Analytical Solution Of Navier-Stokes Equations Research Articles

Performance Assessment of Tesla Expander Using 3D Numerical Simulation

Abstract Bladeless or Tesla turbines consist of several flat parallel disks mounted on a shaft with a narrow gap between them. The analytical solution of Navier-Stokes equations for the flow between disks has been extensively studied in the past. However, there is a significant impact of the stator exit-flow conditions on the performance and flow behavior inside the rotor of the Tesla turbine. There has been limited research on flow characterization and performance evaluation of stator-rotor interaction of the Tesla expander using 3D numerical simulation. The challenge arises due to a very high aspect ratio of the Tesla rotor (diameter to gap ratio > 1000). 3D numerical modeling with a hexahedral mesh of the nozzle/stator with the commercial software is presented. The simulation is performed for a wide range of inlet pressures and rotational speeds. This work focuses on the stator performance, the stator-rotor interaction, the rotor entry losses due to disk tip, the rotor tip velocity ratio and the degree of reaction on the performance of the Tesla expander.The peak efficiency of 58% is predicted for 3 bar inlet pressure and a rotational speed of 30000 rpm for a 3 kW machine with air as a working fluid. The 3D numerical analysis provides insights on flow characterization, mainly stator-rotor interaction and flow between disks at different mass flows. Numerical results are also compared with experimented test results performed on a 100-W and a 3-kW air expander.

Mathematical Model of Flow in a Doubly Constricted Permeable Channel with Effect of Slip Velocity

A mathematical model of steady laminar flow in a channel of varying cross section is studied under the effect of slip velocity at the permeable boundary. The fluid reabsorption at walls is taken care by the assumption of flow rate as a function of the axial coordinate at each cross section. An analytical solution of Navier-Stokes equations is determined by employing the perturbation technique. The graphical results are presented to illustrate the significance of slip velocity and various parameters on the velocity profiles, mean pressure drop, wall shear stress and stream function.

On a new type of non-stationary helical flows for incompressible 3D Navier-Stokes equations

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions indeed.In our presentation, we proceed exploring the case of non-stationary helical flows of the Navier-Stokes equations for incompressible fluids, with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of flow.The main motivation of the current research is the exploring the case when velocity field u is supposed to be perpendicular to the vector ∇α. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained, for which non-stationary helical flow with invariant Bernoulli-function is considered.The spatial part of the pressure field of the fluid flow should be determined via Bernoulli-function, if components of the velocity of the flow are already obtained.

A procedure for the construction of non-stationary Riccati-type flows for incompressible 3D Navier–Stokes equations

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow or 3D case of non-stationary flow of incompressible fluid. But there is an essential deficiency of non-stationary solutions indeed. We explore the ansatz of derivation of non-stationary solution for the Navier-Stokes equations in the case of incompressible flow, which was suggested earlier. In general case, such a solution should be obtained from the mixed system of 2 Riccati ordinary differential equations (in regard to the time-parameter t). But we find an elegant way to simplify it to the proper analytical presentation of exact solution (such a solution is exponentially decreasing to zero for t going to infinity). Also it has to be specified that the solutions that are constructed can be considered as a class of perturbation absorbed exponentially as t going to infinity by the null solution.

Analytical solutions of Navier-Stokes equations for axisymmetric and plane flows of a viscous incompressible fluid

Analytical solutions of Navier-Stokes equations for axisymmetric and plane flows of a viscous incompressible fluid