Heriot ri ot--Watt Universi ni versity ty Chemical & Petroleum Engineering
Multiphase Thermodynamics
Laboratory report 1
Name
Parvin Salamzada
Group number
KM3
Experiment title
Nozzle pressure distribution
Date of Experiment
9.02.2017
Demonstrator
Amir Reza Vakhshouri Vakhshouri
Synopsis In this particular experiment, we are asked to experimentally prove that air is compressible and it possesses special characteristics of compressibility. The purpose of this report is to give more detailed information about the experiment fulfilled in order to see how mass flow rate of the air flow reacts as upstream or downstream pressure changed and at different tapping points, velocity of air flow in mathematical point of view. As we conduct conduct the experiment, experiment, three main objectives objectives provided provided below will will be clarified: 1. Mass flow rate of air through the nozzle as the function of outlet/inlet pressure ratio. 2. Velocity of air flow through the nozzle as the dependence of distance (points). 3. Critical pressure ratios for nozzles for estimation of maximum mass flow rate. Before moving on to explanations of the purposes more clearly, it would be better to deliver the information about the experiment itself. There are three nozzles will be used indicated as Nozzle A, B and C. About the size, and dimensions, all these nozzles have the same cross sectional area of nozzle throat. The conditions are identical for all of them as well. But the differences are their type: whether it is converging diverging or converging. Nozzle A and B are both converging-diverging and Nozzle C is converging type. For each nozzle, we have 4 sets in experiment. For two sets, we stabilize the inlet pressure and change outlet pressure and for other two sets, unlike previous sets, outlet pressure is kept constant and inlet pressures changes. After carrying out the experiment, we obtained the practical mass flow rates, tapping point pressures through the nozzle for each set, with the help of them, it will be reachable to characterize the compressibility of air flow. There is another important specification which is called choked flow. Choked flow is obtained when the mass flow rate reaches its maximum value. As we decrease the downward pressure while keeping inlet pressure constant, mass flow of air flow will become to increase but this rise will continue up to some point which is not related to the values of pressure ratios. Further lessening of pressure ratio will never lead to change in mass flow rate. Then choked flow will begin (straight line for mass flow against pressure ratio). We observe the same situation for the reverse process: Keeping outlet pressure constant and increasing inlet pressure. It is also very important to consider the assumptions before any mathematical operations. First of all, we consider the air as an ideal gas. It is because we are not provided the special formulas or theory that they can be used for air. At lower pressures, the theory from engineering books let us to consider air as ideal gases but here will be some exceptions bout the value of pressures. So that at some sets, pressure will be 3-4 times greater than atmospheric pressure. And it is essential to save in mind that the process is considered as adiabatic although it is neither isothermal nor adiabatic. The process is more close to the adiabatic compression that is why it is selected. In the following sections, the information about the steps to conduct the experiment, theoretical formulas, procedure and the system and equipment that it is composed of, the comparison of theoretical values and experimental values are clearly provided.
Introduction Nozzle used in this experiment as convergent and divergent parts .The graphical representation of flow velocity in the nozzle is the best way of showing wide range of velocities such as subsonic, supersonic and shock wave. The full view of the nozzle is shown in the Figure 1.With help of the lab unit, we get familiar with phenomenal choking effect. After critical pressure ratio it is impossible to rise the mass flow rate .The pressure in the inlet and outlet of the pipe is adjustable .In order to study the behavior o f compressible flow, three different kind of nozzles is used .Converging-Diverging Nozzles are widely used in engineering. These nozzles has applications from civil and mechanical engineering up to aerospace engineering. These nozzles are designed in such a way that increase flow velocity by converging the flow area. In fact, most rockets use help of these nozzles to reach effective propulsion force in order to get recruited speed. From the first look, their operation is simple. However, depending on reacquired speed of the gas at outlet, subsonic and supersonic flows are reached .In this operation, some properties of the flow such as density and temperature changes which makes their operation and working principles more complicated. The performance of these nozzles mainly dependent on pressure ratio between the inlet pressure 0 and outlet (back pressure) . As this ratio decreases, the mass flow rate of the gas will goes up until maximum velocity is achieved .Actually, the maximum velocity is reached when Mach number in the throat is equal to 1 . (sonic flow).This flow is called choked flow . If this ratio reduced further supersonic flow is obtained. After reaching this ratio equal 0.53 and after more complicated flow is obtained.
