Suneet Singh

Flow map and measurement of void fraction and heat transfer coefficient using an image analysis technique for flow boiling of water in a silicon microchannel

The present work focuses on the generation of the flow regime map for two-phase water flow in microchannels of a hydraulic diameter of 140 µm. An image analysis algorithm has been developed and utilized to obtain the local void fraction. The image processing technique is also employed to identify and estimate the percentage of different flow regimes and heat transfer coefficient, as a function of position, heat flux and mass flow rate. Both void fraction and heat transfer coefficient are found to increase monotonically along the length of the microchannel. At low heat flux and low flow rates, bubbly, slug and annular flow regimes are apparent. However, the flow is predominately annular at high heat flux and high flow rate. A breakup of the flow frequency suggests that the flow is bistable in the annular regime, in that at a fixed location, the flow periodically switches from single-phase liquid to annular and vice versa. Otherwise, the occurrence of three regimes—single-phase liquid, bubbly and slug are observed. These results provide several useful insights about two-phase flow in microchannels besides being of fundamental interest.

High-Temperature Receiver Designs for Supercritical CO2 Closed-Loop Brayton Cycles

High-temperature receiver designs for solar powered supercritical CO2 Brayton cycles that can produce ∼1 MW of electricity are being investigated. Advantages of a supercritical CO2 closed-loop Brayton cycle with recuperation include high efficiency (∼50%) and a small footprint relative to equivalent systems employing steam Rankine power cycles. Heating for the supercritical CO2 system occurs in a high-temperature solar receiver that can produce temperatures of at least 700 °C. Depending on whether the CO2 is heated directly or indirectly, the receiver may need to withstand pressures up to 20 MPa (200 bar). This paper reviews several high-temperature receiver designs that have been investigated as part of the SERIIUS program. Designs for direct heating of CO2 include volumetric receivers and tubular receivers, while designs for indirect heating include volumetric air receivers, molten-salt and liquid-metal tubular receivers, and falling particle receivers. Indirect receiver designs also allow storage of thermal energy for dispatchable electricity generation. Advantages and disadvantages of alternative designs are presented. Current results show that the most viable options include tubular receiver designs for direct and indirect heating of CO2 and falling particle receiver designs for indirect heating and storage.Copyright

Pressure Correction–Based Iterative Scheme for Navier-Stokes Equations using Nodal Integral Method

A novel numerical scheme is developed for steady-state, 2-D incompressible Navier-Stokes equations using the nodal integral method (NIM). The NIM-based schemes have been used to solve partial differential equations in different areas of physics and are known to have very high accuracy compared to conventional numerical schemes. The scheme is implemented using a SIMPLE (Semi-Implicit Method for Pressure-Linked Equations)-like algorithm for pressure and velocity correction instead of solving the exact pressure Poisson equation. To verify the results, two well-known test problems, the lid-driven cavity and natural convection of air in a square cavity, are chosen. For both cases, results are in good agreement with the benchmark solutions even for quite coarse grids.

Nodal Integral Method Using Quadrilateral Elements for Transport Equations: Part 1—Convection-diffusion Equation

A generic numerical scheme for solution of the convection-diffusion equation using the nodal integral method (NIM) is developed for complex geometry. Arbitrary-shaped quadrilateral elements fitted to the complex domain are iso-parametrically mapped to unit square elements using bi-linear interpolation function. Approximations for the cross-derivative terms appearing in the transformed equations are developed and incorporated in the scheme. A numerical scheme for Neumann and mixed-type boundary conditions using NIM methodology is developed for an arbitrary-shaped boundary. Continuity conditions at the interface of two adjacent discrete cells are formulated explicitly to deal with generic quadrilateral elements. The developed scheme is verified against the analytical solutions of diffusion and convection-diffusion problems in skewed and curvilinear geometry. The results show the capability of the NIM to produce quite accurate results on a reasonably coarse mesh, even for nonorthogonal and curvilinear geometries.

