EAS 3923 AEROSPACE LABORATORY III (PROPULSION) SEMESTER II 2016/2017
CONVERGENT AND CONVERGENTDIVERGENT NOZZLE PERFORMANCE DATE OF EXPERIMENT: 27/04/2017
NAME
: MUHAMMAD AKMAL AIMAN BIN BIN ALIAS
MATRIC NUM.
: 181051
LECTURER
: PROF. MADYA IR. DR. ABD. RAHIM BIN ABU TALIB
DEMONSTRATOR : MR. HELMEY RAMDHANEY MOHD SAIAH
1. OBJECTIVES
1) To study the convergent and convergent-divergent nozzle behaviors and their pressure distribution over a variety of overall pressure ratios. 2) To observe the choking, over-expansion, and under-expansion phenomena of the compressible flow through nozzles. 3) To identify the corresponding mass flow rate, ̇ , pressure, P, velocity, V , and area, A, relative to the effect of back pressure, P b, variations.
2. INTRODUCTION
Briefly, a technical perspective has been reviewed on the datasheet extracted from an anonymous webpage for an equipment named as F810 No zzle Pressure Distribution Unit, that is engineered and manufactured by P. A. Hilton Ltd, which was generally discussed before performing this experiment of Convergent and Convergent-Divergent Nozzle Performance, as to fulfil the prerequisites syllabus in EAS3923 Aerospace Labo ratory 3. Thus, Fig. 1 below is showing the overall machine of F810.
Fig. 1: F810 Machine of P. A. Hilton Ltd. This machine is solely for the study stud y of inlet and outlet pressure ratio effects on the mass flow and pressure distribution in nozzles. There are two identical 100mm diameter of 0 to 1100N/m2 of compressible air flow pressure, that is to indicate the air inlet and outlet pressures. Operating from a normal laboratory compressed air supply, this unit is supplied
with one convergent and two convergent-divergent nozzles of identical throat diameter. These nozzles can easily be interchanged and are designed to operate at different theoretical expansion ratios or area ratios, which can be defined as nozzle exit area divided by the throat area, or even divided by its entry area. Each nozzle is equipped with axial pressure tapings that can be connected to eight 60mm diameter panel mounted pressure gauges; but, in this Experiment 1, the convergent-divergent Nozzle B is applied with five pressure tapings, whilst using a convergent (conical) Nozzle C with six pressure tapings as shown in Fig. 2. The unit is fully instrumented to measure pressures, mass flow, and temperatures over a wide range of pressure ratios; as in this case, the Nozzle B design pressure ratio of 0.25. Fig. 3 below is illustrating a schematic diagram of the nozzle pressure distribution unit for F810.
Fig. 2: The Nozzles Used with Their Pressure Gauges Tapping Points
Fig. 3: The F810 Nozzle Pressure Distribution Unit Schematic Diagram
In this hands-on experiment, Nozzle B and Nozzle C are used as for the convergent-divergent and convergent types of mechanism, respectively. The convergent nozzle of Nozzle C having the cross section of nozzle tapers to a smaller section allow for changes which occur due changes in velocity – as the flow expands, it has lower expansion ratio and h ence, lower outlet velocities. In Fig. 5, the effect of back pressure, P b, variations for Nozzle C can be depicted as below. Plus, the airflow in the convergent nozzle is assumed only adiabatic. On the other hand, for a convergent-divergent Nozzle B, which may converge to throat and diverges afterwards. It has higher expansion ratio – as addition of divergent portion produces an isentropic assumption airflow of higher velocities. Moreover, the velocity and static pressure along the longitudinal axis of Nozzle B are plotted in Fig. 4 below. This nozzle is also designed with a condition of having the exit pressure equal to the ambient pressure as illustrated in Fig. 6.
