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Morphological instability in rapid directional solidification

Mullins and Sekerka (1964) showed for fixed temperature gradient that the planar interface is linearly stable for all pulling speeds V above some critical value, the absolute stability limit. Near this limit, where solidification rates are rapid, the assumption of local equilibrium at the interface may be violated. Here, nonequilibrium effects are incorporated into a linear stability analysis of the planar front by allowing the segregation coefficient and interface temperature to depend on V in a thermodynamically consistent way. The absolute stability limit of the cellular mode is modified. A new oscillatory state is formed which, in the absence of latent heat, has a critical wavenumber of zero; by itself this instability would lead to the formation of solute bands in the solid. This mode has its own absolute-stability limit determined by solute trapping and kinetics. Under certain conditions, there exists a window of stability above the steady absolute-stability boundary and below the oscillatory-stability boundary; here the planar segregation-free state is restabilized.

Merchant, G. J.↗

The spectrum of random magnetic fields in the mean field dynamo theory of the Galactic magnetic field

The fluctuation spectrum that must arise in a mean field dynamo generation of galactic fields if the initial field is weak is considered. A kinetic equation for its evolution is derived and solved. The spectrum evolves by transfer of energy from one magnetic mode to another by interaction with turbulent velocity modes. This kinetic equation is valid in the limit that the rate of evolution of the magnetic modes is slower than the reciprocal decorrelation time of the turbulent modes. This turns out to be the case by a factor greater than 3. Most of the fluctuation energy concentrates on small scales, shorter than the hydrodynamic turbulent scales. The fluctuation energy builds up to equipartition with the turbulent energy in times that are short compared to the e-folding time of the mean field. The turbulence becomes strongly modified before the dynamo amplification starts. Thus, the kinematic assumption of the mean dynamo theory is invalid. Thus, the galactic field must have a primordial origin, although it may subsequently be modified by dynamo action.

Kulsrud, Russell M.↗

Wave Augmented Diffuser for Centrifugal Compressor

A wave augmented diffuser for a centrifugal compressor surrounds the outlet of an impeller that rotates on a drive shaft having an axis of rotation. The impeller brings flow in in an axial direction and imparts kinetic energy to the flow discharging it in radial and tangential directions. The flow is discharged into a plurality of circumferentially disposed wave chambers. The wave chambers are periodically opened and closed by a rotary valve such that the flow through the diffuser is unsteady. The valve includes a plurality of valve openings that are periodically brought into and out of fluid communication with the wave chambers. When the wave chambers are closed, a reflected compression wave moves upstream towards the diffuser bringing the flow into the wave chamber to rest. This action recovers the kinetic energy from the flow and limits any boundary layer growth. The flow is then discharged in an axial direction through an opening in the valve plate when the valve plate is rotated to an open position. The diffuser thus efficiently raises the static pressure of the fluid and discharges an axially directed flow at a radius that is predominantly below the maximum radius of the diffuser.

Skoch, Gary J.↗

A Review of Sodium-Metal Chloride Battery Activity At JPL

Following the disclosures by Coetzer et al. on the use of transition metal chlorides in chloroaluminates as alternate cathodes to sulfur in rechargeable sodium batteries, several laboratories, including the Jet Propulsion Laboratory, focused their attention on these systems. These systems have certain distinct advantages over sodium-sulfur batteries such as increased safety, inherent overcharge capability, and lower operating temperatures. Two systems, i.e., Na/FeCl2 and NaNiCl2, were developed extensively and evaluated in various applications including electric vehicles and space. Their performance has been very encouraging and warrants a detailed fundamental study on these cathodes. At the Jet Propulsion Laboratory a program was initiated two years back to understand the electrochemical behavior of FeCl2 and NiCl2, and to identify and evaluate other transition metal chlorides of promise. The initial efforts focused on the methods of fabrication of the electrodes and their electrochemical characterization. Subsequent studies were aimed at establishing the reaction mechanism, determining the kinetics, and identifying the rate-limiting processes in te reduction of metal chloride cathodes. Nickel chloride emerged form these studies as the most promising candidate material and was taken up for further detailed study on its passivation- a rate limiting process-under different experimental conditions. Also, the feasibility of using copper chloride, which is expected to have a higher energy density, has been assessed. On the basis of the criteria established from the voltammetric response of FeCl2, NiCl2, and CuCl2, several other transition metal chlorides were screened. Of these, molybdenum and cobalt appear promising.