Experimental and numerical study on the onset of natural convection in a cavity open at the top

The onset of natural convection in a 2D air filled cavity open at the top with adiabatic side walls is studied. The numerical model shows the existence of weak convective flow near the top corner of a cavity due to the thermal gradient between the walls and the atmosphere even at low Rayleigh numbers, as also confirmed by the interferometry-based experimental data. Additionally, a thermally stratified layer is formed on the lower side of the cavity. The onset of convection is seen to be dependent on the interaction of these two features in the cavity. Results of the study show that in low aspect ratio cavities, the thermally stratified layers are clearly formed and are not significantly disturbed by the flow at the corners. The onset of convection takes place in these earlier thermally stratified layers beyond a certain Rayleigh number. This convective movement is characterized by a sudden jump in the heat transfer coefficient at a critical Rayleigh number. However, for high aspect ratio cavities, the flo...

Analytical solution of time-dependent multilayer heat conduction problems for nuclear applications

Analytical solutions for one-dimensional time dependent multilayer heat conduction problems were developed several decades ago. Mathematical theory for such problems in more than one dimensions was also developed during that time. Several of these methods were based on separation of variable and finite integral transform. However, the application of these methods was hindered by the fact that the eigenvalue problems, which are essential for this methodology are difficult to solve. Moreover, in two and three dimensional Cartesian coordinates these eigenvalues were imaginary rendering their solutions even more difficult. It has been recently shown that similar problems in two dimensional cylindrical and spherical coordinates do not have imaginary eigenvalues. It is also helpful that the softwares which are capable of analytical manipulations are now ubiquitous. This paper discusses the methodology as well as possible application in nuclear reactors of analytical solutions of two-dimensional multilayer heat conduction in spherical and cylindrical coordinates.

Experimental Study of Water Boiling in Microchannel

With the reduction in size of electronic devices, the problem of efficient cooling is becoming more and more severe. Boiling heat transfer in microchannels is fast emerging as a promising solution to the problem. In the present work, microchannels were fabricated on a silicon wafer. A chrome-gold micro-heater was integrated and characterized on the other side of the wafer. The change in resistance of the micro-heater in the temperature range of 20 °C – 120 °C was found to be within 10%. Deionized water was used as working fluid in microchannel. The single-phase pressure drop across the microchannel was found to increase linearly with increasing flow rate in confirmation with conventional laminar flow theory. Also, the pressure drop decreases with an increase in heat input due to a reduction in viscosity. The study was extended to two phase flow with flow rate and heat flux as the control parameters. The onset of two phase flow, at a given heat flux, with a decrease in flow rate, can be identified by the departure of linear pressure drop to non-linearity; this point was also confirmed through visual observation. In two-phase region of flow, pressure drop was found to increase initially, passes through a maximum and then decreases, with a decrease in flow rate. The experiments are performed for several heat fluxes. Both the onset of two phase and maximum pressure drop in the two phase region shifts to higher flow rates with an increase in heat input. Such detailed experimental results seem to be missing from the literature and are expected to be useful for modeling of boiling heat transfer in microchannels. Another pertinent observation is presence of instability in two-phase flow. It was found that at higher flow rate and heat flux instability in two-phase flow was more. An attempt to record these instabilities was made and preliminary data on their frequency will be presented. This study may help to choose suitable operating conditions for a microchannel heat sink for use in electronics cooling.Copyright

Flow and heat transfer characteristics of an open cubic cavity with different inclinations

Natural convection of air in an inclined differentially heated open cubic cavity is studied. From the literature, it can be seen that there is no definite relationship between the Nusselt numbers obtained for square and cubic cavities for different Rayleigh numbers (Ra) and cavity inclinations. For some combinations of Ra and cavity inclinations, the Nusselt numbers are significantly lower in the cubic cavity compared to that of the square cavity, while for other combinations, it is quite the opposite. To understand the cause of these variations, a detailed study of the flow patterns is carried out for different Ra and cavity inclination angles. It is seen that for a lower range of Ra, the finiteness of the cavity reduces the flow, resulting in lower heat transfer for the 3D cavity when compared to the 2D cavity. Similar results are seen for larger inclination angles of the cavity (hot wall close to the vertical) even for higher Ra. However, for the cases with higher Ra and small inclination angles (hot wall close to the horizontal), the flow becomes three-dimensional. The three-dimensionality in the flow is attributed to the weak convection currents that rise from the side adiabatic walls and go down from the center of the cavity. The combination of these convection currents with the predominantly strong convection currents, which are going up from the hot wall, results in the complex three dimensional flow patterns. Due to this phenomenon, the cubic cavity with such a configuration has significantly higher Nusselt number compared to that of the square cavity.Natural convection of air in an inclined differentially heated open cubic cavity is studied. From the literature, it can be seen that there is no definite relationship between the Nusselt numbers obtained for square and cubic cavities for different Rayleigh numbers (Ra) and cavity inclinations. For some combinations of Ra and cavity inclinations, the Nusselt numbers are significantly lower in the cubic cavity compared to that of the square cavity, while for other combinations, it is quite the opposite. To understand the cause of these variations, a detailed study of the flow patterns is carried out for different Ra and cavity inclination angles. It is seen that for a lower range of Ra, the finiteness of the cavity reduces the flow, resulting in lower heat transfer for the 3D cavity when compared to the 2D cavity. Similar results are seen for larger inclination angles of the cavity (hot wall close to the vertical) even for higher Ra. However, for the cases with higher Ra and small inclination angles (hot w...

