Unsteady Flow Calculations Research Articles

ОПРЕДЕЛЕНИЕ ТЕПЛОВОГО БАЛАНСА ОДНОПУТНОГО ТОННЕЛЯ И ПРИЛЕГАЮЩЕЙ СТАНЦИИ ДЛЯ РАСЧЕТА АДИАБАТНОГО ОХЛАЖДЕНИЯ ВОЗДУХА

Heat balance for single-track tunnel of underground and adjoining station in warm period of year in terms of Moscow Underground is determined. The calculation of unsteady heat flow is carried out, using software realization of heat transfer calculation by finite elements method, for heat losses determination into the soil at various depth of the tunnel. The phase difference between fluctuations of ambient air temperature and heat flow temperature is determined that should be considered for determination of calculated heat balance and air exchange. In warm period excessive heat in the tunnel cannot be fully removed by ventilation equipment, therefore it is proposed reducing of part of the excessive heat by adiabatic air humidification. In order to efficiency improvement of that method of air cooling, water discharge can be distributed along the tunnel proportionally of heat distribution. With that purpose the numeric experiment with air blowing of car starting-breaking resistors in single-truck tunnel has been carried out. Heat distribution along the tunnel has been found.

Closed vortex lines in fluid and gas

Исследуется непрерывное течение жидкости и газа с замкнутыми вихревыми трубками. Рассмотрена циркуляция вдоль вихревой линии отношения плотности равнодействующей всех сил (приложенных к жидкости или газу) к плотности жидкости или газа. Она совпадает с циркуляцией по той же вихревой линии частной производной вектора скорости по времени и поэтому для стационарных течений равна нулю на любой замкнутой вихревой линии. Для нестационарных течений рассмотрены вихревые трубки, которые остаются замкнутыми по крайней мере в течение некоторого интервала времени. Обнаружена неизвестная ранее закономерность, состоящая в том, что в каждый фиксированный момент времени такая циркуляция одинакова для всех замкнутых вихревых линий, составляющих вихревую трубку. Указанная закономерность верна для течений сжимаемых и несжимаемых, вязких (различных реологий) и невязких жидкостей в поле потенциальных и непотенциальных внешних массовых сил. Поскольку эта закономерность не заложена в современные численные алгоритмы, она может использоваться для верификации численных расчетов нестационарных течений с замкнутыми вихревыми трубками путем проверки равенства циркуляций на разных замкнутых вихревых линиях (в одной трубке). Выражение для плотности распределения равнодействующей всех сил, приложенных к жидкости или газу, может содержать производные высших порядков. В то же время выражение для частной производной вектора скорости по времени и выражение для вектора завихренности, который необходим для построения вихревой линии, содержат только первые производные, что позволяет использовать обнаруженную закономерность для верификации расчетов, проведенных методами не только высокого, но и низкого порядков.

Optimal parameters for a family of flux‐correction methods strongly reducing overshoot in unsteady flow computation

AbstractFlux‐correction allows to reduce or even remove overshoot occuring when Lax‐Wendroff methods are used to calculate one‐dimensional flow. There is a whole family of methods [3] depending on two parameters, whose optimal values are derived. One controls the amount of diffusion to reduce overshoot, the other determines removal of this diffusion as far as overshoot does not reappear, thus largely retaining accuracy of the employed Lax‐Wendroff method.

Calculation of unsteady two-phase quasi-onedimensional channel flow based on the two-fluid model and the artificialviscosity numerical scheme

An example of usage of the artificial viscosity technique for numerical simulation of unsteady one-dimensional two-phase flows based on the two-fluid approach is presented. The governing equations system is written under assumption of equal pressure in the fluids. No interfacial exchange is taken into account. Performance of the artificial viscosity technique suggested has been evaluated via numerical solution of a model problem of two-phase flow in a channel of variable cross-section. It has been shown that the used numerical scheme, implicit and first-order, involving the suggested artificial viscosity model, provides a stable process of getting a numerical solution and predicts a physically adequate flow dynamics without non-physical oscillations.

