Incompressible Wake Research Articles

Two-dimensional numerical simulation of flow around three-stranded rope

Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-e model and Shear-Stress Transport κ-ω (SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3–1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.

Large eddy simulation of passive scalar transport in a high Schmidt number turbulent incompressible wake with experimental validation

Large eddy simulation of the passive scalar transport in a high Schmidt number turbulent confined wake flow has been performed. The results are evaluated by comparison to particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) data, including point-wise data as well as spatial correlations. In the LES simulations, the gradient diffusion hypothesis is used to close the transport equation for the passive scalar. Different discretization schemes are investigated in order to determine the best choice for ensuring boundedness of the passive scalar and to accurately predict the mixing rate. The simulation results compare well to experimental data, demonstrating that the transport mechanisms in this high Schmidt number turbulent flow are well predicted by the LES method. Two-point spatial correlations of passive scalar with velocity predicted by the simulation show good agreement with the experimental results, indicating that the turbulent coherent structures of the flow are reproduced by the simulation.

Effect of inlet conditions on the accuracy of large eddy simulations of a turbulent rectangular wake

Abstract A large eddy simulation (LES) study was performed on a turbulent incompressible wake flow in a rectangular channel. The simulation results were evaluated using particle image velocimetry (PIV) data from a previous experimental study of the same flow (Liu et al., 2013). Comparisons were made of one-point statistics as well as spatial correlations. An extensive pre-simulation study was carried out in which the effect of inlet conditions, grid resolution, time step and subgrid model was investigated and the parameters were optimized. Using the digital filter method of Klein et al. (2003), turbulent inflow velocities were generated based on velocity mean and variance obtained from the experimental data and correlation length scales. It was found that the simulation results in large parts of the domain were strongly dependent on the inlet length scales specified. With a suitable set of length scales, the inlet method was successful at providing inlet conditions that generated accurate simulation results. The very good agreement seen between experiment and simulation demonstrates LES as a method that, with carefully selected inlet conditions, not only can predict the pointwise turbulence statistics of a liquid wake flow, but also capture key features of its large-scale turbulent structures.

Some studies on mechanics of continuous mediums viewed as differential manifolds

The continuous mediums are divided into two kinds according to their geometrical configurations, the first one is related to Euclidian manifolds and the other one to Riemannian manifolds/surfaces in the point of view of the modern geometry. Two kinds of finite deformation theories with respect to Euclidian and Riemannian manifolds have been developed in the present paper. Both kinds of theories include the definitions of initial and current physical and parametric configurations, deformation gradient tensors with properties, deformation descriptions, transport theories and governing equations of nature conservation laws. The essential property of the theory with respect to Euclidian manifolds is that the curvilinear coordinates corresponding to the current physical configurations include time explicitly through which the geometrically irregular and time varying physical configurations can be mapped in the diffeomorphism manner to the regular and fixed domains in the parametric space. It is quite essential to the study of the relationships between geometries and mechanics. The theory with respect to Riemannian manifolds provides the systemic ideas and methods to study the deformations of continuous mediums whose geometrical configurations can be considered as general surfaces. The essential property of the theory with respect to Riemannian manifolds is that the thickness variation of a patch of continuous medium is represented by the surface density and its governing equation is rigorously deduced. As some applications, wakes of cylinders with deformable boundaries on the plane, incompressible wakes of a circular cylinder on fixed surfaces and axisymmetric finite deformations of an elastic membrane are numerically studied.

Stability analysis of wakes with density gradient

This paper investigates the linear stability of wakes with special emphasis on the difference of velocity and density. Velocity and density profiles for laminar flows have gaussian profiles. Incompressible wakes have two generalized inflection points and two unstable modes-sinuous and varicose modes. Sinuous modes are more unstable than varicose modes irrespective of density variation, which shows wakes will be destabilized by sinuous modes. Large velocity difference and density difference lead to more unstable wakes due to large momentum difference.

