Visokotemperaturni spremnici topline predstavljaju najzreliju tehnologiju za centraliziranu
pohranu energije velikih razmjera. Postojeći, komercijalni, visokotemperaturni
spremnici pohranjuju energiju u obliku osjetne topline, a najčešće se koriste u solarnim
termoelektranama gdje omogućuju njihovo upravljanje, bez dodatnih gubitaka pretvorbe
energije, manje-više neovisno o sunčevom zračenju. Daljnji razvoj visokotemperaturnih
spremnika topline može predstavljati jedan od najznačajnijih koraka prema 100% obnovljivim
elektro-energetskim sustavima. Najveći potencijal tog razvoja krije se u latentnim
spremnicima topline koji omogućuju efikasniji rad i mnogo veću gustoću pohrane energije,
no zbog vrlo niskih toplinskih provodnosti materijala za pohranu još nisu dosegli
komercijalnu upotrebu. Ovakav potencijal prepoznat je od znanstvene zajednice, što je,
posljednjih godina, rezultiralo naglim porastom broja istraživanja na temu poboljšanja
procesa punjenja i pražnjenja latentnih spremnika. Nažalost, velik broj numeričkih istra
živanja nije popraćen eksperimentalnim istraživanjima pa je većina korištenih modela
validirana na temelju mjerenja za niskotemperaturne spremnike, temperaturnim mjerenjima
kod vrlo specifičnih geometrija ili uopće nije validirana.
Slijedom navedenog, u ovom je radu sjedinjen numerički i eksperimentalni pristup kako
bi se dobio validiran numerički model koji se može pouzdano i brzo koristiti za analizu i
poboljšavanje dinamičkih značajki visokotemperaturnih spremnika topline. U sklopu istra
živanja razvijen je i implementiran matematički model temeljen na metodi konačnih volumena
i entalpijsko-porozijskoj metodi za simuliranje promjene agregatnog stanja (faze).
U model je uključen i implicitni podmodel spregnutog prijenosa topline izmedu izmjenjiva
ča i materijala za pohranu.
Paralelno je razvijen eksperimentalni postav koji omogućuje dvostruko praćenje procesa
taljenja (temperature i položaja fronte taljenja) materijala za visokotemperaturnu pohranu
latentne topline - natrijeva nitrata u spremniku većih dimenzija. Ukupno su provedena
tri nezavisna eksperimenta taljenja, a dobiveni rezultati iskorišteni su za validaciju
postavljenog numeričkog modela. Usporedbom rezultata pokazano je kako korištenje isklju
čivo temperaturnih mjerenja može dovesti do lažne validacije. Detaljnim pregledom
literature nisu pronadeni izravno dobiveni podatci o napredovanju fronte taljenja u visokotemperaturnim
spremnicima, što ove rezultate čini još vrjednijim.
Primjenom validiranog modela sustavno su analizirane različite geometrije orebrenih spremnika
konstrukcije cijev-u-cijevi. Istraživanje je pokazalo kako reorijentacija rebara s ciljem
maksimiziranja efekta prirodne konvekcije tijekom taljenja kod horizontalnih spremnika
s dva rebra može ubrzati proces taljenja preko 50%. Utvrdeno je i kako vrijeme taljenja
nije najbolji pokazatelj performansi spremnika, jer tijekom procesa taljenja može doći do
zadržavanja krutine u rubnim dijelovima spremnika. Na samom kraju rada predstavljen je
postupak automatske optimizacije položaja rebra korištenjem genetskih algoritama. Njegovim
korištenjem postignuto je povećanje pohranjene energije od 40.3% kod vertikalnih
spremnika s horizontalnim rebrima.
A wider utilization of energy storages is one of the most important steps towards the
100% renewable energy systems. By integrating thermal energy storage (TES) systems
with concentrated solar power (CSP) plants, it is possible to directly store heat and
transform it into electricity later, therefore avoiding additional energy transformations.
