This document summarizes a simulation model developed to analyze heat storage in a thermocline tank for concentrated solar power plants. The model is based on solving convection-diffusion equations for heat transfer in the fluid and between the fluid and filler material. It is validated against experimental data and used to analyze the effects of tank geometry on storage efficiency and compare different heat transfer fluids. The model is then applied to design an alternative storage system for a solar plant called AndaSol I.
This paper gives a short overview of the theoretical and practical aspects of a thermal diffusion column, of the most important applications of 13C and describes a thermal diffusion cascade for enrichment of this isotope.
This paper gives a short overview of the theoretical and practical aspects of a thermal diffusion column, of the most important applications of 13C and describes a thermal diffusion cascade for enrichment of this isotope.
Design and performance of Four-Stage Adsorption SystemIJRES Journal
A design of four-stage adsorption system was proposed to utilize very low temperature waste heat or solar heat. A simulation model for the proposed cycle was developed to analyse the influence of cycle time and driving heat source temperature on the performance of system identifying the specific cooling power (SCP) and coefficient of performance (COP). It was found that the proposed cycle could be driven by waste heat temperature as low as 35oC with the coolant at 30oC. Both SCP and COP of the proposed system is very low at lower heat source temperature, which can be improved through optimization of cycle time with other design parameters.
Numerical Modeling and Simulation of a Double Tube Heat Exchanger Adopting a ...IJERA Editor
The double tube heat exchangers are commonly used in industry due to their simplicity in design and also their
operation at high temperatures and pressures. As the inlet parameters like temperatures and mass flow rates
change during operation, the outlet temperatures will also change. In the present paper, a simple approximate
linear model has been proposed to predict the outlet temperatures of a double tube heat exchanger, considering it
as a black box. The simulation of the heat exchanger has been carried out first using the commercial CFD
software FLUENT. Next the linear model of the double tube heat exchanger based on lumped parameters has
been developed using the basic governing equations, considering it as a black box. Results have been generated
for outlet temperatures for different inlet temperatures and mass flow rates of the cold and hot fluids. The results
obtained using the above two methods have then been discussed and compared with the numerical results
available in the literature to justify the basis for the assumption of a linear approximation. Comparisons of the
predicted results from the present model show a good agreement with the experimental results published in the
literature. The assumptions of linear variation of outlet temperatures with the inlet temperature of one fluid
(keeping other inlet parameters fixed) is very well justified and hence the model can be employed for the
analysis of double tube heat exchangers.
An Offshore Natural Gas Transmission Pipeline Model and Analysis for the Pred...IOSRJAC
The purpose of this paper is to model and analyze an existing natural gas transmission pipeline – the 24-inch, 5km gas export pipeline of the Amenam-Kpono field, Niger Delta, Nigeria – to determine properties such as pressure, temperature, density, flow velocity and, in particular, dew point, occurring at different segments of the pipeline, and to compare these with normal pipeline conditions in order to identify the segments most susceptible to condensation/hydrate formation so that cost-effective and efficient preventive/remedial actions can be taken. The analysis shows that high pressure and low temperature favor condensation/hydrate formation, and that because these conditions are more likely in the lower half of the pipeline system, remedial/preventive measures such as heating/insulation and inhibition injection should be channeled into that segment for cost optimization..
Numerical Study of Entropy Generation in an Irreversible SolarPowered Absorpt...inventionjournals
The ideal three-heat-reservoir (THR) model for absorption refrigeration cycles is extended to include external and internal irreversibilities. Three empirical functions are used to model the internal entropy generation of the cycle. The parameters of these functions are estimated by fitting data obtained by simulation to the predictions of the THR model. The THR model using a linear function or a logarithmic function for the internal entropy generation is able to reproduce performance data for absorption systems with good accuracy
Design and performance of Four-Stage Adsorption SystemIJRES Journal
A design of four-stage adsorption system was proposed to utilize very low temperature waste heat or solar heat. A simulation model for the proposed cycle was developed to analyse the influence of cycle time and driving heat source temperature on the performance of system identifying the specific cooling power (SCP) and coefficient of performance (COP). It was found that the proposed cycle could be driven by waste heat temperature as low as 35oC with the coolant at 30oC. Both SCP and COP of the proposed system is very low at lower heat source temperature, which can be improved through optimization of cycle time with other design parameters.