Fig. 4: Velocity and Static Pressure Distribution in Convergent – Divergent Nozzle
Fig. 5: The Pressure Variations for Flow Through A Convergent Nozzle C
Fig. 6: The Pressure Variations for Flow Through A Convergent-Divergent Nozzle B
Theoretically Fig. 7 below depicting the general behavior of convergent-divergent nozzle, when the exit pressure exceeds the ambient pressure, Pe > Pa, for an under-expansion case with greater Mach number than the its design value, the expansion waves exist on the too small nozzle lip exit area. Whilst, in the opposite case, when the ambient pressure exceeds the exit pressure, Pe < Pa, for an over-expansion, the Mach number is somewhat much lower than its design value, which producing an oblique shock waves that are generated at the excessive exit plane area. By definition, the dimensionless quantity of Mach number is the ratio of the airflow velocity passed the boundary to the lo cal speed of sound, whereas, if M > 1, the flow is supersonic, if M < 1, the flow is subsonic, whilst when M = 1, the flow is sonic. In this experimentation, the ambient pressure is assumed as the back p ressure, Pa = P b.
Fig. 7: The Experiential Study of Over-Expansion and Under-Expansion Phenomena Moreover, the basic variation of area with velocity explained the nature of the flow in subsonic and supersonic nozzles and diffusers, which are summarized in Fig. 8. From Fig. 8(a), as to accelerate a compressible fluid flowing subsonically, a converging nozzle must be used, but once M = 1 is achieved, further acceleration can occur only in a diverging nozzle. Thus, the nozzle would be attaining general parameters as V increases; h, P, and decrease. Whilst, from Fig. 8(b), the converging diffuser is required to decelerate a compressible fluid flowing supersonically, but once M = 1 is achieved, further deceleration can occur onl y in a diverging
diffuser. Hence, the diffusers will be producing counter values of parameters as V decreases; h, P, and increase in subsonic speeds, whilst the velocity is increased in the diffusers as the
supersonic speed is attained.
Fig. 8: Effects of Area Change in Subsonic and Supersonic Flows. In addition, the rotameter is an industrial flowmeter used to measure the flowrate of liquids and gases. The rotameter consists of a tube and float. The float response to flowrate changes is linear, and a 10-to-1 flow range or turndown is standard. For this experiment, the rotameter’s principle of operation is based on mass flow rate,
̇. The greater the flow, the
higher the float is raised, which producing the higher ̇ . The height of the float is directly proportional to the flowrate. With gases as in this case, buoyancy is negligible, and the float responds to the velocity head alone. Fig. 9 showing a typical gravity dependent rotameter which vertically oriented and mounted in the F810 machine.
Fig. 9: The Rotameter for the Mass Flow Rate of the Airflow
3. APPARATUS & EQUIPMENT
1) Hilton F810 Nozzle Pressure Distribution Unit.
Fig. 10: The Machine for the Nozzle Performance Investigations
4. PROCEDURES
1. The pressure gauges were observed. Since some of the readings were not set to zero, therefore, a calibration was made. The correction values were set, these values were ad ded in the experimental data. The values were tabulated appropriately in a table. 2. The Inlet Pressure Control Valve was closed and the Outlet Pressure Control Valve was opened to release any air left inside. The Outlet Pressure Control Valve was closed. 3. The Nozzle unit (A, B, or C) were secured to the Nozzle Pressure Distribution Unit (tightened by hand only). 4. The pressure connectors were secured to the Nozzle unit (tightened by hand only) (8 connectors for Nozzle A, 5 connectors for Nozzle B and 6 connectors for Nozzle C). Hence, Nozzle B and C were chosen. 5. The compressed air supply cable was connected to the Nozzle Pressure Distribution Unit. 6. The Inlet Pressure Control Valve was slowly released to a desired pressure. 7. The Outlet Pressure Control Valve was slowly released to a desired mass flow rate.
8. The pressure gauge readings were observed and noted. 9. The mass flow rate was continue increased until the throat is at choked cond ition (the mass flow rate could not be increased any further, the critical pressure at throat was achieved). The pressure distribution was noted at this point (experiment for Nozzle stopped at this stage). 10. The Outlet Pressure Control Valve was continue released until the exit plane pressure ceases to decrease. 11. The Outlet Pressure Control Valve was continue released, notice that the exit plane pressure will start to increase. The experiment was stopped when the exit plane pressure ceases to increase. 12. The experiment was repeated for several inlet pressure settings. 13. The control valves were opened to release all air in the end of the experiment.
