Search NASA⌕ Search

SEARCH · Search NASA

Results for “Axial Jet”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Fuel Stratification Influence on NO x Emission in a Premixed Axial Reacting Jet-in-Crossflow at High Pressure

Three reacting jet-in-crossflow (JiC) methane/air flames were numerically investigated in a lean axially staged combustor at a pressure of five atmospheres. A detailed chemistry Star-CCM+ computational fluid dynamics (CFD) model was used with 53 species considered and the result of turbulence-governed finite-rate modeling was validated with in-house experimental data. An optically accessible test section features three side windows, allowing local flow and flame analysis with particle image velocimetry (PIV) and CH* chemiluminescence as well as pressure, temperature, and species exit measurements. The research objective was to predict and verify NO x formation of the premixed 12.7 mm axial jet. Three headend temperature levels were investigated along with three premixed jets at lean (φ Jet = 0.75), near-stoichiometric (φ Jet = 1.07), and rich (φ Jet = 1.78) axial fuel line equivalence ratio. Based on the matching exit emission concentration, global emission benefits were investigated by adjustment of the fuel stratification. The perfectly premixed methane/air flames of this study were shown to ignite at the lee-side of the jet. For the elevated headend temperature level T = 1800 K, the flame extended beyond the windward jet trajectory and caused high axial NO production. For industry application, a firing temperature of 1920 K was achieved with a NO x optimized fuel split of 25%, combining a lean headend (φ Headend = 0.61) with a rich (φ Jet = 1.78) jet equivalence ratio. As a result, this operating point allowed minimization of the combustor residence time at temperatures above 1700 K as well as combustion in a compact flame at the jet lee-side along the counter rotating vortex pair.

03 NATURAL GAS↗
DOE OSTI2024

Nonplanar effects in simulations of laser-driven ejecta microjet experiments

Recent experiments of laser-driven ejecta microjets performed at OMEGA 60 reveal tortuous jets whereby the jets appear to deviate from their initial trajectory as they travel in vacuum. To understand these data, we perform two dimensional numerical simulations, considering different target thicknesses, pressures, and models of the drive conditions. In particular, modeling the finite laser spot size appears essential in reproducing qualitatively the non-planar shock observed in the experiment. Simulations capture jet deflection by accounting for a slight misalignment of the laser pointing with respect to the groove axis along with spatial variation of the laser pulse intensity. The principal physical mechanism appears to be that lateral momentum is imparted by release waves arising from the non-planar drive. The induced off-axis velocity is small in comparison to the jet axial velocity but integrates into a pronounced deflection over the course of the experiment. The analysis of jet axial and lateral mass distributions is found to be reproduced reasonably by the simulations. Simulated radiographs are in qualitative agreement with the experiments, though their differences point to potential shortcomings in modeling strictly three-dimensional experiments using two-dimensional hydrodynamic simulations. The simple analysis is able to explain part of the observed discrepancy in simulated vs experimental jet masses.

42 ENGINEERING↗
DOE OSTI2021

The Effect of Pressure on NO x Entitlement and Reaction Timescales in a Premixed Axial Jet-In-Crossflow

This paper investigates the pressure dependency of a lean premixed jet injected into a lean vitiated crossflow with an experimentally verified detailed chemistry computational fluid dynamics (CFD) model and 53 species considered. Experimental data were taken in an axially staged combustor with an optically accessible test section, allowing the use of particle image velocimetry (PIV) and CH* chemiluminescence techniques as well as point measurement of species concentration, temperature, and pressure. The experimental data cases at one, three, and five atmospheres were selected to describe the flame stabilization dependency on pressure and gain the required knowledge for an extrapolation to engine condition. Simulated exit nitrogen oxide levels were validated with experimental emission data, and a global emission trend for the NO reduction at elevated pressure and constant turbine inlet temperature level was defined. The nitrogen oxide benefit at elevated operating pressure was justified with the significantly smaller flame surface area: the analysis of the simulated spanwise and top-view profiles showed a relatively short receded core flame with nitrogen oxide production in the center at high pressure relative to a longer and larger shear layer flame at atmospheric condition that produced NO toward the inner and outer side of the flame. Furthermore, decomposition of the Damköhler number revealed the strong influence of the reaction timescales with higher reaction rates at elevated pressure, along with a moderate influence of the turbulent timescales, showing higher turbulence intensity in the lee-side recirculation zone at lower pressure.

