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DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Opposing Hysteresis Patterns in Flow and Outflow Macroscopic Fundamental Diagrams and Their Implications

Two key aggregated traffic models are the relationship between average network flow and density (known as the network or flow macroscopic fundamental diagram [flow-MFD]) and the relationship between trip completion and density (known as network exit function or the outflow-MFD [o-FMD]). The flow- and o-MFDs have been shown to be related by average network length and average trip distance under steady-state conditions. However, recent studies have demonstrated that these two relationships might have different patterns when traffic conditions are allowed to vary: the flow-MFD exhibits a clockwise hysteresis loop, while the o-MFD exhibits a counter-clockwise loop. One recent study attributes this behavior to the presence of bottlenecks within the network. The present paper demonstrates that this phenomenon may arise even without bottlenecks present and offers an alternative, but more general, explanation for these findings: a vehicle’s entire trip contributes to a network’s average flow, while only its end contributes to the trip completion rate. This lag can also be exaggerated by trips with different lengths, and it can lead to other patterns in the o-MFD such as figure-eight patterns. A simple arterial example is used to demonstrate this explanation and reveal the expected patterns, and they are also identified in real networks using empirical data. Then, simulations of a congestible ring network are used to unveil features that might increase or diminish the differences between the flow- and o-MFDs. Finally, more realistic simulations are used to confirm that these behaviors arise in real networks.

42 ENGINEERING↗

DOE OSTI2022

The influence of intake flow and coolant temperature on gasoline spray morphology during early-injection DISI engine operation

Multi-hole gasoline injectors operating at conditions spanning throttled early-intake stroke operation produce spray plumes that either remained separated or merge and collapse due to flash boiling. Flash boiling occurs due to the sudden expansion of gas bubbles in the liquid fuel at high fuel temperature and low ambient pressure. This study records high-speed images of spray-morphology changes due to in-cylinder flow, thereby revealing operating conditions that do and do not affect the self-induced morphology observed in quiescent vessels. Specifically, in a central-injection, four-valve, high-tumble engine, where the thermodynamic state and in-cylinder cross flow are dynamic. Motivated by cold start and hot restart operation, the fuel pressure, coolant temperature, in-cylinder air pressure, and engine rpm were systematically varied over relevant operating conditions, which bracketed the range from non- to flash-boiling sprays. The results reveal the operating conditions at which the in-cylinder cross flow disrupts the spray morphology as well as the extent of the disruption. At 650 rpm, the spray morphology was similar to that observed in quiescent vessels at nominally equivalent fuel temperature and in-cylinder pressure, indicating that the spray’s self-induced entrainment flow dominated the in-cylinder flow. However, for fuel temperature and ambient pressure near the transition between non- and flash-boiling, the intake cross flow at higher engine speed (1950 rpm) significantly disrupted the spray morphology. The high cross-flow velocity appears to induce plume merging and collapse, whereas none was evident at low rpm (650 rpm). This study led to the postulate that the spray merging and collapse are governed by the rate of atomization near the nozzle exit, presumed to be controlled by either or both aerodynamic atomization and flash-boiling intensity. It would then follow that spray modeling in CFD requires atomization models that blend the effects of both physical processes.

42 ENGINEERING↗

DOE OSTI2022

Integration of Electromagnetic Geophysics Forward Simulation in Coupled Flow and Geomechanics for Monitoring a Gas Hydrate Deposit Located in the Ulleung Basin, East Sea, Korea