ЗНИЖЕННЯ РІВНЯ ДИНАМІЧНИХ НАПРУГ У РОБОЧИХ ЛОПАТКАХ ТУРБІНИ ЗА РАХУНОК ВИБОРУ ГЕОМЕТРІЇ СОПЛОВОГО АПАРАТУ

Interacting between the next rows of the turbine creates a circumferential flow non-uniformity, which leads to origination of resonance dynamic stresses on rotor bladings with frequencies z·fn, where fn - a rotor rotation frequency, z - number of stator vanes. At projection and development of the engine is not always possible detuning from a resonance as the spectrum of eigenfrequencies of rotor blades can be wide enough in relation to a band of working rotor speed. Reduction of exterior exciting forces can be one of ways of a reduction of dynamic stresses in rotor blades. For attenuation of these forces intensity was possibly use of a stator vanes with a different spacing, and also with the blades inclined in a circumferential direction. In the given article numerical research for choice a distribution law of stator vanes spacing and a declivity angle of its blades, allowed to diminish amplitude of the unsteady air forces acting on rotor blades with frequency z·fn are presented. As object for examinations the stage of the air starter turbine, the containing 26 nozzle vanes disposed with different spacings, and 40 rotor blades without a binding has served. Rotor blades and turbine disk of the air starter are made for a single whole of an aluminium alloy. This work was executed stage by stage: in the beginning the angular disposition of vanes blades, giving maximum decrease of exciting forces on rotor blades, by results of unsteady flow calculation in the turbine was chosen; then for the found geometry of a vanes the slope angle of its blades in the circumferential direction, giving the maximum decrease of exciting forces on rotor blades was chosen. The viscous gas unsteady flow was modelled in the computational domain including all blade passages of turbine rows - 26 channels in a nozzle and 40 channels in the rotor wheel. By results of calculation dependence of decrease unsteady force acting on blades and changes of turbine efficiency from a slope angle of vanes is presented. Reduction of dynamic stresses level in rotor blades of the turbine at the expense of decrease of aerodynamic exciting forces amplitude is attained. The numerical result is confirmed experimentally in rig test by decrease of resonance stresses on explored frequencies.

Fully Implicit Chebyshev Time-Spectral Method for General Unsteady Flows

An efficient fully implicit Chebyshev time-spectral method (TSM) is developed to solve general unsteady flows with or without periodicity. High accuracy of the Chebyshev time-spectral operator is demonstrated by simulating the one-dimensional shock motion at constant speed. A space-time lower–upper symmetric Gauss–Seidel (LU-SGS) fully implicit scheme with multigrid acceleration is used to efficiently solve the equations resulting from the Chebyshev TSM. The implicit temporal coupling term is properly split so that the LU-SGS sweeps are extended to the time domain. For cases in which the physical time step is small, a modification to the implicit scheme is suggested to enhance numerical stability. Computational results of nonperiodic flows over a pitching airfoil are presented for different physical time steps and various numbers of Chebyshev collocation points. The fully implicit Chebyshev TSM is also tested to predict the natural vortex shedding frequency for a stationary circular cylinder. This efficient approach can be easily applied to the time-accurate computation of general nonperiodic unsteady flows with a given initial condition.

Multi-GPU parallel computation of unsteady incompressible flows using kinetically reduced local Navier–Stokes equations

Numerical simulations of 2D doubly periodic shear layers and 3D decaying homogeneous isotropic turbulence are presented using Kinetically Reduced Local Navier–Stokes (KRLNS) equations that is applicable to the unsteady incompressible flows without the need for sub-iterations and is capable of capturing the correct transient behavior. To achieve high accuracy, the KRLNS equations is discretized with higher order central difference approximations and 4-stage Runge–Kutta method. The results are compared with the solutions obtained by Lattice Boltzmann method (LBM) and pseudo-spectral method (PSM), which is the standard approach for this problem. Parallel computations are carried out on multiple GPUs (Tesla K40), maximum 4 GPUs available, based on the domain decomposition method and the speedup of the KRLNS equations is investigated. It is found that all three methods can capture the transient flow fields of unsteady incompressible flow and a large speedup for the KRLNS equations is obtained.

