellants impinge at the pintle slots, where the resulting momentum ratio and spray pattern determines the combustion efficiency and thermal effects on the hardware. Another enabling technology used in the design of this thruster is fuel film cooling through a duct, lining the inner wall of the combustion chamber barrel section. The duct is also acts as a secondary fuel injection point. The variation in the amount of LH2 used for the duct allows for adjustments in the cooling capacity for the thruster. The Non-Toxic LOX-LH2 RCS Workhorse Thruster was tested at the NASA Marshall Space Flight Center's Test Stand 500. Hot-fire tests were conducted between March 08, 2002 and April 05, 2002. All testing during the program base period were performed at sea-level conditions. During the test program, 7 configurations were tested, including 2 combustion chambers, 3 LOX injector pintle tips, and 4 LH2 injector stroke settings. The operating conditions that were surveyed varied thrust levels, mixture ratio and LH2 duct cooling flow. The copper heat sink chamber was used for 16 burns, each burn lasting from 0.4 to 10 seconds, totaling 51.4 seconds, followed by Haynes chamber testing ranging from 0.9 to 120 seconds, totaling 300.9 seconds. The total accumulated burn time for the test program is 352.3 seconds. C* efficiency was calculated and found to be within expectable limits for most operating conditions. The temperature on the Haynes combustion chamber remained below established material limits, with the exception of one localized hot spot. The test results demonstrate that both the coaxial liquid-on-liquid pintle injector design and fuel duct concepts are viable for the intended application. The thruster head-e design maintained cryogenic injection temperatures while firing, which validates the concept for minimal heat soak back. By injecting fuel into the duct, the throat temperatures were manageable, yet the split of fuel through the cooling duct does not compromise the overall combustion efficiency, which indicates that, provided proper design refinement, such a concept can be applied to a high-performance version of the thruster. These hot fire tests demonstrate the robustness of the duct design concept and good capability to withstand off-nominal operating conditions without adversely impacting the thermal response of the engine, a key design feature for a cryogenic thruster.

Calvignac, Jacky↗

Design and Testing of Non-Toxic RCS Thrusters for Second Generation Reusable Launch Vehicle

Under NASA sponsorship, Northrop Grumman Space Technology (NGST) designed, built and tested two non-toxic, reaction control engines, one using liquid oxygen (LOX) and liquid hydrogen (LH2) and the other using liquid oxygen and ethanol. This paper presents the design and testing of the LOX/LH2 thruster. The two key enabling technologies are the coaxial liquid-on-liquid pintle injector and the fuelcooling duct. The workhorse thruster was hotfire tested at the NASA Marshall Space Flight Center Test Stand 500 in March and April of 2002. All tests were performed at sea-level conditions. During the test program, 7 configurations were tested, including 2 combustion chambers, 3 LOX injector pintle tips, and 4 LHp injector settings. The operating conditions surveyed were 70 to 100% thrust levels, mixture ratios from 3.27 to 4.29, and LH2 duct cooling from 18.0 to 25.5% fuel flow. The copper heat sink chamber was used for 16 burns, each burn lasting from 0.4 to 10 seconds, totaling 51.4 seconds, followed by Haynes chamber testing ranging from 0.9 to 120 seconds, totaling 300.9 seconds. The performance of the engine reached 95% C* efficiency. The temperature on the Haynes chamber remained well below established material limits, with the exception of one localized hot spot. These results demonstrate that both the coaxial liquid-on-liquid pintle injector design and fuel duct concepts are viable for the intended application. The thruster headend design maintained cryogenic injection temperatures while firing, which validates the selected injector design approach for minimal heat soak-back. Also, off -nominal operation without adversely impacting the thermal response of the engine showed the robustness of the duct design, a key design feature for this application. By injecting fuel into the duct, the throat temperatures are manageable, yet the split of fuel through the cooling duct does not compromise the overall combstion efficiency, which indicates that, provided proper design refinement, such a concept could be applied to a high-performance version of the thruster.