Numerical Modeling and Simulation of a Double Tube Heat Exchanger Adopting a ...IJERA Editor
The double tube heat exchangers are commonly used in industry due to their simplicity in design and also their
operation at high temperatures and pressures. As the inlet parameters like temperatures and mass flow rates
change during operation, the outlet temperatures will also change. In the present paper, a simple approximate
linear model has been proposed to predict the outlet temperatures of a double tube heat exchanger, considering it
as a black box. The simulation of the heat exchanger has been carried out first using the commercial CFD
software FLUENT. Next the linear model of the double tube heat exchanger based on lumped parameters has
been developed using the basic governing equations, considering it as a black box. Results have been generated
for outlet temperatures for different inlet temperatures and mass flow rates of the cold and hot fluids. The results
obtained using the above two methods have then been discussed and compared with the numerical results
available in the literature to justify the basis for the assumption of a linear approximation. Comparisons of the
predicted results from the present model show a good agreement with the experimental results published in the
literature. The assumptions of linear variation of outlet temperatures with the inlet temperature of one fluid
(keeping other inlet parameters fixed) is very well justified and hence the model can be employed for the
analysis of double tube heat exchangers.
An Offshore Natural Gas Transmission Pipeline Model and Analysis for the Pred...IOSRJAC
The purpose of this paper is to model and analyze an existing natural gas transmission pipeline – the 24-inch, 5km gas export pipeline of the Amenam-Kpono field, Niger Delta, Nigeria – to determine properties such as pressure, temperature, density, flow velocity and, in particular, dew point, occurring at different segments of the pipeline, and to compare these with normal pipeline conditions in order to identify the segments most susceptible to condensation/hydrate formation so that cost-effective and efficient preventive/remedial actions can be taken. The analysis shows that high pressure and low temperature favor condensation/hydrate formation, and that because these conditions are more likely in the lower half of the pipeline system, remedial/preventive measures such as heating/insulation and inhibition injection should be channeled into that segment for cost optimization..
Numerical Study of Entropy Generation in an Irreversible SolarPowered Absorpt...inventionjournals
The ideal three-heat-reservoir (THR) model for absorption refrigeration cycles is extended to include external and internal irreversibilities. Three empirical functions are used to model the internal entropy generation of the cycle. The parameters of these functions are estimated by fitting data obtained by simulation to the predictions of the THR model. The THR model using a linear function or a logarithmic function for the internal entropy generation is able to reproduce performance data for absorption systems with good accuracy
Transformación digital: herramientas y estrategias para una transición eficie...HelpSystems
Operaciones manuales, esperas en la sucursal, canales tradicionales… ya son historia antigua. En la Era de la Trasformación Digital el Negocio Financiero está obligado a adaptarse rápidamente para aumentar la productividad, mejorar el servicio a los clientes y reducir sus costos operativos. Mobile banking, biometría, e–wallet, venta online de seguros e iniciativas paperless, son algunos ejemplos de transformaciones tecnológicas muy exitosas para el negocio, pero que conllevan un período de adaptación por parte de los clientes y los usuarios internos. Requieren modificar sistemas, equipos, procesos y dinámicas, por lo que la etapa de transición en general se torna muy difícil
Ante esto, IT necesita asegurarse que los proyectos de transformación digital se lleven a cabo sin riesgos, ni pérdidas de dinero e imagen. Para ello, las tecnologías de monitorización y automatización son herramientas clave para que el negocio fluya sin interrupciones y en forma segura, garantizando el cumplimiento de los niveles de servicio acordados (SLAs) y de las auditorías.
Nicolás Brosky, Director Comercial de Barcelona/04, explica cuáles son las herramientas y estrategias más efectivas para asegurar que su proyecto de transformación digital resulte exitoso.
Optimization of Air Preheater for compactness of shell by evaluating performa...Nemish Kanwar
Designing of an Air Preheater with increased performance from an existing design through alteration in baffle placement. Analysis of 4 Baffle designs for segmented Baffle case was done using Ansys Fluent. The net heat recovery rate was computed by subtracting pump work from heat recovered. Based on the result, Air Preheater design was recommended.
