Experimental and Numerical Analysis of Variable Tube Diameter Circular Central Solar Receiver

CSP (concentrated solar power) is a cutting-edge renewable energy conservation approach. Solar energy has been recognized a one of the providential renewable energy technologies. CSP (long wave range) or PV (short wave range) technologies [1]. At the present time the solar energy the most reliable alternative energy source; however, it cannot be used to create electricity directly owing to its low intensity. By constructing the suitable concentrating systems, it may be used for a far reaching of energy input devices, from domestic to industrial use [2]. Solar energy can be converted directly from the Photovoltaic systems into electricity, which can then be stored in batteries for later use. Both technologies have progressed in diverse ways since a solar energy first arrived in the renewable energy market in the 1970s. PV plants have discovered a way to cut down the costs by seeking more energy-efficient and cost-effective solar cells, allowing for quicker plant- drive times and installation [3].

Another type of solar system gathers solar energy and transmits it to a working fluid by sensible heating of a fluid that continuously passes through tubes. Solar collectors, also known as central solar receivers, are a renewable technology that collects solar radiation and converts it into hightemperature thermal energy for chemical processing and electricity production. Flat plate solar collectors (FPSCs) are the most basic form of collector because they are simple to build, affordable, and low-maintenance [4].

There are several parameters that have a functional link with the thermal efficiency of a solar collector. Collection plate position, coating substance, collector plate coating, glazing material quality, riser tube diameter spacing, flow velocity, incoming radiation intensity, and bottom and side insulation thickness are all factors to consider. Working fluid improves the performance of solar collectors [5]. Nano fluids are cutting-edge working fluids that are attracting a lot of attention from researchers across the world as a method to increase the efficiency of energy absorption and transport systems. To ensure system compatibility, design change is a thorough strategy that influences a wide variety of other properties. The continual and systematic contributions of researchers from all around the world have enabled engineering and technological breakthroughs in FPSC [6]. A solar central receiver (SCR), also known as a solar power tower, powers a traditional steam Rankine cycle and is one of the most common designs for CSP systems. There have been various studies on this design, with several design focusing on economic assessments and thermodynamic [7]. Consequently, to make the key components worthy of their allotted job, modifications in design are always followed by changes in new mechanics, techniques, and even changes in working fluid. In terms of spiral tube collectors, the one used in (S.K. Verma et al) study is novel [8]. Computational Fluid Dynamics (CFD) is a subfield of fluid dynamics that is abbreviated as CFD. The development of high-performance computer hardware, as well as the advent of user-friendly interfaces, has prepared the way for widespread use of CFD in a variety of sectors [9] [10]. Aerodynamics of aircraft and vehicles (improving the mixing capability of a static mixer for use in wastewater treatment or refineries in the oil and gas market), chemical process engineering (improving the mixing capability of a static mixer for use in wastewater treatment or refineries in the oil and gas market), biomedical engineering, and drying technology are examples of such fields [11-14].

The contribution of this paper,

• Thermo-Mechanical Joint Behavior Analyzing CFD model is used to directly solve large-scale transient fluctuation activities, whereas a sub grid scale model is employed to implicitly estimate small-scale movements using NavierStokes equations.

• To measure the pressure difference, the joints are evaluated at five separate segments: maximum diameter junction, minimum diameter junction, average diameter junction, and both inlet and outflow, thereby ensuring thermal behavior of the panel.

The reminder of the paper has been ordered as follows: section 2 presents the recent literatures; section 3 depicts the detail description of the anticipated methodology; section 4 discusses the implementation results; finally, section 5 concludes the paper.

Renewable energy conservation technology is critical for preserving renewable energy and converting it to a usable form where the CFD program is used to model the flow of fluid at the header receiver's gradual convergence and gradual divergence junctions using reported flow parameters at the junctions and to examine the thermal stress concentration caused by fluid flow. Because the design of the receiver has different diameters, determining the exact response of the fluid as a whole is quite challenging. To overcome the abovementioned issue a novel Thermomechanical joint behavior analyzing CFD model has been proposed in which the NavierStokes equations are employed directly to solve large-scale transient fluctuation movements, while a sub-grid-scale model is used implicitly to compute small-scale motions. Furthermore, the joints are an important component of the header that has a greater impact on the functioning of the solar receiver and hence, the joints are examined at five different sections: maximum diameter junction, minimum diameter junction, average diameter junction, and inlet and outflow. The velocity distribution is computed using Bernoulli's theorem, Turbulence with k-epsilon model, wall-adapting local eddyviscosity model, and the transition from laminar to turbulence. The most important component in determining the behavior of the solar receiver is thermal behavior of the panel. Additionally, the temperature is altered to various values, and the thermal concentration is determined at the five joints.

