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At least 1,027 records · Page 57

Numerical analysis of natural convection in liquid droplets by phase change

A numerical analysis is performed on thermocapillary buoyancy convection induced by phase change in a liquid droplet. A finite-difference code is developed using an alternating-direction implicit (ADI) scheme. The intercoupling relation between thermocapillary force, buoyancy force, fluid property, heat transfer, and phase change, along with their effects on the induced flow patterns, are disclosed. The flow is classified into three types: thermocapillary, buoyancy, and combined convection. Among the three mechanisms, the combined convection simulates the experimental observations quite well, and the basic mechanism of the observed convection inside evaporating sessile drops is thus identified. It is disclosed that evaporation initiates unstable convection, while condensation always brings about a stable density distribution which eventually damps out all fluid disturbances. Another numerical model is presented to study the effect of boundary recession due to evaporation, and the 'peeling-off' effect (the removal of the surface layer of fluid by evaporation) is shown to be relevant.

Duh, J. C.↗

Transient analysis of a capillary pumped loop heat pipe

A bench-top Capillary Pumped Loop (CPL) test system has been developed and tested to investigate the transient mode operation of this system by applying a step power input to the evaporators. Tests were conducted at several power input and evaporator inlet subcooling combinations. In addition, a lumped-heat-capacity model of the CPL test system has been presented which is used for predicting qualitatively the transient operation characteristics. Good agreement has been obtained between the predicted and the measured temperature variations. A simple evaporator inlet subcooler model has also been developed to study effects of inlet subcooling on the steady-state evaporator wall temperature. Results were compared with the test data collected.

Kiper, A. M.↗

Understanding land surface evapotranspiration with satellite multispectral measurements

Quantitative use of remote multispectral measurements to study and map land surface evapotranspiration has been a challenging issue for the past 20 years. Past work is reviewed against process physics. A simple two-layer combination-type model is used which is applicable to both vegetation and bare soil. The theoretic analysis is done to show which land surface properties are implicitly defined by such evaporation models and to assess whether they are measurable as a matter of principle. Conceptual implications of the spatial correlation of land surface properties, as observed by means of remote multispectral measurements, are illustrated with results of work done in arid zones. A normalization of spatial variability of land surface evaporation is proposed by defining a location-dependent potential evaporation and surface temperature range. Examples of the application of remote based estimates of evaporation to hydrological modeling studies in Egypt and Argentina are presented.

Menenti, M.↗

Method for controlling protein crystallization

A method and apparatus for controlling the crystallization of protein by solvent evaporation including placing a drop of protein solution between and in contact with a pair of parallel plates and driving one of the plates toward and away from the other plate in a controlled manner to adjust the spacing between the plates is presented. The drop of solution forms a liquid cylinder having a height dependent upon the plate spacing thereby effecting the surface area available for solvent evaporation. When the spacing is close, evaporation is slow. Evaporation is increased by increasing the spacing between the plates until the breaking point of the liquid cylinder. One plate is mounted upon a fixed post while the other plate is carried by a receptacle movable relative to the post and driven by a belt driven screw drive. The temperature and humidity of the drop of protein solution are controlled by sealing the drop within the receptacle and mounting a heater and dessicant within the receptacle.

Noever, David A.↗

Transport phenomena in the micropores of plug-type phase separators

This study numerically investigates the transport phenomena within and across a porous-plug phase separator. The effect of temperature differential across a single pore and of the sidewall boundary conditions, i.e., isothermal or linear thermal gradient, are presented and discussed. The effects are quantified in terms of the evaporation mass flux across the boundary and the mean surface temperature. A two-dimensional finite element model is used to solve the continuity, momentum, and energy equations for the liquid. Temperature differentials across the pore interface of 1.0, and 1.5 K are examined and their effect on evaporation flux and mean surface temperature is shown. For isothermal side boundary conditions, the evaporation flux across the pore is directly proportional and linear with Delta T. For the case of an imposed linear thermal gradient on the side boundaries, Biot numbers of 0.0, 0.15, and 0.5 are examined. The most significant effect of Biot number is to lower the overall surface temperature and evaporation flux.

