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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Bubble Generation in a Flowing Liquid Medium and Resulting Two-Phase Flow in Microgravity

An experimental and theoretical research program is described herein to study bubble generation in a liquid flow in a pipe under reduced gravity conditions. The objective of the work is to study the bubble size and frequency of the generation and the resulting two-phase flow but it also concerns the fluid mechanical aspects of boiling in forced flow in microgravity. By injecting a gas into a liquid flow in a pipe through a small hole in the pipe wall we will investigate how the bubble expands and detaches from the wall, without involving the complexities of boiling. The experiments will be conducted both under isothermal conditions and with heat transfer from the wall. In the experiments with heat transfer the effect of thermocapillarity on the bubble formation and detachment will be the main subject.

Kamotani, Yasuhiro↗
NASA NTRSDate not supplied

Development and Validation of Two-Phase CFD Models for Key Elements of Propellant Tank CFM Operations in 1G and Microgravity – An Overview

This paper presents an overview of the state-of-the-art two-phase CFD models that have been developed for various propellant tank storage and transfer operations in 1g, partial gravity and microgravity. The models are developed in the framework of the industry standard ANSYS/Fluent CFD code, the capabilities of which have been significantly enhanced and customized through incorporation of unique submodels via User Defined Functions (UDF)s to satisfy the requirements of its intended variable gravity Cryogenic Fluid Management (CFM) applications. These models/submodels have been validated against experimental data that cross spatial scales, fluid types, and gravity levels in order to properly anchor the models’ physical and numerical fidelity. The CFM application/processes that have been modeled include tank self-pressurization, tank autogenous pressurization, tank pressure control using both subcooled jet mixing and droplet spray injection mechanisms, tank chilldown/filling, tank drainage, tank slosh for both volatile and non-volatile fluids. The strength and shortcomings of the two-phase models for each application is highlighted and discussed briefly.

Propellant Storage & Pressure Control↗
NASA NTRSDate not supplied

Development and Validation of Two-Phase CFD Models for Key Elements of Propellant Tank CFM Operations in 1G and Microgravity –An Overview

This paper presents an overview of the state-of-the-art two-phase CFD models that have been developed for various propellant tank storage and transfer operations in 1g, partial gravity, and microgravity. The models are developed in the framework of the industry standard ANSYS/Fluent CFD code, the capabilities of which have been significantly enhanced and customized through the incorporation of unique submodels via User Defined Functions (UDF)s to satisfy the requirements of its intended variable gravity Cryogenic Fluid Management (CFM) applications. These models/submodels have been validated against experimental data that cross spatial scales, fluid types, and gravity levels in order to properly anchor the models’ physical and numerical fidelity. The CFM application/processes that have been modeled include tank self-pressurization, tank autogenous pressurization, tank pressure control using both subcooled jet mixing and droplet spray injection mechanisms, tank chilldown/filling, tank drainage, tank slosh for both volatile and non-volatile fluids. The strength and shortcomings of the two-phase models for each application are highlighted and discussed briefly.

Computational Fluid Dynamics↗
NASA NTRS1992

Effect of vaporization on cryogenic spray dropsize measurement

The fluid mechanics of multi-phase flow breakup of liquid nitrogen, LN2, jets injected into sonic velocity nitrogen gasflow, was experimentally investigated. A scattered-light scanning instrument was used to measure the characteristic dropsize, D(sub v.5), of LN2 sprays and to determine the effect of droplet vaporization on experimental dropsize measurements. Under sonic gas-velocity conditions, liquid-jet breakup occurred in the regime of aerodynamic stripping. As a result, the following correlation of volume-median drop diameter, D(sub v.5), with atomizing gas flowrate, W(sub g), was derived for two-fluid atomizers; with atomizing gas flowrate, W(sub g), was derived for two-fluid atomizers; (D(sub v.5))(exp -1) = k(sub c)(W(sub g))(sup n), where proportionally constant k(sub c) and exponent n are functions of droplet vaporization rate. Partially vaporized sprays were investigated and it was found that n = 1.11, which is considerably less than the value of 1.33 that is predicted by atomization theory. This was attributed to the evaporative loss of very small droplets. As a result, the following expression was obtained experimentally: (D(sub v.5e))(exp -1) = 301(W(sub g))(sup 1.11). Values of D(sub v.5), that existed prior to partial vaporization of the LN2 sprays, were calculated and the following expression was derived for originally unvaporized LN2 sprays: (D(sub v.5))(exp -1) = 285(W(sub g))(sup 1.33). This expression agrees well with atomization theory that predicts n = 1.33, for liquid jet breakup in high-velocity gasflow.

