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.     

Numerical simulation of flow past row of square cylinders for various separation ratios

A systematic study for the flow around a row of five square cylinders placed in a side-by-side arrangement and normal to the oncoming flow at a Reynolds number of 150 is carried out through the numerical solution of the two-dimensional unsteady incompressible Navier-Stokes equations. Special attention is paid to investigate the effect of the spacing between the five cylinders on the wake structure and vortex shedding mechanism. The simulations are performed for the separation ratios (spacing to size ratio) of 1.2, 2, 3 and 4. Depending on the separation ratio the following flow patterns are observed: a flip-flopping pattern, in-phase and anti-phase synchronized pattern and non-synchronized pattern. These flow patterns are supposed to be a consequence of the interaction between two types of frequencies viz. the vortex shedding (primary) and the cylinder interaction (secondary) frequencies. At small separation ratio the flow is predominantly characterized by the jet in the gaps between successive cylinders and the secondary frequencies play a role in the resulting chaotic flow. On the contrary, at higher separation ratio the secondary frequencies almost disappear and the resulting flow becomes more synchronized dominated by the primary frequency.     

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.     

Numerical prediction of unsteady vortex shedding for large leading-edge roughness

A full two-dimensional Navier-Stokes algorithm is used to investigate unsteady, incompressible viscous flow past an airfoil leading edge with surface roughness that is characteristic of ice accretion. The roughness is added to the surface through the use of a Prandtl transposition and can generate both small-scale and large-scale roughness. The focus of the study is a detailed flow analysis of the unsteady velocity fluctuations and vortex shedding induced by the surface roughness. The results of this study are compared to experimental data on roughness-induced transition for the same roughness geometry. A comparison is made between “fluctuation intensity” values from the current algorithm to experimentally determined turbulence intensity values. The effects of the roughness Reynolds number, Re_k, are investigated and compared to experimental values of the critical roughness Reynolds number. The authors speculate that there may be a possible correlation between unsteady roughness-induced vortex shedding and the onset of experimentally measured transitional flow downstream of large-scale roughness.     

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.     

No-moving-part hybrid-synthetic jet actuator

In contrast to usual synthetic jets, the “hybrid-synthetic jets” of non-zero time-mean nozzle mass flow rate are increasingly often considered for control of flow separation and/or transition to turbulence as well as heat and mass transfer. The paper describes tests of a scaled-up laboratory model of a new actuator version, generating the hybrid-synthetic jets without any moving components. Self-excited flow oscillation is produced by aerodynamic instability in fixed-wall cavities. The return flow in the exit nozzles is generated by jet-pumping effect. Elimination of the delicate and easily damaged moving parts in the actuator simplifies its manufacture and assembly. Operating frequency is adjusted by the length of feedback loop path. Laboratory investigations concentrated on the propagation processes taking place in the loop.     

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.     

Numerical study on mechanisms of second sweep and positive spikes in transitional flow on a flat plate

Ring-like vortex is a flow structure at late stages of a transitional boundary layer. Independent to the initial disturbance conditions corresponding to K- and N-scenarios of transition, the vortical structure shows some universal features. The nonlinear evolution of the ring-like vortices, detail flow structures around ring-like vortex and their effects on the surrounding flow were studied by direct numerical simulation with high order accuracy. A detailed enforced spatial transition on a flat-plate boundary layer in the compressible flow was studied. This study reveals the mechanism of the second sweep generation, mechanism of the positive spike formation and mechanism of high shear layer distribution.     

On a mechanism of stabilizing turbulent free shear layers in cavity flows

Turbulent free shear flows are subject to the well-known Kelvin–Helmholtz type [Panton RL. Incompressible flow. John Wiley and Sons; 1984. p. 675] instability, and it is well-known that any free shear flow which approximates a thin vorticity layer will be unstable to a wide range of amplitudes and frequencies of disturbance. In fact, much of what constitutes flow control in turbulent free shear layers consists of feeding a prescribed destabilizing disturbance to these layers. The question in the control of free shear flows is not whether the shear layer will be stable, but whether you can influence how the layer becomes unstable. In most cases, since these flows are so receptive to forcing input, and naturally tend toward instability, large changes in flow conditions can be achieved with very small amplitude periodic inputs.

