11 
Comparisons of spherical shell and planelayer mantle convection modelsO'Farrell, Keely Anne 14 January 2014 (has links)
Planelayer geometry convection models remain useful for modelling planetary mantle dynamics however they yield significantly warmer mean temperatures than spherical shell models. For example, in a uniform property spherical shell with the same radius ratio, f, as the Earth's mantle; a bottom heating Rayleigh number, Ra, of 10^7 and a nondimensional internal heating rate, H, of 23 (arguably Earthlike values) are insufficient to heat the mean temperature, θ, above the mean of the nondimensional boundary value temperatures (0.5), the temperature in a planelayer model with no internal heating. This study investigates the impact of this geometrical effect in convection models featuring uniform and stratified viscosity.
To address the effect of geometry, heat sinks are implemented to lower the mean temperature in 3D planelayer isoviscous convection models. Over 100 models are analyzed, and their mean temperatures are used to derive a single equation for predicting θ, as a function of Ra, H and f in spherical and planelayer systems featuring freeslip surfaces.
The inclusion of firstorder terrestrial characteristics is introduced to quantitatively assess the influence of system geometry on planetary scale simulations. Again, over 100 models are analyzed featuring a uniform upper mantle viscosity and a lower mantle viscosity that increases by a factor of 30 or 100. An effective Rayleigh number, Raη, is defined based on the average viscosity of the mantle. Equations for the relationship between θ, Raη, and H are derived for convection in a spherical shell with f = 0.547 and planelayer geometries.
These equations can be used to determine the appropriate heating rate for a planelayer convection model to emulate spherical shell convection mean temperatures for effective Rayleigh numbers comparable to the Earth’s value and greater. Comparing cases with the same H and Raη, the increased lower mantle viscosity amplifies the mismatch in mean temperatures between spherical shell and planelayer models. These findings emphasize the importance of adjusting heating rates in planelayer geometry models and have important implications for studying convection with temperaturedependent parameters in planelayer systems. The findings are particularly relevant to the study of convection in superEarths where full spherical shell calculations remain intractable.

12 
Comparisons of spherical shell and planelayer mantle convection modelsO'Farrell, Keely Anne 14 January 2014 (has links)
Planelayer geometry convection models remain useful for modelling planetary mantle dynamics however they yield significantly warmer mean temperatures than spherical shell models. For example, in a uniform property spherical shell with the same radius ratio, f, as the Earth's mantle; a bottom heating Rayleigh number, Ra, of 10^7 and a nondimensional internal heating rate, H, of 23 (arguably Earthlike values) are insufficient to heat the mean temperature, θ, above the mean of the nondimensional boundary value temperatures (0.5), the temperature in a planelayer model with no internal heating. This study investigates the impact of this geometrical effect in convection models featuring uniform and stratified viscosity.
To address the effect of geometry, heat sinks are implemented to lower the mean temperature in 3D planelayer isoviscous convection models. Over 100 models are analyzed, and their mean temperatures are used to derive a single equation for predicting θ, as a function of Ra, H and f in spherical and planelayer systems featuring freeslip surfaces.
The inclusion of firstorder terrestrial characteristics is introduced to quantitatively assess the influence of system geometry on planetary scale simulations. Again, over 100 models are analyzed featuring a uniform upper mantle viscosity and a lower mantle viscosity that increases by a factor of 30 or 100. An effective Rayleigh number, Raη, is defined based on the average viscosity of the mantle. Equations for the relationship between θ, Raη, and H are derived for convection in a spherical shell with f = 0.547 and planelayer geometries.
These equations can be used to determine the appropriate heating rate for a planelayer convection model to emulate spherical shell convection mean temperatures for effective Rayleigh numbers comparable to the Earth’s value and greater. Comparing cases with the same H and Raη, the increased lower mantle viscosity amplifies the mismatch in mean temperatures between spherical shell and planelayer models. These findings emphasize the importance of adjusting heating rates in planelayer geometry models and have important implications for studying convection with temperaturedependent parameters in planelayer systems. The findings are particularly relevant to the study of convection in superEarths where full spherical shell calculations remain intractable.

