PREFACE
Rationale
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Research aims and Objectives
In this thesis, ANSYS Fluent is simulation software used to simulate the SGHD with 6mx8mx3.5m This type of drying house has been placed in An Giang and Dong Thap province with two categories:
Firstly, the primary objective of this work was to simulate the influence of time on the temperature and humidity distribution inside the SGHD The daily meteorological aspects were considered in the simulation result, and the model was validated through experimental field solar drying data and representing an advance for the accurate prediction of the drying This contributed to the design of a more efficient process Secondly, this research simulates the impact of weather conditions on temperature and humidity distribution inside SGHD by changing a suitable grid by ANSYS Fluent Two types of mesh, including tetrahedral and hexahedral meshing, were conducted in this research, and the number of cells generating a mesh is various values, dependent on the size of the cell.
Outline of thesis
This work is split into 5 chapters: Firstly, A Preface and Literature review in Chapters 1 and 2 with the theoretical portion is discussed Third, the mathematical models part of the thesis is described in Chapter 3 And then, the results and discussion in Chapter 4 and conclusions in Chapter 5.
LITERATURE REVIEW
Solar drying process overview
The greenhouse effect underlies the process of solar drying equipment collecting heat from the sun It involves the accumulation of radiant solar energy beneath glass or a gas layer This phenomenon follows the principle that a glass or gas layer's transparency for shortwave solar radiation differs from its transparency for longwave thermal radiation emitted by the heated objects below.
1 illustrates the solar dryer's heat recovery principle
Figure 1 Principle of heat collection of solar drying equipment [Héliantis: the principle]
2.1.2 Classification of drying methods using solar energy
Figure 2 Classification of solar drying methods [9, 10]
The structure of the forced convection solar drying equipment is shown in Figure
The solar greenhouse dryer (SGHD) operates by capturing solar radiation, which is absorbed by the material within the chamber As the product absorbs radiation, its temperature rises, emitting long-wavelength radiation that is trapped within the chamber due to the dome's insulating properties This elevates the temperature within the chamber, while convection and evaporation contribute to moisture removal through openings The design of SGHD aims to maximize heat availability for the material, enhancing vapor pressure and reducing the relative humidity of drying air, thereby increasing the moisture carrying capacity.
Indirect solar energy drying systems consist of a heat collector and a drying chamber, with products placed within the latter to avoid direct sunlight exposure Natural convection involves passively drawing hot air into the chamber, while forced convection employs a blower and ducting unit to direct heated air precisely Forced airflow enhances water vapor diffusion, reducing drying time Refer to Figure 4 for the structural layout of forced convection solar drying equipment.
Figure 4 The structure of SGHD using the indirect method [9]
2.1.3 Various shapes of the SGHD
The structure of the solar drying house is one of the important factors determining the receipt of radiation from the sun through location and orientation Several studies on the structure of the drying house show that the irregular shape receives higher solar radiation, and the Quonset shape reports the lowest solar radiation in the east-west direction Besides, some irregular shaped drying houses will receive the highest amount of solar radiation in the east and west and the lowest in the north and south directions Unstructured drying houses have lower energy and heat requirements when compared to other shaped greenhouses It had been reported that the uneven shape greenhouse dryer had lower energy and heating requirements in comparison with other shapes of greenhouse dryer [11] The effect of assorted shapes (even, uneven, single, vinery, modified arch, Quonset), and orientation on the performances of the solar greenhouse dryers It was observed that one span-shaped dryer with east-west orientation reported maximum solar incident radiation when put next with others It had also been reported that the radiation loss could be minimized by employing a brick wall at the sun-facing wall of the greenhouse dryer Some researchers compared five different shapes (even, uneven, vinery, semi-circular, elliptical) and orientation with varying the ground area (50 to 400 m 2 ), from which they observed that the elliptical shape performed better than other shapes [12] The varied shapes of the solar greenhouse dryer are shown in Figure
Figure 5 Various shapes of the SGHD [13]
Introduction to computational fluid dynamic (CFD) simulation
CFD or Computational Fluid Dynamic is a fluid mechanic branch that analyzes the fluid flow, heat transfer, mass transfer, and associate chemical reactions CFD uses the numerical method and data structure to solve the set governing mathematical equations such as conservations of momentum, mass, energy, species, or the effect on body forces CFD is now utilized to research and solve engineering problems in various industries, including aerodynamics of aircraft and vehicles, hydrodynamics of ships, power plants, turbomachinery, electrical and electronic engineering, chemical process engineering, etc CFD aid brings a significant potential in saving time in optimization and process design and reduces the cost compared to experimentation and data acquisition [14]
ANSYS FLUENT software was introduced by Ansys Inc company in 2006 to apply for computational fluid dynamics This software supplies all the needed tools for equipment design, optimization, and installation troubleshooting The flexibility of this technology shows insight into how the product performs in the real world before an innovated sample is generated The CFD packages provide solvers that precisely model the behavior of a wide variety of flows that engineers regularly face²from Newtonian to non-Newtonian, from single±phase to multi-phase, and from subsonic to hypersonic Each solver for rapid simulation time is highly stable, well tested, validated, and optimized Tested time and part of a single environment, both precision and speed are provided by highly efficient solvers [15]
2.2.2 Working principle of ANSYS CFD
The finite volume method (FVM) is a widely used method for solving partial differential equations (PDEs) This method involves discretizing the domain into a finite number of control volumes and applying the divergence theorem to solve the conservation equations within each volume FVM's flexibility allows for the use of unstructured grids, making it suitable for complex geometries It has been successfully used to solve various problems in fluid dynamics, heat transfer, and electromagnetism.
