Effects Of Density Ratio Research Articles

Heat Transfer in Internal Cooling Channels of Gas Turbine Blades: Buoyancy and Density Ratio Effects

The present work investigates the effects of buoyancy and wall heating condition on the thermal performance of a rotating two-pass square channel with smooth walls. The U-bend channel has a square cross section with a hydraulic diameter of 5.08 cm (2 in.). The lengths of the first and second passes are 514 mm and 460 mm, respectively. The turbulent flow entered the channel with Reynolds numbers of up to 34,000. The rotational speed varied from 0 to 600 rpm with rotational numbers up to 0.75. For this study, two approaches were considered for tracking the buoyancy effect on heat transfer. In the first case, the density ratio was set constant, and the rotational speed was varied. In the second case, the density ratio was changed in the stationary case, and the effect of density ratio was discussed. The range of buoyancy number along the channel is 0–6. The objective was to investigate the impact of buoyancy forces on a broader range of rotation number (0–0.75) and buoyancy number scales (0–6), and their combined effects on heat transfer coefficient for a channel with an aspect ratio of 1 : 1. Results showed that increasing the density ratio increased the heat transfer ratio in both stationary and rotational cases. Furthermore, in rotational cases, buoyancy force effects were very significant. Increasing the rotation number induced more buoyancy forces, which led to an enhancement in heat transfer. The buoyancy effect was more visible in the turning region than any other region.

Secondary breakup of drops at moderate Weber numbers: Effect of Density ratio and Reynolds number

Breakup of liquid drops occurs in several natural and industrial settings. Fully resolved volume of fluid based simulations presented in this study reveal the complete flow physics and droplet dynamics that lead to the breakup of a drop in the moderate Weber number regime. We have investigated the effects of density ratio and Reynolds number on the initial dynamics of drop deformation. A density ratio-Weber number phase plot is presented that indicates the variation in the deformation of the drop at various density ratios and Weber numbers. We show that the initial deformation and dynamics of the droplets at low density ratios is significantly different from that observed at high density ratios. We also study the temporal characteristics of the initial droplet deformation and motion.

An experimental investigation on streamwise distance and density ratio effects on double-jet film-cooling

In the present study, flow field and film-cooling effectiveness of several double-jet film-cooling geometries on a flat plate are measured. The streamwise distance varies as s/d = 3.0, 4.0, 5.0, and 6.0, while three spanwise distance conditions (p/d) are considered. The density ratio varies as DR = 1.0, 1.5, and 2.5. Both effects of the streamwise distance and the density ratio are focused. Results show, though the streamwise distance effect is not monotonic for all the cases, a general trend is witnessed when comparing with the baseline of s/d = 3.0. For p/d = 0, with an increased streamwise distance, the lateral coverage widens and the laterally averaged effectiveness rises. However, for p/d = 0.5 and 1.0, increasing the s/d may weaken the interaction between the two jets, and reduce the film coverage and effectiveness. With an increased density ratio, the jet momentum decreases, therefore better attachment and higher film-cooling effectiveness are obtained. However, in most cases, the range of lateral coverage is mainly dominated by the spanwise distance, rather than the streamwise distance or the density ratio. By comparing the area averaged effectiveness, an optimal DJFC configuration (among the geometries in this study) is identified for each operation condition.

Agglomeration of Li(NixMnyCoz)O2 particles in Couette–Taylor flow reactor

Couette–Taylor flow reactor is a mixing device that offers wide range of mixing regimes within a single reactor and operates in continuous flow mode. This reactor is recently used in manufacturing the cathode material of lithium ion batteries. Here, we simulate the agglomeration process of Li(NixMnyCoz)O2 particles using computational fluid dynamics. Quadrature method of moments is implemented for modeling of aggregation and breakage in Couette-Taylor flow reactor. We conduct an experiment of the preparation of Li(NixMnyCoz)O2 precursors, and the experimental data are compared with simulated results for the validation of numerical model. The predicted evolutions of mean particle size are well agreed with experimental data. For the practical application, we investigate the effects of density ratio of particle to fluid and initial volume fraction of particles on the particle size. The results show that the particle diameter increases with increasing of density ratio, but it decreases with increasing of initial volume fraction of particles. On the other hand, the particle sizes become similar at high rotational speed.

