Surface-waves, stability, and scattering for a lined duct with flow

We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass-spring-damper boundary model, for which one surface mode has previously been identified as a convective instability; however, we show the stability analysis used in such cases to be questionable. We investigate instead the stability of the surface modes using the Briggs-Bers criterion for a Flügge thin-shell boundary model. For modest frequencies and wavenumbers the thin-shell has an impedance which is effectively that of a mass-spring-damper, although for the large wavenumbers needed for the stability analysis the thin-shell and mass-spring-damper impedances diverge, owing to the thin shell's bending stiffness. The thin shell model may therefore be viewed as a regularization of the mass-spring-damper model which accounts for nonlocally-reacting effects. We find all modes to be stable for realistic thin-shell parameters, while absolute instabilities are demonstrated for extremely thin boundary thicknesses. The limit of vanishing bending stiffness is found to be a singular limit, yielding absolute instabilities of arbitrarily large temporal growth rate. We propose that the problems with previous stability analyses are due to the neglect of something akin to bending stiffness in the boundary model. Our conclusion is that the surface mode previously identified as a convective instability may well be stable in reality. Finally, inspired by Rienstra's recent analysis, we investigate the scattering of an acoustic mode as it encounters a sudden change from a hard-wall to a thin-shell boundary, using a Wiener-Hopf technique. The thin-shell is considered to be clamped to the hard-wall. The acoustic mode is found to scatter into transmitted and reflected acoustic modes, and surface modes strongly linked to the solid waves in the boundary, although no longitudinal or transverse waves within the boundary are excited. Examples are provided that demonstrate total transmission, total reflection, and a combination of the two. This thin-shell scattering problem is preferable to the mass-spring-damper scattering problem presented by Rienstra, since the thin-shell problem is fully determined and does not need to appeal to a Kutta-like condition or the inclusion of an instability in order to avoid a surface-streamline cusp at the boundary change.

Continuous spectrum growth and modal instability in swirling duct flow

We present results on the stability of compressible inviscid swirling flows in an annular duct. Such flows are present in aeroengines, for example in the by-pass duct, and there are also similar flows in many aeroacoustic or aeronautical applications. The linearised Euler equations have a ('critical layer') singularity associated with pure convection of the unsteady disturbance by the mean flow, and we focus our attention on this region of the spectrum. By considering the critical layer singularity, we identify the continuous spectrum of the problem and describe how it contributes to the unsteady field. We find a very generic family of instability modes near to the continuous spectrum, whose eigenvalue wavenumbers form an infinite set and accumulate to a point in the complex plane. We study this accumulation process asymptotically, and find conditions on the flow to support such instabilities. It is also found that the continuous spectrum can cause a new type of instability, leading to algebraic growth with an exponent determined by the mean flow, given in the analysis. The exponent of algebraic growth can be arbitrarily large. Numerical demonstrations of the continuous spectrum instability, and also the modal instabilities are presented.

Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1, - ∞ < x < ∞ with mean flow Mach number M > 0 and a hard wall along x < 0 and a wall of impedance Z along x > 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t), no more singular than h = Ο(x1/2) for x ↓ 0. A mode, incident from x < 0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = Ο(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z (ω) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ω → 0, the modulus fends to |R001| → (1 + M)/(1 -M) without and to 1 with Kutta condition, while the end correction tends to ∞ without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow.

Triple-region structure for turbulent-flow in a square duct - a finite-element approach

The Reynolds-averaged Navier-Stokes equations for describing the turbulent flow in a straight square duct are formulated with two different turbulence models. The governing equations are then expanded as a multi-deck structure in a plane perpendicular to the streamwise direction, with each deck characterized by its dominant physical forces as commonly carried out in analytical work using triple-deck expansion. The resulting equations are numerically integrated using higher polynomial (H-P) finite element technique for each cross-sectional plane to be followed by finite difference representation in the streamwise direction until a fully developed state is reached. The computed results using the two different turbulence models show fair agreement with each other, and concur with the vast body of available experimental data. There is also general agreement between our results and the recent numerical works anisotropic k-epsilon turbulence model.

Computation of turbulent-flow in a square duct - aspects of the secondary flow and its origin

A numerical study of turbulent flow in a straight duct of square cross-section is made. An order-of-magnitude analysis of the 3-D, time-averaged Navier-Stokes equations resulted in a parabolic form of the Navier-Stokes equations. The governing equations, expressed in terms of a new vector-potential formulation, are expanded as a multi-deck structure with each deck characterized by its dominant physical forces. The resulting equations are solved using a finite-element approach with a bicubic element representation on each cross-sectional plane. The numerical integration along the streamwise direction is carried out with finite-difference approximations until a fully-developed state is reached. The computed results agree well with other numerical studies and compare very favorably with the available experimental data. One important outcome of the current investigation is the interpretation analytically that the driving force of the secondary flow in a square duct comes mainly from the second-order terms of the difference in the gradients of the normal and transverse Reynolds stresses in the axial vorticity equation.

New Oncogenic Drivers in Hepatocellular Carcinoma: Role of the RNA Binding Protein Hu antigen R

156 p. : graf.

Three-dimensional growth as multicellular spheroid activates the proangiogenic phenotype of colorectal carcinoma cells via LFA-1-dependent VEGF: implications on hepatic micrometastasis

Background: The recruitment of vascular stromal and endothelial cells is an early event occurring during cancer cell growth at premetastatic niches, but how the microenvironment created by the initial three-dimensional (3D) growth of cancer cells affects their angiogenesis-stimulating potential is unclear. Methods: The proangiogenic profile of CT26 murine colorectal carcinoma cells was studied in seven-day cultured 3D-spheroids of <300 mu m in diameter, produced by the hanging-drop method to mimic the microenvironment of avascular micrometastases prior to hypoxia occurrence. Results: Spheroid-derived CT26 cells increased vascular endothelial growth factor (VEGF) secretion by 70%, which in turn increased the in vitro migration of primary cultured hepatic sinusoidal endothelium (HSE) cells by 2-fold. More importantly, spheroid-derived CT26 cells increased lymphocyte function associated antigen (LFA)-1-expressing cell fraction by 3-fold; and soluble intercellular adhesion molecule (ICAM)-1, given to spheroid-cultured CT26 cells, further increased VEGF secretion by 90%, via cyclooxygenase (COX)-2-dependent mechanism. Consistent with these findings, CT26 cancer cells significantly increased LFA-1 expression in non-hypoxic avascular micrometastases at their earliest inception within hepatic lobules in vivo; and angiogenesis also markedly increased in both subcutaneous tumors and hepatic metastases produced by spheroid-derived CT26 cells. Conclusion: 3D-growth per se enriched the proangiogenic phenotype of cancer cells growing as multicellular spheroids or as subclinical hepatic micrometastases. The contribution of integrin LFA-1 to VEGF secretion via COX-2 was a micro environmental-related mechanism leading to the pro-angiogenic activation of soluble ICAM-1-activated colorectal carcinoma cells. This mechanism may represent a new target for specific therapeutic strategies designed to block colorectal cancer cell growth at a subclinical micrometastatic stage within the liver.