Computation Of Three-dimensional Flows Research Articles

Modeling three-dimensional flow of the polymer melts in a converging channel

Temperature and volume rate impact of the polymer melt on the sizes of the vortex area has been considered. The vortex area appears during the flow at the inlet of the slotted channel. A modified Vinogradov and Pokrovskii rheological model is used for the mathematical modeling of three-dimensional flow of the melt in the convergent plane-parallel channel. This model was extended to take account of the nature of non-monotonic gradient dependence of elongation viscosity. On the solid wall the sticking conditions were used for velocity. The temperature dependence of the initial shear viscosity of the polymer melt has Arrhenius form. The initial relaxation time was rated by comparison with experimental data for agradient based stationary viscosity in uniaxial tension, and on the basis of the molecular-kinetic approach. Discrete analogues of a system of equations of the dynamics for the polymer liquid were obtained via the method of controlling the volume with the division due to physical processes. The numerical algorithm was implemented so that the technology of parallel computing based on GPU was conveniently used. Calculations of hydrodynamic characteristics of polymer melt flows at different temperatures in a convergent channel with a rectangular cross section have shown that the sudden narrowing of the channel leads to the appearance of eddy flows. The sizes of these flows pass through a maximum with increasing melt temperature which is detected in the experiments. It also confirms that the rheological model can be used for the flows of polymer melts in areas with complex geometry. The results are proving the effectiveness of CUDA technology parallel computing for unsteady calculations of three-dimensional flows of nonlinear viscoelastic fluids with rheological law of behavior in differential form. The above calculations show that some convergent flow of polymermelts may show substantial three-dimensional picture, which manifests itself in a velocity component in a neutral flow direction. This should be taken into account when arranging experiments, as there are methods that cannot measure all velocity components. Also note that the velocity profile in the slit of the channel is set at a considerable distance from the entrance to the channel.

ДО ОПТИМАЛЬНОГО ПРОЕКТУВАННЯ ОСЬОВОГО БАГАТОСТУПІНЧАСТОГО КОМПРЕСОРА

The work is devoted to the development of an integrated approach to the aerodynamic improvement of the blade vanes of multistage axial compressors of gas turbine engines. One of the features of the studies carried out to optimize the blade vanes was to take into account the mixing effects by various sources of losses. Thus, minimization of losses sources in compressor blade vanes during their profiling is achieved due to the account of the complex three-dimensional vortex nature of the flow and the use of modern software systems for solving the Navier-Stokes equations. Calculations of the three-dimensional viscous flow in the work are performed with ANSYS software. The profiling of the multi-stage compressor blades is carried out with “Kompress 2.0” software package, the feature of which is the use of parametric models of rotor and stator blade vanes, adapted for their aerodynamic optimization, as well as taking into account the radial unevenness of the incident flow when selecting the tangential blades shape of the stator vanes. As a result, a complex methodology for the optimal design of the blades of a multi-stage compressor with the use of "controlled" diffusivity, S-shaped profiles, lean, and chord variation is developed, with simultaneous variation of geometric parameters according to special plans and the use of the compressor efficiency as an integral efficiency criterion, “Kompress 2.0” for the blades profiling, ANSYS for the calculation of threedimensional viscous flow. Multi-stage axial compressors have been designed, numerically and experimentally investigated. Based on the results of experimental studies of multistage axial compressors, new generalizing relationships are established, that establish a relationship between the geometric parameters of the profiles and their gas dynamic characteristics to take into account the features of the spatial shape of the flow at the stage when solving the inverse design problem. The results of the research were used in the design and improvement of the elements of the flow paths of the ZM multistage compressors. Test aerodynamic optimization of the blade systems of experimentally studied multistage compressors with the use of the proposed approaches made it possible to obtain the efficiency of high-pressure compressor stages at the level of 0.92 ... 0.93 and to increase the efficiency of multistage axial compressors by 1.0-2.4%. The efficiency of the 10-stage compressor is 0.8% (to the level of 0.853), the efficiency of the 6-stage compressor is 1.1% (to the level of 0.825), the efficiency of the 3-stage compressor is 2.4% (to the level of 0.885), and the efficiency of an 8-stage axial compressor is 1.6% (to the level of 0.879).

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas–liquid or gas–solid) and three-phase (gas–liquid–solid) flow of CO2 whose thermodynamic properties are calculated using the Span–Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge–Kutta method. We demonstrate close to fifth-order convergence for advection–diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO2 jets.