Relative Vibration of Suspended Particles With Respect to Microchannel Resonators and Its Effect on the Mass Measurement

In this work, the three-dimensional fluid–solid interaction vibration of particle in the oscillating resonator and its effect on the dynamic characteristics are analyzed and discussed. It demonstrates that the displacement of a particle is composed of two components, one is in phase with the acceleration of resonator and the other is out of phase. The former is responsible for the added mass effect and the latter results in a small damping. A modified measurement principle for detecting the buoyant mass is then presented by considering the in-phase component. The three-dimensional (3D) fluid–solid interaction problem involving the particle, fluid, and resonator is numerically solved, and the effects of density ratio, inverse Stokes number, and the ratio of channel height to particle diameter are studied. Based on the numerical results, a function characterizing the in-phase component is identified through a fitting procedure. According to the modified measurement principle and the analytical expression for the in-phase component, a calibration method is developed for measuring buoyant mass. Using this calibration method, the systematic measurement error induced by the vibration of particles can be effectively reduced.

Effect of density ratio on the dispersion of particles in a submerged liquid jet

A submerged jet is utilized to disperse buoyant particle in a cylindrical receiver. A discrete particle model (DPM) is used for an axisymmetric domain. An unsteady DPM model is used on a steady-state fluid fully developed condition. The primary fluid (a vertical submerged liquid water jet on a cylindrical water bath) jet flow is fully developed and calculated by complete solution of Navier–Stokes equation. The primary flow is validated and verified (published earlier), and then an unsteady DPM is used to investigate the dispersion of particles. For validation, experiments were performed using Doppler velocimetry (LDV) and these data were generated at the Centre for Multiphase Processes, the University of Newcastle. Few turbulence models ( $$k-\in $$ realizable, SST models) generated results were compared. Using the models, dispersion of particle was predicted as a function of particle-to-liquid density ratio. For the same particle-to-liquid density ratio, it was found that the dispersion behavior is similar.

Test cases for comparison of two interfacial solvers

We present novel test cases to study the effect of density ratio on free and forced capillary oscillations at an interface separating two immiscible, inviscid fluids. Using these tests, results obtained from two in-house developed, Volume of Fluid (VoF) based codes for solving the incompressible Euler equations with surface tension, are reported. The first solver (FSS: free surface solver) ignores the dynamics of the lighter phase solving only for the denser phase, explicitly accounting for free surface boundary conditions using the approach presented in Malan et al. (2015). The second is an interfacial solver which implements the one-fluid algorithm (OFS: one fluid solver) for simulating two-phase flows. We present four test cases involving inviscid, free and parametrically forced, capillary oscillations on Cartesian and circular base states. Explicit closed form analytical solutions in the linearised limit are presented for each case. It is found that for small value of the nonlinearity parameter (ϵ or ϵaz < 0.1) and with density ratio (ρr) ranging from 50−103, the FSS shows excellent agreement with linearised analytical predictions. For lower values of density ratio approaching ∼ 10 and below, the FSS results display substantial disagreement with those obtained from the OFS as well as with analytical predictions. At large density ratios ( ∼ 103) (and larger values of ϵ or ϵaz), the FSS shows better accuracy over longer times, when compared to the OFS, partly due to less numerical dissipation. The analytical results presented here add to the repository of test cases in the two-phase CFD literature and are expected to be useful for validating numerical models for surface tension. The comparison of the OFS with the FSS also provides useful rule-of-thumb estimates for choosing between speed (FSS) and accuracy (OFS) in numerical computations of capillary, interfacial flows.

