Study of the Flow and Acoustic Fields in a Rigid-Walled Channel of Circular Cross-Section with a Local Axisymmetric Narrowing: A Theory

Asymptotic expansion for the solution to a boundary-value problem in a thin cascade domain with a local joint

“…In the previous section, we have considered the regular asymptotics taking into account the inhomogeneity of the right-hand side of the differential equation in (1) and the boundary conditions on the horizontal sides of the thin domain Ω ε . In what follows, we construct the boundary part of the asymptotics compensating the residuals of the regular part of the asymptotics at the left side of Ω ε , we seek the boundary asymptotics for the solution in the form Π (1) ∞ :=…”

“…To obtain conditions for the functions {ω (1) k } and {ω (2) k } at the point 0, we introduce an additional internal asymptotics in a neighbourhood of the joint. For this we pass to the following variables ξ = x ε and η = y ε .…”

“…For this we pass to the following variables ξ = x ε and η = y ε . Then forwarding the parameter ε to 0, we see that the domain Ω ε is transformed into the unbounded domain Ξ , which is the union of joint Ξ (0) and two half strips Ξ (1)…”

“…The problem (35) is called limit problem for problem (1). The solution to (35) is given by the following formulas:…”

“…Special interest of researchers is focused on various effects observed in vicinities of local irregularities of the geometry (widening or narrowing) of channels (e.g., adhesion to the walls, welds, and stenosis). Results of recent theoretical, experimental and numerical studies of flows and wall-pressure fluctuations in channels with different types of narrowing are summarized in [1,2,3] and references therein. Also the study of influence of local geometrical irregularities is very important in engineering, since such irregularities often directly affect the strength (stability, resistance, power, etc.)…”