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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Pressure Transient Analyses and Poroelastic Modeling of Hydraulic Fracture Dilation for Multiple Injections at the Devine Fracture Pilot Site

Our team has conducted electromagnetic (EM) surveys for the past six years to monitor hydraulic-fracture behavior at the Devine Fracture Pilot Site (DFPS). The sub-horizontal orientation of a shallow hydraulic fracture at the DFPS provides uniform access to the fracture area for interrogation and data collection. Ahmadian et al. (2023) suggested a possible correlation between spatiotemporal changes in the flow rate, bottomhole pressure (BHP), and the observed surface recorded electric field at the DFPS. In this paper, we present the development of poroelastic forward models and pressure transient analyses (PTAs) to support the development of a multiphysics inverse model for these EM surveys. First, we conducted PTAs of the shut-in periods after six injections out of 10 to determine the fracture closure pressure (FCP) or the overburden pressure used in a poroelastic fracture reopening model. Second, we developed a finite-element poroelastic model throughout five injection cycles to include the effect of the cumulative injected volumes due to the previous injections on current fracture dilation in the presence of highly permeable unpropped and propped zones adjacent to the cohesive layer that models fracture reopening. Fracture reopening in this poroelastic model is based on a calibrated traction-separation response using the bottomhole pressure collected in two injection campaigns in 2020 and 2022. We used the outcomes of a previous simulation study of the primary hydraulic-fracturing stimulation to define the dimension of an unpropped fracture zone ahead of the propped fracture area. The PTAs led to FCPs consistent with those obtained using the injection data collected at the DFPS in 2020. Further, these analyses showed that at later injections, the fracture closure occurred at a later time with respect to the shut-in time, inferring the effect of cumulative injected volumes in previous injections. The simulation results show that considering the propped and unpropped fracture zones improves our poroelastic model in predicting the injection-well BHP. The numerical simulation results demonstrate a significant excess pore pressure near the fracture because of the preceding formation loadings by the previous injections. The obtained fracture dilation area and fluid pressure distribution provide a basis to improve the development of a multiphysics inverse model. Furthermore, in an iteratively coupled scheme, this pressure distribution can be introduced into EM models to render a holistic view of the causative mechanisms for the surface signal anomalies.

02 PETROLEUM↗
DOE OSTI2014

Experimental design applications for modeling and assessing carbon dioxide sequestration in saline aquifers

This project was a computer modeling effort to couple reservoir simulation and ED/RSM using Sensitivity Analysis, Uncertainty Analysis, and Optimization Methods, to assess geologic, geochemical, geomechanical, and rock-fluid effects and factors on CO 2 injectivity, capacity, and plume migration. The project objective was to develop proxy models to simplify the highly complex coupled geochemical and geomechanical models in the utilization and storage of CO 2 in the subsurface. The goals were to investigate and prove the feasibility of the ED/RSM processes and engineering development, and bridge the gaps regarding the uncertainty and unknowns of the many geochemical and geomechanical interacting parameters in the development and operation of anthropogenic CO 2 sequestration and storage sites. The bottleneck in this workflow is the high computational effort of reactive transport simulation models and large number of input variables to optimize with ED/RSM techniques. The project was not to develop the reactive transport, geomechanical, or ED/RSM software, but was to use what was commercially and/or publically available as a proof of concept to generate proxy or surrogate models. A detailed geologic and petrographic mineral assemblage and geologic structure of the doubly plunging anticline was defined using the USDOE RMOTC formations of interest data (e.g., Lower Sundance, Crow Mountain, Alcova Limestone, and Red Peak). The assemblage of 23 minerals was primarily developed from literature data and petrophysical (well log) analysis. The assemblage and structure was input into a commercial reactive transport simulator to predict the effects of CO 2 injection and complex reactions with the reservoir rock. Significant impediments were encountered during the execution phase of the project. The only known commercial reactive transport simulator was incapable of simulating complex geochemistry modeled in this project. Significant effort and project funding was expended to determine the limitations of both the commercial simulator and the Lawrence Berkeley National Laboratory (LBNL) R&D simulator, TOUGHREACT available to the project. A simplified layer cake model approximating the volume of the RMOTC targeted reservoirs was defined with 1-3 minerals eventually modeled with limited success. Modeling reactive transport in porous media requires significant computational power. In this project, up to 24 processors were used to model a limited mineral set of 1-3 minerals. In addition, geomechanical aspects of injecting CO 2 into closed, semi-open, and open systems in various well completion methods was simulated. Enhanced Oil Recovery (EOR) as a storage method was not modeled. A robust and stable simulation dataset or base case was developed and used to create a master dataset with embedded instructions for input to the ED/RSM software. Little success was achieved toward the objective of the project using the commercial simulator or the LBNL simulator versions available during the time of this project. Several hundred realizations were run with the commercial simulator and ED/RSM software, most having convergence problems and terminating prematurely. A proxy model for full field CO 2 injection sequestration utilization and storage was not capable of being developed with software available for this project. Though the chemistry is reasonably known and understood, based on the amount of effort and huge computational time required, predicting CO 2 sequestration storage capacity in geologic formations to within the program goals of ±30% proved unsuccessful.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1973

