1 Motasem Ash, Jafar Samarah, Othman Shnikat

CHAPTER 1

Introduction

Compressible flow is an important field and essential for aircrafts, rocket, and missiles as

well as for cars when they travel at high speeds.

So to investigate the compressible flow, first we have to know its regimes, characteristics,

principles as well as the conditions surrounding the flow.

Compressible flow regimes based on a dimension less number called (Mach number);

due to Mach number flow regime can be determined.

Compressible flow regimes can be summarized as:

1- Subsonic Flow Ma<0.8.

2- Transition Flow 0.8<Ma<1.2.

3- Supersonic Flow 1.0<Ma<5.0.

4- Hypersonic Flow 5.0<Ma<10.

5- High Hypersonic Flow 10<Ma<25.

6- Re-entry speeds Ma>25.

Mach number based on the ration between the speed and speed of sound, but other

parameter can affect the flow, such as:

1- Friction.

2- Heat addition.

3- Shock waves.

These parameters affect the flow in a sensible manner, so to get the solution; we have to

put them in mind.

2 Motasem Ash, Jafar Samarah, Othman Shnikat

CHAPTER 2

Theory

In this chapter we will go through the important principles, equations and parameters that

affect the compressible flow in Venturi tube then to an orifice plate.

2.1 Compressible flow:

Flow is considered to be a compressible flow if the density of the fluid changes with

respect to pressure. This is often the case where the Mach number (the ratio of the flow speed to

the local speed of sound) of the flow exceeds 0.3.

2.2 Mach Number:

Mach Number is the speed of an object moving through air, or any other fluid substance,

divided by the speed of sound as it is in that substance for its particular physical conditions,

including those of temperature and pressure. It is commonly used to represent the speed of an

object when it is travelling close to or above the speed of sound.

Ma =

2.1

a= √ 2.2

Where:

V: speed of the object (m/s).

a: is the speed of sound (m/s).

k: Specific heat ratio(Cp/Cv).

R: Gas constant (287 J/kg.k).

T: temperature at the altitude of the object (K°).

3 Motasem Ash, Jafar Samarah, Othman Shnikat

2.3 Compressible Flow Regimes:

Compressible flow regimes depends on Mach number as the table 2.1 shows, also figure

2.1 shows the how the flow goes.

Table 2.1: Comparison of compressible flow regimes

Regime Mach

number

Mph Km/h m/s General Plane

Characteristics

Subsonic <1.0 <768 <1,230 <340 Most often

propeller-driven

and commercial

turbofan aircraft

with straight

wings.

Transition 0.8-1.2 610-768 980-

1,475

270-410 Sharp intakes;

compressibility

becomes

noticeable;

slightly swept

wings.

Supersonic 1.0-5.0 768-3,840 1,230-

6,150

340-1,710 Sharper edges;

tail plane is a

stipulator.

Hypersonic 5.0-10.0 3,840-7,680 6,150-

12,300

1,710-3,4 Cooled nickel-

titanium skin;

highly

integrated, small

wings.

High-

Hypersonic

10.0-25.0 7,680-16,250 12,300-

30,740

3,415-8,465 Silica thermal

tiles, blunt

wings.

Re-entry

Speeds

Ma>25.0 >16,250 >30,740 >8,465 Ablative heat

shield; no

wings; blunt

capsule shape.

4 Motasem Ash, Jafar Samarah, Othman Shnikat

Figure 2.1: Flow regimes. a-subsonic- critical case, c- transition, d- supersonic, e- hypersonic

5 Motasem Ash, Jafar Samarah, Othman Shnikat

2.3.1 Subsonic Flow

Consider the flow over an airfoil section as sketched in Fig. 2.1 a. Here, the local Mach

number is everywhere less than unity. Such a flow, where M < 1 at every point, and hence the

flow velocity is everywhere less than the speed of sound, is defined as subsonic flow. This flow

is characterized by smooth streamlines and continuously varying properties Note that the initially

straight and parallel streamlines in the free stream begin to deflect far upstream of the body, i e.,

the flow is forewarned of the presence of the body This is an important property of subsonic

flow. Also, as the flow passes over the airfoil, the local velocity and Mach number on the top

surface increase above their free-stream values However, if Ma is sufficiently less than 1, the

local Mach number everywhere will remain subsonic. For airfoils in common use, if Ma < 0 8,

the flow field is generally completely subsonic. Therefore, to the airplane aerodynamicist, the

subsonic regime is loosely identified with a free stream where Ma < 0 8.