We investigate the feasibility of electromagnetic (EM) geophysics methods to detect the dissociation of gas hydrate specifically from a gas hydrate deposit located in the Ulleung Basin, East Sea, Korea via an integrated flow-geomechanics-EM geophysics simulation. To this end, coupled flow and geomechanics simulation is first performed with the multiple porosity model employed, where a mixed formulation with the finite volume (FV) and finite element (FE) methods are taken for the flow and geomechanics, respectively. From the saturation and porosity fields obtained from the coupled flow and geomechanics, the electrical conductivity model is established for the EM simulation. Solving the partial differential equation of electrical diffusion which is linearized using the 3D finite element method (FEM), the EM fields are then computed. For numerical experiments, particularly two approaches in the configuration for the EM methods are compared in this contribution: the surface-to-surface and the surface-to-borehole methods. When the surface-to-surface EM method is employed, the EM is found to be less sensitive, implying low detectability. Especially for the short term of production, the low detectability is attributed to the similarity of electrical resistivity between the dissociated gas (CH4) and hydrate as well as the specific dissociation pattern within the intercalated composites of the field. On the other hand, when the surface-to-borehole EM method is employed, its sensitivity to capture the produced gas flow is improved, confirming its detectability in monitoring gas flow. Hence, the EM geophysics simulation integrated with coupled flow and geomechanics can be a potential tool for monitoring gas hydrate deposits.

depressurization↗

DOE OSTI2020

Determining flow directions in river channel networks using planform morphology and topology

Abstract. The abundance of global, remotely sensed surface water observations has accelerated efforts toward characterizing and modeling how water moves across the Earth's surface through complex channel networks. In particular, deltas and braided river channel networks may contain thousands of links that route water, sediment, and nutrients across landscapes. In order to model flows through channel networks and characterize network structure, the direction of flow for each link within the network must be known. In this work, we propose a rapid, automatic, and objective method to identify flow directions for all links of a channel network using only remotely sensed imagery and knowledge of the network's inlet and outlet locations. We designed a suite of direction-predicting algorithms (DPAs), each of which exploits a particular morphologic characteristic of the channel network to provide a prediction of a link's flow direction. DPAs were chained together to create “recipes”, or algorithms that set all the flow directions of a channel network. Separate recipes were built for deltas and braided rivers and applied to seven delta and two braided river channel networks. Across all nine channel networks, the recipe-predicted flow directions agreed with expert judgement for 97 % of all tested links, and most disagreements were attributed to unusual channel network topologies that can easily be accounted for by pre-seeding critical links with known flow directions. Our results highlight the (non)universality of process–form relationships across deltas and braided rivers.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1953

Smoke Studies of Secondary Flows in Bends, Tandem Cascades, and High-turning Configurations

Flow-visualization studies, using smoke, were made of the secondary flows in rectangular bends, tandem cascades, and high-turning configurations. The roll-up of the wall boundary layer of a rectangular bend forms a passage vortex near the suction surface similar to that previously observed for cascades. The vortex so formed then shifts out into the main stream. Because of leading-edge effects, the boundary-layer flows in bends were found to be sufficiently different from the flows in blade rows to make direct application of bend results to blade rows inadvisable. Passage vortices are shown, in the tandem-cascade study, to resist turning with the main stream through which they pass and to disturb the flow in subsequent blade rows. This disturbance may explain in part the appreciable size of the losses sometimes attributed to secondary flows in turbomachines despite the fact that the energy involvement in vortex formation is slight. Tip-flow studies of high-turning blades with relative motion between blades and end wall indicated that if the relative sizes of the passage vortex forces, the tip clearance forces, and the blade-scraping effects are properly controlled, it may be possible to improve the blade-tip loading characteristics in turbomachine.

CASCADES↗

NASA NTRS2001

Real-time three-dimensional color Doppler echocardiography for characterizing the spatial velocity distribution and quantifying the peak flow rate in the left ventricular outflow tract

Quantification of flow with pulsed-wave Doppler assumes a "flat" velocity profile in the left ventricular outflow tract (LVOT), which observation refutes. Recent development of real-time, three-dimensional (3-D) color Doppler allows one to obtain an entire cross-sectional velocity distribution of the LVOT, which is not possible using conventional 2-D echo. In an animal experiment, the cross-sectional color Doppler images of the LVOT at peak systole were derived and digitally transferred to a computer to visualize and quantify spatial velocity distributions and peak flow rates. Markedly skewed profiles, with higher velocities toward the septum, were consistently observed. Reference peak flow rates by electromagnetic flow meter correlated well with 3-D peak flow rates (r = 0.94), but with an anticipated underestimation. Real-time 3-D color Doppler echocardiography was capable of determining cross-sectional velocity distributions and peak flow rates, demonstrating the utility of this new method for better understanding and quantifying blood flow phenomena.