วารสารวิชาการเทคโนโลยีพลังงานและสิ่งแวดล้อม บัณฑิตวิทยาลัย วิทยาลัยเทคโนโลยีสยาม
Journal of Energy and Environment Technology of Graduate School Siam Technology College
Radial Heat Transport in Packed Beds-III: Correlations of Effective Transport...inventionjournals
The reliability and accuracy of experimental with predictions data of two models ("MC model" Marshall and Coberly model, [1] and modified model by Ibrahim et al. [2] are investigated for the effective radial thermal conductivity (Ker), and the wall heat transfer coefficient (hw) in packed beds in the absence of chemical reactions. The results were evaluated by the modified mathematical model as to the boundary bed inlet temperature; (To) number of terms of the solution series and number of experimental points used in the estimate. Very satisfactory was attained between the predicted and measured temperature profiles for a range of experiments. These cover a range of tube to (equivalent) particle diameter ratios from dt /dp = 4 to 10; Reynolds numbers ranged between 3.8-218 for particle, and elevated pressure from 11 to 20 bar for particle catalyst pellets. In all cases the fluid flowing throughout the bed has been air. The results indicate to the choice of the inlet boundary condition can have a large impact on the values of obtained parameters. And model parameters have been shown to be dependent on the pressure inside the reactor. The following correlations for both (hw) and (Ker) respectively under a given conditions obtained by using multiple regressions of our results that based on the modified mathematical model: Nuw = 67.9Re0.883(dt /dp) -0.635(P/Po) -1.354 Ker = 0.2396 + 0.0041Re The results accuracy of these correlations obtained from the modified mathematical model are more than the results accuracy of correlations obtained from MC model with respect to experimental data; these accuracy of both correlations reach up to 91% and 65% for (hw) and (Ker) respectively; which these results indicate to the reliability
Peltier Thermoelectric Modules Modeling and EvaluationCSCJournals
The purpose of this work is to develop and experimentally test a model for the Peltier effect heat pump for the transient simulation in Spice software. The proposed model uses controlled sources and lumped components and its parameters can be directly calculated from the manufacturer’s data-sheets. In order to validate this model, a refrigeration chamber was designed and fabricated by using the Peltier modules. The overall system was experimentally tested and simulated with Spice. The simulation results were found to be compatible with the experimental results. This model will help designers to better design thermal systems using the Peltier modules.
Theoretical Convective Heat Transfer Model Developement of Cold Storage Using...IJERA Editor
Energy crisis is one of the most important problems the world is facing now-a-days. With the increase of cost of electrical energy operating cost of cold storage storing is increasing which forces the increased cost price of the commodities that are kept. In this situation if the maximum heat energy(Q) is absorbed by the evaporator inside the cold room through convective heat transfer process in terms of –heat transfer due to convection and heat transfer due to condensation, more energy has to be wasted to maintain the evaporator space at the desired temperature range of 2- 8 degree centigrade. In this paper we have proposed a theoretical heat transfermodel of convective heat transfer incold storage using Taguchi L9 orthogonal array. Velocity of air(V), Temperature difference(dT), RelativeHumidity(RH)are the basic variable and three ranges are taken each of them in the model development. Graphical interpretations from the model justifies the reality
There are three modes for heat transfer: convection, conduction, and radiation. The convection heat transfer plays an important role in many industrial applications. The convection heat transfer is usually subdivided into free and forced convection. In the forced convection, the fluid is blown or pumped past the heated surface using a pump or a fan, while in the natural (or free) convection, fluid flow is naturally achieved by buoyancy effects, i.e., density variation in the fluid.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
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Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
Analysis of Heat Storage with a Thermocline Tank for Concentrated Solar Plants: Application to Andasol I
1. Analysis of Heat Storage with a Thermocline Tank for Concentrated
Solar Plants: Application to AndaSol I
Abstract— The storage system in a concentrated solar
plant is considered as an important concern to increase the
capacity factor of the plant by producing power during the
night or in cloudy days. This paper presents the analysis of
a thermocline system, which consists of a single tank that
typically works with molten salt and quartzite rock as
storage media. A simulation model of heat charging and
discharging process is developed with the numerical
solution of non-dimensional convection-diffusion
equations. These equations describe the heat transfer in
the fluid and between the fluid and the filler material. The
model is validated with experimental data, and the results
are compared with other models. The proposed model is
used for the design of an alternative storage system for
AndaSol I. Moreover, the model is used to analyze the
influence of the ratio between height and diameter of the
tank on the energy storage efficiency. Finally, a
comparison between three thermal fluids is made in order
to find out which heat transfer fluid (HTF) is better for the
designed thermal storage tank.
