Shock diffraction in channels with 90° bends

1983 ◽  
Vol 132 ◽  
pp. 257-270 ◽  
Author(s):  
D. H. Edwards ◽  
P. Fearnley ◽  
M. A. Nettleton
Keyword(s):  
Mach Number ◽  
Rectangular Cross Section ◽  
Outer Wall ◽  
Incident Shock ◽  
Radius Of Curvature ◽  
Shock Diffraction ◽  
Expansion Waves ◽  
Concave Wall ◽  
Convex Wall ◽  
Shock Profiles

A study has been made of how initially planar shocks in air propagate around 90° bends in channels of nearly rectangular cross-section. In shallow bends for which the radius of curvature R is much greater than the radius r of the channel, the shock recovers from a highly curved profile at the start of the bend to regain planarity towards the end of the bend. This occurs on account of the acceleration of the triple point across the channel following its interaction with the expansion waves generated at the convex wall. In sharp bends the shock profiles retain their pronounced curvature for some distance downstream of the bend.At the start of a shallow bend (R/r ≈ 6) the shock at the concave wall, initial Mach number M0, accelerates to Mw = 1.15M0 and remains at this value until towards the end of the bend it begins to attenuate. At the convex wall, shocks of M0 > 1.7 attenuate to Mw = 0.7M0 and propagate at this value for some distance around the bend. In the early stages of a sharper bend (R/r ≈ 3) the shock at the concave wall strengthens to Mw = 1.3M0, remaining at this value for some distance downstream of the bend. At the convex wall the shock decelerates to 0.6M0.Whitham's (1974) ray theory is shown to predict with reasonable accuracy the Mach numbers of the wall shocks at both surfaces for both bends tested and the range of incident shock velocities used, 1.2 < M0 < 3. The agreement between the theory and experimental results is particularly close for stronger shocks propagating along the inner bend. Predictions from 3-shock theory (Courant & Friedrichs 1948) of the Mach number at the outer wall are consistently higher than those from Whitham's analysis. In turn, the latter tends to slightly overestimate the strength of the wall shock.A model is developed, based on an extension of Whitham's analysis, and is shown to predict the length of the Mach stem produced by shocks of M0 > 2 over the initial stages of the bend.

Experiments of Compressible Homogeneous and Isotropic Turbulence Interacting With Expansion Waves

2003 ◽  
Author(s):  
Savvas S. Xanthos ◽  
Yiannis Andreopoulos
Keyword(s):  
Mach Number ◽  
Shock Tube ◽  
Total Pressure ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Pressure Fluctuations ◽  
Incident Shock ◽  
Expansion Waves ◽  
Curvature Effects ◽  
Homogeneous And Isotropic Turbulence

The interaction of traveling expansion waves with grid-generated turbulence was investigated in a large-scale shock tube research facility. The incident shock and the induced flow behind it passed through a rectangular grid, which generated a nearly homogeneous and nearly isotropic turbulent flow. As the shock wave exited the open end of the shock tube, a system of expansion waves was generated which traveled upstream and interacted with the grid-generated turbulence; a type of interaction free from streamline curvature effects, which cause additional effects on turbulence. In this experiment, wall pressure, total pressure and velocity were measured indicating a clear reduction in fluctuations. The incoming flow at Mach number 0.46 was expanded to a flow with Mach number 0.77 by an applied mean shear of 100 s−1. Although the strength of the generated expansion waves was mild, the effect on damping fluctuations on turbulence was clear. A reduction of in the level of total pressure fluctuations by 20 per cent was detected in the present experiments.

