Analysis of supersonic flow in Oswatitsch inlet configuration

The aim of this work is a study of the flow parameters relevant for the Oswatitsch intake configuration. Geometry of the cone and inlet are equivalent to those on MiG-21bis fighter aircraft. Supersonic flow parameters for a channeled cone were studied at two different operational Mach numbers. Center body cone is movable along longitudinal axis and analysis is focused on specific positions for supersonic flight regimes. To study the problem, numerical model of axisymmetric two-dimensional Euler flow is applied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical solution of transonic and subsonic flow of compressible inviscid and viscous fluid

The work presents two numerical solutions of compressible flows problems with high and very low Mach numbers. Both problems are numerically solved by finite volume method and the explicit MacCormack scheme using a grid of quadrilateral cells. Moved grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian–Eulerian method. In the first case, inviscid transonic flow through cascade DCA 8% is presented and the numerical results are compared to experimental data. The second case, numerical solution of unsteady viscous flow in the channel for upstream Mach number M_∞=0.012 and frequency of the wall motions 100 Hz is presented. The unsteady case can represent a simplified model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds to the human vocal tract. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

零攻角小钝头钝锥高超音速绕流边界层的稳定性分析和转捩预报

研究了零攻角小钝头圆锥高超音速边界层的稳定性及转捩预测问题．小钝头的球头半径为0.5 mm,锥的半锥角为5°,来流马赫数为6．采用直接数值模拟方法得到了钝锥的基本流场,利用线性稳定性理论分析了等温壁面和绝热壁面条件下的第一、第二模态不稳定波,并用“e-N”方法对转捩位置进行了预测．在没有实验给出N值的情况下,暂取N为10．研究发现,壁面温度条件对于转捩位置有较大影响．绝热边界层的转捩位置比等温边界层的靠后．且尽管高马赫数下第二模态波的最大增长率远大于第一模态波的最大增长率,但绝热边界层的转捩位置是由第一模态不稳定波决定的．研究方法应能推广到有攻角的三维边界层流动的转捩预测．     

Viscous fluid flow at all speeds: analysis and numerical simulation

In [43] a finite volume method for reliable simulations of inviscid fluid flows at high as well as low Mach numbers based on a preconditioning technique proposed by Guillard and Viozat [14] is presented. In this paper we describe an extension of the numerical scheme for computing solutions of the Euler and Navier-Stokes equations. At first we show the high resolution properties, accuracy and robustness of the finite volume scheme in the context of a wide range of complicated transonic and supersonic test cases whereby both inviscid and viscous flow fields are considered. Thereafter, the validity of the method in the low Mach number regime is proven by means of an asymptotic analysis as well as numerical simulations. Whereas in [43] the asymptotic analysis of the scheme is focused on the behaviour of the continuous and discrete pressure distribution for inviscid low speed simulations we prove both the physical sensible discrete pressure field for viscous low Mach number flows and the divergence free condition of the discrete velocity field in the limit of a vanishing Mach number with respect to the simulation of inviscid fluid flow.     

Viscous fluid flow at all speeds: analysis and numerical simulation

In [43] a finite volume method for reliable simulations of inviscid fluid flows at high as well as low Mach numbers based on a preconditioning technique proposed by Guillard and Viozat [14] is presented. In this paper we describe an extension of the numerical scheme for computing solutions of the Euler and Navier-Stokes equations. At first we show the high resolution properties, accuracy and robustness of the finite volume scheme in the context of a wide range of complicated transonic and supersonic test cases whereby both inviscid and viscous flow fields are considered. Thereafter, the validity of the method in the low Mach number regime is proven by means of an asymptotic analysis as well as numerical simulations. Whereas in [43] the asymptotic analysis of the scheme is focused on the behaviour of the continuous and discrete pressure distribution for inviscid low speed simulations we prove both the physical sensible discrete pressure field for viscous low Mach number flows and the divergence free condition of the discrete velocity field in the limit of a vanishing Mach number with respect to the simulation of inviscid fluid flow.     

基于Roe格式的可压与不可压流的统一计算方法

摘要：以Navier-Stokes方程为基础，基于有限体积的时间推进的预处理技术．提出了一个可以用来求解可压与不可压流场的统一的计算方法，原始变量选用压力、速度与温度，通过矩阵变换与重构，使得对流项系数矩阵在可压与小可压条件下都不会奇异．将可压与不可压流场的计算方法统一起来。采用Roe格式计算对流通量，采用中心差分格式计算扩散通量．算例表明，该方法可以进行高Mach数、中等Mach数、低Mach数及不可压流场的计算。由于采用了Roe格式，该方法还可以捕获不连续流场的间断面。     

A low-Mach number method for the numerical simulation of complex flows

A new numerical procedure which considers a modification to the artificial acoustic stiffness correction method (AASCM) is here presented, to perform simulations of low Mach number flows with the compressible Navier–Stokes equations. An extra term is added to the energy fluxes instead of using an energy source correction term as in the original model. This new scheme re-scales the speed of sound to values similar to the flow velocity, enabling the use of larger time steps and leading to a more stable numerical method. The new method is validated performing Large Eddy Simulations on test problems. The effect of a crucial numerical parameter alpha is evaluated as well as the robustness of the method to variations of the Mach number. Numerical results are compared to the existing experimental data showing that the new method achieves good agreement increasing the time-step, and therefore accelerating the computation for low-Mach convective flows.     