5. RESULTS
All the resulting data recorded are tabulated appropriately in Table 1 until Table 8 . Before this experimentation took place, the calibration was performed to make the equivalent values of back pressure (ambient pressure) and the inlet pressure, P b = Pi, as to observe the errors corresponding from each pressure gauges of each nozzle applied and also to indicate the zero ‘0’ mass flow rate. As a result, the overall data recorded is tabulated and graphically represented in Graph 1 until Graph 8 as below. Mass Flow Rate Variation due to Pressure Ration for Nozzle B 3.5 3
) s 2.5 / g ( ṁ
M = 1, P*
2
, e 1.5 t a R 1 w o l F 0.5 s s 0 a M
2.8
1.3
0
0.2
0.4
0.6
0.8
1
1.2
Overall Pressure Ration, P b/ P i Pi = 400kPa
Pi = 200kPa
Graph 1: Graph of Mass Flow Rate Versus Overall Pressure Ration for Nozzle B The representation of the dotted line in Graph 1 above dictating where the throat of the converging-diverging section of the Nozzle B. As the overall pressure ration of the back pressure, P b, to the fixed, static inlet pressure, Pi, keep decreasing further, the maximum mass flow rate, ̇ , is attained for the given stagnation condition, which means there is no changes in the altitude and inlet pressure and temperature. Experimentally, this maximum ̇ , indicates the Mach number unity is attained at M = 1, and as the sonic velocity is attained at the throat, the flow of the nozzle is now choked. Whilst, further decreases in the P b, can just resulted in a constant ̇ as shown in Graph 1 above.
Table 1: The Data Recorded for Convergent-Divergent Nozzle B at Pi = 400kPa Inlet Temp., T (°C)
Outlet Temp., T (°C)
Mass Flow Rate,
̇
25.5 25 25
26 25 25
(g/s) 0 2.6 2.8
25 24.5
25 24.5
2.8 2.8
Tapping Point Pressure (kPa) Inlet Back Pressure, Pressure, Pi (kPa) P b (kPa)
400
P1
P2
P3
P4
P5
400 300 200
410 360 360
400 210 160
430 270 130
440 300 190
420 300 200
100 0
360 360
160 150
70 70
30 30
80 -10
Table 2: The Pressure Ratios Corresponding at Each Tapping Point for Convergent-Divergent Nozzle B
Pressure Ratio, ⁄ (kPa)
Inlet Pressure, Pi = 400kPa Overall Pressure Ration,
1⁄
2⁄
3⁄
4⁄
5⁄
⁄ (kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
400 300
1 0.75
1.025 0.9
1 0.525
1.075 0.675
1.1 0.75
1.05 0.75
200 100 0
0.5 0.25 0
0.9 0.9 0.9
0.4 0.4 0.375
0.325 0.175 0.175
0.475 0.075 0.075
0.5 0.2 -0.025
Back Pressure, P b (kPa)
Table 1 and Table 2 above showing the series of recorded data during the experimentations. These resulting recorded data for the converging-diverging section of Nozz le B which having five local tapping pressure points to be experimented as the inlet pressure is stagnated at Pi = 400kPa, whilst decrementing the back pressure, P b, at a constant rate of 100kPa. The highlighted box in Table 1 is showing the maximum
̇ = 2.8, whereas the choke flow
occurred, the M = 1, and the critical pressure, P*, corresponded to the pressure at the throat incurred. Whilst, the two highlighted boxes in Table 2 showing the crucial data for overex pand
flow ( 5⁄ = 0.2) and underexpand flow ( 5⁄ = -0.025) conditions after passing through a
normal shock wave at the exhaust region outside the nozzle as depicted in Graph 2 above.
