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All sourcesNASA NTRSDOE OSTI
NASA NTRS1934

On the theory of laminar boundary layers involving separation

This paper presents a mathematical discussion of the laminar boundary layer, which was developed with a view of facilitating the investigation of those boundary layers in particular for which the phenomenon of separation occurs. The treatment starts with a slight modification of the form of the boundary layer equation first published by Von Mises. Two approximate solutions of this equation are found, one of which is exact at the outer edge of the boundary layer while the other is exact at the wall. The final solution is obtained by joining these two solutions at the inflection points of the velocity profiles. The final solution is given in terms of a series of universal functions for a fairly broad class of potential velocity distributions outside of the boundary layer. Detailed calculations of the boundary layer characteristics are worked out for the case in which the potential velocity is a linear function of the distance from the upstream stagnation point. Finally, the complete separation point characteristics are determined for the boundary layer associated with a potential velocity distribution made up of two linear functions of the distance from the stagnation point. It appears that extensions of the detailed calculations to more complex potential flows can be fairly easily carried out by using the explicit formulae given in the paper. (author)

Von Karman, TH↗
NASA NTRS1936

General instability criterion of laminar velocity distributions

The present paper describes the results of a stability investigation on symmetrical velocity profiles in a channel and of boundary-layer profiles. The effect of friction was assumed to be vanishing and did not occur in the stability consideration so far as it had been resorted to for preparatory asymptotic considerations. Proceeding on very general premises as regards the form of the velocity distribution, a proof was deduced of the elementary theorem that velocity profiles with inflection points are unstable.

Tollmien, W↗
NASA NTRS1993

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Constantinides, E. D.↗
NASA NTRS1994

Crossflow instability control on a swept-wing: Preliminary studies

The pressure distribution on a swept wing causes the streamlines at the edge of the boundary layer to be curved. This pressure gradient normal to the external streamline creates a velocity component normal to the external streamline within the boundary layer which is referred to as the crossflow velocity. Because the crossflow velocity profile perpendicular to the wing surface has an inflection point, the profile is unstable. The stationary instability mode takes the form of crossflow vortices. Under these conditions, the boundary layer on the wing is extremely unstable and transition to turbulent flow takes place much closer to the leading edge of the wing than it would on an unswept wing. Higher skin friction drag is associated with turbulent flow, and so better aircraft performance could be obtained if the crossflow could be eliminated One method of controlling crossflow that is being investigated is boundary-layer suction. An extensive airfoil suction experiment in the 8 feet Transonic Pressure Tunnel (TPT) at NASA Langley Research Center will begin late in 1994. Because of the size, complexity, and expense associated with this test, a number of 'risk-reduction' tests are currently being conducted. The 20 x 28 in. Shear Flow Control Tunnel at NASA Langley is being used for some of these tests. Prior to the summer of 1994, a flat plate with a swept leading edge was installed in the 20 x 28 in. tunnel, with a displacement body mounted on the tunnel ceiling that created a pressure distribution on the plate similar to the pressure distribution on a swept wing. The flow over the plate was investigated during the summer of 1994 using a laser Doppler velocimeter (LDV) system. The LDV measurements indicated the possible presence of multiple disturbance modes, a rarely-seen phenomena since, in most tests, one disturbance mode dominates. The possible existence of multiple disturbance modes in the flat plate boundary layer, however, means that the flow in the 20 x 28 in. tunnel is of interest itself, and will be investigated more thoroughly in the future. With a view to these investigations, the boundary layer traverse mechanism in the 20 x 28 in. tunnel was modified to improve its performance, and strain gauges were mounted on the traverse in order to monitor its deflection during a test. Other preliminary work conducted in the 20 x 28 in. tunnel included the use of an infrared camera system. Previous work with this system showed that transition indeed could be detected, but the signal produced by the crossflow vortices was too weak to be detected. It was hoped that spraying the flat plate with naphthalene would augment the heat transfer associated with the crossflow vortices so that they would show up in a IR image; however, experiments showed that this would not work. Another set of tests was conducted in the 20 x 28 in. tunnel to determine the tripping requirements for a set of airfoil-shaped struts that will be used in the 8 feet TPT experiment. Since the Reynolds number associated with these struts is small, a laminar boundary layer would separate early, causing large fluctuations in the flow field. A turbulent boundary layer would remain attached further back, but tripping from laminar to turbulent flow at low Reynolds number is very difficult. However, trip strip configurations were found that should effectively trip the boundary layer at the required conditions. Currently underway is an investigation of the data acquisition requirements for the 8 feet TPT experiment, with the purpose of the finding the minimum amount of data needed to characterize sufficiently the swept-wing boundary layer. This study is being conducted using a numerically generated data set.

