A proven methodology to solve multiphase flows is based on the one-fluid formulation of the governing equations, which treats the phase transition across the interface as a single fluid with varying properties and adds additional source terms to satisfy interface jump conditions, e.g., surface tension and mass transfer. Used interchangeably in the limit of non-evaporative flows, recent literature has formalized the inconsistencies that arise in the momentum balance of the non-conservative one-fluid formulation compared to its conservative counterpart when phase change is involved. This translates into an increased sensitivity of the numerical solution to the choice of formulation. Motivated by the fact that many legacy codes using the non-conservative one-fluid formulation have been extended to phase-change simulations, the inclusion of two corrective forces at the interface and a modification of the pressure-velocity solver with an additional predictor-projection step are shown to recover the exact momentum balance in the evaporative non-conservative one-fluid framework for low-viscosity incompressible flows. This has direct implications for obtaining a physically meaningful pressure jump across the interface and is seen to affect the dynamics of two-phase flows. In the high-viscosity domain, the discretization of the viscous term introduces a momentum imbalance which is highly dependent on the chosen method to model the phase transition. In the context of film boiling, this imbalance affects the time scales for the instability growth. Lastly, the need to develop sub-models for heat and mass transfer and for surface tension becomes evident since typical grid resolutions defined as “resolved” in the literature may not be enough to capture interfacial phenomena.@en

Printed circuit heat exchangers (PCHE) are designed to improve heat recovery and energy saving in supercritical CO₂ (S-CO₂) power cycles. In the current study, a modified channel PCHE is proposed based on the regular straight channel and a zigzag channel. The thermal–hydraulic performance of four different types of PCHE is numerically investigated and the methods are verified by both experimental and numerical results. The numerical results are presented for a Reynolds number based on the inlet conditions between 5 000 and 25 000. From the numerical results, the local pressure loss and local heat transfer coefficients are analyzed and discussed. Subsequently, the global Nusselt number and Fanning friction coefficients are discussed. It is found that the inserted straight section contributes to uniform flow, resulted in significant pressure loss reduction with a slight decrease in heat transfer. The modified channel can reduce the Fanning friction coefficient by 33.1%-84.7% while the global Nusselt number reduction is about 3.6%-30.3%. This leads to a maximum performance evaluation criterion (PEC) enhancement of 45.9%.

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An experimental study was conducted to search the reduction of friction in fully developed turbulent pipe flow using different types of polyacrylamides as friction reducing polymers. Pressure drop measurements determined the friction reduction. Three different polymer types Superfloc A110, Superfloc A130 and Superfloc A150 were used to examine the effect of polymer concentration, Reynolds number and polymer type on friction reduction. The Darcy friction factor was obtained for each polymer type at the polymer concentration ranging from 0 to 500 wppm and a Reynolds number range of 10000-80000. It was observed that friction factor decreased with increment in polymer concentration and Reynolds number for each polymer. Higher molecular weight polymers are more effective at reducing friction. With increasing concentration of polymer, the measured data approaches the Virk asymptote, which represents the maximum friction reduction limit by the polymers. The percentage of friction reduction increased with increasing concentration of polymer up to 100 wppm for each polymer type and then began to decrease for polymer concentrations higher than 100 wppm. An empirical formula was obtained to calculate the Darcy friction factor as a function of Reynolds number and polymer concentration for Superfloc A110.