Fazah, M. M.↗

Advanced Multi-phase Flow CFD Model Development for Solid Rocket Motor Flowfield Analysis

A Navier-Stokes code, finite difference Navier-Stokes (FDNS), is used to analyze the complicated internal flowfield of the SRM (solid rocket motor) to explore the impacts due to the effects of chemical reaction, particle dynamics, and slag accumulation on the solid rocket motor (SRM). The particulate multi-phase flowfield with chemical reaction, particle evaporation, combustion, breakup, and agglomeration models are included in present study to obtain a better understanding of the SRM design. Finite rate chemistry model is applied to simulate the chemical reaction effects. Hermsen correlation model is used for the combustion simulation. The evaporation model introduced by Spalding is utilized to include the heat transfer from the particulate phase to the gase phase due to the evaporation of the particles. A correlation of the minimum particle size for breakup expressed in terms of the Al/Al2O3 surface tension and shear force was employed to simulate the breakup of particles. It is assumed that the breakup occurs when the Weber number exceeds 6. A simple L agglomeration model is used to investigate the particle agglomeration. However, due to the large computer memory requirements for the agglomeration model, only 2D cases are tested with the agglomeration model. The VOF (Volume of Fluid) method is employed to simulate the slag buildup in the aft-end cavity of the redesigned solid rocket motor (RSRM). Monte Carlo method is employed to calculate the turbulent dispersion effect of the particles. The flowfield analysis obtained using the FDNS code in the present research with finite rate chemical reaction, particle evaporation, combustion, breakup, agglomeration, and VOG models will provide a design guide for the potential improvement of the SRM including the use of materials and the shape of nozzle geometry such that a better performance of the SRM can be achieved. The simulation of the slag buildup in the aft-end cavity can assist the designer to improve the design of the RSRM geometry.

Liaw, Paul↗

Composition of interstellar clouds in the disk and halo. 2: Gamma(sup 2) Velorum

High-resolution observations of gamma(sup 2) Vel with the Goddard High-Resolution Spectrograph (GHRS) echelle on the Hubble Space Telescope reveal the presence of seven narrow absorption components, with LSR velocities between -23 and +9 km s(exp -1). Three of these show column density ratios N(S(++))/N(S(+)) and N(P(++))/N(P+)) of about 1 or more, and can be identified as H II regions, while the other four are H I regions, consistent with the O I profile and with the overall H(sup 0) column density of 5.9 x 10(exp 19) cm(exp -2), given the usual assumptions that S is undepleted while O has a depletion D(O) = -0.3 dex. The depletions of Fe, Si, and Mn, which could be measure accurately for two of the four H I regions (components 6 and 7), differ somewhat from the values of D(sub ws) found for slowly moving warm clouds in HD 93521; in particular, for the component at 4.0 km s(exp -1) (No. 6), abosolute of D exceeds absolute of D(sub ws) by 0.1-0.4 dex, while for that at 9.3 km s(exp -1) (No. 7), absolute of D equals absolute of D(sub ws) on the average. The observed ratio of Fe + Mg atoms to Si atoms in the grains of component 6 is 2.04 +/-0.10, consistent with an olivine grain composition; the Fe/Mg ratio is 1.5 +/- 0.2. The electron density in component 6, determined from the C II(sup *) feature, is 0.075 +/- 0.013 cm (exp -3), about two-thirds of that found for clouds of this velocity in HD 93521. In the two conspicuous H II regions, components 3 and 4, n(sub e), determined from the Si II(sup *) feature, is about 1 cm(exp -3). From the column density of S(+) + S(++) in these two components, the total H II path length is about 40 pc. With the radius of a wind-blown bubble around gamma(sup 2) Vel set equal to 60 pc, the effective Stromgren radius is about 100 pc, requiring that T approx. equal to 50,000 K for the Wolf-Rayet component of the gamma(sup 2) Vel binary. Since zeta Pup is a comparable source of ionizing radiation, this temperature is an upper limit. The profiles of the strongest H2 absorption features, from Copernicus archives, indicate that the absorbing molecules have a mean velocity identical with that of the strongest H II component (No. 4). We have no explanation for the possible presence of these H2 molecules in a region of ionized H. Alternatively, the H2 profiles can be explained by molecules in the two adjacent (in velocity) H I regions, components 2 and 5, provided their H I gas has densities and temperatures typical of normal cold clouds. The GHRS data show absorption by highly ionized atoms Si(3+) and C(3+), N(4+) in broad features, in addition to the narrow-line absorption by Si(3+) and C(3+) observed in the dominant H II components, Nos. 3 and 4. The broad C(3+) and N(4+) features have widths corresponding to T in the range (4-8) x 10(exp 5) K, consistent with the broad O(5+) line shown in Copernicus data. Despite some observational uncertainties, the ratios of column densities in the broad C(3+), N(4+), and O(5+) features agree to +/- 0.1 dex with theoretical values for warm gas, heating and evaporating by thermal conduction from an adjacent hot region. Outward evaporation from an isolated cloud in a hot ambient gas cannot be distinguished, on the basis of these data, from inward evaporation of a warm shell, compressed by an expanding, hot stellar-wind bubble. For several halo stars, the C IV/O VI ratio has a quite different average value, perhaps consistent with cooling of infalling hot gas instead of conductive heating and evaporation.

