This research study about the character of the fluid of gas flow at the nozzle with the aid of a hydraulic analogy. Characters gas flow varies depending on static pressure, flow rate and nozzle geometry. The gas stream is very difficult to identify because not seen directly by eye. So it requires a special method to observe the shape of the gas flow. The proper way to examine it namely analogized gas medium with water (hydraulic analogy).The study was conducted in three nozzle forms, namely; convergent, parallel and convergent-divergent nozzles. The structure and the shock wave of jet were observed by using topography visualization method. The objectives of this study are to evaluate the jet characteristics, determine the profile of static pressure velocity and variation around the jet, understand the presence of the flow structure and shock waves,and predict the noise intensity of the gas flow. The result revealed that the characteristics and structure of the jet at the water flow is very similar to the gas flow. Flow rate and variation profile of static pressure around the jet at the critical ratio Rh = 1.5 is relative different to the three nozzles that were tested. The structure of the apparent jet was very different at the critical ratio Rh = 1.5 and the ratio of Rh>1.6 were relatively equal. This study obtained that hydraulic analogy technique was capable of providing detailed information about the jet structure, the apparent shock wave and to understand the mechanism of the gas flow noise. This paper recommended that further study of nozzle characteristics and structures is expected to provide detailed information and an overview of the characteristics of the flow and the jet structure.
Keywords: hydraulic analogy, fluid, nozzle, jet, flow structure
Introduction
Nozzle is a tool that functions as a measuring tool to flow the liquid or gas fluid. Characteristics of fluid flow out through the nozzle (jet) has the structure of different flow for any changes in pressure and flow rate.The characteristics and the structure of gas fluid flow are quite complicated to be observed and understood. On the other side, liquid fluid flow (water) is easier to be investigated and observed by means of hydraulic analogy table installation assistance [2,16]. Phenomenon and the structure of the gas flow can be studied in more specific way by analogying the gas and the water flow. Observing and understanding of the characteristic sand the structure of gas fluid flow and the cause of screech tone mechanism is very difficult because the apparent flow structure was difficult to be observed. It is different from the liquid fluid flow (water) that can be observed visually with naked eye or through topography [14].
This study attempted to show the results of research on the characteristics and structure of the water flow of the jet that is analogous to the gas flow to the three forms of the tested nozzle geometries. Several studies have been conducted to study the characteristics of the gas flow, but until now they have not been able to fore see or predict exactly how much noise power that was produced. In particular to gas fluid flow, jet cell structure and shock wave in the specified Mach number, it is the underlying causes of supersonic jet noise (aeroacustic). [12,15]. Andre et al. (2013) also stated that Shock-associated noise is made up of two distinct components: a tonal one, referred to as screech, and a broadband. Therefore, it is required a deepand comprehensive understanding of the characteristics and structure of the flow, shock wave and the apparent screech tone mechanism of the gas flow. Buchanan et al. (2007) then added that the intensity of the screech tone was able to be altered substantially by the positioning of a relatively small cylinder along the centerline of the jet flow. Through the installation of the hydraulic analogy table, it is expected to provide detailed information and an overview of the characteristics of the flow and the jet structure, so that the phenomenon of gas flow of jet can be better understood.
THEORY
The study of the fluid flow structure that flows in the nozzle had been observed through a tool called Hydraulic Analogy Several studies related to fluid flow structures with this method to Brocher & Makhsud (1995), in a research test screech noise on the free surface hydraulic analogy using a convergent nozzle. It was found that the ratio of the critical heights, convergent nozzle showed shock-cell structure. Then Brocher & makhsud (1997), continue their research on the mechanism of sound that is run using the hydraulic analogy. This analogy is designed to utilizing the distribution of the water level does not interfere with jet [8]. So that the sound intensity is found relationship to the gradient of the local static pressure of the shock-second cell. It explains that the greater the intensity of the sound is relative to the shock-cell.
Local static pressure gradient is a function of the ratio pressure jets [2]. So with hydraulic analogy can give better understanding of of the mechanisms of screen tone. Experimental method can show the direct form of jets noise at the nozzle with low pressure ratios. So this research is the right step in predicting the intensity of noise.
