Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers

Transient wake flow patterns and dynamic forces acting on a rotating spherical particle with non-uniform surface blowing are studied numerically for Reynolds numbers up to 300 and dimensionless angular velocities up to Ω=1. This range of Reynolds numbers includes the three distinct wake regimes i.e., the steady axisymmetric, the steady non-symmetrical and the unsteady with vortex shedding. The Navier–Stokes equations for an incompressible viscous flow are solved by a finite volume method in a three-dimensional, time accurate manner. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that unsteady three-dimensional wake flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects and thus, vortex shedding occurs even at Re=200. Global properties, such as the lift and drag coefficients, and the Strouhal number are also significantly affected. It is shown that the present data for the average lift and drag coefficients correlate well with:

C_L/(1+Ω)^3.6=0.11

C_D(1+20V_S)^0.2/(1+Ω)^Re/1000=24(1+Re^2/3/6)/Re

where V_S is the average surface blowing velocity normalized by the free stream velocity.     

Development of a MEMS-based control system for compressible flow separation

A MEMS-based sensor and actuator system has been designed and fabricated for separation control in the compressible flow regime. The MEMS sensors in the system are surface-micromachined shear stress sensors and the actuators are bulk-micromachined balloon vortex generators (VGs). A three-dimensional (3-D) wing model embedded with the shear stress sensors and balloon VGs was tested in a transonic wind tunnel to evaluate the performance of the control system in a range of Mach number between 0.2 and 0.6. At each Mach number tested, the shear stress sensors quantify the boundary layer on the surface of the wing model while the balloon VGs interact with the boundary layer in an attempt to provide flow control. The shear stress measurements indicate the presence of a separated flow on the trailing ramp section of the wing model at all Mach numbers tested when the balloon VGs are not activated. This result is confirmed by total pressure measurements downstream from the wing model where a wake profile is observed. When the balloon VGs are activated, the shear stress level on the trailing ramp increases with the Mach number. At the highest Mach number tested, this increase elevates the shear stress on the ramp to almost the same level as the unseparated flow, suggesting the possibility of a boundary layer reattachment. This result is supported by the downstream pressure measurements which show a large pressure recovery when the balloon VGs are activated. The wind tunnel experiment successfully demonstrated two aspects of the MEMS flow control system: the effectiveness of the microshear stress sensors in measuring the separation characteristics of a high-speed compressible flow and the ability of the microballoons in positively enhancing the aerodynamic performance of a high-speed wing through boundary layer modification.     

Direct numerical simulation of flow separation around a NACA 0012 airfoil

Direct numerical simulation (DNS) for the flow separation and transition around a NACA 0012 airfoil with an attack angle of 4° and Reynolds number of 10⁵ based on free-stream velocity and chord length is presented. The details of the flow separation, detached shear layer, vortex shedding, breakdown to turbulence, and re-attachment of the boundary layer are captured in the simulation. Though no external disturbances are introduced, the self-excited vortex shedding and self-sustained turbulent flow may be related to the backward effect of the disturbed flow on the separation region. The vortex shedding from the separated free shear layer is attributed to the Kelvin-Helmholtz instability.     

Nonlocal vibration and instability analysis of carbon nanotubes conveying fluid considering the influences of nanoflow and non-uniform velocity profile

In this article, the influences of non-uniform velocity profile attributable to slip boundary condition and viscosity of fluid on the dynamic instability of carbon nanotubes (CNTs) conveying fluid are investigated. The nonlocal elasticity theory and the Euler–Bernoulli beam theory are employed to derive partial differential equation of nanotubes conveying fluid. Furthermore, a dimensionless momentum correction factor (MCF) is obtained as a function of Knudsen number (Kn) so as to insert the effects of non-uniform velocity profile into the equation of motion. In continuation, complex eigen-frequencies of the system are attained with respect to different boundary conditions, the momentum correction factor, slip boundary condition and nonlocal parameter. The results delineate that considering the effects of non-uniform velocity profile could diminish predicted critical velocity of flow. Therefore, the divergence instability occurs in the lower values of flow velocity. In addition, the MCF decreases through enhancement of Kn; hence, the effects of non-uniform velocity profile are more noticeable for liquid fluid than gas fluid.     