Figure 6 The fluid region of the pipe flow is discretized into a finite set of control volumes
The important problem of fluid dynamics algorithms is to describe the kinematic properties of fluids To solve this problem, it is necessary to know the physical properties of fluids using the descriptive tools of fluid mechanics Then, mathematical equations (Navier-Stokes equations) can describe these physical properties, which is the governing equation of CFD [17]
The Navier-Stokes equation is general, a system of differential equations, and can be solved analytically However, the problem is usually solved with the help of a computer through numerical methods According to the numerical method, this system of equations will be converted to discrete form by methods such as finite difference, finite element, or finite volume method Accordingly, it is necessary to divide the entire survey domain into several small parts and run the program to calculate iteratively The programming languages used to build the usual solution method are Fortran and C Finally when receiving simulation results, it is possible to compare and analyze these results with other experiments or real experience data If the results are not reliable enough to solve the problem, we must repeat the process until we find a satisfactory solution [18] This is the whole process of CFD This process is depicted in Figure 7
Figure 7 The whole process of CFD simulation stages [19]
MATHEMATICAL MODELS
Conservation equations [20]
The mathematical terms are presented by the governing equations of fluid flow based on the following conservation law of physics:
The mass balance of the fluid elements is presented by:
Rate of increase of mass in fluid element = Net rate of flow of mass into the fluid element (1)
The rate of increase of mass in the fluid element is డ డ௧ሺߩߜݔߜݕߜݖሻ ൌ డఘ డ௧ ߜݔߜݕߜݖ and the second term of the equation is: ቆߩݑ െ߲ሺߩݑሻ ߲ݔ ͳ ʹߜݔቇ ߜݕߜݖ െ ቆߩݑ ߲ሺߩݑሻ ߲ݔ ͳ ʹߜݔቇ ߜݕߜݖ ൬ߩݒ െ߲ሺߩݒሻ ߲ݕ ͳ ʹߜݕ൰ ߜݔߜݖ െ ൬ߩݒ ߲ሺߩݒሻ ߲ݕ ͳ ʹߜݕ൰ ߜݔߜݖ ൬ߩݓ െ߲ሺߩݓሻ ߲ݕ ͳ ʹߜݖ൰ ߜݔߜݕ ൬ߩZ߲ሺߩݓሻ ߲ݕ ͳ ʹߜݖ൰ ߜݔߜݕ The equation (1) is rearranged by divided by element volume ߜݔߜݕߜݖ, then shown in the form of: డఘ డ௧ డሺఘ௨ሻ డ௫ డሺఘ௩ሻ డ௬ డሺఘ௪ሻ డ௭ ൌ Ͳ or డఘ డ௧ ݀݅ݒሺߩݑሻ This equation is unsteady and used for a 3D continuity equation at an incompressible fluid point
Rate of increase of momentum of fluid-particle = Sum of forces on the fluid particle (2)
The left-hand side source term for all dimensions of the coordinate per unit volume of a fluid particle is supplied by: ߩ ௨ ௧, ߩ ௩ ௧ and ߩ ௪ ௧ The forces consist of surface forces and body forces Surface forces include pressure, viscous forces and gravity forces and body forces are centrifugal, Coriolis, and electromagnetic forces Therefore, the equation (2) is illustrated by these equations below for x-, y- and z- components, respectively: ߩܦݑ ܦݐ ൌ߲ሺെߩ ߬ ௫௫ ሻ ߲ݔ ߲߬ ௫௬ ߲ݕ ߲߬ ௭௫ ߲ݖ ܵ ெ௫ ߩܦݒ ܦݐ ൌ߲߬ ௫௬ ߲ݔ ߲ሺെߩ ߬ ௬௬ ሻ ߲ݕ ߲߬ ௭௬ ߲ݖ ܵ ெ௬ ߩܦݓ ܦݐ ൌ߲߬ ௫௭ ߲ݔ ߲߬ ௬௭ ߲ݕ ߲ሺെߩ ߬ ௭௭ ሻ ߲ݖ ܵ ெ௭ Where:
- p is pressure or normal stress, DQGIJLVWKHYLVFRXVVWUHVV
The energy conservation equation is modeled based on the first law of the thermodynamic, which is presented by:
Rate of increase of energy of fluid-particle = Net rate of heat added to fluid-particle + Net rate of work done on the fluid particle (3)
- The rate of heat addition to the fluid particle due to heat conduction: െ ݀݅ݒ ݍ ݀݅ݒሺ ݇ ݃ݎܽ݀ ܶሻ
- The total rate of work done on the fluid particle by surface stresses: ሾെ ݀݅ݒሺݑሻሿ ۏ ێێ ێ ۍ߲ሺݑ߬ ௫௫ ሻ ߲ݔ ߲൫ݑ߬ ௬௫ ൯ ߲ݕ ߲ሺݑ߬ ௭௫ ሻ ߲ݔ ߲ሺݒ߬ ௫௫ ሻ ߲ݔ ߲൫ݒ߬ ௬௫ ൯ ߲ݕ ߲ሺݒ߬ ௭௫ ሻ ߲ݔ ߲ሺݓ߬ ௫௫ ሻ ߲ݔ ߲൫ݓ߬ ௬௫ ൯ ߲ݕ ߲ሺݓ߬ ௭௫ ሻ ߲ݔ ےۑۑۑې
- The total energy equation with SE is the source of energy ߩܦܧ ܦݐ ൌ െ ݀݅ݒ ݑ ۏ ێێ ێ ۍ߲ሺݑ߬ ௫௫ ሻ ߲ݔ ߲൫ݑ߬ ௬௫ ൯ ߲ݕ ߲ሺݑ߬ ௭௫ ሻ ߲ݔ ߲ሺݒ߬ ௫௫ ሻ ߲ݔ ߲൫ݒ߬ ௬௫ ൯ ߲ݕ ߲ሺݒ߬ ௭௫ ሻ ߲ݔ ߲ሺݓ߬ ௫௫ ሻ ߲ݔ ߲൫ݓ߬ ௬௫ ൯ ߲ݕ ߲ሺݓ߬ ௭௫ ሻ ߲ݔ ےۑۑۑې ݀݅ݒሺ ݇ ݃ݎܽ݀ ܶሻ ܵ ா
- For the total enthalpy equation ߲ሺߩ݄ ሻ ߲ݐ ݀݅ݒሺ ߩ݄ ݑሻ ൌ െ ݀݅ݒ ݑ݀݅ݒሺ ݇ ݃ݎܽ݀ ܶሻ ߬ ௫௫ ߲ݑ ߲ݔ ߬ ௬௫ ߲ݑ ߲ݕ ߬ ௭௫ ߲ݑ ߲ݖ ߬ ௫௬ ߲ݒ ߲ݔ ߬ ௬௬ ߲ݒ ߲ݕ ߬ ௭௬ ߲ݒ ߲ݖ ߬ ௫௭ ߲ݓ ߲ݔ ߬ ௬௭ ߲ݓ ߲ݕ ߬ ௭௭ ߲ݓ ߲ݖ ܵ Where:
- ݄ ൌ ݅ ఘ and ݄ ൌ ݄ ଵ ଶሺݑ ଶ ݒ ଶ ݓ ଶ ሻ; h and h0 are respectively specific enthalpies and specific total enthalpy
3.1.4 Heat and mass balances in SGHD:
