Vertical and short takeoff and landing (V/STOL) aircraft have several major categories of engine arrangement. Some of the typical arrangements for high speed aircraft are: the engines may be fixed in a position required to produce thrust for forward flight. Their exhaust systems, however, have built-in variable geometry, making it possible to vector the exhaust nozzle (or nozzles) or divert the exhaust gases by means of valves and auxiliary ducts to nozzles mounted in such a way as to provide vertical thrust or lift.
Another option is the aircraft may include two different sets of engines or propulsors (or both), fixed in position, with one set installed for forward flight and the other for vertical thrust (i. e. , the lift engines). Additionally, the aircraft may use a convertible engine. Supersonic aircraft usually use low bypass turbofans as they give good efficiency below the speed of sound as well as above, or if extended super cruise is needed turbojet engines are desirable as they give less nacelle drag at supersonic speeds.
A supersonic transport (SST) is a civil aircraft designed to transport passengers at speeds greater than the speed of sound. The only supersonic civilian aircraft to see service are the Soviet produced Tupolev Tu-144 which first flew in 1968 and was retired in 1997, and the Franco-British produced Concorde, which first flew in 1969 and remained in service until 2003. Following the cessation of flying by Concorde in 2003, there are no supersonic civilian aircraft in service.
These are succinctly reported in the open literature, which triggered the researchers to make attempts for unconventional lucrative design challenges of supersonic aircraft. In an attempt to resolve some of the technological challenges on supersonic aircraft design, a substantial revision of the existing concept is required. In this paper critical review of the literature is carried out and a conceptual design of short takeoff supersonic aircraft with cold flow multi-purpose rectangular nozzle has been proposed.
Bachelor of Engineering Final Year Student, Department of Aeronautical Engineering, Kumaraguru College of Technology, Coimbatore – 641 049, Tamil Nadu, India (email: vignesh. [email protected] com) 2 Professor and Aerospace Scientist (ISRO), Aeronautical Engineering, Kumaraguru College of Technology, Coimbatore – 641 049, Tamil Nadu, India; Corresponding Author, (phone: +91 – 9150891021 / +91-9388679565, (email: [email protected] co. in) 1
Abstract— In this paper numerical studies have been carried out for the conceptual design of short takeoff supersonic aircraft with cold flow nozzles. As a first step supersonic rectangular CD nozzle with multi-purpose frame is designed in such a way that during the early taxiing time the internal flow choking will be established without forming any shockwave in the divergent region for facilitating the aircraft for a smooth and short takeoff. Immediately after the takeoff the nozzle frame will be converted into rectangular supercritical wing for meeting the high speed aerodynamic design objectives.
Parametric analytical studies have been carried out for both internal and external flows using suitable turbulence models. The results from the parametric study indicate that cold flow choked nozzles with conventional jet engines will compliment for the short takeoff of supersonic aircraft lucratively without having any additional propulsion systems. Keywords— Choked Rectangular Nozzle, Rectangular Supercritical Airfoil, Short Takeoff Aircraft, Supersonic Aircraft. I. INTRODUCTION HE great majority of supersonic aircraft today are military or experimental aircraft.
Most of them, including many military fighter aircraft, are designed to exceed the speed of sound only in certain exceptional flight regimes; a handful of aircraft, such as the SR-71 Blackbird military reconnaissance aircraft and the Concorde supersonic civilian transport, are designed to cruise continuously at speeds above the speed of sound. Supersonic flight brings with it substantial technical challenges, as the aerodynamics of supersonic flight are dramatically different from those of subsonic flight. These challenges have largely been met.
However, political, environmental, and economic obstacles of greater magnitude continue to severely limit the actual deployment of supersonic aircraft, particularly in the civilian world. Additionally, the need and demand for supersonic flight have often been insufficient to justify development or deployment of supersonic aircraft, particularly in the domain of civilian transport. The aforementioned SR-71 and Concorde aircraft are no longer flying today although Concorde was highly profitable in service, but because of the low market among operators (due to sonic booms, relatively high fuel
T Comparisons of 3D computation and experiment for non axi-symmetric nozzles have been carried out by NASA in 1989 . The configurations are selected from a set of the single expansion ramp nozzles which were experimentally investigated by Re and Leavitt . The experiments were performed to analyze the effects of various geometrical 256 3rd International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE’2013) January 8-9, 2013 Kuala Lumpur (Malaysia) parameters and pressure ratios on the static performance of these asymmetric nozzles.
