On the instantaneous cutting of a columnar vortex with non-zero axial flow

1997 ◽  
Vol 351 ◽  
pp. 41-74 ◽  
Author(s):  
J. S. MARSHALL ◽  
S. KRISHNAMOORTHY
Keyword(s):  
Vortex Core ◽  
Flow Model ◽  
Plug Flow ◽  
Axial Flow ◽  
Vortex Rings ◽  
Core Radius ◽  
Expansion Waves ◽  
Columnar Vortex ◽  
Cutting Surface ◽  
Compression And Expansion

A study of the response of a columnar vortex with non-zero axial flow to impulsive cutting has been performed. The flow evolution is computed based on the vorticity–velocity formulation of the axisymmetric Euler equation using a Lagrangian vorticity collocation method. The vortex response is compared to analytical predictions obtained using the plug-flow model of Lundgren & Ashurst (1989). The plug-flow model indicates that axial motion on a vortex core with variable core area behaves in a manner analogous to one-dimensional gas dynamics in a tube, with the vortex core area playing a role analogous to the gas density. The solution for impulsive cutting of a vortex obtained from the plug-flow model thus resembles the classic problem of impulsive motion of a piston in a tube, with formation of an upstream-propagating vortex ‘shock’ (over which the core radius changes discontinuously) and a downstream-propagating vortex ‘expansion wave’ on opposite sides of the cutting surface. Direct computations of the vortex response from the Euler equation reveal similar upstream- and downstream-propagating waves following impulsive cutting for cases where the initial vortex flow is subcritical. These waves in core radius are produced by a series of vortex rings, embedded within the columnar vortex core, having azimuthal vorticity of alternating sign. The effect of the compression and expansion waves is to bring the axial and radial velocity components to nearly zero behind the propagating vortex rings, in a region on both sides of the cutting surface with ever-increasing length. The change in vortex core radius and the variation in pressure along the cutting surface agree very well with the predictions of the plug-flow model for subcritical flow after the compression and expansion waves have propagated sufficiently far away. For the case where the ambient vortex flow is supercritical, no upstream-propagating wave is possible on the compression side of the vortex, and the vortex axial flow is observed to impact on the cutting surface in a manner similar to that commonly observed for a non-rotating jet impacting on a wall. The flow appears to approach a steady state near the point of impact after a sufficiently long time. The vortex response on the expansion side of the cutting surface exhibits a downstream-propagating vortex expansion wave for both the subcritical and supercritical conditions. The results of the vortex response study are used to formulate and verify predictions for the net normal force exerted by the vortex on the cutting surface. An experimental study of the cutting of a vortex by a thin blade has also been performed in order to verify and assess the limitations of the instantaneous vortex cutting model for application to actual vortex–body interaction problems.

The flow induced by periodic vortex rings wrapped around a columnar vortex core

1997 ◽  
Vol 345 ◽  
pp. 1-30 ◽  
Author(s):  
J. S. MARSHALL
Keyword(s):  
Critical Point ◽  
Vortex Core ◽  
Opposite Sign ◽  
Axial Flow ◽  
Inviscid Flow ◽  
Vortex Rings ◽  
Core Radius ◽  
Free Standing ◽  
Columnar Vortex ◽  
Induced Velocity

A study has been performed of the interaction of periodic vortex rings with a central columnar vortex, both for the case of identical vortex rings and the case of rings of alternating sign. Numerical calculations, both based on an adaptation of the Lundgren–Ashurst (1989) model for the columnar vortex dynamics and by numerical solution of the axisymmetric Navier–Stokes and Euler equations in the vorticity–velocity formulation using a viscous vorticity collocation method, are used to investigate the response of the columnar vortex to the ring-induced velocity field. In all cases, waves of variable core radius are observed to build up on the columnar vortex core due to the periodic axial straining and compression exerted by the vortex rings. For sufficiently weak vortex rings, the forcing by the rings serves primarily to set an initial value for the axial velocity, after which the columnar vortex waves oscillate approximately as free standing waves. For the case of identical rings, the columnar vortex waves exhibit a slow upstream propagation due to the nonlinear forcing. The cores of the vortex rings can also become unstable due to the straining flow induced by the other vortex rings when the ring spacing is sufficiently small. This instability causes the ring vorticity to spread out into a sheath surrounding the columnar vortex. For the case of rings of alternating sign, the wave in core radius of the columnar vortex becomes progressively narrower with time as rings of opposite sign approach each other. Strong vortex rings cause the waves on the columnar vortex to grow until they form a sharp cusp at the crest, after which an abrupt ejection of vorticity from the columnar vortex is observed. For inviscid flow with identical rings, the ejected vorticity forms a thin spike, which wraps around the rings. The thickness of this spike increases in a viscous flow as the Reynolds number is decreased. Cases have also been observed, for identical rings, where a critical point forms on the columnar vortex core due to the ring-induced flow, at which the propagation velocity of upstream waves is exactly balanced by the axial flow within the vortex core when measured in a frame translating with the vortex rings. The occurrence of this critical point leads to trapping of wave energy downstream of the critical point, which results in large-amplitude wave growth in both the direct and model simulations. In the case of rings of alternating sign, the ejected vorticity from the columnar vortex is entrained and carried off by pairs of rings of opposite sign, which move toward each other and radially outward under their self- and mutually induced velocity fields, respectively.