Effect of compressibility on the global stability of axisymmetric wake flows

We study the linear dynamics of global eigenmodes in compressible axisymmetric wake flows, up to the high subsonic regime. We consider both an afterbody flow at zero angle of attack and a sphere, and find that the sequence of bifurcations destabilizing the axisymmetric steady flow is independent of the Mach number and reminiscent of that documented in the incompressible wake past a sphere and a disk (Natarajan & Acrivos, J. Fluid Mech., vol. 254, 1993, p. 323), hence suggesting that the onset of unsteadiness in this class of flows results from a global instability. We determine the boundary separating the stable and unstable domains in the (M, Re) plane, and show that an increase in the Mach number yields a stabilization of the afterbody flow, but a destabilization of the sphere flow. These compressible effects are further investigated by means of adjoint-based sensitivity analyses relying on the computation of gradients or sensitivity functions. Using this theoretical formalism, we show that they do not act through specific compressibility effects at the disturbance level but mainly through implicit base flow modifications, an effect that had not been taken into consideration by previous studies based on prescribed parallel base flow profiles. We propose a physical interpretation for the observed compressible effects, based on the competition between advection and production of disturbances, and provide evidence linking the stabilizing/destabilizing effect observed when varying the Mach number to a strengthening/weakening of the disturbance advection mechanism. We show, in particular, that the destabilizing effect of compressibility observed in the case of the sphere results from a significant increase of the backflow velocity in the whole recirculating bubble, which opposes the downstream advection of disturbances.

Role of long waves in the stability of the plane wake

This work is directed toward investigating the fate of three-dimensional long perturbation waves in a plane incompressible wake. The analysis is posed as an initial-value problem in space. More specifically, input is made at an initial location in the downstream direction and then tracing the resulting behavior further downstream subject to the restriction of finite kinetic energy. This presentation follows the outline given by Criminale and Drazin [W. O. Criminale and P. G. Drazin, Stud. Appl. Math. 83, 123 (1990)] that describes the system in terms of perturbation vorticity and velocity. The analysis is based on large scale waves and expansions using multiscales and multitimes for the partial differential equations. The multiscaling is based on an approach where the small parameter is linked to the perturbation property independently from the flow control parameter. Solutions of the perturbative equations are determined numerically after the introduction of a regular perturbation scheme analytically deduced up to the second order. Numerically, the complete linear system is also integrated. Since the results relevant to the complete problem are in very good agreement with the results of the first-order analysis, the numerical solution at the second order was deemed not necessary. The use for an arbitrary initial-value problem will be shown to contain a wealth of information for the different transient behaviors associated to the symmetry, angle of obliquity, and spatial decay of the long waves. The amplification factor of transversal perturbations never presents the trend--a growth followed by a long damping--usually seen in waves with wave number of order one or less. Asymptotical instability is always observed.

Finite point based numerical study on the unsteady laminar wake behind square cylinders

PurposeThe purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.Design/methodology/approachThe numerical method that has been developed is based on a finite point formulation characterised by its weak connectivity requirements. This formulation allows for a patched unstructured approach to computational domain modelling that is of interest for industrial applications. Time evolution of pressure is computed by using a pseudo‐compressibility relaxation model that is based on physical considerations.FindingsThis model is characterised by the fact that no sub‐iterations on a numerical pseudo‐time are required so that computational efficiency is increased. Algorithm stability requires the use of second and fourth order artificial viscosity operators that effectively change the order of the equations. A discussion is included regarding the boundary conditions for these operators that do not influence vortex shedding behaviour.Research limitations/implicationsBearing in mind the industrial drive (MEMS design) that the authors have in mind, solver validation has been addressed at two levels: global coefficients (lift, drag and Strouhal number) were compared with those published in the specialised literature, while local velocity and rms profiles were compared with those obtained after performing a specific low velocity wind tunnel testing campaign (Reynolds numbers in the range from 110 to 268).Practical implicationsA sensitivity analysis of the results obtained is presented and it shows that the solver numerical robustness makes it amenable for project oriented applications.Originality/valueThe formulation being presented is competitive and could be considered as a potential alternative to other approaches.