13 
Investigations On High Rayleigh Number Turbulent Free ConvectionPuthenveettil, Baburaj A 06 1900 (has links)
High Rayleigh number(Ra) turbulent free convection has many unresolved
issues related to the phenomenology behind the flux scaling, the
presence of a mean wind and its effects, exponential probability
distribution functions, the Prandtl number dependence and the nature
of near wall structures. Few studies have been conducted in the high
Prandtl number regime and the understanding of near wall coherent
structures is inadequate for $Ra > 10^9$. The present thesis deals
with the results of investigations conducted on high Rayleigh
number turbulent free convection in the high Schmidt number(Sc)
regime, focusing on the role of near wall coherent structures.
We use a new method of driving the convection using concentration
difference of NaCl across a horizontal membrane between two tanks to
achieve high Ra utilising the low molecular diffusivity of NaCl. The
near wall structures are visualised by planar laser induced
fluorescence. Flux is estimated from transient measurement of
concentration in the top tank by a conductivity probe. Experiments
are conducted in tanks of $15\times15\times 23$cm (aspect ratio,AR =
0.65) and $10\times10\times 23$cm (AR = 0.435). Two membranes of
0.45$\mu$ and 35$\mu$ mean pore size were used. For the fine
membrane (and for the coarse membrane at low driving potentials), the
transport across the partition becomes diffusion dominated, while the
transport above and below the partition becomes similar to unsteady
non penetrative turbulent free convection above flat horizontal
surfaces (Figure~\ref{fig:schem}(A)). In this type of convection,
the flux scaled as $q\sim \Delta C_w ^{4/3}$,where $\Delta C_w$ is
the near wall concentration difference, similar to that in Rayleigh 
B\'nard convection . Hence, we are able to study turbulent free
convection over horizontal surfaces in the Rayleigh Number range of
$\sim 10^ 10 ^$ at Schmidt number of 602, focusing on the
nature and role of near wall coherent structures. To our knowledge,
this is the first study showing clear images of near wall structures
in high Rayleigh Number  high Schmidt number turbulent free
convection.
We observe a weak flow across the membrane in the case of the coarser
membrane at higher driving potentials (Figure \ref(B)).
The effect of this through flow on the flux and the near wall
structures is also investigated. In both the types of convection the
near wall structure shows patterns formed by sheet plumes, the common
properties of these patterns are also investigated. The major
outcomes in the above three areas of the thesis can be summarised as
follows
\subsection*
\label
\subsubsection*
\label
The nondimensional flux was similar to that reported by
Goldstein\cite at Sc of 2750. Visualisations show that the near
wall coherent structures are line plumes. Depending on the Rayleigh
number and the Aspect ratio, different types of large scale flow cells
which are driven by plume columns are observed. Multiple large scale
flow cells are observed for AR = 0.65 and a single large scale flow
for AR= 0.435. The large scale flow create a near wall mean shear,
which is seen to vary across the cross section. The orientation of the
large scale flow is seen to change at a time scale much larger than
the time scale of one large scale circulation
The near wall structures show interaction of the large scale flow with
the line plumes. The plumes are initiated as points and then gets
elongated along the mean shear direction in areas of larger mean
shear. In areas of low mean shear, the plumes are initiated as points
but gets elongated in directions decided by the flow induced by the
adjacent plumes. The effect of near wall mean shear is to align the
plumes and reduce their lateral movement and merging. The time scale
for the merger of the near wall line plumes is an order smaller than
the time scale of the one large scale circulation. With increase in
Rayleigh number, plumes become more closely and regularly spaced.
We propose that the near wall boundary layers in high Rayleigh number
turbulent free convection are laminar natural convection boundary
layers. The above proposition is verified by a near wall model,
similar to the one proposed by \cite{tjfm}, based on the similarity
solutions of laminar natural convection boundary layer equations as
Pr$\rightarrow\infty$. The model prediction of the non dimensional
mean plume spacing $Ra_\lambda^~=~\lambda /Z_w~=~91.7$  where
$Ra_\lambda$ is the Rayleigh number based on the plume spacing
$\lambda$, and $Z_w$ is a near wall length scale for turbulent free
convection  matches the experimental measurements. Therefore, higher
driving potentials, resulting in higher flux, give rise to lower mean
plume spacing so that $\lambda \Delta C_w^$ or $\lambda q^$ is
a constant for a given fluid.