Calvignac, Jacky↗

Propagation of charge-neutral beams in space - Modifications when negative ions are present

Two-dimensional (three velocity component) electrostatic simulations are used to investigate the properties of a charge-neutral beam consisting of H(+), H(-), and electrons which will be used in the Beams on Rockets (BEAR) experiment to be launched in late 1987 or early 1988. For cross-field injection and beam densities much greater than the ambient plasma density, the beam splits into two approximately charge-neutral beams: a H(+)-e(-) beam that propagates down the field lines and a H(+)-H(-) beam that propagates at nearly the initial beam velocity on time scales less than the ion gyroperiod. Because of this splitting, space-charge oscillations are induced in the H(+)-H(-) component, which lead to its breakup. At lower beam densities, particularly when the beam electron density is less than about the density of the ambient plasma, the ambient plasma response reduces the space-charge fields as the beam splits and the space-charge oscillations are suppressed.

Winglee, R. M.↗

Atomization of liquid fuels. Part I

In the present treatise we will consider chiefly the problem of solid injection in comparison with air injection. On leaving the valve or nozzle through one or more small openings, the fuel is split up into innumerable fine drops, which penetrate the combustion chamber in divergent directions in the form of a conical jet. The efficiency of this jet is judged from the following three viewpoints: 1) with respect to the fineness of atomization; 2) with respect to the direction or distribution of sprayed particles; 3) with respect to the penetration of the particles.

FUELS - TESTS↗

Comparison of Combustion Dynamic Characteristics of Two Advanced Multi-Cup Fuel Injectors

An experimental investigation of the combustion dynamic characteristics of two advanced multi-cup lean direct injectors (LDI) under simulated gas turbine combustor conditions was conducted. The objective was to gain a better understanding of the physical phenomena inside a pressurized flame tube combustion chamber and study the effects of injector flow number on combustion dynamics. The injectors are known as Three-zone Injectors one and two or 3ZI-1 and 3ZI-2, respectively. The injectors were experimentally evaluated at inlet pressures up to 1.724 MPa, non-vitiated air temperatures up to 828K, and adiabatic flame temperatures up to 1975K. Dynamic pressure measurements were taken upstream of the injectors and in the combustion zone. The combustion dynamic behavior of the two injectors was measured over a range of inlet pressures, inlet temperatures, fuel air ratios, and fuel flow splits.

Combustion Dynamics↗

Numerical solution for perpendicular sonic hydrogen injection into a ducted supersonic airstream

This note discusses a computer program being developed to study the flow field near opposing perpendicular fuel injectors in scramjets. The MacCormack time-split, finite difference relaxation technique was used to solve the full two-dimensional compressible Navier-Stokes equations along with energy and species equations. By using this technique, a program was developed to consider the turbulent nonreacting flow of hydrogen and air in a rectangular duct. A damping term, proportional to the second derivative of pressure and temperature, was used to produce a stable solution behind the hydrogen jet in the neighborhood of the recompression shock. A case using actual conditions encountered in current scramjet design was analyzed, with results agreeing qualitatively with experimental observations.

Drummond, J. P.↗

Nuclear Thermal Rocket/Vehicle Design Options for Future NASA Missions to the Moon and Mars