Bridges, David H.↗
NASA NTRS1994

Effect of density gradients in confined supersonic shear layers, part 1

The effect of density gradients on the supersonic wall modes (acoustic modes) of a 2-D confined compressible shear layer were investigated using linear analysis. Due to the inadequacies of the hyperbolic tangent profile, the boundary layer basic profiles were used. First a test case was taken with the same parameters as in Tam and Hu's analysis with convective Mach number M(sub c) = 1.836 and density ratio of 1.398. Three generalized inflection points were found giving rise to three modes. The first two show similar properties to the Class A and B modes, and the third is an 'inner mode' which will be called a Class C mode. As the density ratio is increased, the smallest of the three neutral phase speeds tends towards the speed of the lower velocity stream, and the other two eventually coalesce and then disappear. These two effects lead to a linear resonance between the Class B modes which increases the cutoff frequency and growth rate of the lowest mode. In fact, growth rates of 2-4 times the test case were found as the density ratio was increased to 7. A similar trend is observed for the Class A modes when the density ratio is decreased from the test case, but the growth rate is not changed by much from the test case.

Peroomian, Oshin↗
NASA NTRS1995

Meso-beta scale numerical simulation studies of terrain-induced jet streak mass/momentum perturbations

Mesoscale model simulations provide insight into the complex jet streak adjustments on 11-12 July 1981 that preceded the first of two significant gravity wave events to have been generated over the Rocky Mountains in Montana. Simulations employing a variety of terrain treatments indicate that prior to wave formation, geostrophic adjustment processes modified the structure of the mid-upper tropospheric jet streak by creating secondary jetlets to the southeast of the polar jet streak in proximity to the gravity wave generation region. This simulated restructuring of the mid-upper tropospheric jet streak is the result of a four stage process. During stage 1, the wind adjusts to the mass field as the jet streak exit region propagates into the inflection point between the upstream trough and downstream ridge in the height field. Stage 2 is initiated as the mass field is forced to adjust to the new ageostrophic wind field created during stage 1. Stage 3 is defined by a second geostrophic adjustment process occurring in a similar manner but to the south and east of the adjustment which occurs during stage 1. A low-level mesoscale jetlet is formed during stage 4 in response to the low-level pressure falls that are established during stage 3. The perturbation of this jetlet, caused by orographically-induced adiabatic and diabatic physical processes, is the likely mechanism responsible for the generation of the first and second episode of observed gravity waves. The dynamics responsible for this wave episode are discussed as differential surface sensible heating inducing an orographically-forced mountain-plains solenoid, resulting in the formation of additional mesoscale jetlets and internal gravity waves. Also discussed is how convective latent heating modifies the numerically simulated terrain-induced internal gravity waves, especially their amplitude and phase velocities, which provide better agreement with those wave characteristics observed in nature. Finally, the three-dimensional linear response of a zonally uniform barotropic flow in a vertically unbounded, continuously stratified, Boussinesq atmosphere which is perturbed from geostrophic equilibrium is investigated.

Lin, Yuh-Lang↗
NASA NTRS1995

Measuring Q And f(sub r) Of A Microwave Cavity: Part I

Method of measuring quality factor (Q) and frequency of resonance (f(subr)) of microwave cavity exploits two inflection points of power-vs.-frequency resonance curve of cavity. Intended particularly for use with microwave cavity in which sample of lossy dielectric material heated to specified high temperature by microwave power at resonant frequency. Accurate measurement contributes to enhanced monitoring and control in contactless high-temperature processing of materials. Also used with small spherical sample to determine temperature dependence of complex dielectric constant.

