Mixing Planes Research Articles

基于固液两相流的有机肥固液混合施肥装置分析与设计

Organic fertilizer applicator currently has poor versatility toward different properties. A solid-liquid mixed fertilizer device is designed based on the numerical simulation method of solid-liquid two-phase flow. Based on the parameters analysis and viscosity measurement of different organic fertilizer particles, the ribbon-screw type agitator was selected as the basic structure. Using Box-Behnken, three test factors including agitator speed, the mixture ratio of fertilizer and water, agitator height were determined, the agitator was optimized with the test evaluation indexes, the density variation coefficient, and agitator shaft power on 10 mixing planes in the agitator. The result showed that the rotating speed was 80 r/min, the mixing ratio of fertilizer and water was 1.2, and the agitator height was 700 mm, the working parameter combination is optimal. A coarse particle solid-liquid two-phase flow model of the fertilizer discharge pump was established, to obtain the external characteristic curve of the fertilizer pump and analyse the influence of different mixing ratios of fertilizer and rotation speed on the fertilizer pump. In order to prevent the separation of fertilizer and water and achieve better effect, 1140 r/min was comprehensively determined as the working speed of the fertilizer pump. The strength of the agitator meets the working requirements. The solid-liquid deep fertilizer device text bench for organic fertilizer was set up under the optimal working parameters, the result shows that the research results can provide a reference for the design of organic fertilizer solid-liquid mixing fertilizer applicator.

Progresses in Particle-Laden Flows Simulations in Multistage Turbomachinery With OpenFOAM

Abstract Numerical simulations of particle-laden flows have received growing attention in the last decade, due to the broad spectrum of industrial applications in which discrete phases prediction is of interest. Among these, ingestion of particles by turbomachinery is an area that is seeing vivid research and studies. The most common technique to tackle this kind of problem is the Eulerian–Lagrangian method, in which individual particles are tracked inside the domain. At the same time, in multistage turbomachinery simulation interfaces are needed to couple the flow solution in adjacent domains in relative motion. In this work, an open-source extension for Lagrangian simulations in multistage rotating machines is presented in the foam-extend environment. First, a thorough discussion of the implementation is presented, with particular emphasis on particle passage through general grid interfaces (GGI) and mixing planes. Moreover, a mass-conservative particle redistribution technique is described, as such a property is requested at interfaces between multiple reference frame (MRF). The peculiarities of the algorithm are then shown in a relevant test case. Eventually, three turbomachinery applications are presented, with growing complexity, to show the capabilities of the numerical code in real-life applications. Simulation results in terms of erosion and impacts on aerodynamic surfaces are also presented as examples of possible parameters of interest in particle-laden flow computations.

A new Bayesian approach toward improved regression of low-count U[sbnd]Pb geochronology data generated by LA-ICPMS

UPb dating of hydrogenic and fossil material can be a significant challenge because samples often contain low U levels and variable amounts of non-radiogenic Pb. Line scans using LA-ICPMS provide the widest range of ratios available for defining the radiogenic to common Pb mixing line, hence the best age estimate, but extracting this information requires processing many low-count data. Conventional least-squares regression of ratios based on such data can give inconsistent results. A new approach is introduced where data are regressed as count rates in a 3D space rather than ratios on a 2D plot. This is a maximum likelihood approach in that mixing planes covering a range of ages and common 207Pb/206Pb ratios (PbC) are compared to the data set and used to determine a relative probability density surface whose maximum should fix the best-fit age and common 207Pb/206Pb ratio. 95% confidence errors are determined from T and PbC values that cut off 2.5% of the area to the left and right of 2D plots generated by integration of the 3D plot over PbC and age, respectively. Results from a rugose coral fossil show that this approach gives age results similar to regressions of concordia data and more accurate than Tera-Wasserburg regressions on data from natural samples. Tests on randomly generated synthetic data do not show significant discrepancy between Isoplot ages but they do between values of PbC. The 3D approach is the only one that gives accurate results for both age and PbC.