Figure 1. Full view of the nozzle. The main purpose of this report is investigation of this flow by giving this pressure ratio and its effect on mass flow rate of air through the system and determination distribution of pressure in the taping points and respective flow velocities . There are two kind of flows according to their density change. If the density of the flow changes as the pressure changes, then it is compressible flow. Generally, all the fluids are compressible to some extent, however compressibility of gasses is high enough to affect flow pattern. Generally, if pressure change of the gas does not change by more than 20 per cent that fluid could be treated as incompressible and the density could be taken equal to density at mean pressure. Actually equations for compressible flow is much more complicated than equations for incompressible flow. For simplicity, sometimes ideal gas law is used to show behavior of incompressible fluid. It is obvious from the course Process
Industries C that of the fluid density is dependent on temperature and pressure. Actually, in real cases, if we change one of these parameters, the other one will chan ge as well. The heat transfer to the flow should be taken into account as the fluid flows through the pipe. There are two types of these condition for nozzle .Firstly ,isothermal conditions could be achieved if heat transfer between the system and surroundings is very well and if the equipment is small enough and has low flow rate .Of the condition is opposite , such as if there is no exchange of heat between environment and the system and moreover , the fluid flows with high flowrate , then the condition is adiabatic. The main purpose of this experiment are studying the effects inlet and outlet pressures on the mass flowrate of air through various no zzles. In addition the pressure distribution along the nozzles for varying out let pressures is also investigated. One of the outlet and inlet pressures is kept constant for the given run and other o ne is changed. So some properties of t he flow will change.
Dependence of mass flow rate from critical critical pressure and dependence of the flow velocity from the distance is investigated. Three type o f nozzle is used in this experiment. For each type of the nozzle, for first two run , we set Pin and change Pout. For the second two run, we set Pin and changed Pout .
Basic Theory Laval nozzle is used in this experiment . The working principle of Laval nozzle based on the diverse behavior of gases flowing at subsonic and supersonic speeds. Actually, Bernoulli principle and continuity of flow is the main background principles for Laval nozzle. It is known from continuity equation that ,if the pipe converges, the speed of the flow will increase ,because the mass flow rate should be constant . In a subsonic flow the gas is compressible, and sound will propagate through it. At the throat , where the flow area of the pipe is minimum the gas speed will be sonic (Mach number = 1.0).This situation is choked flow. The Bernoulli's principle could be taken as beckground
principle for this experiment. It is obvious from the Bernoulli's principle that an incompressible fluid pass through varying cross section, then the pressure is irreversible proportional to velocity. We know from the continuity equation that high velocity is appropriate to wide area of the pipe and low pressure is suitable for narrow cross sectional area of the pipe . For the incompressible flow , if the friction between the fluid and the pipe is zero then , total pressure (Energy) of the fluid remains constant . Generally , the motion o f the fluids could be represented by help of Bernoulli's Principle, Newtonian lows and continuity equation. This famous equation is derived under same assumptions such fluid must be incompressible and no frictional pressure loss. Moreover ,the flow must be in steady state . Nozzle is a tube of varying flow area used in order to deterimene flow pressure in varying area. The nozzle used in this experiment is steadly decreasing nozzle which gives acceleration to the fluid and a corresponding pressure drop. This convergent entrance is followed by a throat and a divergent outlet. Divergent outlet allows the fluid to nearly recover its previous pressure. The fluid gradually slows dow n in divergent outlet, kinetic energy is converted into Pressure Energy. This phenomenon can be described by Bernoulli's low. The flow area is minimum at the throat. So, here the kinetic energy of fluid is high and pressure energy is low. Pressure energy is determined by pressure so it means that static pressure is low at narrow area or vice versa. Therefore, the equation given below is used.
’
Figure 2.
Figure 3.
Figure 4.