Ingebo, Robert D.↗
NASA NTRS1993

Effect of vaporization on cryogenic spray dropsize measurement

The fluid mechanics of multi-phase flow breakup of liquid nitrogen, LN2, jets injected into sonic velocity nitrogen gasflow, was experimentally investigated. A scattered-light scanning instrument was used to measure the characteristic dropsize, D(sub v.5), of LN2 sprays and to determine the effect of droplet vaporization on experimental dropsize measurements. Under sonic gas-velocity conditions, liquid-jet breakup occurred in the regime of aerodynamic stripping. As a result, the following correlation of volume-median drop diameter, D(sub v.5), with atomizing gas flowrate, W(sub g), was derived for two-fluid atomizers: (D(sub v.5)) (exp -1) = k(sub c) (W(sub g)) (sup n), where proportionally constant k(sub c) and exponent n are functions of droplet vaporization rate. Partially vaporized sprays were investigated and it was found that n = 1.11, which is considerably less than the value of 1.33 that is predicted by atomization theory. This was attributed to the evaporative loss of very small droplets. As a result, the following expression was obtained experimentally: (D(sub v.5e)) (exp -1) = 301 (W(sub g)) (sub 1.11). Values of D(sub v.5), that existed prior to partial vaporization of the LN2 sprays, were calculated and the following expression was derived for originally unvaporized LN2 sprays: (D(sub v.5)) (exp -1) = 285 (W(sub g)) (sub 1.33). This expression agrees well with atomization theory that predicts n = 1.33, for liquid jet breakup in high-velocity gasflow.

Ingebo, Robert D.↗
NASA NTRS1976

Turbulent boundary layer on a full-coverage film-cooled surface: An experimental heat transfer study with normal injection

Heat transfer behavior was studied in a turbulent boundary layer with full-coverage film cooling through an array of discrete holes and with injection normal to the wall surface. Stanton numbers were measured for a staggered hole pattern with pitch-to-diameter ratios of 5 and 10, an injection mass flux ratio range of 0.1 to 1.0, and a range of Reynolds number 170 thousand to 5 million. Air was used as the working fluid with the mainstream velocity varied from .14 to 33.5 m/sec (30 to 110 ft/sec). The data were taken for secondary injection temperatures equal to the wall temperature and also equal to the mainstream temperature. By use of linear superposition theory, the data may be used to obtain Stanton number as a continuous function of the injectant temperature. The heat transfer coefficient is defined on the basis of a mainstream-to-wall temperature difference. This difinition permits direct comparison of performance between film cooling and transpiration cooling.

Choe, H.↗
NASA NTRS2004

Injection Induced Mixing in Flows Separating From Smooth Surfaces

An analytic model for predicting the effect of unsteady local surface injection on the flow separating from a streamlined body at angle of attack is proposed. The model uses the premise that separation control results from enhanced mixing along the shear layer that develops between the main stream and the fluid in the underlying recirculation zone. High-Reynolds-number asymptotic methods are used to connect the unsteady surface injection to an instability wave propagating on the separating shear layer and then to the large-scale coherent structures that produce the increased mixing. The results is a tool that can guide the choice of fluid-actuator parameters to maximize flow-control effectiveness and may also facilitate computer-based numerical experiments.

Adamczyk, John J.↗
NASA NTRS1991

An experimental trace gas investigation of fluid transport and mixing in a circular-to-rectangular transition duct

An ethylene trace gas technique was used to map out fluid transport and mixing within a circular to rectangular transition duct. Ethylene gas was injected at several points in a cross stream plane upstream of the transition duct. Ethylene concentration contours were determined at several cross stream measurement planes spaced axially within the duct. The flow involved a uniform inlet flow at a Mach number level of 0.5. Statistical analyses were used to quantitatively interpret the trace gas results. Also, trace gas data were considered along with aerodynamic and surface flow visualization results to ascertain transition duct flow phenomena. Convection of wall boundary layer fluid by vortices produced regions of high total pressure loss in the duct. The physical extent of these high loss regions is governed by turbulent diffusion.