The description of a more so phisticated hydraulic analogy was described by Carbonaro and Haegen (2002) and Buchanan et al. (2007). Kumar et al. (2009) also stated that the flow behind jet nozzles has been a matter of great interest due to its effects on the aerodynamics, structure and propulsion system of an aircraft. Based on the momentum equations and physical quantities, analogous to the two types of fluid flows are summarized and presented in the Table 1. The characteristics and structure of the fluid that flows out through the nozzle (jet) will be different at each change of pressure and flow rate [3,15]. The difference in the apparent structure depends on the geometry, the size of the width and operating conditions (pressure and flow capacity) of the nozzle. The structure of fluid flow (jet) which comes out through the nozzle depends on the nozzle operating conditions which are in this case divided into:
a. When the fluid pressure inside the nozzle (at the exit) is smaller than the pressure outside the nozzle (outside air), then the jet condition is called “over-expanded” or the “imperfectly expanded”.
b. When the fluid pressure inside the nozzle (at the exit) is equal to the pressure outside the nozzle, the jet in this condition is called “perfectly expanded” or “correctly expanded”.
c. When the fluid pressure inside the nozzle (at the exit) is greater than the pressure outside the nozzle, then the nozzle (jet) at this condition is called “under expanded” or “imperfectly expanded”.
The operation of the nozzle or jet for conditions “correctly expanded” is very rare practically, where the condition of the structure of the jet cell is not visible (has not happened yet) and shock waves. On the nozzle operating conditions where the jet “imperfectly expanded” (over-expanded orunder expanded), the apparent flow structure seems like the shock cell and the shock wave [7,12]. The structure of fluid flow (gas) is very influential on the apparent noise and the level of noise power intensity. As shown by research Zapryagaev (2002) Figure 1a and Makhsud (2009) Figure 1b shows the structure of a shock wave forms supersonic jets of of gas flow and water flow.
In Figures 1a and 1b, it shows clearly that the similarity in jet structure as a result of the visualization of water and gas flow (in this research). A scheme of jet structure was shown in Figure 2 from convergent-divergent nozzle at the nozzle operating condition is over expanded [12].
Eksperimental Setup
The installation of hydraulic analogy table was designed specifically to study the flow characteristics and mechanisms of jet noise. A hydraulic analogy table installation is shown in Figure 3, it consists of a water tank made of stainless steelandis equipped with a water filter that is always kept in clean. To reduce vibration of the pump, so that the foot of the analogy table is propped with vibration-damping (sand) and the installation of the pipe using an elastic plastic pipe installed between the pump and the tank of both channels. For the analogy table, it was made of glass (length =2m, width= 1.4m, thick = 0.015m), it was also supported on each side so that apparent deflection was as small as possible (<1/10 mm). To avoid the reflection of the wave, the mounted corkon both sides of the analogy table or wall and in the downstream (rear) was mounted regulator plate that is tilted lessthan 4o. The regulator plate was also functioned as a regulator of water level on the analogy table
Visualization techniques with the shadow method (shadowgraphy) or topography were used to observe the characteristic structure of jet. The light source (fluorescent lamp) was placed approximately 80 cm above and below the table in which there was a mirror mounted 45o, so that shadows can be seen in the mirror. The shadow that appears on the mirror can easily be seen through the naked eye and can be recorded with a video camera. Capacitor the nozzle flow velocity was measured with the measuring tool namely orificemeter or pitotmeter to determine the velocity profile. Level (high) of water surface on the table was measured with a needle mounted on a micrometer. Fluctuations in water level can be measured with the assistance of optical sensors (fiber optics) MTI model 1000 Fotonic Censor. The captured signals by optical censorsare transferred to the FFT Analyser (HP 3582A), and from this tools, spectrum, coherence and phase angle wave were found. The measured water level fluctuation on the FFT Analyser tool was converted to the value of noise intensity levels produced by water flow (nozzle). There are three (3) nozzles to test : convergent nozzle, parellel nozzle, and convergent-divergent nozzle (Figure 4).
Results and discussion
Profil Jet velocity profile at the nozzle operating conditions with the critical ratio Rh=htot/ha=1.5 is shown in Figure 5a for nozzle N1 and Figure 5b for nozzle N2. Water level on the analogy table was ha=27mm with measurements position that was performed on three (3) vertical points of Z (10 mm, 15mm and 20mm) above the analogy table. Velocity profile was measured on transverse position of Y at nozzle exit section (X =0), it indicated the rate at the same relativity at each point of measurement for height measurements of Z are different. Level ofmeasured velocity in equality was not morethan 5%, and at point toward the nozzle wall, its velocity decreased.It was due to the effect of shear tension on the wall. In the measurement position of Y/W (between -0.2 and 0.2), the transverse direction of the center nozzleshowed the same trend of velocity values and at the position of Y/W about 0.4 velocity changes happened to be relatively higher due to the influence of surface tension (W is the width of the nozzle). For both nozzles (N1 and N2) which were tested showed the velocity profile and the same flow characteristics, while for the convergent-divergent nozzle (N3) the velocity profile was not done because the flow structure was more complicated for Rh=1.5.