Fitzpatrick, Edward L.↗

Charge-induced secondary atomization in diffusion flames of electrostatic sprays

The combustion of electrostatic sprays of heptane in laminar counterflow diffusion flames was experimentally studied by measuring droplet size and velocity distributions, as well as the gas-phase temperature. A detailed examination of the evolution of droplet size distribution as droplets approach the flame shows that, if substantial evaporation occurs before droplets interact with the flame, an initially monodisperse size distribution becomes bimodal. A secondary sharp peak in the size histogram develops in correspondence of diameters about one order of magnitude smaller than the mean. No evaporation mechanism can account for the development of such bimodality, that can be explained only in terms of a disintegration of droplets into finer fragments of size much smaller than that of the parent. Other evidence in support of this interpretation is offered by the measurements of droplet size-velocity correlation and velocity component distributions, showing that, as a consequence of the ejection process, the droplets responsible for the secondary peak have velocities uncorrelated with the mean flow. The fission is induced by the electric charge. When a droplet evaporates, in fact, the electric charge density on the droplet surface increases while the droplet shrinks, until the so-called Rayleigh limit is reached at which point the repulsion of electric charges overcomes the surface tension cohesive force, ultimately leading to a disintegraton into finer fragments. We report on the first observation of such fissions in combustion environments. If, on the other hand, insufficient evaporation has occurred before droplets enter the high temperature region, there appears to be no significant evidence of bimodality in their size distribution. In this case, in fact, the concentration of flame chemi-ions or, in the case of positively charged droplets, electrons may be sufficient for them to neutralize the charge on the droplets and to prevent disruption.

Gomez, Alessandro↗

Numerical Investigation of Slag Behavior for RSRM

It is known that the flow field of the redesigned solid rocket motor (RSRM) is very complicated due to the complex characteristics of turbulent multi-phase flow, chemical reaction, particle combustion, evaporation, breakup and agglomeration etc. It requires multi-phase calculations, chemical reaction simulation, and particle combustion, evaporation, and breakup models to obtain a better understanding of thermophysics for the RSRM design using numerical methods. Also, the slag buildup due to the molten particles is another factor affecting the performance of the RSRM. To achieve this goal, the volume of fluid (VOF) method is used to capture the free surface motion so as to simulate the accumulation of the molten particles (slag) of the RSRM. A finite rate chemistry model is used to simulate the chemical reaction effects. For multi-phase calculations, the Hermsen combustion model is used for the aluminum particle combustion analysis and the Taylor Analogy Breakup (TAB) model is used for the particle breakup analysis. An interphase mas-exchange model introduced by Spalding is used for the evaporation calculation. The particle trajectories are calculated using a one-step implicit method for several groups of particle sizes by which the drag forces and heat fluxes are then coupled with the gas phase equations. The preliminary results predicted a reasonable physical simulation of the particle effects using a simple two dimensional solid rocket motor configuration. It shows that the AL/AL2O3 particle sizes are reduced due to the combustion, evaporation, and breakup. The flow field is disturbed by the particles. Mach number distributions in the nozzle are deformed due to the effect of particle concentrations away from the center line.

Liaw, P.↗

Water Vapor Transport Over the Tropical Oceans During ENSO as Diagnosed from TRMM and SSM/I Data