We also show that the laminar boundary layer assumption is consistent
with the flux scaling obtained from integral relations. Integral
equations for the Nusselt number(Nu) from the scalar variance
equations for unsteady non penetrative convection are derived.
Estimating the boundary layer dissipation using laminar natural
convection boundary layers and using the mean plume spacing relation,
we obtain $Nu\sim Ra^$ when the boundary layer scalar dissipation
is only considered. The contribution of bulk dissipation is found to
be a small perturbation on the dominant 1/3 scaling, the effect of
which is to reduce the effective scaling exponent.
In the appendix to the thesis, continuing the above line of reasoning,
we conduct an exploratory reanalysis (for $Pr\sim 1$) of the Grossman
and Lohse's\cite scaling theory for turbulent Rayleigh  B\'enard
convection. We replace the Blasius boundary layer assumption of the
theory with a pair of externally forced laminar natural convection
boundary layers per plume. Integral equations of the externally forced
laminar natural convection boundary layer show that the mixed
convection boundary layer thickness is decided by a $5^{th}$ order
algebraic equation, which asymptotes to the laminar natural convection
boundary layer for zero mean wind and to Blasius boundary layer at
large mean winds.
\subsubsection*{Effect of wall normal flow on flux and near wall structures}
\label{sec:effectwallnormal}
For experiments with the coarser($35\mu$) membrane, we observe three
regimes viz. the strong through flow regime
(Figure~\ref{fig:schem}(b)), the diffusion regime (Figure
\ref{fig:schem}(a)), and a transition regime between the above two
regimes that we term as the weak through flow regime.
At higher driving potentials, only half the area above the coarser
membrane is covered by plumes, with the other half having plumes below
the membrane. A wall normal through flow driven by impingement of the
large scale flow is inferred to be the cause of this (Figure
\ref{fig:schem}(b)). In this strong through flow regime, only a single
large scale flow circulation cell oriented along the diagonal or
parallel to the walls is detected. The plume structure is more
dendritic than the no through flow case. The flux scales as $\Delta
C_w^n$, with $7/3\leq n\leq 3$ and is about four times that observed
with the fine membrane. The phenomenology of a flow across the
membrane driven by the impingement of the large scale flow of strength
$W_*$, the Deardorff velocity scale, explains the cubic scaling. We
find the surprising result that the nondimensional flux is smaller
than that in the no through flow case for similar parameters.
The mean plume spacings in the strong through flow regime are larger
and show a different Rayleigh number dependence visavis the no
through flow case. Using integral analysis, an expression for the
boundary layer thickness is derived for high Schmidt number laminar
natural convection boundary layer with a normal velocity at the wall.
(Also, solutions to the integral equations are obtained for the
$Sc\sim 1$ case, which are given as an Appendix.) Assuming the
gravitational stability condition to hold true, we show that the plume
spacing in the high Schmidt number strong through flow regime is
proportional to $\sqrt{Z_w\,Z{_{v_i}}}$, where $Z{_{v_i}}$ is a length
scale from the through flow velocity. This inference is fairly
supported by the plume spacing measurements
At lower driving potentials corresponding to the transition regime,
the whole membrane surface is seen to be covered by plumes and the
flux scaled as $\Delta C_w^{4/3}$.
The nondimensional flux is about the same as in turbulent free
convection over flat surfaces if $\frac{1}{2}\Delta C $ is assumed to
occur on one side of the membrane. This is expected to occur in the
area averaged sense with different parts of the membrane having
predominance of diffusion or through flow dominant transport. At very
low driving potentials corresponding to the diffusion regime, the
diffusion corrected non dimensional flux match the turbulent free
convection values, implying a similar phenomena as in the fine
membrane.