A discrete adjoint method for pressure-based algorithms

A discrete adjoint method implemented in a coupled pressure-based RANS solver is presented in this paper. The adjoint equations are solved using an adjoint fixed point iteration that inherits the convergence properties of the primal solver. Automatic differentiation is used extensively for the construction of the adjoint fixed point iteration. The concept of Krylov subspace methods was adopted to stabilize the solution procedure. A common linearization technique in collocated pressure-based algorithms is the introduction of a mass flux variable on the cell faces which is kept constant during the inner iterations. This variable is treated as an independent adjoint variable in related publications. We propose a new method that allows to treat the mass fluxes implicitly in order to take full advantage of the preconditioner of the primal solver. The adjoint solver is general and is not restricted by the commonly used frozen turbulence approximation. It can deal with any turbulence model that is supported by the flow solver as well as any boundary condition. This includes mixing planes and mesh interfaces needed for multi stage turbo machinery simulations. Furthermore, there is no restriction on the choice of objective function. The sensitivities of the adjoint solver have been validated with sensitivities obtained with finite differences.An entirely surface based interpolation method based on radial basis functions (RBF) was developed to deform the surface mesh. We propose the use of discrete geodesics instead of the classical Euclidean distance as the distance measure for the RBF interpolation. As an alternative, a direct deformation method with adjoint consistent smoothing is also described and used in the presented optimization cases.The developed adjoint solver and deformation routines were used to optimize a turbulent bend with different Reynolds numbers as well as the the rotor blade of an axial turbine.

Application of a General Discrete Adjoint Method for Draft Tube Optimization

Automatic optimization is becoming increasingly important in turbomachinery design to improve the performance of machine components and Evolutionary Algorithms (EAs) play a very important role in this task. The main drawback of EAs is the large number of evaluations that are required to obtain an “optimal” result. Consequently, in order to keep the computational time in an affordable frame for design purposes, either the mesh size has to be limited, thus reducing the resolution of the flow phenomena, or the number of free parameters must be kept small. Adjoint optimization does not suffer from these restrictions, i.e. the optimization time is not affected by the number of parameters. The computational effort for the adjoint method scales only with the grid size and is usually in the range of two times the CFD simulation alone. In this paper, a discrete adjoint method based on a coupled pressure based RANS solver is presented and applied to draft tube optimization. The adjoint solver is general and can therefore deal with any turbulence model supported by the CFD solver as well as any boundary condition, including mixing planes and mesh interfaces needed for multi-stage simulations. Furthermore, there is no restriction on the choice of objective function. The adjoint method is first applied to a baseline draft tube geometry and then again to its EA optimized geometry where the objective function was the minimization of losses in the draft tube. To reduce the complexity for this proof of concept but still including multiple operating points in the optimization, only peak efficiency and full-load were optimized simultaneously. The adjoint optimization can significantly improve the draft tube performance in both cases (baseline and EA optimization). The interplay between local and global optimization seems to be a promising strategy to find optimal geometries for multi-operating point/multi-objective optimization and will be further investigated in subsequent research.

A Multifidelity Aero-Thermal Design Approach for Secondary Air Systems

Abstract The paper presents a multidisciplinary approach for aero-thermal and heat transfer analysis for internal flows. The versatility and potential benefit offered by the approach are described through the application to a realistic low pressure turbine assembly. The computational method is based on a run time code-coupling architecture that allows mixed models and simulations to be integrated together for the prediction of the subsystem aero-thermal performance. In this specific application, the model is consisting of two rotor blades, the embedded vanes, the interstage cavity, and the solid parts. The geometry represents a real engine situation. The key element of the approach is the use of a fully modular coupling strategy that aims to combine (1) flexibility for design needs, (2) variable level of modeling for better accuracy, and (3) in memory code coupling for preserving computational efficiency in large system and subsystem simulations. For this particular example, Reynolds averaged Navier–Stokes (RANS) equations are solved for the fluid regions and thermal coupling is enforced with the metal (conjugate heat transfer, CHT). Fluid–fluid interfaces use mixing planes between the rotating parts while overlapping regions are exploited to link the cavity flow to the main annulus flow as well as in the cavity itself for mapping of the metal parts and leakages. Metal temperatures predicted by the simulation are compared to those retrieved from a thermal model of the engine, and the results are discussed with reference to the underlying flow physics.

