An efficient algorithm for compressible flows with real gases

An efficient algorithm is presented for the solution of the Euler equations of gas dynamics with a general convex equation of state. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only one function evaluation in each computational cell is required by using a local parametrization of the equation of state. The scheme is applied to two standard test problems in gas dynamics for some specimen equations of state.     

An efficient shock-capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.     

Laser-induced fluorescence modulation techniques for velocity measurements in gas flows

Broadband fluorescence of iodine, excited at 514.5 nm by a single-mode argon-ion laser tuned to the quasi-linear part of an absorption line, was used to detect the Doppler shift and hence the velocity of iodine molecules seeded in a nitrogen jet flow. The slope of the absorption line profile was measured directly using a frequency shift introduced by acoustooptic modulators (AOMs). A velocity of 36 m/s was measured in a jet of N₂ at 60 Torr in 2 ms with an accuracy of 11%. To reduce experimental noise, the laser beams were switched at 125 KHz and signal-tuned amplification was used.     

Shocklets in compressible flows

The mechanism of shocklets is studied theoretically and numerically for the stationary fluid, uniform compressible flow, and boundary layer flow. The conditions that trigger shock waves for sound wave, weak discontinuity, and Tollmien-Schlichting （T-S） wave in compressible flows are investigated. The relations between the three types of waves and shocklets are further analyzed and discussed. Different stages of the shocklet formation process are simulated. The results show that the three waves in compressible flows will transfer to shocklets only when the initial disturbance amplitudes are greater than the certain threshold values. In compressible boundary layers, the shocklets evolved from T-S wave exist only in a finite region near the surface instead of the whole wavefront.     

Velocity measurement of compressible air flows utilizing a high-speed video camera

PIV-measurements of the flow above a pitching airfoil were conducted in a transonic wind tunnel. An ultra high-speed video camera was used for separate recording of two exposures. The data was analysed using the cross-correlation method. The results show the applicability of the technique in high speed flows.     

Computation of compressible flows with high density ratio and pressure ratio

The WENO method, RKDG method, RKDG method with original ghost fluid method, and RKDG method with modified ghost fluid method are applied to singlemedium and two-medium air-air, air-liquid compressible flows with high density and pressure ratios： We also provide a numerical comparison and analysis for the above methods. Numerical results show that, compared with the other methods, the RKDG method with modified ghost fluid method can obtain high resolution results and the correct position of the shock, and the computed solutions are converged to the physical solutions as themesh is refined.     

Calculations of 3D compressible flows using an efficient low diffusion upwind scheme

A newly suggested E‐CUSP upwind scheme is employed for the first time to calculate 3D flows of propulsion systems. The E‐CUSP scheme contains the total energy in the convective vector and is fully consistent with the characteristic directions. The scheme is proved to have low diffusion and high CPU efficiency. The computed cases in this paper include a transonic nozzle with circular‐to‐rectangular cross‐section, a transonic duct with shock wave/turbulent boundary layer interaction, and a subsonic 3D compressor cascade. The computed results agree well with the experiments. The new scheme is proved to be accurate, efficient and robust for the 3D calculations of the flows in this paper. Copyright © 2005 John Wiley & Sons, Ltd.     

Properties of the iodine molecule relevant to laser-induced fluorescence experiments in gas flows

Laser-induced fluorescence of iodine seed molecules can be used for both flow visualization and accurate measurements of gasdynamic properties. This paper gives an introductory review of the use of iodine in experimental fluid mechanics, including basic formulas for saturated and non-saturated fluorescence (excited with narrowband or broadband lasers), line shape, line strength and quenching behavior. Techniques for the seeding of the molecules into the gas flow and the safe handling of the gas are discussed. Finally, a simple numerical example is given for the calculation of absorption and fluorescence signals with discussion of the measurement of gasdynamic properties.     

Principles and application of velocimetry-based planar pressure imaging in compressible flows with shocks

The paper addresses the computation of pressure fields from velocimetry data, such as provided by Particle Image Velocimetry (PIV), with specific attention to its application in compressible flows with shocks. An essential extension with respect to incompressible flow is that in view of the variable density occurring in compressible flow, the velocimetry data has to be supplemented with additional relations, derived from the flow governing equations. Secondly, compressible flows display specific flow features, notably shocks but also thin shear layers, that pose particular difficulties for the flow velocity measurement itself, as well as for the subsequent determination of the pressure field. The present communication addresses the basic principles of the pressure-field extraction method, as well as its feasibility of application under realistic experimental conditions.     