The assumptions in building a mathematical model for a solar dryer are:
- Do not stratify the air inside the drying house
- Calculation of drying based on thin plate drying model
- The specific heat capacity of the air, the coating and the product is constant The energy transfer diagram inside the solar drying house using the greenhouse effect is shown in Figure 8, and the following heat and mass balances are built as follows [21, 22]:
Figure 8 Distribution of some parameters in SGHD [21]
The rate of heat energy accumulation on the cover = Rate of heat transfer by convection between the air inside the drying house and the polycarbonate cover + the rate of heat transfer between the outdoor air and the cover due to thermal radiation + Heat transfer rate between the roofing sheet and the surrounding air due to thermal convection + Heat transfer rate between the roofing sheet and the product due to thermal radiation + The rate at which solar radiation energy is absorbed into the cladding Energy balance equation: ݉ ܥ ݀ܶ ݀ݐ ൌ ܣ ݄ ǡି ሺܶ െ ܶ ሻ ܣ ݄ ǡି௦ ሺܶ ௦ െ ܶ ሻ ܣ ݄ ௪ ሺܶ െ ܶ ሻ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܣ ן ܫ ௧
3.1.4.2 Energy balance for the air inside the SGHD
The rate of heat energy accumulation of the air inside the drying house = The rate of heat transfer between the product and the air due to convection + The rate of heat transfer between the floor and the air by convection + The rate of heat energy increase of the air from the product due to heat transfer from the product to the air + the rate of heat gain in the air chamber due to the flow and flow of air inside the drying chamber + Rate of heat loss from the drying house air to the surrounding air + Rate of energy absorbed by the air inside the drying house from solar radiation The energy balance equation: ݉ ܥ ௗ் ೌ ௗ௧ ൌ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܦ ܣ ܥ ௩ ߩ ൫ܶ െ ܶ ൯ ௗெ ௗ௧ ൫ߩ ܸ ௨௧ ܥ ܶ ௨௧ െ ߩ ܸ ܥ ܶ ൯ ܷ ܣ ሺܶ െ ܶ ሻ ൣ൫ͳ െ ܨ ൯ሺͳ െ ߙ ி ሻ ൫ͳ െ ߙ ൯Ǥ ܨ ൧Ǥ ܣ ߬ ܫ ௧
3.1.4.3 Energy balance for the product
The rate of heat energy accumulation in product = The rate of heat energy transfer between air and product due to convection + The rate of heat energy transfer between coating and product due to radiation + The rate of heat energy loss from the product due to latent heat loss from the product + The rate at which the product absorbs solar energy
The energy balance equation for the product: ݉ ൫ܥ ܥ ܯ ൯ ௗ் ௗ௧ ൌ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܦ ܣ ߩ ൣܮ ܥ ௩ ൫ܶ െ ܶ ൯൧ ௗெ ௗ௧ ܨ ߙ ܫ ௧ ܣ ߬
3.1.4.4 Energy balance for the concrete
The rate of heat energy accumulation in the floor = Convection heat transfer rate between the air in the dryer and the floor + Heat transfer rate between the floor and the ground + The rate of solar radiation absorption on the floor Energy balance equation: ݉ ൫ܥ ܥ ܯ ൯ ௗ் ௗ௧ ൌ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܦ ܣ ߩ ൣܮ ܥ ௩ ൫ܶ െ ܶ ൯൧ ௗெ ௗ௧ ܨ ן ܫ ௧ ܣ ߬ ݉ ܥ ௗ் ௗ௧ ൌ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ܣ ݄ ǡି ൫ܶ െ ܶ ൯ ሺͳ െ ܨ ሻ ן ܫ ௧ ܣ ߬
The accumulation rate of moisture in the air inside the drying house = The rate of moisture inflow into the drying house due to ambient air ± Rate of moisture loss from the drying house due to venting + The rate of transpiration from the product products inside the drying house Mass balance inside the drying chamber: ߩ ܸ ௗு ௗ௧ ൌ ܣ ߩ ܪ ݒ െ ܣ ௨௧ ߩ ܪ ௨௧ ݒ ௨௧ ܦ ܣ ߩ ௗ ௗெ ௗ௧
3.1.4.6 Heat transfer coefficient and heat loss
Radiant heat transfer coefficient from the roof to the environment (hr, c-s): ݄ ǡି௦ ൌ ߝ ߪሺܶ ଶ ܶ ௦ ଶ ሻሺܶ ܶ ௦ ሻ Radiant heat transfer coefficient between the roofing sheet and the product (hr, c-p): ݄ ǡି ൌ ߝ ߪሺܶ ଶ ܶ ଶ ሻ൫ܶ ܶ ൯ The coefficient of convection heat transfer of the roofing sheet to the surroundings by the wind (hw): ݄ ௪ ൌ ʹǤͺ ͵ǤͲܸ ௪ The convection heat transfer coefficient inside the solar drying house for the cover plate, product, and floor (hc) is determined through the relationship: ݄ ǡି ൌ ݄ ǡି ൌ ݄ ǡି ൌ ݄ ൌ Ǥே௨ Nusselt standard number (Nu), calculated from Reynolds standard number (Re) through the following relationship: ܰݑ ൌ ͲǤͲͳͷͺܴ݁ Ǥ଼
