Thermodynamic optimisation of the integrated design of a small‐scale solar thermal Brayton cycle

The Brayton cycle's heat source does not need to be from combustion but can be extracted from solar energy. When a black cavity receiver is mounted at the focus of a parabolic dish concentrator, the reflected light is absorbed and converted into a heat source. The second law of thermodynamics and entropy generation minimisation are applied to optimise the geometries of the recuperator and receiver. The irreversibilities in the recuperative solar thermal Brayton cycle are mainly due to heat transfer across a finite temperature difference and fluid friction. In a small‐scale open and direct solar thermal Brayton cycle with a micro‐turbine operating at its highest compressor efficiency, the geometries of a cavity receiver and counterflow‐plated recuperator can be optimised in such a way that the system produces maximum net power output. A modified cavity receiver is used in the analysis, and parabolic dish concentrator diameters of 6 to 18 m are considered. Two cavity construction methods are compared. Results show that the maximum thermal efficiency of the system is a function of the solar concentrator diameter and choice of micro‐turbine. The optimum receiver tube diameter is relatively large when compared with the receiver size. The optimum recuperator channel aspect ratio for the highest maximum net power output of a micro‐turbine is a linear function of the system mass flow rate for a constant recuperator height. For a system operating at a relatively small mass flow rate, with a specific concentrator size, the optimum recuperator length is small. For the systems with the highest maximum net power output, the irreversibilities are spread throughout the system in such a way that the internal irreversibility rate is almost three times the external irreversibility rate. Copyright © 2011 John Wiley & Sons, Ltd.     

Thermo‐solutal convection in an inclined porous cavity with various aspect ratios under mixed thermal and species boundary conditions

The problem of laminar thermo‐solutal convective flow of a binary fluid mixture in an inclined rectangular cavity filled with a uniform porous medium is considered. Mixed heat and mass fluxes and uniform temperature and concentration conditions are applied on two opposing walls of the cavity while the other two walls are kept adiabatic and impermeable to mass transfer. The problem is put in terms of the stream function‐vorticity formulation. A numerical solution based on the finite‐difference methodology is obtained. Representative results illustrating the effects of the inclination angle of the cavity, buoyancy ratio, Darcy number, and the cavity aspect ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature, and concentration at mid‐section of the cavity are reported. In addition, numerical results for the average Nusselt and Sherwood numbers as well as some useful correlations are presented for various parametric conditions and discussed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20369     

Numerical study of the effects of lid oscillation on the periodic flow pattern and convection heat transfer in a triangular cavity

This study is concerned with a periodic flow pattern with mixed convection in a triangular cavity caused by the effects of lid oscillation and buoyancy. The dimensionless stream function–vorticity formulation is adopted, and a curvilinear grid method for solving the stream function–vorticity equations in irregular geometries is used. Attention is in particular focused on the flow behaviour under the interaction between the frequency of the oscillation of the lid velocity and the frequency of the natural periodic flow. Meanwhile, numerical predictions of the thermal characteristics represented by local and average Nusselt numbers on the walls as well as the transient flow patterns are also provided. Results show that the frequency of oscillation of lid velocity and the natural periodic flow frequency both appear to be major frequencies in the frequency spectrum of the cavity flow, for cases with a dimensionless lid oscillation frequency less than 0.5. When the dimensionless frequency of the oscillation of the lid velocity is equal to or higher than 0.5, the flow and thermal fields are completely locked-on to the lid oscillation, and the natural periodic flow frequency is no longer visible in the spectrum.     

Numerical study on supersonic combustion with cavity-based fuel injection

The present study describes the numerical investigations concerning the combustion enhancement when a cavity is used for the hydrogen fuel injection through a transverse slot nozzle into a supersonic hot air stream. The cavity is of interest because recirculation flow in cavity would provide a stable flame holding while enhancing the rate of mixing or combustion. Several inclined cavities with various aft wall angle, offset ratio and length are evaluated for reactive flow characteristics. The cavity effect is discussed from a viewpoint of total pressure loss and combustion efficiency. The combustor with cavity is found to enhance mixing and combustion while increasing the pressure loss, compared with the case without cavity. But it is noted that there exists an appropriate length of cavity regarding the combustion efficiency and total pressure loss.     