I. INTRODUCTION
It is widely known that we live in an unsustainable world,
and that the increase of population predicted for the next
decades will require much more amount of energy. Moreover,
the natural resources are limited and some of them are
beginning to disappear. For these reasons, the goals for the
next years in the energy security are clear and a consensus is
reached for the most part among the academia and the public:
significant improvements on the efficiency of energy
processes and an increase in the use of renewable energy
sources which not require limited natural resources are
necessary.
Solar power plants are a good alternative for conventional
thermal power stations to produce sustainable electricity.
However, they should deal with the problem of producing
power during the periods when sun is not available.
Consequently, to improve the efficiency of solar plants, most
of investigations focus efforts on the thermal storage system.
A review of the state of art on thermal energy storage and
important concepts and materials are presented in [1]. There
are already quite a few different types of storage, but the
thermocline tank system has significant advantages compared
to the other systems because of its low-cost in comparison
with the two-tank system. Herrman et al. [2] offer an overview
on different storage systems and Flueckiger et al. [3]
investigated a simulation model for the thermocline tank.
Here, a model is developed in order to simulate charge and
discharge process, and used in the design of an alternative heat
storage system for AndaSol I solar plant. The storage system
currently used in this plant consists of two separate tanks
which store the hot and cold fluid independently. Therefore, a
storage system with one single thermocline tank with the same
heat capacity will be proposed as a low-cost alternative.
II. MODEL DEVELOPMENT
This section presents the governing heat equations of the
model. A detailed explanation of the development of the
dimensionless governing equations for the model can be found
in [4].
Energy balance in the heat transfer fluid is given by the
convection-diffusion equation:
( )* * * *
1f f f
s f eff
r
k
t z z z
∂θ ∂θ ∂θ ∂
+ = θ −θ +
τ∂ ∂ ∂ ∂
(1)
where,
2
r
f f
s
C Ru
H hS
ρ επ
τ = (2)
and
2
(1 )s
s
f R
S
r
π − ε
= (3)
Energy balance between the filler material and the HTF is
given by:
( )*
s CR
s f
r
H
t
∂θ
= − θ − θ
τ∂
(4)
where HCR is the ratio of heat capacities,
(1 )
f f
CR
s s
C
H
C
ρ ε
=
ρ − ε
(5)
and θf and θs are the non-dimensional temperatures of the fluid
and the solid phases:
f c
f
h c
T T
T T
−
θ =
−
, s c
s
h c
T T
T T
−
θ =
−
(6)
Lastly, the non-dimensional position and time are given by:
Serhat Yesilyurt
Mechatronics Department
Sabanci University
Istanbul, Turkey
syesilyurt@sabanciuniv.edu
Albert Graells Vilella
Exchange Student from Technical University of Catalonia
Sabanci University
Istanbul, Turkey
agraellsvilella@gmail.com
2. * *
,
z u
z t t
H H
= =
(7)
A. Numerical solution
The model below is based on dimensionless governing
equations (1) and (4). The aim is to solve two equations with
two unknown vectors with the finite difference method. The
transient term is expressed with the Backward Euler implicit
method and central differences are used for the derivatives
with respect to axial position:
, 1 , 1 * *
* *
* *
,
2
k
f f k f k
k
z z
z k z
z z
+ −
=
∂θ θ − θ
≈ = ∆
∂ ∆
(8)
, 1 , , 1
* * *2
* *
2
k
f f k f k f k
z z
z z z
+ −
=
∂θ θ − θ + θ ∂
≈
∂ ∂ ∆
(9)
As the simulation is considered one dimensional in the axis
direction, the axial position in the tank is represented with N
nodes placed vertically in the axis of the tank. The linear
system of equations that represent the energy balance in the
fluid is obtained as:
( ) ( )*
1 1
2
f
f s f
r zt
∂
+ + = − +
τ ∆∂
θ
B C θ θ θ b (10)
where B is the matrix that corresponds to the second-order
accurate convective term in (8), C is the second-order accurate
conduction term in (9) and ,0 ,0,f = θ b ⋯ is the vector that
helps to impose Dirichlet boundary conditions at the inlet.