Ratnakumar, B. V.↗

An Experimental Study of n-Heptane and JP-7 Extinction Limits in an Opposed Jet Burner

Propulsion engine combustor design and analysis requires experimentally verified data on the chemical kinetics of fuel. Among the important data is the combustion extinction limit as measured by observed maximum flame strain rate. The extinction limit relates to the ability to maintain a flame in a combustor during operation. Extinction limit data can be obtained for a given fuel by means of a laminar flame experiment using an opposed jet burner (OJB). Laminar extinction limit data can be applied to the turbulent application of a combustor via laminar flamelet modeling. The OJB consists of two axi-symmetric tubes (one for fuel and one for oxidizer), which produce a flat, disk-like counter-flow diffusion flame. This paper presents results of experiments to measure extinction limits for n-heptane and the military specification fuel JP-7, obtained from an OJB. JP-7 is an Air Force-developed fuel that continues to be important in the area of hypersonics. Because of its distinct properties it is currently the hydrocarbon fuel of choice for use in Scramjet engines. This study provides much-desired data for JP-7, for which very little information previously existed. The interest in n-heptane is twofold. First, there has been a significant amount of previous extinction limit study and resulting data with this fuel. Second, n-heptane (C7H16) is a pure substance, and therefore does not vary in composition as does JP-7, which is a mixture of several different hydrocarbons. These two facts allow for a baseline to be established by comparing the new OJB results to those previously taken. Additionally, the data set for n-heptane, which previously existed for mixtures up to 26 mole percent in nitrogen, is completed up to 100% n-heptane. The extinction limit data for the two fuels are compared, and complete experimental results are included.

Convery, Janet L.↗

Kinetics of the reaction OH + D yields OD + H

The reaction of OH radicals with D-atoms to form OD has been studied at room temperature in a discharge-flow system utilizing UV resonance fluorescence detection of the molecular species. A rate constant of approximately 1.3 by 10 to the -10th power cu cm per sec is reported where the error limits include systematic error estimates. Astrophysical and kinetic implications are discussed briefly.

Margitan, J. J.↗

Bone Markers, Calcium Metabolism, and Calcium Kinetics During Extended-Duration Space Flight on the Mir Space Station

Bone loss is a current limitation for long-term space exploration. Bone markers, calcitropic hormones, and calcium kinetics of crew members on space missions of 4-6 months were evaluated. Spaceflight-induced bone loss was associated with increased bone resorption and decreased calcium absorption. INTRODUCTION: Bone loss is a significant concern for the health of astronauts on long-duration missions. Defining the time course and mechanism of these changes will aid in developing means to counteract these losses during space flight and will have relevance for other clinical situations that impair weight-bearing activity. MATERIALS AND METHODS: We report here results from two studies conducted during the Shuttle-Mir Science Program. Study 1 was an evaluation of bone and calcium biochemical markers of 13 subjects before and after long-duration (4-6 months) space missions. In study 2, stable calcium isotopes were used to evaluate calcium metabolism in six subjects before, during, and after flight. Relationships between measures of bone turnover, biochemical markers, and calcium kinetics were examined. RESULTS: Pre- and postflight study results confirmed that, after landing, bone resorption was increased, as indicated by increases in urinary calcium (p < 0.05) and collagen cross-links (N-telopeptide, pyridinoline, and deoxypyridinoline were all increased >55% above preflight levels, p < 0.001). Parathyroid hormone and vitamin D metabolites were unchanged at landing. Biochemical markers of bone formation were unchanged at landing, but 2-3 weeks later, both bone-specific alkaline phosphatase and osteocalcin were significantly (p < 0.01) increased above preflight levels. In studies conducted during flight, bone resorption markers were also significantly higher than before flight. The calcium kinetic data also validated that bone resorption was increased during flight compared with preflight values (668 +/- 130 versus 427 +/- 153 mg/day; p < 0.001) and clearly documented that true intestinal calcium absorption was significantly lower during flight compared with preflight values (233 +/- 87 versus 460 +/- 47 mg/day; p < 0.01). Weightlessness had a detrimental effect on the balance in bone turnover such that the daily difference in calcium retention during flight compared with preflight values approached 300 mg/day (-234 +/- 102 versus 63 +/- 75 mg/day; p < 0.01). CONCLUSIONS: These bone marker and calcium kinetic studies indicated that the bone loss that occurs during space flight is a consequence of increased bone resorption and decreased intestinal calcium absorption.

