Experimental and numerical analysis of convergent nozzlex

In this paper the main focus was given to convergent nozzle where both the experimental and numerical calculations were carried out with the support of standardized literature. In the recent years the field of air breathing and non-air breathing engine developments significantly increase its performance. To enhance the performance of both the type of engines the nozzle is the one of the component which will play a vital role, especially selecting the type of nozzle depends upon the vehicle speed requirement and aerodynamic behavior at most important in the field of propulsion. The convergent nozzle flow experimental analysis done using scaled apparatus and the similar setup was arranged artificially in the ANSYS software for doing the flow analysis across the convergent nozzle. The consistent calculation analysis are done based on the public literature survey to validate the experimental and numerical simulation results of convergent nozzle. Using these two experimental and numerical simulation approaches the best fit results will bring up to meet the design requirements. However the comparison also made to meet the reliability of the work on design criteria of convergent nozzle which can entrench in the field of propulsion applications.


Introduction
Today's all the modern aircraft engines are using highly sophisticated components to achieve better fuel efficiency and thrust. These components are highly reliable and giving better service to the aerospace industry. However there are some technical problems which even today facing by all air breathing engines in each and every component like engine intakes, compressor, combustion chamber, turbine and most importantly the nozzle. Nozzle has a vital role in every air breathing and non-air breathing engines, it makes the complete expanded hot gas coming from the turbine to expel with the high acceleration [1]. The more massive expulsion of hot gas gives more forward motion to the aircraft or space craft as per the well-known theory Newton's third law of motion [3]. In general discussion the word propulsion meaning gives the net force that results from imbalanced pressure. To understand more clearly can take the sealed container, gas or air under pressure in a sealed container applies equal forces or pressure on all sides of the container [2]. One more observation that all forces are equally balanced and there is no possibility of container to move. The purpose of this paper is to give straightforward information about the convergent nozzle basic engine operational theory and discussion on experimental results. Apart from this information this paper also describes pertinent information about problems that may phase during the experiment on  nozzle especially those cannot be solved through the simulations well and therefore cause confusion. However the consistent numerical simulation also done for better reliability of convergent nozzle [4]. In common the purpose of the nozzle in terms of the aeronautical applications it converts the chemical thermal energy formed in the combustion chamber into the required kinetic energy [6]. The nozzle makes the high velocity gas of lower temperature and pressure from high pressure, high temperature and low velocity of hot gas. According to the literature survey it is found that the nozzle generally gives exhaust velocity range from 2-4.5 km/sec [5]. If we closely observe the properties of the real fluid in the nozzle the inlet Mach number is less than one and near the throat section the flow is sonic. If we further attach the divergent section we may found that supersonic velocities depends upon the boundary conditions set in the simulation or experiment.

Literature on theoretical analysis on convergent nozzle
The convergent-divergent nozzle, the speed of the gas can increase from end to end, the mean speed of the molecules in the molecular structure of the gas will fall from end to end and at some point the speed of flow will equal the mean speed of the molecules [9]. We have seen that this is a special point where the duct must change from convergence to divergence. Then the flow in the convergence depends on expansion in the direction of flow and in the divergence on expansion across the flow.
Thespeed at the junction, that is, in the throat, is RT  where the absolute temperature at the throat is of course. This immediately raises the issue of the use of the Mach number in connection with nozzles [10]. In the early part of the 20 th century there was great optimism that the use of non-dimensional groups of physical properties would lead to significant improvements in the ways in which we store experimentally gathered data. One of the important groups is the Mach number denoted M and named in honor of Ernst Mach [7,8]. It should be noted that in order to draw graph shown below to start with values for the stagnation conditions. At one time this would have meant that the calculations for drawing the graphs would have been very time consuming. That problem has disappeared with the emergence of mathematics packages on computers. We can draw as many graphs as we like almost instantly like figure 1.

