A non-linear analysis of non-isothermal wave propagation in linear-elastic fluid-saturated porous media

The non-isothermal dynamic behaviour of saturated porous media is analysed numerically employing the finite element method and taking energy convection due to large pore fluid displacements into account. A different pore fluid reference temperature is introduced in order to allow properly for heat convection: this concept is usually neglected in the literature and is discussed and analysed herein. The numerical procedure is validated in a simple problem of hot fluid injection in a steady seepage flow and by comparing the numerical results, neglecting energy convection, with those obtained with a novel solution of the linearised equations, presented herein, which is based on the transfer functions and Fourier transforms method. Finally, the effects of energy convection in wave propagation are analysed: in a pervious porous medium the flux of energy due to energy convection is much greater than the one due to heat conduction; in any case, wave propagation can be considered completely adiabatic even when energy convection is taken into account. Thus the validity of the results presented in the literature and based on the linearised theory is demonstrated.     

A flexible approach to expression evaluation within a computational engineering environment

In many stages of a typical computational simulation, the user has a requirement to extract data which is not always in a readily available form. Typical examples include mesh quality statistics, where the quality measure is typically defined using an expression involving the co-ordinates of each mesh cell, face, edge or node; solution visualisation, where the quantity to be displayed/analysed is an expression involving the resultant variables of the flow solver; and mesh adaption, where the refinement may be driven by a quantity which could be a combination of flow solution variables and the co-ordinates of the mesh edges. A code developer can readily modify source code to meet such requirements but this is not an option to a typical user and, when additionally, codes are embedded within graphical user interfaces. This paper describes EQUATE, a system designed to allow the user to define their own measures at run-time, and how it can be integrated into general interactive, graphical environments. © 1998 John Wiley & Sons, Ltd.     

Instability and Viscous Dissipation in the Horizontal Brinkman Flow through a Porous Medium

The convective instability activated by the sole effect of viscous dissipation in a fluid saturated porous layer is studied. The basic parallel flow in a highly permeable porous medium is analysed by considering the viscous heating contribution in the local energy balance, by assuming a thermally insulated lower boundary and an isothermal upper boundary. The Brinkman model of momentum transfer is adopted. Arbitrarily oriented oblique roll disturbances are considered in the linear stability analysis. Among them, the longitudinal rolls, having axis parallel to the basic flow direction, are shown to be the preferred mode of instability. Some considerations on the reliability of the Brinkman model, when the viscous dissipation contribution is not negligible and when the flow conditions are close to the limiting case of a clear fluid, are finally expressed.     

Combined application of surface flow visualization and laser-Doppler anemometry to engine intake flows

Flow visualization using oil streak techniques and laser-Doppler anemometry were carried out to provide detailed information on the flow through the intake valve of a research (model) engine head under steady flow conditions. The work was partially undertaken to develop the techniques as useful tools for engine research. On the other hand, variations of the flow field with valve lift and with valve location were of interest. In the present paper it is shown that a symmetric geometry does not necessarily result in symmetric flow patterns inside the cylinder; the tendency to asymmetry increases with increasing valve lift. These characteristics of the flow should be taken into account when flow computations are performed necessitating the use of three dimensional codes in the entire flow field, not in a symmetrical half-geometry.     

Study of laminar–turbulent flow transition under pulsatile conditions in a constricted channel

In this paper, direct numerical simulation is performed to investigate a pulsatile flow in a constricted channel to gain physical insights into laminar–turbulent–laminar flow transitions. An in-house computer code is used to conduct numerical simulations based on available high-performance shared memory parallel computing facilities. The Womersley number tested is fixed to 10.5 and the Reynolds number varies from 500 to 2000. The influences of the degree of stenosis and pulsatile conditions on flow transitions and structures are investigated. In the region upstream of the stenosis, the flow pattern is primarily laminar. Immediately after the stenosis, the flow recirculates under an adverse streamwise pressure gradient, and the flow pattern transitions from laminar to turbulent. In the region far downstream of the stenosis, the flow becomes re-laminarised. The physical characteristics of the flow field have been thoroughly analysed in terms of the mean streamwise velocity, turbulence kinetic energy, viscous wall shear stresses, wall pressure and turbulence kinetic energy spectra.     