Traditionally, large-scale water vapor transport [div Q] has been derived directly from circulation statistics in which transport processes are often depicted by mean and eddy motions. Thus detailed and accurate calculations of moisture transport terms over the globe are required. Notably, the lack of systematically spaced conventional measurements of meteorological variables over oceans has hindered understanding of the distribution and transport of water vapor. This motivates the use of indirect calculation methods in which horizontal divergence of water vapor is balanced by the evaporation minus precipitation, assuming the rate of changes of precipitable water and condensates is small over a sufficiently long time period. In order to obtain the water vapor transport, we need evaporation rate minus precipitation (E-P). Focussing on the differences in water vapor transport between El Nino and La Nina periods and their influences on atmospheric circulations, we study January, February, and March of 1998 and 1999 periods which represent El Nino and La Nina respectively. SSM/I-derived precipitation and evaporation rate from SSM/I wind and total precipitable water, in conjunction with NCEP SST and surface air temperature, are used for the calculation of the transport potential function. For the retrieval of evaporation we use a stability-dependent aerodynamic bulk scheme developed by Chou (1993). It was tested against aircraft covariance fluxes measured during cold air outbreaks over the North Atlantic Ocean. Chou et al. (1997) reported that the SSM/I retrieved latent heat flux over the western Pacific warm pool area were found to be comparable with daily mean fluxes of a ship measurements during TOGA/COARE.

Robertson, Franklin R.↗

Investigation of Low Power Operation in a Loop Heat Pipe

This paper presents test results of an experimental study of low power operation in a loop heat pipe. The main objective was to demonstrate how changes in the vapor void fraction inside the evaporator core would affect the loop behavior, The fluid inventory and the relative tilt between the evaporator and the compensation chamber were varied so as to create different vapor void fractions in the evaporator core. The effect on the loop start-up, operating temperature, and capillary limit was investigated. Test results indicate that the vapor void fraction inside the evaporator core is the single most important factor in determining the loop operation at low powers.

Ku, Jentung↗

Water Vapor Tracers as Diagnostics of the Regional Hydrologic Cycle

Numerous studies suggest that local feedback of evaporation on precipitation, or recycling, is a significant source of water for precipitation. Quantitative results on the exact amount of recycling have been difficult to obtain in view of the inherent limitations of diagnostic recycling calculations. The current study describes a calculation of the amount of local and remote sources of water for precipitation, based on the implementation of passive constituent tracers of water vapor (termed water vapor tracers, WVT) in a general circulation model. In this case, the major limitation on the accuracy of the recycling estimates is the veracity of the numerically simulated hydrological cycle, though we note that this approach can also be implemented within the context of a data assimilation system. In this approach, each WVT is associated with an evaporative source region, and tracks the water until it precipitates from the atmosphere. By assuming that the regional water is well mixed with water from other sources, the physical processes that act on the WVT are determined in proportion to those that act on the model's prognostic water vapor. In this way, the local and remote sources of water for precipitation can be computed within the model simulation, and can be validated against the model's prognostic water vapor. Furthermore, estimates of precipitation recycling can be compared with bulk diagnostic approaches. As a demonstration of the method, the regional hydrologic cycles for North America and India are evaluated for six summers (June, July and August) of model simulation. More than 50% of the precipitation in the Midwestern United States came from continental regional tracers, and the local source was the largest of the regional tracers (14%). The Gulf of Mexico and Atlantic 2 regions contributed 18% of the water for Midwestern precipitation, but further analysis suggests that the greater region of the Tropical Atlantic Ocean may also contribute significantly. In general, most North American land regions showed a positive correlation between evaporation and recycling ratio (except the Southeast United States) and negative correlations of recycling ratio with precipitation and moisture transport (except the Southwestern United States). The Midwestern local source is positively correlated with local evaporation, but it is not correlated with water vapor transport. This is contrary to bulk diagnostic estimates of precipitation recycling. In India, the local source of precipitation is a small percentage of the precipitation owing to the dominance of the atmospheric transport of oceanic water. The southern Indian Ocean provides a key source of water for both the Indian continent and the Sahelian region.

Bosilovich, Michael G.↗

Evaporation/SST Sensitivity Over the Tropical Oceans During ENSO Events as Estimated from the da Silva, Young, Levitus Surface Marine Data Set

The da Silva, Young and Levitus Surface Marine Atlas, based on observations from the Comprehensive Ocean Atmosphere Data Set (COADS) Release 1, has been used to investigate the relationship between evaporation and sea-surface temperature (SST) over the global oceans. For the period 1950 to 1987 SST, surface latent heat flux, and other related variables have been filtered to minimize data uncertainties and to focus upon interannual variations associated with warm (El Nino) and cold (La Nina) ENSO events. Compositing procedures have enabled identification of systematic variations in latent heat fluxes accompanying these events and the relationship to spatial anomalies in ocean surface wind speed and humidity. The evaporation response associated with ENSO sea surface temperature (SST) variability is systematic in nature and composed of offsetting contributions from the surface wind and humidity variations. During warm events exceeding 1.0 S.D. delta SST, increases in the surface humidity deficit, delta(qs-qa), between the surface and 2m height dominate regions of positive SST anomalies and lead to increases in evaporation of almost 2 Wm (exp -2) at deltaSST = 0.23 K. Despite the increases in specific humidity, relative humidity decreases slightly in regions of elevated SSTs. For the most part, variations in wind speed are consistent with previous investigations. Weakening of the equatorial easterlies (and generation of westerlies) between 160 degrees E and 140 degrees W dominates during the early phases of warm events. Elevated wind speeds in adjacent subtropical regions and in the eastern equatorial Pacific subsequently develop too. The net contribution of these winds, which reflect adjustments in Hadley and Walker circulation components is toward reduced evaporation. Results for cold periods are approximately similar, but opposite in sign to warm events, though evidence of different temporal evolution is noted.