Reichert, B. A.↗
NASA NTRS1993

SWIRL as a means of liquid management in low gravity

Swirling of a liquid in a container may prove to be a more desirable method of managing liquids in low gravity (space) environments than by rotating the entire container. By injecting a relatively high velocity liquid tangentially into the body of the fluid, swirl can best be started rapidly, however an estimate of the quantity and velocity of jetflow, or mechanical power of a pump impeller required to maintain a given radial acceleration (G force) is needed to assess the feasibility of such a method. While the key aspect of the problem is determining the rate of rotational energy dissipation by wall friction in the container, there are other considerations, and the present study investigates the possible additional effects of axial variation of tangential velocity and secondary (radial and axial) flow components within the rotating fluid.

Steward, W. Gene↗
NASA NTRS2016

Flow Characterization Studies of the 10-MW TP3 Arc-Jet Facility: Probe Sweeps

This paper reports computational simulations and analysis in support of calibration and flow characterization tests in a high enthalpy arc-jet facility at NASA Ames Research Center. These tests were conducted in the NASA Ames 10-MW TP3 facility using flat-faced stagnation calorimeters at six conditions corresponding to the steps of a simulated flight heating profile. Data were obtained using a conical nozzle test configuration in which the models were placed in a free jet downstream of the nozzle. Experimental surveys of arc-jet test flow with pitot pressure and heat flux probes were also performed at these arc-heater conditions, providing assessment of the flow uniformity and valuable data for the flow characterization. Two different sets of pitot pressure and heat probes were used: 9.1-mm sphere-cone probes (nose radius of 4.57 mm or 0.18 in) with null-point heat flux gages, and 15.9-mm (0.625 in) diameter hemisphere probes with Gardon gages. The probe survey data clearly show that the test flow in the TP3 facility is not uniform at most conditions (not even axisymmetric at some conditions), and the extent of non-uniformity is highly dependent on various arc-jet parameters such as arc current, mass flow rate, and the amount of cold-gas injection at the arc-heater plenum. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle and test box, including the models tested. Comparisons of computations with the experimental measurements show reasonably good agreement except at the extreme low pressure conditions of the facility envelope.

Goekcen, Tahir↗
NASA NTRS2016

Flow Characterization Studies of the 10-MW TP3 Arc-Jet Facility: Probe Sweeps

This paper reports computational simulations and analysis in support of calibration and flow characterization tests in a high enthalpy arc-jet facility at NASA Ames Research Center. These tests were conducted in the NASA Ames 10-MW TP3 facility using flat-faced stagnation calorimeters at six conditions corresponding to the steps of a simulated flight heating profile. Data were obtained using a conical nozzle test configuration in which the models were placed in a free jet downstream of the nozzle. Experimental surveys of arc-jet test flow with pitot pressure and heat flux probes were also performed at these arc-heater conditions, providing assessment of the flow uniformity and valuable data for the flow characterization. Two different sets of pitot pressure and heat probes were used: 9.1-mm sphere-cone probes (nose radius of 4.57 mm or 0.18 in) with null-point heat flux gages, and 15.9-mm (0.625 in) diameter hemisphere probes with Gardon gages. The probe survey data clearly show that the test flow in the TP3 facility is not uniform at most conditions (not even axisymmetric at some conditions), and the extent of non-uniformity is highly dependent on various arc-jet parameters such as arc current, mass flow rate, and the amount of cold-gas injection at the arc-heater plenum. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle and test box, including the models tested. Comparisons of computations with the experimental measurements show reasonably good agreement except at the extreme low pressure conditions of the facility envelope.

CFD↗
NASA NTRS1961

On the Induced Flow of an Electrically Conducting Liquid in a Rectangular Duct by Electric and Magnetic Fields of Finite Extent

Reported here are the results of a systematic study of a model of the direct-current electromagnetic pump. Of particular interest is the motion imparted to the electrically conducting fluid in the rectangular duct by the body forces that result from applied electric and magnetic fields. The purpose of the investigation is to associate the observed fluid motion with the characteristics of the electric and magnetic fields which cause them. The experiments were carried out with electromagnetic fields that moved a stream of copper sulphate solution through a clear plastic channel. Ink filaments injected into the stream ahead of the region where the fields were applied identify the motion of the fluid elements as they passed through the test channel. Several magnetic field configurations were employed with a two-dimensional electric current distribution in order to study and identify the magnitude of some of the effects on the fluid motion brought about by nonuniformities in the electromagnetic fields. A theoretical analysis was used to guide and evaluate the identification of the several fluid motions observed. The agreement of the experimental data with the theoretical predictions is satisfactory. It is found that sizable variations in the velocity profile and pressure head of the output stream are produced by the shape of the electric and magnetic fields.