First-order unconditionally stable Backward Euler method
is used for the derivative of the temperature:
( ) ( ), 1 ,
, 1 , 1 , 1
1f j f j
f j s j f j
rt
+
+ + +
−
+ + = − +
∆ τ
θ θ
B C θ θ θ b (11)
Then, (11) is reordered to put the terms , 1f j+θ in the left
side of the equality, and after a few steps we obtain a simple
equation from which we can obtain the solution.
1
, 1f j
−
+ =θ A f (12)
where,
1 1
rt
= + + + ∆ τ
A B C I (13)
and
, 1 , *
1 1 1
2
s j f j
r t z
+= + +
τ ∆ ∆
f θ θ b (14)
A similar, but simpler, procedure is repeated for solving
(4) for the filler material using the first order differences in
time with Backward Euler implicit algorithm.
, 1 ,
*
s j s js
tt
+ −∂
≈
∆∂
θ θθ
(15)
We obtain:
, 1 , , 1
1 1CR CR
s j s j f j
r r
H H
t t
+ +
+ = +
∆ τ ∆ τ
θ θ θ (16)
Finally, the initial and boundary conditions for the
charging and discharging process must be defined. In the
charging period, the boundary conditions show that HTF
enters from the top of the tank at Th, while in the discharging
period the HTF enters from the bottom of the tank at Tc.
Therefore, the initial and boundary conditions for both energy
equations are defined respectively as:
i) Discharge Process:
10 ( )s ft f z= → θ = θ = , ( )*
0 0 0ft z> → θ = = (17)
ii) Charge Process:
20 ( )s ft f z= → θ = θ = , ( )*
0 1 1ft z> → θ = = (18)
III. MODEL VALIDATION
In this section, the results will be compared with
experimental data in order to validate model designed.
Moreover, a comparison with analytical results will be done as
well.
A. Comparisons with Experimental Data
For this comparison, the model is run with parameters
presented in [4]. Fig. 1 shows the predicted dimensionless
temperature distribution of the HTF obtained with our model
every half an hour during 2 hours of discharging process. One
can easily see that the agreement with experimental points is
quite satisfactory.
Figure 1. Comparison of modeling predicted results with experimental data
from [4].
B. Comparison with Analytical Results
Before using the model for new designs, some other
validation studies are needed in order to improve the
reliability of the model. In this case, we will repeat the
analytical results in [4].
First, we simulate the dimensionless fluid temperature in
the tank for 5 cycles. Each cycle includes charging and
discharging which take 4 hours each. Each process is repeated
for 10 cycles and the dimensionless temperature distribution is
plotted every half hour. After 10 cycles, the initial condition
does not affect the temperature distribution in the tank. The
initial condition of the simulation was is an ideal, fully
3. charged tank, for which after several cycles the initial and
final temperature distributions remain constant.
Fig. 2 shows the agreement between the HTF and the filler
material temperatures after a discharge process. As it was
expected, both distributions are practically the same.
However, there is a slight temperature difference from z* =
0.7 to z* = 1 caused by the sudden temperature decrease. The
temperature difference in z* = 1 is 0.03 which is the same as
observed in [4].
The next analysis is the influence under different number
of discretized nodes in the dimensionless temperature
distribution. As one can see in Fig. 3, modeling error increases
considerably with decreasing number of nodes. However, the
accuracy of the model is satisfactory between 100 and 1000
nodes.
Figure 2. HTF and Filler Material dimensionless temperature distribution in
the tank after 4 hours of discharge process.
Figure 3. Comparison of dimensionless temperature distribution after 4 hours
discharging under different number of nodes.