Experimental study on convergent nozzle
For a convergent nozzle where the area of cross-section decreases along the length of the nozzle, velocity increases according to the continuity equation as well as the Bernoulli's equation. It is essential to demonstrate the working of the nozzle and study the velocity and pressure variations as the flow passes through the nozzle. A convergent nozzle with surface/static pressure taps along the length of the nozzle is provided to measure the static pressure variation as the flow passes through the nozzle shown in figure 2-3. An orifice is provided in the upstream direction to measure the volume flow rate. Using the flow rate measurement and the geometry of the nozzle at various locations, it is observed that average velocity is varied along the nozzle. Comparisons can be made theoretically by obtaining the static variation using Bernoulli's and continuity equations and practically using the measurements. Hence the working of the convergent nozzle can be demonstrated.    The set up consists of a blower unit coupled to D.C. motor and is connected to a convergent nozzle through a settling chamber with a hose. The discharge can be controlled by controlling the speed of the D.C. motor. The pressure tap rings (9 nos) are made in the nozzle surface and are connected to the multi-bank manometer. The orifice plate is fitted in the pipeline of the blower outlet, to measure the discharge of flow and is connected to differential manometer. The control panel consists of the mainson indicator, control switch, D.C. motor speed controller, differential manometer and multi-bank manometer. The whole instrument is mounted on a self-contained sturdy table and is isolated from the blower unit so that vibration should not transfer to the study table. After successful iteration of the nozzle requirement in design point of view, numerically and experimentally the appropriate tabulation was formed. After conducting the experiment the observations has tabulated as shown in the table 1 and 2. From the figure 5 it is clear that the port number between 7 and 8 all the pressure lines meeting at one point because the area contacting in the nozzle has more influence. According to the theoretical understanding the exit velocity flow speed and discharge flow speed vary proportionally, same was observed in the experimental graph showed in figure 6 and figure 7. Similar performance also given from the figure 8 and figure 9 that velocity is directly proportional to the pressure head also discharge is proportional to the pressure head because of the area contraction at desired design point is quite good enough to achieve better velocity.

Numerical simulation of convergent nozzle
To The same convergent nozzle used for the experimental work, the numerical simulation has been conducted by creating the similar artificial environment in the ANSYS software. The basic geometric details are shown in figure 4. Once the geometry is created by using proportionate nozzle profile the boundary conditions are given before the meshing. The boundary conditions for the convergent nozzle is shown in table 3. The exit diameter of the nozzle obviously smaller comparatively the inlet diameter, therefore the velocity inlet was given to entry of the nozzle and pressure outlet was given to exit of the nozzle to find the accurate convergence solution. Solution initialisation: Standard compute inlet Run calculation: Enter the number of iteration (50,000), select calculation.
The surface of the nozzle taken as walls so the interference results predicted easily. The meshing plays a vital role in the simulation where the accuracy of the flow parameters like static pressure can found at each location. The mesh elements maintained almost very high density to have better flow characteristics across the nozzle. The mesh density representation over the walls shown in figure 10-11.       The final most important step in the simulation giving boundary conditions. Based on subsonic standardized theory the flow boundary conditions given to convergent nozzle solver. The convergence criteria has been maintained 10 -5 value so that accuracy can be improved. The convergent nozzle for the given set of mesh 2 million cells convergence solution obtained within the 500 iterations. The solution convergence plot as shown in figure 12. For the same boundary conditions the mass and momentum curves are further captured through ANSYS shown in figure 13. The flow aerodynamic behavior in convergent nozzle further explained through the Mach number, total temperature, turbulence model and velocity contour are shown from figure 14-17. The maximum total temperature found to be 3.02x10 2 K, the velocity at the exit of nozzle found to be 2. optimum temperature values that has been shown in figure 19. The average temperature at outlet maintained to be 28 K which is best suitable for subsonic flow conditions in air breathing propulsion.

Conclusions
According to the theory studied on the nozzle and experiment conducted to the convergent nozzle it is understood that the area rule concept perfectly agreed with the numerical simulation results. After successful completion of numerical simulation, convergent nozzle experiment and theoretical calculation the desired mach value achieved at the exit of the convergent nozzle section found to be 1.8x10 2 and also the total temperature also found to be 3.02x10 2 K . Similarly the turbulent intensity was found that 5.50x10 3 which is optimum velocity value for all subsonic air breathing propulsion. Because as the area decreases it increases the velocity especially at throat the flow is sonic and the flow further accelerates to supersonic if we attach additional divergent section. However the given boundary conditions are meeting by conducting the experiment on the convergent nozzle. It is also further understood that there is a scope to improve the same experimental setup to understand the convergent and divergent section nozzle three dimensional flow analysis for better aero mechanical features.