As the gas flows through the nozzle its pressure decreases from the initial value .Let us denote its initial pressure with P1 and the decreased pressure with Pi. In fact , initially the velocity growths more significantly than specific volume so the area of the pipeline needed for the flow reduces .Actually , this velocity of the air in the nozzle is depends on the pressure ratio . If this pressure ratio is low it means the change in the specific volume is more considerable in comparison to the velocity which means area needed for the flow is increasing .In order to expand to flow below critical value ,the pipe should be diverge . Which means in the converging nozzle , the velocity above the sonic velocity could never be achieved .However, if convergingdiverging nozzle is used supersonic velocities could be achieved in the diverging part. Three cases could be seen in the converging-diverging nozzles. The first case is shown in the figure 1
and 2 . Back-pressure is high . The velocity and pressure profile for the case 1 is represented in the figures and denoted by I .As shown in the curves , the pressure of the fluid gets its minimum value at the throat and just after the throat , the pressure begins to increase . In the exit, the back pressure is egual to the exit pressure .In this case , the nozzle performs like Venturi nozzle .The losses pressure is recovered after the throat .The velocity of the fluid reaches its maximum value at the throat , however its value is less than sonic velocity .Then , it begins to decrease just after the throat .For the second case ,the backpressure is decreased .The pressure is reduced up to critical value and sonic velocity is achieved in the throat. Just after the throat, the pressure begins to increase .At the exit , the pressure is equal to back pressure . As mentioned before , sonic velocity is achieved in the throat and decreses The velocity rises to the sonic value at the throat and then decreases. And in the third case, the pressure decreases to the critical value at the throat and continues to decrease in order to get stabilized with low exit pressure .The sonic velocity is achieved in the throat, and as the pressure continues to decrease, the velocity continues to increase as well. Supersonic velocit y is obtained in the diverging part .So, to conclude , if a converging-diverging nozzle is used and if the backpressure is lower than pressure in the throat and sonic velocity is achieved in the throat , then supersonic velocity is achieved in the diverging part .
Apparatus
Air which comes from lab compressor is enters to the filter and flows through the inlet pressure control valve. The inlet pipeline is supplied with temperature sensor that provides inlet temperature of the gas which is used in the calcula tions. Then, the gas enters to the nozzle which is a small metallic section. The nozzle is supplied with taping points which is connected with gauges and allows determination of pressure along the nozzle appropriately. In this experiment, three different kind of nozzles is used. There are two larger gauges which is used to measure inlet and outlet pressures of the nozzle .As seen from the figure above ,Pi is inlet pressure gauge and Po is outlet pressure gauge. There is an outlet pressure control valve which locates after the nozzle and regulates the outlet pressure (the back pressure).In order to measure the flowrate of the flowing gas, a rotameter is used.
Procedure In order to carry out the experiment, the lab unit should be prepared for the operation.
First of all , all gauges should be calibrated against the gauge of inlet pressure of air flow. This procedure is crucial , because each gauge has particular characteristics for the given temperature .In the beginning all the gauges must show the same position . Then , the nozzles which will be used in the experiment is prepared . After adjusting one of the nozzles to the pipeline, the connections of the nozzles with the gauges should be checked. More precisely : 1: Chosen nozzles is settled. 2. Gauges are connected to the nozzle. 3. Inlet and exit valves are opened. 4. Compressor begins and gas begins to pass through the pipe. 6. Measurement of the gauges are noted. 7. The reading of the rotameter is noted.
Results
Table 1. Velocity of the gas in the given distance for first run of Nozzle A .
Table 2. Velocity of the gas in the given distance for second run of Nozzle A.
Table 3. Velocity of the gas in the given distance for third run of Nozzle A.
Table 4. Velocity of the gas in the given distance for fourth run of Nozzle A .
Table 5.Critical pressures for the given mass flow rates for f irst run of Nozzle A.
Table 6.Critical pressures for the given mass flow rates for second run of Nozzle A.
Table 7.Critical pressures for the given mass flow rates for third run of Nozzle A.
Table 8.Critical pressures for the given mass flow rates for f ourth run of Nozzle A.
Plot 1.Velocity versus distance for first run of Nozzle A
Plot 2.Velocity versus distance for second run of Nozzle A.
Plot 3.Velocity versus distance for third run of Nozzle A
Plot 1.Velocity versus distance for fourth run of Nozzle A.
Plot 5.Mass flow rate versus critical pressure for all runs (four) of Nozzle A.
Table 9. Velocity of the gas in the given distance for first run of Nozzle B . Distance Velocity
1.00
2.00
3.00
4.00
5.00
series1
v1
70.62
93.79
93.79
106.64
93.79
series2
v2
165.70
308.77
235.66
215.12
197.10
series2
v3
181.88
314.96
327.34
287.04
264.99
series4
v4
189.59
321.15
411.30
355.44
327.34
series5
v5
197.10
327.34
418.30
440.14
411.30
serise6
v6
204.42
333.54
418.30
440.14
472.01
Table 10. Velocity of the gas in the given distance for second run of Nozzle B .
