Assumption Of Constant Pressure Research Articles

Qualitative Analysis of Drilling Fluid Loss Through Naturally-Fractured Reservoirs

Summary Drilling becomes extremely challenging when dealing with naturally fractured reservoirs (NFR). A comprehensive solution is developed in this study to perform qualitative analysis on drilling fluid loss rate and volume to examine how they can be affected by NFR characteristics, drilling fluid rheology, leakoff phenomenon, and wellbore condition. In this regard, the solution is applied to generate type curves to facilitate the sensitivity analysis (refer to the provided Supplementary Materials). The presented solution accounts for not only drilling fluid pseudoplasticity in the total system but also matrix medium under wellbore constant pressure assumption (by including dimensionless matrix contribution parameter). It is also able to measure mud loss advancement not only through NFR but also through homogeneous reservoirs. The developed solution is validated by reducing it to the preexisting solution (designed for Newtonian fluid case) by incorporating assumptions into it. The result demonstrates the significance of NFR properties and drilling fluid pseudoplasticity on the leakoff phenomenon and total loss volume, especially when constant pressure is established inside the wellbore. The finding reveals that three periods can be identified through generated type curves depending on NFR characteristics, drilling fluid rheology, and leakoff coefficient. Therefore, different drilling fluids with specific pseudoplasticity should be used in each period to mitigate drilling fluid loss effectively. In this regard, the study is supposed to design drilling fluid in a way to maintain its pseudoplasticity at a higher level at early and late times, while being maintained at a lower level during the transient period, a critical aspect for managed pressure drilling techniques, particularly in the context of dual-gradient drilling applications. Additionally, a procedure should be implemented to lessen the transient period while attempting to keep drilling fluid advancement occurrence at a lower rate, which shows that drilling fluid pseudoplasticity can be used as an effective tool to manage this period. The obtained result also indicates that the importance of drilling fluid rheology to control total loss volume is greater for NFR with higher leakoff than with lower leakoff. Furthermore, the greater the differential pressure inside the wellbore, the greater the importance of mud rheology to reduce drilling fluid loss. The outcome of the study not only facilitated qualitative and quantitative analyses through NFR but also enabled decision-makers to instantaneously select optimal wellbore conditions and drilling fluid pseudoplasticity.

One-Dimensional Modeling for Pulsed Flow Twin-Entry Turbine

Abstract One-dimensional (1D) modeling is critical for turbomachinery unsteady performance prediction and system response assessment of internal combustion engines. This paper uses a novel 1D modeling (TURBODYNA) and proposes two additional features for the application to a twin-entry turbocharger turbine. Compared to single-entry turbines, twin-entry turbines enhance turbocharger transient response and reduce engine exhaust valve overlap periods. However, out-of-phase high-frequency pulsating pressure waves lead to an unsteady mixing process from the two flows and pose great challenges to traditional 1D modeling. The present work resolves the mixing problem by directly solving mass, momentum, and energy conservation equations during the mixing process instead of applying constant pressure assumption at the limb–rotor joint. Comparisons of TURBODYNA and an experimentally validated CFD suggest that TURBODYNA cannot only provide a very good agreement on turbine performance but also accurately capture unsteady features due to flow field inertial and pressure wave propagation. Levels of accuracy achieved by TURBODYNA have proved superior to traditional 1D modeling on turbine performance and the generality of the current 1D modeling has been explored by extending the application to other turbine featuring distinct characteristics.

Assessing the impact of pressure drop and leak distribution on ductwork airtightness measurements

Ductwork airtightness test protocols implicitly assume that the pressure across the leaks is identical for all leaks. In fact, the pressure difference at the leaks decreases in absolute value as the distance from the moving air increases, due to friction and dynamic losses. This paper aims to quantify the impact of these pressure losses on airtightness test results, and thereby the measurement error generated by the constant pressure assumption. To this end, we developed an analytical model and performed measurements on an experimental set-up that reproduces residential ductwork at 1:1 scale with dynamic losses that can be modified using dampers. We compared the results obtained using the analytical model and the experimental set-up. The analytical model makes it possible to calculate the maximum “test length” for which the error due to pressure drop remains below 5%. According to this model, the impact of pressure losses on the measured flow rate is very small for airtight ductwork (Class C). In this case, the model shows that a length of 260 m between the measuring device and the far end of the ductwork can be tested at one time, even if the ductwork is quite narrow (average diameter of 200 mm) and the test pressure very high (1000 Pa). However, when testing very leaky ductwork (3*Class A) with an average diameter of 400 mm and a test pressure of 200 Pa, the distance between the measuring device and the far end of the ductwork must be no more than 67 m to limit the error to less than 5%. This model can be used to produce charts giving the maximum length to be tested as a function of the pressure drop and the expected ductwork airtightness class.