2.3.2 Transition Flow:

In figure 2.1 b. Transition flow is illustrated. If Ma remains subsonic, but is sufficiently

near 1, the flow expansion over the top surface of the airfoil may result in locally supersonic

regions, as sketched in Fig. 2.1b. Such a mixed region flow is defined as transonic flow In

Fig.2.1b, Ma is less than 1 but high enough to produce a pocket of locally supersonic flow. In

most cases, as sketched in Fig.2.1b, this pocket terminates with a shock wave across which there

is a discontinuous and sometimes rather severe change in flow properties Shock waves. If Ma is

increased to slightly above unity, this shock pattern will move to the trailing edge of the airfoil,

and a second shock wave appears upstream of the leading edge this second shock wave is called

the bow shock, and is sketched in Fig. 2.1c. In front of the bow shock, the streamlines are

straight and parallel, with a uniform supersonic free-stream Mach number In passing through that

part of the bow shock which is nearly normal to the free stream, the flow becomes subsonic

However, an extensive supersonic region again forms as the flow expands over the airfoil

surface, and again terminates with a trailing-edge shock Both flow patterns sketched in Fig. 2.1b

and c are characterized by mixed regions of locally subsonic and supersonic flow. Such mixed

flows are denned as transonic flows, and 0.8 < Ma < 1.2 is loosely defined as the transonic

regime.

2.3.3 Supersonic Flow:

As in figure 2.1 d. which shows supersonic flow. Supersonic is used to define a speed

that is over the speed of sound (Ma 1). In dry air at 20 °C (68 °F), the threshold value required

for an object to be traveling at a supersonic speed is approximately 343 m/s, (1,125 ft/s, 768 mph

or 1,236 km/h). Speeds greater than 5 times the speed of sound are often referred to as

6 Motasem Ash, Jafar Samarah, Othman Shnikat

hypersonic. Speeds where only some parts of the air around an object (such as the ends of rotor

blades) reach supersonic speeds are labeled transonic (typically somewhere between Mach 0.8

and Mach 1.2).

Sounds are travelling vibrations (pressure waves) in an elastic medium. In gases sound

travels longitudinally at different speeds, mostly depending on the molecular mass and

temperature of the gas; (pressure has little effect). Since air temperature and composition varies

significantly with altitude, Mach numbers for aircraft can change without airspeed varying. In

water at room temperature supersonic can be considered as any speed greater than 1,440 m/s

(4,724 ft/s). In solids, sound waves can be longitudinal or transverse and have even higher

velocities. Supersonic fracture is crack motion faster than the speed of sound in a brittle material.

2.3.4 Hypersonic Flows:

Hypersonic speeds are those that are highly supersonic. Since the 1970s, the term has

generally been assumed to refer to speeds of Mach 5 (5 times the speed of sound) and above. The

hypersonic regime is a subset of the supersonic regime.

The precise Mach number at which a craft can be said to be fully hypersonic is elusive,

especially since physical changes in the airflow (molecular dissociation, ionization) occur at

quite different speeds. Generally, a combination of effects become important "as a whole"

around Mach 5. The hypersonic regime is often defined as speeds where ramjets do not produce

net thrust. This is a nebulous definition in itself, as there exists a proposed change to allow them

to operate in the hypersonic regime.