NASA Discipline Cardiopulmonary↗

NASA NTRS2013

Guide to Flow Measurement for Electric Propulsion Systems

In electric propulsion (EP) systems, accurate measurement of the propellant mass flow rate of gas or liquid to the thruster and external cathode is a key input in the calculation of thruster efficiency and specific impulse. Although such measurements are often achieved with commercial mass flow controllers and meters integrated into propellant feed systems, the variability in potential propellant options and flow requirements amongst the spectrum of EP power regimes and devices complicates meter selection, integration, and operation. At the direction of the Committee on Standards for Electric Propulsion Testing, a guide was jointly developed by members of the electric propulsion community to establish a unified document that contains the working principles, methods of implementation and analysis, and calibration techniques and recommendations on the use of mass flow meters in laboratory and spacecraft electric propulsion systems. The guide is applicable to EP devices of all types and power levels ranging from microthrusters to high-power ion engines and Hall effect thrusters. The establishment of a community standard on mass flow metering will help ensure the selection of the proper meter for each application. It will also improve the quality of system performance estimates by providing comprehensive information on the physical phenomena and systematic errors that must be accounted for during the analysis of flow measurement data. This paper will outline the standard methods and recommended practices described in the guide titled "Flow Measurement for Electric Propulsion Systems."

spacecraft electric propulsion (EP) systems↗

NASA NTRS2015

Capillary Channel Flow (CCF) EU2-02 on the International Space Station (ISS): An Experimental Investigation of Passive Bubble Separations in an Open Capillary Channel

It would be signicantly easier to design fluid systems for spacecraft if the fluid phases behaved similarly to those on earth. In this research an open 15:8 degree wedge-sectioned channel is employed to separate bubbles from a two-phase flow in a microgravity environment. The bubbles appear to rise in the channel and coalesce with the free surface in much the same way as would bubbles in a terrestrial environment, only the combined effects of surface tension, wetting, and conduit geometry replace the role of buoyancy. The host liquid is drawn along the channel by a pump and noncondensible gas bubbles are injected into it near the channel vertex at the channel inlet. Control parameters include bubble volume, bubble frequency, liquid volumetric flow rate, and channel length. The asymmetrically confined bubbles are driven in the cross-flow direction by capillary forces until they at least become inscribed within the section or until they come in contact with the free surface, whereupon they usually coalesce and leave the flow. The merging of bubbles enhances, but does not guarantee, the latter. The experiments are performed aboard the International Space Station as a subset of the Capillary Channel Flow experiments. The flight hardware is commanded remotely and continuously from ground stations during the tests and an extensive array of experiments is conducted identifying numerous bubble flow regimes and regime transitions depending on the ratio and magnitude of the gas and liquid volumetric flow rates. The breadth of the publicly available experiments is conveyed herein primarily by narrative and by regime maps, where transitions are approximated by simple expressions immediately useful for the purposes of design and deeper analysis.

fluid dynamics↗

NASA NTRS2016

Investigation of Multiphase Flow in a Packed Bed Reactor Under Microgravity Conditions

In this paper we study the two-phase flow phenomena in a packed bed reactor using an integrated experimental and numerical method. The cylindrical bed is filled with uniformly sized spheres. In the experiment water and air are injected into the bed simultaneously. The pressure distribution along the bed will be measured. The numerical simulation is based on a two-phase flow solver which solves the Navier-Stokes equations on Cartesian grids. A novel coupled level set and moment of fluid method is used to construct the interface. A sequential method is used to position spheres in the cylinder. Preliminary experimental results showed that the tested flow rates resulted in pulse flow. The numerical simulation revealed that air bubbles could merge into larger bubbles and also could break up into smaller bubbles to pass through the pores in the bed. Preliminary results showed that flow passed through regions where the porosity is high. Comparison between the experimental and numerical results in terms of pressure distributions at different flow injection rates will be conducted. Comparison of flow phenomena under terrestrial gravity and microgravity will be made.