Pressure Profile for Nozzle B ( P i = 400kPa) 1.2
1 i
P / x 0.8 P , o i t 0.6 a R e r 0.4 u s s e 0.2 r P 0 0
1
2
3
4
5
6
-0.2
Five Tapping Pressure Gauges Pb = 400kPa
Pb = 300kPa
Pb = 200kPa
Pb = 100kPa
Pb = 0kPa
Graph 2: Graph of Pressure Ratios Versus Five Tapp ing Pressure Point Gauges (Pi = 400kPa) The resulting data recorded in Table 3 and Table 4 is for the stagnated inlet pressure of Pi = 200kPa, at a constant rate of decrement of P b = 50kPa over the whole process. As previous, the highlighted box in Table 3 is corresponded to the critical pressure, P*, at the nozzle’s throat, sonic flow (M = 1), and flow choking at maximum of ̇ = 1.3 conditions, whilst Table
4 is showing the data of Graph 3’s expansion waves ( 5⁄ = 0.25; -0.1) as P b decreases,
which also occurred when design condition is fail to be achieved. The ideal, properly expanded wave of desired condition is occurred when Pe = P b, whereas Pe is the exit pressure. Table 3: The Data Recorded for Convergent-Divergent Nozzle B at Pi = 200kPa Inlet Temp., T (°C) 24 24.5 24.5 24.5 24.5
Outlet Temp., T (°C) 24 24 24.5 24 24
Mass Flow Rate,
̇ (g/s) 0 1.1 1.1 1.3 1.3
Tapping Point Pressure (kPa) Inlet Back Pressure, Pressure, Pi (kPa) P b (kPa)
200
200 150 100 50 0
P1
P2
P3
P4
P5
210 190 190 180 180
190 120 60 60 50
210 150 80 10 10
220 170 110 30 -30
210 160 100 50 -20
Table 4: The Pressure Ratios Corresponding at E ach Tapping Point for Convergent-Divergent Nozzle B
Pressure Ratio, ⁄ (kPa)
Inlet Pressure, Pi = 200kPa Overall Pressure Ration,
Back Pressure, P b (kPa) 200 150 100 50 0
1⁄
2⁄
3⁄
4⁄
5⁄
⁄ (kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
1 0.75 0.5 0.25 0
1.05 0.95 0.95 0.9 0.9
0.95 0.6 0.3 0.3 0.25
1.05 0.75 0.4 0.05 0.05
1.1 0.85 0.55 0.15 -0.15
1.05 0.85 0.5 0.25 -0.1
Pressure Profile for Nozzle B ( P i = 200kPa) 1.2 1
i 0.8 P / x P 0.6
, o i t 0.4 a R e r 0.2 u s s 0 e r P
0
1
2
3
4
5
6
-0.2 -0.4
Five Tapping Pressure Gage Pb = 200kPa
Pb = 150kPa
Pb = 100kPa
Pb = 50kPa
Pb = 0kPa
Graph 3: Graph of Pressure Ratios Versus Five Tapping Pressure Point Gauges (Pi = 200kPa) Next, in the conical converging section of the Nozzle C, as the back pressure, P b, is decreases at certain decrements of kilo N/m2 under the stagnation conditions at the inlet, the mass flow rate, ̇ , will rises up until a certain maximum amount of g/s at the Rotameter, and stays constant even if the P b keep further decreasing. The dotted lines in Graph 4 below are representing the point where the maximum ̇ is achieved experimentally. These points are where the sonic Mach number unity (M = 1) is also achieved independently, whereas the flow
is choked. The ̇ is stayed constant beyond that point even though if the P b is keep decreasing more and more as shown in Graph 4 below. Mass Flow Rate Variation due to Pressure Ration for Nozzle C 3
2.5
) s / g (
M = 1, P *
2.8
2
ṁ1.5
, e t a R 1 w o 0.5 l F s s 0 a M
1.3
0
0.2
0.4
0.6
0.8
1
1.2
Overall Pressure Ration, P b/ P i Pi = 400kPa
Pi = 200kPa