\subsubsection*{Universal probability distribution of near wall structures}
\label{sec:univprobdistr}
We discover that the probability distribution function of the plume
spacings show a standard log normal distribution, invariant of the
presence or the absence of wall normal through flow and at all the
Rayleigh numbers and aspect ratios investigated. These plume
structures showed the same underlying multifractal spectrum of
singularities in all these cases. As the multifractal curve indirectly represents the processes by which
these structures are formed, we conclude that the plume structures are created by a common
generating mechanism involving nucleation at points, growth along
lines and then merging, influenced by the external mean shear.
Inferring from the thermodynamic analogy of multifractal analysis, we
hypothesise that the near wall plume structure in turbulent free
convection might be formed so that the entropy of the structure is
maximised within the given constraints.

14 
Helium Cryostat for Experimental Study of Natural Turbulent Convection / Helium Cryostat for Experimental Study of Natural Turbulent ConvectionUrban, Pavel January 2010 (has links)
V disertační práci je popsán heliový kryostat s experimentální válcovou konvekční celou pro studium proudění při přirozené konvekci za velmi vysokých Rayleigho čísel Ra (až do řádu 10^15) a Nusseltových čísel Nu (až do řádu 10^4). Pracovní látkou je studené 4He, které umožňuje díky výhodným fyzikálním vlastnostem dosažení velmi vysokých hodnot čísel Ra. Návrh kryostatu je založen na koncepci lázňových NMR kryostatů s nízkým odparem kryokapalin. Ve středu kryostatu je umístěna konvekční cela o průměru 300 mm a výšce 300 mm. Celu tvoří horní a spodní dno a výměnná střední část. Tyto díly jsou spojeny rozebíratelnými přírubami těsněnými indiovým drátem. Výměnná část umožňuje snadnou modifikaci geometrie cely. Hlavní přednost kryostatu spočívá v minimálním vlivu konstrukce cely a použitých materiálů na studovanou konvekci. Cela kryostatu je navržena pro pracovní tlaky do 250 kPa.

15 
Coupled Heat Transfer Processes in Enclosed Horizontal Heat Generating Rod BundlesSenve, Vinay January 2013 (has links) (PDF)
In a nuclear fuel cask, the heat generating spent fuel rods are packed in a housing and the resulting bundle is placed inside a cask of thick outer shell made of materials like lead or concrete. The cask presents a wide variation in geometrical dimensions ranging from the diameter of the rods to the diameter of the cask. To make the problem tractable, first the heat generating rod bundle alone is considered for analysis and the effective thermal conductance of the bundle is correlated in terms of the relevant parameters. In the second part, the bundle is represented as a solid of equivalent thermal conductance and the attention is focused on the modelling of the cask. The first part, dealing with the effective thermal conductance is solved using Fluent software, considering coupled conduction, natural convection and surface radiation in the heat generating rod bundle encased in a hexagonal sheath. Helium, argon, air and nitrogen are considered as working media inside the bundle. A correlation is obtained for the critical Rayleigh number which signifies the onset of natural convection. A correlation is also developed for the effective thermal conductance of the bundle, considering all the modes of transport, in terms of the maximum temperature in the rod bundle, pitchtodiameter ratio, bundle dimension (or number of rods), heat generation rate and the sheath temperature. The correlation covers pitchtodiameter ratios in the range 1.12, number of rods ranging from 19 to 217 and the heat generation rates encountered in practical applications.
The second part deals with the heat transfer modeling of the cask with the bundle represented as a solid of effective (or equivalent) thermal conductance. The mathematical model describes twodimensional conjugate natural convection and its interaction with surface radiation in the cask. Both Boussinesq and nonBoussinesq formulations have been considered for convection. Numerical solutions are obtained on a staggered mesh with a pressure correction method using a custommade Fortran code. The surface radiation is coupled to the conduction and convection at the solidfluid interfaces. Steadystate results are obtained using timemarching. Results for various quantities of interest, namely, the flow and temperature distributions, Nusselt numbers, and interface temperatures, are presented. The Grashof number based on the volumetric heat generation and gap width is varied from 105 to 5 ×109. The emissivities of the interfaces are varied from 0.20.8 for the radiative calculations. The solidtofluid thermal conductivity ratio for the inner cylinder is varied in the range 520 in the parametric studies. Simulations are also performed with thermal conductivity calculated in an iterative manner from bundle parameters. The dimensionless outer wall conductivity ratio is chosen to correspond to cask walls made of lead or concrete. The dimensionless thickness (with respect to gap width) of the outer shell is in the range of 0.08251, while the inner cylinder dimensionless radius is 0.2. Air is the working medium in the cask for which the Prandtl number is 0.71. Correlations are obtained for the average temperatures and Nusselt numbers at the inner interface in terms of the parameters. The radiation heat transfer is found to contribute significantly to the heat dissipation.