Experimental and numerical study of the film cooling performance of the suction side of a turbine blade under the rotating condition

The film cooling performance of the suction side of a turbine blade is experimentally and numerically investigated under the rotating condition. Experiments were performed on a 1.0-stage turbine. In the experiments, the effects of density ratio (0.96 and 1.52) and blowing ratio (0.2–1.0) were studied. The rotational effects were studied by comparing results of three mainstream rotating Reynolds numbers (3528, 4410 and 5292). Three hole positions of 1/4, 1/2 and 3/4 of the total blade height were set on three blades to confirm the mainstream influence. The jets of the holes at 1/4 and 3/4 of the blade height deflect to the mid-span of the blades. The film protection at both hole positions is damaged by the mainstream vortices, resulting in a lower cooling effectiveness. Moreover, as proven by the flow field, the passage vortex influence can be strengthened by the rotation. Thus, as the rotating Reynolds number increases the film cooling performance worsens. An optimal blowing ratio, 0.6, for the mid-span hole film cooling exists. Different from the flat plate film cooling, the film deflection occurs in the blade film cooling and decreases as the blowing ratio. At last, the high density ratio can improve the film cooling performance.

Experimental investigation of the interaction between showerhead coolant jets and main flow

This paper presents the results of an experimental investigation into the thermal and aerodynamic behavior of coolant ejection at the leading edge of a highly loaded nozzle vane cascade. The leading-edge cooling scheme features four rows of cylindrical holes in a staggered configuration (showerhead). Pressure Sensitive Paints (PSP) technique was used to get the adiabatic film cooling effectiveness distribution, while Particle Image Velocimetry (PIV) and flow visualizations were used to investigate the mixing process taking place between coolant and main flow. Tests were run at low speed (Ma2is = 0.2) and low inlet turbulence intensity (Tu1 = 1.6%). PSP tests were conducted by using N2 (Density Ratio DR = 1.0) as coolant at variable blowing ratio (BR = 2.0–4.0). Further tests were run by using CO2 (DR = 1.5) at matching BR and momentum flux ratio (I) in order to investigate the effects of density ratio. The BR = 3.0 injection case was selected for the PIV investigation. Thermal and flow field data consistently show a shift in the position of stagnation line towards the suction side. Jet liftoff close to stagnation and a strong jet to jet as well as jet to mainstream interaction were also observed, resulting in a complex 3D flow characterized by high turbulence levels, with velocity fluctuations as high as 30% of the approaching velocity and with a high degree of anisotropy. No coherent structures were detected, supporting the random nature of mixing process.

Effect of Density Ratio on Film-Cooling Effectiveness Distribution and Its Uniformity for Several Hole Geometries on a Flat Plate

The film cooling effectiveness distribution and its uniformity downstream of a row of film cooling holes on a flat plate are investigated by pressure sensitive paint (PSP) under different density ratios. Several hole geometries are studied, including streamwise cylindrical holes, compound-angled cylindrical holes, streamwise fan-shape holes, compound-angled fan-shape holes, and double-jet film-cooling (DJFC) holes. All of them have an inclination angle (θ) of 35 deg. The compound angle (β) is 45 deg. The fan-shape holes have a 10 deg expansion in the spanwise direction. For a fair comparison, the pitch is kept as 4d for the cylindrical and the fan-shape holes, and 8d for the DJFC holes. The uniformity of effectiveness distribution is described by a new parameter (Lateral-Uniformity, LU) defined in this paper. The effects of density ratios (DR = 1.0, 1.5 and 2.5) on the film-cooling effectiveness and its uniformity are focused. Differences among geometries and effects of blowing ratios (M = 0.5, 1.0, 1.5, and 2.0) are also considered. The results show that at higher density ratios, the lateral spread of the discrete-hole geometries (i.e., the cylindrical and the fan-shape holes) is enhanced, while the DJFC holes is more advantageous in film-cooling effectiveness. Mostly, a higher lateral-uniformity is obtained at DR = 2.5 due to better coolant coverage and enhanced lateral spread, but the effects of the density ratio on the lateral-uniformity are not monotonic in some cases. Utilizing the compound angle configuration leads to an increased lateral-uniformity due to a stronger spanwise motion of the jet. Generally, with a higher blowing ratio, the lateral-uniformity of the discrete-hole geometries decreases due to narrower traces, while that of the DJFC holes increases due to a stronger spanwise movement.