Automatic instrument for chemical processing to detect microorganism in biological samples by measuring light reactions

An automated apparatus is reported for sequentially assaying urine samples for the presence of bacterial adenosine triphosphate (ATP) that comprises a rotary table which carries a plurality of sample containing vials and automatically dispenses fluid reagents into the vials preparatory to injecting a light producing luciferase-luciferin mixture into the samples. The device automatically measures the light produced in each urine sample by a bioluminescence reaction of the free bacterial adenosine triphosphate with the luciferase-luciferin mixture. The light measured is proportional to the concentration of bacterial adenosine triphosphate which, in turn, is proportional to the number of bacteria present in the respective urine sample.

Kelbaugh, B. N.↗
NASA NTRS1978

Low cost solar array project silicon materials task. Development of a process for high capacity arc heater production of silicon for solar arrays

Silicon tetrachloride and a reductant (sodium) will be injected into an arc heated mixture of hydrogen and argon, yielding silicon and gaseous sodium chloride. Detailed characterization of the Sonicore sodium injection nozzle, using water as the test fluid was completed. Results indicated that flow rates of 45 gph sodium and 50 scfm argon should produce sufficiently small droplet sizes. The design effort was also completed for the test system preparation which was divided into two categories: (1) system components and (2) test system-laboratory integration.

Reed, W. H.↗
NASA NTRS1987

Electron heating in a Monte Carlo model of a high Mach number, supercritical, collisionless shock

Preliminary work in the investigation of electron injection and acceleration at parallel shocks is presented. A simple model of electron heating that is derived from a unified shock model which includes the effects of an electrostatic potential jump is described. The unified shock model provides a kinetic description of the injection and acceleration of ions and a fluid description of electron heating at high Mach number, supercritical, and parallel shocks.

Ellison, Donald C.↗
NASA NTRS1998

Analysis of a Rocket Based Combined Cycle Engine during Rocket Only Operation

The all rocket mode of operation is a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. However, outside of performing experiments or a full three dimensional analysis, there are no first order parametric models to estimate performance. As a result, an axisymmetric RBCC engine was used to analytically determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and statistical regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, percent of injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inject diameter ratio. A perfect gas computational fluid dynamics analysis was performed to obtain values of vacuum specific impulse. Statistical regression analysis was performed based on both full flow and gas generator engine cycles. Results were also found to be dependent upon the entire cycle assumptions. The statistical regression analysis determined that there were five significant linear effects, six interactions, and one second-order effect. Two parametric models were created to provide performance assessments of an RBCC engine in the all rocket mode of operation.