On the impulsive blocking of a vortex–jet

1998 ◽  
Vol 369 ◽  
pp. 301-331 ◽  
Author(s):  
J. A. LEE ◽  
O. R. BURGGRAF ◽  
A. T. CONLISK
Keyword(s):  
Vortex Core ◽  
Axial Velocity ◽  
Vortical Structure ◽  
Axial Flow ◽  
Inviscid Flow ◽  
Numerical Results ◽  
Tip Vortex ◽  
Final States ◽  
Core Radius ◽  
The Core

In this paper we consider the flow field within and around a vortex as it ‘collides’ with a thin plate at a right angle to its axis of rotation. We show that based solely on inviscid flow theory, vorticity in the core of the vortex is redistributed significantly. The main cause of this redistribution is the presence of axial flow within the vortex; we call this vortical structure which contains axial flow a vortex–jet. In this work we show that when the axial velocity within the vortex is toward the plate, vorticity is redistributed radially outward from the core resulting in a significant reduction in the axial vorticity there; the vortex is said to ‘bulge’ reflecting an increase in the nominal vortex core radius. A by-product of this interaction is that the suction peak amplitude caused by the presence of the vortex rapidly decreases and the pressure soon returns to a quasi-steady distribution. On the other hand, when the axial velocity within the vortex is directed away from the surface, the suction peak persists and the vortex core radius decreases. The numerical results were validated by comparison with an analytical solution for a sinusoidal vortex jet. Analytical solutions were also derived for the initial and final states of a pure jet; the numerical results are strongly supported by the analysis. In addition, all of these results are consistent with experiments, and their relevance to the interaction between a tip vortex and a helicopter airframe is also discussed.

scholarly journals Transient lift force on a blade during cutting of a vortex with non-zero axial flow

2017 ◽  
Vol 819 ◽  
pp. 258-284 ◽  
Author(s):  
D. Curtis Saunders ◽  
Jeffrey S. Marshall
Keyword(s):  
Vortex Core ◽  
Lift Force ◽  
Lift Coefficient ◽  
Plug Flow ◽  
Axial Flow ◽  
Leading Edge ◽  
Simple Expression ◽  
Navier Stokes ◽  
Wide Range ◽  
The Impact

The problem of orthogonal penetration of a blade into the core of a vortex with non-zero axial flow was studied using a combination of scaling theory, a heuristic plug-flow model and full Navier–Stokes simulations. The particular focus of this paper was to understand the mechanics of the transient lift force that occurs during the initial penetration of the blade leading edge into the vortex core, and the relationship of this transient force to the steady-state lift force that develops due to the difference in vortex core radius over the blade surface. The three modelling approaches all lead to the conclusion that the maximum value of the lift coefficient for the transient blade penetration force is proportional to the impact parameter and inversely proportional to the axial flow parameter. This observation is used to develop a simple expression that collapses the predictions of the full Navier–Stokes simulations for lift coefficient over a wide range of parameter values.

Frequency-Response Approach to Modelling Continuous Reactors

1971 ◽  
Vol 6 (1) ◽  
pp. 249-272
Author(s):  
P.B. Melynk ◽  
J.D. Norman ◽  
A.W. Wilson
Keyword(s):  
Frequency Response ◽  
Flow Model ◽  
Plug Flow ◽  
Order Reaction ◽  
Parameter Estimates ◽  
Second Order Reaction ◽  
Mixing Conditions ◽  
Bode Plot ◽  
Flow Through ◽  
Search Routine

Abstract It is postulated that the mixing conditions in a flow-through reactor can be characterized as having either completely mixed, completely plug flow, or some network of completely mixed and plug flow component vessels. A frequency-response technique is used to obtain an experimental Bodé plot for arbitrarily mixed vessels. The interpretation of the Bodé plot is discussed, and , in light of this interpretation, a network of plug flow and completely mixed components is specified as a flow model. A Rosenbrock search routine is used to improve the parameter estimates of the model. To verify the model, a second order reaction was run through the vessel and the experimentally measured conversion was compared to that predicted by the model. It is shown that the modeling technique, in addition to describing the mixing in the system, will indicate inactive volume, as well as measure the extent of any channeling or short circuiting in the reactor.