Robertson, F. R.↗

On the Regulation of the Pacific Warm Pool Temperature

In the tropical western Pacific, regions of the highest sea surface temperature (SST) and the largest cloud cover are found to have the largest surface heating, primarily due to the weak evaporative cooling associated with weak winds. This situation is in variance with the suggestions that the temperature in the Pacific warm pool is regulated either by the reduced solar heating due to an enhanced cloudiness or by the enhanced evaporative cooling due to an elevated SST. It is clear that an enhanced surface heating in an enhanced convection region is not sustainable and must be interrupted by variations in large-scale atmospheric circulation. As the deep convective regions shift away from regions of high SST due primarily to seasonal variation and secondarily to interannual variation of the large-scale atmospheric and oceanic circulation, both trade wind and evaporative cooling in the high SST region increase, leading to a reduction in SST. We conclude that the evaporative cooling associated with the seasonal and interannual variations of trade winds in the primary factor that prevent the warm pool SST from increasing to a value much higher than what is observed.

Chou, Ming-Dah↗

Tropical Warm Pool Surface Heat Budgets and Temperature: Contrasts Between 1997-98 El Nino and 1998-99 La Nina

Seasonal and interannual variations of the net surface heating F(sub NET) and sea surface temperature tendency (T(sub s)/dt) in the tropical eastern Indian and western Pacific Oceans are studied. The surface heat fluxes are derived from the Special Sensor Microwave/Imager and Japanese Geostationary Meteorological Satellite radiance measurements for the period October 1997-September 2000. It is found that the magnitude of solar heating is lager than that of evaporative cooling, but the spatial variation of the latter is significantly large than the former. As a result, the spatial variations of seasonal and interannual variability of F(sub NET), follow closely that of evaporative cooling. Seasonal variations of F(sub NET) and T(sub s)/dt are significantly correlated, except for the equatorial western Pacific. The high correlation is primarily attributable to high correlation between seasonal cycles of solar heating and T(sub s)/dt. The change of F(sub NET) between 1997-98 El Nino and 1998-99 La Nina is significantly larger in the tropical eastern Indian Ocean than tropical western Pacific. For the former region, the reduced evaporative cooling arising from weakened winds during the El Nino is generally associated with enhanced solar heating due to decreased cloudiness, and thus increases the interannual variability of F(sub NET). For the latter region, the reduced evaporative cooling due to weakened winds is generally associated with but exceeds the reduced solar heating arising from increased cloudiness, and vise versa. Thus the interannual variability of F(sub NET) is reduced due to this offsetting effect. Interannual variations of F(sub NET) and T(sub s)/dt have very low correlation. This is most likely related to interannual variability of ocean dynamics, which includes the variations of solar radiation penetrating through oceanic mixed layer, upwelling of cold thermocline water, Indonesian throughflow for transporting heat from the Pacific to Indian Ocean, and interhemispheric transport in the Indian Ocean.

Chou, Shu-Hsien↗

Influence of Transient Atmospheric Circulation on the Surface Heating of the Pacific Warm Pool