Laminar natural convection in an inclined cavity with a wavy wall

In the present work, a numerical study of the effect of a hot wavy wall of a laminar natural convection in an inclined square cavity, differentially heated, was carried out. This problem is solved by using the partial differential equations, which are the vorticity transport, heat transfer and stream function in curvilinear co-ordinates. The tests were performed for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. Two geometrical configurations were used namely one and three undulations.The results obtained show that the hot wall undulation affects the flow and the heat transfer rate in the cavity. The mean Nusselt number decreases comparing with the square cavity. The trend of the local heat transfer is wavy. The frequency of the latter is different from the undulated wall frequency.     

Peristaltic flow of a Williamson fluid in an inclined asymmetric channel with partial slip and heat transfer

The present article deals with the peristaltic flow of a Williamson fluid in an inclined asymmetric channel. The relevant equations have been modeled. Analysis has been carried out in the presence of velocity and thermal slip conditions. Expressions for stream function, temperature, pressure gradient and heat transfer coefficients are derived. The solutions are compared with the existing available results in a limiting sense. Numerical integration has been performed for pressure rise per wavelength. Plots are presented and analyzed for various embedded parameters into the problem. Comparison between the solutions is also shown.     

A study of the ventilation performance of a series of connected solar chimneys integrated with building

A series of connected solar chimneys consisting of an inclined section on the roof and a vertical section near the south wall was studied in a typical two-floor house. Specifically, the effects of the total length and width of the chimney, the inclined angle of the second floor inlet, the length ratio of the vertical to inclined section, and the chimney inclined angle on the chimney ventilation performance were numerically studied. The results showed that the ventilation was improved with the increase of the total chimney length. The air mass flow rate increased firstly then decreased with the chimney width, indicating that there existed an optimal length to width ratio, which was 12:1. Similarly, the mass flow rate increased firstly then decreased with the inclined angle of the second floor chimney inlet. The optimal inclined angle was found to be 4° from the horizontal. At the fixed total chimney length, the air mass flow rate also varied with the length ratio of the vertical to inclined section, and the maximum mass flow rate can be achieved by choosing the longest vertical length within the restriction of the building code. Finally, with the increase of chimney inclined angle, the velocity distribution inside the chimney was improved and the air flow rate increased. These results may provide the theoretical basis for the practical solar building design.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Exergy optimization of flow rates in flat-plate solar collectors

The optimal flat-plate collector mass flow rate is determined by maximizing the exergy (available energy) delivery of the collector as the objective function. Collector and storage dynamics are neglected. Although the case where the pumping power loss is ignored results in bang-bang control, the case where this loss is included in the exergy equation results, after some assumptions, in an optimal mass flow rate that is a function of collector parameters, inlet and ambient temperatures and solar heat gain. Daily performance of a typical flat-plate solar collector with optimum mass flow rate is compared with the performance of the same collector using the mass flow rate obtained by maximizing the difference between the collected thermal energy and the required pumping power.     

Exergy analysis and parametric study of concentrating type solar collectors

The exergetic performance of concentrating type solar collector is evaluated and the parametric study is made using hourly solar radiation. The exergy output is optimized with respect to the inlet fluid temperature and the corresponding efficiencies are computed. Although most of the performance parameters, such as, the exergy output, exergetic and thermal efficiencies, stagnations temperature, inlet temperature, ambient temperature etc. increase as the solar intensity increases but the exergy output, exergetic and thermal efficiencies are found to be the increasing function of the mass flow rate for a given value of the solar intensity. The performance parameters, mentioned above, are found to be the increasing functions of the concentration ratio but the optimal inlet temperature and exergetic efficiency at high solar intensity are found to be the decreasing functions of the concentration ration. On the other hand, for low value of the solar intensity, the exergetic efficiency first increases and then decreases as the concentration ratio is increased. This is because of the reason that the radiation losses increase as the collection temperature and hence, the concentration ratio increases. Hence, for lower value of solar intensity, there is an optimal value of concentration ratio for a given mass flow rate at which the exergetic efficiency is optimal. Again it is also observed that the mass flow rate is a critical parameter for a concentrating type solar collector and should be chosen carefully.     

Effect of uniform inclined magnetic field on natural convection and entropy generation in an open cavity having a horizontal porous layer saturated with a ferrofluid

Numerical analysis of natural convection combined with entropy generation in a square open cavity partially filled with a porous medium has been performed for a ferrofluid under the effect of inclined uniform magnetic field. Governing equations with corresponding boundary conditions formulated in dimensionless stream function and vorticity using Brinkman–extended Darcy model for porous layer have been solved numerically using finite difference method. An influence of key parameters on ferrofluid flow and heat transfer has been analyzed. It has been found that an inclusion of spherical ferric oxide nanoparticles can lead to a diminution of entropy generation in the case of similar flow and heat transfer structures.     