2.4 Shock Waves:

Shock wave is type of propagating disturbance. Like an ordinary wave, it carries energy

and can propagate through a medium (solid, liquid, gas or plasma) or in some cases in the

absence of a material medium, through a field such as the electromagnetic field. Shock waves are

characterized by an abrupt, nearly discontinuous change in the characteristics of the medium.[1]

Across a shock there is always an extremely rapid rise in pressure, temperature and density of the

flow. In supersonic flows, expansion is achieved through an expansion fan. A shock wave travels

through most media at a higher speed than an ordinary wave.

There are two types of shock waves,

1- Normal shock waves.

2- Oblique Shock Waves.

7 Motasem Ash, Jafar Samarah, Othman Shnikat

2.4.1 Normal Shock Waves:

Normal shock wave is a shock wave that is traveling through a fluid (often gaseous)

medium with a velocity relative to the velocity of the fluid already making up the medium. As

such, the normal shock relations require modification to calculate the properties before and after

the moving shock. Knowledge of moving shocks is important for studying the phenomena

surrounding detonation, among other applications.

Figure 2.2: Shock Wave is a pressure disturbance over the time.

2.4.2 Oblique Shock Wave:

An oblique shock wave, unlike a normal shock, is inclined with respect to the incident

upstream flow direction. It will occur when a supersonic flow encounters a corner that

effectively turns the flow into itself and compresses. The upstream streamlines are uniformly

deflected after the shock wave. The most common way to produce an oblique shock wave is to

place a wedge into supersonic, compressible flow. Similar to a normal shock wave, the oblique

shock wave consists of a very thin region across which nearly discontinuous changes in the

thermodynamic properties of a gas occur. While the upstream and downstream flow directions

are unchanged across a normal shock, they are different for flow across an oblique shock wave.

8 Motasem Ash, Jafar Samarah, Othman Shnikat

It is always possible to convert an oblique shock into a normal shock by a Galilean

transformation.

Figure 2.3 Oblique Shock Wave.

2.5 Differential Pressure Device (Orifice Plate):

An orifice meter is a device used for measuring the rate of fluid flow. It uses the same

principle as a Venturi nozzle, namely Bernoulli's principle which says that there is a relationship

between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the

pressure decreases and vice versa.

An orifice plate is basically a thin plate with a hole in the middle. It is usually placed in a

pipe in which fluid flows. As fluid flows through the pipe, it has a certain velocity and a certain

pressure. When the fluid reaches the orifice plate, with the hole in the middle, the fluid is forced

to converge to go through the small hole; the point of maximum convergence actually occurs

shortly downstream of the physical orifice, at the so-called vena contracta point (see drawing to

the right). As it does so, the velocity and the pressure changes. Beyond the vena contracta, the

fluid expands and the velocity and pressure change once again. By measuring the difference in

fluid pressure between the normal pipe section and at the vena contracta, the volumetric and

mass flow rates can be obtained from Bernoulli's equation.

2.6 Venturi Tube:

The Venturi effect is the reduction

in fluid pressure that results when a fluid

flows through a constricted section of

pipe. Figure 2.4: Venturi Tube

9 Motasem Ash, Jafar Samarah, Othman Shnikat

CHAPTER 3

Experimental Setup

In this chapter the devices used in the experiment will be mentioned and explained.

Aim of the experiment is to get the pressure values, along Venturi tube with orifice plate

at one side.

To accomplish the experiment the following devices has been used:

1- Air Compressor (10 bar).

2- Venture Tube (Converging- Diverging Nozzle).

3- Orifice Plate (pressure differential device).

4- Bourdon Pressure Gage.

Figure 3.1 shows the drawing of the set-up used in the experiment.

Figure 3.1: Drawing of the set-up used in the experiment

10 Motasem Ash, Jafar Samarah, Othman Shnikat

3.1 Air Compressor:

Figure 3.2 shows the air compressor used in the experiment, the compressor capacity up

to 11 bar (11 *105 Pa).

Figure 3.2: Air Compressor.