An assessment of pressure variations in artificially ventilated cavities

In this work, the character of the pressure within artificially ventilated cavities is investigated in detail using computational fluid dynamics. The efforts explore the details of the pressure inside both twin- and toroidal-vortex cavities through histograms of the internal cavity pressure. Rather than a uniform pressure, detailed interrogation of the pressure indicates a multi-peak distribution of cavity pressure. Further interrogation of these peaks suggests that such pressure variations align with distinct regions within the cavity. Additionally, the character of these distributions are found to be dependent on the cavity closure mode (Campbell and Hilborne, 1958; Karn et al., 2016; Logvinovich, 1972). In evaluating these small, yet present, pressure variations, it is hypothesized that they are the driving force for the internal, re-circulatory flow. Lastly, the importance of these distinct regions of pressure regions is investigated with respect to semi-empirical theory, which aims to directly evaluate the level of validity of the constant pressure assumption. The results indicate that the constant pressure assumption remains valid, but may lead to small inaccuracies when evaluating other cavity characteristics through semi-empirical theory.

Intermediate-line Emission in AGNs: The Effect of Prescription of the Gas Density

Abstract The requirement of an intermediate-line component in the recently observed spectra of several active galactic nuclei (AGNs) points to the possible existence of a physically separate region between the broad-line region (BLR) and narrow-line region (NLR). In this paper we explore the emission from the intermediate-line region (ILR) by using photoionization simulations of the gas clouds distributed radially from the center of the AGN. The gas clouds span distances typical for the BLR, ILR, and NLR, and the appearance of dust at the sublimation radius is fully taken into account in our model. The structure of a single cloud is calculated under the assumption of constant pressure. We show that the slope of the power-law radial profile of the cloud density does not affect the existence of the ILR in major types of AGNs. We found that the low-ionization iron line, Fe ii, appears to be highly sensitive to the presence of dust and therefore becomes a potential tracer of dust content in line-emitting regions. We show that the use of a disk-like cloud density profile computed for the upper part of the atmosphere of the accretion disk reproduces the observed properties of the line emissivities. In particular, the distance of the Hβ line inferred from our model agrees with that obtained from reverberation mapping studies in the Sy1 galaxy NGC 5548.

THE PROBLEMS OF HYDRODYNAMIC NON-ISOTHERMAL LUBRICATION

The classical hydrodynamic theory of slide bearing lubrication has been constituted on the assumption of constant pressure and viscosity perpendicular to the thin oil layer thickness. These fundamental assumptions are in contradiction to contemporary achievements connected with new devices such as micro-bearing, nano-bearing, magnetic bearings, artificial joints in humanoid robots, micro-motors. Therefore, new methods of measurements and calculations using AFM and a new mathematical computer programs are needed. Energy conservation equations after boundary layer simplifications confirm the fact that temperature gradient variations across the film thickness have the same order of magnitude as the variations in longitudinal or circumferential directions. The fact that temperature gradient variations across the bearing gap height can be significantly large are evident, despite the temperature differences across the film thickness that are negligibly small. This statement cannot be compliant with the assumption of a constant viscosity value in the gap height direction. It has been proven that hydrodynamic pressure is not constant across the film thickness for non-Newtonian oils with Rivlin Erickson constitutive equations. For pseudo-plastic non-Newtonian oils, the apparent dynamic viscosity significantly decreases with shear rate increases. However, for pseudo-plastic oils, the shear rate increments during the oil flow are strictly connected with the average flow velocity increments. Therefore, the apparent dynamic viscosity depends strongly on the oil velocity gradients. It is evident that flow velocity gradients across the film thickness have intensive variations, particularly in regions where gap height attains the least value. In these places, the dynamic viscosity attains the largest variations in gap height directions. If gap height in micro-bearing is smaller than one micrometre, than the largest oil dynamic viscosity increments caused by the velocity variations across the film thickness are located near the superficial layer of the movable journal surfaces in the case of the hydrodynamic lubrication by rotation, but in the neighbourhood where each of two come near lubricated surfaces during the squeezing. Hence, in these places, dynamic viscosity increases across the film thickness and attains the local maximum values. A gap height smaller than one micrometre has the largest oil dynamic viscosity increments caused by the adhesion force variations across the film thickness located near the motionless sleeve surfaces. In a similar manner, the influences on the viscosity variations caused by the cluster points of concentrations of nano particles as oil inhibitors or oil additives smaller than 5 nm occurring in micro-bearing gaps and the cluster concentration regions of collagen fibres occurring in human joint gap are observed. This paper describes and comments on the above-mentioned problem of oil viscosity changes in the gap height direction, and it presents the apparent dynamic viscosity functions for Newtonian and non-Newtonian oils as well indicates the largest viscosity variations in bearing gap height direction and gives examples of initial calculation results.