Simulation of Multistage Compressor at Off-Design Conditions

Computational fluid dynamics (CFD) has been widely used for compressor design, yet the prediction of performance and stage matching for multistage, high-speed machines remains challenging. This paper presents the authors' effort to improve the reliability of CFD in multistage compressor simulations. The endwall features (e.g., blade filet and shape of the platform edge) are meshed with minimal approximations. Turbulence models with linear and nonlinear eddy viscosity models are assessed. The nonlinear eddy viscosity model predicts a higher production of turbulent kinetic energy in the passages, especially close to the endwall region. This results in a more accurate prediction of the choked mass flow and the shape of total pressure profiles close to the hub. The nonlinear viscosity model generally shows an improvement on its linear counterparts based on the comparisons with the rig data. For geometrical details, truncated filet leads to thicker boundary layer on the filet and reduced mass flow and efficiency. Shroud cavities are found to be essential to predict the right blockage and the flow details close to the hub. At the part speed, the computations without the shroud cavities fail to predict the major flow features in the passage, and this leads to inaccurate predictions of mass flow and shapes of the compressor characteristic. The paper demonstrates that an accurate representation of the endwall geometry and an effective turbulence model, together with a good quality and sufficiently refined grid, result in a credible prediction of compressor matching and performance with steady-state mixing planes.

Filtering Mixing Planes for Low Reduced Frequency Analysis of Turbomachines

A class of problems in turbomachinery is characterized by unsteady interactions at low reduced frequencies. These interactions are often the result of perturbations with length-scale on the order of the machine circumference and examples include axial compressors operating with inlet distortion, fans with downstream pylons, and turbine rotors downstream of midframe struts. Typically, this unsteadiness is accompanied by higher frequency fluctuations caused by perturbations with a length-scale on the order of a blade pitch. Conventional numerical analysis of this class of problem requires computations with a time step governed by the high-frequency content but a greatly reduced run time could be achieved if the time step was dictated solely by the low reduced frequency, long length-scale, interaction of interest. In this paper, a filtering mixing plane technique is proposed that removes unwanted short length-scale perturbations at the interfaces between blade rows. This approach gives the user control over the amount of mixing that occurs at these interfaces with the limits being fully mixed-out to pitchwise uniformity (conventional mixing plane) or no mixing (conventional sliding plane). By choosing to retain only enough harmonics to resolve the low reduced frequency interaction of interest, an order of magnitude reduction in run time can be achieved.

Unsteady Half-Annulus Computational Fluid Dynamics Calculations of Thermal Migration Through a Cooled 2.5 Stage High-Pressure Turbine

This paper presents an industrial perspective on the potential use of multiple-airfoil row unsteady computational fluid dynamics (CFD) calculations in high-pressure turbine design cycles. A sliding-mesh unsteady CFD simulation is performed for a high-pressure turbine section of a modern aviation engine at conditions representative of engine take-off. The turbine consists of two stages plus a center-frame strut upstream of the low-pressure turbine. The airfoil counts per row are such that a half-annulus model domain must be simulated for periodicity. The total model domain size is 170 MM computational grid points and the solution requires approximately nine days of clock time on 6288 processing cores of a Cray XE6 supercomputer. Airfoil and endwall cooling flows are modeled via source term additions to the flow. The endwall flowpath cavities and their purge/leakage flows are resolved in the computational meshes to an extent. The time-averaged temperature profile solution is compared with static rake data taken in engine tests. The unsteady solution shows a considerable improvement in agreement with the rake data, compared with a steady-state solution using circumferential mixing planes. Passage-to-passage variations in the gas temperature prediction are present in the 2nd stage, due to nonperiodic alignment between the nozzle vanes and rotor blades. These passage-to-passage differences are quantified and contrasted.