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Figure 1. Block diagram of the proposed Thermo mechanical joint behavior

The mechanical characteristics that alter as a function of the thermal behavior are also thoroughly examined. The block diagram of the proposed methodology is depicted in Figure 1.

3.1 Thermo mechanical joint behavior analyzing CFD model

Thermo-Mechanical Joint Behavior Analyzing CFD model is used to analyse the circular header receiver with varied diameter for its performance under various conditions. The Navier-Stokes equations are used to solve large-scale transient fluctuation movements, while a sub grid size model is used to compute small-scale motions implicitly. As a result, the parallel plate model is widely practiced to determine the fracture permeability m, which was derived by applying the Navier—Stokes equation to laminar incompressible flow between two parallel smooth plates. The hydraulic aperture, which is the joint's effective opening to fluid flow, is also depicted as a function of its permeability. The hydraulic aperture of the fracture does not match its mechanical aperture because actual fractures deviate substantially from ideal parallel plates.

$m=\frac{e_i{ }^2}{12}$              (1)

where, $e_i \rightarrow$ Hydraulic aperture of the joint.

To estimate the hydraulic aperture from the mechanical aperture, the following empirical connection is shown in Eq. (2).

$e_i=\frac{e_n^2}{J R C}$             (2)

where, JRC→ Joint roughness coefficients.

$e_i$ and $e_n$ are in $\mu m \rightarrow$ Mechanical aperture of the joint. In addition, a linear link between mechanical apertures and hydraulic are shown in Eq. (3).

$e_i=e_{i 0}+g \Delta e_n$         (3)

where, $e_{i 0}$ is the initial hydraulic aperture, $\Delta e_n$ is the variation in mechanical aperture owing to the combined effects of compression and shear, and g is a proportionality factor. When, g ranges between 0.5 to 1. The roughness of the joint surfaces contributes to this component. The limiting ideal case of parallel smooth plates has a factor g=1, this circumstance exists only when the joint is relatively open, with apertures of the order of mm are shown in Eq. (4). In the majority of other circumstances, $g<1$ the shape of the flow path has a significant influence on g. Where, g is often close to 0.8 for rectilinear laminar flow.

$g=g_{0 \exp }\left.\left(-\int_0^{u^q} d_g d u^q\right)\right.$     (4)

where, $d_g$ is a production gauge factor. Where, the additional parameters $g_0$ and $d_g$ presented in this section are extremely likely to be experimentally connected to JRC, JCS, and q. To get to specific correlations, a detailed experimental design will be required.

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Figure 2. Design of Thermomechanical joint behaviour using CFD model

Autodesk CFD was used to simulate the solar central receiver with thermo-mechanical joint behavior. The diameter of the upper header inlet and outlet is 15 mm and 50 mm and the diameter of the bottom header inlet and outlet is 15 mm and 50 mm, the diameter of the upper header inlet and outlet is 15 mm and 50 mm, the number of tubes is 15, the area of the receiver is 0.6 m2, the heat flux is 3500 w/m2, and the material of the receiver and frame is copper. Also, the simulation fluid is water, which has a constant density of 997 kg/m3 and a dynamic viscosity of 0.0008 kg/ms are shown in Figure 2. The fluid is assumed to be incompressible, with mass flow at the input and pressure at the output chosen as the boundary conditions. Hence, the experimental procedure is explained in the below subsection.

3.2 Experimental procedure

The joints are an important component of the header that has a greater impact on the functioning of the solar receiver. Hence, the joints are examined at five different sections: maximum diameter junction, minimum diameter junction, average diameter junction, and inlet and outflow.

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Figure 3. Circular solar receiver

The following procedures were taken throughout the testing method to investigate the influence of outlet inclination on the phase split:

• The outlet branches were angled as required.

• The suitable air inlet control valve was changed to provide the necessary air inlet flow rate. Therefore, the necessary air outlet control valves were simultaneously adjusted to achieve the target junction pressure of 2.0 atm (abs).

• The water pump was twisted on when the suitable water inflow rotameter valve was entirely opened where, the flow rate was set by adjusting the control valve.