The nuclear thermal rocket (NTR) provides a unique propulsion capability to planners/designers of future human exploration missions to the Moon and Mars. In addition to its high specific impulse (approximately 850-1000 s) and engine thrust-to-weight ratio (approximately 3-10), the NTR can also be configured as a 'dual mode' system capable of generating electrical power for spacecraft environmental systems, communications, and enhanced stage operations (e.g., refrigeration for long-term liquid hydrogen storage). At present the Nuclear Propulsion Office (NPO) is examining a variety of mission applications for the NTR ranging from an expendable, single-burn, trans-lunar injection (TLI) stage for NASA's First Lunar Outpost (FLO) mission to all propulsive, multiburn, NTR-powered spacecraft supporting a 'split cargo-piloted sprint' Mars mission architecture. Each application results in a particular set of requirements in areas such as the number of engines and their respective thrust levels, restart capability, fuel operating temperature and lifetime, cryofluid storage, and stage size. Two solid core NTR concepts are examined -- one based on NERVA (Nuclear Engine for Rocket Vehicle Application) derivative reactor (NDR) technology, and a second concept which utilizes a ternary carbide 'twisted ribbon' fuel form developed by the Commonwealth of Independent States (CIS). The NDR and CIS concepts have an established technology database involving significant nuclear testing at or near representative operating conditions. Integrated systems and mission studies indicate that clusters of two to four 15 to 25 klbf NDR or CIS engines are sufficient for most of the lunar and Mars mission scenarios currently under consideration. This paper provides descriptions and performance characteristics for the NDR and CIS concepts, summarizes NASA's First Lunar Outpost and Mars mission scenarios, and describes characteristics for representative cargo and piloted vehicles compatible with a reference 240 t-class heavy lift launch vehicle (HLLV) and smaller 120 t HLLV option. Attractive performance characteristics and high-leverage technologies associated with both the engine and stage are identified, and supporting parametric sensitivity data is provided. The potential for commonality of engine and stage components to satisfy a broad range of lunar and Mars missions is also discussed.

Borowski, Stanley K.↗

Spin Start Line Effects on the J2X Gas Generator Chamber Acoustics

The J2X Gas Generator engine design has a spin start line connected near to the turbine inlet vanes. This line provides helium during engine startup to begin turbomachinery operation. The spin start line also acts as an acoustic side branch which alters the chamber's acoustic modes. The side branch effectively creates 'split modes' in the chamber longitudinal modes, in particular below the first longitudinal mode and within the frequency range associated with the injection-coupled response of the Gas Generator. Interaction between the spin start-modified chamber acoustics and the injection-driven response can create a higher system response than without the spin start attached to the chamber. This work reviews the acoustic effects of the spin start line as seen throughout the workhorse gas generator test program. A simple impedance model of the spin start line is reviewed. Tests were run with no initial spin start gas existing in the line, as well as being initially filled with nitrogen gas. Tests were also run with varying spin start line lengths from 0" to 40". Acoustic impedance changes due to different spin start gas constituents and line lengths are shown. Collected thermocouple and static pressure data in the spin start line was used to help estimate the fluid properties along the line length. The side branch impedance model was coupled to a chamber impedance model to show the effects on the overall chamber response. Predictions of the spin start acoustic behavior for helium operation are shown and compared against available data.

Kenny, R. Jeremy↗

GC/MS Method Development for Separating Lunar Volatile Ice Simulant Headspace Gases