Recently, it has been discovered that turbulent free shear flows can also be stabilized using periodic forcing. This is, at first glance, counter-intuitive, considering our long history of considering these flows to be very unstable to forcing input. It is a phenomenon not described in modern fluid dynamic text books. The forcing required to achieve this effect (which we will call turbulent shear layer stabilization) is of a much higher amplitude and frequency than the more traditional type of shear layer flow control effect seen in the literature (which we will call turbulent shear layer destabilization).

A numerical study is undertaken to investigate the effect of frequency of pulsed mass injection on the nature of stabilization, destabilization and acoustic suppression in high speed cavity flows. An implicit, 2nd-order in space and time flow solver, coupled with a recently developed hybrid RANS-LES (Reynolds Averaged Navier Stokes-Large Eddy Simulation) turbulence model by Nichols and Nelson [Nichols RH, Nelson CC. Weapons bay acoustic predictions using a multi-scale turbulence model. In: Proceedings of the ITEA 2001 aircraft-stores compatibility symposium, March 2001], is utilized in a Chimera-based parallel format. This tool is used to numerically simulate both an unsuppressed cavity in resonance, as well as the effect of mass-addition pulsed jet flow control on cavity flow physics and ultimately, cavity acoustic levels.

Frequency (and in a limited number of cases, amplitude) of pulse is varied, from 0 Hz (steady) up to 5000 Hz. The change in the character of the flow control effect as pulsing frequency is changed is described, and linked to changes in acoustic levels. Limited comparison to 1/10th scale experiments is presented.

The observed local stabilization of the cavity turbulent shear layer, when subjected to high frequency pulsed blowing, is shown in simulation to be the result of a violent instability and breakdown of a pair of opposite sign vortical structures created with each high frequency “pulse”. This unique shear layer stabilization behavior is only observed in simulation above a certain critical pulsing frequency. Below this critical frequency, pulsing is shown in simulation to provide little benefit with respect to suppression of high cavity acoustic levels.     

Numerical study of passive and active flow separation control over a NACA0012 airfoil

This paper is focused on numerical investigation of subsonic flow separation over a NACA0012 airfoil with a 6° angle of attack and flow separation control with vortex generators. The numerical simulations of three cases including an uncontrolled baseline case, a controlled case with passive vortex generator, and a controlled case with active vortex generator were carried out. The numerical simulation solves the three-dimensional Navier-Stokes equations for compressible flow using a fully implicit LU-SGS method. A fourth-order finite difference scheme is used to compute the spatial derivatives. The immersed-boundary method is used to model both the passive and active vortex generators. The characteristic frequency that dominates the flow is the natural frequency of separation in the baseline case. The introduction of the passive vortex generator does not alter the frequency of separation. In the case with active control, the frequency of the sinusoidal forcing was chosen close to the natural frequency of separation. The time- and spanwise-averaged results were used to examine the mean flow field for all three cases. The passive vortex generators can partially eliminate the separation by reattaching the separated shear layer to the airfoil over a significant extent. The size of the averaged separation zone has been reduced by more than 80%. The flow control with active vortex generator is more effective and the separation zone is not visible in the averaged results. The three-dimensional structures of the flow field have also been studied.     