Analyses of data on clouds, winds, and surface heat fluxes show that the transient behavior of basin-wide large-scale circulation has a significant influence on the warm pool sea surface temperature (SST). Trade winds converge to regions of the highest SST in the equatorial western Pacific. These regions have the largest cloud cover and smallest wind speed. Both surface solar heating and evaporative cooling are weak. The reduced evaporative cooling due to weakened winds exceeds the reduced solar heating due to enhanced cloudiness. The result is a maximum surface heating in the strong convective and high SST regions. Data also show that the maximum surface heating in strong convective regions is interrupted by transient atmospheric and oceanic circulation. Due to the seasonal variation of the insolation at the top of the atmosphere, trade winds and clouds also experience seasonal variations. Regions of high SST and low-level convergence follow the Sun, where the surface heating is a maximum. As the Sun moves away from a convective region, the strong trade winds set in, and the evaporative cooling enhances, resulting in a net cooling of the surface. During an El Nino, the maximum SST and convective region shifts eastward from the maritime continent to the equatorial central Pacific. Following the eastward shift of the maximum SST, the region of maximum cloudiness and surface heating also shift eastward. As the atmospheric and oceanic circulation returns to normal situations, the trade winds increase and the surface heating decreases. We conclude that the evaporative cooling associated with the seasonal and interannual variations of trade winds is one of the major factors that modulate the SST distribution of the Pacific warm pool.

Chou, Ming-Dah↗

Sensitivity of a Cloud-Resolving Model to the Bulk and Explicit Bin Microphysical Schemes

A cloud-resolving model is used to study sensitivities of two different microphysical schemes, one is the traditional bulk type, and the other is an explicit bin scheme, in simulating a mid-latitude squall line case (PRE-STORM, June 10-1 1,1985). Simulations using different microphysical schemes are compared with each other and also with the observations. Both the bulk and bin models reproduce the general features during the developing and mature stage of the system. Furthermore, the observations and the well-proven bulk scheme simulation serve as validations for the newly incorporated bin scheme. However, it is also shown that the bulk and bin simulations have distinct differences, most notably in the stratiform region of the squall line system. Weak convective cells exist in the stratiform region in the bulk simulation, but not in the bin simulation. These weak convective cells in the stratiform region simulated in the bulk scheme model are remnants of the stronger convections previously at the leading edge of the system, sustained by horizontal vorticity generated by its own cool pool near the surface. The bin simulation, on the other hand, has a horizontally homogeneous stratiform cloud structure, which agrees better with the observations. Examinations of the downdraft core strength, the potential temperature perturbation, and the evaporative cooling rate show that the differences between the bulk and bin models are due mainly to the stronger low-level evaporative cooling in the convective zone simulated in the bulk microphysical scheme, which is unrealistic because of the assumptions made in raindrop size distribution. Further sensitivity tests that reduce the evaporation rate in bulk scheme artificially produce more upright convective core and less weak cores in stratiform region. However, they produce weaker upper level outflow and consequently less stratiform rain area. The addition of a more realistic raindrop breakup scheme in the bin scheme results more realistic radar reflectivity and stronger surface rainfall. Despite the increase of the rain evaporation and strengthening of the near surface cool pool, bin scheme with rain breakup shows homogeneous stratiform rain. These sensitivity tests prove the robustness of the bin microphysical scheme and the difficulty of tuning the limited parameters in the bulk microphysical scheme to realistically reproduce detail structures in a mid-latitude squall line case study.

Li, Xiao-Wen↗

An Impact Triggered Runaway Greenhouse on Mars

When a planet is in radiative equilibrium, the incoming solar flux balances the outgoing longwave flux. If something were to perturb the system slightly, say the incoming solar flux increased, the planet would respond by radiating at a higher surface temperature. Since any radiation that comes in must go out, if the incoming is increased, the outgoing must also increase, and this increase manifests itself as a warmer equilibrium temperature. The increase in solar flux would correspond to an increase in temperature, which would increase the amount of water vapor in the atmosphere due to increased evaporation. Since water vapor is a greenhouse gas, it would absorb more radiation in the atmosphere leading to a yet warmer equilibrium temperature. The planet would reach radiative equilibrium at this new temperature. There exists a point, however, past which this positive feedback leads to a "runaway" situation. In this case, the planet does not simply evaporate a little more water and eventually come to a slightly higher equilibrium temperature. Instead, the planet keeps evaporating more and more water until all of the planet's available liquid and solid water is in the atmosphere. The reason for this is generally understood. If the planet's temperature increases, evaporation of water increases, and the absorption of radiation increases. This increases the temperature and the feedback continues until all water is in the atmosphere. The resulting equilibrium temperature is very high, much higher than the equilibrium temperature of a point with slightly lower solar flux. One can picture that as solar flux increases, planetary temperature also increases until the runaway point where temperature suddenly "jumps" to a higher value, in response to all the available water now residing in the atmosphere. This new equilibrium is called a "runaway greenhouse" and it has been theorized that this is what happened to the planet Venus, where the surface temperature is more than 700 K (427 C).

Segura, T. L.↗