computational fluid dynamics↗

NASA NTRS2017

Experimental and Numerical Investigation of Air Radiation in Superorbital Expanding Flow

To investigate air radiation in expanding flows and provide experimental data for validating associated computational models, experiments were conducted in the X2 expansion tunnel facility at the Centre for Hypersonics of the University of Queensland. A 54 turning angle wedge model was employed to generate steady expanding flows with in flow total enthalpies of 50.7, 63.4 and 75.4 MJkg. VUV spectra from 118 to 180 nm were acquired across the wedge at three equispaced distances away from the top of the model, as well as through its top surface. High speed filtered images were also obtained by coupling a Shimadzu 1 MHz high speed camera to a bandpass filter to obtain calibrated images of the 777 nm oxygen triplet. Both the across-wedge VUV spectra and filtered images of the 777 nm atomic oxygen were compared with NEQAIR simulations, which were performed using flow field data from two-dimensional CFD simulations with two-temperature 11-species air chemistry utilizing the in-house Navier-Stokes flow solver Eilmer3. Data extracted from consecutive frames of the filtered high speed images confirmed up to 8 s of available test time for the flow conditions tested. For the strongly radiating 149 and 174 nm atomic nitrogen lines, large disagreement between experimental data and NEQAIR predictions can be observed from the start of the expansion fan where the electron-ion recombination process commences. The spatial extent, or spans of the radiance profiles of the 149 and 174 nm N lines are significantly under predicted by NEQAIR, and are very close to those of N, N+ and electron number density profiles, which follow that of flow density. The electron-ion recombination process is proposed as the main reason for these discrepancies. The comparisons between NEQAIR simulations and filtered images of the 777 nm oxygen triplet show good agreement in the post-shock compression region and the start of the expansion fan for the 63.4 MJkg condition, but with up to a factor of three over prediction by NEQAIR further downstream, which is attributed to electron-impact excitation. Similar trends are found with the 75.4 MJkg condition, with reduced level of agreement in the compression region, which can be due to uncertainties in inflow condition.

Earth entry↗

NASA NTRS2017

Experimental and Numerical Investigation of Air Radiation in Superorbital Expanding Flow

To investigate air radiation in expanding flows and provide experimental data for validating associated computational models, experiments were conducted in the X2 expansion tunnel facility at the Centre for Hypersonics of the University of Queensland. A 54deg turning angle wedge model was employed to generate steady expanding flows with in flow total enthalpies of 50.7, 63.4 and 75.4 MJ/kg. VUV spectra from 118 to 180 nm were acquired across the wedge at three equispaced distances away from the top of the model, as well as through its top surface. High speed filtered images were also obtained by coupling a Shimadzu 1 MHz high speed camera to a bandpass filter to obtain calibrated images of the 777 nm oxygen triplet. Both the across-wedge VUV spectra and filtered images of the 777 nm atomic oxygen were compared with NEQAIR simulations, which were performed using flow field data from two-dimensional CFD simulations with two-temperature 11-species air chemistry utilising the in-house Navier-Stokes flow solver Eilmer3. Data extracted from consecutive frames of the filtered high speed images confirmed up to 8 s of available test time for the flow conditions tested. For the strongly radiating 149 and 174 nm atomic nitrogen lines, large disagreement between experimental data and NEQAIR predictions can be observed from the start of the expansion fan where the electron-ion recombination process commences. The spatial extent, or spans of the radiance profiles of the 149 and 174 nm N lines are significantly underpredicted by NEQAIR, and are very close to those of N, N+ and electron number density profiles, which follow that of flow density. The electron-ion recombination process is proposed as the main reason for these discrepancies. The comparisons between NEQAIR simulations and filtered images of the 777 nm oxygen triplet show good agreement in the post-shock compression region and the start of the expansion fan for the 63.4 MJ/kg condition, but with up to a factor of three overprediction by NEQAIR further downstream, which is attributed to electron-impact excitation. Similar trends are found with the 75.4 MJ/kg condition, with reduced level of agreement in the compression region, which can be due to uncertainties in inflow condition.