Extension of the Wall-Driven Enclosure Flow Problem to Toroidally Shaped Geometries of Square Cross-Section

1996 ◽  
Vol 118 (4) ◽  
pp. 779-786 ◽  
Author(s):  
L. M. Phinney ◽  
J. A. C. Humphrey
Keyword(s):  
Cross Section ◽  
Fluid Motion ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Coordinate Direction ◽  
Concave Wall ◽  
Center Vortex ◽  
Convex Wall ◽  
Two Dimensional Flow ◽  
Moving Fluid

The two-dimensional wall-driven flow in an enclosure has been a numerical paradigm of long-standing interest and value to the fluid mechanics community. In this paradigm the enclosure is infinitely long in the x-coordinate direction and of square cross-section (d × d) in the y-z plane. Fluid motion is induced in all y-z planes by a wall (here the top wall) sliding normal to the x-coordinate direction. This classical numerical paradigm can be extended by taking a length L of the geometry in the x-coordinate direction and joining the resulting end faces at x = 0 and x = L to form a toroid of square cross-section (d × d) and radius of curvature Rc. In the curved geometry, axisymmetric fluid motion (now in the r-z planes) is induced by sliding the top flat wall of the toroid with an imposed radial velocity, ulid, generally directed from the convex wall towards the concave wall of the toroid. Numerical calculations of this flow configuration are performed for values of the Reynolds number (Re = ulidd/ν) equal to 2400, 3200, and 4000 and for values of the curvature ratio (δ = d/Rc) ranging from 5.0 · 10−6 to 1.0. For δ ≤ 0.05 the steady two-dimensional flow pattern typical of the classical (straight) enclosure is faithfully reproduced. This consists of a large primary vortex occupying most of the enclosure and three much smaller secondary eddies located in the two lower corners and the upper upstream (convex wall) corner of the enclosure. As δ increases for a fixed value of Re, a critical value, δcr, is found above which the primary center vortex spontaneously migrates to and concentrates in the upper downstream (concave wall) corner. While the sense of rotation originally present in this vortex is preserved, that of the slower moving fluid below it and now occupying the bulk of the enclosure cross-section is reversed. The relation marking the transition between these two stable steady flow patterns is predicted to be δcr1/4 = 3.58 Re-1/5 (δ ± 0.005).

Shear-Driven Flow in a Toroid of Square Cross Section

2003 ◽  
Vol 125 (1) ◽  
pp. 130-137 ◽  
Author(s):  
J. A. C. Humphrey ◽  
J. Cushner ◽  
M. Al-Shannag ◽  
J. Herrero ◽  
F. Giralt
Keyword(s):  
Cross Section ◽  
Finite Length ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Radius Of Curvature ◽  
Infinite Length ◽  
Core Flow ◽  
Reynolds Number Flow ◽  
End Wall

The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature Rc reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length. These include: the recirculating core flow and its associated counterrotating corner eddies; above a critical value of the Reynolds (or corresponding Goertler) number, the appearance of Goertler vortices aligned with the recirculating core flow; at higher values of the Reynolds number, flow unsteadiness, and vortex meandering as precursors to more disorganized forms of motion and eventual transition to turbulence. Present calculations also show that, for any fixed location in a toroid, the Goertler vortex passing through that location can alternate its sense of rotation periodically as a function of time, and that this alternation in sign of rotation occurs simultaneously for all the vortices in a toroid. This phenomenon has not been previously reported and, apparently, has not been observed for the wall-driven flow in a finite-length parallelepiped where the sense of rotation of the Goertler vortices is determined and stabilized by the end wall vortices. Unlike the wall-driven flow in a finite-length parallelepiped, the shear-driven flow in a toroid is devoid of contaminating end wall effects. For this reason, and because the toroid geometry allows a continuous variation of the curvature parameter, δ=D/Rc, this flow configuration represents a more general paradigm for fluid mechanics research.

Influence of Skewing of Contact Face on Performance of Wave Rotor Refrigerators and Superchargers

2013 ◽  
Author(s):  
Yuqiang Dai ◽  
Fengxia Liu ◽  
Jintao Wu ◽  
Wei Wei ◽  
Dapeng Hu ◽  
...  
Keyword(s):  
High Pressure ◽  
Mach Number ◽  
Shock Waves ◽  
Rotational Speed ◽  
Channel Width ◽  
Wave Rotor ◽  
Coriolis Forces ◽  
Local Loss ◽  
Expansion Waves ◽  
Pressure Port