Unsteady Effects in Axial Compressors: A Multistage Simulation

This work presents a numerical simulation of a four-stage axial compressor with cantilevered stators and repeating stages. Two simulations have been accomplished, namely, unsteady with sliding plane and steady with mixing plane, over a wide range of operating conditions. The solver is an unsteady Reynolds-averaged Navier–Stokes code with the Spalart–Allmaras turbulent model. It has been found that the greatest effect of unsteadiness is near the end walls. The stall point for the unsteady simulation is 40% closer to the experimental data when compared with the steady one with mixing planes. This is due to the recovery and segregation of the rotor tip vortex near the casing, which has a stabilizing effect in terms of stall limit. The unsteady simulation is able to reproduce total pressure loss experimentally observed near the hub at the stator exit but not found in the steady simulation. A previous experimental campaign suggested this loss was generated by the wakes of upstream inlet guide vanes propagating through the machine. However, this work found that it is generated by the migration of hub leakage flow induced by the incoming rotor wakes. The unsteady simulation shows higher performance at midspan. This has been found to be related to the rotor wake rectification with a 70% inviscid recovery of wake.

Multistage three-dimensional Navier-Stokes computation of off-design operation of a four-stage turbine

In this paper a three-dimensional computational methodology for multistage turbomachinery flows is developed, validated and applied in analysing the reduced mass flowrate operation of a four-stage turbine. The flow is modelled by the three-dimensional Favre-Reynolds-averaged Navier-Stokes equations using the Launder-Sharma near-wall k-ɛ turbulence closure, which are integrated using an implicit third-order upwind solver. The computation models the eight blade rows, including the tip clearance gaps of the rotors, using a 6 × 106 points grid, and computes the time-averaged flow using mixing planes between rows. Computational results are compared with measurements for various operating points. After this validation the method is used in a first attempt to analyse the three-dimensional flow at reduced-mass-flow operation.

Numerical calculation of torque converter flow using interrow mixing model

In this study, a steady three-dimensional incompressible turbulent flow within a torque converter was numerically analyzed with the introduction of interrow mixing model. Mixing planes were introduced to exchange the flow informations between two adjacent elements of the torque converter. The mixing planes were installed among three elements of the torque converter. Therefore, in the present method, it could be possible to calculate the flow-filed within the torque converter without any assumption of circulating flow rates or any extension of boundaries toward the upstream and the downstream for each element. The numerically calculated performances of the torque converter were in good agreement with experimental results, and the complex flow patterns were be observed according to design and off-design condition. As a conclusion, it was found that the present numerical method was very effective in the steady flow analysis of torque converters.

Helium and Argon in Ore Fluids: So What?

The isotopic composition of He and Ar trapped in crustal fluids and fluid inclusions carries a signature of the source of the fluids and the processes which have affected them. There are three distinct sources of the noble gases; atmosphere, crust and mantle. Atmospheric gases carried in groundwaters are characterised by the presence of 36Ar and 4~ and minor amounts of helium (3He/4He = 1.39 x 10 _6 = Ra). The crust is a source of radiogenic 4~ and 4He, very low levels of3He (-0.01-0.05 Ra) and no 36Ar. The prime signature of the mantle is helium with a high 3He content (e.g. 3He/4HeMoRB ~ 8 Ra), together with 4~ and, in most situations, negligible 36Ar (4~ ~ 40,000). Fluids trapped in ore minerals frequently carry all three components (Stuart et al., 1995). We have investigated He and Ar isotopes, sometimes in combination with halogens, trapped in ore fluids from a variety of areas and types of mineralisation. Our aims have been to see what qualitative aspects of the mineralisation processes are reflected in noble gas patterns and to what extent these can be used to resolve conflicting interpretations, what aspects can be understood in a quantitative way, and whether these can be used, for example, to model the large scale features of specific ore deposits. In this report we contrast the He and Ar isotope observations from two widely separated porphyry-Cu deposits (PCD) with those from an MVT deposit. The Machangqing PCD deposit in West Yunnan province, China, is part of the Ailaoshan-Jinshajiang alkali-porphyry intrusive zone of Eocene age formed in an extensional setting. The mantle derived magmas intrude lower Ordovician microelastic rocks and Devonian limestone and appear to have assimilated some crustal material. The Sungun PCD is located in NW Iran and is associated with a series of calc-alkaline hypabyssal igneous intrusions of Oligo-Miocene age. The magma was emplaced in a continental margin tectonic setting related to the subduction and assimilation of the Persian plate during the major Alpine orogenic phase. The Sungun porphyries occur as stocks and dykes intruding a series of Oligocene dacitic breccias, tufts and trachyandesitic lavas, Eocene arenaceous-argiUaceous rocks, and UpperCretaceous limestones. The He and Ar compositions of gases released by crushing sulphides from the two deposits are shown in Figs. 1 and 2. 4~ is the only isotope present in high abundance in all components and consequently this is the only method of representing all the data, end members and processes in a single figure. Mixtures of three end members define a mixing plane, while elemental fractionation of He and Ar drive compositions radially from, and perpendicular to, the ASW axis. In both figures the data lie on 3component mixing planes. The three end members are fluids enriched respectively in atmosphere (ASW), mantle helium and argon ( label led EARLY) and crustal helium (labelled LATE). The 3He/4He ratios, 1.2 Ra (Machangqing) and 2.25 Ra