Three-dimensional solutions obtained with their code have been presented for two asymmetric, single expansion ramp nozzles at a pressure ratio of 10. The computed flow consists of the internal expansion region in the converging / diverging sections and the external supersonic exhaust in a quiescent ambient environment. The fundamental characteristics existing at the prescribed flow condition have been captured successfully for the present nozzle / exhaust flow field. These features include expansion fans, Mach wave reflections, mixing layers, and nonsymmetrical, multiple inviscid cell, supersonic exhausts.
Comparison has been made with experimental data for wall pressure distributions at the center planes with good agreement. Applications of numerical methods to the nozzle complex flow field have been reported by investigators. Some of these studies have focused on the interaction of the exhaust plume and the external stream, and the consequent effects on the nozzle afterbody [3, 4]. In several other studies, the jet plume has been analyzed independently [5, 6]. The flow inside the nozzle is treated as a separate problem, and is generally well understood for a simple two-dimensional symmetrical nozzle.
In the case of the nozzle considered in this paper, however, the independent treatment of the exhaust plume may not be adequate, since the initial part of the exhaust plume bordered by its free shear layer can change the flow structure near the upper external expansion surface. Simultaneously solving the flow field to account for the strongly interactive nature thus becomes necessary. Works related to this type of nozzle, in which the computations include a complete domain of the internal nozzle, the external exhaust plume and the ambient stream, have been performed by several other investigators .
Independent calculation of a similar nozzle had also been reported for a two-dimensional case . Other results based on the full Navier- Stokes (NS) equations, parabolized NavierStokes (PNS) equations or method of characteristics in two and three dimensions have been calculated for a variety of nozzle conditions including supersonic, subsonic and quiescent external streams [12-16]. In addition, these previous analyses have demonstrated the simplicity of the simulation procedures as applied to the nozzle / exhaust problem, in which the geometry is complex and the flow is highly nonuniform.
The importance of investigating rectangular turbulent jets is determined by both their practical importance and ? ow complexity. In fact, a rectangular turbulent jet is a typical example of a 3D turbulent ? ow, which is strongly influenced by initial conditions. Several papers have been written on rectangular turbulent jets [17-21]. It is difficult to compare the experimental data presented in these papers because of the considerable difference between the particular initial conditions, including the nozzle geometry and the experimental set-up itself. Hence it is almost impossible to summarize the results obtained by different authors.
In addition most papers treat a particular geometry and specific initial conditions without investigating their influence. It should be noted that in recent years the number of publications on this topic has increased because of the need to 257 investigate the turbulent structure of the flow for various practical applications . III. CONCEPTUAL DESIGN Turbulent jet flows issuing from rectangular nozzles are used in many technological and practical applications. Understanding their development and mechanics is important to the design and performance improvement of these applications.
Therefore, rectangular jets have been Fig. 1 Supersonic aircraft with rectangular CD nozzle with adjustable frame facilitated for converting it into the rectangular supercritical airfoil after takeoff. studied extensively over the past decades. Fig. 1 shows the proposed design of military aircraft with CD rectangular nozzle under the wing and shifted laterally. A rectangular CD nozzle is an altered type of a De Laval nozzle where we can have reduced frontal surface area. Fig. 2(a-b) represents the physical model of a rectangular CD nozzle. The ultimate idea of this study is to reduce the take-off distance.
Note that by placing the CD nozzle under the wing we can accelerate the cold flow at the choked flow condition during taxiing, resulting the sudden increase in thrust and short take-off. Though the idea is very simple the design optimisation of a rectangular CD nozzle is a difficult task. In order to control how much mass is moving and how fast it moves, the ratio of the exit to the throat is the key design component of a CD nozzle. In the divergent session of the CD nozzle the supersonic flow accelerates as the area gets bigger. This region of supersonic acceleration is terminated by a normal shock wave. (a) Physical Model b) Idealized Physical Model Fig. 2 (a-b) Physical models of the rectangular CD nozzle. 3rd International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE’2013) January 8-9, 2013 Kuala Lumpur (Malaysia) The shock wave produces a near-instantaneous deceleration of the flow to subsonic speed. This shock wave is the major concern in designing a CD nozzle. The size of the nozzle throat effectively sets the mass flow rate through the nozzle. Next, the area of the exit is important because it will determine how much the fluid is allowed to expand. This expansion will then determine the Mach number of the exiting flow.