I. SIZING THERMAL STORAGE TANKS
The design of a thermocline tank consists of determination
of the size (length and diameter) that satisfies the required
energy storage of the solar plant. The size of the storage tank
is dictated by the required operational conditions which are:
electrical power output, thermal efficiency, duration of heat
discharge period, high temperature of the HTF and low
temperature of HTF returned, properties of HTF, properties of
the filler material, and the packing porosity [5].
A. Tank Sizing
The first step is to consider the tank as an ideal
thermocline tank and to calculate the baseline volume for this
case. The difference between an ideal thermocline tank and
the real one is the presence of a filler material in the
thermocline. The presence of a packed bed will explain why
the distribution of the temperature is stratified, as it can be
seen in Fig. 4. In order to avoid the temperature degradation, it
is necessary to use an ideal thermocline tank or to have a
system which stores much more thermal energy than needed.
Thus, during the discharge time period, the temperature
degradation must be minimal. However, in a real thermal
energy storage system, when the cold fluid is pumped into the
bottom of the tank, it extracts heat from the filler material.
After some time, the HTF could not heat up because the filler
material would become cold as well. Therefore, in a thermal
storage design, the goal is to minimize the temperature
degradation during the required operational period of time
such that the temperature of the HTF varies from the filler
temperature, Th, minimally.
Figure 4. Illustration of a single tank thermal storage system, [4]
Required total energy storage is obtained from the values
of the electric power output, Pe, the thermal efficiency, ηT, of
the power plant and the operation time period:
( ) ( ) e
total P h cf
T
P
Q V C T T t= ρ − = ∆
η
(19)
Moreover, to meet the requirement of minimum
temperature degradation, one needs to store large amount of
thermal energy than in an ideal tank. The mathematical
expression of this requirement is given by:
( ) ( )1s s f f real f f idealC C V C V ρ −ε +ρ ε = ρ (20)
The second step consists of using a model in order to evaluate
the heat transfer and observe the temperature degradation for a
fully charged tank with packed bed.
B. Alternative Design for AndaSol I
First, we determined the minimum required volume for a
single storage tank based on the ideal thermocline. We use
(19) in order to obtain the total heat storage required, which is
1000 MWhth.
The operation time period is 7.5 hours because it is the
same storage capacity of AndaSol I plant [6]. Here we aim to
optimize the design of the tank maintaining the same required
4. operational conditions. With (23) we get the ideal volume
which is 14.695 m3
for the specifications of the AndaSol I
plant.
( ) ( )
total
ideal
P h cf
Q
V
C T T
=
ρ −
(21)
Moreover, in order to consider a bigger volume which
minimizes the temperature degradation, we use the following
requirement:
( )1
f f
real ideal
s s f f
C
V V
C C
ρ
=
ρ − ε + ρ ε
(22)
The next step is to choose the diameter, D, and the height,
H, that satisfy the minimum volume. With these dimensions,
the parameters τr and HCR can be evaluated and the
temperature distribution in the tank can be simulated during a
discharge process. The dimensions of the tank with a volume
of 17.611 m3
are: H = 15.2 m and D = 38.5 m. For choosing
these dimensions, we considered the same diameter/height as
the previous tank which was 36/14.
In Table I, model parameters and values are presented. The
HTF used in AndaSol has the same composition as the fluid
used in the comparison with the experimental data presented
in [4]. For this reason, the thermodynamic properties of the
HTF and the filler material are obtained from the literature.
The flow rate, the hot and cold temperatures, and the required
time period of energy discharge are operational parameters are
fixed for the AndaSol I plant as design constraints.
Surprisingly, the first design has better results than we
expected. In Fig. 5, one can see the dimensionless temperature
distribution of the HTF during a discharge process. The
simulation was run for 10 cycles in order to stabilize the initial
conditions.