Measurement of water level (head pressure) on the table was done with two objectives. First, to compare the water level at the measurement point to circumstances beyond the nozzle (ha), so that the flow was detected over pressure or under pressure conditions, it was due to the principle of analogy (h/ha)2=(p/pa). Second, to determine the local surface in flux velocity, to determine the local Froude number Fr=V/√gh. In Figure 6a nozzle N1 and in Figure 6b nozzle N2, it is shown that the distribution of water level (static pressure) along jet was at the nozzle operating condition with the critical ratio Rh=htot/ha=1.5.
Fluctuations of static pressure ratio (h/ha) along the jet for three measurement positions of Y/W on the nozzle N1 and N2 showed different relatively profile. At the nozzle N2 generated static pressure profile along the jet nozzle stend to be similar (X direction) and have not seen any visual shockcell and the shock wave, while the nozzle N1 was visible (displayed) the shock cells with long specific cell structure as shown in thefigure nozzle (jet).
The jet structure which is out through the nozzle highly depends on the capacity of the nozzle flow and geometry. This study has been conducted to test several variations of discharge or flow capacity, ranging from critical head ratio with Rh=1.5 to Rh=2.2. When the nozzle head was operated on head ratio with Rh>1.6 for nozzle N1, then at the flow structure would become clearly visible the presence of shock cell and the shock wave which is the main causeof aerodynamic noise. The apparent shock cell or shock wave on cell emission was interesting to be observed and studied deeply with the assistance of more accurate measuring tools. The nozzle structure and length of the shockcells that have been recorded from a video camera were happened because of the shadow method assistance as shown in the Figure 7. Nozzle structure and shock cell which were recorded from the installation of the hydraulic analogy table showed the same phenomenon with nozzle of gas flow. In the Figure7a, it is clearly seen that the jet flow structure showed the same structure and characteristics with the fluid flow of gas that has been observed by previous researchers. This phenomenon reinforced our belief that thefluid flow of liquid (water) can be analogous to fluid flow of gas. For all the three forms of the tested nozzle geometry on a particular nozzle operating conditions showed that the jet characteristics and structure is relatively the same, except in the nozzle operating conditions with the critical ratio is the head ratio Rh=1.5or pressure ratio Rp=2.25(as seen on the figures 7).
When the nozzle is operated at critical ratio, in the head ratio Rh=1.5 or at the pressure ratio Rp=2.25, then the shock cell structure and the shock wave on jet seemed to be very clear to the nozzle N1 (Figure7a), while for nozzle N2 (Figure 7b) shock cells has not appeared yet, and for nozzle N3 Mach disc is visible (Figure 7c). Shock cells will appear on the nozzle N2 when the flow capacity was enlarged from a height ratio approximately Rh1.6. Similarly, what happened on the nozzle N3, when the flow capacity is still low (critical ratio) which first appeared in the jet is Mach disc and when the flow capacity is increased with Rh1.65, then on the jet emerged shock cells and the shock wave which is similar or identical to the nozzle N1 and N2 (Figure 8).
At the installation under the analogy table has been placed striped transparent paper that is useful to know or measure the length of the shockcells that occurs in nozzle. On the nozzle operating conditions through specified flow capacity with Rh>1.9 generally jet nozzle has oscillated on the third tested nozzle.When the jet oscillated laterally as result of the flow interaction and shock waves, the shock cell length varies periodically, so the average value of the length of the cell can be recorded. In the Figure 9a for nozzle N1 it is clearly to see the first and second shock cell, while the third cell seen to be relatively less clear, especially when the jet oscillated. Results of previous studies (Makhsud, 1995 & 1996), it was found that the interaction of the flow and the shock wave at the second shock cell was a source and cause of the jet noise at hydraulic analogy. The gas flow has also been described by Tam (1995). That the apparent shock wave on jet is the cause of the aerodynamic noise’s presence. Tam also explained that for gas fluid flow, it has been identified cell and the shock wave to the fourth shock cell. Thus, in this study shock cell can be observed to the second shock cell obviously.
