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On the dynamical buoyancy of vortices
In this paper we consider the effect of dynamical buoyancy (Parker) on the motion of stratified fluid vortex tubes. We find that the dynamical buoyancy force does not necessarily lead to a buoyant rise if there exists a flow field external to a tube. In particular, the vortex tubes presented in our previous work are shown to have a pressure force exactly canceling the buoyancy force so that they do not move vertically (i.e., parallel to gravity) at all. Moreover, we construct a more general class of vortex tubes and find that their vertical motion can be either up or down, depending on the detailed vorticity distribution, regardless of the fact that they are all dynamically buoyant. We find that the vertical motion is intimately related to the horizontal self-motion of stratified fluid vortex tubes. Finally, we note that the presence of dynamical buoyancy implies that steady state compressible flow solutions for isolated fluid regions in a gravitational field do not exist. These results may have relevance to astrophysical convection.
Experimental and analytical studies in fluids
The first objective was to analyze and design a true airspeed sensor which will replace the conventional pitot-static pressure transducer for small commercial aircraft. The second objective was to obtain a numerical solution and predict the frequency response which is generated by the vortex whistle at a certain airspeed. It was concluded flow rate measurements indicate that the vortex tube sound frequency is linearly proportional to the frequency response. The vortex tube whistle frequency is dependent upon geometrical parameters to such an extent that: an increase in vortex tube length produces a decrease in frequency response and that an increase in the exhaust nozzle length produces an increase in the frequency precession. An increase in the vortex tube diameter produces a decrease in frequency precession. An increase in swirler diameter produces a decrease in frequency. An increase in the location distance of the microphone pickup signal point from the inside edge of the exit nozzle produces an increase in frequency response. The experimental results indicate that those parameters most significantly effecting frequency are in descending order of importance microphone location, vortex tube diameter, exit nozzle length, vortex tube length, and swirler diameter.
A visual investigation of turbulence in stagnation flow about a circular cylinder
A visual investigation of turbulence in stagnation flow around a circular cylinder was carried out in order to gain a physical insight into the model advocated by the corticity-amplification theory. Motion pictures were taken from three different viewpoints, and a frame by frame examination of selected movie strips was conducted. Qualitative and quantitative analyses of the flow events focused on tracing the temporal and spatial evolution of a cross-vortex tube outlined by the entrained smoke filaments. The visualization supplied evidence verifying: (1) the selective stretching of cross-vortex tubes which is responsible for the amplification of cross vorticity and, hence, of streamwise turbulence; (2) the streamwise tilting of stretched cross-vortex tubes; (3) the existence of a coherent array of vortices near the stagnation zone; (4) the interaction of the amplified vorticity with the body laminar boundary layer; and, (5) the growth of a turbulent boundary layer.
Local forced convection boiling heat transfer of wetting mercury in a single tube with vortex insert
Local forced convection heat transfer data and empirical correlations for boiling Hg in single wetted Ta tube with composite helical inserts
3D visualization of unsteady 2D airplane wake vortices
Air flowing around the wing tips of an airplane forms horizontal tornado-like vortices that can be dangerous to following aircraft. The dynamics of such vortices, including ground and atmospheric effects, can be predicted by numerical simulation, allowing the safety and capacity of airports to be improved. In this paper, we introduce three-dimensional techniques for visualizing time-dependent, two-dimensional wake vortex computations, and the hazard strength of such vortices near the ground. We describe a vortex core tracing algorithm and a local tiling method to visualize the vortex evolution. The tiling method converts time-dependent, two-dimensional vortex cores into three-dimensional vortex tubes. Finally, a novel approach calculates the induced rolling moment on the following airplane at each grid point within a region near the vortex tubes and thus allows three-dimensional visualization of the hazard strength of the vortices. We also suggest ways of combining multiple visualization methods to present more information simultaneously.
Study of the velocity gradient tensor in turbulent flow
The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.
