Constant Property Flow Research Articles

Numerical simulation of drag on local particle cluster within a high void fraction environment in supercritical water

The drag of particle cluster within a high void fraction environment in supercritical water (SCW) is investigated by numerical simulation. The results show that the description pattern of particle drag in SCW is the same as that in constant property flow (CPF). The diffusion of pressure in the phenomenon of fluid flow around particle cluster caused that the variation pattern of drag coefficient is contrary to the classical conclusion. The normalized drag coefficient is mainly depending on the thermal properties. The internal flow characteristics of the particle cluster further confirm the effects of fluid flow around it. After separating the effects of thermal properties, the exponent -β representing the effects of void fraction in SCW is similar to that in CPF. A correlation for calculating the particle drag in SCW is developed based on this result.

DNS investigation of flow and heat transfer characteristics of supercritical carbon dioxide over a backward-facing step

This study employed direct numerical simulation to investigate the turbulent flow and heat transfer characteristics of supercritical carbon dioxide (SCO2) in a vertical backward-facing step (BFS). Three cases were considered: constant property flow, SCO2 forced convection, and SCO2 mixed convection. All cases were conducted with an inlet Reynolds number of 4805, and the expansion rate of BFS is set at 1.5. Mean statistics like velocity, temperature, Reynolds stress, turbulent heat flux, and thermophysical properties are given and discussed. The results show that the turbulent and heat transfer characteristics of SCO2 over a backward-facing step are significantly different from those of conventional fluids due to the dramatic changes in its thermophysical properties near the pseudo-critical temperature. In the case of SCO2 forced convection, though the large thermophysical property variations do not have an obvious impact on the mean flow field, the near-wall mean density decreases largely and thus Reynolds stress and turbulent heat flux near the wall are reduced significantly, which in turn leads to a substantial reduction in the local skin friction coefficient and Nusselt number. In the SCO2 mixed convection, buoyancy substantially distorts the flow, resulting in a significant reduction in the size of the recirculation zone. Simultaneously, buoyancy acts as an additional driving force leading to the formation of a wall jet. These combined effects induce intensified turbulence near the heated wall, which enhances the turbulent heat flux and facilitates efficient heat transfer. The instantaneous vortical structures based on Q criterion also clearly show the intensified turbulence in the near-wall region.

Effects of physical properties of supercritical water on coarse graining of particle cluster

The coarse graining of particle cluster is of great significance to the study of a fluidized bed. The effects of variations in the physical properties of supercritical water on the coarse graining of particle cluster are investigated in this work. The drag coefficient distributions of the particle cluster are not influenced by the physical properties. However, the physical properties have effects on the values of drag coefficient. The effects of physical properties are weaker in the case of large particle concentrations. Furthermore, the physical properties lead to that the effect of particle cluster wake on the drag of downstream particles being significantly different from that of constant property flow. The variation trend of drag of coarse graining particle is consistent with that of isolated particle. The physical properties lead to significant differences in the values of drag. In this paper, the dominance of the effects of physical properties in a variety of cases is confirmed. Finally, a physical properties effect model is developed accordingly.

Drag of a single particle within a multi-particle system in supercritical water

Particle drag is a very important factor in reactor simulation. The complex physical properties of supercritical water (SCW) prevent some modeling methods of reactor simulation from being able to accurately simulate an SCW reactor. Therefore, in this work, the effects of particle interaction on single particle drag within a multi-particle system in SCW are investigated. The results show that the variation in the drag coefficient in SCW is special. This work indicates a control mechanism for the Reynolds number, volume fraction, temperature, and pressure on drag specificity of a single particle. This mechanism essentially exhibits an interaction of viscosity and velocity gradient. Furthermore, through a comparison of SCW and constant property flow, a drag specificity model can be initially developed. The results for SCW can be obtained by calculating the constant property flow, coupled with a drag specificity model. This model can be applied to modeling methods of reactor simulation after further improvement.