Effects of inlet conditions on film evaporation along an inclined plate

The evaporation of falling water liquid film in air flow is used in different solar energy applications as drying, distillation and desalination, and desiccant systems. The good understanding of the hydrodynamics and heat exchange in falling liquid film and gas flow, with interfacial heat and mass transfer, can be applied in improving solar systems performance. The solar system performance is dependent on the operating conditions, system conception and related to several physical parameters, where the effects of some of these parameters are not completely clarified. In the present numerical study, we examine the effects of inlet conditions on the evaporation processes along the gas–liquid interface. The liquid film streams over an inclined plate subjected to different thermal conditions. Liquid and gas flows are approached by two coupled laminar boundary-layers. The numerical solution is obtained by utilizing an implicit finite-difference box method. In this analysis an air–water system is considered and the coupled effects of inclination, inlet liquid mass flow rate and gas velocity are examined. The results show that, for imposed heat flux or uniform wall temperature, the effect of inclination is highly dependent on the liquid mass flow rate and gas velocity. An increase in the liquid mass flow rate causes an enhancement of the effect of inclination on the heat and mass transfer. The inclination affects the heat and mass transfer, especially at lower gas velocities. In the range of inclination angles of 0–10°, an increase in the inclination improves the evaporation by increasing the vapor mass flow rate. The maximum effect of inclination is nearly achieved at an inclination angle of 10°.     

Finite element simulation of mixed convection heat and mass transfer in a right triangular enclosure

A simulation of mixed convection heat and mass transfer in a right triangular enclosure is investigated numerically. The bottom surface of the enclosure is maintained at uniform temperature and concentration that are higher than that of the inclined surface. Moreover, the left wall of cavity moves upward (case 1) and downward (case 2) directions, which have constant flow speed, and is kept adiabatic. The enclosure represents the most common technology utilizing solar energy for desalination or waste-water treatment. A simple transformation is employed to transfer the governing equations into a dimensionless form. A finite-element scheme is used for present analysis. Comparison with the previously published work is made and found to be an excellent agreement. The study is performed for pertinent parameters such as buoyancy ratio, Richardson number and the direction of the sliding wall motion. The effect of aforesaid parameters on the flow and temperature fields as well as the heat and mass transfer rate examined. The results show that the increase of buoyancy ratio enhances the heat and mass transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the direction of the sliding wall motion can be a good control parameter for the flow and temperature fields.     

Simulation of thermal and velocity slip on the peristaltic flow of a Johnson–Segalman fluid in an inclined asymmetric channel

This research is concerned with the peristaltic motion of a Johnson–Segalman fluid in an inclined asymmetric channel. The equations for a magnetohydrodynamic fluid in an inclined asymmetric channel are developed. Both the thermal and velocity slip conditions are used. Series solutions for stream function, temperature, pressure gradient and heat transfer coefficients are derived. The solutions are compared with the previous published work. Numerical integration has been performed for pressure rise per wavelength. Graphical results are presented and discussed for some embedded parameters. A comparative study with the existing available results is shown.     

Numerical Study of Effects of Inclination on Buoyancy-Induced Flow Oscillation in a Lid-Driven Arc-Shaped Cavity

ABSTRACT

Numerical predictions of the inclination effects on the buoyancy-induced oscillatory flow in a lid-driven arc-shaped cavity are presented in this report. Governing equations in terms of the stream function–vorticity formulation expressing the laws of conservation in mass, momentum, and energy are solved by the finite-volume method in curvilinear coordinates. Computations have been performed for various combinations of physical parameters. The inclination angle of the cavity (θ) is varied from 0° to 15°, the Reynolds number (Re) is assigned to be 100, 200, and 500, and the Grashof number (Gr) ranges from 3 × 10⁵ to 1 × 10⁷, while the Prandtl number is fixed at 0.71 for air. In these above ranges of the parameters, two kinds of oscillatory flow pattern have been observed, namely, the traversing-periodic and the half-periodic patterns. Attention has been focused on the effects of the inclination effects on the occurrence of these two different oscillatory flow patterns. Meanwhile, periodic variation in the mixed-convection heat transfer accompanying the oscillatory flow field has also been studied, and the results for the local and the overall Nusselt numbers are presented.     