03 NATURAL GAS↗
DOE OSTI2021

The Influence of Pressure on Flame-Flow Characteristics of a Reacting Jet in Crossflow

This work experimentally investigates the effects of elevated combustor pressures on the characteristics of a lean premixed reacting methane/air jet injected into a lean vitiated crossflow using a 12.7 mm axial jet. Experiments were conducted in an axially staged combustor, which implements a reacting jet in crossflow (RJIC) configuration and operates over a pressure range of 1–5 atmospheres. Simultaneous CH* chemiluminescence and particle image velocimetry (PIV) are used to study the flow field and flame behavior. The results show that the reacting jet trajectory exhibits greater penetration with elevated pressure, which is a novel finding compared to available data in the literature. However, the flame liftoff point and ignition delay time both decreased with elevated pressure, which was attributed to decreased vorticity along the flame boundary which corresponds to increased Damköhler numbers (Da). Emissions measurements confirm the NOx increase with pressure as reported in the literature for single-stage gas turbine combustors. Concurrently, emission measurements for the staged configuration show the strong NOx benefit of the RJIC system: the data prove a reduction of global outlet emission levels at elevated pressure with the axially staged configuration. Here, the axial emission reduction was attributed to the decreasing liftoff at elevated pressure levels. Hence, the research emphasizes that the flame and emission characteristics are coupled; they are not only dependent on the geometric parameters and momentum flux ratios but are also a function of pressure.

03 NATURAL GAS↗
DOE OSTI2022

Controlling pollutant emissions in a high-pressure combustor with fuel-diluent blending

This paper investigates the formation of nitric oxide (NO) and carbon monoxide (CO) emissions as a function of nitrogen (N 2 ) or carbon dioxide (CO 2 ) diluent content, added to a premixed reacting jet in crossflow. Here, reaction characteristics of a rich methane-air jet injected into a lean vitiated crossflow were analyzed at an elevated pressure of 5 atm. The jet was pre-heated and enriched with 0%, 15%, 30%, and 50% mass fraction to quantify the effect on pollutant emissions. Simulated results of the full chemistry Star-CCM+CFD model were verified with data taken in the experimental high-pressure combustion facility, which provides pressure, temperature and velocity profiles, as well as line-of-sight chemiluminescence and exit emission measurements. The analysis revealed the significant influence of the diluent to delay axial combustion; this mixing delay increased the axial flame lift-off and controlled any thermal ignition limitations. Increasing the diluent content increased the timescale for the flame to stabilize, which allowed for greater entrainment of crossflow oxidizer into the axial jet stream, and led to decreased pollutant emissions. Hence, crossflow entrainment is a critical driving force at high diluent content. Local nitric oxide (NO) emission formation in the axial stage was predicted numerically, showing the correlation between diluent addition, axial heat release, and the formation of nitric oxide pollution. The high diluent levels leaned out the jet mixture and delayed axial combustion, while reducing prompt and thermal NOx by mitigating flame hotspots and minimizing the timescale that the products remain at high temperatures.

03 NATURAL GAS↗
DOE OSTI2024

Structure and dynamics of magneto-inertial, differentially rotating laboratory plasmas

We present a detailed characterization of the structure and evolution of differentially rotating plasmas driven on the MAGPIE pulsed-power generator (1.4 MA peak current, 240 ns rise time). The experiments were designed to simulate physics relevant to accretion discs and jets on laboratory scales. A cylindrical aluminium wire array Z pinch enclosed by return posts with an overall azimuthal off-set angle was driven to produce ablation plasma flows that propagate inwards in a slightly off-radial trajectory, injecting mass, angular momentum and confining ram pressure to a rotating plasma column on the axis. However, the plasma is free to expand axially, forming a collimated, differentially rotating axial jet that propagates at ${\approx }100\,{\rm km}\,{\rm s}^{-1}$ . The density profile of the jet corresponds to a dense shell surrounding a low-density core, which is consistent with the centrifugal barrier effect being sustained along the jet's propagation. We show analytically that, as the rotating plasma accretes mass, conservation of mass and momentum implies plasma radial growth scaling as $r \propto t^{1/3}$ . As the characteristic moment of inertia increases, the rotation velocity is predicted to decrease and settle on a characteristic value ${\approx }20\,{\rm km}\,{\rm s}^{-1}$ . We find that both predictions are in agreement with Thomson scattering and optical self-emission imaging measurements.