Bone and Bones/metabolism/pathology↗

A comparison of limited-area energetic processes between observations and primitive equation model predictions

Energetic analyses of the NMC initial conditions and NMC six-layer primitive equation operational prediction model 12-hr forecast for a developing cyclone are presented. Consideration is given to the total kinetic energy, the energetics of the divergent and nondivergent flows and the baroclinic (vertical shear flow) and barotropic (vertical mean flow) components of the kinetic energy. It is found that the model initial conditions lose 10-15% of the kinetic energy at various levels compared to a limited-area multivariate statistical analysis of the observational data, leading to a decrease in the horizontal kinetic energy flux, a misrepresentation of the synoptic scale wave system in the 12-hr forecast. Similar results are obtained for the nondivergent flow, while the divergent flow energetics are not reproduced accurately by the model. The horizontal flux terms of the vertical mean and vertical shear energetics are also not found to be reproduced in the upper levels, although horizontal flux contributions to the baroclinic component are improved at middle and lower levels. Finally, vertical shear kinetic energy generation is found to be well represented in the model prediction, however kinetic energy conversion between vertical shear and mean flow is not reproduced in the lower layer.

Alpert, J. C.↗

A theory for the Langmuir waves in the electron foreshock

A comprehensive theory for the Langmuir waves in the earth's foreshock involving saturation of the kinetic version of the beam instability by quasi-linear relaxation is proposed in this paper. Reactive and kinetic beam instabilities are shown to be the two limiting versions of a single instability whose analytically and numerically derived descriptions are shown to form a consistent picture. It is pointed out that the reactive instability gives rise only to narrow-band growth while the kinetic instability gives rise to wide-band growth. Arguments for describing the Langmuir wave growth in terms of the kinetic instability are given, and four suppression mechanisms for the kinetic instability are discussed. It is suggested that quasi-linear relaxation limits the Langmuir growth and gives rise to distributions qualitatively similar to the observed distribution functions, and arguments in favor of this hypothesis are presented.

Cairns, Iver H.↗

Analytical and Numerical Modeling of Flame-Balls in Hydrogen-Air Mixtures

Flame-balls are stationary spherical premixed flames observed in certain near-limit mixtures. It is believed that radiative heat losses are an important stabilizing influence. Numerical solutions of flame balls are constructed for hydrogen-air mixtures using an accurate description of the chemical kinetics, diffusive transport, and radiation losses. A lean limit equivalence ratio of 0.0866 is predicted and a rich limit of 2,828. For any equivalence ratio between the two limits there are two solutions. One is characterized by a small flame, incomplete reactant consumption, and negligible radiation losses. The other by a large flame, complete consumption of one of the reactants, and significant radiation losses. The maximum temperature varies between 1200 and 900 K as the two solution branches are traversed. Much of our discussion is a reprise and modification of previously published analytical results, for these provide physical insight into the nature of the solutions, and suggest that a portion of the large flame branch near the lean limit is stable and so corresponds to observable flames.

Buckmaster, J.↗

Morphological evolution of growing crystals - A Monte Carlo simulation

The combined effects of nutrient diffusion and surface kinetics on the crystal morphology were investigated using a Monte Carlo model to simulate the evolving morphology of a crystal growing from a two-component gaseous nutrient phase. The model combines nutrient diffusion, based on a modified diffusion-limited aggregation process, with anisotropic surface-attachment kinetics and surface diffusion. A variety of conditions, ranging from kinetic-controlled to diffusion-controlled growth, were examined. Successive transitions from compact faceted (dominant surface kinetics) to open dendritic morphologies (dominant volume diffusion) were obtained.