Particle dispersion in turbulent mixing layer at supercritical pressure

The heterogeneous structures of particles are generated due to the significant temperature changes when cold particles-dilute jet injects into a supercritical water fluidized bed, which is unfavorable for the reaction of coal particles. We expect to promote the particle dispersion by entrainment mechanism of large-scale vortical structures. The Eulerian-Lagrangian point-source method is used to numerically investigate the dynamics of dilute particles in mixing layer sustained by supercritical water with different temperatures. The effects of density ratio and velocity ratio between two streams are analyzed. In addition to the smaller particle numbers at high-density side, the particle clustering in the vortex core regions is found due to the inhibition of vortical structures by increasing density ratio. With increasing velocity ratio, however, the enhanced vortex stretching promotes the entrainment of particles. As a result, the increase in particle number density at high-density side is up to 26% compared with the constant-property flow. • Study on variable-density effect on dynamics of particle-laden mixing layer. • Enhancement of vortical structure by increasing velocity ratio between two streams. • Particle acceleration decrease with increasing density ratio between two streams. • Improvement of particle dispersion due to the entrainment of vortical structures.

Laminar flow and pressure loss in planar Tee joints: Numerical simulations and flow analysis

This paper presents a numerical investigation of the laminar flow and pressure drop characteristics of planar Tee joints, a canonical flow of interest for the thermal-hydraulic design of oil-immersed power transformer windings. After formulating the problem in nondimensional form, the steady, constant property flow in planar 90∘ Tee joints is computed numerically by integrating the Navier–Stokes equations with fully developed upstream and downstream boundary conditions. The analysis assumes a straight-through configuration in which the straight duct holds flow in the same direction before and after the junction, whereas the flow in the side branch can either divide from the incoming flow or combine with it. The analysis starts with the description of the flow patterns that emerge in the dividing and combining flow cases for all mass split ratios, 0≤ṁ1≤1, and a wide range of straight duct to side branch width ratios, 1≤α≤3, and Reynolds numbers of the common branch, 0 ¡ Re3≤ 200, representative of the cooling oil flow in oil-immersed transformer winding. Flow maps for planar Tee joints are then presented, showing the existence of different regions in the (Re3, ṁ1)-plane that exhibit different number and location of recirculation zones. Pressure distributions and secondary loss coefficients are then computed and analyzed, providing a numerical database that is used to develop new local pressure loss correlations for planar Tee joints in an accompanying paper.

CFD study of Convective Heat Transfer of Water Flow Through Micro-Pipe with Mixed Constant Wall Temperature and Heat Flux Wall Boundary Conditions

The dissipation of heat in tiny engineering systems can be achieved with fluid flow through micro pipes. They have the advantage of less volume to large surface ratio convective heat transfer. There are deep-rooted analytical relations for convective heat transfer available for fluid flow through macro size pipes. But differences exist between the convective heat transfer for fluid flow through macro and micro pipes. Therefore, there is a good scope of work in micro convection heat transfer to study the mechanism of fundamental flow physics. There have been studies with either constant heat flux wall boundary conditions or constant wall temperature boundary conditions with constant and variable property flows. In this article, first, the numerical simulations are validated with the experimental data for 2D axisymmetric conventional pipe with pipe diameter of 8 mm is taken with laminar, steady, and single-phase water flows with constant wall heat flux boundary condition of 1 W/cm2. The computed Nusselt number is compared to the experimental results at different Reynolds numbers of 1350, 1600 and 1700. In the next study, three-dimensional micropipe laminar flow is studied numerically using water with an inlet velocity of 3 m/s and pipe diameter of 100 µm. The mixed wall boundary conditions with upper half pipe surface subjecting to constant wall temperature of 313 K and lower half surface subjecting to 100 W/cm2 are used in the simulations. The focus of research would be to consider the effect of temperature-dependent properties like thermal conductivity, viscosity, specific heat, and density (a combined effect we call it as variable properties) on micro-pipe flow characteristics like Nusselt number at mixed wall boundary conditions and compare it with the constant property flows. The conventional pipe showed no significant difference with variable and constant property flows with different Reynolds numbers. On contrary the flow through 3D micropipe shows that the Nusselt number with variable property flows is less as compared to the constant property flows.