Barmatz, Martin B.↗
NASA NTRS1995

An experimental investigation of flow-induced oscillations of the Bruel and Kjaer in-flow microphone

One source contributing to wind tunnel background noise is microphone self-noise. An experiment was conducted to investigate the flow-induced acoustic oscillations of Bruel & Kjaer (B&K) in-flow microphones. The results strongly suggest the B&K microphone cavity behaves more like an open cavity. Their cavity acoustic oscillations are likely caused by strong interactions between the cavity shear layer and the cavity trailing edge. But the results also suggest that cavity shear layer oscillations could be coupled with cavity acoustic resonance to generate tones. Detailed flow velocity measurements over the cavity screen have shown inflection points in the mean velocity profiles and high disturbance and spectral intensities in the vicinity of the cavity trailing edge. These results are the evidence for strong interactions between cavity shear layer oscillations and the cavity trailing edge. They also suggest that beside acoustic signals, the microphone inside the cavity has likely recorded hydrodynamic pressure oscillations, too. The results also suggest that the forebody shape does not have a direct effect on cavity oscillations. For the FITE (Flow Induced Tone Eliminator) microphone, it is probably the forebody length and the resulting boundary layer turbulence that have made it work. Turbulence might have thickened the boundary layer at the separation point, weakened the shear layer vortices, or lifted them to miss impinging on the cavity trailing edge. In addition, the study shows that the cavity screen can modulate the oscillation frequency but not the cavity acoustic oscillation mechanisms.

Fields, Richard S., Jr.↗
NASA NTRS1996

Electrochemical Impedance Spectroscopy of Conductive Polymer Coatings

Electrochemical impedance spectroscopy (EIS) was used to investigate the corrosion protection performance of twenty nine proprietary conductive polymer coatings for cold rolled steel under immersion in 3.55 percent NaCl. Corrosion potential as well as Bode plots of the data were obtained for each coating after one hour immersion, All coatings, with the exception of one, have a corrosion potential that is higher in the positive direction than the corrosion potential of bare steel under the same conditions. Group A consisted of twenty one coatings with Bode plots indicative of the capacitive behavior characteristic of barrier coatings. An equivalent circuit consisting of a capacitor in series with a resistor simulated the experimental EIS data for these coatings very well. Group B consisted of eight coatings that exhibited EIS spectra showing an inflection point which indicates that two time constants are present. This may be caused by an electrochemical process taking place which could be indicitive of coating failing. These coatings have a lower impedance that those in Group A.

Calle, Luz Marina↗
NASA NTRS1997

Grapevine Remote Sensing Analysis of Phylloxera Early Stress (GRAPES): Remote Sensing Analysis Summary

High spatial resolution airborne imagery was acquired in California's Napa Valley in 1993 and 1994 as part of the Grapevine Remote sensing Analysis of Phylloxera Early Stress (GRAPES) project. Investigators from NASA, the University of California, the California State University, and Robert Mondavi Winery examined the application of airborne digital imaging technology to vineyard management, with emphasis on detecting the phylloxera infestation in California vineyards. Because the root louse causes vine stress that leads to grapevine death in three to five years, the infested areas must be replanted with resistant rootstock. Early detection of infestation and changing cultural practices can compensate for vine damage. Vineyard managers need improved information to decide where and when to replant fields or sections of fields to minimize crop financial losses. Annual relative changes in leaf area due to phylloxera infestation were determined by using information obtained from computing Normalized Difference Vegetation Index (NDVI) images. Two other methods of monitoring vineyards through imagery were also investigated: optical sensing of the Red Edge Inflection Point (REIP), and thermal sensing. These did not convey the stress patterns as well as the NDVI imagery and require specialized sensor configurations. NDVI-derived products are recommended for monitoring phylloxera infestations.