Mixed Convection in Lid-Driven Trapezoidal Cavities with an Aiding or Opposing Side Wall

Mixed convection heat transfer and fluid flow fields inside a lid-driven trapezoidal cavity were studied numerically. The cavity horizontal walls were thermally insulated while the inclined side walls were maintained isothermally at different temperatures. Forced convection was induced by moving the hotter right inclined side wall. The problem is formulated using the stream function–vorticity procedure. Together with the established boundary conditions on the right moving wall, the problem is solved by the finite difference method. The Richardson number Ri (0.01–10) and inclination angle of the side walls Φ (66–80°) were considered as pertinent parameters and investigated in two lid-driven cases: aiding and opposing directions. The results show that the behavior of Nusselt number is different from Richardson number depending on the direction of the lid. The inclination angle of the side walls was found to have a significant effect on Nusselt number when Ri was relatively low (≤1); otherwise, a negligible effect of Φ on Nusselt number was recorded.     

THERMOSOLUTAL TRANSFER WITHIN TRAPEZOIDAL CAVITY

The heat and mass transfer problem in a trapezoidal cavity is treated in this article. The lower part of the cavity is heated and the top inclined part is cooled. Phenomenological equations are solved using the alternating direction implicit (ADI) method combined with a fourth-order compact Hermitian method. The results are compared to those obtained experimentally and numerically by other authors in the triangular and trapezoidal cavity cases. The thermoconvective instabilities obtained are similar to those obtained in rectangular cavities. The influence of geometric parameters, global solicitations, and Lewis numbers on fluid flow configurations and on heat and mass transfer ratios is also studied.     

Thermal performance simulation of a solar cavity receiver under windy conditions

Solar cavity receiver plays a dominant role in the light-heat conversion. Its performance can directly affect the efficiency of the whole power generation system. A combined calculation method for evaluating the thermal performance of the solar cavity receiver is raised in this paper. This method couples the Monte-Carlo method, the correlations of the flow boiling heat transfer, and the calculation of air flow field. And this method can ultimately figure out the surface heat flux inside the cavity, the wall temperature of the boiling tubes, and the heat loss of the solar receiver with an iterative solution. With this method, the thermal performance of a solar cavity receiver, a saturated steam receiver, is simulated under different wind environments. The highest wall temperature of the boiling tubes is about 150 °C higher than the water saturation temperature. And it appears in the upper middle parts of the absorbing panels. Changing the wind angle or velocity can obviously affect the air velocity inside the receiver. The air velocity reaches the maximum value when the wind comes from the side of the receiver (flow angle α = 90°). The heat loss of the solar cavity receiver also reaches a maximum for the side-on wind.     

Some aspects of modelling the energy balance of a room in regard to the impact of solar energy

The architecture of a building is crucial in determining its thermal energy balance and indoor comfort conditions. Knowledge of solar radiation availability and its transmission through a building envelope to the interior of the building helps an architect to design the building in an energy efficient way. Nowadays, in highly populated urban areas, attics are used as living spaces and the building envelope includes inclined external walls and windows in roofs. This paper presents some aspects of modelling the energy balance of rooms with different orientations and with vertical or inclined surfaces of building envelope, with stress on the impact of solar energy. The dynamics of energy flow through windows is analysed in more detail. One dimensional energy flow through the centre of glass area (based on a thermal resistance model), two-dimensional energy flow through the edge of glass area and two-dimensional heat flow through the opaque frame are analysed. The third dimension is also considered in a simplified way by taking into account the specific perimeter of the edge or frame. Stress is put on modelling the solar energy input. Solar radiation is modelled as short wave radiation that is transmitted directly to the room through glazing and as energy absorbed by the building envelope (glass panes, frame and opaque external walls) that becomes internal heat sources and is transferred indirectly to the room. The model developed has been used for numerical simulation using MATLAB as the programming language. This model predicts (amongst other things) the solar energy impact on the energy balance of a room in a building. It allows many cases of rooms and their envelopes to be run and evaluated and as a result both general and detailed conclusions can be drawn. Some results are presented in both graphical and tabular form.     

Local thermal nonequilibrium effect on nanofluid filled porous cavity subject to mixed convection heat transfer

In this study, a numerical study is performed to determine the significance of local thermal nonequilibrium on mixed convection heat transfer of a copper water-based nanofluid in an inclined porous cavity. By employing the nonequilibrium hypothesis, the governing equations for nanofluid flow in a porous medium are solved by the Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm. From the obtained results, the nanofluid flow and thermal characteristics are analyzed through streamlines and isothermal plots whereas the heat-transfer rate of the system is scrutinized via the average Nusselt number.