A linear system for pipe flow stability analysis allowing for boundary condition modifications

Abstract

An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer & Trefethen (2000), while providing flexibility to amend the boundary conditions without a need to modify the formulation. The accuracy is achieved by formulating the state variables to behave as analytic functions. We show that the resulting system retains the regular singularity at the pipe centre with a multiplicity of poles such that the wall boundary conditions are complemented with precisely the needed number of regularity conditions for obtaining unique solutions. In the case of axisymmetric and axially constant perturbations the computed eigenvalues match, to double precision accuracy, the values predicted by the analytical characteristic relations. The derived system is used to obtain the optimal inviscid disturbance pattern, which is found to hold similar structure as in plane shear flows.

Viscoelastic laminar drag bounds in pipe flow

“…Indeed, we proved that U and the components of the tensor C exhibit even or odd symmetries with respect to r. As an outlook, these symmetries can be exploited to derive conditions for the regularity of perturbations at the pipe center as derived in the Newtonian case 32 . These are expected to be valuable for the study of the stability and transition of viscoelastic pipe flows.…”

“…The last point in this sequence could be perceived as shear-thinning by introducing a variable viscosity as a factoring function together with ∇ 2 U , which balances the total dissipation. Indeed, we proved that U and the components of the tensor C exhibit even or odd symmetries with respect to r. As an outlook, these symmetries can be exploited to derive conditions for the regularity of perturbations at the pipe center as derived in the Newtonian case 32 . These are expected to be valuable for the study of the stability and transition of viscoelastic pipe flows.…”

“…show that they exhibit even or odd symmetries with respect to r. These parities can assist when analyzing the symmetries of small perturbations close to the wall as performed for the case of Newtonian flows 30 and when deploying them in the numerical calculations 31,32 . Figure 1(a) shows the velocity profiles in the Newtonian case (β = 1) and three non-Newtonian cases (β = 0.8 and increasing Wi).…”

Computation Analysis of Flow in a Round Pipe with Navier-Stokes Equations

“…They applied initial velocity and pressure at the pipe inlet and implemented a zero-pressure gradient at the pipe outlet. By employing these boundary conditions, researchers were able to model realistic flow in the pipe [8]. The researchers also took into account the energy loss in the fluid flow inside the pipe.…”

Compressor Piping Design Effect on Vibration Data

“…The piping system on the nitrogen compressor shows that there is possibility backflow to the standby equipment [3][4]. Besides, the phenomenon of turbulence in pipe flow caused by boundary condition on pipe-wall and also appears confluence of two flows and the influence of flow velocity [5][6][7][8][9][10][11][12]. The pressure on the backflow flow is very high, and it will cause nitrogen gas leading to standby equipment being condensate [13][14][15][16].…”