Lobitz, Brad↗
NASA NTRS1999

Swept-Wing Receptivity Studies Using Distributed Roughness

Transition to turbulence in swept-wing flows has resisted correlation with linear theory because of its sensitivity to freestream conditions and 3-D roughness and because one of the principal instability modes quickly 'becomes nonlinear. In the face of such a formidable problem, two rather long-term fundamental efforts have been underway at DLR Gottinberg and Arizona State University that address swept-wing transition. These efforts have been recently reviewed by Bippes (1997) and Reibert and Saric (1997). Thus, the present work is a continuation of a series of studies on swept-wing boundary layers which have led to a better understanding of the transition process. In particular, we have taken advantage of the sensitivity to 3-D roughness and the modal nature of the instability in order to propose a particular control strategy. Complementing the two aforementioned reviews, general reviews of the swept-wing transition problem are found in Arnal (1997) and Kachanov (1996). Other recent reviews include Reshotko (t997), Crouch (1997), and Herbert (1997a,b). The failure of linear theory is discussed in Reed et al. (1996). The historical work is found in Reed and Sar-ic (1989). The basic idea is that the combination of sweep and chordwise pressure gradient within the boundary layer creates a velocity component perpendicular to the inviscid streamline. This crossflow profile is inflectional and exhibits both traveling and stationary unstable waves called crossflow vortices that are (approximately) aligned along the inviscid streamlines. Under conditions of low freestream turbulence levels, the dominant crossflow wave is stationary (Reibert and Saric t997) while moderate to high turbulence levels initiate dominant traveling waves (Dehle and Bippes 1996; Bippes 1997). 'Me mechanism is relatively insensitive to sound and 2-D surface roughness (Radeztsky et al. 1993) but very sensitive to 3-D roughness near the attachment line. We concentrate our work on low-turbulence freestream flows and stationary crossflow waves. Although the v' and w' components of the disturbances are very small, by convecting streamwise momentum in the wall-normal direction, they produce 0(l) changes inu'.Thus the mean flow is highly distorted with localized inflection points. Transition is then triggered by a high-frequency secondary instability of the distorted mean profile.

Saric, William S.↗
NASA NTRS2000

Generation and Radiation of Acoustic Waves from a 2D Shear Layer

A thin free shear layer containing an inflection point in the mean velocity profile is inherently unstable. Disturbances in the flow field can excite the unstable behavior of a shear layer, if the appropriate combination of frequencies and shear layer thicknesses exists, causing instability waves to grow. For other combinations of frequencies and thicknesses, these instability waves remain neutral in amplitude or decay in the downstream direction. A growing instability wave radiates noise when its phase velocity becomes supersonic relative to the ambient speed of sound. This occurs primarily when the mean jet flow velocity is supersonic. Thus, the small disturbances in the flow, which themselves may generate noise, have generated an additional noise source. It is the purpose of this problem to test the ability of CAA to compute this additional source of noise. The problem is idealized such that the exciting disturbance is a fixed known acoustic source pulsating at a single frequency. The source is placed inside of a 2D jet with parallel flow; hence, the shear layer thickness is constant. With the source amplitude small enough, the problem is governed by the following set of linear equations given in dimensional form.

Dahl, Milo D.↗
NASA NTRS2003

Foliar Reflectance and Fluorescence Responses for Plants Under Nitrogen Stress Determined with Active and Passive Systems