Rossow, Vernon J.↗
NASA NTRS2003

Mixing and Transport in the Solar Nebula

Boss & Vanhala (2000, 2001) prepared reviews of triggered collapse and injection models, using Prudence Foster's finite differences code at very high spatial resolution (440 x 1440 cells) to demonstrate the convergence of the R-T fingers in triggered injection models. A two dimensional hydrodynamical calculation with unprecedentedly high spatial resolution (960 x 2880 zones, or almost 3 million grid points) demonstrated that it suitable shock front can both trigger the collapse of an otherwise stable presolar cloud, and inject shock front particles into the collapsing cloud through the formation of what become Rayleigh-Taylor fingers of compressed fluid layers falling into the gravitational potential well of the growing protostar. These calculations suggest that heterogeneity derived from these R-T fingers will persist down to the scale of their injection onto the surface of the solar nebula. Haghighipour developed a numerical code capable of calculating the orbital evolution of dust grains of varied sizes in a gaseous nebula, subject to Epstein and Stokes drag as well as the self-gravity of the disk. In collaboration with the PI and George W. Wetherill, Haghighipour has been involved in development of a new idea on the possibility of rapid formation of ice giant planets via the disk instability mechanism. Haghighipour studied the stability of a five-body system consisting of the Sun and four protoplanets by numerically integrating their equations of motions. Using Levison and Duncan s SWIFT integrator, Haghighipour showed that, depending on the orbital parameters of the bodies, such a system can be stable for 0.1-10 Myr. Time periods of 1 Myr or more are long enough to be consistent with the time scale proposed for the formation of giant planets by the disk instability mechanism and the photoevaporation of the gaseous envelopes of the outermost protoplanets by a nearby OB star, resulting in the formation of ice giant planets. The PI has used his three dimensional models of marginally gravitationally unstable disks to study the preservation of isotopic heterogeneity in evolving protoplanetary disks. Such heterogeneity might arise from the infall onto the disk s surface of solids processed in the X-wind region of the disk, or derived from stellar nucleosynthesis and injected by R-T fingers. The technique used consists of solving a color equation, identical to the gas continuity equation, which follows the time evolution in three space dimensions of an arbitrarily placed initial color field, i.e., a dye inserted the disk. The models show that significant concentrations of color could persist for time periods of about a thousand years or more, even in the most dynamically active region of such a disk. Such a time period might be long enough for solids to coagulate and grow to significant sizes while retaining the isotopic signature of their birth region in the nebula.

Boss, Alan P.↗
NASA NTRS1996

Analysis of Supercritical-Extracted Chelated Metal Ions From Mixed Organic-Inorganic Samples

Organic and inorganic contaminants of an environmental sample are analyzed by the same GC-MS instrument by adding an oxidizing agent to the sample to oxidize metal or metal compounds to form metal ions. The metal ions are converted to chelate complexes and the chelate complexes are extracted into a supercritical fluid such as CO2. The metal chelate extract after flowing through a restrictor tube is directly injected into the ionization chamber of a mass spectrometer, preferably containing a refractory metal filament such as rhenium to fragment the complex to release metal ions which are detected. This provides a fast, economical method for the analysis of metal contaminants in a sample and can be automated. An organic extract of the sample in conventional or supercritical fluid solvents can be detected in the same mass spectrometer, preferably after separation in a supercritical fluid chromatograph.