The overall heat loss coefficient of the drying house roof sheet is determined as follows: ܷ ൌ ఋ
3.1.4.7 The drying equation for thin layer: ெିெ ெ ିெ ൌ ݁ݔሺെܣݐ ሻ
In there: í M is the moisture content of the dried material at time t (%) í M0 is the initial moisture content of the drying material (%) í Me is the equilibrium moisture content of the dried material (%) í The parameters A and B are given as follows: ܣ ൌ ͲǤͲͲͻͷͷ ͲǤͲͲͲ͵ʹܶ െ ͲǤͲͳͳʹݎ݄ െ ͵Ǥʹ ൈ ͳͲ ି ܶ ଶ ͲǤͲͳʹͶͲͺݎ݄ ଶ ͲǤͲͲͶ͵ܸ െ ͲǤͲͲ͵ͺͳܸ ଶ ܤ ൌ ͶǤͺͻͶͺ െ ͲǤͳ͵Ͷͷͻܶ ͲǤ͵ͺͲͲʹݎ݄ ͲǤͲͳ͵Ͷͷܶ ଶ െ ͳǤͳͶʹͶͶͷܸ ͲǤͻʹͲͶͶͶܸ ଶ ܯ ൌ െͷǤʹʹͲ െ ͲǤͲͻʹʹܶ ͲǤͲʹʹ͵Ͷܶ ଶ െ ʹͻǤͶͲͻݎ݄ ͺǤ͵ͳͳͻ͵ݎ݄ ଶ െ ͵ǤͶʹͷܸ ͷǤͶʹͻܸ ଶ
In which T is the temperature ( o C), Va (m/s) is the speed of the air inside the drying house, and rh is the relative humidity (%), [21].
Viscous Model [20]
The viscous model in ANSYS FLUENT is used to set the parameter for inviscid, laminar, and turbulent flow Many models are supplied, such as inviscid, laminar, Spalert-Allmaras, k-epsilon, k-omega, LES, etc However, this study concentrates on k- epsilon models because there is no turbulent flow inside this spray dryer
The turbulent k-İFRQVLVWVRIstandard types, RNG and realizable k-İPRGHOV These models have a VLPLODUIRUPZLWKWKHWUDQVSRUWHTXDWLRQVIRUNDQGİ+RZHYHU there are three significant differences among these models The first difference comes from the calculation method of the turbulent viscosity Secondly, there is also a change in the turbulent Prandtl number, ZKLFKJRYHUQVWKHWXUEXOHQWRINDQGİ)LQDOO\WKHİ equation has some differences in generation and destruction terms
The turbulent length and time scale are investigated using two separate transport equations This model is commonly applied in the industrial flow and heat transfer equation because of robustness, economy, and nearly accuracy for a variety of turbulent flow The standard k-İ PRGHO LV D VHPL-empirical model based on model transport HTXDWLRQVIRUWKHWXUEXOHQFHNLQHWLFHQHUJ\NDQGLWVGLVVLSDWLRQUDWHİ7KHPRGHO transport equation for k is derived from the exact equation, while the model transport
HTXDWLRQIRUİZDVREWDLQHGXVLQJSK\VLFDOUHDVRQLQJDQGEHDUVOLWWOe resemblance to its mathematically exact counterpart
+ Gk: the generation of turbulence kinetic energy due to the mean velocity gradients
+ Gb: the generation of turbulence kinetic energy due to buoyancy
+ YM: the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
+ Cİ, CİCİ: constants; Cİ=1.44, Cİ=1.92, Cİ=0.09
- 7KHWXUEXOHQWYLVFRVLW\ȝt is calculated by: ߤ ௧ ൌ ߩܥ ఓ మ ఌ where Cȝ is a constant
The performance of realizable k-İ PRGHO EHWWHU WKDQ VWDQGDUG N-İ PRGHO DW DQ alternative formulation of turbulent viscosity Also, it comes from the modified transport equation for dissipation rate, derived from an exact equation for the transport of the mean-square vorticity fluctuation Same as the RNG k-İPRGHOWKHUH DUH VXEVWDQWLDO improvements for the flow performing the vortices or rotation Some current research has provided the realizable k-İPRGHOVKRZVWKHRYHrweight performance compared to other models
Same as the other k-İPRGHOVWKHHGG\YLVFRVLW\LVFDOFXODWHGE\ ߤ ௧ ൌ ߩܥ ఓ ݇ ଶ ߝ However, in this model Cȝ is not constant, determined by: ܥ ఓ ൌ ͳ ܣ ܣ ௦ ܷ݇ כ ߝ Where:
+ ߗ LM : mean rate-of-rotation tensor, ߱ : angular velocity
+ A0 and As: constants which are determined by: Ͳ ൌ ͶǤͲͶǡ ܣ ௦ ൌ ξ ܿݏ ߮ ߮ ൌͳ ͵ܿݏ ିଵ ൫ξܹ൯ ǡ ܹ ൌܵ LM ܵ MN ܵ NL ܵሚ ଷ ǡ ܵሚ ൌ ටܵܵ ǡ ܵ ൌͳ ʹቆ߲ݑ ߲ݔ ߲ݑ ߲ݔ ቇ
- Turbulent production in the k-İPRGHO ܩ ൌ െߩݑ Ԣݑ Ԣ߲ݑ ߲ݔ
- Effects of Buoyancy ܩ ൌ ߚ݃ ߤ ௧ ܲݎ ௧ ߲ܶ ߲ݔ + Prt: turbulent Prandtl number
+ Gi: component of the gravitational vector
Species model [16]
The conservation equation for species is solved by predicting each local mass fraction, Yi, within the solution of a convection-diffusion of each species The general form of the conservation equation is presented by: ߲ ߲ݐሺߩ߭Ԧܻ ሻ ߘ ڄ ሺߩݒԦܻ ሻ ൌ െߘ ڄ ܬሬሬԦ ܴ ప ܵ Where:
+ Ri: net rate of species i generation by chemical reaction
+ Si: The rate of creation by addition from the dispersed phase
In a system with n fluid phase species, n-1 species can be calculated using equations The remaining species, denoted as Nth, is defined as 1 minus the total mass fraction of the other species This ensures consistency of the total mass fraction For high accuracy, Nth should have the largest overall mass fraction.
