Search NASA⌕ Search

SEARCH · Search NASA

Results for “gas turbine engine”

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

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

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Ab Initio Design of High-Entropy Thermal/ Environmental Barrier Coatings

Next generation thermal/environmental barrier coatings (TEBC) require carefully balancing various properties including phase stability, thermal conductivity, coefficient of thermal expansion (CTE), mechanical properties, and resistance against hot corrosion and water vapor recession. This work mainly focuses on rapid design of cost-effective high entropy rare-earth disilicates and aluminum garnets to protect SiC-based ceramic matrix composites and nickel-based superalloys in the hot section of gas turbine engines using density functional theory methods. Our calculations identify several low-cost high entropy TEBC exhibiting ultralow thermal conductivity at 1500 K and desirable CTE while maintaining good mechanical properties, including Er1/2Y3/4Yb3/4Si2O7, Gd1/4Er1/4Y3/4Yb3/4Si2O7, Eu1/4Er1/4Y3/4Yb3/4Si2O7, and (Y1/4Gd1/4Er1/4Yb1/4)3Al5O12. This work also aims to gain fundamental understanding of oxygen diffusion in model disilicates. Minimizing oxidizer (such as water vapor and oxygen) permeability through the EBC layer can significantly decrease the growth rate of thermally grown oxide and extend the service life of the coating system. Oxygen diffusion mechanisms including formation energy of defects under varying oxygen conditions and defect migration energy barriers will be presented.

coefficient of thermal expansion↗
DOE OSTI2024

Quench process modeling & simulation in the heat-treatment of critical aerospace components

To manufacture light-weight, advanced metal alloy components for gas turbine engines, quench heat-treatment processes are typically used. By quenching the component from elevated tempera-tures, the alloy sometimes undergoes a solid-state phase transformation which produces special microstructures with the required, enhanced mechanical properties. However, the quenching can also lead to cracks forming in the component. Addressing the quench cracking problems adds a significant burden to the cost, schedule, and energy demand of manufacture. Currently, optimizing the quench process to mitigate or avoid the cracking is performed largely by trial-and-error, relying heavily on costly experimental (thermocouple) trials to understand the local thermal gradients which cause the cracks to form. In this first part (Phase 1) of the work, high-performance computing is employed to establish the ability of modern CFD (computational fluid dynamics) to alleviate or wholly replace the experimental quenching trials by virtual testing. A baseline CFD model is defined and its accuracy established to be comparable to (and which usually exceeds) the accuracy of existing HTC (heat-transfer correlation) based simulation methods of quenching. As a first-principles based approach, “calibration” of the Baseline CFD model is independent of the quench process itself, but instead relies on the accuracy of the underlying (modeled), generic two-phase fluid processes which cannot be currently resolved by CFD for large, industrial-scale cases. A novel, high-fidelity DNS capability has been developed and verified to examine and further improve upon the mean-field closure submodels on which the Baseline CFD approach is based.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Enhancing CMC Temperature Performance in High Hydrogen Environments using Field Assisted Sintering Technology

This final report summarizes the developments in field assisted sintering technology (FAST) for rapid fabrication of ceramic matrix composite (CMC) materials with integrated environmental barrier coatings (EBCs), as well as their performance in a representative gas turbine combustor environment including stagnant flame zones, and high velocity product zones. CMCs are a possible high temperature tolerant material system for gas turbine engines, which are currently the dominant source of electric power production and the primary source of aircraft propulsion. However, CMCs are costly and time-consuming (on the order of weeks to months) to fabricate, and CMCs based on silicon carbide (SiC) ceramics are susceptible to water vapor degradation requiring the use of specialized EBCs. The manufacturing technique known as FAST can create consolidated parts in as little as a few hours using high pressure and temperature, and may be useful to integrate EBCs into CMCs directly during consolidation.

