Transient compressible flow in a compliant viscoelastic tube

Abstract

Motivated by problems arising in the pneumatic actuation of controllers for micro-electromechanical systems, labs-on-a-chip or biomimetic soft robots, and the study of microrheology of both gases and soft solids, we analyze the transient fluid–structure interactions (FSIs) between a viscoelastic tube conveying compressible flow at low Reynolds number. We express the density of the fluid as a linear function of the pressure, and we use the lubrication approximation to further simplify the fluid dynamics problem. On the other hand, the structural mechanics is governed by a modified Donnell shell theory accounting for Kelvin–Voigt-type linearly viscoelastic mechanical response. The fluid and structural mechanics problems are coupled through the tube’s radial deformation and the hydrodynamic pressure. For small compressibility numbers and weak coupling, the equations are solved analytically via a perturbation expansion. Three illustrative problems are analyzed. First, we obtain exact (but implicit) solutions for the pressure for steady flow conditions. Second, we solve the transient problem of impulsive pressurization of the tube’s inlet. Third, we analyze the transient response to an oscillatory inlet pressure. We show that an oscillatory inlet pressure leads to acoustic streaming in the tube, attributed to the nonlinear pressure gradient induced by the interplay of FSI and compressibility. Furthermore, we demonstrate an enhancement in the volumetric flow rate due to FSI coupling. The hydrodynamic pressure oscillations are shown to exhibit a low-pass frequency response (when averaging over the period of oscillations), while the frequency response of the tube deformation is similar to that of a bandpass filter.

Continuous dependence and convergence for a Kelvin–Voigt fluid of order one

“…As such, the equations for such fluids present many mathematical challenges, see e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Competitive Double Diffusive Convection in a Kelvin–Voigt Fluid of Order One

“…Straughan [2]. The field of viscoelastic fluids which includes fading memory fluids is vast, as is witnessed by the work of Amendola and Fabrizio [3], Amendola et al [4], Anand et al [5], Anand and Christov [6,7], Anh and Nguyet [8], Christov and Christov [9], Fabrizio et al [10], Franchi et al [11][12][13][14], Gatti [15], Jordan et al [16], Jordan and Puri [17], Payne and Straughan [18], Yang et al [19].…”

Lattice Boltzmann method for fluid-structure interaction in compressible flow

“…Interaction between fluid and deformable or moving bodies is important area of research in computational mechanics. Behavior of solid structures under the influence of fluid flow, and vice versa, is of special interest in the fields of bio-mechanics, mechanical engineering and aerospace engineering with applications ranging from blood flow inside the heart and blood vessels [1], material erosion due to bubble cavitation [2,3], effect of shock or blast waves on solid structures [4,5], and vibration or deformation of aircraft wings at high speeds [6][7][8]. For aerospace vehicle design, the study of fluid structure interactions (FSI) at transonic and supersonic speeds is especially important in order to detect shock induced vibrations and deformations such as aeroelastic flutter.…”