• The right test section the pressure of 2.0 atm (abs) was conserved by continually changing the air control valves. The water level in the separation tanks was kept constant by managing the exit water flow rates via valves. The exact test conditions of test section pressure, correct extraction ratio, input flow rate and constant water level in the separation tanks necessitated this repeating technique.

• The mass split ratio (W3/W1) was evaluated with the appropriate test section pressure, intended intake flow rate, and a stable level of liquid in the separation tanks. If it differed from the required value, the air control valves downstream from the separation tanks were used to correct it. Also, the mass split ratio was adjusted in such a way that the right intake mass flow rate and pressure were maintained. Iterative procedures were used until the required operational conditions were totally met.

The quantity of period required to alter the flow variables in the loop was resolute by the intake flow conditions and the value of the mass split ratio (W3/W1). Before capturing any phase distribution data during the steady-state period, the following parameters required to remain fixed:

• The pressure at the intersection (Ps).

• The water and air mass flow rates at the inlet and outlet.

• The water level in the filter tanks.

• The air and water pressures and temperatures throughout the system. By, using the required parameters of WG1, WL1, WG2, WL2, WG3, and WL3, the following criteria were calculated.

$W_j=W_{H j}+W_{M j} \quad j=1,2, \ldots n$          (5)

The inlet and the outlet qualities were calculated by,

$y_j=\frac{W_{H j}}{W_i} \quad j=1,2 \ldots . n$

where, W be the mass flow rate $\left(K g s^{-1}\right)$

H be the gravitational acceleration

M be the liquid

j be the superficial velocity $\left(\mathrm{ms}^{-1}\right)$

y be the quality

Therefore, the fraction of total inlet liquid entering outlet and the fraction of total inlet gas entering outlet were calculated using above equations.

A beam problem may be reduced to a simple harmonic oscillator differential equation retaining linear material features hypothesis and eigenvalues solution because of structural dynamic theory. Hence, bending deformations are examined when the Euler-Bernoulli hypothesis is used. All of these hypotheses lead to a set of equations corresponding to an equivalent damped harmonic oscillator solution for each Eigen mode.

$N_{e q}=\int N \overline{V^2} d V$       (6)

$K_{e q}=\int F J\left(\frac{d^2 \bar{V}}{d y^2}\right)^2 d V$         (7)

$H_{e q}=\int H \bar{V} d V, \omega=\sqrt{\frac{K_{e q}}{N_{e q}}}$             (8)

Assuming statistical independence of the forces at each ring, the equivalent force term may be defined as square sum. This model provides an estimate of the supreme movement of the rods, allowing users to determine whether moving frame simulations are required are shown in table 1.

Table 1. Dimensions of proposed experimental setup

Thus the velocity distribution is determined via wall adapting eddy viscosity and k-epsilon turbulence model is explained in the below section.

3.2.1 Turbulence and velocity distribution model

The K-epsilon $(\mathrm{k}-\varepsilon)$ turbulence model is the most frequently used model in computational fluid dynamics (CFD) to simulate mean flow characteristics under turbulent flow conditions. It is a two-equation model that uses two transport equations to provide a broad characterization of turbulence (partial differential equations, or PDEs). The K-epsilon model was created to improvise the mixing-length model to provide an alternative to algebraically dictating turbulent length scales in moderate to high-complexity flows.

The velocity is parted into a mean flow component and a fluctuating component with a zero temporal average because of the Reynolds decomposition. As a consequence, the Reynolds Stress terms $u_i u_j$ have a closure issue. For algebraic models, the $u_i u_j$ are supposed isotropic, so that all of the tensor cross components may be attributed to the generation and dissipation of turbulent kinetic energy. A kinetic turbulence energy balance equation and a dissipation rate equation are derived from this assumption. In addition, the turbulent eddy viscosity $\mu_t$ is the ratio using a simple algebraic equation the relationship between kinetic turbulent energy and dissipation rate are shown in Eqs. (9) and (10).