Visualization of turbulence in flow about a bluff body
A visual diagnostic investigation of turbulence in flow about a circular cylinder was conducted in order to gain a physical insight into the model for the structure of turbulence in flow around a bluff body advanced by the vorticity-amplification theory. A frame-by-frame qualitative and quantitative examination of selected movie strips over time intervals up to more than 800 ms was performed. The selective stretching of cross-vortex tubes, their streamwise tilting, the emergence of an organized turbulent flow pattern near the stagnation zone and the growth of a turbulent boundary layer were clearly revealed by the visualization. In particular, the visualization indicated that the cross-vortex tubes conveyed by the diverging stagnation flow constitute a coherent substructure within the overall turbulent flow that is triggered to its fullest manifestation by the stretching mechanism.
CVS Decomposition of 3D Homogeneous Turbulence Using Orthogonal Wavelets
This paper compares the filtering used in Coherent Vortex Simulation (CVS) decomposition with an orthogonal wavelet basis, with the Proper Orthogonal Decomposition (POD) or Fourier filtering. Both methods are applied to a field of Direct Numerical Simulation (DNS) data of 3D forced homogeneous isotropic turbulence at microscale Reynolds number R(sub lambda) = 168. We show that, with only 3%N retained modes, CVS filtering separates the coherent vortex tubes from the incoherent background flow. The latter is structureless, has an equipartition energy spectrum, and has a Gaussian velocity probability distribution function (PDF) and an exponential vorticity PDF. On the other hand, the Fourier basis does not extract the coherent vortex tubes cleanly and leaves organized structures in the residual high wavenumber modes whose PDFs are stretched exponentials for both the velocity and the vorticity.
Turbulent Compressible Convection with Rotation: Flow Structure and Evolution - Part 1
The effects of Coriolis forces on compressible convection are studied using three-dimensional numerical simulations carried out within a local modified f-plane model. The physics is simplified by considering a perfect gas occupying a rectilinear domain placed tangentially to a rotating sphere at various latitudes, through which a destabilizing heat flux is driven. The resulting convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers, evaluating conditions where the influence of rotation is both weak and strong. Given the computational demands of these high-resolution simulations, the parameter space is explored sparsely to ascertain the differences between laminar and turbulent rotating convection. The first paper in this series examines the effects of rotation on the flow structure within the convection, its evolution, and some consequences for mixing. Subsequent papers consider the large-scale mean shear flows that are generated by the convection, and the effects of rotation on the convective energetics and transport properties. It is found here that the structure of rotating turbulent convection is similar to earlier nonrotating studies, with a laminar, cellular surface network disguising a fully turbulent interior punctuated by vertically coherent structures. However, the temporal signature of the surface flows is modified by inertial motions to yield new cellular evolution patterns and an overall increase in the mobility of the network. The turbulent convection contains vortex tubes of many scales, including large-scale coherent structures spanning the full vertical extent of the domain involving multiple density scale heights. Remarkably, such structures align with the rotation vector via the influence of Coriolis forces on turbulent motions, in contrast with the zonal tilting of streamlines found in laminar flows. Such novel turbulent mechanisms alter the correlations which drive mean shearing flows and affect the convective transport properties. In contrast to this large-scale anisotropy, small-scale vortex tubes at greater depths are randomly orientated by the rotational mixing of momentum, leading to an increased degree of isotropy on the medium to small scales of motion there. Rotation also influences the thermodynamic mixing properties of the convection. In particular, interaction of the larger coherent vortices causes a loss of correlation between the vertical velocity and the temperature leaving a mean stratification which is not isentropic.
Optimization of a Cyclone Using Multiphase Flow Computational Fluid Dynamics
The U.S. Department of Energy National Energy Technology Laboratory's (NETL) 50 kW th chemical looping reactor (CLR) has an underperforming cyclone, which was designed using empirical correlations. To improve the performance of this cyclone using computational fluid dynamics (CFD)-based modeling simulations, four critical design parameters including the vortex tube radius and length, barrel radius, and the inlet width and height were optimized. Here, NETL's open source multiphase flow with interphase exchange (MFiX) CFD code has been used to model a series of cyclones by systematically varying the geometric design parameters. To perform the optimization process, the surrogate modeling and sensitivity analysis followed by the optimization capability in nodeworks was used. The basic methodology for the process is to employ a statistical design of experiments (DOE) method to generate sampling simulations that fill the design space. Corresponding CFD models are then created, executed, and postprocessed. A response surface is created to characterize the relationship between input parameters and the quantities of interest (QoI). Finally, the CFD-surrogate is used by an optimization method to find the optimal design condition based on the objective and constraints prescribed. The resulting optimal cyclone has a larger diameter and longer vortex tube, a larger diameter barrel, and a taller and narrower solids inlet. The improved design has a predicted pressure drop 11 times lower than the original design while reducing the mass loss by a factor of 2.3.