The Analysis of Global Stability Boundary and Multistability in the Nonlinear Dynamical System of an Advanced Heavy Water Reactor

Abstract The nonlinear stability analysis of an advanced heavy water reactor (AHWR) is performed to investigate global stability. The global stability perspective predicts the exact stability boundary of the system, which is valid for small as well as large disturbances in the system. Recently, the local or linear stability boundary and bifurcation of limit cycles has been discussed for an AHWR. However, the studies were not sufficient to predict global stability of the system. In this work, advanced bifurcation analysis is carried out for an AHWR, which unfolds multistable or unstable states. The region of multistability is observed due to the presence of steady states and multiple limit cycles. The global stability boundary is marginally away from the local stability boundary, the region beyond which the global stability boundary is safe for operation due to the nonexistence of nonlinear phenomena, such as limit cycles. The local stability boundary is basically a Hopf bifurcation boundary as limit cycles (i.e., nonlinear phenomena) emerge from these points. Subcritical or supercritical Hopf bifurcations excite unstable limit cycles (ULCs) or stable limit cycles (SLCs), respectively, and these limit cycles end on the global stability boundary. The subcritical Hopf bifurcation is considered as hard or dangerous bifurcation due to the presence of ULCs in the linearly stable region, which gains stability on the global stability boundary and in which SLCs surround ULCs. Therefore, a region of bistability between the local and global stability boundary is present for subcritical Hopf. The supercritical Hopf is generally considered as the soft and safe bifurcation because of SLCs in the linearly unstable region. Due to this fact, it is assumed that in the supercritical Hopf region the global and local stability boundaries are the same. However, in this work ULCs in the linearly stable region for supercritical Hopf bifurcation are observed along with SLCs, which is an uncommon phenomenon in nuclear reactors. The presence of ULCs surrounding SLCs are observed both in the stable and unstable side on the parameter plane for supercritical Hopf. For the safe operation of a nuclear reactor, identification of the region of global stability is of paramount interest.

Two Phase Flow Stability Analysis of Multiple Horizontal Uniformaly Heated Channel

Two-phase flow in multiple horizontal heated channels has wide applications in heat exchangers, solar heating systems, nuclear systems etc. The theoretical study of the two-phase flow instability analysis for parallel channel was carried by Zhang et al. [1]. This was done for vertical channels and they used nodal method to analyze stability of the system. Similar analysis was done by Lee et al. [2, 3] and Nayak and Vijayan [10], for multiple, vertical boiling channels with forced flows. Following the Zhang et al. [1] and Lee et al. [2, 3], the stability analysis of multiple horizontal channels with uniform heat flux has been carried out. The system is mathematically represented by non-linear PDEs using mass, momentum and energy equations in single as well as two-phase regions. Coupling equation is being used under the assumption that pressure drop in each channel is same and the total mass flow rate is equal to sum of individual mass flow rates. The homogeneous equilibrium model is assumed to be valid in the two phase region. Stability boundary is obtained in terms of phase change number (N pch ) and Sub-cooling Number (N sb ) and is validated by comparing it with result obtained by MatCont using the same parametric values. Numerical simulation of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter space to obtain the actual damped and growing oscillations in terms of the channel inlet velocity which verifies the stability behavior across the stability map.