Table 11. Velocity of the gas in the given distance for third run of Nozzle B .
Table 12. Velocity of the gas in the given distance for fourth run of Nozzle B .
Table 13.Critical pressures for the given mass flow rates for first run of Nozzle B.
Table 14.Critical pressures for the given mass flow rates for second run of Nozzle B.
Table 15.Critical pressures for the given mass flow rates for fourth run of Nozzle B.
Table 16.Critical pressures for the given mass flow rates for fourth run of Nozzle B.
Plot 6.Velocity versus distance for first run of Nozzle B.
Plot 7.Velocity versus distance for second run of Nozzle B.
Plot 8.Velocity versus distance for third run of Nozzle B.
Plot 9.Velocity versus distance for fourth run of Nozzle B.
Plot 10.Mass flow rate versus critical pressure for all runs (four) of Nozzle B.
Table 17. Velocity of the gas in the given distance for first run of Nozzle C.
Table 18. Velocity of the gas in the given distance for second run of Nozzle C .
Table 19. Velocity of the gas in the given distance for third run of Nozzle C .
Table 20. Velocity of the gas in the given distance for fourth run of Nozzle C.
Table 21.Critical pressures for the given mass flow rates for first run of Nozzle C.
Table 22.Critical pressures for the given mass flow rates for second run of Nozzle C.
Table 23.Critical pressures for the given mass flow rates for third run of Nozzle C.
Table 24.Critical pressures for the given mass flow rates for fourth run of Nozzle C.
Plot 11.Velocity versus distance for first run of Nozzle C.
Plot 12.Velocity versus distance for second run of Nozzle C.
Plot 13.Velocity versus distance for third run of Nozzle C.
Plot 14.Velocity versus distance for fourth run of Nozzle C.
Plot 15.Mass flow rate versus critical pressure for all runs (four) of Nozzle C.
The main objective of the report is investigation of behavior of compressible fluid in the nozzle. In order to carry out the experiment the nozzle is used. By help of this nozzle , behavior of the air under different inlet and outlet pressure is studied. In order to demonstrate the flow condition for the air three type of the nozzle is used . They are convergent, convergent-divergent, convergentdivergent. For each nozzle, the one of the inlet and outlet pressure is kept constant and the other one is changed . And the velocity and mass flow rate of the nozzle is calculated by using equations given in the theory part . However, as all lab experiments , this experiments contains some deviation and errors. In this part, the main deviation and the main reasons behind that deiavtions will be investigated . Theoretical values of the mass flow rate is calculated by using the given data and real mass flowrates is obtained from the rotameter .The maoxiumum flow rate is taken from rotameter reading in order to co mpare with calculated maximum flowrate .In fact , there are always inaccuracies associated with lap experiments which is impossible to avoid In the nozzle as we increase the difference between the inlet and outlet pressure the mass flow rate of the gas increase significantly up to a point . After that point , it is impossible to increase the flow rate , which is called critical pressure. This flow case is called “choked flow”. The above tables indicate the theoretical values for the maximum mass flow rate air in Nozzle A. The Practical values for the same quantities are below: S o, first of all, without using of the graphs, we are able to compare the values for maximum mass flow rate: For instance , for run set 1 ,3.72 g/s maximum mass flow rate is obtained theoretically. However, maximum mass flow rate obtained by rotameter is 3.60 g/s. Actually deviation isn’t significant .However, a considerable deviation is seen in the Run Set 3. 3.72 g/s mass flow rate calculated theoreticall y , while 2.80 g/s is rotameter reading. The reason of this noticeably difference lies on thermodynamics. As it is
known from the thermodynamics course as the pressure increase the temperature of the gas increase .However, this fact isn’t taken into accou nt while calculations and the unit was supplied with only one thermocouples in order to determine temperature of the gas in the inlet. Moreover, the flow is turbulent and there should be some pressure losses which will result in increase in the temperature. As the density of the gas decreases as the temperature increase , the value shown in the rotameter isn’t exact . The critical values could be determined from mass flow rate versus / ratio plots . They are given in the table below: Nozzle A
Run1 S /
Run2
Run3
3.72
2.98
3.6
2.9
g( et ar w ol f s s a M
Practical value
Run4 1.49 1.87 2.24 2.61 2.98 3.35 3.72 2.8
2.98 3.35 3.72 3.94
3.8
6.00 ) r 5.00 h ? g k ( 4.00 e k a r 3.00
Run set 1 Run set 2
w o l f 2.00 s s a M1.00
Run set 3 Run set 4
0.00 0.00
0.20
0.40
0.60
0.80
1.00
1.20
Pout/Pin
As seen from the graph, in the beginning the pressure ratio is equal to 1 . It is obvious that in the beginning, the inlet pressure is equal to the outlet pressure. As seen from the graphs, for all pf the runs the pressure ratio 1 is appropriate to the lowe st flow rate . If we increase the inlet pressure, it finds enough energy to overcome the backpressure. But as it seen from the graph after some point, the pressure ratio has no effect on the mass flowrate . For the run 1 , this ratio is approximately 0.77 . As seen from the graph ,after reaching the maximum mass flow rate , the maxium flow rate is decreasing. This phenomenon is opposite to the working principle of the nozzle and is result of inaccuracies associated with the experiment . For the run 2, the at the pressure ratio approximately 0.82,the flow rate riches its maximum value and it stays constant .