Numerical investigation of heat transfer characteristics between two particles and supercritical water

This work takes two particles as an example to study the effect of distance and angle between two particles on the average Nusselt number Nu, average heat transfer rate ηb, local Nusselt number Nuφ, and local heat transfer rate ηaφ. It was found that the variation trend of Nu and Nuφ in supercritical water is the same as that in constant property flow, thus indicating that the variation trend of heat transfer between particles and fluid in supercritical water is the same as in constant property flow. The change in physical properties of supercritical water does not have any special effect on the variation trend of heat transfer. The heat transfer is mainly affected by the overlap of temperature field and the overlap of flow field. However, the results of ηb and ηaφ indicate that the variation trend of heat transfer rate is affected by temperature gradient changes and physical property changes.

Computational fluid dynamic simulations and heat transfer characteristic comparisons of various arc-baffled channels

Abstract In this analysis, the baffling method is used to increase the efficiency of channel heat exchangers (CHEs). The present CFD (computational fluid dynamics)-based work aims to analyze the constant property, steady, turbulent, Newtonian, and incompressible fluid flow (air), in the presence of transverse-section, arc-shaped vortex generators (VGs) with two various geometrical models, i.e., arc towards the inlet section (called arc-upstream) and arc towards the outlet section (called arc-downstream), attached to the hot lower wall, in an in-line situation, through a horizontal duct. For the investigated range of Reynolds number (from 12,000 to 32,000), the order of the thermal exchange and pressure loss went from 1.599–3.309 to 3.667–21.103 times, respectively, over the values obtained with the unbaffled exchanger. The arc-downstream configuration proved its superiority in terms of thermal exchange rate by about 14% than the other shape of baffle. Due to ability to produce strong flows, the arc-downstream baffle has given the highest outlet bulk temperature.

Toward Exascale: Overview of Large Eddy Simulations and Direct Numerical Simulations of Nuclear Reactor Flows with the Spectral Element Method in Nek5000

At the beginning of the last decade, Petascale supercomputers (i.e., computers capable of more than 1 petaFLOP) emerged. Now, at the dawn of exascale supercomputing, we provide a review of recent landmark simulations of portions of reactor components with turbulence-resolving techniques that this computational power has made possible. In fact, these simulations have provided invaluable insight into flow dynamics, which is difficult or often impossible to obtain with experiments alone. We focus on simulations performed with the spectral element method, as this method has emerged as a powerful tool to deliver massively parallel calculations at high fidelity by using large eddy simulation or direct numerical simulation. We also limit this paper to constant-property incompressible flow of a Newtonian fluid in the absence of other body or external forces, although the method is by no means limited to this class of flows. We briefly review the fundamentals of the method and the reasons it is compelling for the simulation of nuclear engineering flows. We review in detail a series of Petascale simulations, including the simulations of helical coil steam generators, fuel assemblies, and pebble beds. Even with Petascale computing, however, limitations for nuclear modeling and simulation tools remain. In particular, the size and scope of turbulence-resolving simulations are still limited by computing power and resolution requirements, which scale with the Reynolds number. In the final part of this paper, we discuss the future of the field, including recent advancements in emerging architectures such as GPU-based supercomputers, which are expected to power the next generation of high-performance computers.

Velocity and Temperature Profiles in Turbulent Channel Flow at Supercritical Pressure

Understanding the effects of property variations on velocity and temperature profiles is important for the accurate prediction of supercritical heat transfer in regenerative cooling channels. In this study, direct numerical simulations of a planar turbulent channel flow with a wall-normal temperature gradient were conducted to understand the mean temperature profiles that are affected by property variations at supercritical pressure. The working fluid used was supercritical nitrogen. The density ratios between two walls were four and eight. The Van Driest transformation for the mean velocity profiles holds true in the present conditions. This result implies that discussions based on a mixing length hypothesis are valid for the conditions that were studied. Mean temperature profiles in the viscous sublayer are correlated to those of incompressible constant-property flows using a local Prandtl number. For the mean temperature profiles in the logarithmic region, a new temperature transform equation that accounts for the variation in mean density and isobaric specific heat was introduced. It was demonstrated that the gradients of temperature profiles transformed by the transform equation coincide with the ones in incompressible constant-property flows in the logarithmic region.