Stability of a family of flux‐correction methods as a remedy against overshoot in unsteady flow computation

AbstractStill Lax‐Wendroff schemes are occasionally used calculating one‐dimensional flow. Supplementary flux‐correction allows to reduce or even prevent unphysical overshoot occuring with discontinuous initial conditions. There is a whole family of variants [4] based on damping or smoothing with different stability limits, which will be considered here in more detail. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

High-order non-inertial computation method for helicopter rotor flows in forward flight

Purpose This paper aims to improve the computational efficiency and to achieve high-order accuracy for the computation of helicopter rotor unsteady flows in forward flight during the industrial preliminary design stage. Design/methodology/approach The integral arbitrary Lagrangian–Eulerian form of unsteady compressible Navier–Stokes equations with low Mach number preconditioned pseudo time terms based on non-inertial frame of reference undergoing rotating and translating was derived and discretized in the framework of multi-block structured finite volume grid using three types of spatial reconstruction schemes, i.e. the third-order accurate monotonic upwind scheme for conservation laws, the fifth-order accurate weighted essentially non-oscillatory and the fifth-order accurate weighted compact nonlinear schemes. Findings The results show that the present non-inertial computational method can obtain comparable results with other methods, such as the dynamic overset method, and make sure that the higher-order spatial schemes can significantly improve the tip vortex resolution. Originality/value The computational grid used by the present method remained static during the whole unsteady computation process, with only local deformations induced by blade cyclic pitch and other operating motions, which greatly reduced the complexity of grid motion and enhanced the efficiency and robustness.

Evaluation of Fully Implicit Runge Kutta Schemes for Unsteady Flow Calculations

This paper presents the formulation of a dual time stepping procedure to solve the equations of fully implicit Runge–Kutta schemes. In particular the method is applied to Gauss and Radau 2A schemes with either two or three stages. The schemes are tested for unsteady flows over a pitching airfoil modeled by both the Euler and the unsteady Reynolds averaged Navier Stokes equations. It is concluded that the Radau 2A schemes are more robust and less computationally expensive because they require a much smaller number of inner iterations. Moreover these schemes seem to be competitive with alternative implicit schemes.

Efficient Gridless Method Using Constrained Weights Optimization for Two-Dimensional Unsteady Inviscid Flows at Low Angles of Attack

AbstractAn accurate and efficient gridless method is presented for calculation of unsteady flows at low and high reduced frequencies. A central gridless scheme is applied to solve unsteady flow equ...

Implicit second-order CUSP gridless method for unsteady moving boundary simulations

Efficient first-order and second-order gridless method is presented for calculation of unsteady compressible flows. The convective upwind split pressure (CUSP) gridless scheme is applied for solving unsteady fluid flow equations in the arbitrary Lagrangian–Eulerian (ALE) formulation. In order to manage dynamic cloud and nodes movement, the nodes are moved based on the boundary movements using the segment spring analogy. Discretization of spatial derivatives are done by using the Taylor series least squares at each node. For increasing the accuracy, second-order Taylor series (SOTS) expansion is also used on the CUSP gridless method. For time advancement, implicit dual-time and explicit schemes are used. The accuracy of the methods is compared with the AGARD experimental data and finite volume results for some test cases in steady and unsteady flows. Results show that the CUSP gridless scheme is accurate in steady and unsteady flows and using the second-order discretization increases the accuracy a little bit and also the gridless schemes reduce the computational time as compared with finite volume method. Numerical results are in good agreement with the experimental data.

Implementation of dual time-stepping strategy of the gas-kinetic scheme for unsteady flow simulations.

In our study, the dual time-stepping strategy of the gas-kinetic scheme is constructed and used for the simulation of unsteady flows. In comparison to the previous implicit gas-kinetic scheme, both the inviscid and viscous flux Jacobian are considered in our work, and the linear system of the pseudo-steady-state is solved by applying generalized minimal residual algorithm. The accuracy is validated by several numerical cases, the incompressible flow around blunt bodies (stationary circular cylinder and square cylinder), and the transonic buffet on the NACA0012 airfoil under hybrid mesh. The numerical cases also demonstrate that the present method is applicable to approach the fluid flows from laminar to turbulent and from incompressible to compressible. Finally, the case of acoustic pressure pulse is carried out to evaluate the effects of enlarged time step, and the side effect of enlarged time step is explained. Compared with the explicit gas-kinetic scheme, the proposed scheme can greatly accelerate the computation and reduce the computational costs for unsteady flow simulations.

Turbulent and Unsteady Flows on Unstructured Line-Based Hamiltonian Paths and Strands Grids

A solution algorithm using Hamiltonian paths and strand grids is presented for turbulent flows and unsteady flow calculations around representative geometries initially consisting of a mixed-element unstructured surface mesh. Line-based reconstruction schemes and approximate factorization techniques are robustly implemented on unstructured grids. The Baldwin–Lomax and Spalart–Allmaras turbulence models are integrated to the present method for both two- and three-dimensional flows, and the predicted aerodynamic flows are validated by comparing against those obtained from established solvers and/or experiments. In addition, time-accurate methods with dual-time-stepping strategies are explored to predict flows over canonical time-dependent problems. It is observed that a various high-order-type reconstruction scheme can be used on “lines” constructed from purely unstructured grids in the current framework, along with good spatial and temporal accuracy.