Verification of Complex Transonic Phenomena with CFD Codes

Classical analytic models for the theoretical behavior of transonic flows have guided the development of numerical simulation of practically relevant flows. But while operational successfully for the usual applications (conventional configuration high speed aerodynamics), CFD codes fail frequently once detailed information regarding even just inviscid flow structure for freestream Mach number close to unity is needed. In this contribution shock configurations are computed verifying analytical results for both the far field behavior of detached bow waves and the local structure of attaching bow waves. The first example is challenging the ability of a CFD code (DLR‐τ) to adapt its unstructured grid to a weak bow wave detached from the airfoil. Known analytical results for the asymptotic bow wave behavior at decreased Mach number → 1 serve for judging numerical results where practical case studies neither from CFD nor from experiment are available. In the second example the behavior of a bow wave attaching to a wedge for increased Mach number is studied, with grid adaption allowing for a verification of both the singular analytical model when attachment takes place and also the transition to plain supersonic wedge flow.     

A conservative pressure-correction scheme for transient simulations of reacting flows

An algorithm is presented for numerical simulations of time-dependent low Mach number variable density flows with an arbitrary amount of scalar transport equations and a complex equation of state. The pressure-correction type algorithm is based on a segregated solution formalism. It is conservative and guarantees stable results, regardless of the difference in density between neighboring cells. Furthermore, states are predicted which exactly match the equation of state. In the one-dimensional example, considering non-premixed flames, a simplified flamesheet model is used to describe the combustion of fuel and oxidizer. We demonstrate that the predicted states exactly correspond to the equation of state. We illustrate the accuracy improvement due to higher order formulation and demonstrate grid convergence.     

Cellular articular cartilage replacement tissues: Modeling and analysis

Long-term studies reveal that mechanical stimulation causes growth and remodeling phenomena within biological tissues. The main aim of this research is to fully understand and control these phenomena. For accomplishing that, two steps are considered: first, we determine a suitable numerical model based on different approaches by a comparative study using experimental validations, and second, investigate the mechanical properties of the tissue specimens after a remodeling process. We start with the first step by choosing a convenient model that mimics the biotissue for running the numerical simulations in the second step. There are different models available that determine the mechanical properties of soft replacement tissues seeded with human chondrocytes in modern medical applications. It is our objective to achieve a common methodology of theory and experiments that allows the determination of the mechanical properties of the native material. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation on the effect of trailing edge ejection on a turbine cascade

This paper presents a detailed experimental and numerical investigation for a turbine cascade with different trailing edge ejection. The numerical simulation is based on Three-Dimensional Navier–Stokes equations coupled with an effective ejection model, where a high resolution non-oscillatory scheme, LU-SGS implicit algorithm and Baldwin-Lomax turbulence model are employed. The experiments presented in this paper focused on a transonic turbine cascade performance with different ejection to validate the numerical simulation results. The results show that the blowing ratio has a small effect on the Mach number distribution and exit flow angle with two slot types. However the energy loss coefficient increases initially, and subsequently has a decrease tendency with the increasing of blowing ratio. The ejection from the symmetry slot blows away the vortex at the blade trailing edge and strengthens the mixing between the wake and main flow. The ejection from the pressure side cutback only clears up the vortex near the slot surface, and has small effect on the flow field near the trailing edge.     

Minimum quench energies of uncooled low temperature superconductors with temperature dependent thermophysical parameters

An analytical method for calculation of minimum quench energies (MQEs) of uncooled composite low temperature superconductors is presented. The method takes into account transient heat transfer in the conductor as well as temperature dependent ohmic heat generation and temperature dependent thermophysical properties of the conductor. MQE of the conductor is calculated based on the analysis of evolution of peak temperature in the normal zone. The method is validated by comparison of the obtained results with the experimental data as well as with analytical and numerical results taken from literature.     

Premature in-bore separation of sabot-jacketed projectiles

The premature separation of saboted projectiles undergoing high-mach-number in-bore acceleration is investigated. Results from a simplified numerical model for the problem are presented. Measured short-term velocity history for a typical projectile is used to describe the motion of a nonuniformly accelerating piston. Two numerical algorithms for calculating the shocked flow in tront of the accelerating piston are presented. Mach number and pressure time histories for the flow afford corrective input to the sabot design process. © 1993 John Wiley & Sons, Inc.     