08 HYDROGEN↗
DOE OSTI2025

Phase-field predictions of the influence of cooling rates during AM on the Evolution of Microstructures in Nickel-Based Single Crystal Superalloys

Additive manufacturing of single crystals made of Ni-based superalloys offers major cost savings for gas turbine engines with the inclusion of internal cooling channels. However, the lack of understanding of the effect of transient thermal conditions on solidification grain structure during additive manufacturing hinders the potential for process control to maintain the single crystal quality. The use of high-fidelity simulations through high performance computing to predict the evolution of the solidification microstructure will enhance the abilities to tailor the microstructures through process optimization. Phase field simulations are used to determine the effect local thermal conditions and defects on the stability of the solidification morphology, specifically with respect to the onset of columnar-to-equiaxed transition that results in the loss of the single crystal. The results are expected to be instrumental for developing future surrogate models to speed up the integration of design and manufacturing of turbine blades under the harsh in-service conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Theoretical Prediction of Thermal Expansion Anisotropy for Y 2 Si 2 O 7 Environmental Barrier Coatings Using a Deep Neural Network Potential and Comparison to Experiment

Environmental barrier coatings (EBCs) are an enabling technology for silicon carbide (SiC)-based ceramic matrix composites (CMCs) in extreme environments such as gas turbine engines. However, the development of new coating systems is hindered by the large design space and difficulty in predicting the properties for these materials. Density Functional Theory (DFT) has successfully been used to model and predict some thermodynamic and thermo-mechanical properties of high-temperature ceramics for EBCs, although these calculations are challenging due to their high computational costs. In this work, we use machine learning to train a deep neural network potential (DNP) for Y 2 Si 2 O 7 , which is then applied to calculate the thermodynamic and thermo-mechanical properties at near-DFT accuracy much faster and using less computational resources than DFT. We use this DNP to predict the phonon-based thermodynamic properties of Y 2 Si 2 O 7 with good agreement to DFT and experiments. We also utilize the DNP to calculate the anisotropic, lattice direction-dependent coefficients of thermal expansion (CTEs) for Y 2 Si 2 O 7 . Molecular dynamics trajectories using the DNP correctly demonstrate the accurate prediction of the anisotropy of the CTE in good agreement with the diffraction experiments. In the future, this DNP could be applied to accelerate additional property calculations for Y 2 Si 2 O 7 compared to DFT or experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Closed-loop brayton cycle system with turbine blade cooling

A closed-loop Brayton cycle system utilizes supercritical carbon dioxide as the working fluid for the system to achieve higher efficiencies than can be achieved with traditional open-loop gas turbine engines. A bleed channel is used to direct a flow of cooling fluid to cool the turbine blades during operation of the system, preventing damage to the turbine blades during operation of the system. The bleed channel includes a bleed inlet fluidly coupled between a first recuperator and a second recuperator and a bleed outlet fluidly coupled to the turbine blades. The bleed channel is configured to direct the flow of cooling fluid to the turbine blades at a desired temperature and pressure.

Taylor, Stephen H.↗
DOE OSTI2021

Novel Temperature Sensors and Wireless Telemetry for Active Condition Monitoring of Advanced Gas Turbines

The objective of the program is to develop and engine test hardware and software technologies that will enable active condition monitoring to be implemented on hot gas path turbine blades in large industrial gas turbines. The specific objectives are (1) to fabricate and install Smart Turbine Blades with thermally sprayed sensors and high temperature wireless telemetry systems in a gas turbine engine, (2) to integrate the component engine test data with remaining useful life (RUL) models and develop an approach for networking the component RUL data with Siemens' Power Diagnostics® engine monitoring system. These significant advances carried out in Phase 1 in temperature wide bandgap telemetry, along with new induced power driver and receiver geometry combined with an innovative approach to transmit digital data wirelessly will enable the opportunity to proceed with more technical innovation. The Phase 2 program focused on validation testing of sensor-wireless telemetry package in spin rig and advanced operation-based assessment (OBA) model utilizing artificial intelligence. Significant efforts were dedicated on the download of the technology onto components to be tested an actual gas turbine engine for full realization of active condition monitoring for Smart Turbine Blades.