Sinha, Mahadeva P.↗
NASA NTRS1999

Experimental Investigation of Pool Boiling Heat Transfer Enhancement in Microgravity in the Presence of Electric Fields

In boiling high heat fluxes are possible driven by relatively small temperature differences, which make its use increasingly attractive in aerospace applications. The objective of the research is to develop ways to overcome specific problems associated with boiling in the low gravity environment by substituting the buoyancy force with the electric force to enhance bubble removal from the heated surface. Previous studies indicate that in terrestrial applications nucleate boiling heat transfer can be increased by a factor of 50, as compared to values obtained for the same system without electric fields. The goal of our research is to experimentally explore the mechanisms responsible for EHD heat transfer enhancement in boiling in low gravity conditions, by visualizing the temperature distributions in the vicinity of the heated surface and around the bubble during boiling using real-time holographic interferometry (HI) combined with high-speed cinematography. In the first phase of the project the influence of the electric field on a single bubble is investigated. Pool boiling is simulated by injecting a single bubble through a nozzle into the subcooled liquid or into the thermal boundary layer developed along the flat heater surface. Since the exact location of bubble formation is known, the optical equipment can be aligned and focused accurately, which is an essential requirement for precision measurements of bubble shape, size and deformation, as well as the visualization of temperature fields by HI. The size of the bubble and the frequency of bubble departure can be controlled by suitable selection of nozzle diameter and mass flow rate of vapor. In this approach effects due to the presence of the electric field can be separated from effects caused by the temperature gradients in the thermal boundary layer. The influence of the thermal boundary layer can be investigated after activating the heater at a later stage of the research. For the visualization experiments a test cell was developed. All four vertical walls of the test cell are transparent, and they allow transillumination with laser light for visualization experiments by HI. The bottom electrode is a copper cylinder, which is electrically grounded. The copper block is heated with a resistive heater and it is equipped with 6 thermocouples that provide reference temperatures for the measurements with HI. The top electrode is a mesh electrode. Bubbles are injected with a syringe into the test cell through the bottom electrode. The working fluids presently used in the interferometric visualization experiments, water and PF 5052, satisfy requirements regarding thermophysical, optical and electrical properties. A 30kV power supply equipped with a voltmeter allows to apply the electric field to the electrodes during the experiments. The magnitude of the applied voltage can be adjusted either manually or through the LabVIEW data acquisition and control system connected to a PC. Temperatures of the heated block are recorded using type-T thermocouples, whose output is read by a data acquisition system. Images of the bubbles are recorded with 35mm photographic and 16mm high-speed cameras, scanned and analyzed using various software packages. Visualized temperature fields HI allows the visualization of temperature fields in the vicinity of bubbles during boiling in the form of fringes. Typical visualized temperature distributions around the air bubbles injected into the thermal boundary layer in PF5052 are shown. The temperature of the heated surface is 35 C. The temperature difference for a pair of fringes is approximately 0.05 C. The heat flux applied to the bottom surface is moderate, and the fringe patterns are regular. In the image a bubble penetrating the thermal boundary layer is visible. Because of the axial symmetry of the problem, simplified reconstruction techniques can be applied to recover the temperature field. The thermal plume developing above the heated surface for more intensive heating is shown. The temperature distribution in the liquid is clearly 3D, and tomographic techniques have to be applied to recover the temperature distribution in such a physical situation. A sequence of interferometric images showing the temperature distribution around the rising bubble, recorded with a high-speed camera is shown. Again, the temperature distribution is 3D, and a more complex approach to the evaluation, the tomographic reconstruction has to be taken. Measurement of the temperature distribution from the fringe pattern temperature distributions that yield important information regarding heat transfer are determined. Two algorithms that allow the quantitative evaluation of interferometric fringe patterns and the reconstruction of temperature fields during boiling have been developed at the Heat Transfer Laboratory of the Johns Hopkins University. In the first algorithm the bubble is assumed to be axially symmetrical, which significantly reduces the computational effort for quantifying the temperature distribution around the bubble. For this purpose the thermal boundary layer around the bubble is divided into equidistant concentric shells, and the refractive index is assumed to be constant in each of the shells. Since large temperature gradients are expected in the vicinity of the bubble during boiling, the deflection of the light beam cannot be neglected in boiling experiments. Since the exit angle of the light beam is known, this allows to account for the deflections and phase shifts outside the boundary layer (in the bulk fluid and in the windows of the test cell). Three dimensional temperature distributions in the vicinity of the bubble are reconstructed using tomographic techniques. In tomography, the measurement volume is sliced into 2D planes. In the present study these planes are parallel to the heated surface. The objective is to determine the values of the field parameter of interest in form of the field function in these 2D planes. The field parameter is the change of the refractive index of the liquid in the measurement volume caused by temperature changes. By superimposing data for many 2D planes recorded at the same time instant, the 3D temperature distribution in the measurement volume is recovered.