Flow-visualization studies of a confined, jet- driven water vortex
Flow visualization of confined jet driven water vortex tube
Ground evaluation of seeding an in-flight wingtip vortex using infrared imaging flow visualization technique
An experimental simulation of an in-flight wingtip vortical flow visualization technique uses infrared imaging to observe strong and concentrated vortices. This experiment is phase 1 of a two-phase infrared evaluation program. The system includes a vortex generator (model 320 Vortec Vortex Tube) which generates the required vortex. The mouth of the unit is mounted close to the free end of a half-inch diameter, sixteen and a half foot long stainless steel tubing (sized after tubing currently installed in the wings of an experimental Beechcraft Sundowner 180 aircraft). Dichloro difluoromethane (Freon-12) is entrained into the generated vortex. A breakdown of the vortices is indicated by the rapid diffusion and the resulting pattern is tracked using the infrared imager and video systems. Flow rates (volume and mass) are estimated at the laboratory and proposed flight conditions. The nominal flight altitude is expected to be 2500 feet.
Simulation of vortex breakdown in tubes
The breakdown of a vortex flow in a tube is studied for a slightly diverging tube by means of a numerical solution of the Navier-Stokes equations for a quasi-stationary, incompressible, laminar flow. Numerical results are compared to experiments of Faler and Leibovich. The numerical data display features similar to the experimental results concerning breakdown conditions, location, and structure.
Evolution of a vortical structure associated with the bursting event in a channel flow
The temporal evolution of a horseshoe vortex structure in a channel is investigated by a numerical simulation. A spectral numerical method is employed to integrate the time-dependent, three-dimensional Navier-Stokes equations. The initial vortical structure is obtained by applying a conditional sampling technique to a data base generated from a direct simulation of a turbulent channel flow. The evolution of this vortical structure under the influence of the self-induced motion and the mean shear is presented. It is shown that the initial sheet-like vortical structure rolls up into a vortex tube as it is convected downstream. Turbulence structures associated with the vortex stretching are investigated. Production of vorticity stretching is high inside the vortex legs, although it is also substantial in the tip region and above the legs. High Reynolds shear stress is produced near the tip of the vortex.
Three-dimensional simulations of reshocked inclined Richtmyer-Meshkov instability: Effects of initial perturbations
The effect of initial perturbations on the evolution of the inclined Richtmyer-Meshkov turbulent mixing layer before and after reshock initiated by a shock wave with Mach number 1.55 is investigated through three-dimensional (3D) simulations using the flash code. The 3D simulations aim to reproduce both predominantly single-mode and multimode interfaces between light and heavy gases (N 2 -CO 2 , Atwood number, A≈0.22; amplitude to wavelength ratio of 0.088) which were created in an inclined shock tube facility to analyze the effects of initial conditions on mixing development in the entire flow field. The two-dimensional center slices of 3D simulations are compared with the experimental results to validate the computational code. Mixing width, mixed mass, mixed-mass thickness, and circulation in addition to concentration fields are shown to be in good agreement with the experimental data. The three-dimensional density and vorticity fields are first presented to qualitatively describe the flow behavior before and after reshock. Several measured density/velocity-related quantities indicate that the growth of the mixing material is strongly dependent on initial conditions. Before reshock and at early times after reshock, flow is clearly maintaining the memory of initial perturbations. However, at late time after reshock, although the large wavelength feature still dominates the flow motion, and the morphology of the two different interfaces indicates several differences, by breakdown of large-scale coherent structures to much finer scales, the memory of small scales of the multimode initial perturbation is not as clear as pre-reshock. Regarding three-dimensionality of the flow, before reshock in the multimode case, the baroclinic vorticity production, circulation, turbulent kinetic energy, and turbulent mass flux suggest that the small-scale roll-up features along the large inclined wavelength quickly evolves in all three dimensions. The coherent vortex tubes break down to smaller wormlike vortex structures, and turbulent fluctuations in the out-of-plane dimension are comparable to the spanwise direction. After reshock, this three-dimensionality of mixing growth was observed in the flow for both initial conditions. The results of this work represent a significant extension of previous computational studies performed on this specific topic. A different code with a different numerical method is validated through comparison with the experimental data. The initial perturbations are directly measured from the experimental results. Moreover, the entire three-dimensional experimental shock tube domain is simulated, and more quantities are investigated to understand the mixing mechanism and instability evolution in all three dimensions.