As a novel generation of rotational gas wave machines, wave rotor machines such as wave rotor refrigerators (WRR) and wave rotor superchargers (WRS) are unsteady flow devices. In their passages two gas streams (with different pressure or even different phases) comes into direct contact can exchange energy due to the movement of shock waves and expansion waves. A detailed study shows that, when rotor channels open to the high pressure port gradually, the contact face in rotor channels inevitably skews, which is always accompanied with reflection of shockwaves. This causes very large energy dissipation and influences adversely on the refrigeration performance of WRR or the supercharging performance of WRS. In this work, factors such as centrifugal forces, Coriolis forces, gradual channel opening and gradual channel closing, etc, which influence the wave transportation and skewing of shock waves and contact faces are studied by means of computational fluid dynamics and experiments. The skewing of contact faces causes uneven distribution of velocity and large local loss. With rotation Mach number smaller than 0.3, the skewing of contact face can be alleviated. To reduce the adverse influence of rotation Mach number, a smaller rotor channel width or higher rotational speed is necessary. The rotation effect plays an important role for the skewing of gas discontinuities. Both the centrifugal and Coriolis forces of wave rotor cannot be ignored with the Rossby number of 1.3∼3.5. To reduce the skewing loss of contact face, a lower rotational speed seems necessary. The rotation speed of wave rotors has dialectical influences on the skewing of shock waves and contact faces. The jetting width of high pressure port is the key factor of the gradual opening of rotor channels. A feasible way to reduce skewing losses of gas waves is to optimize the ratio between high pressure port width and channel width. The validation experiments have got at least 3∼5% rise of isentropic efficiency for WRRs.

Heat Transfer for Laminar Flow in Spiral Ducts of Rectangular Cross Section

2005 ◽  
Vol 127 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Michael W. Egner ◽  
Louis C. Burmeister
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Aspect Ratios ◽  
Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

Particle Dispersion and Deposition in a Curved Duct

2009 ◽  
Author(s):  
C. M. Winkler ◽  
S. P. Vanka
Keyword(s):  
Particle Deposition ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Outer Wall ◽  
Particle Dispersion ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Particle Volume ◽  
Particle Tracking Method ◽  
Dean Vortex

Particle transport in ducts of square cross-section with constant streamwise curvature is studied using numerical simulations. The flow is laminar, with Reynolds numbers of Reτ = 40 and 67, based on the friction velocity and duct width. The corresponding Dean numbers for these cases are 82.45 and 184.5, respectively, where De = Rea/R, a is the duct width and R is the radius of curvature. A Lagrangian particle tracking method is used to account for the particle trajectories, with the particle volume fraction assumed to be low such that inter-particle collisions and two-way coupling effects are negligible. Four particle sizes are studied, τp+ = 0.01, 0.05, 0.1, and 1. Particle dispersion patterns are shown for each Dean number, and the steady-state particle locations are found to be reflective of the Dean vortex structure. Particle deposition on the walls is shown to be dependent upon both the Dean number and particle response time, with the four-cell Dean vortex pattern able to prevent particle deposition along the center of the outer wall.

Numerical Study of Turbulent Flow and Convective Heat Transfer Characteristics in Helical Rectangular Ducts

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Yunfei Xing ◽  
Fengquan Zhong ◽  
Xinyu Zhang
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Axial Direction ◽  
Outer Wall ◽  
Centrifugal Effect

Three-dimensional turbulent forced convective heat transfer and its flow characteristics in helical rectangular ducts are simulated using SST k–ω turbulence model. The velocity field and temperature field at different axial locations along the axial direction are analyzed for different inlet Reynolds numbers, different curvatures, and torsions. The causes of heat transfer differences between the inner and outer wall of the helical rectangular ducts are discussed as well as the differences between helical and straight duct. A secondary flow is generated due to the centrifugal effect between the inner and outer walls. For the present study, the flow and thermal field become periodic after the first turn. It is found that Reynolds number can enhance the overall heat transfer. Instead, torsion and curvature change the overall heat transfer slightly. But the aspect ratio of the rectangular cross section can significantly affect heat transfer coefficient.