expansion tube↗

NASA NTRS2016

Flow Boiling and Condensation Experiment (FBCE) for the International Space Station

An effective means to reducing the size and weight of future space vehicles is to replace present mostly single-phase thermal management systems with two-phase counterparts. By capitalizing upon both latent and sensible heat of the coolant rather than sensible heat alone, two-phase thermal management systems can yield orders of magnitude enhancement in flow boiling and condensation heat transfer coefficients. Because the understanding of the influence of microgravity on two-phase flow and heat transfer is quite limited, there is an urgent need for a new experimental microgravity facility to enable investigators to perform long-duration flow boiling and condensation experiments in pursuit of reliable databases, correlations and models. This presentation will discuss recent progress in the development of the Flow Boiling and Condensation Experiment (FBCE) for the International Space Station (ISS) in collaboration between Purdue University and NASA Glenn Research Center. Emphasis will be placed on the design of the flow boiling module and on new flow boiling data that were measured in parabolic flight, along with extensive flow visualization of interfacial features at heat fluxes up to critical heat flux (CHF). Also discussed a theoretical model that will be shown to predict CHF with high accuracy.

flow boiling↗

NASA NTRS2018

Orientation Effects in Two-Phase Microgap Flow

The high power density of emerging electronic devices is driving the transition from remote cooling, which relies on con-duction and spreading, to embedded cooling, which extracts dissipated heat on-site. Two-phase microgap coolers employ the forced flow of dielectric fluids undergoing phase change in a heated channel within or between devices. Such coolers must work reliably in all orientations for a variety of applications (e.g., vehicle-based equipment), as well as in microgravity and high-g for other applications (e.g., spacecraft and aircraft). The lack of acceptable models and correlations for orientation- and gravity-independent operation has limited the use of two-phase coolers in such applications. Previous research has revealed that gravita-tional acceleration plays a diminishing role in establishing flow regimes and transport rates as the channel size shrinks, but there is considerable variation among the proposed microscale criteria and limited research on two-phase flows in low aspect ratio mi-crogap channels. Reliable criteria for achieving orientation- and gravity-independent flow boiling would enable emerging sys-tems to exploit this thermal management technique and streamline the technology development process. As a first step toward understanding the effect of gravity on two-phase microgap flow and transport, in the present effort the authors have studied the effect of evaporator orientation and mass flux on near-saturated flow boiling of HFE7100 in a 1.01 mm tall by 13.0 mm wide by 12.7 mm long microgap channel. Orientation-independence, defined as achieving similar critical heat fluxes, heat transfer coefficients, and flow regimes across evaporator orientations, was achieved for mass fluxes of 400 kg/m2-s and greater. The present results are compared to pub-lished criteria for achieving gravity-independence.

orientation↗

NASA NTRS2019

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D for Axisymmetric Jet Flow

Two full seven-equation turbulence models have been implemented into the FUN3D code to evaluate their ability to improve the computation of challenging flows encountered in aerospace propulsion, including mixing flows. These models are the SSG/LRR and Wilcox full second-moment Reynolds stress models. They solve equations for the six components of the Reynolds stress and a seventh equation for the mixing length. Two standard eddy viscosity models are also evaluated for comparison, the Spalart-Allmaras (SA) one-equation model and the Menter Shear Stress Transport (SST-V) two-equation turbulence model. Flow through an axisymmetric reference nozzle is examined at three flow conditions: subsonic unheated, subsonic heated, and near sonic unheated. Centerline profiles of velocity and turbulent kinetic energy and radial profiles of velocity, turbulent kinetic energy and turbulent stresses are examined. characteristics, no significant changes in the downstream flow behavior compared to the baseline case are observed. Furthermore, the total power consumed by the fans for different incoming flow conditions also remain marginally the same. It is hoped that the results, albeit obtained at very low speeds. would serve as a database for this technologically interesting flow field that has not been explored adequately before.