03 NATURAL GAS↗
DOE OSTI2024

Evaluation of methods for characterizing the fine particulate matter emissions from aircraft and other diffusion flame combustion aerosol sources

The U. S. Environmental Protection Agency in collaboration with the U. S. Air Force Arnold Engineering Development Complex conducted the VAriable Response In Aircraft nvPM Testing (VARIAnT) 3 and 4 test campaigns to compare nvPM emissions measurements from a variety of diffusion flame combustion aerosol sources (DFCASs), including a Cummins diesel engine, a diesel powered generator, two gas turbine start carts, a J85-GE-5 turbojet engine burning multiple fuels, and a Mini-CAST soot generator. The VARIAnT research program has conducted four test campaigns to date with the VARIAnT 3 and 4 test campaigns focusing on BC mass instrument performance, use of gas turbine engine sources for BC mass instrument calibration, and the characterization of the aerosols produced from the combustion sources. Results from both campaigns revealed agreement of about 20% between the AVL Micro-Soot Sensor, the Cavity Attenuated Phase Shift (CAPS PMSSA) monitor and the thermal-optical reference method for elemental carbon (EC), independent of the calibration source used. For the Artium LII-300, the measured mass concentrations in VARIAnT3 fall within 18% and in VARIAnT4 fall within 32% of the reference EC mass concentration when calibrated on a combustor rig in VARIAnT3 and on a LGT-60 start cart in VARIAnT4, respectively. It was also found that the three mass instrument types (MSS, CAPS PMSSA, and LII-300) can exhibit different BC to reference EC ratios depending on the emission source that appear to correlate to particle geometric mean mobility diameter, morphology, or some other parameter associated with particle geometric mean diameter (GMD) with the LII-300 showing a slightly stronger apparent trend with GMD. Systematic differences in LII-300 measured mass concentrations have been reduced by calibrating with a turbine combustion source (combustor or turbine engine). With respect to the particle size measurements made, the sizing instruments (TSI SMPS, TSI EEPS, and Cambustion DMS 500) were found to be in general agreement in terms of size distributions and concentrations with some exceptions. Teflon filter measurements of the total aerosol mass produced by the various DFCASs differed from the reference EC, BC, and integrated particle sized distribution measured aerosol masses. The Teflon filter measured mass was 30 to 40% greater than the reference EC and 50 to 60% greater than the BC mass for the J85 in both test campaigns. The measurements of particle size distributions and single particle analysis by miniSPLAT indicated the presence of large particles (>100 nm) having more compact morphologies, higher effective density, and a composition dominated by OC and ash. This increased large particle fraction is also associated with higher values of single scattering albedo measured by the CAPS PMSSA instrument and higher OC/EC measurements. These measurements indicate gas turbine engine emissions can be a more heterogeneous mix of particle types beyond the original E31 assumption that it is mainly composed of black carbon.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Challenges in Kinetic modeling of ammonia pyrolysis

Ammonia pyrolysis reactions have implications for its ignition and oxidation in engines and gas turbines. In the present work, the chemistry of ammonia pyrolysis is investigated by kinetic modeling and theory. Rate constants for key reactions are carefully evaluated based on available experimental and theoretical results. The high pressure limit k1,∞ for NH 2 + H (+M) ⇄ NH 3 (+M) (R1) is calculated to be essentially the collision frequency, indicating that dissociation of ammonia in combustion processes will be at or close to the low pressure limit even at engine and gas turbine conditions. The chemical kinetic model is validated against reported shock tube measurements of NH 3 , NH 2 , and NH in ammonia pyrolysis. Predictions are in good agreement with observations for dilute conditions (≤ 0.5% NH 3 ), but the model appears to underpredict the NH 3 consumption rate at longer times in less dilute mixtures. At short reaction times, thermal dissociation of NH3, together with the NH 3 + H reaction, controls conversion. At longer times, secondary reactions involving NH 2 and NH become important due to their impact on the radical pool. Predictions become sensitive to formation and consumption of diazene (tHNNH and cHNNH). Several of the key steps in the ammonia pyrolysis mechanism are radical-radical reactions that are difficult to measure accurately and challenging to calculate theoretically, and a more comprehensive experimental characterization is desirable to support further model development.