Graph 4: Graph of Mass Flow Rate Versus Overall P ressure Ration for Nozzle C As the experiential progresses, the data to observe the behavior performance of converging nozzle section. At a constant decrement of P b, at 100kPa, the static inlet pressure, Pi is fixed at 400kPa in first case. Hence, the nozzle is equipped with six local tapping pressure gauges as to observe the P b at each region of nozzle length. In Table 5, the experimental choking condition is where speed of sound is obtained in the flow (highlighted) as the sonic throat (M = 1), critical pressure, P*, and maximum ̇ = 2.8 is arrived but stayed constant beyond that. Table 5: The Data Recorded for Convergent Nozzle C at Pi = 400kPa Inlet Temp., T (°C)
24.5
Outlet Temp., T (°C) 24.5 24.5 24 24 24
Mass Flow Rate,
̇ (g/s) 0 2.1 2.8 2.8 2.8
Tapping Point Pressure (kPa) Inlet Back Pressure, Pressure, Pi (kPa) P b (kPa)
400
400 300 200 100 0
P1
P2
P3
P4
P5
P6
410 390 380 370 370
390 360 340 330 340
410 370 330 330 330
420 350 270 270 270
400 310 190 180 180
410 320 190 170 170
Table 6: The Pressure Ratios Corresponding at Each Tapping Point for Convergent Nozzle C
Pressure Ratio, ⁄ (kPa)
Inlet Pressure, Pi = 400kPa Overall Pressure Ration,
1⁄
2⁄
3⁄
4⁄
5⁄
6⁄
⁄ (kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
400
1
1.025
0.975
1.025
1.05
1
1.025
300 200 100
0.75 0.5 0.25
0.975 0.95 0.925
0.9 0.85 0.825
0.925 0.825 0.825
0.875 0.675 0.675
0.775 0.475 0.45
0.8 0.475 0.425
0
0
0.925
0.85
0.825
0.675
0.45
0.425
Back Pressure, P b (kPa)
In addition to this experiential recorded data evaluation in Table 5 and Table 6, as this experimentation went further for a converging conical section of nozzle like Nozzle C only, the supersonic speed or velocity cannot be achieved beyond the Mach disk (choked flow) at the nozzle’s throat, instead the sonic velocity (M = 1) is incurred by the nozzle at the ver y end its exit lips. So, there are no shock wave nor expansion wave occurred during this hands-on process, which producing a nozzle steady-state flow of graphical representation in Graph 5 below. Even if the converging section of nozzle is further extended b y reducing its flow area as in favor of producing supersonic flow velocity, the sonic velocity will eventually be transferred to the exit of the converging extension, rather than the original nozzle exit, which making the mass flow rate, ̇ , to be decreased because of the reduced exit area.
Pressure Profile for Nozzle C ( P i = 400kPa) 1.2
1 i
P / x 0.8 P , o i t 0.6 a R e r 0.4 u s s e r P 0.2 0 0
1
2
3
4
5
6
7
Six Tapping Pressure Gage Pb = 400kPa
Pb = 300kPa
Pb = 200kPa
Pb = 100kPa
Pb = 0kPa
Graph 5: Graph of Pressure Ratios Versus Six Tapping Pressure Point Gauges (Pi = 400kPa) Furthermore, upon completing this observation, evaluation, and analyzation of the nozzle behavior performance, the last condition of the converging Nozzle C is when the static inlet pressure is fixed throughout the nozzle at Pi = 200kPa. The highlighted box in Table 7 is reflecting to the highest possible value of
̇ , at which the choked flow occurred, and
beginning to achieve the sonic speed of sound, practically at the exit of the nozzle. From Table 8, the pressure ratios of every tapping point pressure gauge have plotted the graph as in Graph 6 below. As observed, both of the plotted graphs in Graph 5 and Graph 6 tend to remain constant as it can be understood that the converging section of the Nozzle C will limit its speed to only M = 1, which explained why there is no expansion line plotted in these graphs as depicted for Graph 2 and Graph 3 of previous Nozzle B.