Xiao, Rong-Fu↗

Safer Roadside Crash Walls Would Limit Deceleration

The figure depicts the aspects of a proposed deceleration-limiting design for crash walls at the sides of racetracks and highways. The proposal is intended to overcome the disadvantages of both rigid barriers and kinetic-energy-absorbing barriers of prior design. Rigid barriers can keep high-speed crashing motor vehicles from leaving roadways and thereby prevent injury to nearby persons and objects, but they can also subject the occupants of the vehicles to deceleration levels high enough to cause injury or death. Kinetic-energy-absorbing barriers of prior design reduce deceleration levels somewhat, but are not designed to soften impacts optimally; moreover, some of them allow debris to bounce back onto roadways or onto roadside areas, and, in cases of glancingly incident vehicles, some of them can trap the vehicles in such a manner as to cause more injury than would occur if the vehicles were allowed to skid along the rigid barriers. The proposed crash walls would (1) allow tangentially impacting vehicles to continue sliding along the racetrack without catching them, (2) catch directly impacting vehicles to prevent them from injuring nearby persons and objects, and (3) absorb kinetic energy in a more nearly optimum way to limit decelerations to levels that human occupants could survive.

Schneider, William C.↗

Nitric Oxide and Oxygen Air-Contamination Effects on Extinction Limits of Non-Premixed Hydrocarbon-Air Flames for a HIFiRE Scramjet

Unique nitric oxide (NO) and oxygen air-contamination effects on the extinction Flame Strength (FS) of non-premixed hydrocarbon (HC) vs. air flames are characterized for 7 gaseous HCs, using a new idealized 9.3 mm straight-tube Opposed Jet Burner (OJB) at 1 atm. FS represents a laminar strain-induced extinction limit based on cross-section-average air jet velocity, Uair, that sustains combustion of a counter jet of gaseous fuel just before extinction. Besides ethane, propane, butane, and propylene, the HCs include ethylene, methane, and a 64 mole-% ethylene / 36 % methane mixture, the writer s previously recommended gaseous surrogate fuel for HIFiRE scramjet tests. The HC vs. clean air part of the work is an extension of a May 2008 JANNAF paper that characterized surrogates for the HIFiRE project that should mimic the flameholding of reformed (thermally- or catalytically-cracked) endothermic JP-like fuels. The new FS data for 7 HCs vs. clean air are thus consolidated with the previously validated data, normalized to absolute (local) axial-input strain rates, and co-plotted on a dual kinetically dominated reactivity scale. Excellent agreement with the prior data is obtained for all 7 fuels. Detailed comparisons are also made with recently published (Univ. Va) numerical results for ethylene extinction. A 2009-revised ethylene kinetic model (Univ. Southern Cal) led to predicted limits within approx. 5 % (compared to 45 %, earlier) of this writer s 2008 (and present) ethylene FSs, and also with recent independent data (Univ. Va) obtained on a new OJB system. These +/- 5 % agreements, and a hoped-for "near-identically-performing" reduced kinetics model, would greatly enhance the capability for accurate numerical simulations of surrogate HC flameholding in scramjets. The measured air-contamination effects on normalized FS extinction limits are projected to assess ongoing Arc-Heater-induced "facility test effects" of NO production (e.g., 3 mole-%) and resultant oxygen depletion (from 21 to 19.5 %), for testing the "64/36" surrogate fuel in Langley s Arc-Heated Scramjet Test Facility for HIFiRE engine designs. The FS results show a generally small (< 4 %) "nitric oxide enhancement" effect, relative to clean air, for up to 3 % NO (freestream Mach number up to 7 in Arc Jet testing). However, a progressively large "oxygendeficiency weakening" effect develops. For 3 % NO, a net weakening of 26 % in FS is derived for the "64/36" fuel vs. air. The corresponding net weakening for pure ethylene is 20 %. A number of practical recommendations regarding facility test effects are offered.