Analysis of Draw Bead Geometry on Wall Thinning and Concave/Convex Feature in Rectangular Deep Drawn Parts

2011 ◽  
Vol 189-193 ◽  
pp. 2704-2707 ◽  
Author(s):  
Wiriyakorn Phanitwong ◽  
Sutasn Thipprakmas
Keyword(s):  
Finite Element Method ◽  
Bead Geometry ◽  
Distribution Analysis ◽  
The Finite Element Method ◽  
Bead Width ◽  
Wall Thinning ◽  
Concave Wall ◽  
Straight Wall ◽  
Convex Wall ◽  
Bead Height

The application of the draw bead could reduce the concave/convex wall features. However, it also affected the wall thinning. Therefore, it is difficult to determine the suitable draw bead geometry to obtain a straight wall without the wall thinning. In this study, the effects of draw bead geometry of height and width on concave/convex wall feature and wall thinning were investigated by using the finite element method (FEM) and experiments. Based on the stress distribution analysis, the increasing in draw bead width and the decreasing in draw bead height lead to the concave wall feature increased; however, the application of the too small draw bead width and the too large draw bead height generated the convex wall feature. The wall thinning also decreased as the draw bead width increased as well as the draw bead height decreased. Therefore, the application of suitable draw bead height and width significantly suppressed the concave/convex wall feature and wall thinning, which resulted in the straight wall with the smallest wall thinning could be achieved.

Experimental investigation of diaphragm material combinations in a small-scale shock tube

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Anugya Singh ◽  
Aravind Satheesh Kumar ◽  
Kannan B.T.
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Shock Tube ◽  
Production Capacity ◽  
Incident Shock ◽  
Small Scale ◽  
Content Type ◽  
Shock Mach Number ◽  
Reinforcing Material ◽  
Shock Wave Mach Number

Purpose The purpose of this study is to experimentally investigate the trends in shock wave Mach number that were observed when different diaphragm material combinations were used in the small-scale shock tube. Design/methodology/approach A small-scale shock tube was designed and fabricated having a maximum Mach number production capacity to be 1.5 (theoretically). Two microphones attached in the driven section were used to calculate the shock wave Mach number. Preliminary tests were conducted on several materials to obtain the respective bursting pressures to decide the final set of materials along with the layered combinations. Findings According to the results obtained, 95 GSM tracing paper was seen to be the strongest reinforcing material, followed by 75 GSM royal executive bond paper and regular 70 GSM paper for aluminium foil diaphragms. The quadrupled layered diaphragms revealed a variation in shock Mach number based on the position of the reinforcing material. In quintuple layered combinations, the accuracy of obtaining a specific Mach number was seen to be increasing. Optimization of the combinations based on the production of the shock wave Mach number was carried out. Research limitations/implications The shock tube was designed taking maximum incident shock Mach number as 1.5, the experiments conducted were found to achieve a maximum Mach number of 1.437. Thus, an extension to further experiments was avoided considering the factor of safety. Originality/value The paper presents a detailed study on the effect of change in the material and its position in the layered diaphragm combinations, which could lead to variation in Mach numbers that are produced. This could be used to obtain a specific Mach number for a required study accurately, with a low-cost setup.

The effect of biased plates on transport of vacuum arc plasma through rectangular curved magnetic filter

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740006
Author(s):  
W. Y. Bi ◽  
L. H. Li ◽  
H. T. Liu ◽  
G. Zhao
Keyword(s):  
Rectangular Cross Section ◽  
Outer Wall ◽  
Vacuum Arc ◽  
Arc Plasma ◽  
Transport Efficiency ◽  
Magnetic Filter ◽  
Coating Efficiency ◽  
Vacuum Arc Deposition ◽  
Ion Current Density ◽  
Arc Deposition

Filtered cathode vacuum arc deposition can remove the macroparticles produced from the cathode. Positively biasing the whole filter or inserting a biased plate in the filter can increase the plasma transport efficiency. We developed a curved magnetic filter with rectangular cross-section to improve the coating efficiency. In this study, the effect of biased plates at outer-wall and inner-wall on the transport efficiency of vacuum arc plasma through rectangular curved magnetic filter was investigated. A Langmuir probe system is used to measure the distribution properties of the filtered plasma at 15 places in the outlet plane of the filter. The results showed that a positively biased plate at inner-wall would increase the output ion current density and make the plasma concentrate to the middle of the outlet plane.

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