Microfluidic two-phase interactions under variable liquid to cross-flow gas momentum flux ratios

Volume of fluid (VOF) and large eddy simulations (LES) are coupled to investigate the microfluidic two-phase interactions during the liquid emergence into the cross-flow gas in a super-hydrophobic micro-channel. Spatio-temporal evolution of the gas/liquid interface is presented for nine different cases of the liquid to gas momentum flux ratios, gas/liquid Reynolds numbers and gas/liquid Weber numbers. With increased momentum of the gas flow, the liquid topology is found deflected towards the downstream. Under variable gas resistance effects, the liquid flow emerging through the square pore may or may not develop a circular cross-section governed by the axis-switching phenomenon. At strong gas inertia, vortex shedding in the downstream of the liquid generates vorticular ligaments in the wake region. Shearing effects on the liquid surface are increased at higher liquid injection velocities and/or gas densities. Depending on the competing effects of the viscous diffusion versus gas/liquid inertia, different combinations of the interactions among the three building blocks of the fluid flow problems (boundary layer, shear layer and wake) are described in microfluidics scales. The complexity of the liquid topology is found correlated with the occurrence of the phenomena such as the Kelvin–Helmholtz (KH) instability, the horseshoe vortex system, stationary/shedding vortices in the wake of the liquid topology as well as their interaction with the micro-channel wall boundary layers.     

Numerical simulation of the flow around rows of cylinders

Two-dimensional, laminar, unsteady, water flow around cylinder arrays of unequal sizes was simulated using FLUENT™ at Reynolds numbers below 150 (based on the free-stream velocity and first row cylinder diameter). The flow pattern through two rows of inline cylinders showed incomplete vortex shedding behind the first row at a separation distance less than 2d. Karman vortices were not formed and a near-stagnant separated flow region appeared between the aligned cylinders. Cylinders in staggered arrangements shed Karman vortices regardless of the separation between the two rows. This research has shed light on the detailed flow through paper machine forming fabrics.     

Implicit multigrid computation of unsteady flows past cylinders of square cross-section

An implicit, multigrid scheme has been extended to treat unsteady flows using the concept of temporal subiteration (or dual-time stepping, as it sometimes is called). The efficiency and accuracy of the subiterated, multigrid approach has been discussed in a previous paper. Here, the scheme is applied to compute the unsteady flow past fixed cylinders of square cross-section at moderate Reynolds numbers. The observed pattern of periodic vortex shedding is computed and the dimensionless frequency of this phenomenon (the Strouhal number) is compared with experimentally determined values. Results of coupled aeroelastic computations also are presented that illustrate a hysteresis phenomenon as the structural frequency is varied.     

LES of synthetic jets in boundary layer with laminar separation caused by adverse pressure gradient

In the development of synthetic jet actuators (SJAs) for active flow control, numerical simulation has played an important role. In controlling the boundary layer flow separation, an integrated numerical model which includes both the baseline flow and the SJA is still in its initial stage of development. This paper reports preliminary results of simulating the interaction between a synthetic jet and a laminar separation bubble caused by adverse pressure gradient in a boundary layer. The computational domain was three-dimensional and Large-eddy simulation (LES) was adopted. The initial and boundary conditions were defined using or referring to our wind tunnel experimental results. Prior to numerically simulating the interaction between the synthetic jets and the baseline flow, a numerical model for simulating the separation bubble was developed and verified. In the numerical model including the SJA, the synthetic jet velocity at the exit of the SJA was defined as an input. The numerical model was further verified by comparing the simulation with experimental results. Based on reasonable agreement between the numerical and experimental results, simulations were carried out to investigate the dependency of flow control using synthetic jets on the forcing frequency, focused on the lower frequency range of the Tollmien-Schlichting (T-S) instability, and on the forcing amplitude which was represented by the maximum jet velocity at the exit of the SJA. Supporting the hypothesis based on the experiment, LES results showed that the forcing frequency had stronger influence on SJA’s effective elimination of the separation bubble than the forcing amplitude did.     

Incompressible flow calculations with a consistent physical interpolation finite volume approach

The computation of incompressible three-dimensional viscous flow is discussed. A new physically consistent method is presented for the reconstruction for velocity fluxes which arise from the mass and momentum balance discrete equations. This closure method for fluxes allows the use of a cell-centered grid in which velocity and pressure unknowns share the same location, while circumventing the occurrence of spurious pressure modes. The method is validated on several benchmark problems which include steady laminar flow predictions on a two-dimensional cartesian (lid driven 2D cavity) or curvilinear grid (circular cylinder problem at Re = 40), unsteady three-dimensional laminar flow predictions on a cartesian grid (parallelopipedic lid driven cavity) and unsteady two-dimensional turbulent flow predictions on a curvilinear grid (vortex shedding past a square cylinder at Re = 22,000).     