Scaling Properties and Wave Interactions in Confined Supersonic Turbulent Bluff-Body Wakes

Results are presented from an experimental study that compares the large-scale structure, mean velocities, and scaling properties of confined, supersonic, planar, turbulent, bluff-body wakes at M∞ ≈ 2 and 3 with corresponding results from incompressible wakes. The large-scale structure of incompressible planar turbulent wakes is recovered at downstream locations x where the local relative Mach number Mr(x) has decreased to about 0.4. Interactions between these large-scale structures and reflected expansion waves from the near-field recompression region lead to substantial changes in the scaling properties of the flow. Wave interactions with the flow create local self-induced forcing as the large-scale structures pass through the reflected expansion waves. In the M∞ ≈ 2 wake, a subsonic upstream path exists from the first wave interaction point that allows upstream propagation of the wave-induced forcing, and consequently the measured wake scaling constants match values reported from forced incompressible wakes. In the M∞ ≈ 3 wake, no subsonic upstream path exists from the first interaction point, and as a consequence the measured scaling constants match values reported from unforced incompressible wakes. Downstream of each wave interaction point, the self-induced forcing leads to an increase in the wake growth rate and in the entrainment of free-stream fluid. The wake subsequently detrains this fluid and returns to its original growth rate. This local forcing mechanism and its effects on the wake scaling properties repeat at each downstream location where the reflected expansion waves intersect the wake.

Asymptotic Expansions for Two Dimensional Symmetrical Laminar Wakes

A non parallel extension of the Gaussian asymptotic representation of the two dimensional laminar incompressible far wake past a symmetrical body is presented. Under the one and only condition that the middle and far field be governed by the thin shear layer theory that keeps the complete non linearity of the equation of motion, we determined a solution in terms of an infinite power series of the streamwise space variable with fractional negative exponents. The general n-th order term has been analytically established. The behaviour of these expansions inserted into the Navier-Stokes equations was analyzed to verify the consistency of the approximation in the intermediate region of the wake. At the third order the correction due to pressure variations identically vanishes while the contribution of the longitudinal diffusion is still two-three order of magnitude smaller than that of the transversal diffusion, depending on the Reynolds number.

Lagrange identification of absolutely unstable regimes in wakes

The development of a pulsewise perturbation in a two-dimensional incompressible wake is simulatd numerically using a vortex dynamics method. The main attraction of using vortex methods lies in their Lagrangian nature, which in inviscid flows preserves the identity of rotational fluid elements and thereby allows for the tracking of individual vortex lines or tubes. Because of the non-linearity of this novel approach to identify regions of local absolute and local converctive instability, the analysis is not restricted tio small amplitudes. Moreover the basic state does not have to be locally parallel, and the method is easily applicable to unsteady flows. A comparison of the resulting stability features of the symmetric wake profiles as determined by the numerical simulation with the prediction of the Orr-Sommerfeld analysis confirms the validity of the linear, local stability theory. An extension of the vortex dynamics method to rotational flow fields in which the effects of viscosity become important is enabled by the particle strength exchange scheme.

An interferometric study of organized structures in wakes of circular cylinders

Double-pulse, diffuse-illumination interferometry has been used to study the organized structures in the wake of a circular cylinder (M = 0.6,Red = 300,000). The interferograms show striking similarities to the flow visualization pictures of the incompressible wakes of circular cylinders as obtained by other investigators. In particular, the interferograms taken with very short pulse intervals show concentrations of fine scale turbulence in the von Karman vortices and the existence of streamwise vortices between these counter-rotating largescale vortices. The fact that most of the features observed in low speed wakes using a variety of techniques can be observed in the interferograms illustrated the potential of interferometry for the study of turbulent structures in compressible flows.