10 SYNTHETIC FUELS↗
DOE OSTI2020

Transcritical diffuse-interface hydrodynamics of propellants in high-pressure combustors of chemical propulsion systems

Rocket engines and high-power new generations of gas-turbine jet engines and diesel engines oftentimes involve the injection of one or more reactants at subcritical temperatures into combustor environments at high pressures, and more particularly at pressures higher than those corresponding to the critical points of the individual components of the mixture, which typically range from 13 to 50 bars for most propellants. This class of trajectories in the thermodynamic space has been traditionally referred to as transcritical. However, the fundamental understanding of fuel atomization, vaporization, mixing, and combustion processes at such high pressures remains elusive. In particular, whereas fuel sprays are relatively well characterized at normal pressures, analyses of dispersion of fuel in high-pressure combustors are hindered by the limited experimental diagnostics and theoretical formulations available. The description of the thermodynamics of hydrocarbon-fueled mixtures employed in chemical propulsion systems is complex and involves mixing-induced phenomena, including an elevation of the critical point whereby the coexistence region of the mixture extends up to pressures much larger than the critical pressures of the individual components. As a result, interfaces subject to surface-tension forces may persist in multicomponent systems despite the high pressures, and may give rise to unexpected spray-like atomization dynamics that are otherwise absent in monocomponent systems above their critical point. In this article, the current understanding of this phenomenon is reviewed within the context of propulsion systems fueled by heavy hydrocarbons. Emphasis is made on analytical descriptions at mesoscopic scales of interest for computational fluid dynamics. In particular, a set of modifications of the constitutive laws in the Navier–Stokes equations for multicomponent flows, supplemented with a high-pressure equation of state and appropriate redefinitions of the thermodynamic potentials, are introduced in this work based on an extended version of the diffuse-interface theory of van der Waals. The resulting formulation involves revisited forms of the stress tensor and transport fluxes of heat and species, and enables a description of the mesoscopic volumetric effects induced by transcritical interfaces consistently with the thermodynamic phase diagram of the mixture at high pressures. Additionally, applications of the theory are illustrated in canonical problems, including dodecane/nitrogen transcritical interfaces in non-isothermal systems. The results indicate that a transcritical interface is formed between the propellant streams that persists downstream of the injection orifice over distances of the same order as the characteristic thermal-entrance length of the fuel stream. The transcritical interface vanishes at an edge that gives rise to a fully supercritical mixing layer.

02 PETROLEUM↗
DOE OSTI2020

A statistical model to predict ignition probability

Ignition capability is a critical design constraint for aeronautical gas turbines. However the current trend toward overall lean burn is detrimental to the engine ignition and relight and the ignition system must be adapted to ensure a fast and reliable light-round in all circumstances. As ignition is a stochastic phenomenon, the optimization of an ignition system requires to build ignition probability maps, which is difficult and costly with either experiment or numerical simulation as both require many tests. Here, this work proposes a model to predict the ignition probability map, knowing only flow statistics in non-reacting conditions, i.e., with only one test. The originality of the model is to construct statistics of the flame kernel trajectory, which are then combined with local flow indicators to evaluate the ignition probability at the considered sparking location. Application to a swirled burner operated in premixed, non-premixed and spray combustion modes illustrates the model concepts and demonstrates its ability to recover the experimental ignition map with good accuracy.

42 ENGINEERING↗
DOE OSTI2023

Laminar Burning Speed Measurements of Hydrogen/Natural Gas Mixtures

Abstract To address the shortage of fossil fuels and the environmental impact of exhaust emissions, research efforts in combustion seek to identify candidates for sustainable fuels. Hydrogen is an example, from which water is produced as the main combustion product. However, when used as neat hydrogen, it is very difficult to control hydrogen combustion due to its high flame speed, pre-ignition propensity, and flashback characteristics. One method to control hydrogen combustion is to blend it with a well-established fuel. Natural gas is a common fuel for use in engines or gas turbines. Natural gas is characterized by slow flame speeds and poor lean-burn ability; thus, engine power is decreased in the lean-burn region. Consequently, natural gas engines are typically operated at stoichiometric conditions to maximize output. Blending hydrogen to natural gas has several advantages: (i) Control of hydrogen’s ignition characteristics, (ii) extension of Natural gas’s lower flammability limit — making it easier to ignite, and (iii) reduced greenhouse gas emissions. In this study, the laminar burning speed (LBS) for neat natural gas and natural gas/hydrogen mixtures at 5 atm and 296 K were measured. Schlieren optical imaging was utilized to validate laminar flame conditions and further investigate the structure of natural gas/hydrogen flames. Results indicate that replacing 50% of natural gas with hydrogen increases the peak laminar burning velocity by a factor of ∼1.6 times. LBS simulations were conducted with NUI 1.1 and UCF NG/H2 mechanisms; Predictions by both mechanisms were found to be satisfactory for neat NG mixtures. However, for 50% NG/ 50% H2 mixture, the true LBS for fuel-lean conditions was under-predicted by both models, while predictions for fuel-rich conditions were satisfactory. Additionally, a literature review and similar experimental analysis will be performed for methane, ammonia, and hydrogen fuel blends to better understand the combustion phenomena of natural gas fuels.