computational fluid dynamics↗

DOE OSTI2024

The Onset of Nucleate Boiling Prediction in a Mini Channel with the Eulerian Multiphase Flow

The prediction of boiling incipience is a critical issue for a reactor. Vapor lock causes operating instability and undesirable temperature rise, especially for small channels. This study uses the Eulerian multiphase flow boiling model to predict the onset of nucleate boiling in a millimeter scale rectangular channel. Two wall boiling models, namely the RPI (Rensselaer Polytechnic Institute) and the non-equilibrium sub cooled model are applied. Computational fluid dynamics is employed for this study to investigate the impact of operating conditions like liquid flow rate, operating pressure, heat flux, velocity profile, turbulence model, and inlet liquid temperature. Here, the effect of fundamental boiling parameters on the surface wall temperature and vapor volume fraction is also studied. The parameters under consideration are the bubble departure diameter, bubble departure frequency, nucleate site density, quenching time period, and interface heat transfer coefficients. A series of CFD calculations is conducted by varying the considered variables systematically in a wide range of flow conditions covering laminar, transition, and turbulent flows. The sub-component heat fluxes like the liquid convective, the vapor convective, the evaporative, and the quenching terms are monitored to infer the boiling dynamics in the transition region from the single-phase flow to the nucleate boiling zone. It is found that the CFD approach to detecting the boiling incipience point agrees reasonably with available experimental data. However, its limitations, like inaccuracy for lower flow rates and early transition to boiling flow, are also noticed due to the nature of the considered RPI model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Modeling and simulation of transitional Rayleigh–Taylor flow with partially averaged Navier–Stokes equations

In this work, the partially averaged Navier–Stokes (PANS) equations are used to predict the variable-density Rayleigh–Taylor (RT) flow at Atwood number 0.5 and maximum Reynolds number 500. This is a prototypical problem of material mixing, featuring laminar, transitional, and turbulent flow, instabilities and coherent structures, density fluctuations, and production of turbulence kinetic energy by both shear and buoyancy mechanisms. These features pose numerous challenges to modeling and simulation, making the RT flow ideal to develop the validation space of the recently proposed PANS Besnard–Harlow–Rauenzahn-linear eddy viscosity model closure. The numerical simulations are conducted at different levels of physical resolution and test three approaches to set the parameters $f_\phi$ defining the range of physically resolved scales. The computations demonstrate the efficiency (accuracy vs cost) of the PANS model predicting the spatiotemporal development of the RT flow. Results comparable to large-eddy simulations and direct numerical simulations are obtained at significantly lower physical resolution without the limitations of the Reynolds-averaged Navier–Stokes equations in these transitional flows. The data also illustrate the importance of appropriate selection of the physical resolution and the resolved fraction of each dependent quantity $\phi$ of the turbulent closure, $f_\phi$. These two aspects determine the ability of the model to resolve the flow phenomena not amenable to modeling by the closure and, as such, the computations’ fidelity.

Navier Stokes equations↗

DOE OSTI2025

Effect of nozzle translation on a bounded vortex flow

A bounded vortex flow is generated by a nozzle that combines azimuthally tilted downward jets in a circular array and a central suction port. When the nozzle is directed toward a bottom surface (called the impingement surface), the flow develops a strong intake vortex spanning from the impingement surface to the suction port, which acts to generate strong shear stress on the impingement surface. This strong shear stress can aid in removing particles attached to the impingement surface or in enhancement of heat or mass transfer, where in typical applications, the nozzle would be translated along the impingement surface. This paper reports on a computational study of the effect of nozzle translation on the bounded vortex flow field. The nozzle translation induces a bending of the bounded vortex in the downstream flow direction, which becomes larger with increase in the nozzle translation speed. We identify an interesting oscillatory phenomenon by which the bounded vortex can resist the bending induced by the translational flow and rotate about a mean position downstream of the suction port. At sufficiently high translation speeds, the oscillatory process can no longer resist the downwash effect from nozzle translation and the vortex eventually detaches from the impingement surface, limiting the effectiveness of this flow device.

42 ENGINEERING↗