Vegetation productivity is driven by nitrogen (N) availability in soils. Both excessive and low soil N induce physiological changes in plant foliage. In 2001, we examined the use of spectral fluorescence and reflectance measurements to discriminate among plants provided different N fertilizer application rates: 20%, 50%, 100% and 150% of optimal N levels. A suite of optical, fluorescence, and biophysical measurements were collected on leaves from field grown corn (Zea mays L.) and soybean plants (Glycine max L.) grown in pots (greenhouse + ambient sunlight daily). Three types of steady state laser-induced fluorescence measurements were made on adaxial and abaxial surfaces: 1) fluorescence images in four 10 nm bands (blue, green, red, far-red) resulting from broad irradiance excitation; 2) emission spectra (5 nm resolution) produced by excitation at single wavelengths (280,380 or 360, and 532 nm); and 3) excitation spectra (2 nm resolution), with emission wavelengths fixed at wavelengths centered on selected solar Fraunhofer lines (532,607,677 and 745 nm). Two complementary sets of high resolution (less than 2 nm) optical spectra were acquired for both adaxial and abaxial leaf surfaces: 1) optical properties (350-2500 nm) for reflectance, transmittance, and absorptance; and 2) reflectance spectra (500-1000 nm) acquired with and without a short pass filter at 665 nm to determine the fluorescence contribution to apparent reflectance in the 650-750 spectrum, especially at the 685 and 740 nm chlorophyll fluorescence (ChIF) peaks. The strongest relationships between foliar chemistry and optical properties were demonstrated for C/N content and two optical parameters associated with the red edge inflection point. Select optical properties and ChIF parameters were highly correlated for both species. A significant contribution of ChIF to apparent reflectance was observed, averaging 10-25% at 685 nm and 2 - 6% at 740 nm over all N treatments. Discrimination of N treatment groups was possible with specific fluorescence band ratios (e.g., F740/F525 obtained with 380EX). From all measurements assessing fluorescence, higher ChIF and blue/green emissions were measured from the abaxial leaf surfaces; Abaxial surfaces also produced higher reflectances in the 400-800 nm spectrum. Fluorescence information collected in Fraunhofer regions located on the shoulders of ChIF features compared favorably with peak emissions. This supports the potential capability of a future space-born interferometer sensor to capture plant canopy fluorescence.

Middleton, E. M.↗
NASA NTRS1961

Investigation of an Axisymmetric Internal Compression Inlet at a Mach Number of About 3.8

An idealized axisymmetric, all-internal compression inlet was designed for a Mach number of 3.75. The objective of the design was to obtain a steady, one-dimensional transonic flow and a high over-all total pressure recovery. Boundary-layer removal was employed in the vicinity of the inflection point of the supersonic contour. Static and total-pressure fluctuations were measured in the transonic flow region. A total pressure recovery of about 90 percent was obtained with a boundary-layer-removal mass flow rate of 15 percent of the inlet mass flow rate. The accompanying root-mean-square total pressure fluctuation in the throat region was only 1 percent of the free stream total pressure. The test Mach number was 3.80 and the Reynolds number based on inlet diameter was 2.63 x 10(exp 6).

Lundell, John H.↗
NASA NTRS2013

Atmospheric Entry Studies for Venus Missions: 45 Sphere-Cone Rigid Aeroshells and Ballistic Entries

The present study considers direct ballistic entries into the atmosphere of Venus using a 45deg sphere-cone rigid aeroshell, a legacy shape that has been used successfully in the past in the Pioneer Venus Multiprobe Mission. For a number of entry mass and heatshield diameter combinations (i.e., various ballistic coefficients) and entry velocities, the trajectory space in terms of entry flight path angles between skip out and -30deg is explored with a 3DoF trajectory code, TRAJ. From these trajectories, the viable entry flight path angle space is determined through the use of mechanical and thermal performance limits on the thermal protection material and science payload; the thermal protection material of choice is entry-grade carbon phenolic, for which a material thermal response model is available. For mechanical performance, a 200 g limit is placed on the peak deceleration load experienced by the science instruments, and 10 bar is assumed as the pressure limit for entry-grade carbon-phenolic material. For thermal performance, inflection points in the total heat load distribution are used as cut off criteria. Analysis of the results shows the existence of a range of critical ballistic coefficients beyond which the steepest possible entries are determined by the pressure limit of the material rather than the deceleration load limit.

Prabhu, Dinesh K.↗
NASA NTRS2013

Geologic Interpretation of Data Sets Collected by Planetary Analog Geology Traverses and by Standard Geologic Field Mapping: A Comparison Study - Part 1