Smith, T. D.↗
NASA NTRS2002

Flow field measurements in the cell culture unit

The cell culture unit (CCU) is being designed to support cell growth for long-duration life science experiments on the International Space Station (ISS). The CCU is a perfused loop system that provides a fluid environment for controlled cell growth experiments within cell specimen chambers (CSCs), and is intended to accommodate diverse cell specimen types. Many of the functional requirements depend on the fluid flow field within the CSC (e.g., feeding and gas management). A design goal of the CCU is to match, within experimental limits, all environmental conditions, other than the effects of gravity on the cells, whether the hardware is in microgravity ( micro g), normal Earth gravity, or up to 2g on the ISS centrifuge. In order to achieve this goal, two steps are being taken. The first step is to characterize the environmental conditions of current 1g cell biology experiments being performed in laboratories using ground-based hardware. The second step is to ensure that the design of the CCU allows the fluid flow conditions found in 1g to be replicated from microgravity up to 2g. The techniques that are being used to take these steps include flow visualization, particle image velocimetry (PIV), and computational fluid dynamics (CFD). Flow visualization using the injection of dye has been used to gain a global perspective of the characteristics of the CSC flow field. To characterize laboratory cell culture conditions, PIV is being used to determine the flow field parameters of cell suspension cultures grown in Erlenmeyer flasks on orbital shakers. These measured parameters will be compared to PIV measurements in the CSCs to ensure that the flow field that cells encounter in CSCs is within the bounds determined for typical laboratory experiments. Using CFD, a detailed simulation is being developed to predict the flow field within the CSC for a wide variety of flow conditions, including microgravity environments. Results from all these measurements and analyses of the CSC flow environment are presented and discussed. The final configuration of the CSC employs magnetic stir bars with angled paddles to achieve the necessary flow requirements within the CSC.

Cell Culture↗
DOE OSTI2012

Production and delivery of a fluid mixture to an annular volume of a wellbore

The methods described herein generally relate to preparing and delivering a fluid mixture to a confined volume, specifically an annular volume located between two concentrically oriented casing strings within a hydrocarbon fluid producing well. The fluid mixtures disclosed herein are useful in controlling pressure in localized volumes. The fluid mixtures comprise at least one polymerizable monomer and at least one inhibitor. The processes and methods disclosed herein allow the fluid mixture to be stored, shipped and/or injected into localized volumes, for example, an annular volume defined by concentric well casing strings.

42 ENGINEERING↗
DOE OSTI2014

Secondary air injection system and method

According to one embodiment of the invention, a secondary air injection system includes a first conduit in fluid communication with at least one first exhaust passage of the internal combustion engine and a second conduit in fluid communication with at least one second exhaust passage of the internal combustion engine, wherein the at least one first and second exhaust passages are in fluid communication with a turbocharger. The system also includes an air supply in fluid communication with the first and second conduits and a flow control device that controls fluid communication between the air supply and the first conduit and the second conduit and thereby controls fluid communication to the first and second exhaust passages of the internal combustion engine.

42 ENGINEERING↗
DOE OSTI2021

A coupled thermo-hydro-mechanical model for simulating leakoff-dominated hydraulic fracturing with application to geologic carbon storage

A potential risk of injecting CO2 into storage reservoirs with marginal permeability (≲ 10 mD (1 mD = 10 –15 m 2 )) is that commercial injection rates could induce fracturing of the reservoir and/or the caprock. Such fracturing is essentially fluid-driven fracturing in the leakoff-dominated regime. Recent studies suggested that fracturing, if contained within the lower portion of the caprock complex, could substantially improve the injectivity without compromising the overall seal integrity. Modeling this phenomenon entails complex coupled interactions among the fluids, the fracture, the reservoir, and the caprock. Here, we develop a simple method to capture all these interplays in high fidelity by sequentially coupling a hydraulic fracturing module with a coupled thermal-hydrological-mechanical (THM) model for nonisothermal multiphase flow. The model was made numerically tractable by taking advantage of self-stabilizing features of leakoff-dominated fracturing. The model is validated against the PKN solution in the leakoff-dominated regime. Moreover, we employ the model to study thermo-poromechanical responses of a fluid-driven fracture in a field-scale carbon storage reservoir that is loosely based on the In Salah project's Krechba reservoir. The model reveals complex yet intriguing behaviors of the reservoir-caprock-fluid system with fracturing induced by cold CO 2 injection. We also study the effects of the in situ stress contrast between the reservoir and caprock and thermal contraction on the vertical containment of the fracture. The proposed model proves effective in simulating practical problems on length and time scales relevant to geological carbon storage.