Investigation on fluctuations in full-size Molten Salt Reactor with coupled neutronic/thermal-hydraulic model

In this paper, the fluctuations in neutron fluxes, delayed neutron precursors, fuel salt temperature and velocity in a full-size MSR are investigated by coupling the neutronic and thermal-hydraulic models. The neutronic model is established based on two-group diffusion theory with one averaged group of delayed neutron precursors. The balance equations for mass and energy are chosen to build the thermal-hydraulic model, while the momentum equation is neglected in the assumption of constant pressure. The group constants, including the cross sections and diffusion coefficients, are generated by means of the HELIOS code and fitted as functions of temperature to build the thermal feedback. The equations for fluctuations are derived based on linear perturbation theory, assuming the perturbation is small enough. All the equations are discretized and numerically solved with the help of a developed code. The static results show that the neutron flux distributions are almost independent of the fuel recirculation, and the distribution of precursors is not that sensitive to the fuel velocity change, due to the small delayed neutron fraction and large decay constant of the fuel material. In the dynamic case, it is found that the thermal feedback effect is important at low frequencies, i.e. when the point kinetic effect is prominent and the neutronic power is significantly perturbed. Similar to the static case, the fuel recirculation has apparent influence on the precursor noise, whereas its effect on the neutron noise is very small. Moreover, due to the interference among the effects of fluctuations in various group constants, the fast and thermal neutron noise are in opposite phases. Such out-phase behavior has been first observed in the case of traditional reactors and reconfirmed in the present study for a closed-loop MSR system.

Theoretical and experimental investigation of a closed sorption thermal storage prototype using LiCl/water

A 1 kWh lab-scale sorption prototype using LiCl-water was theoretically and experimentally investigated for sorption thermal energy storage. A type of consolidated composite matrix is developed for the system by using AC (activated carbon), LiCl, expanded natural graphite treated with sulphuric acid (ENG-TSA) to increase heat transfer and SS (silica solution) to enhance mechanical strength. Thermal conductivity and permeability were measured first. A two-dimensional model considering the combined heat and mass transfer was developed to predict the sorption kinetics of the reactor. Under the operation condition of a charging temperature of 85 °C and a discharging temperature of 40 °C, the experimentally recovered heat is 2517 kJ, resulting a heat storage efficiency of 93%. The heat storage density is 874 kJ/kg consolidated sorbent or 2622 kJ/kg LiCl. The experimental results of the prototype were compared with the simulated results. The established two-dimensional model proves to be effective since the general evolution trends of experimental and simulated outlet fluid temperatures are in good agreement. An average gap of about 0.4 °C between the experimental and simulated outlet temperature may be caused by the heat loss and the constant pressure assumption.

English

Determining the composition of a mixture of combustion gases at a given temperature is based on chemical equilibrium, when the equilibrium constants are calculated on the assumption of constant pressure and temperature. In this paper, an analysis of changes occurring when combustion takes place at constant volume is presented, deriving a specific formula of the equilibrium constant. The simple reaction of carbon combustion in pure oxygen in both cases (constant pressure and constant volume) is next considered as example of application, observing the changes occurring in the composition of the combustion gases depending on temperature.