Relationship between multibody dynamics computation and nonlinear vibration theory

This paper presents the ground-work of implementing the multibody dynamics codes to analyzing nonlinear coupled oscillators. The recent developments of the multibody dynamics have resulted in several computer codes that can handle large systems of differential and algebraic equations (DAE). However, these codes cannot be used in their current format without appropriate modifications. According to multibody dynamics theory, the differential equations of motion are linear in the acceleration, and the constraints are appended into the equations of motion through Lagrange's multipliers. This formulation should be able to predict the nonlinear phenomena established by the nonlinear vibration theory. This can be achieved only if the constraint algebraic equations are modified to include all the system kinematic nonlinearities. This modification is accomplished by considering secondary nonlinear displacements which are ignored in all current codes. The resulting set of DAE are solved by the Gear stiff integrator. The study also introduced the concept of constrained flexibility and uses an instantaneous energy checking function to improve integration accuracy in the numerical scheme. The general energy balance is a single scalar equation containing all the energy component contributions. The DAE solution is then compared with the solution predicted by the nonlinear vibration theory. It also establishes new foundation for the use of multibody dynamics codes in nonlinear vibration problems. It is found that the simulation CPU time is much longer than the simulation of the original equations of the system.     

Theoretical investigation of combustion characteristics in ram-jet dump combustor with side-inlet

The combustion flow of a sudden-expansioin dump combustor with injecting side-inlet is analysed using the SIMPLE-C algorithm and the Jones-Launder k-? two-equation turbulence model. The transport properties of velocity, turbulence kinetic energy, temperature and combustion efficiency as a function of the injected mass fraction and the number of side-inlet nozzles are solved in this paper. The axial velocities of the sudden-expansion dump combustor without injected side-inlet flow are solved first and found to be in good agreement with the experimental data of Moon and Rudinger. For a fixed value of the side-inlet number the wall temperature and combustion efficiency of the dump combustor are decreased when the injected mass fraction is increased. For a fixed value of the injected mass fraction the wall temperature and combustion efficiency are decreased when the number of side-inlet nozzles is increased.     

Three-dimensional disturbances of planar viscometric flow

This paper examines three-dimensional disturbances of a plane steady shear flow of simple fluids with short memory. Under the assumption of nearly-viscometric flow, constitutive equations are derived and then a general form of the Reynolds-Orr energy equation is obtained. With the aid of this derived energy formula, sufficient conditions are generated for the stability of three-dimensional disturbances of the planar viscometric flow. These conditions are analysed and a comparison is made with the corresponding two-dimensional stability problem. There is a strong indication that the basic flow is less stable against three-dimensional disturbances than against two-dimensional ones.     

Energy distribution from vertical impact of a three-dimensional solid body onto the flat free surface of an ideal fluid

Hydrodynamic impact phenomena are three dimensional in nature and naval architects need more advanced tools than a simple strip theory to calculate impact loads at the preliminary design stage. Three-dimensional analytical solutions have been obtained with the help of the so-called inverse Wagner problem as discussed by Scolan and Korobkin in 2001. The approach by Wagner provides a consistent way to evaluate the flow caused by a blunt body entering liquid through its free surface. However, this approach does not account for the spray jets and gives no idea regarding the energy evacuated from the main flow by the jets. Clear insight into the jet formation is required. Wagner provided certain elements of the answer for two-dimensional configurations. On the basis of those results, the energy distribution pattern is analysed for three-dimensional configurations in the present paper.     

Velocity measurements on highly turbulent free surface flow using ADV

The 3D instantaneous velocity recorded with an acoustic Doppler velocimeter (ADV) in a highly turbulent free surface flow is analysed using several filters in order to eliminate the corrupted data from the sample. The filters used include the minimum/maximum threshold, the acceleration threshold, and the phase-space threshold. Following some ideas of the phase-space filter, a new method based on the 3D velocity cross-correlation is proposed and tested. A way of computing the constants of the acceleration threshold method is proposed, so no parameters need to be fixed by the user, which makes the filtering process simpler, more objective and more efficient. All the samples analysed are highly turbulent. Nevertheless, the turbulence intensity and the air entrainment vary widely in the flow under study, which produces data records of different quality depending on the measurement point. The performance of the filtering methods when applied to samples of different quality, and the effects of the filtering process in the mean velocity, turbulent kinetic energy and frequency spectra are discussed.     