Compressible laminar flow around a wall-mounted cubic obstacle

The fully-compressible, viscous and non-stationary Navier-Stokes equations are solved for the subsonic flow over a block placed on the floor of a channel. The Reynolds number is varied from 50 to 250. The Mach number is varied between 0.1 and 0.6. In all cases studied the flow field proves to be steady. Several distinct flow features are identified: a horseshoe vortex system, inward bending flow at the side walls of the obstacle, a horizontal vortex at the downstream upper-half of the obstacle and a downstream wake containing two counter-rotating vortices. The shape and size of these flow features are mainly dominated by the Reynolds number. For higher Reynolds numbers, both the horseshoe vortex and the wake region extend over a significantly larger area. The correlation of the position of the separation and attachment point with the Reynolds number has been calculated. Increasing the Mach number (at a fixed Reynolds number of 150) shows its influence in the reduced size, due to compression, of both the wake region and the horseshoe vortex.     

Spectral simulations of an unsteady compressible flow past a circular cylinder

An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an ‘improper’ boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.     

Optimal control of cylinder wakes via suction and blowing

A general method based on adjoint formulation is discussed for the optimal control of distributed parameter systems (including boundary parameter) which is especially suitable for large dimensional control problems. Strategies for efficient and robust implementation of the method are described. The method is applied to the problem of controlling vortex shedding behind a cylinder (through suction/blowing on the cylinder surface) governed by the unsteady two-dimensional incompressible Navier-Stokes equations space discretized by finite-volume approximation with time-dependent boundary conditions. Three types of objective functions are considered, with regularization to circumvent ill-posedness. These objective functions involve integration over a space-time domain. The minimization of the cost function uses a quasi-Newton DFP method.A complete control of vortex shedding is demonstrated for Reynolds numbers up to 110. The optimal values of the suction/blowing parameters are found to be insensitive to initial conditions of the model when the time window of control is larger than the vortex shedding period, the inverse of the Strouhal frequency. Although this condition is necessary for robust control, it is observed that a shorter window of control may suffice to suppress vortex shedding.     

Experimental investigation on the flow transition in different pin-fin arranged microchannels

The flow characteristics of water through the in-line and staggered pin-fin microchannels with length of 25 mm, width of 2.4 mm and height of 0.11 mm were studied experimentally. The flow transition was identified as a sudden increasing slope in both pressure drop versus mass flow rate curve and friction factor versus Reynolds number curve for in-line pin-fin microchannels, but it did not occur for staggered pin-fin microchannels. The effect of pin-fin arrangements on the flow transition was not reported in the previous literature. With the aid of microparticle image velocimetry (Micro-PIV) technology, the streamlines, velocity fields and velocity fluctuation fields of flow through the pin-fin microchannels were captured to explain the flow transition, and the effect of pin-fin arrangements on the flow transition was analyzed for the first time. It was found that at the critical Reynolds number where the flow transition occurred for the in-line pin-fin microchannels, the steady double-vortex wake flow changed to the unsteady vortex-shedding wake flow. The occurrence of vortex shedding caused an obvious change in main stream from straight flow to wavy flow and further induced significant increases of transversal velocity and velocity fluctuations, which induced strong flow disturbance in transversal directions and large additional pressure drop, and finally caused the flow transition in the in-line pin-fin microchannels. For the staggered pin-fin microchannels, the main stream through the pin-fin arrays was found to be already the wavy flow before the vortex shedding. Thus, the transversal velocity and velocity fluctuations induced by the vortex shedding were relatively small, and therefore, the flow transition with an abrupt pressure drop increase was not observed in the staggered pin-fin microchannels.     

Pressure-driven diffusive gas flows in micro-channels: from the Knudsen to the continuum regimes

Despite the enormous scientific and technological importance of micro-channel gas flows, the understanding of these flows, by classical fluid mechanics, remains incomplete including the prediction of flow rates. In this paper, we revisit the problem of micro-channel compressible gas flows and show that the axial diffusion of mass engendered by the density (pressure) gradient becomes increasingly significant with increased Knudsen number compared to the pressure driven convection. The present theoretical treatment is based on a recently proposed modification (Durst et al. in Proceeding of the international symposium on turbulence, heat and mass transfer, Dubrovnik, 3–18 September, pp 25–29, 2006) of the Navier–Stokes equations that include the diffusion of mass caused by the density and temperature gradients. The theoretical predictions using the modified Navier–Stokes equations are found to be in good agreement with the available experimental data spanning the continuum, transition and free-molecular (Knudsen) flow regimes, without invoking the concept of Maxwellian wall-slip boundary condition. The simple theory also results in excellent agreement with the results of linearized Boltzmann equations and Direct Simulation Monte Carlo (DSMC) method. Finally, the theory explains the Knudsen minimum and suggests the design of future micro-channel flow experiments and their employment to complete the present days understanding of micro-channel flows.     