A low-Mach methodology for efficient direct numerical simulations of variable property thermally driven flows

Abstract Thermally driven flows can be approximated as constant property flows only when temperature differences are relatively small. In that case, the Oberbeck-Boussinesq approximation holds and the set of governing equations is simplified. For larger temperature differences, the variation of the fluid properties with temperature cannot be ignored and in the case of gasses the governing equations take the low-Mach form. This significantly complicates the numerical solution of variable property against constant property flows because of the emergence of a variable coefficient Poisson equation for the pressure. In the present study, a numerical methodology for the direct numerical simulation of thermally driven low-Mach flows is presented. In this framework, a pressure-splitting scheme is utilised to transform the variable coefficient Poisson equation for the pressure into a constant coefficient Poisson equation, improving the efficiency of the numerical solution. The consistent boundary conditions for the pressure are derived and presented. Furthermore, the proposed methodology is validated for the natural convection of air inside a differentially heated cavity, for a wide range of temperature differences, both within and outside the limits of applicability of the Oberbeck-Boussinesq approximation. Finally, to demonstrate the potential of this methodology, the three-dimensional natural convection of air inside a differentially heated cavity is simulated for a Rayleigh number Ra = 2.0 × 10 9 and for temperature differences Δ T = 50 K, 100 K, and 200 K. It is found that, with increasing temperature difference, the symmetry around the centre of the cavity that characterises the Oberbeck-Boussinesq solution is lost. In addition, the laminar-turbulent transition point on the heated and cooled walls changes position, moving to a more upstream position on the heated wall and a more downstream position on the cooled wall.

High-order fully implicit solver for all-speed fluid dynamics

We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below $$M=10^{-5}$$ , which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the $${\mathrm{AUSM}}^{+}$$ -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.

Fluidization in Supercritical Water: Heat Transfer between Particle and Supercritical Water

Abstract Supercritical water fluidized bed reactor, which is used to gasify biomass and produce hydrogen, is a new member of fluidized bed family. Forced convection heat transfer between supercritical water and particles is a major basic heat transfer mechanism in supercritical water fluidized bed reactor. The object of this paper was to determine the heat transfer characteristics for a forced convection between a spherical particle and supercritical water (SCW) in a range of pressure from 23 to 27 MPa and temperature from 637 to 697 K. A numerical model fully accounting for thermal physical property variation of SCW has been solved using a finite volume method with Reynolds number up to 200. Comparing with constant property flow, high velocity and temperature gradient in the vicinity of the particle surface were observed when the variable thermal physical property of SCW was incorporated in calculation. Based on the numerical results, a correlation that takes into account the large thermal physical property variation was proposed for predicting Nusselt number.

Physical Effects of Variable Fluid Properties on Laminar Gas Microconvective Flow

AbstractThe physical effects of variable fluid properties on heat transfer and frictional flow characteristics of laminar gas microconvective flow are investigated in this research. The fully developed flow through a microtube is studied numerically by using 2D continuum‐based governing equations. The physical effects induced due to variations in gas density with pressure and temperature, and gas viscosity, thermal conductivity, and specific heat with temperature are analyzed. Numerical results reveal that the heat transfer and frictional flow characteristics of laminar gas microflow are drastically affected by these physical effects. Hence, this research suggests that these physical effects need to be well considered in the applications of laminar gas microconvection based on large temperature gradients, for example, the design of microchannel heat sinks, and the flow cannot be generally considered as a constant property flow, as in conventional channels.

Periodic reactive flow simulation: Proof of concept for steam cracking coils

Streamwise periodic boundary conditions (SPBCs) have been successful in reducing the computational cost of simulating high aspect ratio processes. Extending beyond the classic assumptions of constant property flows, a novel approach incorporating non‐equilibrium kinetics was developed and implemented for the simulation of an industrial propane steam cracker. Comparison with non‐periodic benchmarks provided validation as relative errors on the main product yields were consistently below 1% for different reactor configurations. A further order‐of‐magnitude reduction of the radial errors on product concentrations was obtained via an intuitive correction method based on the concept of local fluid age. The computational speedup achieved through application of SPBCs was a factor 16–250 compared to the non‐periodic simulations. The presented methodology thus serves as a quick screening tool for the development of novel reactor designs and unlocks the potential for using more elaborate kinetic models or a more fundamental approach toward turbulence modeling. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1715–1726, 2017

Nusselt number correlations for simultaneously developing laminar duct flows of liquids with temperature dependent properties

