## Natural Circulation Loop with Heat Exchanger Boundary Conditions

The basic natural circulation loop case is modeled with heat source and sink. The high and low temperatures for the fluid are expressed in terms of the source and sink temperatures and the characteristics of the heat exchangers. The transient and steady state model equations are developed, the steady state solution presented, the model equations are given in dimensionless form, and the linearized versions of the equations developed.

Additional work is required to finish analyses of the stability of the system.

A file is here.

## Coupled Natural Circulation Loops

Coupled natural circulation loops (NCLs) have not been much investigated. Single natural circulation loops, on the other hand, have been the subject of experimental, analytical and numerical research for several decades since the early 1950s. The literature is very extensive with investigations continuing to this day. Much of the research has been directed toward various systems of electric power generation by nuclear power plants.

The objectives of the present notes include; (1) development of model equations for steady-state and transient flows in coupled NCLs, (2) giving the steady state solutions for the steady state equations, (3) linearization of the transient equations for use in stability analyses, and (4) incorporation of realistic boundary-condition representations into the model equation systems for coupled NCLs.

The results are distilled to a system of equations that will be used for investigations into the stability of coupled natural circulation loops.

The design of such systems, also an interesting problem, is not addressed here.

I have uploaded a file here.

## Moto Road Trip Travel Logs

I have posted travel logs, with photos, for our Moto Road Trips across America here.

## Verify the Methods: Conservation of Water Mass

Professor Pielke Sr. has posted a comment on this paper. The complete paper is available at the URL. The citation for the paper is:

Beate G Liepert and Michael Previdi, 2012: Inter-model variability and biases of the global water cycle in CMIP3 coupled climate models, 2012: Environmental Research Letters Volume 7 Number 1 014006 doi:10.1088/1748-9326/7/1/014006

Abstract

Observed changes such as increasing global temperatures and the intensification of the global water cycle in the 20th century are robust results of coupled general circulation models (CGCMs). In spite of these successes,model-to-model variability and biases that are small in first order climate responses, however, have considerable implications for climate predictability especially when multi-model means are used. We show that most climate simulations of the 20th and 21st century A2 scenario performed with CMIP3 (Coupled Model Inter-comparison Project Phase 3) models have deficiencies in simulating the global atmospheric moisture balance. Large biases of only a few models (some biases reach the simulated global precipitation changes in the 20th and 21st centuries) affect the multi-model mean global moisture budget. An imbalanced flux of −0.14 Sv exists while the multi-model median imbalance is only −0.02 Sv. Moreover, for most models the detected imbalance changes over time. As a consequence, in 13 of the 18 CMIP3 models examined, global annual mean precipitation exceeds global evaporation, indicating that there should be a ‘leaking’ of moisture from the atmosphere whereas for the remaining five models a ‘flooding’ is implied. Nonetheless, in all models, the actual atmospheric moisture content and its variability correctly increases during the course of the 20th and 21st centuries. These discrepancies therefore imply an unphysical and hence ‘ghost’ sink/source of atmospheric moisture in the models whose atmospheres flood/leak. The ghost source/sink of moisture can also be regarded as atmospheric latent heating/cooling and hence as positive/negative perturbation of the atmospheric energy budget or non-radiative forcing in the range of −1 to +6 W m−2(median +0.1 W m−2). The inter-model variability of the global atmospheric moisture transport from oceans to land areas, which impacts the terrestrial water cycle, is also quite high and ranges from 0.26 to 1.78 Sv. In the 21st century this transport to land increases by about 5% per century with a model-to-model range from 1 to 13%. We suggest that this variability is weakly correlated to the land–sea contrast in air temperature change of these models. Spatially heterogeneous forcings such as aerosols contribute to the variability in moisture transport, at least in one model. The polewards shifts of dry zones in climate simulations of the 21st century are also assessed. It is shown that the multi-model means of the two subsets of models with negative and positive imbalances in the atmospheric moisture budget produce spatial variability in the dry zone positions similar in size to the spatial shifts expected from 21st century global warming. Thus, the selection of models also affects the multi-model mean dry zone extension. In general, we caution the use of multi-model means of E − P fields and suggest self-consistency tests for climate models.