A Derivation of the Volume-Averaged Boussinesq Equations for Flow in Porous Media with Viscous Dissipation

The volume-averaged equations are derived for convective flow in porous media. In the thermal energy equation viscous dissipation is taken into account, and a suitable form is obtained which is valid when Brinkman effects are significant.     

花岗岩破坏过程能量演化机制与能量屈服准则

为了明确岩石破坏的能量演化特性，结合单轴实验和颗粒流程序获得花岗岩的细观力学参数，进行不同应力状态的花岗岩实验，研究不同围压下花岗岩破坏过程的能量演化机理并推导能量屈服准则。获得以下主要结论:花岗岩破坏过程中低围压下内部损伤出现较早而高围压较晚，表明低围压花岗岩内部损伤是渐进发展过程，而高围压下内部损伤一旦出现便快速发展破坏；高围压花岗岩峰值前一定应变范围弹性应变能基本保持不变，吸收的能量全部转化为耗散能，表明高围压破坏时花岗岩内部损伤程度严重；弹性应变能经历不断积累并达到弹性储能极限而后减小的变化过程，而弹性储能极限与围压之间存在线性变化规律，因此高围压下岩体开挖卸荷时极易诱发大量弹性应变能的急剧释放，引起围岩失稳甚至发生岩爆；花岗岩峰值破坏时的能量比与围压无关，为一定值；基于能量原理导出了能量屈服准则，该准则包含岩性参数和所有主应力，能够综合反映岩石破坏影响因素。     

微重力环境下Marangoni对流的有限元数值模拟

本文以悬浮区为背景研究液桥中气液交界面上由表面张力所驱动的流体对流。我们采用有限元方法对轴对称、定常运动方程,能量方程,自由面切向、法向应力平衡条件迭代求解,首次考虑了边界形状的影响,得到了自洽的流区位形和流场、温度场、表面压强分布。一般说来,流区自由面呈弯月形。结果表明,只要表面张力数 C_a<1,静态平衡的流区位形就是动态情况的良好近似。本文还分析了C_a数及G_r 数对流区位形的影响,得到了不同 M_a 数及散热条件下的温度场和流函数分布。     

High performance parallel computing of flows in complex geometries

Efficient numerical tools taking advantage of the ever increasing power of high-performance computers, become key elements in the fields of energy supply and transportation, not only from a purely scientific point of view, but also at the design stage in industry. Indeed, flow phenomena that occur in or around the industrial applications such as gas turbines or aircraft are still not mastered. In fact, most Computational Fluid Dynamics (CFD) predictions produced today focus on reduced or simplified versions of the real systems and are usually solved with a steady state assumption. This article shows how recent developments of CFD codes and parallel computer architectures can help overcoming this barrier. With this new environment, new scientific and technological challenges can be addressed provided that thousands of computing cores are efficiently used in parallel. Strategies of modern flow solvers are discussed with particular emphases on mesh-partitioning, load balancing and communication. These concepts are used in two CFD codes developed by CERFACS: a multi-block structured code dedicated to aircrafts and turbo-machinery as well as an unstructured code for gas turbine flow predictions. Leading edge computations obtained with these high-end massively parallel CFD codes are illustrated and discussed in the context of aircrafts, turbo-machinery and gas turbine applications. Finally, future developments of CFD and high-end computers are proposed to provide leading edge tools and end applications with strong industrial implications at the design stage of the next generation of aircraft and gas turbines.     

Two-phase flow phenomena along an adiabatic riser – An experimental study at the test-facility GENEVA

Long adiabatic riser geometries with low system pressures are present in a lot of energy and petrochemical processes. Natural-circulation systems are an appropriate solution to save operating and maintenance costs. Under certain circumstances natural-circulation systems tend to unstable mass flow, especially in the riser section. The pressure gradients can stress the construction materials and affect the heat transfer. This paper focuses on GENEVA test-facility and its natural-circulation circuit with heat input by steam condensation. The GENEVA test-facility is explained in detail with focus on the local void fraction measurement system in the adiabatic riser section. The differences to former natural circulation test-facilities are particular emphasized. Therefore a transient experiment is presented and analysed. Moreover the influence of flow restrictions at the downcomer outlet is explained and an experimental method is presented, to determine the maximum natural circulation mass flow of the natural-circulation circuit. Besides, a comparison between the two different riser inner diameters, which were used during the experiments, is presented. The convective heat transfer is analysed by taking into account different dimensionless numbers. A variety of experiments were performed up to 100 kW_el input power from the evaporators. Flashing and geysering as two types of occurred instabilities are stated and discussed in comparison to former test-facilities. Further phenomena like water hammer and counter current liquid flow are investigated. Based on these analyses constructive solutions can be derived, to stabilize the presented natural-circulation two-phase flow system.     