Various investigators propose the lunar surface contains widely distributed volatiles, especially water- like species, i.e. OH and H2O. Surface volatiles are theorized to exist as a hydrated regolith layer, concentrated in extremely cold polar permanently shadowed regions (PSR), and/or solar wind implantation reservoirs in lunar glasses. The proposed sources of lunar surface volatiles range from cometary impacts, solar wind, or a supply present during moon formation. Future Artemis missions aim to collect and return the samples containing volatiles collected near lunar polar craters or PSRs. We, as advanced curation scientists, are responsible for developing techniques and methodologies for preserving returned sample integrity as much as possible. Pristine volatile-bearing samples are invaluable to the scientific community seeking to unravel the history of the solar system. Realistically, a sample will experience alteration during collection, transportation back to earth, and storage. The Planetary Exploration and Astromaterials Research Lab (PEARL) seeks to understand temperature and pressure effects on high-fidelity volatile-containing regolith simulants, the foundation for the future of cold curation. This abstract outlines the separation, identification, and quantification of headspace gases over volatile ice feed stock material using gas chromatography/mass spectrometry (GC/MS). Preliminary objectives concentrated on sample handling, reproducibility, and understanding the elution characteristics for each analyte. Initial GC/MS method development experiments utilized diluted static headspace sample preparation. Diluted samples were used because sampling headspace gases directly from a vial containing liquid analyte resulted in overloading of the column and detector. Overloading is evident based on chromatogram peak shapes and instrument contamination, or carry over, between experiments. A mixture of three alcohols were used for a majority of the sample handling and reproducibility studies. Reproducibility was tested via multiple users, calibration curves, and check standards. Stock solutions of condensed lunar volatile analytes included methanol, ammonia in methanol, hydrogen sulfide in water, and an equal volume mixture of methanol, ethanol, and isopropanol. Current samples use room air as the headspace sample matrix, however future experiments will incorporate an inert purge gas, such as argon or nitrogen. Three mL of each analyte solution were capped in separate 20 mL crimp top GC vials. Dilutions were carried out by removing an aliquot of headspace gases with a calibrated 1 mL gastight syringe and immediately transferring to a 20 mL capped crimp top vial. The GC/MS is a Thermo Fisher Trace 1310/ISQ 7000 with a TriPlus RSH autosampler and split/splitless injector module. The experiments outlined in this abstract use the following hardware: a 2.5 mL gastight headspace syringe tool, 1 mm ID x 78.5 mm length ultra-inert straight injection liner, and a TG-BondQ 30 m × 0.32 mm × 10 μm column. Various parameters, such as hardware selection and the temperature, pressure, and split ratio set points, continue to evolve as the overall experiment is refined. Diluted headspace chromatograms were collected for the individual stock solutions. Retention times, peak shapes, and mass spectra were evaluated and added to the data processing method for each molecule of interest. Figure 1 shows the total ion chromatograms for the three major lunar volatile simulant stock solutions: methanol, 7 N ammonia in methanol, and 0.4% hydrogen sulfide in water. Tailing peak shapes for ammonia (2.98 min rt) and water (4.06 min rt) indicate the molecules are not properly eluting from the selected column with the current separation method. Additionally, hydrogen sulfide and ammonia have overlapping peak windows, which could impact quantification. Ongoing experiments aim to address the peak shape and overlapping via the separation method and hardware selection. Sample preparation reproducibility experiments used stock solution containing equal volumes of a non- interactive mixture of methanol, ethanol, and isopropanol. Mass spectrum ion traces were used to identify and quantify all three alcohols. Peaks were automatically detected, identified, and integrated through the mass spectra detection and processing parameters. Calibration response curves and check standards were used to evaluate the validity of the sample preparation procedure. Figure 2 shows the methanol chromatogram peak area versus total headspace dilution volume transferred from the alcohol mixture vial. The calibration response curves and check standards validate sample preparation procedure. Continuing data analysis efforts are working towards correlating the peak area and instrument response factor to the headspace analyte concentration and condensed phase composition. Static headspace gas chromatography theory relies on Dalton’s law, Raoult’s law, Henry’s Law, and the Kolb and Ettre equation to associate peak area to the analyte composition in a non-ideal solution. Equation 1 is a simplified expression derived from the aforementioned theories. Future experiments involve liquid injections of the individual stock solutions, liquid and headspace analysis of various stock solution combinations, and the addition of regolith simulants to the mixtures. Temperature is another variable expected to affect reaction rates and will be explored.

Cecilia L. Amick↗

Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, Linda Neergaard↗

Modeling of Particle Acceleration at Multiple Shocks via Diffusive Shock Acceleration: Preliminary Results

Successful forecasting of energetic particle events in space weather models require algorithms for correctly predicting the spectrum of ions accelerated from a background population of charged particles. We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box. We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (E(sub max)) appropriate for quasi-parallel and quasi-perpendicular shocks and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, L. Neergaard↗

Active control of asymmetric vortical flows around cones using injection and heating

The effectiveness of certain active-control methods for asymmetric flows around circular cones is investigated by using computational solution of the unsteady, compressible full Navier-Stokes equations. Two main methods of active control which include flow injection and surface heating are used. For the flow-injection-control method, flow injection is used either in the normal direction to the surface or in the tangential direction to the surface. For the surface-heating-control method, the temperature of the cone surface is increased. The effectiveness of a hybrid method of flow control which combines normal injection with surface heating has also been studied. The Navier-Stokes equations, subjected to various surface boundary conditions, are solved by using an implicit, upwind, flux-difference splitting, finite-volume scheme for locally-conical flow solutions.

Kandil, Osama A.↗