58 GEOSCIENCES↗
DOE OSTI2021

NRAP-Open-IAM Multisegmented Wellbore Reduced-Order Model

Geologic carbon storage is one of the promising strategies to mitigate climate change by reducing the emission of carbon dioxide to the atmosphere. As part of the National Risk Assessment Partnership (NRAP), a systems-level stochastic analysis tool called the open source integrated assessment model, NRAP-Open-IAM, has been developed to estimate and manage the risk of containment loss at a geological carbon sequestration site. NRAP-Open-IAM contains several wellbore leakage model components that estimate the fluid leak rate that may occur through compromised legacy wells due to the increase in pressure resulting from CO 2 injection activities. Coupled to a reservoir component model, these components estimate the leakage of CO 2 and/or brine from a storage reservoir to overlying aquifer layers and the atmosphere through legacy wells. This report presents the theoretical framework and quality testing of the multisegmented wellbore reduced-order model. The model allows for segmenting of the legacy wells passing through the overlying stratigraphy into several intervals to simulate a site’s specific stratigraphic and hydrogeologic properties. For quality assurance, the analytical model is validated against numerical reservoir flow simulations for single and multiple aquifer(s) models. The results indicate that the model accurately predicts the transport of two-phase fluids (brine and injected CO 2 ) through the well over time. A detailed description of the model helps users to understand the model and provides a basis for future improvements.

58 GEOSCIENCES↗
DOE OSTI2013

Development of an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs

In this study, we have developed an analytical solution for thermal single-well injection-withdrawal tests in horizontally fractured reservoirs where fluid flow through the fracture is radial. The dimensionless forms of the governing equations and the initial and boundary conditions in the radial flow system can be written in a form identical to those in the linear flow system developed by Jung and Pruess [Jung, Y., and K. Pruess (2012), A Closed-Form Analytical Solution for Thermal Single-Well Injection-Withdrawal Tests, Water Resour. Res., 48, W03504, doi:10.1029/2011WR010979], and therefore the analytical solutions developed in Jung and Pruess (2012) can be applied to compute the time dependence of temperature recovery at the injection/withdrawal well in a horizontally oriented fracture with radial flow.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Highly resolved Eulerian simulations of fuel spray transients in single and multi-hole injectors: Nozzle flow and near-exit dynamics

In high pressure fuel injectors, needle opening and closing transients cause complex off-design fluid dynamics behaviors that profoundly impact the spray and mixture formation processes. These dynamics are completely different from what is known to occur in steady state conditions. In this study, diesel spray transients have been investigated in single-hole and 3-hole nozzles, encompassing internal and external nozzle flow and including needle motion, performing highly resolved (2.5 μm) computational fluid dynamics (CFD) simulations. We focused on end-of-injection (EOI) and start-of-injection (SOI) processes, in order to provide insights in to the physics. The liquid fuel, vapor and gas species are modeled with a single-fluid multiphase mixture approach, with diffuse interface, and with large eddy simulations (LES) of the turbulence. Occurrence of phase change due to cavitation is accounted for, and the spray dispersion is described with a turbulent dispersion model. Detailed needle motion data and orifice internal surface are available from xray synchrotron source measurements carried out at Argonne National Laboratory, and shared through the Engine Combustion Network (ECN) community. Simulations are compared against x-ray phase contrast imaging and radiography of the internal and near-exit flow, in addition to optical microscopy data of the near-exit sprays. Simulation results are found to agree well with available experimental data, and are able to realistically capture local and global features. The simulations allow to gain insight into the physics of gas ingestion and dribbles at EOI, for different hole diameters, operating conditions and number of holes. At SOI, timing of liquid appearance out of the injector and spray tip penetration are adequately predicted, by using the EOI flow field as in-nozzle initialization, and by prescribing the measured tip needle displacement with an informed effective valve opening point inferred from the x-ray observations. Lastly, the variation of spreading angle over time is also discussed in detail for the multi-hole case, including hole-to-hole variations. Due to real geometry features and asymmetric needle motion with eccentric components, it is found that the three holes exhibit swirling flows of increasing intensity as the lift decreases, causing the near cone angle to open and spread, in a quasi-hollow cone structure. These features are not observed in axial single-hole injectors because of their relative simplicity and intrinsic symmetry.