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We use direct numerical simulations (DNS) to investigate the turbulent modulation due to the presence of bubbles in vertical channels flowing downward. The Reynolds number for single-phase flow based on half channel height h^* and friction velocity is Re_τ= 180. A density and viscosity ratio of ρ_d^*/ρ_c^*=0.01 and μ_d^*/μ_c^*=0.018 is chosen for two void fractions of ϵ=1.2% and ϵ=2.4%. For each void fraction three different bubble sizes are simulated: D/h=0.2130, 0.2684 and 0.3382, where D denotes the diameter of the bubbles. Numerical simulations are based on multiple markers Coupled Level-Set/Volume-of-Fluid (CLSVOF) method. To improve the efficiency of this method, a fast pressure-correction method is used in order to enable the simulation to exploit a constant coefficient Poisson equation which can be solved with FFT-based technique. Extensive verification and validation were performed and perfect accuracy and agreement are obtained. In all the simulations performed in this work, the new Poisson solver showed a minimum speedup of 22 times. Accumulation of bubbles in the core region of the channel for all cases is observed, which forms a bubble-free layer in the near-wall region. The presence of bubbles resulted in considerable modification in the mean velocity profile compared to single-phase flow. Another common observation is that all the components of velocity fluctuations in the near-wall region decrease with increasing void fraction and decreasing wall layer thickness. The opposite happens in the core region, where the presence of bubbles favours turbulence. With respect to the bubble size, the wall-normal and spanwise velocity fluctuations decrease in the near-wall region for smaller bubbles, however, the streamwise velocity fluctuations remained almost unaffected. The investigation of turbulent kinetic budgets shows that, unlike single-phase flow, the dissipation terms rises to large values in the core region of the channel. This behaviour is referred to the presence of bubbles and hence enhancement of turbulent kinetic energy in the core region.

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In a conventional continuous annealing line, the energy supplied to steel strip during heating is not recovered while cooling it. Therefore, an alternative heat transfer technology for energy efficient continuous annealing of steel was developed. This technology enables reusing the heat extracted during cooling of the strip in the heating part of the process. This is achieved by thermally linking the cooling strip to the heating strip via multiple rotating heat pipes. In this context, the dynamic simulation of a full heat pipe assisted annealing line is performed. The dynamic simulation consists of the interaction of computational building blocks, each comprising of a rotating heat pipe and strip parts wrapped around the heat pipe. The simulations are run for different installation configurations and operational settings, with the heat pipe number varying between 50 and 100 and with varying strip line speed and dimensions. The heat pipes are sized to be 0.5 m in diameter and 3 m in length. The simulation results show that the equipment is capable of satisfying the thermal cycle requirements of annealing both at steady-state and during transition between steady-states following changes in boundary conditions. With this concept, energy savings of up to 70% are feasible.

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Flow and heat transfer of merging and bouncing droplets are studied for different Weber and Reynolds numbers and eccentricities of droplets by means of direct numerical simulation. Droplets are allowed to deform under the hydrodynamic forces of the surrounding flow. A coupled level-set and volume of fluid (CLSVOF) method is used to capture the highly deformable topology of the droplets. The method is coupled with a fast pressure solver, developed by Dodd and Ferrante, 2014, in order to circumvent the expensive iterative solvers commonly used. The temperature distribution inside the droplet and its consequent effect on the Nusselt number is studied. The results show that the Reynolds number and the initial configuration of droplets is of more important than the effect of the surface tension which governs the extent of deformations.

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Fuel efficiency improvement and harmful emission reduction are the paramount driving forces for development of gas turbine combustors. Lean-burn combustors can accomplish these goals, but require specific flow topologies to overcome their sensitivity to combustion instabilities. Large Eddy Simulations (LES) can accurately capture these complex and intrinsically unsteady flow fields, but estimating the appropriate numerical resolution and subgrid model(s) still remain challenges. This paper discusses the prediction of non-reacting flow fields in the DLR gas turbine model combustor using LES. Several important features of modern gas turbine combustors are present in this model combustor: multiple air swirlers and recirculation zones for flame stabilisation. Good overall agreement is obtained between LES outcomes and experimental results, both in terms of time-averaged and temporal RMS values. Findings of this study include a strong dependence of the opening angle of the swirling jet inside the combustion chamber on the subgrid viscosity, which acts mainly through the air mass flow split between the two swirlers in the DLR model combustor. This paper illustrates the ability of LES to obtain accurate flow field predictions in complex gas turbine combustors making use of open-source software and computational resources available to industry.

