Direct Numerical Simulation Of Hypersonic Boundary-Layer Transition Over A Blunt Cone

Direct numerical simulation of transition How over a blunt cone with a freestream Mach number of 6, Reynolds number of 10,000 based on the nose radius, and a 1-deg angle of attack is performed by using a seventh-order weighted essentially nonoscillatory scheme for the convection terms of the Navier-Stokes equations, together with an eighth-order central finite difference scheme for the viscous terms. The wall blow-and-suction perturbations, including random perturbation and multifrequency perturbation, are used to trigger the transition. The maximum amplitude of the wall-normal velocity disturbance is set to 1% of the freestream velocity. The obtained transition locations on the cone surface agree well with each other far both cases. Transition onset is located at about 500 times the nose radius in the leeward section and 750 times the nose radius in the windward section. The frequency spectrum of velocity and pressure fluctuations at different streamwise locations are analyzed and compared with the linear stability theory. The second-mode disturbance wave is deemed to be the dominating disturbance because the growth rate of the second mode is much higher than the first mode. The reason why transition in the leeward section occurs earlier than that in the windward section is analyzed. It is not because of higher local growth rate of disturbance waves in the leeward section, but because the growth start location of the dominating second-mode wave in the leeward section is much earlier than that in the windward section.

Thermocapillary Migration Of Nondeformable Drops

In this paper, we present a numerical study on the thermocapillary migration of drops. The Navier-Stokes equations coupled with the energy conservation equation are solved by the finite-difference front-tracking scheme. The axisymmetric model is adopted in Our simulations, and the drops are assumed to be perfectly spherical and nondeformable. The benchmark simulation starts from the classical initial condition with a uniform temperature gradient. The detailed discussions and physical explanations of migration phenomena are presented for the different values of (1) the Marangoni numbers and Reynolds numbers of continuous phases and drops and (2) the ratios of drop densities and specific heats to those of continuous phases. It is found that fairly large Marangoni numbers may lead to fluctuations in drop velocities at the beginning part of simulations. Finally, we also discuss the influence of initial conditions on the thermocapillary migrations. (C) 2008 American Institute of Physics.

A Pressure-Correction Method And Its Applications On An Unstructured Chimera Grid

In this paper, an unstructured Chimera mesh method is used to compute incompressible flow around a rotating body. To implement the pressure correction algorithm on unstructured overlapping sub-grids, a novel interpolation scheme for pressure correction is proposed. This indirect interpolation scheme can ensure a tight coupling of pressure between sub-domains. A moving-mesh finite volume approach is used to treat the rotating sub-domain and the governing equations are formulated in an inertial reference frame. Since the mesh that surrounds the rotating body undergoes only solid body rotation and the background mesh remains stationary, no mesh deformation is encountered in the computation. As a benefit from the utilization of an inertial frame, tensorial transformation for velocity is not needed. Three numerical simulations are successfully performed. They include flow over a fixed circular cylinder, flow over a rotating circular cylinder and flow over a rotating elliptic cylinder. These numerical examples demonstrate the capability of the current scheme in handling moving boundaries. The numerical results are in good agreement with experimental and computational data in literature. (C) 2007 Elsevier Ltd. All rights reserved.

A Linear Stability Analysis Of Large-Prandtl-Number Thermocapillary Liquid Bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 <= Pr <= 50). We focus on the relationships between the critical Reynolds number Re-c, the azimuthal wave number m, the aspect ratio F and the Prandtl number Pr. A detailed Re-c-Pr stability diagram is given for liquid bridges with various Gamma. In the region of Pr > 1, which has been less studied previously and where Re, has been usually believed to decrease with the increase of Pr, we found Re-c exhibits an early increase for liquid bridges with Gamma around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the "effective" part of liquid bridge. (c) 2008 Published by Elsevier Ltd on behalf of COSPAR.

Thermocapillary Motion Of Droplets At Large Marangoni Numbers

In this paper, the thermocapillary motion problem of drops is investigated using the axisymmetric model. The front-tracking method is employed to capture the drop interface. We find that the migration velocity of the drop is greatly influenced by the temperature field in the drop when Ma is fairly large (>100), which leads to an increase-decrease migration velocity at the beginning of our simulations. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Dns Of Compressible Turbulent Boundary Layer Around A Sharp Cone

Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20 degrees cone angle (or 10 degrees half-cone angle) is performed by using the mixed seventh-order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent energy budget is studied. The computed results show that the effect of circumferential curvature on turbulence characteristics is not obvious.