Numerical Flow Analysis of Torque Converter Using Interrow Mixing Model.

In this study, a steady, three-dimensional incompressible turbulent flow within a torque converter was numerically analyzed by introducing an interrow mixing model. Mixing planes were introduced to exchange the flow information between two adjacent elements of a torque converter. By installing the mixing planes among the three elements of a torque converter, the flow field within the torque converter could be calculated without any assumptions concerning circulating flow rates or any upstream and / or downstream extension of boundaries for each element. The numerically calculated performances of the torque converter were in good agreement with the experimental results, and the complex flow patterns could be observed according to the given working conditions. It was concluded that the present numerical method was ver effective in the steady flow analysis of torque converters.

Time series studies of vent fluids from the TAG and MARK sites (1986, 1990) Mid-Atlantic Ridge: a new solution chemistry model and a mechanism for Cu/Zn zonation in massive sulphide orebodies

Abstract The hot springs at TAG and MARK on the Mid-Atlantic Ridge have been resampled after an interval of four years (1986–1990). The fluid compositions show the same temporal stability as observed elsewhere, e.g. 21°N, East Pacific Rise (EPR) and the Guaymas Basin. Although the MARK fluids have no chemical characteristics that would distinguish them from those on the faster spreading ridges of the Pacific, TAG has pronounced differences. The depletion in B and the small shift in δ 11 B indicate a substantial degree of reaction at intermediate temperatures along the recharge path that is unique to TAG. In addition, the TAG mound contains a large cluster of sphalerite-rich ‘onion domes’ that have been formed from an approximately 5:1 mixture of the primary hydrothermal end-member fluid and seawater that is formed within the deposit. This has resulted in the extensive precipitation of FeS within the mound and a resulting decrease in pH to values below 3. The low pH causes the large-scale remobilization of Zn from the interior of the deposit and its reprecipitation on the surface as the domes. Such compositional zoning is a common feature of ophiolite-type massive sulphide ore bodies and probably results by the same mechanism. The end-member data from both hydrothermal areas fall on the mixing planes defined by the EPR and Juan de Fuca data in a new three-component mixing model, indicating the presence of a phase-separated brine pool at depth under these Mid-Atlantic Ridge systems which is very similar in composition to those on the Pacific ridges.

Toward Improved Throughflow Capability: The Use of Three-Dimensional Viscous Flow Solvers in a Multistage Environment

A methodology is presented for simulating turbomachinery blade rows in a multistage environment by deploying a standard three-dimensional Navier–Stokes solver simultaneously on a number of blade rows. The principal assumptions are that the flow is steady relative to each blade row individually and that the rows can communicate via inter-row mixing planes. These mixing planes introduce circumferential averaging of flow properties but preserve quite general radial variations. Additionally, each blade can be simulated in three-dimensional or axisymmetrically (in the spirit of throughflow analysis) and a series of axisymmetric rows can be considered together with one three-dimensional row to provide, cheaply, a machine environment for that row. Two applications are presented: a transonic compressor rotor and a steam turbine nozzle guide vane simulated both isolated and as part of a stage. In both cases the behavior of the blade considered in isolation was different to when considered as part of a stage and in both cases was in much closer agreement with the experimental evidence.