Yovino, Louis↗
DOE OSTI2024

On the importance of species immiscibility in mixing-layer dynamics at supercritical pressures

The mixing dynamics of injected propellants is a key factor in determining the ignition performance and combustion-instability response of rocket engines, internal combustion engines, and gas turbines. A key source of uncertainty in the prediction of phase-exchange dynamics is the immiscibility of the injected propellants at supercritical pressure conditions, which induces liquid/vapor phase separation and surface-tension dynamics. While experimental observations indicate the presence of liquid/vapor interfacial structures, this interfacial dynamics is typically neglected in numerical analyses. To address this issue, the objective of the present study is to systematically evaluate the importance of species immiscibility on the phase-exchange dynamics of cryogenic LOX/GH2 mixing layers at typical rocket engine injection conditions. This is accomplished by comparing simulations of (i) a recently developed interface-capturing Regularized-Interface Method (RIM) formulation, and (ii) the commonly employed Diffuse-Interface Method (DIM) formulation. Analysis shows that the interfacial dynamics significantly impact the atomization and mixing of the propellants in the near-injector region, which is not captured by the DIM formulation. The findings of this study extend to other immiscible injection systems, such as LOX/kerosene and hydrocarbon-fuel/air, thereby highlighting the importance of resolving species immiscibility in simulating high-pressure combustion engines.

diffused-interface method↗
DOE OSTI2023

Large Eddy Simulation of Rotationally Induced Ingress and Egress around an Axial Seal between Rotor and Stator Disks

In gas turbines, the hot gas exiting the combustor can have temperatures as high as 2000 °C, and some of this hot gas enter into the space between the stator and rotor disks (wheelspace). Since the entering hot gas could damage the disks, its ingestion must be minimized. This is carried out by rim seals and by introducing a cooler flow from the compressor (sealing flow) into the wheelspace. Ingress and egress into rim seals are driven by the stator vanes, the rotor and its rotation, and the rotor blades. This study focuses on the ingress and egress driven by the rotor and its rotation. This is carried out by performing wall-resolved large eddy simulation (LES) around an axial seal in a rotor–stator configuration without vanes and blades. Results obtained show the mechanisms by which the rotor and its rotation induce ingress, egress, and flow trajectories. Kelvin–Helmholtz instability was found to create a wavy shear layer and displacement thickness that produces alternating regions of high and low pressures around the rotor side of the seal. Vortex shedding on the backward-facing side of the seal and its impingement on the rotor side of the seal also produces alternating regions of high and low pressures. The locations of the alternating regions of high and low pressures were found to be statistically stationary and to cause ingress to start on the rotor side of the seal. Vortex shedding and recirculating flow in the seal clearance also cause ingress by entrainment. With the effects of the rotor and its rotation on ingress and egress isolated, this study enables the effects of stator vanes and rotor blades to be assessed.