Modeling the water decarbonization processes in atmospheric deaerators

A mathematical model of the water decarbonization processes in atmospheric deaerators is proposed to calculate the thermal decomposition degree of hydrocarbonates in a deaerator, pH of a deaerated water sample, and the mass concentration of free carbonic acid in it on a carbon dioxide basis. The mathematical description of these processes is based on the deaeration tank water flow model implemented in the specialized software suite for the calculation of three-dimensional liquid flows, where a real water flow is a set of parallel small plug-flow reactors, and the rate constant of the reaction representing a generalized model of the thermal decomposition of hydrocarbonates with consideration for its chemical and diffusion stages is identified by experimental data. Based on the results of experimental studies performed on deaerators of different designs with and without steam bubbling in their tanks, an empirical support of this model has been developed in the form of recommended reaction order and rate constant values selected depending on the overall alkalinity of water fed into a deaerator. A self-contained mathematical description of the water decarbonization processes in deaerators has been obtained. The proposed model precision has been proven to agree with the specified metrological characteristics of the potentiometric and alkalimetric methods for measuring pH and the free carbonic acid concentration in water. This allows us to recommend the obtained model for the solution of practical problems of forming a specified amount of deaerated water via the selection of the structural and regime parameters of deaerators during their design and regime adjustment.

Numerical investigation of a HPT with different rotor tip configurations in terms of pressure ratio and efficiency

The choice of the most appropriate rotor tip configuration is important, because it helps to avoid high blade tip losses due to the leakage flow that are responsible for efficiency and pressure ratio drops, mainly in High Pressure Turbine (HPT). This subject has been investigated to improve the axial turbines performance. The HPT used in this work is the turbine designed during the Energy Efficient Engine Program (E3 Program). This HPT was evaluated with different rotor tip geometry configurations: without tip clearance (hypothetical condition), with standard tip clearance geometry (flat-tip), with squealer, with winglet and squealer with winglet. Results were obtained based on the three-dimensional turbulent flow calculations making the use of a commercial CFD RANS equation-based solver with the addition of a two-equation turbulence model, in which the numerical solutions were compared with data available in the open literature for a HPT design-point operation. It was determined that for the HPT studied in this work, the machine efficiency can be improved using the rotor tip geometry equipped with winglet tip configuration. However, the rotor tip geometry equipped with squealer–winglet tip configuration presented a better pressure ratio compromise.

Multiscale approach to computation of three-dimensional gas mixture flows in engineering microchannels

A multiscale approach to computing real gas flows in engineering microchannels on high-performance computer systems in a wide range of Knudsen numbers is described. The numerical implementation of the approach combines the solution of quasigasdynamic equations and the molecular dynamics method. Following the approach, the parameters of the real gas equation of state are found at the molecular level, the kinetic gas properties are calculated, and the form of boundary conditions on the microchannel walls are determined. The technique is verified by computing several test problems. The results agree well with available theoretical and experimental data.

Modelling 3D Steam Turbine Flow Using Thermodynamic Properties of Steam Iapws-95

Abstract An approach to approximate equations of state for water and steam (IAPWS-95) for the calculation of three-dimensional flows of steam in turbomachinery in a range of operation of the present and future steam turbines is described. Test calculations of three-dimensional viscous flow in an LP steam turbine using various equations of state (perfect gas, Van der Waals equation, equation of state for water and steam IAPWS-95) are made. The comparison of numerical results with experimental data is also presented.

A Comparative Study of Numerical Methods on Aerodynamic Characteristics of a Compressor Rotor at Near-stall Condition

The present work performs three-dimensional flow calculations based on Reynolds Averaged Navier-Stokes (RANS) and Delayed Detached Eddy Simulation (DDES) to investigate the flow field of a transonic rotor (NASA Rotor 37) at near-stall condition. It is found that the DES approach is likely to predict well the complex flow characteristics such as secondary vortex or turbulent flow phenomenon than RANS approach, which is useful to describe the flow mechanism of a transonic compressor. Especially, the DES results show improvement of predicting the flow field in the wake region and the model captures reasonably well separated regions compared to the RANS model. Besides, it is discovered that the three-dimensional vortical flows after the vortex breakdown from the rotor tip region are widely distributed and its vortex structures are clearly present. Near the rotor leading edge, a part of the tip leakage flows in DES solution spill over into next passage of the blade owing to the separation vortex flow and the backflow is clearly seen around the trailing edge of rotor tip. Furthermore, the DES solution shows strong turbulent eddies especially in the rotor hub, rotor tip section and the downstream of rotor trailing edge compared to the RANS solution.

A Dimension Splitting Method for 3-D Incompressible Thermal Flow

This work deals with the computation of three-dimensional incompressible thermal flow, and a dimension splitting method is proposed for this. First, a time-space iterative method is adopted to obtains Euler implicit/explicit scheme. For the remaining Stokes equations we present a projection method to deal with the incompressibility constraint. In conclusion, only three independent linear elliptic equations need to be calculated at each step. Furthermore, on account of the splitting property of the method, all the computations are carried out on two-dimensional manifolds, which greatly reduces the difficulty and the computational cost in mesh generation, and a coarse-grained parallel algorithm can be constructed.