Table 7: The Data Recorded for Convergent Nozzle C at Pi = 200kPa Inlet Temp., T (°C)
Outlet Temp., T (°C)
24.5
24
Mass Flow Rate,
̇ (g/s) 0 0.8 1.2
Tapping Point Pressure (kPa) Inlet Back Pressure, Pressure, Pi (kPa) P b (kPa)
200
1.3 1.3
P1
P2
P3
P4
P5
P6
200 150 100
220 210 200
210 190 170
230 200 180
230 180 150
210 160 110
220 160 120
50 0
190 190
170 170
170 170
130 130
80 70
70 70
Table 8: The Pressure Ratios Corresponding at Each Tapping Point for Convergent Nozzle C
Pressure Ratio, ⁄ (kPa)
Inlet Pressure, Pi = 200kPa Overall Pressure Ration,
1⁄
2⁄
3⁄
4⁄
5⁄
6⁄
⁄ (kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
200 150
1 0.75
1.1 1.05
1.05 0.95
1.15 1
1.15 0.9
1.05 0.8
1.1 0.8
100 50 0
0.5 0.25 0
1 0.95 0.95
0.85 0.85 0.85
0.9 0.85 0.85
0.75 0.65 0.65
0.55 0.4 0.35
0.6 0.35 0.35
Back Pressure, P b (kPa)
Consequently, the plotted graphical representations of Graph 2 and 3, with Graph 5 and 6 is thoroughly discussed in the following discussion section, which also reflects to the performance of the nozzles’ operations due to its nature behavior and the effect of back pressure variations.
Pressure Profile for Nozzle C (Pi = 200kPa) 1.4 1.2
i 1 P / x P 0.8 ,
o i t 0.6 a R e r 0.4 u s s 0.2 e r P 0
0
1
2
3
4
5
6
7
Six Tapping Pressure Gage Pb = 200kPa
Pb = 150kPa
Pb = 100kPa
Pb = 50kPa
Pb = 0kPa
Graph 6: Graph of Pressure Ratios Versus Six Tapping Pressure Point Gauges (Pi = 200kPa)
6. DISCUSSIONS AND QUESTIONS
In this laboratory report, the results of this experiment of Convergent and ConvergentDivergent Nozzle Performance are presented by thorough discussing on all the flows’ behavior performances for maximum optimization ranging from the tabulated data visualizations in the Table 1 until 8, with the corresponding graphical representations of Graph 1 until 6. From the primary convergent-divergent Nozzle B graphs plotted analyses, the effect of back pressure, P b, variations to the stagnation conditions of its inlet pressure, Pi or P0, and temperature, T i or T 0, can be observed as in Fig. 11 below, whereby, this simplicity of onedimensional flow model analysis has derived a flow b ehavior at which each pressure ratio can be represented in the denotation of case (a), (b), (c), (d), (e), and (f). In cases (a) and (b), the mass flow rate, ̇ , increases as P b is reduced in consecutive steps of certain decrement of 100kPa and 50kPa in two levels of fixed inlet pressure, Pi = 400kPa; 200kPa, respectively from P0 to P(a), P(b), and P(c). Thus, the flow accelerates in the converging section with lowest pressure and then decelerates subsonically with greatest pressure in the diverging section of Nozzle B. Eventually, when P b = P(c), the pressure at the throat reaches the critical pressure, P*, corresponding to a Mach number of unity (M = 1) there. At this condition, the flow is
choked, and ̇ cannot increases with further decrease in P b, where the greatest velocity and
lowest pressure occurred. Then, as the P b is reduced below P(c), the flow in the converging section or the upstream is unchanged. Practically, at this point of P(c), the normal shock wave would appear in the diverging section which technically increases the pressure abruptly and irreversibly to match the P b imposed at the exit of the nozzle, and also decreases the flow speed abruptly from supersonic to subsonic flow. The normal shock wave appeared in the pressure distribution for Nozzle B for which indicated the starting condition of over-expanded flow detaching from the nozzle’s wall; however, as the P b is reduced more to be lesser than case (c) in the downstream, the pressure then, increases inside the nozzle which forms an oblique compression shock wave, that is somewhat referred to as overexpansion for case (d). Then, there is a virtual dotted line of a unique P b in case (e) for which no shock waves occur within or outside of the nozzle, whereas the flow is properly expanded as to be indicated for the desired design condition of any nozzle flow behavior performances optimization, when Pe = P b, where Pe is the exit pressure; but, not acquired in this experiment due to certain
erroneous. After that, an underexpansion situation had appeared at the downstream when the flow expands more outside the nozzle through an oblique expansion shock wave for which in case (f). Practically, these experiential results did reflect accordingly to the theoretical concepts, because the overexpansion and underexpansion conditions will just only appear at the downstream region of the nozzle. To be details based on theory concepts, overexpansion is happening when the pressure decreases continuously as the flow expands isentropically through the nozzle and then increases to match the P b outside the nozzle, whilst, in underexpansion, the flow expands isentropically through the nozzle and then expands outside the nozzle to the P b. Regarding the ̇ , once M = 1 is achieved at the throat, the ̇ is fixed at its critical, maximum value for the given stagnation conditions, so the ̇ is the same for P b corresponding to cases (c) through (f).
