The Importance of Aerodynamic Flow Quantities in Engineering Design

Introduction

The study of aerodynamics focuses on how air interacts with objects and includes examining different quantities that determine air flow around surfaces. In this article, we explore the important aerodynamic flow quantities that engineers and researchers consider when designing aircraft and improving performance during flight.

1.Pressure

When you hold your hand outside the window of a moving automobile, with your palm perpendicular to the incoming airstream, you can feel the air pressure exerting a force and tending to push your hand rearward in the direction of the airflow. The force per unit area on your palm is defined as the pressure .The pressure exists basically because air molecules (oxygen and nitrogen molecules) are striking the surface of your hand and transferring some of their momentum to the surface. More precisely,Pressure is the normal force per unit area exerted on a surface due to the time rate of change of momentum of the gas molecules impacting on that surface.
It is important to note that even though pressure is defi ned as force per unit area (for example, newtons per square meter or pounds per square foot), you do not need a surface that is actually 1 m 2 or 1 ft 2 to talk about pressure. In fact, pressure is usually defi ned at a point in the gas or a point on a surface and can vary from one point to another. We can use the language of differential calculus to see this more clearly. Referring to Fig. 1,we consider a point B in a volume of gas. Let

dA=An incremental area around B

dF=Force on one side of dA due to pressure

Then the pressure p at point B in the gas is defined as

`p=limleft(frac{dF}{dA}right)dArightarrow0`

Above Equation says that, in reality, the pressure p is the limiting form of the force per unit area where the area of interest has shrunk to zero around point B . In this formalism, it is easy to see that p is a point property and can have a different value from one point to another in the gas.

Figure 1

Pressure is one of the most fundamental and important variables in aerodynamics, as we will soon see. Common units of pressure are newtons per square meter, dynes per square centimeter, pounds per square foot, and atmospheres.Abbreviations for these quantities are N/`m^2`, dyn/c`m^2`, lb/f`t^2` , and atm, respectively.

2.Density

The density of a substance (including a gas) is the mass of that substance per unit
volume.

Density will be designated by the symbol ρ . For example, consider air in a room that has a volume of 250 `m^3`.If the mass of the air in the room is 306.25 kg and is evenly distributed throughout the space, then ρ = 306.25 kg/250 `m^3`=1.225 kg/`m^3` and is the same at every point in the room.

Analogous to the previous discussion of pressure, the defi nition of density does not require an actual volume of 1 m 3 or 1 ft 3.Rather, ρ is a point property and can be defi ned as follows. Referring to Fig. 2.4 , we consider point B inside a volume of gas. Let

dv=Elemental volume around point B

dm=Mass of gasinside dv

Then ρ at point B is

`p=limleft(frac{dm}{dv}right)dvrightarrow0`

Therefore, ρ is the mass per unit volume where the volume of interest has shrunk to zero around point B . The value of ρ can vary from point to point in the gas.Common abbreviated units of density are kg/`m^3`, slug/`ft^3`, g/`cm^3`, and `lb_m`/`ft^3`.

3.Temperature

Consider a gas as a collection of molecules and atoms. These particles are in constant motion, moving through space and occasionally colliding with one another. Because each particle has motion, it also has kinetic energy. If we watch the motion of a single particle over a long time during which it experiences numerous collisions with its neighboring particles, we can meaningfully defi ne the average kinetic energy of the particle over this long duration.
If the particle is moving rapidly, it has a higher average kinetic energy than if it were moving slowly. The temperature T of the gas is directly proportional to the average molecular kinetic energy. In fact, we can defi ne T as follows.
Temperature is a measure of the average kinetic energy of the particles in the gas. If KE is the mean molecular kinetic energy, then temperature is given by KE = `frac{3}{2}` kT,where k is the Boltzmann constant.
The value of k is `1.38times10^{-23}` J/K, where J is an abbreviation for joule and K is
an abbreviation for Kelvin.
Hence we can qualitatively visualize a high-temperature gas as one in which the particles are randomly rattling about at high speeds, whereas in a low temperature gas, the random motion of the particles is relatively slow. Temperature is an important quantity in dealing with the aerodynamics of supersonic and hypersonic fl ight, as we will soon see. Common units of temperature are the kelvin (K), degree Celsius (°C), degree Rankine (°R), and degree Fahrenheit (°F).

4.Velocity

The concept of speed is commonplace: It represents the distance traveled by some object per unit time. For example, we all know what is meant by traveling at a speed of 55 mi/h down the highway. However, the concept of the velocity of a flowing gas is somewhat more subtle.
First, velocity connotes direction as well as speed. The automobile is moving at a velocity of 55 mi/h due north in a horizontal plane.To designate velocity, we must quote both speed and direction.For a flowing gas, we must further recognize that each region of the gas does not necessarily have the same velocity; that is, the speed and direction of the gas may vary from point to point in the flow. Hence, flow velocity, along with p, ρ, and T, is a point property.
To see this more clearly, consider the flow of air over an airfoil or the flow of combustion gases through a rocket engine, as sketched in Fig. 3,4 . To orient yourself, lock your eyes on a specific, infinitesimally small element of mass in the gas, and watch this element move with time.
Both the speed and direction of this element (usually called a fluid element) can vary as it moves from point to point in the gas. Now fix your eyes on a specific fixed point in the gas flow, say point B in Fig. 3,4 . We can now define flow velocity as follows:

The velocity at any fixed point B in a flowing gas is the velocity of an infinitesimally small fluid element as it sweeps through B .

Again we emphasize that velocity is a point property and can vary from point to point in the flow.
Referring again to Fig. 3,4 , we note that as long as the flow is steady (as long as it does not fl uctuate with time), a moving fluid element is seen to trace out a fixed path in space. This path taken by a moving fluid element is called a streamline of the flow. Drawing the streamlines of the flow field is an important way of visualizing the motion of the gas; we will frequently sketch the streamlines of the flow about various objects.
For example, the streamlines of the flow about an airfoil are sketched in Fig. 3,4 and clearly show the direction of motion of the gas. Figure 5 is an actual photograph of streamlines over an airfoil model in a low-speed subsonic wind tunnel.
The streamlines are made visible by injection of filaments of smoke upstream of the model; these smoke filaments follow the streamlines in the flow. Using another flow field visualization technique, Fig. 6 shows a photograph of a flow where the surface streamlines are made visible by coating the model with a mixture of white pigment in mineral oil. Clearly, the visualization of flow streamlines is a useful aid in the study of aerodynamics.

Figure 3

Figure 4

Figure 5

Figure 6

Conclusion

In the ever-changing field of aerodynamics, flow quantities serve as the fundamental elements, leading engineers and researchers towards effective and secure flight. Velocity, pressure, density, temperature, Mach number, Reynolds number, and angle of attack are interconnected, influencing how air behaves when in contact with aircraft surfaces. A thorough comprehension of these aerodynamic flow quantities is crucial for achieving precise and efficient navigation through the skies as aviation advances.