Quantum size effects on classical thermosize effects

Thermosize effects have been proposed in literature by considering the quantum size effects (QSE) induced by the wave character of particles. These effects appear only if nano and macro domains are connected to each other when they are under a temperature gradient. QSE are noticeable in nano domain while they are almost negligible in macro domain. This difference causes thermosize effects, which may be called quantum thermosize effects (QTSE) because of their pure quantum origin. On the other hand, also classical thermosize effects (CTSE) appear as a result of different transport regimes in nano and macro domains, and they can be noticeable even if QTSE are negligible. As long as the mean free path (l) is much greater than the mean de Broglie wave length of particles (λ), which is almost the case in practice λ/l < 1, the principal effects are CTSE. QSE cause only small corrections on CTSE when the scale is down to nanoscale. On the other hand, in literature, QTSE and CTSE have been examined individually although it is not possible to observe QTSE alone in practice except for the extreme case of $${\lambda /l \gg 1}$$ . Furthermore, the constant pressure assumption and the Knudsen law have been used during the derivations of QTSE and CTSE, respectively, although the proper assumption at nanoscale is the modified Knudsen law, which considers QSE. In this study, QSE on CTSE are considered and the modified Knudsen law is derived and used to obtain the more realistic results for thermosize coefficients. The results can be used for a possible experimental verification of thermosize effects as well as to design some new devices based on these effects.

Modeling the influences of pressure and velocity variations on the microwave‐induced pyrolysis of wood

AbstractA detailed two‐dimensional mathematical model is studied for the unsteady heat‐and mass‐transfer equations coupled with a quasi‐steady formulation of the electromagnetic field for the microwave‐induced pyrolysis of a wood block. The aspects examined include the description of the flow field based on either the assumption of constant pressure and one‐dimensional flow velocity directed along the wood fibers or the linked two‐dimensional variation of pressure and velocity in accordance with the Darcy law and deviations from the assumptions of local thermal equilibrium between the solid and gas/vapor phase. © 2011 American Institute of Chemical Engineers AIChE J, 52: 610–624, 2012

Human cortical bone: Computer method for physical behavior at nano scale constant pressure assumption

It is well known that long term behavior of implants depends on bone remodeling. In the absence of a model of this phenomenon, few numerical simulations take into account bone remodeling. Some laws have been proposed but they cannot be used in the essential area surrounding the implant. We propose a multi-scale approach: cortical bone is structured in a hierarchical way consisting of five levels. The cortical part of a given bone is made up of various areas having different physical properties adapted to locally existing conditions. A Bony Elementary Volume denotes the elementary part of such a zone which constitutes our first level. The other levels are in conformity with our previous studies: osteon, lamella, fibre and fibril. This latter is composed by collagen and hydroxyapatite (Hap) occurring in a viscous liquid containing mineral ions. Mathematical homogenisation theory is used to determine equivalent macroscopic properties of a BEV, knowing the physical properties of collagen and Hap and the architectural description of this bony structure. For improving the performance of our simulation software, a new behavior law has been introduced with no continuity between the various levels. The effect of the fluid at the nanoscopic scale is modeled by a constant pressure. Recent developments allow us to determine the magnitude of various entities at nanoscopic scale from information at the macroscopic level. Realized simulations show that the assumption of constant pressure is not sufficient to characterize the nanoscopic mechanical behaviour. This point needs a more complex model with the introduction of a coupling between structure and fluid. This aspect is in development.

Models for solar magnetic loops

The present work describes a detailed comparison between SOHO-CDS observations of active region loops with a static, isobaric loop model developed assuming a temperature-independent heating function in the energy balance equation and a variable loop cross-section. The loop model is described in Landini & Landi (2002). Observations of an active region recorded by CDS have been analyzed. Additional data from the EIT and MDI instruments on board the SOHO satellite, and broad band soft X-rays images from the Yohkoh satellite, have been used to complement the CDS dataset. CDS monochromatic images from lines at different temperatures have been co-aligned with EIT, MDI and Yohkoh images and a loop structure has been identified. Two other loop structures are visible but their footpoints are not clearly identified, and have not been analyzed. Electron density, temperature and pressure along the selected loop structure have been measured by means of line ratio techniques. These quantities have been used to test the assumption of constant pressure adopted in the theoretical model, and to compare their values with its predictions. The loop filling factor has also been estimated from the CDS data after assumptions on the loop geometry have been made. Comparison with CDS data has shown that a classical model is not able to reproduce the observations; despite the large uncertainties, mainly given by the limited CDS spatial resolution, indications suggest that agreement occurs only if an ad hoc isothermal region is added on top of the loop and a large conductive flux at the base is assumed. Suggestions for improvements of theoretical loop models and further studies with the EIS instrument on Solar-B, due for launch in 2005, are given.