Hybrid vortex method for high Reynolds number flows around three-dimensional complex boundary

The hybrid vortex method, in which the vortex particle method was combined with the vortex sheet method, was extended to flows around a three-dimensional complex geometry boundary at high Reynolds number of O(10⁶). The computing domain was decomposed into an interior domain of vortex blobs and a thin numerical boundary layer of vortex sheets. The core radii of shedding blobs were related to the size of the vortex sheets. As the result of numerical experiments on the flow over a ship propeller, the hybrid vortex method was found to be acceptable for simulations of unsteady separated flows around a solid body at high Reynolds number, since the computed results showed reasonable agreement with the measured data.     

GPU acceleration for general conservation equations and its application to several engineering problems

In the this paper, shock/shock and shock/boundary layer interactions in thermochemical nonequilibrium flow have been analyzed. The analysis is limited to flow at Mach 9 around a double-wedge selected to generate an interaction of type IVr that does not fit into Edney’s classification. It is generally known that the interaction of type IV are associated with very high local loads in pressure and heat transfer. The numerical resolution of the Navier Stokes equations allows the prediction of the structure of flow field. The numerical method used is based on a finite volume formulation defined on a structured multi block mesh. Particular emphasis is given to the contribution of real gas effects on the topological characteristics and dynamic structure of the flow field. A comparative study of the contours of Mach numbers and pressure is shown. The results obtained showed that the flow field is highly sensitive to real gas effects.     

LES of bubble dynamics in wake flows

The results of large eddy simulations (LES) of turbulent bubbly wake flows are presented. The LES technique was applied together with the Lagrangian particle dynamics method and a random flow generation (RFG) technique to the cases of a two-phase bubbly mixing layer and the high-Reynolds number bubbly ship-wake flows. The validation was performed on the experimental data for the bubbly mixing layer. Instantaneous distributions and probability density functions of bubbles in the wake were obtained using a joint LES/RFG approach. Separate estimates of bubble decay due to dissolution and buoyancy effects were obtained. The analysis of bubble agglomeration effects was done on the basis of experimental data for a turbulent vortex to satisfy one-way coupling that is used in this study.     

Improved Incompressible Smoothed Particle Hydrodynamics method for simulating flow around bluff bodies

In this article, we present numerical solutions for flow over an airfoil and a square obstacle using Incompressible Smoothed Particle Hydrodynamics (ISPH) method with an improved solid boundary treatment approach, referred to as the Multiple Boundary Tangents (MBT) method. It was shown that the MBT boundary treatment technique is very effective for tackling boundaries of complex shapes. Also, we have proposed the usage of the repulsive component of the Lennard-Jones Potential (LJP) in the advection equation to repair particle fractures occurring in the SPH method due to the tendency of SPH particles to follow the stream line trajectory. This approach is named as the artificial particle displacement method. Numerical results suggest that the improved ISPH method which is consisting of the MBT method, artificial particle displacement and the corrective SPH discretization scheme enables one to obtain very stable and robust SPH simulations. The square obstacle and NACA airfoil geometry with the angle of attacks between 0° and 15° were simulated in a laminar flow field with relatively high Reynolds numbers. We illustrated that the improved ISPH method is able to capture the complex physics of bluff-body flows naturally such as the flow separation, wake formation at the trailing edge, and the vortex shedding. The SPH results are validated with a mesh-dependent Finite Element Method (FEM) and excellent agreements among the results were observed.     

Steady flow around and through a permeable circular cylinder

The steady flow around and through a porous circular cylinder was studied numerically. The effects of the two important parameters, the Reynolds and Darcy numbers, on the flow were investigated in details. The recirculating wake existing downstream of the cylinder is found to either penetrate into or be completely detached from the cylinder. It is also found that, contrary to that of the solid cylinder, the recirculating wake develops downstream of or within the porous cylinder, but not from the surface of it. These new findings provide additional evidence to Leal’s conclusion (Leal LG. Vorticity transport and wake structure for bluff bodies at finite Reynolds number. Phys Fluids A 1989;1:124) that the appearance of recirculating wakes at finite Reynolds number is due to vorticity accumulation, but not a result of the same physical phenomena associated with separation in boundary layers in adverse pressure gradients. Also presented in the current study are the variation of the critical Reynolds number for the onset of a recirculating wake as a function of Darcy number and the variation of a newly defined parameter, the penetration depth, as a function of the Reynolds number and Darcy number.     