3.3.1 Mass diffusion in turbulent flow
In turbulent flow, the mass diffusion is determined by: ܬ ప ሬሬԦ ൌ െ ቀߩܦ ǡ ఓ ௌ ቁ ߘܻ െ ܦ ்ǡ ఇ் ் Where:
+ ܵܿ ௧ : turbulent Schmidt number calculated by ܵܿ ௧ ൌ ఓ ఘ
3.3.2 Treatment of Species Transport in the Energy Equation
The species diffusion can lead to the transport of enthalpy, which may have a dramatical impact on the field of enthalpy: ߘ ڄ ݄ ୀଵ ܬ ప ሬሬԦ൩
When the Lewis number of each specie is far from the unity, if the transport of enthalpy is skipped, it can lead to errors ܮ݁ ൌ ఘ ǡ where k is the thermal conductivity.
Radiation model [20]
The model selection is an important issue to simulate the heat radiation process of the drying house by the greenhouse effect Here, the discrete coordinate radiation model (also known as the DO model) will be used to simulate the effect of radiation rays from the sun entering the area to be calculated In addition, the thermal radiation model will determine the sun's position over a period, day and time By design, the DO model is the appropriate model for the radiation case for semi-transparent objects
The DO radiation model assumes that radiant energy is propagated simultaneously through the medium at its speed in all directions It can model various applications except for gases, such as absorbing CO2 vapor or H2O vapor and emitting energy at different wavelengths This model is suitable for use with participating media where the VSHFWUDO DEVRUSWLRQ FRHIILFLHQW ĮȜ YDULHV DFURVV VSHFWUDO EDQGV ,Q WKLV FDVH WKH absorption coefficient is assumed to be constant throughout the spectral bands
The DO model solves the radiation transfer equation (RTE) for a finite number of discrete solid angles, each associated with a fixed vector r direction in a Cartesian (x, y, z) coordinate system It transforms the RTE equation into a transformation equation for the radiation intensity in spatial coordinates (x, y, z) DO is a solution model for many types of directed transport equations For example, the RET radiation transfer equation (for spectral intensity) is written: ߘሺܫ ఒ ሺݎԦǡ ݏԦሻݏԦሻ ሺߪ ఒ ߪ ௦ ሻܫ ఒ ሺݎԦǡ ݏԦሻ ൌ ߙ ఒ ݊ ଶ ܫ ఒ ሺݎԦሻ ఙ ೞ ସగ ସగ ܫ ఒ ሺݎറǡ ݏԦሻߔ ቀݏԦǡ ݏԢሬሬԦቁ ݀ߗԢ (18) Where: о ݎԦ is the position vector о ݏԦ is the direction vector о ݏԢሬሬԦ is the vector indicating the scattering direction о ߪ is the Stefan-Boltzman constant о ܫ ఒ is the radiation intensity of the wavelength о ߙ ఒ is the spectral absorption coefficient о ܫ ఒ is the blackbody intensity given by the Planck function о ߙ ௦ is the scattering coefficient о ݊is the refractive index о ߔ is the phase function ߗԢ is the cube angle (radians).
SIMULATION OF SOLAR GREENHOUSE DRYER
Bench-scale of solar greenhouse dryer
The actual drying house is designed as shown in Figure 6 with the dimensions of 6mx8mx3.5m, and the storage capacity is about 200-300 kg of raw materials/batch The SGHD construction includes polycarbonate (PC) sheets, metal frames, aluminum (Al) trays, and a concrete ground in Dong Thap province, Viet Nam The cover plates prevent the agricultural product from rain, bug and permit solar radiation into the dryer Solar radiation was measured by a Kipp and Zonen pyranometer placed on the roof of the dryer In addition, thermocouples (type K) and a digital probe Bioblock thermohygrometer with ± 3% precision was used to measure air temperatures and ambient air relative humidity in the dryer
Based on the above real drying house, a mathematical model is established based on the problem of energy balance and matter balance inside the drying house
Computer-aided design (CAD) software, such as SpaceClaim, Design Modeler, Autodesk Inventor, and Solidwork, is commonly used to create the 3D geometry of a problem In this study, SpaceClaim was chosen to generate the geometry The geometry is then imported into a flow model, which represents the flow path of the fluid in the problem The flow model must be carefully designed to ensure that all the boundary conditions and domains of the problem are properly defined The geometry used in this work is shown in Table 1 and Figure 9.