Pellett, Gerald L.↗

Influence of Nucleation Mechanisms on the Radiative Properties of Deep Convective Clouds and Subvisible Cirrus in CRYSTAL/FACE

During the past few years we have conducted work on several different topics, as reflected by our publications. As one of the Co-Project scientists for The Cirrus Regional Study of Tropical Anvils and Cirrus Layers - Florida Area Cirrus Experiment (CRYSTAL FACE) we worked to help design the mission and then conduct it in the field. Another major activity during the past two years has been to pull together various groups to formulate plans for follow on missions to CRYSTAL FACE. We organized a workshop at the University of Colorado during the summer of 2003 to assess the best locations for future missions. Working with a group of about 10 scientists from around the country we prepared a science-planning document (Tropical Composition, Cloud and Climate Coupling Experiment (TC(sup 4)) that outlined the rationale, locations, strategy to accomplish the goals, and possible payloads for a set of three tropical missions. We also prepared background materials for various NRAs being prepared at NASA Headquarters for missions in Costa Rica, Darwin and Guam. In conjunction with the group at NASA Ames we have helped build a new numerical model for deep convection and have applied that model to simulate the CRYSTAL data. Our goal in particular has been to better understand how convection distributes water vapor isotopes. CRYSTAL observations of water isotopes are very different from those suggested by previous workers who assumed the isotopes would obey Rayleigh fractionation. The water isotope study has several implications. First it is a check on the realism of the deep convection model. Second, the isotopes are a measure of the precipitation removal in the atmosphere. Hence they provide a constraint on a parameter that is difficult to otherwise measure. Finally it has been suggested that isotopes may be the key to unraveling the water transport into the stratosphere and upper troposphere. Such transport is critical both for the radiation balance and for stratospheric chemistry. Ours is the first model that is able to treat this transport. Our initial results have just been submitted to Geophys. Res. Lett (Smith et al., 2005). Essentially we are able to explain the vertical profiles of isotopes in the tropical tropopause transition layer. We are also able to account for stratospheric humidity and isotope abundances with this model. We have also been heavily involved in trying to improve our understanding of nitric acid condensation on ice. Gao et al (2004) have shown that water supersaturations above ice occur when the atmosphere is supersaturated with respect to nitric acid trihydrate. As one of the co-authors of that work, we suggested the mechanism that may explain why this is occurring. Essentially, ice does not like to grow near unit supersaturation, but does so because the water molecules can find sites on the ice surface to attach themselves to before they fly off the ice surface. This phenomena was well known in the 1960s when it was a source of debate about whether condensation and evaporation coefficients for ice would be the same. Evaporation does not require any molecular orientation, while condensation does, so it was possible that the coefficients would differ. They don't differ because the water molecules rapidly move across the surface and find places to attach. Nitric acid may be occupying these preferred sites and therefore the water molecules can't find a desirable place to attach. We anticipate that this research will be the subject of laboratory work during the coming few years. Another possibility that has been suggested is that cubic ice is forming in clouds. We have measured the vapor pressure of cubic ice, and plan to publish that result in the next few months. We have also been working on additional aspects of the condensation of nitric acid on ice. With Y. Kondo we studied the condensation of NOy on ice using the SOLVE data. Gamblin et al. have continued this work. The CRYSTAL NOy and HNO, groups have shown th their data can be fit using standard Langmuir isotherms as suggested in some, but not all, laboratory studies. We have found in the SOLVE data set that this is not the case. Moreover some laboratory studies show there are important kinetic effects that may be occurring in the atmosphere limiting the transfer of nitric acid to the ice. The SOLVE data seem consistent with these studies. We are currently re-analyzing the CRYSTAL data to look for these kinetic effects. There are a number of implications of these studies. One of the more interesting is that the nitric acid coating on ice can be used as a cloud clock to determine how long the cloud parcel has been in existence. We have also been involved with several laboratory studies. We have worked to improve the database on ice optical constants, which are critical for remote sensing. We have also studied the ways in which ice nucleates on clays. We suspect now that the standard theories used for depositional ice nucleation are completely incorrect. Further work will be needed to develop a new theory.