An experimental study of gas phase back mixing under the counter-current gas-liquid flow on a vertical expanded metal sheet packing by static tracer technique

1980 ◽  
Vol 45 (1) ◽  
pp. 214-221
Author(s):  
Jan Červenka ◽  
Mirko Endršt ◽  
Václav Kolář
Keyword(s):  
Gas Phase ◽  
Flow Model ◽  
Plug Flow ◽  
Packed Bed ◽  
Metal Sheet ◽  
Concentration Profiles ◽  
Expanded Metal ◽  
Gas Liquid Flow ◽  
Counter Current ◽  
Back Mixing

Gas phase back mixing has been measured in a column packed with vertical expanded metal sheet under the counter-current flow of gas and liquid by the static method using a tracer. The observed experimental concentration profiles has not confirmed our earlier proposed model of back mixing, based on the concentration profiles in absorption runs. These profiles do not even conform with the axially dispersed plug flow model currently used to describe axial mixing in packed bed columns. The concentration profiles may be described by a combination of the axially dispersed plug flow model with back flow.

scholarly journals Measurement of the vortex-core radius by scanning tunneling microscopy

1994 ◽  
Vol 194-196 ◽  
pp. 387-388 ◽  
Author(s):  
U. Hartmann ◽  
A.A. Golubov ◽  
T. Drechsler ◽  
M.Yu. Kupriyanov ◽  
C. Heiden
Keyword(s):  
Scanning Tunneling Microscopy ◽  
Vortex Core ◽  
Scanning Tunneling ◽  
Core Radius ◽  
Tunneling Microscopy

Hydrogen Production from Ethanol Steam Reforming: Fixed Bed Reactor Design

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Pablo Giunta ◽  
Norma Amadeo ◽  
Miguel Laborde
Keyword(s):  
Steam Reforming ◽  
Flow Model ◽  
Multicomponent Mixture ◽  
Plug Flow ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Ethanol Steam Reforming ◽  
Heterogeneous Model ◽  
Ethanol Steam ◽  
Hydrogen Stream

The aim of this work is to design an ethanol steam reformer to produce a hydrogen stream capable of feeding a 60 kW PEM fuel cell applying the plug flow model, considering the presence of the catalyst bed (heterogeneous model). The Dusty-Gas Model is employed for the catalyst, since it better predicts the fluxes of a multicomponent mixture. Moreover, this model has shown to be computationally more robust than the Fickian Model. A power law-type kinetics was used. Results showed that it is possible to carry out the ethanol steam reforming in a compact device (1.66 x 10 -5 to 5.27 x 10 -5 m3). It was also observed that this process is determined by heat transfer.

The Aerodynamic Characteristics of the Pantograph When the Train Passes Through the Tunnel

2017 ◽  
Author(s):  
Dilong Guo ◽  
Wen Liu ◽  
Junhao Song ◽  
Ye Zhang ◽  
Guowei Yang
Keyword(s):  
High Speed ◽  
Aerodynamic Force ◽  
Maximum Amplitude ◽  
Aerodynamic Characteristics ◽  
High Speed Train ◽  
Expansion Waves ◽  
Compression And Expansion ◽  
High Speed Trains ◽  
Current Characteristics ◽  
Pass Through

The aerodynamic force acting on the pantograph by the airflow is obviously unsteady and has a certain vibration frequency and amplitude, while the high-speed train passes through the tunnel. In addition to the unsteady behavior in the open-air operation, the compressive and expansion waves in the tunnel will be generated due to the influence of the blocking ratio. The propagation of the compression and expansion waves in the tunnel will affect the pantograph pressure distribution and cause the pantograph stress state to change significantly, which affects the current characteristics of the pantograph. In this paper, the aerodynamic force of the pantograph is studied with the method of the IDDES combined with overset grid technique when high speed train passes through the tunnel. The results show that the aerodynamic force of the pantograph is subjected to violent oscillations when the pantograph passes through the tunnel, especially at the entrance of the tunnel, the exit of the tunnel and the expansion wave passing through the pantograph. The changes of the pantograph aerodynamic force can reach a maximum amplitude of 106%. When high-speed trains pass through tunnels at different speeds, the aerodynamic coefficients of the pantographs are roughly the same.

Interaction of a singular surface with a strong shock in the interstellar gas clouds

2021 ◽  
Vol 63 ◽  
pp. 342-358
Author(s):  
Jasobanta Jena ◽  
Sheena Mittal
Keyword(s):  
Strong Shock ◽  
Singular Surface ◽  
Acceleration Wave ◽  
Interstellar Gas ◽  
Surface Theory ◽  
Expansion Waves ◽  
Lie Group Of Transformations ◽  
Compression And Expansion ◽  
Particular Solution ◽  
Flow Variables

We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.   doi:10.1017/S1446181121000328

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