In order to figure out the temperature degradation of HTF
during discharge, we plotted the dimensionless temperature
TABLE I. DIMENSIONS AND PARAMETERS OF THE THERMOCLINE TANK
Parameters Values
H [m] 15.2
D [m] 38.5
ε 0.22
dT [ h ] 7.5
Heat Transfer Fluid
ᆑf [ kg / m3
] 1733
kf [ W / (m K) ] 0.57
Cf [ J / (kg K) ] 1520
µf [ Pa s ] 0.0021
݉ሶ [ kg / s ] 948
Th [ ºC ] 384
Tc [ºC ] 291
Filler Material
ᆑs [ kg / m3
] 2500
ks [ W / (m K) ] 5
Cs [ J / (kg K) ] 830
dr [ m ] 0.015
histories of at the exit, z* = 1, during a discharge process,
which can be seen in Fig. 6. The temperature degradation is
not significant and it seems that this design would work well.
However, improvements are necessary for the design
observing the effects produced by the modification of some
parameters, based on the thermal energy efficiency which is
expressed in:
( )
arg
( , )
0
arg
disch et
f x H t c
h c disch e
T T dt
T T t
= −
η =
−
∫
(23)
In the first attempt, the thermal energy efficiency was
0.9928. Therefore, when improving the design, we should pay
attention not to deteriorate this parameter.
C. Optimization Studies
1) Ratio H/D:
First, the ratio between height and diameter of the tank is
varied in order to find out if the geometry could affect the
efficiency of the thermal storage. Simulations are carried out
with the model for different values of this ratio, and the effect
on the thermal storage efficiency is calculated.
Figure 5. Dimensionless temperature of HTF every 30 min during a discharge
process
Table II shows the results for different ratios which are
plotted in Fig. 7 as well. As one can see, the energy storage
efficiency increases with the H/D-ratio. In other words, higher
energy efficiencies are obtained for taller tanks.
The principal conclusion inferred from this observation is
that, if we need to increase the volume of the tank in order to
reduce the temperature degradation, it is better to increase it
by increasing the height, and consequently, the ratio H/D.
Therefore, the first design is modified based on this
observation. In order to decrease the HTF temperature
degradation, volume needs to be increased. Thus, we decided
to increase the height to 18 m. With this adjustment, the HTF
temperature degradation shown in Fig. 8 is considerably
reduced and the thermal storage efficiency is increased to
0.9992.
2) Heat Transfer Fluid:
The last investigation is about the HTF. The aim of this
last question is to analyze two alternatives for the solar salt as
storage fluid. The two fluids selected are called: Hitec XL and
Therminol . The last one is a heat conductive oil. Hitec XL is
a molten salt composed with 7% NaNO3, 45% KNO3 and 48%
5. Ca(NO3)2. Table III illustrates the average properties at 300ºC
for the thermal energy storage (TES) materials.
TABLE II. THERMAL STORAGE EFFICIENCY UNDER DIFFERENT RATIOS
Figure 6. Dimensionless temperature histories of exit fuid at z* = 1 for a
discharge process
Figure 7. Effect of the Ratio H/D on the Thermal Storage Efficiency
Figure 8. Dimensionless temperature histories of exit fuid at z* = 1 for a
discharge process with the new design
The simulation of the new tank designed previously is
repeated for the three storage materials, and the results are
shown in Fig. 9. Each graph is the result of the same
simulation, only changing the properties of the HTF. The fluid
temperature distribution plotted represents the inside
temperature after 20 cycles of charge and discharge process
from a fully tank. 20 cycles are required in order to be sure
that the initial condition does not affect the temperature
distribution. The melting point and the upper temperature are
also indicated in Table III because the HTF must work in a
temperature range between the two temperatures in order to
remain in liquid phase during the charge-discharge processes.
As Th is 384 ºC and Tc is 291 ºC [6], all three fluids fulfill this
requirement.
As one can see in the Fig. 9, if the mass flow rate is kept
the same the Solar Salt seems to be the choice for the HTF.
However, for constant thermal mass flow rate, i.e. ,p lmcɺ , all
three HTF are comparable, with lowest mass flow rate for
Therminol, which will also have the least parasitic pumping
loss.
Moreover, Table IV sums up the energy storage efficiency
for each example. For the same thermal mass flow rate all
three have comparable efficiencies. However, if one considers
the cost of each HTF, the Solar Salt becomes the best thermal
energy storage material. Furthermore, complete analysis is
necessary by considering the effect of parasitic pumping loses
and other properties of the fluids.