Figure 9 The SGHD model designed by SpaceClaim
Table 1 The dimension of the SGHD
One of the most important characteristics of simulations is to generate the mesh
It means to discretize the spatial domain in small cells connected between them to compute the variables with numerical methods A fine mesh can be related to the computational cost and the solution's accuracy and convergence However, the low quality of meshes can lead to bad results Therefore, this approach is used to generate the fine mesh, which is fine enough and adequately represents all important features of the geometry The mesh can be drawn by some CAD programs, GAMBIT, ANSYS ICEM, or ANSYS Meshing, as long as satisfying with the mesh quality Conventionally, the mesh is divided into two types: structured, unstructured mesh, and hybrid mesh
It is identified by regular connectivity between the elements, and it is composed of elements like quadrilateral in 2D and hexahedra in 3D A good characteristic is that space is divided with such efficiency Each point can be defined by indexes (i,k,k) in the cartesian coordinate system so that the neighborhood relationships are defined by storage arrangement In addition, we can have an orthogonal or non-orthogonal mesh
In contrast to orthogonal grids where lines intersect at right angles, structural meshes adopt a non-orthogonal approach where lines intersect at non-perpendicular angles While this flexibility allows for adaptability in complex geometries, the implementation of non-orthogonal meshes presents challenges due to the increased difficulty in handling intricate designs.
The characteristic of unstructured mesh is the intermittent connectivity between the elements It is easy to generate from an algorithm of the program Consequently, the nodes are not ordered, and we cannot identify these by indexes A mix of quadrilaterals and triangles elements are generally used in 2D simulations, while tetrahedra and hexahedrons in 3D problems Then, the main advantage of unstructured grids is that the complex geometry can be easily discretized However, we have to be careful to get a suitable mesh because it is easy to generate a bad quality grid In addition, a large amount of space can take up the computer's memory
This type of mesh is an efficient combination of structured and unstructured meshes It is adapted in an irregular domain so that the structured grids can be used in a regular region, while it is convenient to use unstructured meshes in complex areas
4.1.3 Physical properties and boundary conditions
Table 2 Properties of the drying agent materials
Table 3 The properties of the solid material
Table 4 The boundary conditions of the SGHD
Boundary conditions Material Parameters Value
Outlet Moist air Pressure [at] 1.0
4.1.4 Simulation method and the operating conditions
Inflow kinematics calculations, nonlinear descriptive equations, and unknown variables are often very large Under these conditions, implicitly constructed equations are mostly solved by iterative methods
An iterative method is used to progress a solution through a sequence of steps from the starting state to the final convergent state This is true for cases where the solution is a step in a transient problem or where the result is in the final steady state In both cases, the iterations are like a timed process Of course, the iterations are usually independent of the actual time In fact, this aspect of an implicit method makes it attractive for steady-state computations because the number of iterations required for a solution is often much smaller than the number of time steps required for a correct process
For a time-dependent simulation problem, the management equations must be discrete in both space and time Therefore, the spatial discretization for the time- dependent equations resembles the transient-state case This involves integrating every WHUPLQWKHGLIIHUHQWLDOHTXDWLRQVLQWRDWLPHVWHSǻW
Numerical simulations were conducted using ANSYS Fluent R19.2, employing the SIMPLEC method to solve the CFD model Second-order spatial discretization was used for momentum equations, while first-order discretization was applied for other variables The computations were performed on a cluster computer with 24 cores and 32 GB RAM, ensuring accurate and efficient solution of the model.
Table 5 The operating condition of the SGHD
The operating conditions Governing Equations
3D simulation Implicit formulation Absolute velocity formation Transient state analysis
Radiation model Discrete Ordinate (DO)
RESULTS AND DISCUSSION
Profile temperature and relative humidity inside the SGHD
A series of 3D numerical computations, achieved using the commercially available ANSYS Fluent CFD code, produced results including temperature and velocity profiles relative to the time in a dryer Figure 10 shows the humid air temperature simulation results with the variation over time The simulated maximum temperature inside the drying house is 339.1 K at 2:00 PM, and the temperature inside the dryer in the range of 11:00 AM to 4:00 PM remains above 328 K For the experimental results in Figure 11, the highest temperature is 335.3 K at 11:00 AM and 334.1 K at 2:00 PM In addition, the experimental temperature provides more consistent results than simulation Although the simulation results are slightly higher than the experimental values, the numerical results are generally consistent with the experimental data Therefore, the simulation model of SGHD can fully predict the behavior of the experimental design understudy
Figure 10 Simulation temperature profile inside the SGHD from 7:00 AM to 6:00 PM
Figure 11 Experimental temperature inside the SGHD from 7:00 AM to 6:00 PM
From sunrise (7:00 AM) to sunset (6:00 PM), the roof and inside of the dryer absorb solar radiation and are heated As this heated air rises and exits the dryer through three fans, fresh air will be drawn in from the other end of the dryer This causes a change in the humid air temperature in the dryer, making the temperature in the dryer higher than that of the environment Figure 12 shows the typical temperature distribution inside the dryer across three locations at 9:00 AM Dark blue represents the lowest value while red represents the highest value Green, yellow, and orange lie in the middle, showing the lowest and highest values range The figure below demonstrates the strong relation of solar irradiation through the polycarbonate wall on the temperature distribution The lowest temperature is near the region of inlet air because ambient temperature was lower (303.1 K) than the temperature inside the dryer According to the simulation result, the temperature of moist air is almost identical in the exhaust area
