Computational Fluid Dynamics
At some point in our lives, we have wondered about some things like how to planes fly or how those sneaky submarines go about their business. There are simple explanations for these questions but some feel the need to dive deeper into these topics and are greeted with oddly coloured lines going all over the place or in scientific terms Computational Flow Diagrams. These may seem difficult at the first glance but with minimal effort can be understood to a good extent. Today we will try to make this topic a little more manageable for you folks.
Computational Fluid Dynamics, a widely used modelling process which us used for physical phenomenon which includes fluid flow, heat transfer with an ability of solving it in numerical ways with computational process. In the growing technology and increase in computers with ever-growing computational power, Computational Fluid Dynamics field is becoming a very common tool which is applied in numerous solutions for problems which has relation with fluid flow. In Computational Fluid Dynamics software analysis, the fluid flow is examined considering its physical properties. Physical properties are velocity, pressure, temperature, density and viscosity.
The technique of CFD is so useful and is exaggerated in a huge span of industrial and non-industrial application areas. Some of the examples are:
1. It is widely used in aerodynamics of aircraft and vehicles with relation to lift and drag
2. Used in hydrodynamics of ships
3. It also plays an important role in power plant focused on combustion in internal combustion engines and gas turbines
4. turbomachinery: flows inside rotating passages, diffusers etc.
CFD working:
To work around fluid flow problems, the codes of Computational Fluid Dynamics are designed as per numerical algorithms. For solving problems, easy access is provided. CFD packages includes some great deals of user interfaces in order to input some problem parameters and to analyze the result. Hence all codes contain three main elements:
a. pre-processor
b. solver
c. a post-processor
Pre-processor: The input of the flow problem is associated with pre-processing to a CFD program by means of an operator-friendly interface and the subsequent transformation of this input into a form suitable for use by the solver.
Solver: For solver, three different streams of numerical solution techniques are there: finite difference, finite element and spectral methods.
Post-processor: As per the work in pre-processing, in post-processing also a good amount of development work is being done in this field. Because of the drastic change in trends of engineering workstations, there are many of whom which have outstanding graphics capabilities and now the top CFD packages are now equipped with versatile data visualization tools.
Governing Equations:
The three main equations that are used are based on the law of conservation of fluids physical property [1,2]:
1. Continuity equation
2. Newton’s Second law
3. First law of thermodynamics/ Energy Equation
The most important part is Fluid flow must be analyzed to know vector v, p and T at each and every point of flow regime. The investigation of movement of fluid can be done with either Lagrangian or Eulerian methods.
While formulating Lagrangian for motion, it is time-dependent. So, a, b, and c are assumed as initial coordinates and x, y, and z are assumed to be the final coordinates of the same particle at time t.
Description of motion for a Lagrangian flow:
X = x(a,b,c,t)
Y = y(a,b,c,t)
Z = z(a,b,c,t) ……………………….(1)
Description of motion for a Eulerian flow for any particular time t:
u=u(x,y,z,t) v=v(x,y,z,t) w=w(x,y,z,t) ……………………….(2)
Conservation of Mass equation is given by [3]:
Dρ/Dt + ρ(∇⋅v⃗) = 0 ………………………. (3)
Navier-Stokes Equation which is referred as Conservation of Momentum is given by:
………………………. (4)
Here
p is static pressure
τ is viscous stress tensor
ρg⃗ is the gravitational force per unit volume
the roman numerals denote:
a. Local change with time
b. Momentum convection
c. Surface force
d. Diffusion term
e. Mass force
The first law of thermodynamics which is Conservation of Energy states that the summation of the work and heat which is added to the system generally results in the energy increase in the system:
dEt = dQ + dW ………………………. (5)
where dQ is the heat added to the system, dW is the work done on the system and dEt is the increment in the total energy of the system. The most common energy equation is given as:
… ……………. (6)
a. Local change with time
b. Convective term
c. Pressure work
d. Heat flux
e. Source term
Partial Differential Equation (PDE):
When we talk about mathematical modelling, we get the interrelation of transport parameters. The equation has a relative effect on physical phenomenon but still the changes in the parameters has to be taken into the consideration simultaneously through the numerical solutions which includes differential equations, vector, and tensor notations.
A Partial Differential Equation has more than one variable which is denoted by “∂”. If the derivation of the equation is conducted with “d”, then these equations are termed as ODE: Ordinary Differential Equations.
It contains a single variable and its derivation. The PDEs are implicated to transform the differential operator (∂) into an algebraic operator in order to get a solution.
Example:
d2x/dt2 = x → x(t) ……… ………. where T is single variable
Example of PDE:
∂f/∂x + ∂f/∂y = 5 → f(x,y) ……………where x and y are variables
Different Types of CFD Applications
Computational Fluid Dynamics tools diversify in accordance with mathematical models, numerical methods, computational equipment, and post-processing facilities. As a physical phenomenon could be modelled with completely different mathematical approaches, it would also be integrated with unlike numerical methods simultaneously. So, an awareness and responding of an establishment or resumption is an essential factor on the path to developing CFD tools.
Number of licensed commercial software solutions are present with open-source software. One of the most used open-source solvers for CFD is OpenFOAM12[12].
SimScale and OpenFOAM are most used simulation platform which are integrated for the solvers.
References:
[1] Frank M. White, Viscous Fluid Flow, McGraw-Hill Mechanical Engineering, 3rd Edition, ISBN-10: 0072402318
[2] http://www3.nd.edu/~gtryggva/CFD-Course/2011-Lecture-9.pdf
[4]http://www.brockmann-consult.de/CloudStructures/karman-vortex-examples-9.html
Authors:
56, 119112589, Ayush Sudhakar Kohade
59, 11910168, Darshan Kulkarni
60, 11910418, Vedang Kulkarni
62, 11910975, Gautam Lunkad
65, 11911259, Archis Mahore