Exergy and energy analysis of a biogas-fuelled micro-tubular flame fuel cell

In the present study, a combination of 60% CH4 and 40% CO2 was used as the fuel. The performance of the fuel cell was studied at three different equilibrium ratios of fuel to air entering the burner. The effects of current density and equivalence ratio were investigated on the fuel cell voltage, voltage drops, output power, methane molar flow rate, and efficiency. The results indicated that a maximum power of 0.724 W, 0.955 W, and 1.201 W was achieved for a single fuel cell at the equivalence ratios of 1.2, 1.3, and 1.4, respectively. Exergy efficiency was increased from 21.93% to 46.68% by reducing the current density from 1800 A/m2 to 100 A/m2 at the equivalence ratio of 1.4. The maximum efficiency and the minimum inlet methane molar flow rate were observed at the equivalence ratio of 1.4.

Turbine vane endwall film cooling from mid-chord or downstream rows and upstream coolant injection

Endwall film cooling investigations were carried out in a four-passage linear turbine vane cascade. The endwall film cooling is designed with two cooling-hole configurations: the mid-chord row and the downstream row. Two-row of staggered cylindrical holes in front of the vane leading edge is implemented for providing the upstream coolant injection. In this study, the injection angle of the upstream cooling hole and the endwall cooling hole are fixed at 30°. The mainstream Reynolds number at the cascade inlet is measured at 380,000 based on the vane axial chord length, and the corresponding cascade exit Ma number is 0.5. The turbulence intensity at the mainstream inlet is kept at 19% with an integral length scale of 1.7 cm. The mass flow rate of the coolant for upstream injection and the endwall injection are varying from MFR = 0, 0.5%, 1.0% to 1.5% respectively to optimize the coolant distribution. The coolant-to-mainstream density ratio effects are investigated by feeding three different coolants with DR = 1.0, 1.5 and 2.0. The film cooling effectiveness on the endwall is determined by using the PSP measurement technique. Results will provide useful information about the endwall cooling design with the mid-chord row and downstream row, especially on how to distribute the coolant consumption from the upstream or the endwall locations, which efficiently saves the coolant.

Velocimetry during depressurized conduction cooldown events in the HTTF

Abstract The High Temperature Test Facility (HTTF) is a quarter-scale integral-effect facility designed to study pressurized and depressurized conduction cooldowns (PCC and DCC, respectively) in high temperature, gas-cooled reactors (HTGR). This study focuses on DCC and aims to characterize the gas exchange between the reactor core and the reactor cavity to assess the risk for air ingress and subsequent potential for natural circulation core cooldowns. High-resolution velocity profile measurements are performed at the coolant pipe break location over a long time-scale using molecular tagging velocimetry. This non-intrusive, laser-based technique is applied for the first time in the field of nuclear thermal hydraulics, providing new insights for understanding the underlying phenomena at play during a DCC event. Such data are also valuable for validation of numerical simulations such as Reactor Excursion and Leak Analysis Program (RELAP). Results are reported here for various gas mixtures of helium (the coolant) and nitrogen (surrogate for air) to study the effect of density ratio. The short transient (30 s) lock-exchange phase is well captured with helium flow velocity between 0.8 and 2 m/s. The flow is shown to persist over much longer time-scales (hours) at a velocity of about 0.2 m/s, a likely consequence of gas mixing in the hot leg and in the lower plenum of the reactor. Flow visualization at the exit of the hot leg shows shear instabilities, which supports the hypothesis of significant mixing.

Characterization of flow mixing and structural topology in supersonic planar mixing layer