Valenzuela-Villaseca, V. (ORCID:0000000167721441)↗
DOE OSTI2023

Numerical Simulations of High Prandtl Number Liquid Jets Impinging on a Flat Plate

In this work, 3D simulations of oil jets impinging on a flat, heated wall are presented. The numerical setup uses the Volume of Fluid (VoF) method to model the two-phase flow. A careful grid definition across the liquid film, along with the use of the Conjugate Heat Transfer (CHT) approach allowed local heat transfer to be solved with fine resolution at the wall. Variations of liquid flow rate, liquid temperature and surface temperature allow to cover a wide range of local Reynolds and Prandtl numbers (226 < Re < 2850, 77 < Pr < 161). Resulting surface-averaged heat transfer compares very well with experimental measurements conducted in a previous study. In-depth analysis of the flow has identified expected features from the literature. In particular, the impact of jet axial velocity profiles on the heat transfer distribution in the stagnation zone was clearly stated. The increase in heat transfer when warming the liquid film was also reproduced and explained by a decrease in oil viscosity and an increase in film velocity. All those effects were taken into account in correlations for stagnation and local values of Nusselt number. A grid sensitivity study was also conducted, showing that if the grid solving the thermal boundary layer in the stagnation zone can be coarsened without impacting local and surface-averaged predictions of heat transfer, a minimum resolution (2 to 3 cells) within the thermal boundary layer is however required for an accurate prediction of heat transfer.

conjugate heat transfer↗
DOE OSTI2020

An Efficient 1-D Thermal Stratification Model for Pool-Type Sodium-Cooled Fast Reactors

Investigating thermal stratification in the upper plenum of a sodium fast reactor (SFR) is presently a technology gap in SFR safety analysis. Understanding thermal stratification will promote safe operation of the SFR before its commercial deployment. Stratified layers of liquid sodium with a large vertical temperature gradient could be established in the upper plenum of an SFR during a down-power or a loss-of-flow transient. These stratified layers are unstable and could result in uncertainties for the core safety of an SFR. In order to predict the occurrence of the thermal stratification efficiently, we developed a one-dimensional (1-D) transport model to estimate the temperature profile of the ambient fluid in the upper plenum. This model demands much less computational effort than computational fluid dynamics (CFD) codes and provides calculations with higher fidelity than historical system-level codes. Two flow conditions were considered separately in the current study depending on if in-vessel components are presented in the upper plenum. For the condition where in-vessel components, specifically the upper internal structure, are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the distance between the bottom of the in-vessel component and the jet inlet surface. For the condition where no in-vessel components are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the jet length, which was determined through data-driven trainings. The newly developed 1-D model showed similar performance with the CFD model in both cases. However, due to the assumption of flat profiles of the impinging jet axial dispersion rate, nonnegligible discrepancies between the 1-D prediction and the measured data were observed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

NO PLIF flow visualization and time-resolved temperature distributions in laser induced breakdown plumes