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Rotating wickless and stationary capillary cylindrical heat pipes are widely used heat transfer devices. Transient behavior of such heat pipes has been investigated numerically with computational fluid dynamics and lumped parameter models. In this paper, the advantages of both methods are combined into a novel engineering model that is low in computational cost but still accurate and rich in the details it provides. The model describes the interior dynamics of the heat pipe with a 2D representation of a cylindrical heat pipe. Liquid and vapor volumes are coarsely meshed in the axial direction. The cells are allowed to change in size in the radial direction during simulation. This allows for tracking the liquid/vapor interface without having to implement fine meshing. The model includes the equations for mass, momentum and energy and is applicable to both rotating and stationary heat pipes. The predictions of the model are validated with other experimental, numerical, and analytical works having an average deviation of less than 4%. The effects of various parameters on the system are explored. The presented model is suitable for the simulation of heat pipe systems in which both the level of detail and the computational cost are crucial factors.

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A new concept for energy efficient annealing of steel strip comprises of multiple rotating heat pipes. Each heat pipe extracts heat from the cooling strip which is reused to increase the temperature of the heating strip. In this context, the heat transfer between the steel strip and the rotating heat pipe is investigated. When the strip is transported over the heat pipe, gas entrains in the gap. The gas compresses into a uniform gas layer. The contact heat transfer deteriorates due to this phenomenon. A numerical model to quantify the heat transfer between the surfaces is developed. Since there is no direct way to quantify the heat transfer between two moving surfaces, the problem is divided into a gas entrainment and a heat transfer part. The model is validated with experiments executed on a rotating heat pipe test rig. The validation was made varying the strip thickness, specific tension and strip velocity. The results show a uniform gas layer forming within the first 1° of the 180° wrap angle in all cases. The heat transfer is dominated by gas conduction. Results for the uniform gas layer region yield heat transfer coefficients in the range between 4000 and 20,000 W/m2·K.@en

We investigate the effectiveness of the semi-local Reynolds number Re τ to parametrize wall-bounded flows with strong density, ρ, and viscosity, µ, gradients. Several cases are considered, namely, volumetrically heated low-Mach-number turbulent channel flows, a simultaneously heated and cooled flow with CO2 at supercritical pressure, and heated and cooled supersonic boundary layer flows. The mean density and viscosity in some of these cases vary up to a factor of nine and six, respectively. We show that, even for such high gradients in mean properties, the velocity transformation based on the semi-local Reynolds number is able to collapse the mean streamwise velocity profiles. We further-more provide evidence that the turbulent kinetic energy and streamwise vorticity budget equations are also governed by the semi-local Reynolds number. For cases with strong property variations, additional mechanisms appear that are caused by individual density (e.g., baroclinicity) or viscosity gradients. However, in the cases investigated herein, these additional mechanisms are small. The insights gained are used to improve a wall model, which is then tested in a wall-modeled large-eddy simulation (LES) of a compressible channel flow with isothermal walls.@en

Heat transfer to fluids at supercritical pressure is different from heat transfer at lower pressures due to strong variations of the thermophysical properties with the temperature. We present and analyze results of direct numerical simulations of heat transfer to turbulent CO2 at 8 MPa in an annulus. Periodic streamwise conditions are imposed so that mean streamwise acceleration due to variations in the density does not occur. The inner wall of the annulus is kept at a temperature of 323 K, while the outer wall is kept at a temperature of 303 K. The pseudocritical temperature Tpc=307.7 K, which is the temperature where the thermophysical properties vary the most, can be found close to the inner wall. This work is a continuation of an earlier study, in which turbulence attenuation due to the variable thermophysical properties of a fluid at supercritical pressure was studied. In the current work, the direct effects of variations in the specific heat capacity, thermal diffusivity, density, and the molecular Prandtl number on heat transfer are investigated using different techniques. Variations in the specific heat capacity cause significant differences between the mean nondimensionalized temperature and enthalpy profiles. Compared to the enthalpy fluctuations, temperature fluctuations are enhanced in regions with low specific heat capacity and diminished in regions with a large specific heat capacity. The thermal diffusivity causes local changes to the mean enthalpy gradient, which in turn affects molecular conduction of thermal energy. The turbulent heat flux is directly affected by the density, but it is also affected by the mean molecular Prandtl number and attenuated or enhanced turbulent motions. In general, enthalpy fluctuations are enhanced in regions with a large mean molecular Prandtl number, which enhances the turbulent heat flux. While analyzing the Nusselt numbers under different conditions it is found that heat transfer deterioration or enhancement can occur without streamwise acceleration or mixed convection conditions. Finally, through a combination of a relation between the Nusselt number and the radial heat fluxes, a quadrant analysis of the turbulent heat flux, and conditional averaging of the heat flux quadrants, it is shown that heat transfer from a heated surface depends on the density and the molecular Prandtl number of both hot fluid moving away from a heated surface as well as the thermophysical properties of relatively cold fluid moving towards it.@en