High-temperature sensible TES systems are already commercially utilized, mostly as twotank
molten salt design, together with large CSP plants. High-temperature latent heat
storages (HTLES), on the other hand, have numerous advantages such as higher energy
density and (near) isothermal energy transfer, but due to some inherited drawbacks which
are characteristic for high temperature phase change materials (PCM), they are not yet
commercially used in CSP plants. Most PCMs suitable for HTLES are salts. Salts are
characterized by low thermal conductivity which severely limits achievable heat transfer
rates in HTLES. To increase commercial appeal of the high temperature PCM, achievable
heat transfer rates need to be increased, either by improving the effective thermal conductivity
of PCMs (material modifications), improving heat exchanger geometry or by
Traditional heat exchanger design methods are limited by high non-linearity and transient
nature of the problem, therefore, detailed numerical models of the high temperature
PCMs are used. As a result, there are different models which can be distinguished based
on dimensionality (1D, 2D or 3D), heat transfer mechanism (conduction or conduction +
convection), usage of fixed or adaptive grid, phase boundary modeling, etc. However, an
increasing number of papers concerning high temperature LTES numerical modeling is
not accompanied by the increase of experimental papers that can be used for model validation.
These few papers with experimental results are limited to temperature data for
very specific geometries while model validation with that data usually results in relatively
large temperature errors which occur during the period of melting front propagation.
In this thesis a finite volume numerical model based on the enthalpy-porosity approach
is proposed and implemented in open source computational fluid dynamics toolbox
OpenFOAM. A dedicated experimental setup for more reliable measurements of high temperature PCMs is developed. Setup allows both melting front propagation measurements
and temperature measurements at different points during the melting. New model is successfully
validated by acquired data. In the final part of the thesis, the validated model
is used for analysis of different parameters of finned shell-and-tube storages and, finally,
for optimization of HTLES by geometry modifications of the heat exchanger.
A numerical model for simulation of high-temperature phase change materials based on
the transient modified Navier-Stokes equations was used in this thesis. The following simplifications
of natural phenomena were introduced: density change due to the temperature
and phase changes was neglected; radiation heat transfer was ignored; liquid fraction was
assumed to be a linear function of the temperature; solid PCM is homogeneous material
with isotropic (although temperature dependent) properties and without porosity;
influence of the crystal orientation is neglected. Equations were discretized using the finite
volume approach and implemented in the open source computational fluid dynamics
toolbox OpenFOAM. The flow is assumed to be incompressible while Boussinesq approximation
is used to account for body forces from temperature-caused density variations. A
widely accepted fixed-mesh enthalpy-porosity method proposed by Woller was implemented
for phase-change modeling.
Conjugate heat transfer is modeled implicitly. For all equations and for both solid (heat
exchanger) and PCM the same mesh was used. Unmodified heat equation is solved for the
whole domain whereas velocity is set to 0 during solution of the momentum equation (that
is, during PIMPLE steps). The geometry of heat exchanger - PCM interface coincides
with mesh faces. Harmonic interpolation is used for discretization of the heat equation
on interface cells, while no slip boundary condition is implemented for the momentum
Following the idea of a simple geometry and numerical reproducibility, experimental setup
is constructed as a simple rectangular cavity. The cavity is heated from the isothermal
left side and cooled from the isothermal right side, while other sides are adiabatic. The
identification of the melting front is achieved visually, using a commercial digital camera,
therefore the front plate of experimental setup is transparent.
The dimensions of the cavity are 300 x 300 x 110 mm. A relatively large height is chosen
to allow high Grashof numbers and a possibility of turbulent flow. Sodium nitrate, a very
popular high-temperature PCM, with well-known properties is chosen. PCM is enclosed
in an inner case which is constructed from stainless steel with borosilicate glass at the
front and copper heaters on left and right. Heaters are built by fixing a 1 kW electric
heater plates on 15 mm thick copper plates. Thick copper plates are used to achieve a
uniform temperature distribution and to avoid significant vertical temperature variations.
Sealing the inner case proved to be very challenging as a very elastic gasket is necessary to
avoid high forces acting on the glass and breaking it due to the temperature deformations
of the case. Since >300 ◦C temperature range is too high for most elastic gaskets, 3mm
graphite sheets with thin layer of high temperature silicone were used. Silicone is known
to react with strong oxidizing materials (such as sodium nitrate) which results in PCM
leakage after more than 10-15 hours of system operation (above melting point). To prevent
leakage, the sealant was replaced after every experiment.