The investigations on mixing process and structural topology properties of supersonic planar mixing layer with different inflow conditions are conducted by employing direct numerical simulation. First, the present high-order accuracy numerical methods are validated by comparing the simulation results with the data gained from previous well characterized experimental and numerical cases. Then the high-resolved three-dimensional numerical visualizations of supersonic mixing layer are presented by utilizing Q-criterion. The visualization results show the full development and evolution process of mixing layer, including the shear action, the transition process populated sequentially by Λ-vortices, hairpin vortices and braid structures and the establishment of self-similar turbulence. The effects of density ratio, velocity ratio and convective Mach number between the two parallel streams on mixing layer growth rate are evaluated by examining the indexes including velocity thickness and momentum thickness represented the mixing process. The results indicate that for the only variation of density ratio, the velocity thickness growth rates do not significantly vary, while the momentum thickness becomes larger when the upper and lower streams possess the same density. With the increase of only velocity ratio, the mixing layer becomes more stable and the velocity and momentum thickness are both drastically depressed in the whole flow field. As only convective Mach number increases, the mixing layer growth is inhibited in the near field through the transition delay of the flow, while in the far field, the growth rates are nearly the same for different convective Mach numbers. The spatial correlation analysis of structural topology indicates that the effects of each of the three main flow parameters on vortex topology lead to different mean structure sizes and shapes. The present research is useful for evaluating the effects of different flow parameters on mixing properties, which is important for the future scramjet combustor design and evaluation in engineering.

Effect of density ratio on velocity fluctuations in dispersed multiphase flow from simulations of finite-size particles

Velocity fluctuations in the carrier phase and dispersed phase of a dispersed multiphase flow are studied using particle-resolved direct numerical simulation. The simulations correspond to a statistically homogeneous problem with an imposed mean pressure gradient and are presented for $${Re}_{m}=20$$ and a wide range of dispersed phase volume fractions $$\left( 0.1 \le \phi \le 0.4 \right) $$ and density ratios of the dispersed phase to the carrier phase $$\left( 0.001 \le \rho _\mathrm{p}/\rho _\mathrm{f} \le 1000 \right) $$ . The velocity fluctuations in the fluid and dispersed phase at the statistically stationary state are quantified by the turbulent kinetic energy (TKE) and granular temperature, respectively. It is found that the granular temperature increases with a decrease in the density ratio and then reaches an asymptotic value. The qualitative trend of the behavior is explained by the added mass effect, but the value of the coefficient that yields quantitative agreement is non-physical. It is also shown that the TKE has a similar dependence on the density ratio for all volume fractions studied here other than $$\phi =0.1$$ . The anomalous behavior for $$\phi =0.1$$ is hypothesized to arise from the interaction of particle wakes at higher volume fractions. The study of mixture kinetic energy for different cases indicates that low-density ratio cases are less efficient in extracting energy from mean flow to fluctuations.

Overlimiting current due to electro-diffusive amplification of the second Wien effect at a cation-anion bipolar membrane junction.

Numerical simulations are presented for the transient and steady-state response of a model electrodiffusive cell with a bipolar ion-selective membrane under electric current. The model uses a continuum Poisson-Nernst-Planck theory including source terms to account for the catalytic second Wien effect between ionogenic groups in the membranes and resolves the Debye layers at interfaces. The resulting electric field at the membrane junction is increased by as much as four orders of magnitude in comparison to the field external to the membrane. This leads to a significant amplification of the second Wien effect, creating an increased ionic flux due to the catalytic decomposition of water. The effect also induces an exaltation effect wherein the salt ion flux undergoes a concomitant increase as well. The interplay of effects results in a unique over-limiting current mechanism due to concentration polarization internal, rather than external, to the membranes. In addition to the case of two equal but oppositely charged membranes under the standard simplifying assumption of equal ionic diffusivities, two variations on this model are studied. Asymmetric diffusivities, representative of the actual mobility difference in dissociated water ions, and the effect of the membrane charge density ratio were also considered. The latter elucidates an overlimiting current shift mechanism for DNA adsorption on anion-selective membranes proposed by Slouka et al. [Langmuir 29, 8275 (2013)]. The former provides more realistic picture of multi-ion transport and demonstrates a surprising steady-state effect due to the asymmetry in the diffusivity of hydroxide and hydronium.