42 ENGINEERING↗
DOE OSTI2025

Plasma assisted NH 3 /H 2 /air ignition in nanosecond discharges with non-equilibrium energy transfer

Ammonia (NH 3 ), with its high energy density and easiness to store and transport as a hydrogen carrier, has become a promising alternative green fuel. However, its adoption in power generation is hindered by challenges such as low burning velocity, slow low-temperature oxidation, high NO x emissions, and ignition difficulty. Here, this work computationally investigates the effects of non-equilibrium energy transfer by nanosecond discharges on NH 3 ignition and flame propagation in an NH 3 /H 2 /air flow at 700 K and 1 atm. The simulation results demonstrate that NH 3 /air mixtures require a large ignition energy due to their large critical ignition radius. It is shown that adding 30 % hydrogen significantly reduces the critical ignition radius and minimum ignition energy. Two-dimensional modeling further shows a non-monotonic dependence of ignition kernel volume on the applied voltage and reduced electric field. The optimum ignition enhancement occurs at 200 Td where the generation of electronically excited species and radicals including N 2 (B), O( 1 D) and OH becomes most efficient. Higher voltages divert electron energy toward ionization, which makes it less effective for NH 3 ignition. The study also identifies an optimal electrode gap size for a given pulse energy. Smaller gap sizes increase deposited energy density, raising temperature and radical concentrations. However, excessive reduction of the gap distance reduces flame propagation speed due to the flame stretch effect in rich mixtures with the effective Lewis number greater than unity. A nonlinear relationship between pulse repetition frequency and ignition kernel volume is observed in a nanosecond pulsed high frequency discharge (NPHFD). An optimal frequency range of 200 kHz to 2 MHz is found when two pulses are used. In addition, an optimal number of pulses exists for each pulse repetition frequency, with higher frequencies requiring more pulses to maximize the overlap region. These findings provide critical insights on developing controlled plasma discharge techniques for efficient NH 3 ignition in reactive flows within internal combustion engines and gas turbines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Understanding the role of flow dynamics in thermoacoustic combustion instability

Thermoacoustic combustion instability is one of the most challenging operational issues in several high-performance, low-emissions combustion technologies, including gas turbines, aircraft engines, rockets, and industrial boilers. Driven by the coupling between combustor acoustics and flame heat release rate fluctuations, thermoacoustic combustion instability can lead to reduced operability, increased emissions, and, in the most extreme cases, catastrophic failure of combustor components. The feedback loop between acoustics and combustion is often facilitated by fluid mechanic oscillations, referred to as “velocity coupling,” whereby acoustic oscillations drive flow fluctuations, which in turn create fluctuations in the flame. The character of these fluid mechanic oscillations is highly dependent on the structure of the flow field and the receptivity of the flow to external excitation. Combustor flow fields use features like fluid recirculation and shear to enhance flame holding and reduce emissions, but these are also the same features that can make the flow receptive to acoustic excitation or even drive self-excited oscillations. Here, in this paper, we discuss the basics of thermoacoustic instability with a focus on the role of hydrodynamic oscillations in typical combustor flows. To facilitate this discussion, we explore the hydrodynamic instability characteristics of several key combustor unit flows (wakes, swirling jets, etc.) and show how the hydrodynamic stability of a flow is an important consideration in determining a combustor’s propensity for thermoacoustic oscillations. Several examples of coupling between hydrodynamics and thermoacoustics are discussed to illustrate this important link. The paper concludes by discussing the potential for designing flow fields that are thermoacoustic instability resistant, either through a reduction in the receptivity of the flow or through nonlinear coupling mechanisms by which self-excited flow instabilities can suppress velocity-coupled combustion oscillations.

42 ENGINEERING↗
DOE OSTI2020

Progress and Prospective of Nitrogen-Based Alternative Fuels

Alternative fuels are essential to enable the transition to a sustainable and environmentally friendly energy supply. Synthetic fuels derived from renewable energies can act as energy storage media, thus mitigating the effects of fossil fuels on environment and health. Their economic viability, environmental impact, and compatibility with current infrastructure and technologies are fuel and power source specific. Nitrogen-based fuels pose one possible synthetic fuel pathway. In this paper, we discuss the progress and current research on utilization of nitrogen-based fuels in power applications, covering the complete fuel cycle. We cover the production, distribution, and storage of nitrogen-based fuels. We assess much of the existing literature on the reactions involved in the ammonia to nitrogen atom pathway in nitrogen-based fuel combustion. Furthermore, we discuss nitrogen-based fuel applications ranging from combustion engines to gas turbines, as well as their exploitation by suggested end-uses. Thereby, we evaluate the potential opportunities and challenges of expanding the role of nitrogen-based molecules in the energy sector, outlining their use as energy carriers in relevant fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