NO planar laser induced fluorescence (PLIF) is used to obtain images of laser-induced breakdown plasma plumes in NO-seeded nitrogen and dry air at near atmospheric pressure. Single-shot PLIF-images show that the plume development 5–50 μs after the breakdown pulse is fairly reproducible shot-to-shot, although the plume becomes increasingly stochastic on longer timescales, 100–500 μs. The stochastic behavior of the plume is quantified using probability distributions of the loci of the plume boundary. Analysis of the single-shot images indicates that the mixing of the plume with ambient gas on sub-ms time scale is insignificant. The induced flow velocity in the plume is fairly low, up to 30 m s –1 , suggesting that laser breakdowns are ineffective for mixing enhancement in high speed flows. The ensemble-averaged PLIF images indicate the evolution of the plume from an initially elongated shape to near-spherical to toroidal shape, with a subsequent radial expansion and formation of an axial jet in the center. Temperature distributions in the plume in air are obtained from the NO PLIF images, using two rotational transitions in the NO(X, v' = 0 → A, v'' = 0) band, J'' = 6.5 and 12.5 of the Q R 12 + Q 2 branch. The results indicate that the temperature in the plume remains high, above 1000 K, for approximately 100 μs, after which it decays gradually, to below 500 K at 500 μs. The residual NO fraction in the plume is ~0.1%, indicating that repetitive laser-assisted ignition may result in significant NO-generation. Furthermore, these measured temperature and velocity distributions can be used for detailed validation of kinetic models of laser-induced breakdown and assessment of their predictive capability.

42 ENGINEERING↗
DOE OSTI2021

Partial Premixing Effects on the Reacting Jet of a High-Pressure Axially Staged Combustor

The effects of partial premixing on a reacting jet-in-crossflow is investigated in a five atmosphere axially staged combustor at stationary gas turbine relevant conditions. The facility consists of a dump style headend burner that provides a crossflow with a quasi-uniform velocity and temperature profile to the axial stage to isolate the effects of the jet-in-crossflow. The headend burner is run with methane and air at a lean equivalence ratio to match industry emission standards. For this work, the total air to the headend and axial stage is kept constant, and fuel is split between the headend and axial stage to represent different gas turbine loading conditions. For the cases analyzed, the fuel split to the axial stage went up to 25%. The axial stage consists of an optically accessible test section with a coaxial injector that provides variability to how long the methane and air can mix before entering the facility. Three different premixed levels are studied: fully premixed, nonpremixed, and partially premixed. The flow-field characteristics of the reacting jet-in-crossflow are analyzed using particle image velocimetry (PIV), and flame behavior is quantified by employing CH* chemiluminescence. NO measurements are made at the exit of the facility using a Horiba emissions analyzer. Furthermore, two different flames are observed: flames that burn in the leeward recirculation region and flames that burn at the core of the jet.

03 NATURAL GAS↗
DOE OSTI2021

Simulation of Premixed and Partially Premixed Jet-in-Crossflow Flames at High Pressure

In this paper, we explore the operational map of a lean axial-staged combustor of premixed and partially premixed reacting jet-in-crossflow flames at high -pressure (5 atm). This study attempts to expand the data to relatively high pressure and could significantly aid scaling to real gas turbine engine conditions at 20–30 atm. High-speed camera, particle image velocimetry (PIV), CH* chemiluminescence, temperature, and pressure measurements were taken and processed to allow accurate reconstruction of six operating points relative to computational fluid dynamics (CFD) simulations under minimal adjustments. Variation of lean main stage (φ = 0.575 and 0.73) and rich jet (φ = 1.1, 4, and 8) equivalence ratio has been investigated for a four mm axial jet. The fully premixed flames were found to be controlled by the crossflow temperature before ignition and the crossflow oxygen content during combustion. Analysis of flame shape and position for the partially premixed operating points describes a lee stabilized as well as a more unsteady windward flame branch. Adjustment of added jet fuel and crossflow temperature along with its corresponding oxygen level is required to attain a compact flame body. Here, the risk of delaying combustion progress is significantly increased at a richer jet φ = 8 and an overshooting, spatially divided flame was attained with a main stage φ = 0.73. Control toward a compact flame body is critical to allow combustion at reasonable reaction rate.

03 NATURAL GAS↗
DOE OSTI2022

Improving NO x Entitlement with Axial Staging

Manufacturers are constantly under pressure to increase the efficiency of air breathing gas turbines for the next generation of ground based combined cycle power plants without a significant increase in NO x emissions. Axially staging some of the fuel and air is one method manufacturers are exploring to increase the firing temperature with a minimal NO x increase. This project used a high-pressure combustion facility to systematically explore the axial stage design space at conditions relevant to engine manufacturers. Chemiluminescence and PIV images of the reacting jets were obtained as well as exit emissions. This data was used to create correlations for reacting jets-in-crossflow, analogous to what currently exists for non-reacting jets-in-crossflow. Two CFD programs were used to model these results to quantifying the accuracy of the codes and help elucidate the underlying physics that governs the high-pressure reacting jet in crossflow. This report indicates a change in flame/flow-field behavior, and emissions characteristics with increasing pressure from 1-5.5 atm. Additionally, the effects of preheating and premixing the axial jet are explored at various conditions and show increased jet liftoff leads to a decrease in NO x emissions.