M=1
(a)
(b) (c) Choke
Overexpansion P*
(d) (e) (f) Underexpansion
(a) (b)
(c) Overexpansion
Choke
(d)
P*
(e) (f) Throat
Underexpansion
Fig. 11: Effect of Back Pressure Variation on the Operation of Convergent – Divergent Nozzle B On the other hand, as from the resulting graphs plotted in the Convergent Nozzle C, the onedimensional flow model analysis on the flow performance behavior under the stagnation condition of the converging section alone has dictated in several crucial cases in the nozzle length itself as (a), (b), (c), (d), and (e) in Fig. 12. Particularly, in case (a), when
̇ = 0, it is
proven that P b = Pe = P0, whereas the P0 is the initial or often referred as Pi. Then, as the P b, is decreased more as in cases (b) and (c), the
̇ will started to increases and the flow speed
throughout the nozzle length is subsonic, whereby the pressure at the nozzle exit equals the P b. This resulted in greater ̇ and new pressure variations within the nozzle. Now, as the area
of the nozzle is decreasing with decrements of P b at 100kPa and 50kPa for two amounts of static Pi = 400kPa; 200kPa, respectively, the velocity of the flow at the downstream will be increases until eventually a Mach number unity (M = 1) is attained at the nozzle exit plane. The corresponding pressure there is denoted by P*, whereas since the velocity at the exit equals the velocity or speed of sound, reductions in P b below P* have no effect on flow conditions in the nozzle. Neither the pressure variation within the nozzle nor the ̇ is affected. Thus, under this critical situation in case (d) and (e), the nozzle is said to be choked at the sonic throat by the Mach disk, making a maximum possible ̇ , with decreasing area and pressure within the nozzle. These constant lines of graphs plotted are also depicted the limitation of M < 1 at the throat of the converging nozzle section based on the theoretical concept on the downstream section. The possibility of certain errors may have occurred during this experimentation, thus, to overcome those errors, one must take some precaution steps; such as, setting up the complicated equipments and apparatus correctly, that involves from installing the nozzles in the machine, calibrating the flow conditions appropriately, and using much smaller decrement of P b variations. The smaller decrement could produce a nice, detailed kind of graphical representations which point to each behavior in the flow performances. Moreover, all the resulting recorded data are obtained by the observers’ very own eyes, which somehow may not be perpendicularly to the needle reading of each local pressure gauge, as in parallax error.
