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• Oshin Mittal

# Introduction to CFD | Computational Fluid Dynamics | Tool to analyze airflow

As a kid, we all have admired planes at some point of time in our life. There is a certain level of fascination towards these flying objects. But do you know what goes behind making these aircraft? What’s the maths and physics behind it?

To begin with, thanks to technology, we have computer-aided engineering. Different software assists in the designing as well as the analysis of the objects. We have different equations and models to study different factors and circumstances. After completion of designing, we begin with the CFD (computational fluid dynamics) analysis which gives us the final verdict about our design.

So today, we will discuss mainly CFD. Let's head on then !!

BASICS OF COMPUTER-AIDED ENGINEERING (CAE):

Inferences:

From the perspective of fundamental logic, engineering reasoning is categorized into the following three types of inference given the rule, cause, and effect of the physical quantity:

• Deduction- Given the rule and the cause, we deduce the effect. E.g., Simulations and analysis.

• Induction- Cause and effects are known and from this information, we induce the rule. E.g., Interpretation.

• Abduction- Rule and the effect is pre-defined through which we abduct the cause. It's just the reverse of deduction. E.g., Diagnosis and synthesis.

Important engineering tasks are simulation, diagnosis, synthesis, and interpretation of

information. All of these tasks transform one type of information to another through

inference.

• Simulation- In this, causes are applied to particular structures in order to observe effects under the effect of a rule.

• Analysis- It is a special case of simulation. The analysis is performed when behavioral parameters are required for a given physical configuration in a particular environment.

• Diagnosis- Diagnosis can be thought of as the reverse of simulation. For this task, observed effects are considered with the physical configuration and the environment to infer causes.

• Synthesis- synthesis is the reverse of analysis, where target behavior is used to infer a physical configuration within an environment.

• Interpretation- Interpretation of information includes a wide range of engineering activities. Interpretation of information refers to tasks that infer knowledge from activities.

MATHEMATICAL MODELS INVOLVED IN CFD:

The main structure of thermo-fluids examination is directed by governing equations that are based on the conservation law of fluid’s physical properties. The basic equations are the three laws of conservation.

• Conservation of Mass: Continuity Equation

• Conservation of Momentum: Newton’s Second Law

• Conservation of Energy: First Law of Thermodynamics or Energy Equation

Euler Equation:

There are driving as well as the resistive force which comes into the picture when fluid flow is considered. One such basic resistive force is the viscous force.

The motivation behind this equation:

When a fluid flows across a solid body at a very high velocity, the effect of the wall will be felt on the very thin layer, called the boundary layer. The momentum disturbance due to the viscous effects won’t propagate to the outer layer and hence, here, the flow would be governed by the laws of motion. Shear stress is a combined product of the rate of deformation and viscosity so if the rate of deformation is negligible, shear stress tends to 0. So, Euler’s equation is an equation to study fluid flow under such conditions.

Equation: Euler Equation

Navier-Stokes:

The following assumptions about fluids are made while dealing with the Navier-Stokes equation:

• Newtonian

• Incompressible

• Isothermal

Equation: Navier-Stokes Equation

Application:

This equation is used to

• predict weather forecast

• model airplanes and rockets

• predict the flow of water currents.

But due to the chaotic nature of fluids, we can’t predict the weather for more than 7 days or predict when the turbulence will happen.

Reynold’s Transport Theorem:

Purpose:

Not always do we have a fixed mass flowing. At times we need observation in terms of volume or the region of observation is control volume. All the equations discussed above are with respect to control mass. Now, when we have to make the shift from the control mass approach to control volume, certain adjustments or alterations need to be made in our mathematical equations which are realized through this theorem.

Equation: Reynold's Transport Theorem

Reynolds Average Navier-Stokes (RANS) Equation:

Motivation:

Navier Stokes equation for turbulent flow exhibits certain characteristics like they are highly sensitive to initial conditions and they must address a wide range of length scales and time scales. Whereas we can reduce those complexities by considering the statistical average form of the equation.

Equation: Closure Equations:

In RANS, Reynold’s stress tensor gives additional unknowns but there are no additional governing equations for them. We have 10 unknowns and 4 equations; hence the equation is indeterminant and therefore one needs to close the problem i.e., obtain additional or derive additional equation or model equation if necessary, so as to come up with a matching condition w.r.t. no. of equations and no. of terms.