For turbulent kinetic energy,

$\frac{\partial(\rho l)}{\partial t}+\frac{\partial \rho u_i}{\partial x_i}=\frac{\partial}{\partial x_j}\left[\frac{u_t}{\sigma_k} \frac{\partial l}{\partial x_j}\right]+2 \mu_t F_{i j}^2-P \varepsilon$               (9)

For dissipation,

$\frac{(\partial P \varepsilon)}{\partial t}+\frac{\partial\left(P \varepsilon u_i\right)}{\partial x_i}=\frac{\partial}{\partial x_j}\left[\frac{\mu_t}{\sigma \varepsilon} \cdot \frac{\partial \varepsilon}{\partial x_j}\right]+D_1 \varepsilon \frac{\varepsilon}{l} 2 \mu_t F_{i j}^2-D 2 \varepsilon \rho \frac{\varepsilon^2}{l}$            (10)

Where, $u_i$ denotes the component of velocity in the relevant direction.

$F_{i j}$ denotes a rate of deformation component.

$\mu_t$ denotes the eddy viscosity.

$\mu_t=\rho D_\mu \frac{l^2}{\varepsilon}$                (11)

$\sigma_k, \sigma_{\varepsilon}, C_{1 \varepsilon}$ and $C_{2 \varepsilon}$  are constants. Thus the pressure difference is mentioned via Bernoulli’s model are explained in the below subsection.

3.2.2 Pressure difference model

Bernoulli's principle of fluid dynamics circumstances i.e. an increase in fluid speed occurs simultaneously with a decrease in static pressure or potential energy. As a consequence, fluid particles are simply impacted by their own weight and pressure. If a fluid is flowing horizontally along a section of a streamline, it can only increase in speed because the fluid has moved from a higher pressure region to a lower pressure region and it can only decrease in speed because the fluid has moved from a lower pressure region to a higher pressure region. the quickest speed occurs where the pressure is lowest, and th e slowest speed occurs at pressure is highest in a horizontally flowing fluid. In most cases gases and liquids flowing at low Mach numbers, the density of a fluid packet may be considered to remain constant, regardless of pressure variations in the flow. As a result, the fluid can be termed incompressible, and incompressible flows are the outcome. The following is a common variation of Bernoulli's equation that may be used at any point along a streamline:

$\frac{w^2}{2}+h z+\frac{p}{\rho}=Constant $       (12)

where, w denotes the velocity of fluid flow at a location on a streamline.

h be the acceleration due to gravity.

z be the Elevation of a point above a reference plane, with the positive z-direction pointing upward - that is, in the opposite direction of gravitational acceleration.

p be the pressure at the particular point.

For this Bernoulli equation to operate, the assumptions are followed.

The flow is stable, which means that the flow characteristics (velocity, density, and so on) at any point cannot fluctuate over time. The flow is incompressible i.e., even if pressure fluctuates, the density must remain constant along a streamline. Also, viscous force friction is to be minimal.

Bernoulli's equation may be generalized to conservative force fields as follows:

$\frac{w^2}{2}+\varphi+\frac{p}{\rho}=Constant $           (13)

where, $\varphi$ be the force potential at the location on the streamline under consideration. $\varphi=h x$

Equation (12) may be expressed as follows by multiplying by the fluid density:

$\frac{1}{2} \rho w^2+\rho h x+p=$ constant       (14)

(or) $\quad q+\rho h i=p_0+\rho h x=$ constant                 (15)

where, $q=\frac{1}{2} \rho w^2$ is a dynamic pressure $i=x+\frac{P}{\rho h}$ is a hydraulic head $P_0=P+q$  is a Stagnation pressure The Bernoulli equation's constant can be normalized. A typical method is to express total head or energy head H:

$H=x+\frac{p}{\rho h}+\frac{w^2}{2 h}=i+\frac{w^2}{2 h}$            (16)

According to the preceding equations, Pressure is zero at a certain flow speed, while pressure is negative at higher rates. Bernoulli's equation is plainly no longer valid before zero pressure reached since gases and liquids seldom achieve negative absolute pressure, let alone zero pressure. When the pressure in a liquid drops too low, cavitation occurs. The equations above take use of a linear relationship between pressure and flow speed squared. Higher gas flow rates or sound waves in water liquids, because considerable variations in mass density, making the premise of constant density invalid. Consequently, the temperature is varied to different values and the thermal concentration is defined at the defined five joints. Also the mechanical characteristic changes based on the thermal behavior is also analyzed thoroughly. In this, we have compared our results with CFD software packages with classical formula and made an attempt to analyze the geometrical Configuration. Hence, the experiment is carried out to carefully quantify the pressure differential, turbulence, and velocity distribution caused by the flow of a micro fluid medium in a solar convergent divergent header configuration. The further implementation particulars of the proposed SCR with thermos mechanical joint behavior have been presented in the next section.