Two Problems of Waveguides Carrying Mean Fluid Flow

Mahmood-ul-Hassan,; Rawlins, A. D.

doi:10.1006/jsvi.1998.1711

Cited by 13 publications

(16 citation statements)

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“…We validate our solution by comparing with existing results. We obtain identical solutions for the reflection coefficients as were obtained in [19] for specific dimensions of the ducts. We observe that the mode matching method is significantly easy to implement than the Wiener-Hopf technique.…”

Section: Introductionmentioning

confidence: 56%

“…In addition, we have the radiation conditions that insure the solution to be bounded and the scattered waves to be outgoing. Moreover, we have edge conditions

ϕ (x, \pm a) = O (1) and ϕ_{y} (x, \pm a) = O ((), x^{- \frac{1}{2}}),

as x →0 at the end of the semi‐infinite plates. These conditions play a significant role for the uniqueness of the solution for the Wiener–Hopf technique but are not required for the current method.…”

Section: Trifurcated Waveguide Problemmentioning

confidence: 99%

“…Figure shows | R | versus k a . Here, dashed line (data 2) is plotted for | R | using the Wiener–Hopf technique by taking Mach number M = 0, and it is given by

| R | = \frac{8 π^{2} (\frac{1}{2} - M / (1 + M))}{3 {|\frac{3 ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{9 k^{2} a^{2}}{1 - M^{2}} - 4 π^{2})}|}^{2}} .

In Figure , the solid line (data 1) shows the graph of | R | against ka by using the mode matching method. In Figure , | R | is plotted for fixed c = 3/2 and (i) a = 1 and (ii) a = 0.5.…”

Section: Trifurcated Waveguide Problemmentioning

confidence: 99%

“…Figure represents the graph of | R | against ka for the Wiener–Hopf technique and mode matching technique. Here, the dashed line (data 5) for M = 0 is for Wiener–Hopf method where | R | for c = 3 a is defined by

| R | = \frac{64 π^{2} {|\frac{ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{k^{2} a^{2}}{1 - M^{2}} - \frac{π^{2}}{4})}|}^{2}}{243 {|\frac{ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{k^{2} a^{2}}{1 - M^{2}} - \frac{π^{2}}{9})}|}^{2}} \times \frac{(\frac{1}{2} - \frac{M}{M + 1})}{{|\frac{ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{k^{2} a^{2}}{1 - M^{2}} - \frac{4 π^{2}}{9})}|}^{2}} .

InFigure , data 4 (solid line) is the graph of reflection coefficient against the wave number for the mode matching method. In Figure , data 4 represented by the solid line is for a = 1, and data 6 (dotted line) is for a = 0.5 for fixed c = 3.…”

Section: Trifurcated Waveguide Problemmentioning

confidence: 99%

“…Some worked on bifurcated waveguide , while others considered trifurcated problems . Many authors used the Wiener–Hopf technique, which involves complicated split functions. While the Wiener–Hopf method can lead to simple formula for quantities like the reflection coefficient, it is difficult to derive and to generalize, often a more straightforward method that can be easily generalized is more useful in practice.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Mode matching analysis for wave scattering in triple and pentafurcated spaced ducts

Mahmood-ul-Hassan

Meylan

Bashir

et al. 2015

Math Methods in App Sciences

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We present solutions to both trifurcated and pentafurcated spaced waveguides using the mode matching (or eigenfunction expansion) method. While the trifurcated problem with mean fluid flow has been solved previously using the Wiener-Hopf technique, we solve this problem to validate and demonstrate our method. We then show how we can easily generalize the method to the pentafurcated problem that has not been solved previously. We observe that mode matching method is easier to derive and generalize than the Wiener-Hopf technique. We also investigate the numerical solution in detail for various geometries to model practical exhaust systems.

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Section: Introductionmentioning

confidence: 56%

“…In addition, we have the radiation conditions that insure the solution to be bounded and the scattered waves to be outgoing. Moreover, we have edge conditions

ϕ (x, \pm a) = O (1) and ϕ_{y} (x, \pm a) = O ((), x^{- \frac{1}{2}}),

Section: Trifurcated Waveguide Problemmentioning

confidence: 99%

“…Figure shows | R | versus k a . Here, dashed line (data 2) is plotted for | R | using the Wiener–Hopf technique by taking Mach number M = 0, and it is given by

| R | = \frac{8 π^{2} (\frac{1}{2} - M / (1 + M))}{3 {|\frac{3 ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{9 k^{2} a^{2}}{1 - M^{2}} - 4 π^{2})}|}^{2}} .

In Figure , the solid line (data 1) shows the graph of | R | against ka by using the mode matching method. In Figure , | R | is plotted for fixed c = 3/2 and (i) a = 1 and (ii) a = 0.5.…”

Section: Trifurcated Waveguide Problemmentioning

confidence: 99%

| R | = \frac{64 π^{2} {|\frac{ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{k^{2} a^{2}}{1 - M^{2}} - \frac{π^{2}}{4})}|}^{2}}{243 {|\frac{ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{k^{2} a^{2}}{1 - M^{2}} - \frac{π^{2}}{9})}|}^{2}} \times \frac{(\frac{1}{2} - \frac{M}{M + 1})}{{|\frac{ka}{\sqrt{1 - M^{2}}} + \sqrt{(\frac{k^{2} a^{2}}{1 - M^{2}} - \frac{4 π^{2}}{9})}|}^{2}} .

Section: Trifurcated Waveguide Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mode matching analysis for wave scattering in triple and pentafurcated spaced ducts

Mahmood-ul-Hassan

Meylan

Bashir

et al. 2015

Math Methods in App Sciences

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Wave propagation in a waveguide

Rawlins

Mahmood-ul-Hassan

2003

Z Angew Math Mech

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MSC (2000) 74J15, 78A40, 78A50We shall consider the sound radiation of a surface wave mode which propagates towards the mouth of a semi-infinite waveguide which supports surface waves. This semi-infinite waveguide is symmetrically located inside an infinite waveguide whose surface is lined with an absorbent surface. The whole system constitutes a new trifurcated waveguide boundary value problem. This model results in a scalar Wiener-Hopf problem. An exact closed form solution is obtained with the aid of the Wiener-Hopf technique. The theoretical problem solved has application in acoustics and electromagnetism.

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