Rotor Wake Vortex Definition Using 3C-PIV Measurements: Corrected for Vortex Orientation
Three-component (3-C) particle image velocimetry (PIV) measurements, within the wake across a rotor disk plane, are used to determine wake vortex definitions important for BVI (Blade Vortex Interaction) and broadband noise prediction. This study is part of the HART II test program conducted using a 40 percent scale BO-105 helicopter main rotor in the German-Dutch Wind Tunnel (DNW). In this paper, measurements are presented of the wake vortex field over the advancing side of the rotor operating at a typical descent landing condition. The orientations of the vortex (tube) axes are found to have non-zero tilt angles with respect to the chosen PIV measurement cut planes, often on the order of 45 degrees. Methods for determining the orientation of the vortex axis and reorienting the measured PIV velocity maps (by rotation/projection) are presented. One method utilizes the vortex core axial velocity component, the other utilizes the swirl velocity components. Key vortex parameters such as vortex core size, strength, and core velocity distribution characteristics are determined from the reoriented PIV velocity maps. The results are compared with those determined from velocity maps that are not corrected for orientation. Knowledge of magnitudes and directions of the vortex axial and swirl velocity components as a function of streamwise location provide a basis for insight into the vortex evolution.
Zero-Gravity Vortex Vent and PVT Gaging System
Space Station and satellite reservicing will require the ability to vent gas on orbit from liquid supply or storage tanks and to gage liquid quantity under microgravity conditions. In zero gravity, (zero-g) the vortex vent is capable of venting gas from a tank of liquid containing gas randomly distributed as bubbles. The concept uses a spinning impeller to create centrifugal force inside a vortex tube within a tank. This creates a gas pocket and forces the liquid through a venturi and back into the tank. Gas is then vented from the gas pocket through a liquid detector and then out through an exhaust port. If the liquid detector senses liquid in the vent line, the fluid is directed to the low-pressure port on the venturi and is returned to the tank. The advantages of this system is that it has no rotating seals and is compatible with most corrosive and cryogenic fluids. A prototype was designed and built at the NASA Johnson Space Center and flown on the KC-135 zero-g aircraft. During these test flights, where microgravity conditions are obtained for up to 30 sec, the prototype demonstrated that less than 0.10 percent of the volume of fluid vented was liquid when the tank was half full of liquid. The pressure volume temperature (PVT) gaging system is used in conjunction with the vortex vent to calculate the amount of liquid remaining in a tank under microgravity conditions. The PVT gaging system is used in conjunction with the vortex vent to gage liquid quantity in zero or low gravity. The system consists of a gas compressor, accumulator, and temperature and pressure instrumentation. To measure the liquid in a tank a small amount of gas is vented from the tank to the compressor and compressed into the accumulator. Pressure and temperature in the tank and accumulator are measured before and after the gas transfer occurs. Knowing the total volume of the tank, the volume of the accumulator, the volume of the intermediate lines, and initial and final pressures and temperatures, the mass of the gas leaving the tank is equated to the mass of the gas entering the accumulator. The volume of liquid remaining in the tank is calculated using the ideal gas law.