Clearly the GCMs considered in the paper do not conserve water mass, where water means the phases of water. The ‘leaking’ and ‘flooding’ are nothing more or less than sinks and sources for water due to lack of conservation of mass for these aspects of the numerical solution methods.

Verify the methods.

## More on Entropy, MEP, and Climate . . . and more

HISASHI OZAWA AND ATSUMU OHMURA Thermodynamics of a Global-Mean State of the Atmosphere—A State of Maximum Entropy Increase

ABSTRACT

Vertical heat transport through thermal convection of the earth’s atmosphere is investigated from a thermo- dynamic viewpoint. The postulate for convection considered here is that the global-mean state of the atmosphere is stabilized at a state of maximum entropy increase in a whole system through convective transport of sensible and latent heat from the earth’s surface into outer space. Results of an investigation using a simple vertical gray atmosphere show the existence of a unique set of vertical distributions of air temperature and of convective and radiative heat fluxes that represents a state of maximum entropy increase and that resembles the present earth. It is suggested that the global-mean state of the atmospheric convection of the earth, and that of other planets, is stabilized so as to increase entropy in the universe at a possible maximum rate.

OLIVIER PAULUIS AND ISAAC M. HELD Entropy Budget of an Atmosphere in Radiative–Convective Equilibrium. Part II: Latent Heat Transport and Moist Processes

ABSTRACT

In moist convection, atmospheric motions transport water vapor from the earth’s surface to the regions where condensation occurs. This transport is associated with three other aspects of convection: the latent heat transport, the expansion work performed by water vapor, and the irreversible entropy production due to diffusion of water vapor and phase changes. An analysis of the thermodynamic transformations of atmospheric water yields what is referred to as the entropy budget of the water substance, providing a quantitative relationship between these three aspects of moist convection. The water vapor transport can be viewed as an imperfect heat engine that produces less mechanical work than the corresponding Carnot cycle because of diffusion of water vapor and irreversible phase changes.

The entropy budget of the water substance provides an alternative method of determining the irreversible entropy production due to phase changes and diffusion of water vapor. This method has the advantage that it does not require explicit knowledge of the relative humidity or of the molecular flux of water vapor for the estimation of the entropy production. Scaling arguments show that the expansion work of water vapor accounts for a small fraction of the work that would be produced in the absence of irreversible moist processes. It is also shown that diffusion of water vapor and irreversible phase changes can be interpreted as the irreversible counterpart to the continuous dehumidification resulting from condensation and precipitation. This leads to a description of moist convection where it acts more as an atmospheric dehumidifier than as a heat engine.

RICHARD GOODY Maximum Entropy Production in Climate Theory

ABSTRACT

R. D. Lorenz et al. claim that recent data on Mars and Titan show that planetary atmospheres are in unconstrained states of maximum entropy production (MEP). Their model as it applies to Venus, Earth, Mars, and Titan is reexamined, and it is shown that their claim is not justified. This does not necessarily imply that MEP is incorrect, and inapplicable to atmospheres, but it does mean that the difficult and unexplored problem of dynamical constraints on the MEP solution must be understood if it is to be of value for climate research.

Here’s some recent info on the topic.

I ran across this issue of Philosophical Transactions of The Royal Society B: Biological Sciences, May 12, 2010; 365 (1545):

Theme Issue ‘Maximum entropy production in ecological and environmental systems: applications and implications’ compiled and edited by Axel Kleidon, Yadvinder Malhi and Peter M. Cox. doi:10.1098/rstb.2010.0018

Full papers are available at no cost.

This paper:

G Grinstein and R Linsker, “Comments on a derivation and application of the ‘maximum entropy production’ principle” 2007 J. Phys. A: Math. Theor. 40 9717. doi:10.1088/1751-8113/40/31/N01

reports errors in these recent papers by Dewar:

Dewar R 2003. “Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states” J. Phys. A: Math. Gen. 36 631. doi: 10.1088/0305-4470/36/3/303

Dewar R C 2005, “Maximum entropy production and the fluctuation theorem” J. Phys. A: Math. Gen. 38 L371. doi: 10.1088/0305-4470/38/21/L01

Finally, additional papers here. And even more here.