M=1
(a) (b)
(c) (d) (e)
Choke P*
(a)
(b) (c) (d) (e)
Choke P*
Throat Fig. 12: Effect of Back Pressure Variation on the Operation of Convergent Nozzle C
7. CONCLUSION
Therefore, in this experiment of Propulsion – Convergent and Convergent-Divergent Nozzle Performance which is conducted in the Propulsion Laboratory, all of the objectives are achieved successfully, which is by studying the convergent and convergent-divergent nozzle behaviors and their pressure distribution over a variety of overall pressure ratios. Now that it is concluded that the pressure profile for Convergent-Divergent Nozzle B is somehow plotting an erroneous form of graphical representation in this practical experiment rather than in the theoretical concepts of the converging-diverging section of nozzle. Whilst, the pressure profile for Convergent Nozzle C did plotted the converging section of nozzle graphs that match with the theory representation. Furthermore, many phenomenon which included in this experiential condition have been observed from the graphs plotted; for instance, the flow choking, over-expansion, and underexpansion phenomena of the compressible flow through both nozzles. Technically, the choked flow is when the Mach disk appeared at some region inside the nozzle length; but, not necessarily at the minimum area, A, of the nozzle and achieved its sonic speed of M = 1. This corresponding speed also has declared the critical pressure, P*, occurred in the nozzle, though. Fig. 13 below is showing the real-time situations whereas the overexpansion and underexpansion phenomena had occurred. As been discussed previously, the design condition of Pe = P b, whereas the P b is also referred to as ambient pressure, Pa, for which represented experimentally in the graphs plotted of Fig. 11 above in case (e) is crucially desirable for most rocket model applying the nozzle medium for thrust acceleration optimum efficiencies. When overexpansion occurred, the compressible flow at the exhaust of the nozzle is ‘pinched’ inwards as the Pa surrounding it is greater than the Pe, making the useless implementation of the spaces between the flow and the nozzle’s wall to additionally generate the thrust force. On the other hand, the hot flow is somehow overly expanding outside the nozzle’s wall in underexpansion, which then producing the flow to be expand outwards the exit area of the nozzle (exhaust region) as the Pa surrounding it is smaller than the Pe, making the thrust force to be lost in spa ce and not efficiently used for the optimum usage inside the nozzle’s wall itself.
Fig. 13: The Rocket Compressible Flow Phenomena; for, (a) Overexpansion (b) Underexpansion The third objectives have been also identified rigorously from the resulting graphs corresponding to the mass flow rate, ̇ , pressure, P, velocity, V , and area, A, relative to the effect of back pressure, P b, variations. As for the flow rate, the
̇ will linearly rises up into a
highest possible point where it stays constant when it reached the sonic speed of Mach number equal to one and P* throughout the P b variations, because of the conservation of mass theory, whereas the amount of mass remains constant – neither created nor destroyed. Theoretically, the quantity of × × has the dimensions of mass/time and is called the mass flow rate or
̇. This quantity is an important parameter in determining the thrust produced by a propulsion system as the conservation of mass makes easier to determine the velocity at any region of a flow in a nozzle when the density,
, is constant at low speed (subsonic) and changing
independently at near to beyond speed of sound (transonic to sonic to supersonic) due to compressibility effects of the compressible flow. Therefore, the objectives are achieved successfully, despite the erroneous.
8. REFERENCES
1. Compressible Fluid Flow. F810 Nozzle Pressure Distribution Unit . Retrieved 30 April 2017, from http://www.alfarez.com/frames/hilton/compressible-fluid.html 2. Omega. Rotameters – Introduction to Pressure Measurement with Rotameters. Retrieved 30 April 2017, from http://www.omega.com/prodinfo/rotameters.html 3. Mass
Flow
Rate.
(2015). Grc.nasa.gov.
Retrieved
30
April
2017,
from
https://www.grc.nasa.gov/www/K-12/airplane/mflow.html 4. El-Sayed, A. F. (2008). Aircraft propulsion and gas turbine engines. New York City: CRC Press. 5. Abdul Ahad Noohani (n.d.). Nozzle. Class lecture for Thermodynamics-II, MIT Department of Mechanical Engineering, Mehran University of Engineering and Technology (MUET), Jamshoro, Pakistan. 6. Dávila, A. L. P. (2016, February 13). Compressible Flow in Nozzles. Class lecture for WI15-ME4111-35 – Thermal Engineering Laboratory, Mechanical Engineering Department, Polytechnic University of Puerto Rico (PUPR), San Juan, Puerto Rico. 7. Moran, M. J., Shapiro, H. N., Boettner, D. D., & Bailey, M. B. (2014). Fundamentals of engineering thermodynamics. New York City: John Wiley & Sons, Inc.