Investigation of the Flow Around Two Interacting Ship-Like Sections

This paper reports calculations of three-dimensional (3D) unsteady cross flow over two ship sections in close proximity and compares the results with measurements. The ship sections have different breadth and draft conditions which represent typical situations in a ship-to-ship marine operation in a cross current. The behavior of the vortex-shedding around the two different ship hull sections is investigated numerically by computational fluid dynamics (CFD) methods. For the two sections, simulations are done for Reynolds number Re = 68,000, Froude number Fr = 0.25, and Re = 6800, Fr = 0.025 by using the dynamic Smagorinsky large eddy simulation (LES) turbulence model. The simulations are performed by using the software ansysfluent and the numerical results are compared with particle image velocimetry (PIV) results taken from the literature. The hydrodynamic forces acting on the two ship sections are predicted by numerical simulations and interaction effects between the two ships are evaluated.

Residual Least-Squares Error Estimate for Unstructured h-Adaptive Meshes

An a posteriori error estimate suitable for finite-volume adaptive computations is presented. The error estimate combines the least-squares method regressions with the residual computation, which provides information from the grid quality and the governing equations for a better local adaptation of the unstructured grid. The decision algorithm uses the information provided by the error estimate and does not require problem-dependent constants; it also uses a grid interface correction step to provide a smoother and a high-quality adaptive grid. The proposed error estimate and the adaptive refinement algorithm are verified against analytic solution for different two-dimensional problems. In addition, calculations of three-dimensional laminar flows with different types of unstructured grids have demonstrated the applicability of the adaptive method.

Multi-objective shape optimization of runner blade for Kaplan turbine

Automatic runner shape optimization based on extensive CFD analysis proved to be a useful design tool in hydraulic turbomachinery. Previously the authors developed an efficient method for Francis runner optimization. It was successfully applied to the design of several runners with different specific speeds. In present work this method is extended to the task of a Kaplan runner optimization. Despite of relatively simpler blade shape, Kaplan turbines have several features, complicating the optimization problem. First, Kaplan turbines normally operate in a wide range of discharges, thus CFD analysis of each variant of the runner should be carried out for several operation points. Next, due to a high specific speed, draft tube losses have a great impact on the overall turbine efficiency, and thus should be accurately evaluated. Then, the flow in blade tip and hub clearances significantly affects the velocity profile behind the runner and draft tube behavior. All these features are accounted in the present optimization technique. Parameterization of runner blade surface using 24 geometrical parameters is described in details. For each variant of runner geometry steady state three-dimensional turbulent flow computations are carried out in the domain, including wicket gate, runner, draft tube, blade tip and hub clearances. The objectives are maximization of efficiency in best efficiency and high discharge operation points, with simultaneous minimization of cavitation area on the suction side of the blade. Multiobjective genetic algorithm is used for the solution of optimization problem, requiring the analysis of several thousands of runner variants. The method is applied to optimization of runner shape for several Kaplan turbines with different heads.

Design Work of a Compressor Stage Through High-To-Low Speed Compressor Transformation

Low-speed model testing has advantages such as great accuracy and low cost and risk, so it is widely used in the design procedure of the high pressure compressor (HPC) exit stage. The low-speed model testing project is conducted in Nanjing University of Aeronautics and Astronautics (NUAA) to represent aerodynamic load and flow field structure of the seventh stage of a high-performance ten-stage high-pressure compressor. This paper outlines the design work of the low speed four-stage axial compressor, the third stage of which is the testing stage. The first two stages and the last stage provide the compressor with entrance and exit conditions, respectively. The high-to-low speed transformation process involves both geometric and aerodynamic considerations. Accurate similarities demand the same Mach number and Reynolds number, which will not be maintained due to motor power/size and its low-speed feature. Compromises of constraints are obvious. Modeling principles are presented in high-to-low speed transformation. Design work was carried out based on these principles. Four main procedures were conducted successively in the general design, including establishment of low-speed modeling target, global parameter design of modeling stage, throughflow aerodynamic design, and blading design. In global parameter design procedure, rotational speed, shroud diameter, hub-tip ratio, midspan chord, and axial spacing between stages were determined by geometrical modeling principles. During the throughflow design process, radial distributions of aerodynamic parameters such as D-factor, pressure-rise coefficient, loss coefficients, stage reaction, and other parameters were obtained by determined aerodynamic modeling principles. Finally, rotor and stator blade profiles of the low speed research compressor (LSRC) at seven span locations were adjusted to make sure that blade surface pressure coefficients agree well with that of the HPC. Three-dimensional flow calculations were performed on the low-speed four-stage axial compressor, and the resultant flow field structures agree well with that of the HPC. It is worth noting that a large separation zone appears in both suction surfaces of LSRC and HPC. How to diminish it through 3D blading design in the LSRC test rig is our further work.