42 ENGINEERING↗
NASA NTRS2008

An Idealized, Single Radial Swirler, Lean-Direct-Injection (LDI) Concept Meshing Script

To easily study combustor design parameters using computational fluid dynamics codes (CFD), a Gridgen Glyph-based macro (based on the Tcl scripting language) dubbed BladeMaker has been developed for the meshing of an idealized, single radial swirler, lean-direct-injection (LDI) combustor. BladeMaker is capable of taking in a number of parameters, such as blade width, blade tilt with respect to the perpendicular, swirler cup radius, and grid densities, and producing a three-dimensional meshed radial swirler with a can-annular (canned) combustor. This complex script produces a data format suitable for but not specific to the National Combustion Code (NCC), a state-of-the-art CFD code developed for reacting flow processes.

Iannetti, Anthony C.↗
DOE OSTI2019

Performance, Fuel Economy, and Economic Assessment of a Combustion Concept Employing In-Cylinder Gasoline/Natural Gas Blending for Light-Duty Vehicle Applications

In current production natural gas/gasoline bi-fuel vehicles, fuels are supplied via port fuel injection (PFI). Injecting a gaseous fuel in the intake port significantly reduces the volumetric efficiency and consequently torque as compared to gasoline. In addition to eliminating the volumetric efficiency challenge, direct injection (DI) of natural gas (NG) can enhance the in-cylinder flow, mixing, and combustion process resulting in improved efficiency and performance. A computational fluid dynamics (CFD) approach to model high-pressure gaseous injection was developed and validated against X-ray data from Argonne’s Advanced Photon Source. NG side and central DI of various designs and injection strategies were assessed experimentally along with CFD correlation. Significant effects on combustion metrics were quantified and explained via improved understanding of the in-cylinder flow effects due to NG injection. On-demand in-cylinder blending using E10 PFI and NG DI provides an additional lever to adjust in-cylinder turbulence as well as knock resistance across the engine speed and load range. NG DI improves part-load dilution tolerance due to higher in-cylinder turbulence and the high knock resistance of NG compared to E10 improves wide open throttle (WOT) performance while enabling increased compression ratios (CR). Vehicle level simulations suggest that implementing this strategy on a ½ ton pick-up truck with a naturally aspirated engine at 12.5:1 CR improves energy consumption on the aggressive US06 drive cycle by 15.5% compared to E10 operation, and gives a petroleum reduction of 78% over the blended range. There are challenges regarding market acceptance and widespread adoption of dual-fuel NG-gasoline vehicle applications beyond the performance degradation when the vehicle runs out of natural gas. Furthermore, those challenges include practical concerns such as loss of cargo volume and payload due to the NG storage tank, extended NG refueling times, fueling convenience due to gasoline and NG fuel tanks, and limited NG fueling infrastructure.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2014