Vortex shedding from confined micropin arrays

The hydrodynamics in microcavities populated with cylindrical micropins was investigated using dynamic pressure measurements and fluid pathline visualization. Pressure signals were Fourier-analyzed to extract the flow fluctuation frequencies, which were in the kHz range for the tested flow Reynolds numbers (Re) of up to 435. Three different sets of flow dependent characteristic frequencies were identified, the first due to vortex shedding, the second due to lateral flow oscillation and the third due to a transition between these two flow regimes. These frequencies were measured at different locations along the chip (e.g. inlet, middle and outlet). It is established that vortex shedding initiates at the outlet and then travels upstream with increase in Re. The pathline visualization technique provided direct optical access to the flow field without any intermediate post-processing step and could be used to interpret the frequencies determined through pressure measurements. Microcavities with different micropin height-to-diameter aspect ratios and pitch-to-diameter ratios were tested. The tests confirmed an increase in the Strouhal number (associated with the vortex shedding) with increased confinement (decrease in the aspect ratio or the pitch), in agreement with macroscale measurements. The compact nature of the microscale geometry tested, and the measurement technique demonstrated, readily enabled us to investigate the flow past 4,420 pins with various degrees of confinements; this makes the measurements performed and the techniques developed here an important tool for investigating large arrays of similar objects in a flow field.     

DNS for flow separation control around an airfoil by pulsed jets

Direct numerical simulation (DNS) for flow separation and transition around a NACA-0012 airfoil with an attack angle of 4° and Reynolds number of 100,000 has been reported in our previous paper. The details of flow separation, formation of the detached shear layer, Kelvin-Helmholtz instability (inviscid shear layer instability) and vortex shedding, interaction of nonlinear waves, breakdown, and re-attachment are obtained and analyzed. The power spectral density of pressure shows the low frequency of vortex shedding caused by the Kelvin-Helmholtz instability still dominates from the leading edge to trailing edge. Based on our understanding on the flow separation mechanism, we try to reveal the mechanism of the flow separation control using blowing jets and then optimize the jets. DNS simulations for flow separation control by blowing jets (pulsed and pitched and skewed jets) are reported and analyzed. The effects of different unsteady blowing jets on the surface at the location just before the separation points are studied. The length of separation bubble is significantly reduced (almost removed) after unsteady blowing technology is applied. The mechanism of early transition caused by the blowing jets was found. A blowing jet with K-H frequency, sharp shape function (very small mass blowing), pitching and skewing obtained the best efficiency based on the increase of the ratio of lift over drag and decrease of blowing mass flow. In this work, a DNS code with high-order accuracy and high-resolution developed by the computational fluid dynamics group at University of Texas at Arlington is applied.     

Numerical solution of incompressible Navier–Stokes equations using a fractional-step approach

A fractional step method for the solution of steady and unsteady incompressible Navier–Stokes equations is outlined. The method is based on a finite-volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (third and fifth) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when fifth-order upwind differencing and a modified production term in the Baldwin–Barth one-equation turbulence model are used with adequate grid resolution.     

Effects of slip on sheet-driven flow and heat transfer of a non-Newtonian fluid past a stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian fluid due to a stretching surface subject to partial slip is considered. The constitutive equation of the non-Newtonian fluid is modeled by that for a third grade fluid. The heat transfer analysis has been carried out for two heating processes, namely, (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHFcase) in presence of a uniform heat source or sink. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip, magnetic field, heat source (sink) parameter and the third grade fluid parameters on the velocity, skin friction coefficient and the temperature field. It is interesting to find that slip decreases the momentum boundary layer thickness and increases the thermal boundary layer thickness, whereas the third grade fluid parameter has an opposite effect on the thermal and velocity boundary layers.     

Effect of the skimming layer on electro-osmotic��Poiseuille flows of viscoelastic fluids

An analytical solution is derived for the micro-channel flow of viscoelastic fluids by combined electro-osmosis and pressure gradient forcing. The viscoelastic fluid is described by the Phan-Thien–Tanner model with due account for the near-wall layer depleted of macromolecules. This skimming layer is wider than the electric double layer (EDL) and leads to an enhanced flow rate relative to that of the corresponding uniform concentration flow case. The derived solution allows a detailed investigation of the flow characteristics due to the combined effects of fluid rheology, forcing strengths ratio, skimming layer thickness and relative rheology of the two fluids. In particular, when the EDL is much thinner than the skimming layer and simultaneously the viscosity of the Newtonian fluid inside this layer is much lower than that of the fluid outside, the flow is dominated by the characteristics of the Newtonian fluid. Outside these conditions, proper account of the various fluid layers and their properties must be considered for an accurate prediction of the flow characteristics. The analytical solution remains valid for the flow driven by a pressure gradient and its streaming potential, which is determined in the appendix.