The Extreme‐Ultraviolet Structure and Properties of a Newly Emerged Active Region

The structure and properties of a newly emerged solar active region (NOAA Active Region 7985) are discussed using the Coronal Diagnostic Spectrometer (CDS) and the Extreme-Ultraviolet Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory. CDS obtained high-resolution EUV spectra in the 308-381 ? and 513-633 ? wavelength ranges, while EIT recorded full-disk EUV images in the He II (304 ?), Fe IX/X (171 ?), Fe XII (195 ?), and Fe XV (284 ?) bandpasses. Electron density measurements from Si IX, Si X, Fe XII, Fe XIII, and Fe XIV line ratios indicate that the region consists of a central high-density core with peak densities of the order of 1.2 ? 1010 cm-3, which decrease monotonically to ~5.0 ? 108 cm-3 at the active region boundary. The derived electron densities also vary systematically with temperature. Electron pressures as a function of both active region position and temperature were estimated using the derived electron densities and ion formation temperatures, and the constant pressure assumption was found to be an unrealistic simplification. Indeed, the active region is found to have a high-pressure core (1.3 ? 1016 cm-3 K) that falls to 6.0 ? 1014 cm-3 K just outside the region. CDS line ratios from different ionization stages of iron, specifically Fe XVI (335.4 ?) and Fe XIV (334.4 ?), were used to diagnose plasma temperatures within the active region. Using this method, peak temperatures of 2.1 ? 106 K were identified. This is in good agreement with electron temperatures derived using EIT filter ratios and the two-temperature model of Zhang et al. The high-temperature emission is confined to the active region core, while emission from cooler (1-1.6) ? 106 K lines originates in a system of loops visible in EIT 171 and 195 ? images. Finally, the three-dimensional geometry of the active region is investigated using potential field extrapolations from a Kitt Peak magnetogram. The combination of EUV and magnetic field extrapolations extends the core-halo picture of active region structure to one in which the core is composed of a number of compact coronal loops that confine the hot, dense, high-pressure core plasma while the halo emission emerges from a system of cooler and more extended loops.

Unsteady Effects in Droplet Vaporization Lifetimes at Subcritical and Supercritical Conditions

The heating and vaporization of a pure cold fluid package in a hot environment of the same fluid has been analyzed. The model applies to subcritical as well as supercritical fluid conditions and relics on the assumption of constant pressure and quasisteady conditions in the gas phase (in a reference system receding with the cold front). An asymptotic analysis is performed using the ratio of the hot fluid density to the density of the cold fluid package as the smallness parameter. Then, a transcendental equation is obtained which provides the evolution of the cold package radius. For longer times when isothermal conditions are achieved in the cold region, the d2 law is obtained. Some deviations from this law. due to the unsteadiness of the heating process in the cold region, are evaluated and discussed.

Spatio-temporal development of the filaments due to the thermal self-focusing instability near the critical surface in ionospheric plasmas

We study fully nonlinear spatio-temporal development of the thermal self-focusing instability of high-power radio waves near the critical surface of the ionosphere. These simulations improve on our earlier work by including an evolution equation for the density instead of using the assumption of constant pressure to determine the perturbed density connected with the known temperature perturbation. Using our two-dimensional nonlinear code we analyze the time scale and associated velocity for the development of the field-aligned irregularities as they spread from the critical surface both in the underdense as well as the overdense regions. The scaling of this velocity as a function of the radiated power of the heater electromagnetic wave (ERP) is determined. We also study the characteristic size of the self-focused filament as a function of ERP. Finally, the spectrum of the density and temperature fluctuations as well as modifications in the equilibrium values of these parameters for different values of ERP are presented.