Impact of the dogleg geometry on displacement efficiency during cementing; an integrated modelling approach

In the dogleg section of directional wells, casing strings bend to fit the borehole trajectory, which may lead to complicated contact areas with the borehole. The severity of dogleg in combination with casing properties may make the formed annulus space so complex that cement may not displace mud remnants very well. While current simulation methods only consider constant eccentricity, we propose a model for a more general geometry defined by the well trajectory and casing properties. We have developed a three-dimensional finite element model (FEM) to simulate large-deformations of the casing while running into the dogleg. The casing deformation determines the annulus geometry that is supposed to be filled with cements. We utilized a computational fluid dynamics (CFD) model to simulate cement-mud displacement in the resultant annulus space. The effects of density ratio and rheology on the displacement efficiency are analyzed here. The obtained numerical results show the complicated contact geometry of the casing and borehole at the dogleg, which may worsen in casing strings with small thickness and large curvature doglegs. Results show that the magnitude of the stress developed along the casing can considerably increase due to friction. Complicated geometry of the annulus induced by casing deformation makes mud displacement by cement in the dogleg difficult. Continuous drilling mud pockets are formed due to the cement reverse flow. However, increasing density difference helps development of a steady and shorter displacement interface. We also noticed the phenomenon of reverse flow occurred during the cementing, which prevents sweeping or perfect displacement of the cement in the annulus space. The outcome will help us to prevent any potential damage that might happen due to large pressure fluctuations during fracturing through casing by minimum costs and avoid such potential integrity problems by setting a packer and tubing or using more appropriate cement recipes.

Lattice Boltzmann Simulation of Fluid Flow Characteristics in a Rock Micro-Fracture Based on the Pseudo-Potential Model

Slip boundary has an important influence on fluid flow, which is non-negligible in rock micro-fractures. In this paper, an improved pseudo-potential multi-relaxation-time (MRT) lattice Boltzmann method (LBM), which can achieve a large density ratio, is introduced to simulate the fluid flow in a micro-fracture. The model is tested to satisfy thermodynamic consistency and simulate Poiseuille flow in the case of large liquid-gas density ratio. The slip length is used as an index for evaluating the flow characteristics, and the effects of wall wettability, micro-fracture width, driving pressure and liquid-gas density ratio on the slip length are discussed. The results demonstrate that the slip length increases significantly with the increase of the wall contact angle in rock micro-fracture. And the liquid-gas density ratio has an important impact on the slip length, especially for the hydrophobic wall. Moreover, under the laminar flow regime the driving pressure and the micro-fracture width has little effect on the slip length.

Two-phase SPH simulation of vertical water entry of a two-dimensional structure

In view of the fact that the SPH model is easy to handle the flows with the free surface of large deformation, a 2-D flow induced by vertical water entry of a 2-D structure is simulated using the two-phase SPH model. The local pressure of the boundary particles is obtained by pressure of the fluid particles nearby through a modified kernel approximation. To evaluate the accuracy of the method, water entry of a 2-D symmetric wedge with fixed separation point of the free surface on the wedge surface is simulated. The pressure distribution of the wedge at the initial stage agrees well with the analytical results available. Evolution of the free surface and the air flow in the cavity induced by the water entry are obtained. A higher speed air jet is found at the neck of the cavity when the neck of the cavity becomes smaller. For the case of a horizontal cylinder entering the water with an unknown separation point of flow on the model surface, the early stage of the water entry is simulated for the rigid body with different density. Evolution of the free surface deformation of the half-buoyant cylinder and neutrally buoyant cylinder water entry is compared with the experimental data. The effects of the density ratio and Froude number on the pinch-off of the cavity are discussed. It is found that the pinch-off time remains almost constant for different density ratio and Froude number. Meanwhile, for a given Froude number, the dimensionless pinch-off depth and the location of the cylinder at the time of pinch-off increase with the density ratio. Further, for a given density ratio, these two parameters increase with the Froude number and, however, the relative cavity shape appears to be a self-similar shape when Fr ≥ 8.35.

Thin double-layer film development over a flat stretching sheet

Development of thin double-layer film over a stretching sheet is studied. Similarity variables have been applied to transform the guiding Navier–Stokes equations into a set of coupled unsteady nonlinear partial differential equations. These equations along with moving boundary conditions are solved using the asymptotic method. We have presented analytically obtained long time solution for smaller values of Reynolds number. For small and moderate values of Reynolds number, guiding equations were solved using the finite difference method. Effects of density ratio, viscosity ratio, thickness ratio and Reynolds number are analyzed.