An extension of the TV-HLL scheme for multi-dimensional compressible flows

This paper investigates a very simple method to numerically approximate the solution of the multi-dimensional Riemann problem for gas dynamics, using the literal extension of the Toro Vazquez-Harten Lax Leer (TV-HLL) scheme as its basis. Indeed, the present scheme is obtained by following the Toro–Vazquez splitting, and using the HLL algorithm with modified wave speeds for the pressure system. An essential feature of the TV-HLL scheme is its simplicity and its accuracy in computing multi-dimensional flows. The proposed scheme is carefully designed to simplify its eventual numerical implementation. It has been applied to numerical tests and its performances are demonstrated for some two-dimensional and three-dimensional test problems.     

Modelling far-field entrainment in compressible flows

A procedure that generates steady-states with accurate far-field entrainment is described here. It can be applied to any existing code originally designed for unsteady simulations. Such steady-states are obtained with physical-time damping, introduced through a dual time stepping methodology to effectively eliminate all transient fluctuations without affecting spatial resolution. Far-field entrainment is guaranteed by using properly selected local boundary conditions. Hence, reference profiles with accurate far-field entrainment are generated from the very same code that will eventually use them in unsteady simulations. This new procedure is tested on an unsteady code designed for compressible planar mixing-layer simulations at arbitrary Mach numbers. It is numerically stable for a wide range of Mach numbers and velocity ratios.     

An implicit Lagrangian lattice Boltzmann method for the compressible flows

In this paper, we propose a new Lagrangian lattice Boltzmann method (LBM) for simulating the compressible flows. The new scheme simulates fluid flows based on the displacement distribution functions. The compressible flows, such as shock waves and contact discontinuities are modelled by using Lagrangian LBM. In this model, we select the element in the Lagrangian coordinate to satisfy the basic fluid laws. This model is a simpler version than the corresponding Eulerian coordinates, because the convection term of the Euler equations disappears. The numerical simulations conform to classical results. Copyright © 2006 John Wiley & Sons, Ltd.     

An immersed boundary method for simulation of inviscid compressible flows

In this paper, an immersed boundary method for simulating inviscid compressible flows governed by Euler equations is presented. All the mesh points are classified as interior computed points, immersed boundary points (interior points closest to the solid boundary), and exterior points that are blanked out of computation. The flow variables at an immersed boundary point are determined via the approximate form of solution in the direction normal to the wall boundary. The normal velocity is evaluated by applying the no‐penetration boundary condition, and therefore, the influence of solid wall in the inviscid flow is taken into account. The pressure is computed with the local simplified momentum equation, and the density and the tangential velocity are evaluated by using the constant‐entropy relation and the constant‐total‐enthalpy relation, respectively. With a local coordinate system, the present method has been extended easily to the three‐dimensional case. The present work is the first endeavor to extend the idea of hybrid Cartesian/immersed boundary approach to compressible inviscid flows. The tedious task of handling multi‐valued points can be eliminated, and the overshoot resulting from the extrapolation for the evaluation of flow variables at exterior points can also be avoided. In order to validate the present method, inviscid compressible flows over fixed and moving bodies have been simulated. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

An efficient algorithm for hypersonic viscous flows

The CSCM-S algorithm proposed by Lombard et al. is a very attractive tool for solving multidimensional Euler and Navier-Stokes equations. However, it is not economical due to the use of global sweeps in the whole computational domain. In this paper we suggest a modified strategy, which combines a single-marching technique for supersonic dominated region with a multi-sweep procedure for pure subsonic and complex flowfield. The new algorithm may save significantly CPU time and is more suitable for engineering applications. The project supported by National Natural Science Foundation of China     

An effective limiting algorithm for particle-based numerical simulations of compressible flows

Eulerian computational fluid dynamics (CFD) and Lagrangian computational structural dynamics (CSD) are used extensively in the aerospace industry. Combined mesh-based Eulerian and particle-based Lagrangian algorithms arevery effective for modelling and simulation due to the increased efficiency of combining the two numerical simulations. However, when compressible flows are simulated using a particle-based algorithm, calculations of strong discontinuity, such as a shock wave, may become unstable. In the present study, a numerical limiter is integrated with a particle-based CFD code to remedy this instability. The limiting algorithm incorporates an ‘averaging’ technique which calculates average values using the properties of neighbouring particles (also known as material points), including mass, momentum and energy. These averaged values are then input to a min-mode limiter to eliminate numerical noise and incur dissipation in the flow in areas with steep property gradients. The results of this algorithm show very stable solutions with minimal oscillations when applied to the one-dimensional shock tube problem and an increased accuracy with reduced oscillations for a two-dimensional cylinder cross-flow problem.     