Time Correlations Of Pressure In Isotropic Turbulence

The time correlations of pressure modes in stationary isotropic turbulence are investigated under the Kraichnan and Tennekes "random sweeping" hypothesis. A simple model is obtained which predicts a universal form for the time correlations. It implies that the decorrelation process of pressure fluctuations in time is mainly dominated by the sweeping velocity, and the pressure correlations have the same decorrelation time scales as the velocity correlations. These results are verified using direct numerical simulations of isotropic turbulence at two moderate Reynolds numbers; the mode correlations collapse to the universal form when the time separations are scaled by wavenumber times the sweeping velocity, and the ratios of the correlation coefficients of pressure modes to those of velocity modes are approximately unity for the entire range of time separation. (c) 2008 American Institute of Physics.

Control Of Vortex Shedding From A Square Cylinder

Small circular, square, and thin-strip cross-sectional elements are used to suppress vortex shedding from a square cylinder at Reynolds numbers in the range of 1.12 x 10(4)-1.02 x 10(5). The axes of the element and cylinder are parallel. The element's size, position, and angle of attack are varied. Measurements of the fluctuating surface pressures and wake velocities, together with smoke flow visualization, show that vortex shedding from both sides of the cylinder is suppressed and the mean drag and fluctuating lift on the cylinder is reduced if the element is installed in an effective zone downstream of the cylinder. The effective zone of the circular element is shown to be much smaller than those of the other elements. The effects of Reynolds number and blockage ratio are investigated. A phenomenon of monoside vortex shedding is observed. The role of the element's bluffness is investigated and the suppression mechanism is discussed.

A Note On The Numerical Simulations Of Flow Past A Wavy Square-Section Cylinder

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Karman vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.

On separated shear layer of blunt circular cylinder

Separated shear layer of blunt circular cylinder has been experimentally investigated for the Reynolds numbers (based on the diameter) ranging from 2.8 x 10(3) to 1.0 x 10(5), with emphasis on evolution of separated shear layer, its structure and distribution of Reynolds shear stress and turbulence kinetic energy. The results demonstrate that laminar separated shear layer experiences 2 similar to 3 times vortex merging before it reattaches, and turbulence separated shear layer takes 5 similar to 6 times vortex merging. In addition, relationship between dimensionless initial frequencies of K-H instability and Reynolds numbers is identified, and reasons for the decay of turbulence kinetic energy and Reynolds shear stress in reattachment region are discussed.

MILU-CG method and the numerical study on the flow around a rotating circular cylinder

A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder at Re = 200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed. to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number.

Supersonic dusty-gas flows with Knudsen effect in interphase momentum exchange

On the basis of the two-continuum model of dilute gas-solid suspensions, the dynamic behavior of inertial particles in supersonic dusty-gas flows past a blunt body is studied for moderate Reynolds numbers, when the Knudsen effect in the interphase momentum exchange is significant. The limits of the inertial particle deposition regime in the space of governing parameters are found numerically under the assumption of the slip and free-molecule flow regimes around particles. As a model problem, the flow structure is obtained for a supersonic dusty-gas point-source flow colliding with a hypersonic flow of pure gas. The calculations performed using the full Lagrangian approach for the near-symmetry-axis region and the free-molecular flow regime around the particles reveal a multi-layer structure of the dispersed-phase density with a sharp accumulation of the particles in some thin regions between the bow and termination shock waves.

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise characteristic length linear stable mode may dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding. At Re = 250 and 300 it is found that the streamwise vortices evolve into a new type of mode - "dual vortex pair mode" downstream. The streamwise vortex structures switch among mode A, mode B and dual vortex pair mode from near wake to downstream wake. At Re = 250, an independent low frequency f(m) in addition to the vortex shedding frequency f(s) is identified. Frequency coupling between f(m) and f(s) occurs. These result in the irregularity of the temporal signals and become a key feature in the transition of the wake. Based on the formation analysis of the streamwise vorticity in the vicinity of cylinder, it is suggested that mode A is caused by the emergence of the spanwise velocity due to three dimensionality of the incoming flow past the cylinder. Energy distribution on various wave numbers and the frequency variation in the wake are also described.