Fluid Simulation Project for Educational Purposes

Lab Auxiliary UET Peshawar

Introduction

This is a web app that simulates the fluid flow around a falling sphere, taking into account the dynamic effects of fluid viscosity, sphere radius and density, along with static parameters such as gravity, buoyancy and drag. The simulation measures the time taken for the sphere to travel 15cm at terminal velocity. It is meant as a lab auxiliary for the Chemical Engineering branch at the UET Peshawar.

Usage

The simulation parameters can be changed from the menus at the top of the screen. The time can be altered from real time to 4 times slower or 4 times faster. The viscosity is measured in centistokes (cSt). Any sphere can be selected by clicking on it. The radius is provided in imperial measurements, like the laboratory resources. At the bottom of the screen is the table for physical, dynamic parameters. On the right is the data log that outputs the measurements. The Jacobi iterations parameter represents the number of calculations for the fluid movement. A higher number of iterations provides higher fidelity in the fluid flow, but requires more power from the GPU.

Technicalities

The graphical fluid flow is modelled using the Navier-Stokes equations: $$\frac{\partial \vec{u}}{\partial t} = -\vec{u} \cdot \nabla \vec{u} - \frac{1}{\rho}\nabla \rho + \nu \nabla^2\vec{u} + \vec{F}$$ $$\nabla \cdot \vec{u} = 0$$ However, for purely graphical purposes, leaving the viscosity term out provides a very good trade-off in terms of computational efficiency and graphical fidelity. The equations are solved numerically for pressure using Jacobi iterations.

The graphical sphere movement is modelled using gravitational acceleration, drag force and buoyancy. The sphere moves in discrete time-steps of around 0.065ms. Therefore, at terminal velocity, the following is true: $$ m g = C_d A \frac {\rho u^2}{2} + \rho V g $$ The drag coefficient C_d is defined in terms of the Reynolds Number: $$ Re = \frac {\rho u d}{\mu} $$

• For Stokes' flow (Re < 0.2) $$C_d = \frac{24}{Re}$$
• For Allen flow (0.2 < Re < 1000) $$C_d = \frac{24}{Re} (1 + 0.15 Re^{0.687})$$
• For Newton flow (1000 < Re < 2x10⁵) $$C_d = 0.44$$
• For Re > 2x10⁵ $$C_d= 0.11$$

Dynamic Parameters

The simulation parameters can be changed from the menus at the top of the screen

Time Alteration

The time can be altered from real time to 4 times slower or 4 times faster

Tabular Data

At the bottom of the screen is the table for physical, dynamic parameters and output data

CSV Data Export

Data calculated after experiments can be exported as CSV or XLSX for further operations

Diverse Material Spheres

Any sort of material sphere can be selected by clicking on it ranging from steel to nylon

Lab Auxiliary

A perfect lab auxiliary for the Chemical Engineering streams