International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 5, September–October 2016, pp.221–240, Article ID: IJMET_07_05_024 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=7&IType=5 Journal Impact Factor (2016): 9.2286 (Calculated by GISI) www.jifactor.com ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication
CONCEPTS AND CFD ANALYSIS OF DE-LAVAL NOZZLE Malay S Patel, Sulochan D Mane and Manikant Raman Mechanical Engineering Department, Dr. D.Y Patil Institute of Engineering and Technology, Pune, India. ABSTRACT Anozzle is a device designed to control the characteristics of fluid. It is mostly used to increase the velocity of fluid. A typical De-Laval nozzle is a nozzle which has a converging part, throat and diverging part. This paper aims at explaining most of the concepts related to De Laval nozzle. In this paper the principle of working of nozzle is discussed. Theoretical analysis of flow is also done at different points of nozzle. The variation of flow parameters like Pressure, Temperature, Velocity and Density is visualized using Computational Fluid Dynamics. The simulation of shockwave through CFD is also done. Key words: Rocket engine nozzle, De-Laval nozzle, Ideal gas, Computational Fluid dynamics, Ansys-Fluent. Cite this Article: Malay S Patel, Sulochan D Mane and Manikant Raman, Concepts and CFD Analysis of De-Laval Nozzle. International Journal of Mechanical Engineering and Technology, 7(5), 2016, pp. 221–240. http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=7&IType=5
1. INTRODUCTION Nomenclature: F= Force (N) P=Pressure (Pa) T=Temperature (K) V=Velocity (m/s) C= Velocity of sound (m/s) g=Gravitational acceleration (m/s2) m= Mass flow rate (kg/s) ρ= Density (kg/m3) A=Cross sectional area (m2) CP=Specific heat at constant pressure (J/kgK) h- Enthalpy (J) = Isentropic index
http://www.iaeme.com/IJMET/index.asp 221
[email protected]
Malay S Patel, Sulochan D Mane and Manikant Raman
R= Specific gas constant (J/kgK) Ma=Mach number Nozzle is a device which is designed to control properties of fluid like pressure, density, temperature and velocity. The major application of nozzle is to increase the velocity of flow by converting pressure and heat into kinetic energy. Mostly in rockets or air breathing engines, it is used to produce thrust to gain lift. Fluid of subsonic velocities can be accelerated to supersonic velocities using a rocket engine nozzle. To design a nozzle the major requirement is the magnitude of thrust produced by the nozzle. The altitude at which it operates and the properties of working fluid which govern the flow are its molecular weight, specific heat at constant pressure or volume and specific heat ratio.
2. LITERATURE REVIEW •
•
“Theoretical and CFD Analysis of De Laval Nozzle” by Nikhil Deshpande and Suyash Vidwans. In this paper total CFD analysis of a model of De Laval nozzle has been done. In this paper comparison is done based on theoretical and CFD values. In our paper we have explained all the basic concepts of De Laval nozzle along with providing the CFD of each and every case(1). “Modeling and simulation of Supersonic nozzle using computational fluid dynamics, by Venkatesh V and C Jayapal Reddy. In this paper theoretical and CFD analysis of various types of nozzles is given. Also thrust conditions and design parameters are discussed in this nozzle. We have taken diagrams and certain theory relevant to our topic(2).
2.1. Rocket or Air Breathing Nozzle
Figure 1 Thrust Operation
The ultimate purpose of nozzle is to expand a gas as efficiently as possible to maximize the exit velocity. This will increase the thrust produced. The thrust produced is given by the equation. F = mV + (P − P )A
For equation 1and figure 1, [Ref
(1)
(2)
]
2.2. Expansion Ratio The expansion ratio of the nozzle is the ratio of exit area to throat area. ε=
∗
(2)
A rocket generally does not travel through a single altitude, thus while designing a path over which a rocket is to travel is considered so that the expansion ratio that maximizes the performance is selected. Other factors like nozzle weight, length, manufacturability, heat transfer and aerodynamic characteristic are also considered, while designing thus altering the shape of nozzle.