New correlations, suitable for engineering applications, for the mean Nusselt number in the entrance region of circular tubes and square ducts with uniform heat flux boundary conditions specified at the walls are proposed. These correlations are obtained on the basis of the results of a previous parametric investigation on the effects of temperature dependent viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight ducts of constant cross-sections. In these studies, a finite element procedure has been employed for the numerical solution of the parabolized momentum and energy equations. Viscosity and thermal conductivity are assumed to vary with temperature according to an exponential and to a linear relation, respectively, while the other fluid properties are held constant. Axial distributions of the mean Nusselt number, obtained by numerical integration from those of the local Nusselt number, are used as input data in the derivation of the proposed correlations. A superposition method is proved to be applicable in order to estimate the Nusselt number by considering separately the effects of temperature dependent viscosity and thermal conductivity. Therefore, for each of the considered cross-sectional geometries, two distinct correlations are proposed for flows of liquids with temperature dependent viscosity and with temperature dependent thermal conductivity, in addition to that obtained for constant property flows.

A Numerical Investigation of Localized and Steady Energy Addition to High Speed Airflows

ABSTRACT This work presents a numerical analysis of the gas dynamic problem of localized and steady energy addition to uniform high-speed airflows. Firstly, the general effects caused by a localized energy deposition on the flow were investigated, then an extensive parametric analysis concerning the effects of energy deposition rate and dispersion for different free stream flow speeds was performed. As a general result, localized and steady energy deposition generates compression waves and constant property flow stream tube downstream to the source. The parametric analysis results have shown that either increasing the rate or decreasing dispersion in the orthogonal direction to the flow of the deposited energy has the effect of enhancing property flow changes, which is even more pronounced for lower flow speeds. In contrast, energy dispersion in the flow direction has presented very little effect on the flow changes. The results of this numerical analysis should be very helpful in studies of energy addition applications in hypersonic.

HEAT TRANSFER ENHANCEMENT DUE TO SWIRL EFFECTS IN OVAL TUBES TWISTED ABOUT THEIR LONGITUDINAL AXIS

Periodically fully developed swirl flow and heat transfer in axially helically twisted tubes with elliptical cross sections are computationally modeled. The tubular geometry is described by its twist ratio y (ratio of 180°wist-pitch H to hydraulic diameter dh), and flow cross-section aspect ratio a (ratio of minor to major axis of ellipse). Constant-property flows of water (Prandtl number ~3.0) in the laminar Reynolds number regime (10 ≤ Re ≤ 1000) are considered for several different duct geometries (3.0 ≤ y ≤ 6.0 and 0.3 ≤ α ≤ 0.7). The parametric study delineates the effect of swirl on the velocity distribution, isothermal Fanning friction factor f, the temperature field, and Nusselt number Nu for a tube maintained at a uniform wall temperature (T condition). The dominant vortex structure has a spiral formation with a rotating fluid nucleus and two counter-rotating cells as spiral arms in the flatter section of the oval cross section. Both f and Nu are found to be highest for more tightly twisted tubes (y = 3.0) with a flatter elliptical cross section (α = 0.3). Moreover, relative to an equivalent straight oval tube, up to 2.5 times higher heat transfer rates can be achieved for fixed pumping power to render a more compact heat exchanger with a smaller volume or high surface-area density.

A Novel Model of Turbulent Convective Heat Transfer in Round Tubes at Supercritical Pressures

In the present study, a novel model was established to investigate the enhanced heat transfer to turbulent pipe flow of supercritical pressure fluids. The governing equations for the steady turbulent compressible pipe flow were simplified into the one-dimensional nondimensionalized forms based on the boundary layer theory. A conventional mixing length turbulence model for constant-property pipe flows was modified by introducing the effect of density fluctuations into the equations of turbulent transport, and the modified turbulence model was applicable to both constant-property and variable-property pipe flows. With the suggested model, which was a combination of the nondimensional governing equations and the modified turbulence model, the numerical calculations were carried out for the turbulent convective heat transfer of water in round tubes at supercritical pressures. The results showed that the present model can provide a relatively precise prediction about the effect of pressure, mass flux, and wall heat flux on heat transfer for supercritical fluid flows and greatly reduce the calculation workload. The modified turbulence model showed a much better agreement with the experimental results than the original turbulence model.