It also determines the exit pressure, temperature, and velocity of the fluid coming out. The proposed CD nozzle is an over expanded nozzle with P b /P c value of 0. 6 which will cause the flow to choke and will reduce the possibility of forming shock waves within the nozzle. Immediately after the takeoff it is proposed to transform the CD rectangular nozzle into a rectangular supercritical wing for reducing the wave drag during the transonic regime. IV. NUMERICAL METHOD OF SOLUTION Numerical simulations for internal flow have been carried out with the help of a two-dimensional standard k-epsilon model.
It is a two equation turbulence model in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined. The turbulence kinetic energy, k, and its rate of dissipation, ? , are obtained from the following transport equations: (a) 3D Grid system (b) 2D Grid system Fig. 3(a-b) Grid systems in the computational domain of the rectangular CD nozzle. and G k represents the generation of turbulence kinetic energy due to the mean velocity gradients. G b is the generation of turbulence kinetic energy due to buoyancy.
Y M represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. C 1? , C 2? , and C 3? are constants. ? k and ? ? are the turbulent Prandtl numbers for k and ? , respectively. S k and S ? are user-defined source terms. Compressibility effects are encountered in gas flows at high velocity and/or in which there are large pressure variations. When the flow velocity approaches or exceeds the speed of sound or when the pressure change in the system is large, the variation of the gas density with pressure has a ignificant impact on the flow velocity, pressure, and temperature. Compressible flows create a unique set of flow physics for which one must be aware of the special input requirements and appropriate solution techniques. Compressible flows are typically characterized the total pressure P o and total temperature T o of the flow. In this model the compressible flows are described by the standard continuity and momentum equations with the inclusion of the compressible treatment of the density. The energy equation solved by the code will incorporate the coupling between the flow velocity and the static temperature.
The viscosity is determined from the Sutherland formula. All boundary conditions for wall-function meshes will correspond to the wall function approach, but in the case of fine meshes the appropriate low-Reynolds number boundary 258 conditions will be applied. At the solid walls a no-slip boundary condition is imposed. An idealized physical model is required for the simplification of the analysis. Concurrently, decisions are made as to the extent of the finite flow domain in which the flow is to be simulated. Portions of the boundary of the flow domain coincide with the surfaces of the body geometry.
Other surfaces are free boundaries over which flow enters or leaves. The geometry is modeled in such a manner as to provide input for the grid generation. Thus, the modeling often takes into account the structure and topology of the grid generation. Fig. 3(a-b) shows the grid systems in the computational domain for 3D and 2D cases. In this paper numerical results are generated using the 2D mesh for fast computation without sacrificing the accuracy much. Initial wall temperature (300 K), inlet total pressure (101325 Pa) and temperature (300 K) are specified. Ideal gas is selected as the working fluid.
The turbulent intensity is selected as 5 % and inlet velocity is obtained as 150 m/s. The code has successfully validated with the help of benchmark solutions. In another attempt numerical studies for external flows have been carried out using two dimensional density based steady one-equation Spalart – Allmaras model for the geometrical optimizing of a supercritical aerofoil, transformed from the rectangular nozzle, aiming for reducing the drag at wide range of operating conditions. The Sutherland law for viscosity is well suited for high-speed compressible flow.
Though Cp and thermal conductivity are temperature dependent, for simplicity, initially we assumed it as constants at high speed flows . V. RESULTS AND DISCUSSION The numerical results presented in this session are a pointer towards for the design optimization of a supersonic aircraft with rectangular CD nozzle for short takeoff. Fig. 4 shows the variations of pressure and velocity inside the CD nozzle. It is evident from these figures that the CD nozzle design is acceptable owing to the fact that shock waves are not encountered in the divergent session of the nozzle. rd International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE’2013) January 8-9, 2013 Kuala Lumpur (Malaysia) (a) Static Pressure (b) Velocity Magnitude Fig. 7 Comparison of the takeoff distance of a typical supersonic aircraft with and without CD nozzle. Fig. 4 Demonstrating the pressure and velocity variations inside the CD nozzle. Fig. 5 Demonstrating the wall pressure coefficient variations in the CD nozzle. with and without CD nozzle under ideal conditions. We observed through the parametric analytical studies that the average outlet velocity is approximately 5 to 6 times the inlet velocity.
