Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates

Through the Lie symmetry analysis method, the axisymmetric, incompressible, and inviscid fluid is studied. The governing equations that describe the flow are the Euler equations. Under intensive observation, these equations do not have a certain solution localized in all directions $(r,t,z)$ ( r , t , z ) due to the presence of the term $\frac{1}{r}$ 1 r , which leads to the singularity cases. The researchers avoid this problem by truncating this term or solving the equations in the Cartesian plane. However, the Euler equations have an infinite number of Lie infinitesimals; we utilize the commutative product between these Lie vectors. The specialization process procures a nonlinear system of ODEs. Manual calculations have been done to solve this system. The investigated Lie vectors have been used to generate new solutions for the Euler equations. Some solutions are selected and plotted as two-dimensional plots.

Developing and applying Mach 4.5 nozzle in hypersonic wind tunnel

Mach 4.5 tests in a conventional trans-supersonic wind tunnel are often accompanied by the air liquefaction phenomenon, resulting in the low reliability of test data. The Mach 4.5 nozzle developed in a hypersonic wind tunnel is able to heat airflow and provide more accurate test data. At present, China does not have the capability to test the Mach 4.5 nozzle in the 0.5-meter hypersonic wind tunnel. This gap may be filled by developing the Mach 4.5 nozzle in the hypersonic wind tunnel. The axisymmetric nozzle profile was calculated by the inviscid flow calculation method, and the boundary layer was modified by the Sivells-Payne method. Then, the numerical simulation was carried out, and the simulation results prove that the nozzle profile thus calculated meets the design requirements of the Mach number. For its structural design, a three-section design method is adopted to ensure the continuity and smoothness of the inner surface so as to better calibrate the flow field. Standard model tests were also carried out. The test results show that the velocity field of the Mach 4.5 nozzle we developed meets technical requirements. The standard model test data provide data reliable support for the development of aircraft.

Numerical Simulation of Cascade Flow: Vortex Element Method for Inviscid Flow Analysis and Axial Turbine Blade Design

This study aims to design an axial turbine rotor blade and predict the turbine performance at preliminary design stage. Quasi three dimensional method was applied to design including blade to blade flow analysis. The blade profile uses a NACA 0015 airfoil by varying the profile thickness from hub to tip. The profile is divided into eleven segments which has different parameters. The profile was analysed using blade to blade flow/cascade flow analysis called vortex panel method to obtain lift coefficient. The analysis of cascade flow was performed in potential flow and prediction of turbine perfomance is carried out involving common best practice to give drag effect on the blade. The design of the turbine was applied on three different rotors, which also have a different discharge, head, and design rotation. The outer diameter of turbine 1 is 0.65 m, while turbine 2 and turbine 3 have an outer diameter of 0,60 m. The calculation result show that the efficiency of turbines 1, 2, and 3 were 88,32%, 89,67%, and 89,04%, respectively.

On the Verification of the Pedestrian Evacuation Model

In this article we deal with numerical solution of macroscopic models of pedestrian movement. From a macroscopic point of view, pedestrian movement can be described by a system of first order hyperbolic equations similar to 2D compressible inviscid flow. For the Pedestrian Flow Equations (PFEs) the density ρ and the velocity v are considered as the unknown variables. In PFEs, the social force is also taken into account, which replaces the outer volume force term used in the fluid flow formulation, e.g., the pedestrian movement is influenced by the proximity of other pedestrians. To be concrete, the desired direction μ of the pedestrian movement is density dependent and is incorporated in the source term. The system of fluid dynamics equations is thus coupled with the equation for μ. The main message of this paper is the verification of this model. Firstly, we propose two approaches for the source term discretization. Secondly, we propose two splitting schemes for the numerical solution of the coupled system. This leads us to four different numerical methods for the PFEs. The novelty of this work is the comparative study of the numerical solutions, which shows, that all proposed methods are in the good agreement.

Parametric Evaluation of Forces Due to a Passing Ship on a Moored Ship Using CFD Simulation

Over the years, with advancements in the shipping industry, there has been considerable increase in size, numbers and speed of ships. Ports and harbours have to handle these larger ships and increased ship traffic within the limited space especially in matured ports. Due to the above mentioned issues at the ports and harbours, passing ship interactions with a moored ship is eventual. Pressure variations around the passing ship may cause additional forces and moments on the ship moored in the vicinity. Though there is literature from past research available on the subject, only few parameters have been investigated. The passing ship forces on a moored ship has been evaluated using Computational Fluid Dynamics (CFD), based on a double-body flow model. Simulations were carried out for three-dimensional, unsteady, inviscid flow using overset meshing technique to facilitate the movement of the vessel. The results obtained from CFD simulations were compared with the existing results obtained by experiments (Remery, 1974) for the validation of the CFD model. Detailed parametric studies were carried out for parameters such as velocity ratio and displacement ratio, spacing ratio, and water depth ratio. Empirical equations for force and moment coefficients are derived based on the present study and recommendations for passing vessel distances from moored vessel has been made in the article.