In Figure 9b, it shows that the length of the first shockcell (L1) are relatively similar for all the three tested nozzles at flow conditions with the head ratio htot/ha>1.65. Similarly the length number of the first and second cell (L) for the three nozzles is relatively similar in flow conditions htot/ha>1.8. The length distinction of shock cell for the three nozzles is relatively small and it will also affect the produced noise intensity. The research results of Brocher & Makhsud (1997), and Makhsud (1996) showed that the length of the cell and the shock wave will affect the strength or the caused noise intensity. On the flow conditions for (Rh =htot/ha) is lower the structure and length of the shock cells for the three tested nozzles are different, so that the influence of the noise strength which is generated will be different.
The results in the analogy table indicated that the mechanism of screech noise is a loop of acoustic pure (acoustic wave) which propagated downstream to the boundary between the jet shear layer at the local sound velocity and the wave propagated upstream into the acoustic velocity on the outside or around the jet. Loop phenomenon that appears on the analogy table is purely acoustic that in contrast to the findings of previous researchers, where the vortex is instability waves. The results of this study indicated that the loop length is considered as the distance L (the noise source) is the distance between the tip of the nozzle and the end of the second shock cell (Figure 9a). Assuming that the noise velocity around the jet is equal to the local noise velocity (atmosphere), then the frequency of screech noise is written as:
1/f = L (1)
or f =
Where M is the Mach number average around the jet boundary. In Figure 10, it showed that the value of the noise intensity that was produced by the jet for nozzle N1 and N2, showed the average of noise intensity for the nozzle N1 is higher than nozzle N2 (Makhsud, 2006). Acoustic intensity differences to the two nozzles morethan 10 decibels on test conditions with pressure ratio( ) which is low at (Rp≤3.8), and relatively similar to the test conditions of the pressure ratio Rp≥4. This difference occurred because the produced flows structure (the length of shock cell and shock waves) is different, although the flow capacity is the same.
The gas flow instability described by Seineretal.(1987) also occured at the tested jet on the installation of the hydraulic analogy table. In Figure 11, it is shown that the movement of an unstable jet (oscillating to the right and left) recordings through photos on the camera head ratio Rh=1.85 or pressure ratio Rp= 3.4 for convergen-divergen nozzle N3. In Figure 11 it is clear that the jet oscillated to the right (Figure 11a) in certain and under the next condition the jet oscillated to the left (Figure 11b). The jet showed a relatively stable movement on the condition head ratio Rh<1.85 and oscillating movements of jet occurred when the flow capacity increased with the head ratio between Rh=1.85 to 2.1. Further more, when the flow capacity is increased to reach head ratio Rh>2.1, then the movement of the jet will best able. Conditions like this can be happenned because when the flow capacity increases, the flow velocity and energy movement will also increase so that the energy is able to penetrate and leadback the movement of jet to best able. Nozzle operation under the conditions where the screech noise is dominant, then the nozzle flow (jet) visually demonstrated the phenomenon of lateral oscillation motion. This phenomenon is clearly seen witht he naked eye (without any tools) to test the installation of the hydraulic analogy table.
Conclussion
Data processing and discussion of the results of research that has been done, can be concluded that:
a. Hydraulic analogy installation can provide a more detailed information on the characteristics and structure of the jet flow, the apparent shock wave, and the screech noise mechanism. Jet structure of water flow resulted from the use of hydraulic analogy table installations is visually similar to the results of research of jet flow of gas.
b. Jet velocity profile is relatively the same, while the water level variations (static pressure) around the jet for the three tested nozzles showed the condition and different relative value especially for nozzle operating conditions, for the critical ratio Rh=htot/ha=1.5 or pressure ratioRp=2.25.
c. Characteristics and structure of the jet flow as seen in the three tested nozzles are very different for nozzle operating condition with critical ratio Rh =1.5, but for the nozzle operating conditions with ratio of Rh≥1.6 (nozzle N1 and N2), and the ratio Rh≥1.65 (nozzle N3) has shown the overall structure of the jet and shock waves are relatively similar.
d. Screech noise mechanism found on analogy table was pure loop of acoustic wave that propagates downstream in the boundary layer around the jet and the wave propagates upstream on the outside of the jet. Intensity values for screech noise resulted by the jet for nozzle N1 was higher average than the nozzle N2. Nozzle operation under conditions where the screech noise is dominant, so that the jet visually showed the phenomenon of lateral oscillation movement. Hydraulic analogy technique is capable of providing detailed information about the jet structure, the apparent shock wave and to understand the mechanism of the gas flow noise. Future work should be reduce screech noise of the jet characteristics
Unknowledgement
The authors gratefully acknowledge the financial support of the Fundamental Research Grant (2008) DP2M-DIKTI Jakarta for building the water table of hydraulic analogy.