高超声速飞行器前体压缩性能研究

用数值模拟的方法研究了高超声速飞行器前体不同型面与进气性能的关系,分析了二级压缩构型在不同压缩角组合和来流攻角下的流场品质和产生的压缩效果．研究结果表明,对于高超声速飞行器,采用多级压缩的前体构型可以得到较好的预压缩效果和优良的流场品质;同时,攻角和不同的压缩角组合会对压缩性能产生影响．因此,采用多级压缩的前体构型、优化各级压缩角的组合是决定飞行器前体预压缩性能的重要因素,同时也是开展前体/发动机一体化设计的关键．     

Mathematical modeling of temperature pulsation in a thick anode in optoelectronic systems

A numerical method is applied to analyze the one-dimensional model of temperature pulsation inside a two-layer anode with temperature-dependent thermophysical coefficients. The analysis allows for surface thermal radiation, secondary electron emission, and distribution of electron energy losses by penetration depth into the target. Penetration of pulsations deep into the target is observed.Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach Matematicheskoi Fiziki, pp. 215–217, 1993.     

Methods of critical value reduction for type-2 fuzzy variables and their applications

A type-2 fuzzy variable is a map from a fuzzy possibility space to the real number space; it is an appropriate tool for describing type-2 fuzziness. This paper first presents three kinds of critical values (CVs) for a regular fuzzy variable (RFV), and proposes three novel methods of reduction for a type-2 fuzzy variable. Secondly, this paper applies the reduction methods to data envelopment analysis (DEA) models with type-2 fuzzy inputs and outputs, and develops a new class of generalized credibility DEA models. According to the properties of generalized credibility, when the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we can turn the proposed fuzzy DEA model into its equivalent parametric programming problem, in which the parameters can be used to characterize the degree of uncertainty about type-2 fuzziness. For any given parameters, the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers. Finally, one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed DEA model.     

Numerical Simulation of Spot-Weld Joints under Crash Loading

This paper compares FE simulations of spot-weld joints for dual-phase steel under different load cases by using damage models of Gurson-Tvergaard-Needleman (GTN) and its two extensions, GTN-Johnson-Cook and GTN-Hutchinson. Spot-weld specimens have three zones depending with different material properties: Base material, heat-affected zone and fusion zone. The characterization of the base material is straightforward. The other two zones are characterized with specifically heat-treated specimens. For each zone, flat smooth tensile, flat notched tensile and Iosipescu-shear specimen are used in order to obtain the damage behavior for different triaxiality values. GTN damage model parameters are calibrated with the help of smooth and notched flat tensile specimens. The parameters of the above mentioned extensions of GTN damage model are identified with the help of Iosipescu-shear specimen. Finally, the calibrated material models are used in the FE simulation of the spot-weld specimens under quasi static-load case (10 mm/min) for loading directions of 0°, 30°, 60°, 90°. The numerical force-displacement results are in good agreement with experimental results. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical solution of transient heat conduction equation with variable thermophysical properties by the Tau method

In this article, we proposed the operational approach to the Tau method for solving linear and nonlinear one‐dimensional transient heat conduction equations with variable thermophysical properties which can involve heat generation term. To solve heat conduction equation, first we recall the Tau method to obtain a matrix form of the governing differential equation. Then boundary and initial conditions are transformed into a matrix form. Finally the resulting systems of linear or nonlinear algebraic equations are given. Afterwards, efficient error estimation is also introduced for this method. Some numerical examples are given to illustrate the efficiency and high accuracy of the proposed method and also results are compared with solutions obtained by other methods. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 964–977, 2014     

Modelling of material and structural inhomogeneities in timber structures

The numerical simulation of timber structures by means of FEM has been an object of recent research. Most of the material models developed so far are based on idealized assumptions by disregarding inhomogeneities. Here, models to capture structural inhomogeneities in terms of branches and knots and the resulting deviation in grain course in a three-dimensional FE analysis are presented. Besides, naturally varying material properties referred to as material inhomogeneities have to be considered in the structural analysis. Due to the insufficient experimental data, the uncertainty model fuzziness is applied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of the spherical metric tensor to grid adaptation and the solution of applied problems

New results concerning the construction and application of adaptive numerical grids for solving applied problems are presented. The grid generation technique is based on the numerical solution of inverted Beltrami and diffusion equations for a monitor metric. The capabilities of the spherical metric tensor as applied to adaptive grid generation are examined in detail. Adaptive hexahedral grids are used to numerically solve a boundary value problem for the three-dimensional heat equation with a moving boundary in a continuous medium with discontinuous thermophysical parameters; this problem models the interaction of a thermal wave with a thermocouple embedded in the solid.