350 300 250
) s / m200 ( y t i c 150 o l e V
Series1 Series2 Series3
100
Series4 50 0 0
1
2
3
4
5
6
7
Distance (mm)
As seen from the graph, there is a significant rise i in velocity from point 1 to point 2 for all runs. This is due to considerable decrease of the flow area from point 1 to point 2.However , as the pipeline begins to diverge, the velocity begins to decrease. For the series 1 , the velocity of the fluid is zero in the outlet of the nozzle. The reason for this is at that tapping pint the pressure at that point becomes equal to the outlet pressure and there is no driving force. Analysis of experimental error. As discussed above, there are some inaccuracies and deviations associated with the lab experiment. This a great deal of these deviations are endemic for the lab experiments and impossible to avoid. Let us discuss some of the factors which could lead to these deviations. Actually , we have no information about the type of the compressor . If positive displacement compressor is used in the system it doesn’t give stable flowrate. Inload and outload operation of the compressor results in fluctuation in the flowrate and associated errors . Moreover , there may be some leaks in the rig . These leaks could cause significant deviation . Actually , the fluid is air and it is impossible to determine these leaks by eye . Moreover , the gauges could be the reasons of the deviation . The calibration of the gauges is very important .However, there could be some inaccuracies in the calibration process . On the other hand , there could be meniscus errors made by students when reading rotameter
Conclusion As mentioned in synopsis, the aim of this report was to practically prove the compressibility of air flow. In order to reach our goal, we needed to obtain mass flow rates of air flow at different inlet and outlet pressure values, and also velocity values at different tapping points inside the nozzle. All the information required to professionally fulfill experiment such as about experiment, air flow and its areas of use, the theoretical data, equations, and hypothesis, procedure and instruments had been clearly indicated in Introduction, Theory, Procedure and Equipment sections of this report. In Results section, the evaluated values for needed quantities had been provided, all the tables
and graphs for mass flow rates and velocity of air flow for all sets given one by one. But it is necessary to not forget the fact that, there were several assumptions accepted by those who conduct the experiment such as Air condition outside, temperature of air flow, and the size of nozzles did not change as any external changes done on nozzles. In fact temperature cannot be constant as the pressure inside the nozzle change. But as stated in the above sections, we assumed that air was ideal and the compression was adiabatic: no heat gain or lose with surroundings and all the pressure increase was used to compress the air not for heating of air. There were some deviations in results, when we compared the theoretical and practical values, these undesirable differences might be the reason of assumptions. All the reasons lead to errors had been provided above. But to clarify the reasons leaded to errors, it can be said that Bernou lli’s principle is followed to carry out the experiment: Conservation of pressures energies. As the static pressure decreases, velocity of air flow should increase to the same extent simultaneously. But keep in mind that, in real life, there are always environmental energy losses. No doubt that, some of the pressure energy converted into the internal energy of air. The errors are not too big, and they can be disregarded in engineering applications. Indeed, it is not achievable to have the same values in experiment as theoretical values. There will always be some deviations.
Referance 1. Coulson & Richardson, Chemical Engineering, vol. 1, (chapter on compressible flow page 155) 2.
Douglas, Gasiorek, Swaffield, “Fluid Mechanics”. Chapter 2
3. http://physics.stackexchange.com/questions/283628/de-laval-nozzle-geometry 4. http://web.mit.edu/16.unified/www/SPRING/fluids/Spring2008/LectureNotes/f20.pdf 5.
Perry’s Chemical Engineers Handbook