http://www.iaeme.com/IJMET/index.asp 222
[email protected]
Concepts and CFD Analysis of De-Laval Nozzle
3. DE-LAVAL NOZZLE De-Laval nozzle is mainly used to achieve supersonic velocities. De-Laval nozzle or Converging Diverging Nozzle is the most widely used type of nozzle. It is in the shape of a tube pinched at the middle, making a perfectly balanced asymmetric hourglass shape. It is widely used in supersonic jet engines and steam turbines. They also have certain application in jet stream within astrophysics. Converging nozzle has a cross section reducing up to the throat at which the fluid gains maximum velocity. However in a converging nozzle the fluid can be accelerated up to sonic speed [Ma=1]. Thus to increase the velocity of fluid up to supersonic speed [Ma>1] a diverging part is attached to the nozzle. This type of nozzle is known as Converging Diverging Nozzle or De-Laval Nozzle.
3.1. Operation The speed of a gas (subsonic flow) will increase if the pipe carrying it narrows, because the mass flow rate is constant. The gas flowing is assumed to be isentropic. In a subsonic flow the gas is compressible and sound will propagate. At the throat, where cross section area is at its minimum, the gas velocity locally becomes sonic [Ma=1], a condition called chocked flow. As the nozzle cross sectional area increases the gas begins to expand, and the gas flow increase to supersonic velocities, where a sound wave will not propagate backwards through the gas as viewed in the frame of reference of the nozzle [Ma>1] It is not sufficient to force a fluid through nozzle to gain the supersonic velocity. Sometimes, the fluid may decelerate in the diverging section instead of accelerating if the back pressure is not in the range. Thus the state of nozzle flow is determined by the Overall Pressure Ratio O. P. R =
(3)
Consider the following conditions, (Ref Figure. 2) 1. When P0=Pb When P0=Pb, There is no pressure difference and thus no flow through nozzle. 2. When P0>Pb>Pc The flow remains subsonic through the nozzle. The fluid velocity increases in converging section and reaches to maximum at the throat, but the velocity is still subsonic at the throat. Thus in the diverging part, fluid loses its energy and diverging part acts as diffuser. The pressure reduces up to throat and again increases in the diverging section. 3. When Pb=Pc The throat pressure becomes P* and fluid gains the sonic velocity at the throat. P* is the minimum pressure at the throat and the velocity obtained is maximum velocity achieved by converging nozzle. Further reduction does not influence flow through the converging section, but influences flow through diverging section. 4. When PC>Pb>Pe The fluid that achieves the sonic velocity continues to accelerate to supersonic velocities in the diverging section. As pressure decreases, acceleration comes to sudden stop. Normal shocks are developed at the section between throat and exit plane and thus there is sudden drop in the velocity and flow gets decelerated. Flow through shock is highly irreversible and cannot be approximated as isentropic flow. When Pb=Pe shockwave forms at exit plane. Thus the supersonic flow through the nozzle becomes subsonic before leaving the nozzle as it crosses the normal shock. 5. When Pe>Pb>0 The flow in diverging section is supersonic and fluid expands to PF at the nozzle exit with no normal shock. Thus analysis of flow can be done as isentropic flow. When Pb=PF however, the pressure inside the nozzle increases from PF to Pb irreversibly in the wake of nozzle creating oblique shocks. The behavior of
http://www.iaeme.com/IJMET/index.asp 223
[email protected]
Malay S Patel, Sulochan D Mane and Manikant Raman
fluid expansion process is governed by exhaust pressure as well as pressure of external environment into which it exhausts. For minimum conversion of thermal energy into thrust, the exit pressure will be equal to t the ambient pressure. Where Pb is back pressure, Pe is exit pressure. PA , PB, PC are pressures at points A, B and C.
Figure 2 Pressure conditions
3.2. Expansion Analysis of Nozzle ozzle There are four cases too be taken into consideration (Ref ( Figure 3): Pe is exit pressure and Pamb is atmospheric pressure. 1. Pe