This work investigates fully developed turbulent flows of carbon-dioxide close to its vapour-liquid critical point in a channel with a hot and a cold wall. Two direct numerical simulations are performed at low Mach numbers, with the trans-critical transition near the channel centre and the cold wall, respectively. An additional simulation with constant transport properties is used to selectively investigate the effect of the non-linear equation of state on turbulence. Compared to the case where the pseudo-critical transition occurs in the channel center, the case with the pseudo-critical transition close to the cold wall reveals that compressibility effects can exist in the near-wall region even at low Mach numbers. An analysis of the velocity streaks near the hot and the cold walls also indicates a greater degree of streak coherence near the cold wall. A comparison between the constant and variable viscosity cases at the same Reynolds number, Mach number and having the same isothermal wall boundary conditions reveals that variable viscosity increases turbulence near the cold wall and also causes higher velocity gradients near the hot wall. We also show that the extended van Driest transformation results in a better agreement of the velocity profile with the log-law of the wall compared to the standard van Driest transformation. The semi-locally scaled turbulent velocity fluctuations and the turbulent kinetic energy budgets on the hot and the cold sides of the channel collapse on top of each other, thereby establishing the validity of Morkovin’s hypothesis.

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Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive relations for density ρ, viscosity μ, and thermal conductivity λ as a function of temperature are prescribed in order to characterize the turbulent scalar statistics. It is shown that the dominant effect caused by property variations on scalar statistics can be parameterized by two nondimensional parameters, namely the semilocal Reynolds number Re★τ≡Reτ√(¯ρ/ρw)/(¯¯μ/μw) (the bar and subscript w denote Reynolds averaging and wall value respectively, while Reτ is the friction Reynolds number based on wall values), and the local Prandtl number Pr★=Prw(¯¯μ/μw)/(¯λ/λw) (Prw is the molecular Prandtl number based on wall values). Near-wall gradients in Re★τ modulate the turbulent heat flux generation mechanism because of structural changes in turbulence. However, the influence of these modulations on the inner scaling of turbulent heat conductivity normalized by local mean viscosity is shown to be weak. Using this observation, a temperature transformation is derived that is invariant of Re★τ variations and only exhibits a Pr★-dependent shift.@en

The influence of near-wall density and viscosity gradients on near-wall turbulence in a channel is studied by means of direct numerical simulation of the low-Mach-number approximation of the Navier-Stokes equations. Different constitutive relations for density and viscosity as a function of temperature are used in order to mimic a wide range of fluid behaviours and to develop a generalised framework for studying turbulence modulations in variable-property flows. Instead of scaling the velocity solely based on local density, as done for the van Driest transformation, we derive an extension of the scaling that is based on gradients of the semilocal Reynolds number, defined as (the bar and subscript denote Reynolds averaging and wall value respectively, while is the friction Reynolds number based on wall values). This extension of the van Driest transformation is able to collapse velocity profiles for flows with near-wall property gradients as a function of the semilocal wall coordinate. However, flow quantities like mixing length, turbulence anisotropy and turbulent vorticity fluctuations do not show a universal scaling very close to the wall. This is attributed to turbulence modulations, which play a crucial role in the evolution of turbulent structures and turbulence energy transfer. We therefore investigate the characteristics of streamwise velocity streaks and quasistreamwise vortices and find that, similarly to turbulence statistics, the turbulent structures are also strongly governed by profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in show significant changes in inclination and tilting angles of quasistreamwise vortices. These structural changes are responsible for the observed modulation of the Reynolds stress generation mechanism and the inter-component energy transfer in flows with strong near-wall gradients.

