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Computational Modeling of a Typical Supersonic Converging-Diverging Nozzle and Validation by Real Measured Data

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Computational Modeling of a Typical Supersonic Converging-Diverging Nozzle and Validation by Real Measured Data Computational Modeling of a Typical Supersonic Converging-Diverging Nozzle and Validation by Real Measured Data Omid Joneydi Shariatzadeh, Afshin Abrishamkar, and Aliakbar Joneidi Jafari parameters such as mass flow rate, outlet pressure and outlet Abstract—The converging-diverging nozzles play a velocity of the engine might be various [3], [4]. significant role in a supersonic wind tunnel, where they draw air Based on the configurations, nozzles can be divided into from a gas reservoir. Due to the back pressure conditions three general types: through the convergent section, air reaches sonic conditions at 1) Cone nozzles which are conical and linear [5]; throat. These conditions lead this stream to flow further through the divergent section where the flow Mach number increases. 2) Bell nozzles which are contoured, shaped and classical Manipulating the determinative variables such as area ratio and converging-diverging [6]; back pressure, the obtained Mach number may be regulated. In 3) Annular nozzles which are spike, aerospike, plug, this work a comprehensive simulation of a flow in a typical expansion and expansion-deflection [7]. supersonic converging-diverging nozzle has been reported. In Each of the mentioned nozzles has advantages and the respective nozzle, flow suddenly contracts at a certain point disadvantages against the others and according to the and then expands after throat. All the simulation endeavors have been carried out by ANSYS FLUENT® utilizing the mesh configurations, each could be beneficial for different geometries previously and precisely accomplished in GAMBIT®. applications [8]. The simulations have been conducted in either 2D or 3D The nozzle configuration which is the topic of this research domains to provide better comparative platform. Also, the is converging-diverging nozzle. Converging-diverging nozzle influence of the turbulence model, differentiation and was first used on steam turbines by a Swedish inventor called computational grid to the solution has been studied. Gustaf de Laval which is now also well known as de Laval Furthermore, the numerical comparison between CFD modeling nozzle or Converging-Diverging Nozzle [9]. In a converging- results and corresponding available measured data has been presented. The comparison analysis of the data demonstrates an diverging nozzle, the hot exhaust leaves the combustion accurate enough coordination between the experimental data chamber and converges down to the minimum area, or throat, and the simulation results, which is applied more to the 3D of the nozzle. The converging part is subsonic while in the endeavors than 2Ds. throat Mach number is 1 and in the diverging part it reaches over unity. Mach number usually increases even after throat to ® Index Terms—ANSYS FLUENT , computational fluid the end while in some cases a small decrease in Mach number dynamics, converging-diverging nozzle, numerical validation, has been reported [10]. When the back pressure ratio is large turbulence models. enough, the flow within the entire device will be subsonic and isentropic. When the back pressure ratio reaches a critical value, the flow will become choked with subsonic flow in the I. INTRODUCTION converging section, sonic flow at the throat, and subsonic A nozzle is a proportionally plain device, specifically a flow in the diverging section [11]. formed tube which can lead hot and fast gases through. Aerospace shuttles basically use a fixed convergent section followed by a fixed divergent section as the configuration design of the nozzle [1]. There are different applications where nozzle is used to accelerate hot exhaust to generate thrust which works based on the Newton’s 3rd law of motion such as in Ramjets, scramjets, and rockets [2]. Nozzle design specifies the amount of thrust since for different nozzle designs, several Manuscript received February 14, 2014; revised June 26, 2014. O. Joneydi Shariatzadeh is with the Department of Energy Technology, Lappeenranta University of Technology, Skinnarilankatu 34, 53850 Lappeenranta, Finland (e-mail: [email protected],). A. Abrishamkar is with the Department of Chemical Technology, Lappeenranta University of Technology, Skinnarilankatu 34, 53850 Fig. 1. Schematic view and a qualitative diagram of pressure versus the Lappeenranta, Finland (e-mail: [email protected]) length axis for a converging-diverging nozzle with fully supersonic flow [1]. A. Joneidi Jafari is with the Department of Energy Technology, School of Technology, Aalto University, PO Box 14400, FI-00076 Espoo, Finland. He Basically, a supersonic converging-diverging nozzle has is also with the Department of Energy Technology, Lappeenranta University two sorts of flow trends: of Technology, Skinnarilankatu 34, 53850 Lappeenranta, Finland (e-mail: 1) Fully supersonic flow (M>1): As shown in Fig. 1, nozzle [email protected], [email protected]). is choked; flow accelerates through the converging role in a supersonic wind