03 NATURAL GAS↗
DOE OSTI2021

Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

Here, proper scaling for the mean transverse flow and Reynolds shear stress in a turbulent plane jet is determined using a scaling patch approach. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity equation, a proper scale for the mean transverse flow in a turbulent plane jet is found as V ref = –δdU ctr /dx, where δ is the jet half width and dU ctr /dx is the decay rate of the mean axial velocity at the jet centerline. By seeking an admissible scaling for the mean axial momentum equation, a proper scale for the kinematic Reynolds shear stress is found as R uv,ref =U ctr V ref , which is a mix of the velocity scales in the axial and transverse directions. Approximation functions for the scaled mean transverse flow and Reynolds shear stress are developed and found to agree well with experimental and numerical data. Similarities and differences between the scales of the mean transverse flow and Reynolds shear stress in turbulent plane jets and zero-pressure-gradient turbulent boundary layer flows are clarified.

42 ENGINEERING↗
DOE OSTI2024

Breakup dynamics in a pressure-swirl injector for urea-water solution applications: A computational study

The co-optimization of in-cylinder combustion and after-treatment technology has become a major aspect in engine design and development, with the goal of meeting the increasingly restrictive emission regulations in the transportation industry. Selective Catalytic Reduction is a robust technology to control the emission of NO x , and the injection of urea in water solution is the exhaust tailpipe is a key aspect of its operation. The proposed work uses high-fidelity Computational Fluid Dynamics to characterize the atomization dynamics of the liquid jet in relevant cross-flow conditions. The study focuses on a commercial low-pressure (9 bar) pressure-swirl injector which is characterized in its internal geometry through high-resolution X-ray micro-computational tomography. The internal two-phase flow has been modeled according to the volume-of-fluid approach in a large eddy simulation framework and validated against near-nozzle X-ray radiography measurement. Moreover, characterizing the breakup dynamics for the swirling hollow cone formation, and assessing the influence of the cross-flow in the breakup dynamics was completed. The results have been reported proposing Re-Oh maps and probability density functions of the spray kinematics. Higher cross-flow momentum generates an increase in the jet intact length and a reduction of the liquid droplet diameters. The axial momentum of the jet is affected by the cross-flow already in the near-nozzle region, determining a relevant deviation of the spray velocities. In conclusion, this work aims to inform the initialization of Eulerian-Lagrangian spray models through the assignment of droplet kinematics and static one-way coupling between volume-of-fluid results and Lagrangian spray parcels, to be used for system-size domain simulations.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Time-domain self-broadened and air-broadened nitrogen S-branch Raman linewidths at 80–200 K recorded in an underexpanded jet

We report pure-rotational N 2 –N 2 , N 2 –air, and O 2 –air S-branch linewidths for temperatures of 80–200 K by measuring the time-dependent decay of rotational Raman coherences in an isentropic free-jet expansion from a sonic nozzle. We recorded pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps CARS) spectra along the axial centerline of the underexpanded jet, within the barrel shock region upstream of the Mach disk. The dephasing of the pure-rotational Raman coherence was monitored using probe-time-delay scans at different axial positions in the jet, corresponding to varying local temperatures and pressures. The local temperature was obtained by fitting CARS spectra acquired at zero probe time delay, where the impact of collisions was minimal. The measured decay of each available Raman transition was fit to a dephasing constant and corrected for the local pressure, which was obtained from the CARS-measured static temperature and thermodynamic relationships for isentropic expansion from the known stagnation state. Nitrogen self-broadened transitions decayed more rapidly than those broadened in air for all temperatures, corresponding to higher Raman linewidths. In general, the measured S-branch linewidths deviated significantly in absolute and relative magnitudes from those predicted by extrapolating the modified exponential gap model to low temperatures. The temperature dependence of the Raman linewidth for each measured rotational state of nitrogen (J ≤ 10) and oxygen (N ≤ 11) was fit to a temperature-dependent power law over the measurable temperature domain (80–200 K) and extrapolated to both higher rotational states and room temperature. Furthermore, the measured and modeled low-temperature linewidth data provided here will aid low temperature gas-phase pressure measurements with fs/ps CARS.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Computational Fluid Dynamics analysis of a jet-induced attrition