Toon, Owen B.↗

New Reduced Two-Time Step Method for Calculating Combustion and Emission Rates of Jet-A and Methane Fuel With and Without Water Injection

A simplified kinetic scheme for Jet-A, and methane fuels with water injection was developed to be used in numerical combustion codes, such as the National Combustor Code (NCC) or even simple FORTRAN codes that are being developed at Glenn. The two time step method is either an initial time averaged value (step one) or an instantaneous value (step two). The switch is based on the water concentration in moles/cc of 1x10(exp -20). The results presented here results in a correlation that gives the chemical kinetic time as two separate functions. This two step method is used as opposed to a one step time averaged method previously developed to determine the chemical kinetic time with increased accuracy. The first time averaged step is used at the initial times for smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, initial water to fuel mass ratio, temperature, and pressure. The second instantaneous step, to be used with higher water concentrations, gives the chemical kinetic time as a function of instantaneous fuel and water mole concentration, pressure and temperature (T4). The simple correlations would then be compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates were then used to calculate the necessary chemical kinetic times. Chemical kinetic time equations for fuel, carbon monoxide and NOx were obtained for Jet-A fuel and methane with and without water injection to water mass loadings of 2/1 water to fuel. A similar correlation was also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium concentrations of carbon monoxide and nitrogen oxide as functions of overall equivalence ratio, water to fuel mass ratio, pressure and temperature (T3). The temperature of the gas entering the turbine (T4) was also correlated as a function of the initial combustor temperature (T3), equivalence ratio, water to fuel mass ratio, and pressure.

Molnar, Melissa↗

Simplified Two-Time Step Method for Calculating Combustion Rates and Nitrogen Oxide Emissions for Hydrogen/Air and Hydorgen/Oxygen

A simplified single rate expression for hydrogen combustion and nitrogen oxide production was developed. Detailed kinetics are predicted for the chemical kinetic times using the complete chemical mechanism over the entire operating space. These times are then correlated to the reactor conditions using an exponential fit. Simple first order reaction expressions are then used to find the conversion in the reactor. The method uses a two-time step kinetic scheme. The first time averaged step is used at the initial times with smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, temperature, and pressure. The second instantaneous step is used at higher water concentrations (> 1 x 10(exp -20) moles/cc) in the mixture which gives the chemical kinetic time as a function of the instantaneous fuel and water mole concentrations, pressure and temperature (T4). The simple correlations are then compared to the turbulent mixing times to determine the limiting properties of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. This time is regressed over the complete initial conditions using the Excel regression routine. Chemical kinetic time equations for H2 and NOx are obtained for H2/air fuel and for the H2/O2. A similar correlation is also developed using data from NASA s Chemical Equilibrium Applications (CEA) code to determine the equilibrium temperature (T4) as a function of overall fuel/air ratio, pressure and initial temperature (T3). High values of the regression coefficient R2 are obtained.

Molnar, Melissa↗

Simplified Two-Time Step Method for Calculating Combustion and Emission Rates of Jet-A and Methane Fuel With and Without Water Injection

A simplified kinetic scheme for Jet-A, and methane fuels with water injection was developed to be used in numerical combustion codes, such as the National Combustor Code (NCC) or even simple FORTRAN codes. The two time step method is either an initial time averaged value (step one) or an instantaneous value (step two). The switch is based on the water concentration in moles/cc of 1x10(exp -20). The results presented here results in a correlation that gives the chemical kinetic time as two separate functions. This two time step method is used as opposed to a one step time averaged method previously developed to determine the chemical kinetic time with increased accuracy. The first time averaged step is used at the initial times for smaller water concentrations. This gives the average chemical kinetic time as a function of initial overall fuel air ratio, initial water to fuel mass ratio, temperature, and pressure. The second instantaneous step, to be used with higher water concentrations, gives the chemical kinetic time as a function of instantaneous fuel and water mole concentration, pressure and temperature (T4). The simple correlations would then be compared to the turbulent mixing times to determine the limiting rates of the reaction. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates are used to calculate the necessary chemical kinetic times. Chemical kinetic time equations for fuel, carbon monoxide and NOx are obtained for Jet-A fuel and methane with and without water injection to water mass loadings of 2/1 water to fuel. A similar correlation was also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium concentrations of carbon monoxide and nitrogen oxide as functions of overall equivalence ratio, water to fuel mass ratio, pressure and temperature (T3). The temperature of the gas entering the turbine (T4) was also correlated as a function of the initial combustor temperature (T3), equivalence ratio, water to fuel mass ratio, and pressure.

Molnar, Melissa↗