Tem pe ra tu re ( K )
Figure 12:Temperature distribution of moist air in the volume (a) at various locations and (b) in the middle of the SGHD
In order to investigate the effect of times on the profile temperature of moisture air inside the SGHD, this study includes an investigation of the distribution temperature of moist air inside the SGHD The results of this analysis are presented in Figure 13 and prove that the profile temperature is closely related to location and time a) b) c) d) e) f)
Figure 13:Temperature distribution of moist air in the volume of the SGHD at various times : (a): 8:00 AM; (b): 10:00 AM; (c): 12:00 PM; (d): 1:00 PM; (e): 2:00 PM; and (f): 4:00 PM
As shown in Figure 13, through the effect of heat transfer associated with solar irradiance through the upper semi-transparent wall, the temperature of moist air increases in the large volume of the SGHD, and the highest temperature area depends on the solar direction This result is also similar to the experimental results measured at the dryer located in the An Giang province When the air temperature in the dryer is fairly high, the temperature distribution in this section is relatively homogeneous, and the low-temperature zone accounts for a relatively small proportion area However, when the indoor air temperature is not high, the temperature distribution of moist air on the surface containing the drying material is still greater than the outside air temperature This means that the greenhouse understudy is suitable for a better drying process
5.1.2 The distribution of relative humidity
In the SGHD, the properties of moist air change not only the temperature but also the relative humidity The relative humidity of moisture was strongly affected by the energy SGHD absorbed, and the amount of fresh air was flown to SGHD The velocity vector of the airflow is one of the effects of the important factors on the properties of the dryer, and the behavior of the air movement inside the dryer is presented in Figure
Figure 14: Velocity vectors of the airflow inside the SGHD
It can be realized that air can circulate throughout the whole dryer, and air speed is independent of time The velocity distribution of moist air inside the SGHD is similar at the highest and lowest temperatures The simulation results demonstrate that the internal velocity value ranges 0.5 m/s and the highest point at the outlet is over 1.7 m/s Further, in order to probe the properties of moist air inside the dryer, a relative humidity simulation was conducted inside the SGHD for a one-day experimental run The results of this investigation are illustrated in Figure 15 Relative humidity decreases with time inside the dryer from sunrise to sunset, which is caused by the decreased relative humidity of the ambient air and increased water-holding capacity of the drying air due to temperature increase The relative humidity of the air inside the dryers is always lower than that of the ambient air and the lower relative humidiW\5+LQVLGHWKH6*+' This normally occurs from 11:00 AM and can carry on for 6 h The air leaving the dryer has lower relative humidity than the ambient air, which indicates that the exhaust air from the dryer still has drying potential a) b) c) d) e) f)
Figure 15:RH distribution of moist air in the volume of the SGHD at various time: (a):
8:00 AM; (b): 10:00 AM; (c): 12:00 PM; (d): 1:00 PM; (e): 2:00 PM; and (f):
To analyze the moisture distribution within the SGHD, a 3D numerical simulation was employed to simultaneously calculate RH values at various locations The RH variation is dependent on the temperature distribution of humid air within the SGHD volume The lowest air temperature, corresponding to the highest RH, occurs at the air inlet and gradually decreases as the air temperature increases inside the dryer This temperature variation explains the configured RH values observed during typical test runs.
Figure 16: RH distribution of moist air in the volume of the SGHD at various locations
The sensitive mesh
The CFD analyzed the temperature and relative humidity distribution inside the SGHD A mesh sensitivity analysis was conducted to find the relation of size and number of cells suitable for this analysis The correct cell size will accurately resolve every gradient in inflows Tetrahedral cells are more adaptive to a flow domain with a complicated boundary However, a tetrahedron is not as accurate as a hexahedron with the same grid number The grid number of a tetrahedral mesh is larger than that of a hexahedral mesh with the same cell dimensions Compared with tetrahedral, hexahedral meshes can be aligned with the predominant direction, decreasing numerical diffusion The relation between different grids, sizes, and the number of cells in this research is shown in Table 6
Table 6 The type of mesh
Mesh type Abbreviation Size of cell [m] Number of cells
The role of grid type was investigated by using hexahedral, tetrahedral as shown in Figure 17 For evaluating grid number, a mesh of at least a hundred thousand elements is necessary in order to describe dryer details that are important for simulating the temperature and relative humidity distribution Because of limitations on our computing resources, the maximum cell number used was about 7 million
Figure 17 Mesh distribution of SGHD for different mesh grid types: (a) hexahedral mesh H01, (b) hexahedral mesh H005, (c) tetrahedral mesh T01, and (d) tetrahedral mesh T005
In Figure 9, the grid distributions of hexahedral and tetrahedral mesh types had similar However, the distribution with different sizes of cell investigation defined the large mesh dimension used in the main flow region as the global mesh dimension.