TABLE III. CHARACTERISTICS OF TWO MOLTEN SALTS (SOLAR SALT AND
HITEC XL) AND ONE HEAT CONDUCTIVE OIL (THERMINOL) [7]
TES materials Solar Salt Hitec XL Therminol
Density, kg/m3
1899 1992 815
Heat Capacity, J/kg·K 1460 1800 2300
Thermal conductivity, W/m·K 0.52 0.53 0.21
Viscosity, Pa·s 0.00326 0.00637 0.0002
Melting Point, ºC 220 120 13
Upper Temperature, ºC 600 500 400
Cost of the material, $/kg 0.49 1.19 2.20
Cost of the heat storage, $/kWh 5.8 15.2 57.5
TABLE IV. ENERGY STORAGE EFFICIENCY FOR EACH HTF
HTF
η (constant
flow rate)
η (constant thermal
flow rate)
Solar Salt 0.9979 0.9899
Hitec XL 0.9925 0.9911
Therminol 0.8369 0.9814
CONCLUSIONS
This work presents the modeling of a thermocline storage
tank with a solid-filler packed bed. We developed and
validated a model that can be used for future storage systems
designs. Moreover, the model is also useful to investigate the
influence of different parameters of the tank. In this paper we
studied the influence of the ratio between the height and the
diameter of the tank to the thermal storage efficiency. We
conclude that an increase in this ratio causes an increase in the
thermal storage efficiency. The scientific justification is that a
smaller diameter corresponds to a higher flow velocity for the
HTF trough the filler material, and consequently, the heat
transfer coefficient would be also higher.
The model has also been used to propose a new
configuration of storage system for a real solar power plant.
H/D η H/D η
0.3948 0. 9928 2.3948 0.9995
1.3948 0.9994 3.3948 0.9995
6. AndaSol I has been the solar plant selected because its storage
system contains two separate tanks which store the hot and
cold fluid independently. Thus, a thermocline storage tank
would be a low-cost alternative to the current, because a single
tank requires a lower quantity of materials and space.
Moreover, the HTF in AndaSol I is the same molten salt used
in the model. Therefore, a storage system consisting on a
thermocline tank with 18 m height and 38.5 m diameter has
been obtained in this work as an alternative storage system for
AndaSol I. Moreover, the new design offers smaller fluid
temperature degradation.
Furthermore, a comparison between a Solar Salt, Hitec XL
and Therminol is presented here. This evaluation shows that
the best thermal storage fluid for this design seems to be Solar
Salt because of its lower temperature degradation and its low
cost. However, other factors such as pumping of the fluid and
melting point must be considered as well: for the former
Therminol is best because of its low viscosity and high heat
capacity (but also costs higher), and for the latter Hitec XL
would be a good alternative because its lower melting point.
Figure 9. Dimensionless temperature distribution and exit histories at z* = 1
during a discharge process for each HTF for constant mass flow rate.
Figure 10. Dimensionless temperature distribution and exit histories at z* = 1
during a discharge process for each HTF for constant thermal mass flow rate.
ACKNOWLEDGMENT
The author gratefully acknowledges the financial help
received from the Erasmus Mundus and the hospitality of the
Sabanci University.
NOMENCLATURE
CP Specific heat (J/kg·K)
D Diameter of the storage tank (m)
fs Surface shape factor (2-3)
H Height of the storage tank (m)
HCR Dimensionless parameter
k Thermal conductivity (W/m·K)
mɺ Mass flow rate (kg/s)
N Number of nodes
R Radius of the storage tank (m)
r Equivalent radius of a rock (m)
S Surface area (m2
)
T Temperature (K)
t Time (s)
u Fluid velocity in the axial tank direction (m/s)
z Location along the axis of the tank
Greek symbols
ε Porosity of packed bed in storage tank
η Efficiency
µ Dynamic viscosity (Pa·s)
τr Dimensionless parameter
ρ Density (kg/m3
)
θ Dimensionless temperature
Subscript
c Cold
eff Effective
f Thermal fluid
h Hot
j Discretized variable of time
k Discretized variable of space, Node position
s Filler material
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