Loop Models from SOHO Observations

The Coronal Diagnostic Spectrometer (CDS) on SOHO is a grazing/normal incidence spectrograph, aimed to produce stigmatic spectra of selected regions of the solar surface in six spectral windows of the extreme ultraviolet from 150 A to 785 A (Harrison et al. 1995). In the present work, CDS, EIT, MDI and Yohkoh observations of active region lops have been analyzed. These observations are part of JOP 54. CDS monochromatic images from lines at different temperatures have been co-aligned with EIT and MDI images, and loop structures have been clearly identified using Fe XVI emission lines. Density sensitive lines and lines from adjacent stages of ionization of Fe ions have been used to measure electron density and temperature along the loop length; these measurements have been used to determine the electron pressure along the loop and test the constant pressure assumption commonly used in loop modeling. The observations have been compared with a static, isobaric loop model (Landini and Monsignori Fossi 1975) assuming a temperature-constant heating function in the energy balance equation. Good agreement is found for the temperature distribution along the loop at the coronal level. The model pressure is somewhat higher than obtained from density sensitive line ratios.

The Electron Pressure in the Solar Lower Transition Region Determined from Ovand SiiiiDensity‐sensitive Line Ratios

We determine the electron density at the temperatures of formation of O+4 and Si+2 ions, which are about 2.5 × 105 and 3.2 × 104 K in ionization equilibrium, respectively. These temperatures occur in the lower transition region of the Sun's atmosphere and allow a test of the often invoked assumption of constant pressure in quiet-Sun models. The O+4 density is determined from a density-sensitive spectroscopic O V line ratio involving 2s2p3P-2p23P transitions that fall near 760 A. The Si+2 density is determined from a density-sensitive Si III line ratio within the 3s3p3P-3p23P multiplet near 1300 A. There are few available line ratio techniques for determining the density and hence electron pressure in the quiet-Sun and coronal hole transition regions using lines emitted by the same ion, and determining these quantities is the principal motivation for this work. The spectra used in our analysis were obtained from the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) experiment on the Solar and Heliospheric Observatory (SOHO). We determine the electron density and pressure in typical quiet-Sun/coronal hole regions, and densities in active region brightenings and in an explosive event. Our O V and Si III results indicate that constant pressure is valid or nearly valid in quiet-Sun lower transition regions, although there are complications arising from the weakness of a key Si III line in the quiet-Sun disk spectra. We also discuss our results in light of other density measurements and theories regarding the structure and heating of the transition region.

Mass flux measurements for burning rate determination of premixed turbulent flames

A method for measuring the burning rate integral B T in turbulent premixed flames and data obtained from several V-flames via the method are reported. B T is determined by integration over the flame brush of data for the mass fluxes normal and tangent to c¯ constant surfaces. The determination of both convective and turbulent mass fluxes is made by simultaneous two-component velocity (axial and lateral) and temperature measurements using a combination of laser Doppler velocimetry (LDV) and compensated, finewire thermocouples, where the instantaneous gas density is obtained from the instantaneous temperature through the equation of state and the assumption of constant pressure. B T data for turbulent premixed CH 4 -air flames, with equivalence ratios between 0.7 and 0.75, mean axial flow velocities between 2 and 6.37 m/s, and ratios of turbulence intensities to laminar burning velocities between 0.643 and 3.16, are reported. The data demonstrate the utility of simultaneous velocity and temperature measurements for determining the burning rate integral for premixed flames in laboratory burners. They further show (1) that conditional velocity data alone cannot be used with confidence to estimate mass fluxes in the flamelet regime, (2) that the use of velocity data from the reactant side of the turbulent flame brush to estimate B T (or the turbulent burning velocity) results in estimates that are quite high, and (3) that B T is a strong function of u′/S L .

Simulation of the transient, compressible, gas-dynamic behavior of catalytic-combustion ignition in stagnation flows

This paper develops and uses a computation model to explore the transient ignition dynamics of catalytic combustion in a stagnation-flow configuration. The analysis considers the elementary heterogeneous chemistry associated with catalytic behavior at the surface. It also considers gas-dynamic effects in the boundary layer, including temporal and spatial pressure variations. The gas-dynamic effects are included through the axial momentum equation, which has been neglected in previous analyses of unsteady stagnation flows. In addition to the physical interpretation of ignition transients, the paper presents a mathematical and computational analysis and comparison of the constant-pressure and compressible stagnation-flow equations. The constant-pressure equations, as commonly formulated and used, are a system of differential-algebraic equations (DAE) that have an index greater than two. This high-index behavior is responsible for severe numerical difficulties in regions of fast transients or stringent numerical error control. This paper relaxes the constant-pressure assumption using a compressible-flow formulation, which extends the range of physical validity and reduces the index of the transient stagnation-flow problem while preserving stagnation-flow “similarity”.