Analysis of a propeller in compressible, steady flow

THIS Synoptic describes an analytical method for solving the equation governing the inviscid, irrotational, compressible, potential flow about a propeller. The equation and boundary conditions are transferred to a noninertial system of coordinates rotating with the propeller, in which the basic problem becomes a steady one. The solution method takes advantage of the linearity of the model by superposing a compressible solution to the potential equation on an incompressible wake solution. In addition, the boundary conditions are satisfied by dividing the flowfield at the propeller plane, solving the equations separately ahead of and behind this plane, and enforcing continuity matching conditions. Applying the final boundary condition yields an infinite-series integral equation for the unknown circulation distribution. A lifting-line method is used to produce numerical results. Presented results establish the effect of compressibility on the induced field. Contents Except in the vicinity of the propeller and its wake, the flowfield caused by an advancing propeller in an inertial coordinate system may be considered irrotational and isentropic. This approach treats the viscous drag on the blade as inconsequential to the general induction theory. Consider a transformation of the linearized convective wave equation to a bladefixed coordinate system that rotates with the propeller at angular velocity w. This noninertial, cylindrical system (r, 6, z, t) is defined by r = r, 6 = 0 + ui, z = z, and t = t. Tildes represent quantities in the inertial, translating coordinate system. Performing these coordinate transformations gives the unsteady, linearized potential equation in the rotating system. Although the general methodology works for unsteady flows, this Synoptic focuses on the aerodynamics of the steady propeller, that is, a rigid propeller experiencing a uniform freestream. This allows the time-dependent terms to be excluded, since the flow now appears steady in the rotating, translating coordinates. Converting the dimensional spatial variables to dimensionless form (p = a>/-/£/and z = uz/U) and dropping the bar over the dimensionless z variable, the steady, potential equation becomes - M2p2 (1)

The effect of Mach number on the stability of a plane supersonic wake

Recent interest in supersonic combustion and problems of transatmospheric flight has prompted renewed research efforts in laminar–turbulent free-shear flow transition. In the present work, the influence of Mach number on the stability of supersonic planar wake flows is investigated to gain insight into the physics of linear, nonlinear, and three-dimensional (3-D) stages of transition. The effect of varying the relative phase difference between a fundamental instability mode and its subharmonic is investigated as a possible means of controlling the evolution of a wake. From a linear stability analysis, it is found that the influence of increasing Mach number is stabilizing, resulting in a growth rate at a Mach number of 3 which is 60% that of an incompressible wake. Direct numerical simulations of the time-dependent compressible Navier–Stokes equations in two and three dimensions are performed for a forced time-developing wake using a spectral collocation method. The results of the two-dimensional (2-D) simulations show the slow rollup of spanwise vortices at high Mach numbers that is attributed to the influence of baroclinic and dilatational effects. Finally, the results of three-dimensional simulations forced with the most unstable Kelvin–Helmholtz wave and a pair of oblique three-dimensional waves show that, depending on the initial phasing between the 2-D and 3-D waves, vortex loops may or may not form as a result of the interaction between the streamwise and spanwise vorticity.

A calculation method for two-dimensional wall-bounded turbulent flows

SummaryA method to calculate two-dimensional or axisymmetric, compressible, wall-bounded viscous flows is described. The solution procedure involves a finite-difference discretisation of the governing flow equations. A number of novel normal co-ordinate transformations are used to enable efficient use to be made of the computational grid points. The implementation of zero-, one- and two-equation turbulence models is described. Results are presented for a range of compressible boundary-layer flows, and for an incompressible wake/ boundary layer mixing flow.