16 
Beeinflussung der thermomagnetischen Konvektion in Ferrofluidschichten durch den magnetischen SoretEffektSprenger, Lisa 02 December 2013 (has links) (PDF)
Diese Arbeit stützt sich auf die theoretische und experimentelle Untersuchung der Thermodiffusion im Magnetfeld. Bei magnetischen Flüssigkeiten als kolloidalen Suspensionen versteht man unter der Thermodiffusion einen durch einen Temperaturgradienten angestoßenen unidirektionalen Partikeltransport, der zur Separation des Fluids führt. Beschrieben wird die Thermodiffusion theoretisch über das Konzentrationsprofil der Partikel in Abhängigkeit von Zeit und Ort in einer Fluidschicht. Die Experimente detektieren die Separation des Fluids über die Konzentrationsdifferenz zwischen zwei Fluidkammern. Die Bestimmung des SoretKoeffizienten erfolgt über einen Datenfit zwischen experimentellen und theoretischen Daten. Für das kerosinbasierte Ferrofluid EMG905 wurden zwei Effekte festgestellt. Bei kleinen Magnetfeldstärken wandern die Partikel zum kalten Rand der Schicht (ST>0), bei steigenden Feldstärken kehrt sich diese Richtung um (ST<0). Die Ergebnisse der Untersuchungen zur Thermodiffusion gehen dann in eine lineare Stabilitätsanalyse einer Ferrofluidschicht bei anliegendem Temperaturgradienten und Magnetfeld ein. Dabei wird festgestellt, dass die kritische RayleighZahl als charakteristische Größe zum Einsetzen von Konvektion von dem SoretKoeffizienten abhängt. Ist letzterer positiv, wird das Einsetzen von Konvektion begünstigt, ist er wiederum negativ, so kann Konvektion vollständig unterdrückt werden.

17 
Beeinflussung der thermomagnetischen Konvektion in Ferrofluidschichten durch den magnetischen SoretEffektSprenger, Lisa 25 October 2013 (has links)
Diese Arbeit stützt sich auf die theoretische und experimentelle Untersuchung der Thermodiffusion im Magnetfeld. Bei magnetischen Flüssigkeiten als kolloidalen Suspensionen versteht man unter der Thermodiffusion einen durch einen Temperaturgradienten angestoßenen unidirektionalen Partikeltransport, der zur Separation des Fluids führt. Beschrieben wird die Thermodiffusion theoretisch über das Konzentrationsprofil der Partikel in Abhängigkeit von Zeit und Ort in einer Fluidschicht. Die Experimente detektieren die Separation des Fluids über die Konzentrationsdifferenz zwischen zwei Fluidkammern. Die Bestimmung des SoretKoeffizienten erfolgt über einen Datenfit zwischen experimentellen und theoretischen Daten. Für das kerosinbasierte Ferrofluid EMG905 wurden zwei Effekte festgestellt. Bei kleinen Magnetfeldstärken wandern die Partikel zum kalten Rand der Schicht (ST>0), bei steigenden Feldstärken kehrt sich diese Richtung um (ST<0). Die Ergebnisse der Untersuchungen zur Thermodiffusion gehen dann in eine lineare Stabilitätsanalyse einer Ferrofluidschicht bei anliegendem Temperaturgradienten und Magnetfeld ein. Dabei wird festgestellt, dass die kritische RayleighZahl als charakteristische Größe zum Einsetzen von Konvektion von dem SoretKoeffizienten abhängt. Ist letzterer positiv, wird das Einsetzen von Konvektion begünstigt, ist er wiederum negativ, so kann Konvektion vollständig unterdrückt werden.

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