The flow dynamics, collisional behavior and attrition rates of a grid jet attrition unit are computationally investigated using a kinetic theory-based approach. Profiles of the flow statistical properties are presented and discussed to describe the jet dynamics. Attrition behavior and rates are analyzed from the local reconstruction of the collision energy spectra. The commonly used jet-induced attrition mechanisms which involve the entrainment of the particles into the jet followed by their acceleration and collision at the jet tip is reproduced by the CFD calculations in this work. Here, supported by the local attrition rates, it is shown that the shear-based collisions around the jets, due to counter-current particle axial motions, are an additional jet-induced mechanism generating more fines than at the jet tips.

42 ENGINEERING↗
DOE OSTI2021

Preheating and premixing effects on NO x emissions in a high-pressure axially staged combustor

NO x emissions remain a primary concern for modern and future gas turbines, particularly as we progress towards a net-zero carbon future. It is critical to identify novel strategies to mitigate environmental pollutants for both modern turbines operated on natural gas and future turbines projected to use carbon-free fuels (such as hydrogen). In the current study, NO x emissions of a reacting methane-air jet in a vitiated crossflow are experimentally investigated in a model axially staged combustor at 5 atm. The combustion products from the main stage combustor flow into the axial stage at temperatures ranging from 1580 to 1650 °C. The axial stage contains a reacting jet in crossflow, which provides an overall temperature rise ranging from 50 to 220 °C to generate exit temperatures similar to gas turbine engines. The focus of this paper is to explore the effects of flame liftoff and ignition timescales on the NO x contribution of this secondary jet. This is done by varying the premixed level and preheat temperature of the axial jet. The effects are explored at different momentum flux ratios (J), jet equivalence ratios (φ jet ), exit temperatures (T exit ), and main stage (headend) temperatures (T HE ). High-speed CH* chemiluminescence imaging is employed for each test case to determine the flame stabilization point. For a given temperature rise and combustor exit temperature, an increase in ignition delay was observed with a decrease in jet temperature. This provided a NO x benefit, particularly for jets that are injected at or close to an ignitable mixture fraction. Similarly, the coaxial injector caused a significant ignition delay compared to the fully premixed injector; this also led to a NO x benefit. Overall, the results show that a thermally driven delay in the axial stage provides a greater NO x reduction than a mixing delay.

03 NATURAL GAS↗
DOE OSTI2022

Near-field acoustical holography and acoustic power analysis of a simulated, highly heated supersonic jet

Although near-field acoustical holography (NAH) and acoustic intensity analysis have previously been used to investigate the apparent jet noise sources produced by military aircraft, explicit connections to supersonic jet characteristics cannot be made due to a lack of information about the exhaust plume. Here, to begin to bridge this gap and better understand the source information yielded by NAH, the current study instead applies NAH to a virtual measurement of the near-field pressures of a highly heated laboratory-scale supersonic jet generated by large-eddy simulation (LES). The holographic reconstructions of the pressure, particle velocity, and acoustic intensity are found to match the LES-generated acoustic field well and are used to calculate the acoustic power of the jet. The jet's calculated overall acoustic power is compared to the free-stream mechanical power, resulting in an acoustic efficiency of 1.5%. Ray-tracing of the acoustic intensity to the jet centerline generates an axial distribution of the acoustic power origin, showing that almost all the power originates from the supersonic portion of the flow and with the distribution peak upstream of the potential core tip. Holographic reconstruction of the pressures along the nozzle lipline captures the general spectral shape of the LES-generated pressures, though it underestimates the amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