On Direct and Semi-Direct Inverse of Stokes, Helmholtz and Laplacian Operators in View of Time-Stepper-Based Newton and Arnoldi Solvers in Incompressible CFD

AbstractFactorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability. It is shown that the Stokes operator can be inversed within an acceptable computational effort. This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix. It is shown, additionally, that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers, as well as for other problems where convergence of iterative methods slows down. Implementation of the Stokes operator inverse to time-stepping-based formulation of the Newton and Arnoldi iterations is discussed.

Simulation and Optimization of Turbine Blade Shape Modification

Thickness thinning repair analog simulated using fluid mechanics research tool ANSYS-CFX of mixed-flow turbine runner blade,Through the three-dimensional flow and numerical calculation and analysis of energy distribution on the blade after featheredging. Leaf blade repair thickness thinning after 0.5CM in the cavitation performance, vibration performance and operation performance of the performance indicators to achieve the ideal state, The new method for reducing wheel vibration, vortex row, There is a certain positive significance in improving the efficiency of turbine, make full use of new energy.

Modeling of gas flow in the cylindrical channels of high-voltage plasma torches with rod electrodes

The article is devoted to the calculation of gas dynamic parameters of gas flow in various areas of low-temperature plasma generator, therefore, target area's grid was built for the simulation of plasma gas flow in channels of studied high-voltage AC plasma torches and calculations of three-dimensional gas flow was made using GAMBIT and FLUENT soft-ware and Spalart-Allmares turbulence model, air flow was simulated in the tangential feed's areas, in the cylindrical channel, in the tapering nozzle chamber and in the mixing chamber of plasma torches and outside (in the environment); thus, 3D-modelling of the cold plasma-forming gas flow was performed in cylindrical channels of studied high-voltage AC plasma torches with rod electrodes for the first time.

A discrete‐mechanical approach for computation of three‐dimensional flows

AbstractDynamical processes modeled with a suitable set of differential equations can be approximately computed with finite element method. However, especially in fluid dynamics, numerical instabilities may occur. In order to circumvent such problems many techniques have been realized over the last four decades. Often the lack of stability is linked to numerical insufficiency, therefore the solution is sought by tuning functional spaces, cf. [5] or by adding stabilizing terms, cf. [18, 19, 41]. Stabilizing terms are needed and helpful, however, they involve coefficients to be found depending on the underlying problem. The purpose of this work is to propose another approach based on first principles producing similar terms so that the numerical approximation converges without using any other parameter but the material constants, which are measurable. The approach eliminates stability problems, first, by setting the primary variables in a fundamental way and, second, by using the balance equations in their global form in a discrete manner instead of a continuous one. Some applications at the end emphasize the usefulness of the lengthy calculations, which we develop in a straightforward and consistent way.

Regeneratively cooled scramjet heat transfer calculation and comparison with experimental data

Regeneratively cooled scramjet heat transfer calculation method was developed using three-dimensional calculation for engine solid wall heat conduction. The scramjet thermal environment was determined by engine heat flux measurement and the engine three-dimensional combustion flow calculations. Different heat transfer relationships in the laminar, transition and turbulence fuel flow regions were applied. The cooling fuel flow distribution data inside combustion chamber side panel were obtained by three-dimensional fuel cooling flow calculation. The results of a light weight regeneratively cooled combustion chamber heat transfer tests were adopted to verify the calculation method. The comparisons showed good agreement, indicating that the calculation method is applicable.

3D numerical analysis of flow in Francis turbine in sandy river

Three-dimensional turbulent flow calculation of the flow in Francis turbine in sandy river was conducted by using body-fitted coordinates, tetrahedral grid system and SIMPLE algorithm based on the solid-liquid two-phase flow equation of motion in Eulerian coordinate system. The flow mechanism of sandy water in the turbine was analyzed through numerical simulation of flow in the turbine in several different sand water concentrations. In sandy water with various concentrations, the erosion area of turbine are basically concentrated at the lateral wall of the whole flow passage and the heads of guide vanes and blades.

Transient simulation of hydropower station with consideration of three-dimensional unsteady flow in turbine

To study the interaction between the transient flow in pipe and the unsteady turbulent flow in turbine, a coupled model of the transient flow in the pipe and three-dimensional unsteady flow in the turbine is developed based on the method of characteristics and the fluid governing equation in the accelerated rotational relative coordinate. The load-rejection process under the closing of guide vanes of the hydraulic power plant is simulated by the coupled method, the traditional transient simulation method and traditional three-dimensional unsteady flow calculation method respectively and the results are compared. The pressure, unit flux and rotation speed calculated by three methods show a similar change trend. However, because the elastic water hammer in the pipe and the pressure fluctuation in the turbine have been considered in the coupled method, the increase of pressure at spiral inlet is higher and the pressure fluctuation in turbine is stronger.