A segregated method for compressible flow computation Part I: isothermal compressible flows

Traditionally, coupled methods have been employed for the computation of compressible flows, whereas segregated methods have been preferred for the computation of incompressible flows. Compared to coupled methods, segregated solvers present the advantage of reduced computer memory and CPU time requirements, although at the cost of an inferior robustness. Therefore, in a series of papers we present unified computational techniques to compute compressible and incompressible flows with segregated stabilized methods. The proposed algorithms have an increased robustness compared to existing techniques, while possessing additional benefits such as employing standard pressure boundary conditions. In this first part, the thermodynamics of isothermal, thermally perfect compressible flows is set up in the framework of symmetric systems and the corresponding segregated algorithms are introduced. Copyright © 2005 John Wiley & Sons, Ltd.     

Self-similar turbulent compressible gas flows in a channel

In this study we establish for turbulent compressible gas flow (to within a constant factor) the laws governing the variation of the height (radius) and the static pressure along the length of a planar or axisymmetric channel for which the longitudinal velocity component and gas temperature are functions only of the transverse dimensionless coordinate. In such channels the gas density decrease due to friction is compensated by the increase of the cross-sectional area so that the velocity and temperature profiles remain unchanged at all sections of the channel.The results obtained are a generalization to the gas case of the known laws governing the turbulent flow of an incompressible fluid in a cylindrical channel.The author wished to thank A. P. Byrkin for helpful discussions.     

Friction characteristics of compressible gas flows in microtubes

The characteristics of a gaseous flow of nitrogen in commercial stainless steel microtubes for gas chromatography having a nominal inner diameter of 762, 508, 254 and 127 μm are experimentally investigated. The friction factor is calculated as a function of the Reynolds number and plotted in a Moody chart. A comparison among three different methods to calculate the friction factor is made in order to evidence limitations and advantages of each method. It was observed that in the laminar regime the Poiseuille law correctly predicts the value of the pressure drop. It has been evidenced that in order to make accurate experiments on the frictional characteristics of commercial microtubes the value of the inner diameter given by the manufacturer has to be always verified. The experimental data presented in this work remark how in microtubes the compressibility effects related to the axial variation of the gas density tend to become important at large Reynolds numbers and small diameters even if the average Mach number is low. The effects due to the gas acceleration on the laminar-to-turbulent transition in microtubes are investigated by evidencing the role of the L/D (length to diameter) ratio on the transition to turbulence. No early transition to turbulence has been evidenced in the tests, instead it takes place at Reynolds numbers ranging between 1800 and 2900.     

An efficient unstructured WENO method for supersonic reactive flows

An efficient high-order numerical method for supersonic reactive flows is proposed in this article. The reactive source term and convection term are solved separately by splitting scheme. In the reaction step, an adaptive time-step method is presented, which can improve the efficiency greatly. In the convection step, a third-order accurate weighted essentially non-oscillatory (WENO) method is adopted to reconstruct the solution in the unstructured grids. Numerical results show that our new method can capture the correct propagation speed of the detonation wave exactly even in coarse grids, while high order accuracy can be achieved in the smooth region. In addition, the proposed adaptive splitting method can reduce the computational cost greatly compared with the traditional splitting method.     

A segregated method for compressible flow computation. Part II: general divariant compressible flows

Typically, segregated methods have been used for the computation of incompressible flows whereas coupled solvers, for compressible flows. Compared to coupled solvers, segregated methods present the advantage of computational savings in RAM memory and CPU time, although at the cost of an inferior robustness. However, previously published segregated algorithms for general compressible flows are known to present pitfalls, like convergence to wrong solutions, lack of robustness in the presence of strong discontinuities, such as normal and oblique shocks, and complicated boundary condition imposition. Therefore, in this paper a segregated method for non‐isothermal compressible flows is proposed that preserves the thermodynamic coupling and overcomes the criticisms of existing methods. Copyright © 2005 John Wiley & Sons, Ltd.