Contribution to the theory of laminar momentumless wakes

The self-similar laws of decay of the velocity field in a plane momentumless viscous incompressible wake of a hydrodynamic propulsion system were first analyzed in [1]. Turbulent wakes in the near and far flow regions were investigated in [2] on the basis of an integral calculation method. In [3] the asymptotic laws of degeneration of the passive admixture concentration, temperature and velocity fields were obtained, making it possible to estimate the effect of purely molecular diffusion and convective transfer o the passive impurity concentration distribution in the wake. In the present paper the limiting self-similar solutions of the problem of a swirled momentumless viscous incompressible wake are obtained, together with the self-similar solutions of the problem of the development of a plane momentumless wake in a medium nonuniform with respect to temperature (passive admixture concentration).

Stability of an incompressible two-dimensional wake

In experimental investigations of the wake flow behind a plate, a monochromatic (in time) signal is usually observed immediately behind the end of the plate. Downstream, the signal is distorted and then becomes random, i.e., a turbulent flow regime is realized. Theoretically, a branch point is found at the experimentally observed frequency in the spectrum of three-dimensional perturbations of the problem linearized with respect to the steady solution [1]. Mattingly and Criminale [1] attribute all the characteristics of the observed signal to this point. As in other similar investigations, the mechanism of the appearance of the monochromatic signal in the near wake was not elucidated in [1]. In the present paper, the problem of the characteristic oscillations of the flow in the near wake is studied. The appearance of the monochromatic signal is explained by the presence in the near wake of a standing wave of the required frequency, the wave being formed by two scattering points. The first is the end of the plate, and the second the branch point in the spectrum of linear three-dimensional perturbations.

Blade Loading and Spanwise Effects on Wake Characteristics of Compressor Rotor Blade

An experimental investigation of the blade loading and spanwise effects on the rotor wake is presented. The investigation was limited to a study of a low subsonic and incompressible wake flow found downstream of a lightly loaded rotor. Measurements were made with a triaxial hot wire probe mounted in the stationary frame of reference at six radial and nine axial positions. At each measurement location, the rotor was run at different operating conditions to discern the effects of blade loading on the wake. Nearand far-wake measurements are given, including mean velocity and turbulence intensity characteristics. The loading and spanwise effects on rotor-wake characteristics were found to be substantial.

Calculation of axisymmetric jets and wakes with a three-equation model of turbulence

The concept of diffusion by bulk convection formulated by Bradshaw is applied to the transport equations for the turbulent kinetic energy, turbulent shear stress and an integral length scale. The resulting set of hyperbolic partial differential equations is solved by an explicit finite-difference scheme for the cases of incompressible axisymmetric wakes and jets in a coflowing air stream. It is found that the profiles of mean velocity and shear stress are almost insensitive to the empirical input whereas the profiles of kinetic energy are very sensitive.

The stability of an incompressible two-dimensional wake

The growth of small disturbances in a two-dimensional incompressible wake has been investigated theoretically and experimentally. The theoretical analysis is based upon inviscid stability theory wherein small disturbances are considered from both temporal and spatial reference frames. Through a combined stability analysis, in which small disturbances are permitted to amplify in both time and space, the relationship between the disturbance characteristics for the temporal and spatial reference frames is shown. In these analyses a quasi-uniform assumption is adopted to account for the continuously varying mean-velocity profiles that occur behind flat plates and thin airfoils. It is found that the most unstable disturbances in the wake produce transverse oscillations in the mean-velocity profile and correspond to growing waves that have a minimum group velocity.Experimentally, the downstream development of the wake of a thin airfoil and the wave characteristics of naturally amplifying small disturbances are investigated in a water tank. The disturbances that develop are found to produce transverse oscillations of the mean-velocity profile in agreement with the theoretical prediction. From the comparison of the experimental results with the predictions for the characteristics of the most unstable waves via the temporal and spatial analyses, it is concluded that the stability analysis for the wake is to be considered solely from the more realistic spatial viewpoint. Undoubtedly, this conclusion is also applicable to other highly unstable flows such as jets and free shear layers.In accordance with the disturbance vorticity distribution as determined from the spatial model, a description of the initial development of a vortex street is put forth that contrasts with the description given by Sato & Kuriki (1961).