tunnel, where they draw air from a section, reaches its maximum speed at the throat and gas reservoir which might be either at atmospheric conditions accelerates through the diverging section [12]. or even contains compressed and pressurized air. 2) Shock wave (supersonic flow with shock wave): As In this work a comprehensive simulation of a flow in a illustrated in Fig. 2, nozzle is choked; flow accelerates typical supersonic converging-diverging nozzle has been through the converging section, reaches its maximum reported. Simulations have been carried out by ANSYS speed at the throat, accelerates through the diverging FLUENT® where meshing of geometries have been generated section and decelerates through the diverging section in GAMBIT® prior to that. Two different turbulence models [12], [13]. of k-ε and k-ω have been applied to the solution. Further on, the comparison of turbulence models, grid differentiation and computational methods have been analyzed and even compared to the experimental data to give better overview of the similar applications for future purposes. The outcomes of this research demonstrate an accurate enough coordination between the experimental data and the simulation results, which is exerted more to the 3D endeavors than 2Ds. II. GEOMETRY AND THEORY Converging-diverging nozzle has a non-swirling axisymmetric geometry. The 2D layout of the nozzle studied Fig. 2. Schematic view and a qualitative diagram of pressure versus the is illustrated in Fig. 3. High-pressure low velocity gas, which length axis for a converging-diverging nozzle with supersonic flow with shock wave. is air, flows through the convergent section in a subsonic condition and contracts in the throat. Then, the low- pressure As the matter of fact, a shock occurs after throat and the high velocity air expands in divergent section in supersonic most important questions in this regard are where the shock conditions [20]. Discretized method should be employed; actually happens and what the minimum pressure is after therefore, the geometry in the shape of mesh has been throat. To this end, there are several governing equations developed in GAMBIT®. associated with converging-diverging nozzles that are taken into consideration in theoretical calculations, which also form the fundamentals of majority of computational fluid dynamics software such as ANSYS FLUNET®, which has been applied in this work [13]. Conservation of mass [12], [14]: V A constant (1) Fig. 3. 2D layout of the studied converging-diverging nozzle. where ρ = density (kg/m3), V = velocity (m/s), A = area (m2). Conservation of momentum [12], [14]: p 1 2 (2) u V constant 2 where u = velocity magnitude (m/s), p = pressure (N/m2 (Pa)). Conservation of energy [12], [15]: 1 h V 2 constant (3) 2 where h = enthalpy (kj/kg) In fact, the reason to use converging-diverging nozzles is to reach supersonic velocities to make the thrust even larger [16]. In converging nozzles sonic velocity is the highest velocity Fig. 4. Utilized geometries and meshes: a) 2D axisymmetric grid, b) 2D accessible with the extreme point at the throat, while in complete (planner) grid, and c) 3D complete grid. converging-diverging nozzles due to the increase in volume after the throat in diverging area, density drops down which In addition to the 2D axisymmetric, 2D complete (planner) causes the velocity to augment even more and reach case and 3D meshes were also generated to collate them in supersonic speeds [17], [18]. Manipulating the determinative order to study the different cases. In terms of the type of mesh, variables such as area ratio and back pressure, the obtained the structured meshes were utilized for execution of the Mach number at the end of the nozzle may be regulated. simulation. The simulations are resolved with a very fine Important applications of the converging-diverging nozzle are mesh for all the cases (e.g. with 670000 cells for 3D cases) to aerodynamics especially in jet engines where high speed predict the most accurate data. The schematic view of the aircrafts or rocket engines work [19]. They play a significant studied grids is depicted in Fig. 4. III. METHODOLOGY The cases are not performing under low Reynolds number; Solver type was chosen as Density-Based because fluid is hence, k–ε model has been mostly used as the viscous model compressible also high-speed flow. Different pressure inlets for all the present CFD calculations. However, other viscous were examined i.e. 0.4, 1, 4 and 8 atm. The corresponding models like k-ω were also examined and it was practically pressure outlets are then 0.2, 0.5, 2 and 4 atm. Note that, total discovered that obtained results for temperature are less pressure should be considered since total pressure is sensitive to model choice. However, the results for pressure summation of static pressure and dynamic pressure and may were very sensitive to model choice. be calculated as (4). TABLE I: MEASUREMENT DATA 2 (4) X p X p Total pressure p V X p X 2 throat t, in throat pt, in 0.33 0.958 1.413 0.438 The studied fluid is air, which must be defined as ideal gas; 0.44 0.942 1.456 0.447 due to the supersonic flow density, that is not constant during 0.55 0.927 1.5 0.451 passing through the nozzle.
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