A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows

Abstract The present paper aims at building a fast and accurate phase transition solver dedicated to unsteady multiphase flow computations. In a previous contribution (Chiapolino et al. 2017), such a solver was successfully developed to compute thermodynamic equilibrium between a liquid phase and its corresponding vapor phase. The present work extends the solver’s range of application by considering a multicomponent gas phase instead of pure vapor, a necessary improvement in most practical applications. The solver proves easy to implement compared to common iterative procedures, and allows systematic CPU savings over 50%, at no cost in terms of accuracy. It is validated against solutions based on an accurate but expensive iterative solver. Its capability to deal with cavitating, evaporating and condensing two-phase flows is highlighted on severe test problems both 1D and 2D.

Application of a new cavitation model for computations of unsteady turbulent cavitating flows around a hydrofoil

In the present work, a cavitation model based on a new truncated form of the full Rayleigh-Plesset (R-P) equation for the source terms controlling vapor generation and destruction has been developed and implemented in the ANSYS FLUENT platform. Coupled with a Filter-based density corrected model (FBDCM), the cavitating flow over a 2-D Clark-Y hydrofoil is investigated numerically with particular emphasis on understanding the effect of cavitation structures and the shedding dynamics on the hydrodynamics coefficients and surrounding flow velocity structures. The hydrofoil has a fixed angle of attack of α = 8° with a moderate Reynolds number of Re = 7.0×105. Simulations have been carried out for various cavitation numbers ranging from non-cavitating flows to the cloud cavitation regime (σ = 0.80). In particular, we compared the lift and drag coefficients, the cavitation dynamics and the time-averaged velocity with available experimental data for two cavitation models, i.e. the proposed model and Schnerr-Sauer model. The comparisons between the numerical and experimental results show that the proposed model has a better capability than Schnerr-Sauer model to capture the characteristics of lift and drag coefficients under cavitation conditions. Meanwhile, the proposed model is sufficiently robust to predict the initiation of the sheet/cloud cavity, growth towards the trailing edge, and subsequent shedding downstream, which is in accordance with the experimental quantitative features in literature.

A simple turbulent two-fluid model

We present in this paper a simple turbulent two-phase flow model using the two-fluid approach. The model, which relies on the classical ensemble averaging, allows the computation of unsteady flows including shock waves, rarefaction waves, and contact discontinuities. It requires the definition of adequate source terms and interfacial quantities. The hyperbolic turbulent two-fluid model is such that unique jump conditions hold within each field. Closure laws for the interfacial velocity and the interfacial pressure comply with a physically relevant entropy inequality. Moreover, source terms that account for mass, momentum and energy interfacial transfer are in agreement with the entropy inequality. Particular attention is also given to the jump conditions when assuming a perfect gas equation of state within each phase; this enables us to recover expected bounds on the mean density through shock waves.

Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL) in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD) Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.

A simple phase transition relaxation solver for liquid–vapor flows

SummaryDetermining liquid–vapor phase equilibrium is often required in multiphase flow computations. Existing equilibrium solvers are either accurate but computationally expensive or cheap but inaccurate. The present paper aims at building a fast and accurate specific phase equilibrium solver, specifically devoted to unsteady multiphase flow computations. Moreover, the solver is efficient at phase diagram bounds, where non‐equilibrium pure liquid and pure gas are present. It is systematically validated against solutions based on an accurate (but expensive) solver. Its capability to deal with cavitating, evaporating, and condensing two‐phase flows is highlighted on severe test problems both 1D and 2D. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical analysis of the dynamics of distributed vortex configurations

A numerical algorithm is proposed for analyzing the dynamics of distributed plane vortex configurations in an inviscid incompressible fluid. At every time step, the algorithm involves the computation of unsteady vortex flows, an analysis of the configuration structure with the help of heuristic criteria, the visualization of the distribution of marked particles and vorticity, the construction of streamlines of fluid particles, and the computation of the field of local Lyapunov exponents. The inviscid incompressible fluid dynamic equations are solved by applying a meshless vortex method. The algorithm is used to investigate the interaction of two and three identical distributed vortices with various initial positions in the flow region with and without the Coriolis force.