Geologic maps integrate the distributions, contacts, and compositions of rock and sediment bodies as a means to interpret local to regional formative histories. Applying terrestrial mapping techniques to other planets is challenging because data is collected primarily by orbiting instruments, with infrequent, spatiallylimited in situ human and robotic exploration. Although geologic maps developed using remote data sets and limited "Apollo-style" field access likely contain inaccuracies, the magnitude, type, and occurrence of these are only marginally understood. This project evaluates the interpretative and cartographic accuracy of both field- and remote-based mapping approaches by comparing two 1:24,000 scale geologic maps of the San Francisco Volcanic Field (SFVF), north-central Arizona. The first map is based on traditional field mapping techniques, while the second is based on remote data sets, augmented with limited field observations collected during NASA Desert Research & Technology Studies (RATS) 2010 exercises. The RATS mission used Apollo-style methods not only for pre-mission traverse planning but also to conduct geologic sampling as part of science operation tests. Cross-comparison demonstrates that the Apollo-style map identifies many of the same rock units and determines a similar broad history as the field-based map. However, field mapping techniques allow markedly improved discrimination of map units, particularly unconsolidated surficial deposits, and recognize a more complex eruptive history than was possible using Apollo-style data. Further, the distribution of unconsolidated surface units was more obvious in the remote sensing data to the field team after conducting the fieldwork. The study raises questions about the most effective approach to balancing mission costs with the rate of knowledge capture, suggesting that there is an inflection point in the "knowledge capture curve" beyond which additional resource investment yields progressively smaller gains in geologic knowledge.

Eppler, Dean B.↗
NASA NTRS2015

Altitude Compensating Nozzle

The dual-bell nozzle (fig. 1) is an altitude-compensating nozzle that has an inner contour consisting of two overlapped bells. At low altitudes, the dual-bell nozzle operates in mode 1, only utilizing the smaller, first bell of the nozzle. In mode 1, the nozzle flow separates from the wall at the inflection point between the two bell contours. As the vehicle reaches higher altitudes, the dual-bell nozzle flow transitions to mode 2, to flow full into the second, larger bell. This dual-mode operation allows near optimal expansion at two altitudes, enabling a higher mission average specific impulse (Isp) relative to that of a conventional, single-bell nozzle. Dual-bell nozzles have been studied analytically and subscale nozzle tests have been completed.1 This higher mission averaged Isp can provide up to a 5% increase2 in payload to orbit for existing launch vehicles. The next important step for the dual-bell nozzle is to confirm its potential in a relevant flight environment. Toward this end, NASA Marshall Space Flight Center (MSFC) and Armstrong Flight Research Center (AFRC) have been working to develop a subscale, hot-fire, dual-bell nozzle test article for flight testing on AFRC's F15-D flight test bed (figs. 2 and 3). Flight test data demonstrating a dual-bell ability to control the mode transition and result in a sufficient increase in a rocket's mission averaged Isp should help convince the launch service providers that the dual-bell nozzle would provide a return on the required investment to bring a dual-bell into flight operation. The Game Changing Department provided 0.2 FTE to ER42 for this effort in 2014.

Ruf, Joseph H.↗
NASA NTRS2018

Temperature Oscillations in Loop Heat Pipes - A Revisit

Three types of temperature oscillation have been observed in the loop heat pipes. The first type is an ultra-high frequency temperature oscillation with a period on the order of seconds or less. This type of temperature oscillation is of little significance in spacecraft thermal control because the amplitude is in the noise level. The second type is a high frequency, low amplitude temperature oscillation with a period on the order of seconds to minutes and an amplitude on the order of one Kelvin. It is caused by the back-and-forth movement of the vapor front near the inlet or outlet of the condenser. The third type is a low frequency, high amplitude oscillation with a period on the order of hours and an amplitude on the order of tens of Kelvin. It is caused by the modulation of the net heat load into the evaporator by the attached large thermal mass which absorbs and releases energy alternately. Several papers on LHP temperature oscillation have been published. This paper presents a further study on the underlying physical processes during the LHP temperature oscillation, with an emphasis on the third type of temperature oscillation. Specifically, equations governing the thermal and hydraulic behaviors of LHP operation will be used to describe interactions among LHP components, heat source, and heat sink. The following sequence of events and their interrelationship will also be explored: 1) maxima and minima of reservoir and thermal mass temperatures; 2) the range of the vapor front movement inside the condenser; 3) rates of change of the reservoir and thermal mass temperatures; 4) the rate of heat absorption and heat release by the thermal mass and the rate of vapor front movement; and 5) inflection points of the reservoir and thermal mass temperatures.

Fluid Mechanics and Thermodynamics↗