3.2 Venturi Tube:

Venturi tube is a converging- diverging nozzle, they are connecting to each other at the

throat.

Venturi tube used to measure the flow rates using the following equation:

Q= A1√

= A2√

………………………………..……….3.1

Figure 3.3 shows the Venturi tube used.

11 Motasem Ash, Jafar Samarah, Othman Shnikat

Figure 3.3: Venturi Tube

3.3 Orifice Plate:

An orifice meter is a device used for measuring the rate of fluid flow. It uses the same

principle as a Venturi nozzle, namely Bernoulli's principle which says that there is a relationship

between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the

pressure decreases and vice versa.

An orifice plate is basically a thin plate with a hole in the middle. It is usually placed in a

pipe in which fluid flows. As fluid flows through the pipe, it has a certain velocity and a certain

pressure. When the fluid reaches the orifice plate, with the hole in the middle, the fluid is forced

to converge to go through the small hole; the point of maximum convergence actually occurs

shortly downstream of the physical orifice, at the so-called vena contracta point. As it does so,

the velocity and the pressure changes. Beyond the vena contracta, the fluid expands and the

velocity and pressure change once again. By measuring the difference in fluid pressure between

the normal pipe section and at the vena contracta, the volumetric and mass flow rates can be

obtained from Bernoulli's equation.

Orifice plate also can be used as pressure differential device as well as flow measuring device by

using the following equation:

m° = ρ1Q1 = C*Y*A2√ …………………………………………………………………………..3.

Y = √

……………………………………………………………………….3.3

r=

………………………………………………………………………………………3.4

Where:

Y: is the expansion factor of the gas.

k: Specific heat ratio.

Note: Equation 3.2 is valid for gas flow only.

12 Motasem Ash, Jafar Samarah, Othman Shnikat

3.4 Bourdon Pressure Gage:

The Bourdon gauge. Bourdon Gauge the Bourdon gauge is shown in figure3.4. It works

on the same principle as that of the snakelike, paper party whistle you get at a New Year party,

which straightens when you blow into it. Within the Bourdon gauge is a thin-walled metal tube,

somewhat flattened and bent into the form of a C. Attached to its free end is a lever system that

magnifies any motion of the free end of the

tube. On the fixed end of the gauge is a

fitting you thread into a boiler system. As

pressure increases within the boiler, it

travels through the tube. Like the snakelike

paper whistle, the metal tube begins to

straighten as the pressure increases

inside of it. As the tube straightens, the

pointer moves around a dial that indicates

the pressure in psi. The Bourdon gauge is a

highly accurate but rather delicate instrument.

You can easily damage it. In addition, it malfunctions if pressure varies rapidly. This

problem was overcome by the development of another type of gauge, the Schrader. The Schrader

gauge is not as accurate as the Bourdon, but it is sturdy and suitable for ordinary hydraulic

pressure measurements. It is especially suitable for fluctuating loads. In the Schrader gauge,

liquid pressure actuates a piston. The pressure moves up a cylinder against the resistance of a

spring, carrying a bar or indicator with it over a calibrated scale. The operation of this gauge

eliminates the need for cams, gears, levers, and bearings.

Figure 3.4: Bourdon Gage

13 Motasem Ash, Jafar Samarah, Othman Shnikat

CHAPTER 4

Experiments & Results

In the experiments, Pressure at different locations (see figure 4.1) is to be determined by

using Bourdon Gage Pressure devices.

Figure 4.1: The Location of Pressure Measurement along the tube.

Results:

At location one(x=0) the reading was

At location two (x=95mm) the reading was

At location three (x=162 mm) the reading was

At location four (x= 435 mm) the reading was

At location five (x=465mm) the reading was

x

1 2 3

4 5

14 Motasem Ash, Jafar Samarah, Othman Shnikat

Conclusion:

There are many conditions that may affect the results, such as:

1- Roughness of the tube.

2- Losses through the tube.

3- Outside pressure.