The low Reynolds number turbulent flow and mixing in a confined impinging jet reactor

Turbulent mixing takes an important role in chemical engineering, especially when the chemical reaction is fast compared to the mixing time. In this context a detailed knowledge of the flow field, the distribution of turbulent kinetic energy (TKE) and its dissipation rate is important, as these quantities are used for many mixing models. For this reason we conduct a direct numerical simulation (DNS) of a confined impinging jet reactor (CIJR) at Re = 500 and Sc = 1. The data is compared with particle image velocimetry (PIV) measurements and the basic flow features match between simulation and experiment. The DNS data is analysed and it is shown that the flow is dominated by a stable vortex in the main mixing duct. High intensities of turbulent kinetic energy and dissipation are found in the impingement zone which decrease rapidly towards the exit of the CIJR. In the whole CIJR the turbulence is not in equilibrium. The strong mixing in the impingement zone leads to a rapid development of a monomodal PDF. Due to the special properties of the flow field, a bimodal PDF is generated in cross-sections downstream the impingement zone, that slowly relaxes under relaminarising conditions. The time required for meso-mixing is dominating the overall mixing performance.     

Flow and geometry induced scattering of high frequency acoustic duct modes

Cut-on cut-off transition of acoustic modes in hard-walled ducts with irrotational mean flow is well understood for Helmholtz numbers of order unity. Previous finite-element simulations of this phenomenon, however, appear to indicate the possibility of energy scattering into neighbouring modes at moderately large Helmholtz numbers. In this paper, such scattering phenomena are explained and predicted in slowly varying aeroengine ducts using a multiple-scales approach. It is found that, for sufficiently high frequencies, two mechanisms exist whereby energy can be scattered into neighbouring modes by an incident propagating mode. One mechanism occurs only when there is a mean flow inside the duct and induces scattering at significantly lower frequencies than the other mechanism which remains present without mean flow. A coupled system of ordinary differential equations is derived and then solved numerically for a number of example cases to obtain the corresponding transmitted and reflected amplitudes of the scattered modes as well as the overall acoustic pressure field. The theory appears to demonstrate that some exchange of energy between the acoustic and mean flow fields occurs during scattering.     

Stereoscopic multi-planar PIV measurements of in-cylinder tumbling flow

The non-reacting flow field within the combustion chamber of a motored direct-injection spark-ignition engine with tumble intake port is measured. The three-dimensionality of the flow necessitates the measurement of all three velocity components via stereoscopic particle-image velocimetry in multiple planes. Phase-locked stereoscopic PIV is applied at 15 crank angles during the intake and compression strokes, showing the temporal evolution of the flow field. The flow fields are obtained within a set of 14 axial planes, covering nearly the complete cylinder volume. The stereoscopic PIV setup applied to engine in-cylinder flow and the arising problems and solutions are discussed in detail. The three-dimensional flow field is reconstructed and analyzed using vortex criteria. The tumble vortex is the dominant flow structure, and this vortex varies significantly regarding shape, strength, and position throughout the two strokes. The tumble vortex center moves clockwise through the combustion chamber. At first, the tumble has a c-shape which turns into an almost straight tube at the end of the compression. Small-scale structures are analyzed by the distribution of the turbulent kinetic energy. It is evident that the symmetry plane only represents the 3D flow field after 100 CAD. For earlier crank angles, both kinetic energy (KE) and turbulent kinetic energy (TKE) in the combustion chamber are well below the KE and TKE in the symmetry plane. This should be taken into account when the injection and breakup of the three-dimensional fuel jet are studied. The mean kinetic energy is conserved until late compression by the tumble motion. This conservation ensures through the excited air motion an enhancement of the initial air-fuel mixture which is of interest for direct-injection gasoline engines.