A numerical analysis of two-dimensional flow past a rectangular prism by a discrete vortex model

A discrete vortex model is developed to analyse the two-dimensional fully separated unsteady flow past a rectangular prism. The effects of viscous diffusion of vortices and the loss in vorticity after the stationary prism with a thickness ratio ranging from 0.5 to 2.0. The formation of Karman vortices, the vortex shedding frequency, and the fluid forces acting on the body are favourably compared with the experimental results by various research workers. The method of analysis is also shown to be applicable to the flow past a prism that is in forced vibration.     

Implementation of a transient adaptive sub-cell module for the parallel-DSMC code using unstructured grids

A method of transient adaptive sub-cells (TAS) suitable for unstructured grids that is modified from the existing one for the structured grids of DSMC is introduced. The TAS algorithm is implemented within the framework of a parallelized DSMC code (PDSC). Benchmarking tests are conducted for steady driven cavity flow, steady hypersonic flow over a two-dimensional cylinder, steady hypersonic flow over a cylinder/flare and the unsteady vortex shedding behind a two-dimensional cylinder. The use of TAS enables a reduction in the computational expense of the simulation since larger sampling cells and less simulation particles can be employed. Furthermore, the collision quality of the simulation is maintained or improved and the preservation of property gradients and vorticity at the scale of the sub-cells enables correct unsteady vortex shedding frequencies to be predicted. The use of TAS in a parallel-DSMC code allows simulations of unsteady processes at a level to be carried out efficiently, accurately and with acceptable computational time.     

Direct computation of the noise induced by a turbulent flow through a diaphragm in a duct at low Mach number

A direct computation of the noise radiated by a turbulent flow in a duct obstructed by a diaphragm is performed by compressible large-eddy simulation. For the low Mach number configuration considered, a two-step hybrid method could be less expensive, but would fail at characterizing sound-flow interactions. The application of direct calculation is thus challenging but gives both the acoustic and aerodynamic fields in the same computation in order to shed light on the noise generation mechanisms. Acoustic energy is produced and dissipated in the asymmetric jet-type flow issuing from the diaphragm. A low-frequency radiation is correlated with the breakdown of the coherent jet-column structures as the plane jet reattaches the upper wall. The Kelvin-Helmholtz vortices in the shear layers of the jet constitute the primary instabilities but do not radiate sound. On the contrary, this vorticity shedding seems to dissipate waves propagating upstream by enforcing the unsteady Kutta condition.     

Unsteady pulsating characteristics of the fluid flow through a sudden expansion microvalve

This paper investigates the unsteady characteristics of flow in a specific type of microvalve with sudden expansion shape. The resultant vortex structures cause different flow resistance in forward and backward flow directions. This may be used in applications such as a microvalve in micropump system and MEMS-based devices. A time-varying sinusoidal pressure was set at the inlet of the microchannel to produce unsteadiness and simulate the pumping action. The existence of block obstacle and expansion shoulders leads to various sizes of vortex structures in each flow direction. All simulation results are based on the numerical simulation of two-dimensional, unsteady, incompressible and laminar Navier–Stokes equations. Two fundamental parameters were varied to investigate the vortex growth throughout the time: the frequency of the inlet actuating mechanism (1 Hz ≤ f ≤ 1,000 Hz) and the amplitude of the inlet pressure. In this way, one can see the effect of actuation mechanism on the onset of separation and follow the size and duration of the vortex growth. In order to better understand the effect of geometry and frequency on flow field, the pressure and velocity distributions are studied through one cycle. Strouhal number is calculated for frequency, and a critical value of f = 250 Hz is found for St = 1. The obtained results provide a deep insight into the physics of unsteady flow in valveless micropumps and leads to better use of current design as a part of microfluidic system.     

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.