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Heated or cooled fluids at supercritical pressure show large variations in thermophysical properties, such as the density, dynamic viscosity and molecular Prandtl number, which strongly influence turbulence characteristics. To investigate this, direct numerical simulations were performed of a turbulent flow at supercritical pressure (CO2 at 8 MPa) in an annulus with a hot inner wall and a cold outer wall. The pseudo-critical temperature lies close to the inner wall, which results in strong thermophysical property variations in that region. The turbulent shear stress and the turbulent intensities significantly decrease near the hot inner wall, but increase near the cold outer wall, which can be partially attributed to the mean dynamic viscosity and density stratification. This leads to decreased production of turbulent kinetic energy near the inner wall and vice versa near the outer wall. However, by analysing a transport equation for the coherent streak flank strength, it was found that thermophysical property fluctuations significantly affect streak evolution. Near the hot wall, thermal expansion and buoyancy tend to decrease streak coherence, while the viscosity gradient that exists across the streaks interacts with mean shear to act as either a source or a sink in the evolution equation for the coherent streak flank strength. The formation of streamwise vortices on the other hand is hindered by the torque that is the result of the kinetic energy and density gradients. Near the cold wall, the results are reversed, i.e. the coherent streak flank strength and the streamwise vortices are enhanced due to the variable density and dynamic viscosity. The results show that not only the mean stratification but also the large instantaneous thermophysical property variations that occur in heated or cooled fluids at supercritical pressure have a significant effect on turbulent structures that are responsible for the self-regeneration process in near-wall turbulence. Thus, instantaneous density and dynamic viscosity fluctuations are responsible for decreased (or increased) turbulent motions in heated (or cooled) fluids at supercritical pressure.@en

We use direct numerical simulations to study the effect of thermal boundary conditions on developing turbulent pipe flows with fluids at supercritical pressure. The Reynolds number based on pipe diameter and friction velocity at the inlet is Reτ0=360 and Prandtl number at the inlet is Pr0=3.19. The thermodynamic conditions are chosen such that the temperature range within the flow domain incorporates the pseudo-critical point where large variations in thermophysical properties occur. Two different thermal wall boundary conditions are studied: one that permits temperature fluctuations and one that does not allow temperature fluctuations at the wall (equivalent to cases where the thermal effusivity ratio approaches infinity and zero, respectively). Unlike for turbulent flows with constant thermophysical properties and Prandtl numbers above unity – where the effusivity ratio has a negligible influence on heat transfer – supercritical fluids shows a strong dependency on the effusivity ratio. We observe a reduction of 7 % in Nusselt number when the temperature fluctuations at the wall are suppressed. On the other hand, if temperature fluctuations are permitted, large property variations are induced that consequently cause an increase of wall-normal velocity fluctuations very close to the wall and thus an increased overall heat flux and skin friction.@en

Heated or cooled fluids at supercritical pressure show large variations in thermophysical properties, such as the density, dynamic viscosity and molecular Prandtl number, which strongly influence turbulence characteristics. To investigate this, direct numerical simulations were performed of a turbulent flow at supercritical pressure (CO2 at 8 MPa) in an annulus with a hot inner wall and a cold outer wall. The pseudo-critical temperature lies close to the inner wall, which results in strong thermophysical property variations in that region. We aim to obtain a better theoretical understanding of how the variable thermophysical properties attenuate both the flow field, as well as the heat transfer. Turbulence in the near wall cycle can be thought of as a cycle of events or coherent structures; near wall streaks (coherent low speed fluid regions) become unstable, which results in the formation of quasi streamwise vortices that in turn may create streaks. The disruption of a component of this cycle may lead to laminarization of the flow. First, we will present how the generation of streaks is affected by variable density effects (such as local thermal expansion and buoyancy) as well as variable viscosity effects. We will also present a similar analysis for the generation of streamwise vorticity. Secondly, we will focus on the effect of the (highly) variable molecular Prandtl number. The turbulent heat flux can be interpreted as the result of different turbulent events. The effectiveness of these turbulent events with respect to heat transfer is modulated due variations in the density, as well as the Prandtl number. We believe that the presented insights may be of use in developing better heat transfer prediction models for heated fluids at supercritical pressure.@en