Mesh quality
In this study, unstructured mesh and structured mesh were combined As mentioned before, the unstructured grid can lead to a high cost during the computation Hence structured mesh accounted for most of this model The quality standard of the mesh is illustrated in Figure 20
Figure 18 and Figure 19 show the orthogonality and skewness values of the parameters related to mesh quality Both orthogonality and skewness values go from 0 to 1 On the one hand, if the value of orthogonality is near 0, the mesh has low quality
On the other hand, the values near 0 correspond to a high quality in the skewness case Skewness is defined as the difference between the shape of the cell and an equilateral cell of equivalent volume
Figure 18 and Figure 19 (a) and (c) show the orthogonal quality and skewness of hexahedral mesh H01, H005 with the distribution of highest the number of elements in the region are 0.95 ± 1 and over 0.06, respectively With the tetrahedral (b) T01 and (c) T005 mesh model, the orthogonal quality results with the highest number of elements in the region is 0.5 ± 1 and 0.44 ± 0.06, respectively Based on the standard quality of mesh in Figure 20, the results show that the hexahedral mesh has excellent quality and is favorable for this model than the tetrahedral mesh The results are as good as the hexahedral mesh, ensuring that the mesh is essential to producing reliable and accurate results
Figure 18 The orthogonal quality mesh (a) hexahedral mesh H01, (b) tetrahedral mesh T01, (c) hexahedral mesh H005 and (d) tetrahedral mesh T005
Figure 19 The skewness of mesh (a) hexahedral mesh H01, (b) tetrahedral mesh T01, (c) hexahedral mesh H005 and (d) tetrahedral mesh T005
Figure 20 The skewness and orthogonal mesh quality (2015 ANSYS, Inc.)
5.3.1 Influence of number of cells on the simulated results
Modeling internal conditions in solar dryers is crucial for assessing dryer efficiency, with location and time impacting these conditions Besides temperature, airflow velocity influences dryer properties significantly Simulations of temperature and airflow vector in a solar dryer with tetrahedral meshes of varying cell numbers showed improved agreement with measured temperature distributions as cell numbers increased.
Figure 21 Temperature distribution and velocity of air inside SGHD at 10 AM for different mesh grid sizes: (a) and (c): tetrahedral mesh T01, (b) and (d) tetrahedral mesh T005 The roof and dryer absorbed the solar radiation from morning to afternoon and were heated due to the greenhouse effect This figure shows the strong relation of solar irradiation through the polycarbonate wall on the temperature distribution To investigate the effects of grids number on the temperature simulation, the average temperature and maximum air temperature inside SGHD for different mesh grid sizes were conducted and shown in Figure 22
Figure 22 Comparison of the average temperature profiles (a) and the maximum temperature profiles (b) computed using different tetrahedral meshes The simulation results implied that the different grid numbers led to different temperature simulated results As a result, the average temperature distribution results were very similar, and the error value was less than 5% However, the simulation results of the maximum temperature inside the dryer were different from those with finer grids Hence, a further increase in grid number influenced the simulated temperature profiles
5.3.2 Influent of mesh type on the simulated results
The simulated temperature distributions and the temperature volume rendering of the air inside the SGHD using hexahedral mesh type with two sizes of the cell are shown in Figure 23, and the comparison of the average temperature and the maximum temperature of the air inside SGHD using different mesh type is shown in Figure 24
Figure 23 Temperature distribution and the temperature volume rendering of air inside SGHD at 10 AM using hexahedral mesh type, (a) and (c): hexahedral mesh H01,
Figure 24 Comparison of the average temperature profiles (a) and the maximum temperature profiles (b) computed using hexahedral mesh type T01 and tetrahedral mesh type H01
In this research, when the size of the cell is similar, the number of cells by using tetrahedral mesh type was more than 7 times the number of cells by using hexahedral mesh type In Figure 24 and Figure 25, the result of temperature distribution of air in the SGHD using the hexahedral grid had a higher accuracy than the result which was used the tetrahedral grid, and at sufficiently high grid numbers, the effect of mesh type on the simulation results was small In Figure 24, the different value of average temperature profiles was not significant, and the maximum air temperature of the air in the SGHD
T01H01 of hexahedral mesh type was normally lower than the maximum air temperature of the air in the SGHD hexahedral mesh type
Further, the influence of mesh type on the relative humidity of the air inside the GHSD was investigated The humidity of moist air inside the SGHD differs widely in space and depends on time The simulation results with various mesh types are illustrated in Figure 25
Figure 25 Relative humidity distribution of air inside SGHD at 10 AM using tetrahedral mesh type T01 (a) and hexahedral mesh H01 (b)
Relative humidity in the dryer decreases over time due to both falling ambient humidity and increased water-holding capacity of the drying air as temperatures rise Variations in humidity levels can be simulated using mesh types such as hexahedral or tetrahedral, as illustrated in Figure 26.
The relative humidity simulated using hexahedral (H01) and tetrahedral meshes (T01) with similar cell sizes yielded comparable results The error between the two mesh types was minimal The relative humidity distribution closely aligns with the temperature distribution of moist air within the greenhouse solar dryer (GHSD) The air inside the dryer cools overnight, but the relative humidity remains lower than the ambient air The computational time for simulations increases with mesh density and node count, and among the mesh types tested, hexahedral meshes require the longest computation time.
RELA TIV E H UM ID ITY (% )
CONCLUSION
This thesis created a computational model of SGHD in SpaceClaim with simulation using ANSYS Fluent The results indicate the complex models in which 3D geometry is favorable for predicting the dryer's performance with several incident solar radiations in various weather conditions The temperature distribution and the velocity of moist air inside the dryer from sunrise to sunset have been simulated Additionally, numerically obtained results are consistent with experimental results The highest temperature and lowest RH at 2:00 PM are 66.1°C (339 K) and 23.70%
Moreover, the velocity distribution of the air is more uniform The simulation results also present the relation of RH inside the dryer at the location and time at which the maximum value of RH is 79.55%, and the minimum value is 23.70% The results of the simulation distribution temperature and distribution RH prove that the SGHD could be operated throughout an entire day and can be a prime for building dryers in agricultural countries
CFD simulation can accurately predict temperature and air flow distribution within the GSHD under varying operating conditions Hexahedral and tetrahedral mesh types yield similar airflow distribution results, suggesting that increasing the number of cells is the most effective means of enhancing GSHD simulation accuracy and efficiency.
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