Herman, Cila↗
NASA NTRS1996

Fluid Dynamic Verification Experiments on STS-70

Fluid dynamic experiments were flown on STS-70 as phase two of the engineering evaluation of the first bioreactor Engineering Development Unit (EDU#1). The phase one experiments were comparative cell cultures in identical units on earth and onboard STS-70. In phase two, two types of fluid dynamic experiments were performed. Qualitative comparisons of the basic flow patterns were evaluated with the use of 'dye' streaklines formed from alternate injections of either a mild acid or base solution into the external flow loop that was then perfused into the vessel. The presence of Bromothymol Blue in the fluid then caused color changes from yellow to blue or vice versa, indicating the basic fluid motions. This reversible change could be repeated as desired. In the absence of significant density differences in the fluid, the flow patterns in space should be the same as on earth. Video tape records of the flow patterns for a wide range of operating conditions were obtained. The second type of fluid dynamic experiment was the quantitative evaluation of the trajectories of solid beads of various densities and sizes. The beads were introduced into the vessel and the paths recorded on video tape, with the vessel operated at various rotation rates and flow perfusion rates. Because of space limitations, the video camera was placed as close as possible to the vessel, resulting in significant optical distortion. This report describes the analysis methods to obtain comparisons between the in-flight fluid dynamics and numerical models of the flow field. The methods include optical corrections to the video images and calculation of the bead trajectories for given operating conditions and initial bead locations.

Kleis, Stanley J.↗
NASA NTRSDate not supplied

Numerical Prediction of Heat Transfer Coefficients during Xenon Tank Fill in Microgravity

NASA’s Gateway will serve as an orbital outpost to enable sustained human lunar exploration and facilitate access to destinations beyond the Moon. To maintain sustainable deep space missions, on-orbit propellant transfer and refueling must be realized. One of Gateway’s critical components, the Power and Propulsion Element (PPE), will use solar electric propulsion to perform attitude control maneuvers and orbit transfers. Xenon will be used as the propellant for the PPE and stored in a composite overwrapped pressure vessel (COPV). During the propellant refueling process, xenon will compress causing the fluid and tank walls to warm. There is concern that the bond between the tank liner and composite may degrade at elevated temperatures, along with the possibility of the tank exceeding design pressure. While on-orbit testing is being proposed, numerical models are being used to predict the thermal response and reduce risk during a refueling operation in microgravity where natural convection is diminished. Accurate numerical models may be used to inform decisions for follow-on testing, or design and operation of refueling architectures. Challenges of modeling xenon tank fill in microgravity include non-ideal gas behavior, operating near the fluid’s critical point, and lack of experimental flight data. This study presents a computational fluid dynamics (CFD) model with conjugate heat transfer that is used to predict averaged heat transfer coefficients during tank filling. At the anticipated injection flow rates, the CFD results showed that forced convection dominates in microgravity. Initial results from a multi-node Thermal Desktop model that assumed a purely conducting fluid (Nu=1) over-predicted the CFD fluid temperature and pressure, while a similar model allowing for natural convection under-predicted. The heat transfer coefficients predicted by CFD were implemented into the multi-node model, and the COPV thermal response from the two computational approaches were compared with good agreement.

Heat Transfer↗
NASA NTRS1991

An experimental trace gas investigation of fluid transport and mixing in a circular-to-rectangular transition duct

An ethylene trace gas technique was used to map out fluid transport and mixing within a circular-to-rectangular transition duct. Ethylene gas was injected at several points in a cross stream plane upstream of the transition duct. Ethylene concentration contours were determined at several cross stream measurement planes spaced axially within the duct. The flow involved a uniform inlet flow at a Mach number level of 0.5. Statistical analyses were used to quantitatively interpret the trace gas results. Also, trace gas data were considered along with aerodynamic and surface flow visualization results to ascertain transition duct flow phenomena. Convection of wall boundary layer fluid by vortices produced regions of high total pressure loss in the duct. The physical extent of these high loss regions is governed by turbulent diffusion.

Reichert, B. A.↗