Thermal insulation, 100 mm of rock wool, is placed on the outside of the outer case while
empty space between inner and outer case is also filled with rock wool. The front of the
outer case is a triple insulated glass with removable insulation baffle between the outer
and the inner glass. The baffle is filled with rock wool and can be removed to take photos.
On top of both the inner and outer case, a square orifice is created. The orifice provides
sufficient light inside the inner case for taking photos. The square shape of the orifice
results in the light sheet that highlights melting front form.
Three different experiments were run, distinct by the hot wall temperature (Rayleigh
number) and cavity orientation. In all experiments, the shape of the melting front is
characterized by very fast propagation near the top (free surface), and insignificant front
movement in the lower part of the domain.
Validation and verification
Accuracy of the finite volume numerical simulation depends on model accuracy, discretization
methods, mesh quality and case parameters (boundary and initial conditions etc.).
Enthalpy-porosity method is also characterized by the ”unphysical” constant C which defines
the flow in mushy region and for which there are no consensual values in literature.
For each experiment, a series of simulations with different meshes and parameters such
as melting temperatures and C values was run. The model was successfully validated on
all three cases and some interesting observations were made. Value of the heat transfer
coefficient differs significantly from the literature which deals with pure sodium nitrate
properties. A similar observation was already reported by some authors, therefore the
corrected heat transfer coefficient was calculated using iterative approach and used in
Contrary to some authors, it is shown that the value of constant C has significant effect
on the melting process, especially for coarser meshes. Good choice of C value can lead
to accurate simulations on coarser meshes, thus significantly reducing the run time for
simulation which can be of huge importance in optimization studies. It is also shown that
temperature data comparison can lead to false validation.
Heat transfer rate improvement
Different finned shell-and-tube configurations were numerically analyzed to asses influence
of the number of fins, fin positioning and fin material on charging and discharging
process. Both quantitative and qualitative differences between different fin materials and
configurations are observed. Two and four finned configurations were explored. It can
be concluded that melting (charging) time varies greatly with different heat exchanger
geometries. Bad utilization of natural convection can prolong melting for more than 50%.
Also it can be observed that the melting time is not the most appropriate characteristic
for determining the performances of the storage, as it is shown that melting time for one
case is 64% longer than in the other case, while the stored energy during the charging
is almost the same (within 10%). This is very important to note since the melting time
is frequently used for measuring storage performances. The effect of heat transfer improvement
by utilizing natural convection with fin reorientation is nullified during the
storage discharge. However, in some specific work regimes where the available charging
time varies and the discharging is slow (CSP with inconsistent energy surplus during the
day and low night consumption), those modifications can be advantageous.
Last part of this thesis considers the application of genetic algorithm for geometry optimization
of the LHTES heat exchanger. Optimization is performed on the finned vertical
shell-and-tube storage. Geometry is described using eight variables (height and length of
each of the four fins). Benchmark geometry with four equally spaced and equally long
fins was defined as the starting point for the optimization. Overall stored energy during
50 minutes of simulation is used as fitness function, which is equal to 53.5 kJ or around
50% melting for the benchmark geometry. The optimized HTLES can store 75.1 kJ or
40.3% more energy than the referent HTLES in the same time.
Conclusion and scientific contribution
• Unique, front propagation experimental data is provided that can be used for validation
of HTLES models in general.
• By comparing both front propagation data and temperature measurements with
experiments, it is proven that using only temperature data can lead to false validation
of the model. Influence of the constant C on simulation results can be
significant for coarser meshes.
• Different finned HTLES shell-and-tube geometries were analyzed. It is shown that
influence of fin orientation plays a crucial role during charging. Significant improvement
of charging performance can be achieved by positioning fins with respect
to maximizing natural convection. Influence of the fin material (thermal conductivity)
is not only quantitative (i.e. higher conductivity - faster charging): changing
fin orientations of steel fins plays an insignificant role compared to aluminum fins,
where right orientation can reduce melting time significantly.