Gulf of Mexico miocene CO₂ site characterization mega transect

This project characterized the Miocene-age sub-seafloor stratigraphy in the near-offshore portion of the Gulf of Mexico adjacent to the Texas coast. The large number of industrial sources of carbon dioxide (CO₂) in coastal counties and the high density of onshore urbanization and environmentally sensitive areas make this offshore region extremely attractive for long-term storage of carbon dioxide emissions from industrial sources (CCS). The study leverages dense existing geologic data from decades of hydrocarbon exploration in and around the study area to characterize the regional geology for suitability and storage capacity. Primary products of the study include: regional static storage capacity estimates, sequestration “leads” and prospects with associated dynamic capacity estimates, experimental studies of CO₂-brine-rock interaction, best practices for site characterization, a large-format ‘Atlas’ of sequestration for the study area, and characterization of potential fluid migration pathways for reducing storage risks utilizing novel high-resolution 3D (HR3D) seismic surveys. In addition, three subcontracted studies address source-to-sink matching optimization, offshore well bore management and environmental aspects. The various geologic data and interpretations are integrated and summarized in a series of cross-sections and maps, which represent a primary resource for any near-term commercial deployment of CCS in the area. The regional study characterized and mapped important geologic features (e.g., Clemente-Tomas fault zone, the regionally extensive Marginulina A and Amphistegina B confining systems, etc.) that provided an important context for regional static capacity estimates and specific sequestration prospects of the study. A static capacity estimate of the majority of the Study area (14,467 mi 2 ) was estimated at 86 metric Gigatonnes. While local capacity estimates are likely to be lower due to reservoir-scale characteristics, the offshore Miocene interval is a storage resource of National interest for providing CO₂ storage as an atmospheric emissions abatement strategy. The natural petroleum system was used as an analog to infer seal quality and predict possible migration pathways of fluids in an engineered system of anthropogenic CO₂ injection and storage. The regional structural features (e.g., Clemente-Tomas fault zone) that exert primary control on the trapping and distribution of Miocene hydrocarbons are expected to perform similarly for CCS. Industrial-scale CCS will require storage capacity utilizing well-documented Miocene hydrocarbon (dominantly depleted gas) fields and their larger structural closures, as well as barren (unproductive, brine-filled) closures. No assessment was made of potential for CO₂ utilization for enhanced oil and gas recovery. The use of 3D numerical fluid flow simulations have been used in the study to greatly assist in characterizing the potential storage capacity of a specific reservoir. Due to the complexity of geologic systems (stratigraphic heterogeneity) and inherent limitations on producing a 3D geologic model, these simulations are typically simplified scenarios that explore the influence of model property variability (sensitivity study). A specific site offshore San Luis Pass (southern Galveston Island) was undertaken successfully, indicating stacked storage potential. Downscaling regional capacity estimates to the local scale (and the inverse) has proven challenging, and remains an outstanding gap in capacity assessments. In order to characterize regional seal performance and identify potential brine and CO₂ leakage pathways, results from three high-resolution 3D (HR3D) seismic datasets acquired by the study using novel HR3D (P-Cable) acquisition system showed steady and significant improvements in data quality because of improved acquisition and processing technique. Finely detailed faults and stratigraphy in the shallowest 1000 milliseconds (~800 m) of data allowed for the identification and mapping of unconformable surfaces including what is probably a surface associated with the last Pleistocene glacial lowstand. The identification of a previously unrecognized (in commercial seismic data) gas chimney that was clearly defined in the 2013 HR3D survey, indicates that HR3D surveys may be useful as both a characterization tool for the overburden of a potential carbon sequestration site and as an additional monitoring tool for future engineered injection sites. Geochemical modeling indicated that injection of CO₂ would result in minor dissolution of calcite, K-feldspar and albite. In addition, modeling of typical brines in Miocene age rocks indicate that approximately 5% of injection capacity would result from CO₂ dissolution into the brine. After extensive searches, no rock samples of the Marginulina A and Amphistegina B seals (“caprocks”) were obtained, but analyses of available core samples of other Miocene age mudrocks (seals or caprocks) indicate that they have sealing ability sufficient for potential CO 2 storage in underlying sandstone units.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2016

Systems and methods for preventing flashback in a combustor assembly

Embodiments of the present application include a combustor assembly. The combustor assembly may include a combustion chamber, a first plenum, a second plenum, and one or more elongate air/fuel premixing injection tubes. Each of the elongate air/fuel premixing injection tubes may include a first length at least partially disposed within the first plenum and configured to receive a first fluid from the first plenum. Moreover, each of the elongate air/fuel premixing injection tubes may include a second length disposed downstream of the first length and at least partially disposed within the second plenum. The second length may be formed of a porous wall configured to allow a second fluid from the second plenum to enter the second length and create a boundary layer about the porous wall.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1992

Time-dependent cosmic ray shocks with injection - A progress report

The study presents preliminary results of a two-fluid hydrodynamical simulation of cosmic-ray-modified shock structure by extending the steady-state calculations of Zank et al. (1991) to the time-dependent case. The present simulations model diffusive shock acceleration of the energetic particle component at planar shocks. A new model for the injection of cosmic ray particles is presented. The quadratic artificial viscosity algorithm is found to be numerically unstable and therefore unusable for strong cosmic ray shocks. There is visible ringing and overshoot in the various profiles. A large enhancement in the fluid density appears downstream of the subshock. This 'overcompression' results from the upstream fluid being compressed in the precursor, then traversing a strong shock with compression ratio near the adiabatic limit of four.

Donohue, D. J.↗