During the external flow simulation we have observed that when the free stream Mach number exceeds the critical Mach number a pocket of supersonic flow occurs over the top surface as usual; but because of the top surface is relatively flat, the local supersonic Mach number is a lower value than would exist in the case of a conventional aerofoil. As a result, the shock wave that terminates the pocket of supersonic flow is weaker. In turn, the supercritical airfoil can penetrate closer to Mach 1 before drag divergence occurs. Admittedly, considerable amount of drag has been encountered during the transonic regime.
Therefore one should propose more meaningful design for the drag reduction while proposing for the integrated approach for the design optimization of a supersonic aircraft for the smooth and short takeoff, which is beyond the scope of this paper. Fig. 8 shows the grid system in the computational domain of the supercritical airfoil. Fig. 9 shows the contours of the static pressure and the velocity magnitude over the supercritical airfoil. We observed that with the same inflow conditions the proposed supercritical airfoil could reduce the drag coefficient by 5 % than the conventional geometry.
This supercritical airfoil can be further optimized for reducing the drag without affecting the structural and aerodynamics design requirements. The basic design approach behind supercritical shapes is to flatten the upper surface of the airfoil to reduce flow acceleration and to use a highly cambered aft section to generate the majority of the lift. The disadvantage of this approach is that aft-loaded wings shift the center of lift back, Fig. 6 Demonstrating the velocity variations in the CD nozzle. Fig. 5 shows the wall pressure coefficient variations and Fig. shows the velocity variations inside the CD nozzle. Based on the numerical data an analytical exercise has been carried out to estimate the take of velocity of a typical aircraft with T/W = 0. 85, Max. take-off weight = 46200 Kg, Thrust = 152 KN, C d = 0. 153, Wing span = 13. 46 m). We observed that with the rectangular CD nozzle with inlet velocity 150 m/s one can accelerate the aircraft for a short takeoff with 50 % reduction in the takeoff distance. Fig. 7 shows the comparison of the takeoff distance of an aircraft 259 Fig. Grid system in the computational domain of the supercritical airfoil. 3rd International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE’2013) January 8-9, 2013 Kuala Lumpur (Malaysia)  L. E. Putnam, and J. Hodges, “Assessment of NASA and RAE Vicous –     Fig. 9 Pressure and velocity contours over the supercritical airfoil.  which necessitates moving the wings forward. This design tradeoff results in larger pitching moments, the need for larger and heavier control surfaces, and the need for stronger and heavier wing structures.
VI. CONCLUDING REMARKS Successful numerical studies have been carried out for the conceptual design and optimization of short takeoff supersonic aircraft with cold flow nozzles. As a first step supersonic rectangular CD nozzle with multi-purpose frame is designed in such a way that during the early taxiing time the internal flow choking will be established without forming any shockwave in the divergent region for facilitating the aircraft for a smooth and short takeoff.
Immediately after the takeoff the nozzle frame will be converted into rectangular supercritical wing for meeting the high speed aerodynamic design objectives. Parametric analytical studies have been carried out for both internal and external flows using suitable turbulence models. As speed increases, the compressibility (or ability to be squeezed into a smaller volume) of air increases. It implies that the density of air increases at high speeds resulting in greater drag on an airfoil.
A supercritical airfoil is designed to delay the speed at which the compressibility effect becomes significant so that drag will be reduced. Note that any attempt for retaining the rectangular CD nozzle after the takeoff will be counter productive to the flight performance owing to the fact that its frame induces additional drag and the supersonic inflow will be shocked down by the CD nozzle at its throat leading to the formation of subsonic flow at its exit. Therefore design optimization of a short takeoff supersonic aircraft with cold flow nozzles is a daunting task and however must be attempted with caution.
We concluded that the fluid-structural interactive code can possibly optimize the proposed conceptual design of a supersonic aircraft with flexible rectangular CD nozzle frames for the lucrative commercial applications. REFERENCES                Inviscid Interaction Methods for Predicting Transonic Flow over Nozzle Afterbodies, AIAA Paper No. 83-1789, July 1983. R. Wilmoth, Aerodynamics Interactions with Turbulent Jet Exhaust Plumes, JANNAF 13th Plume Technology Meeting, April 1982, Houston, Texas.
E. Venkatapathy, and W. J. Feiereisen, “3-D Plume Flow Computations with an Upwind Solver,” AIAA Paper No. 88-3158, AIAA/ASME/SAE/ASEE 24th Joint Propulsion Conference, July 1988, Boston, MA, USA. G. A. Hasen, “Navier-Stokes Solutions for an Axisymmetric Nozzle,I1 AIAA Journal, Vol. 20, Sept. 1982, pp. 1219-1227. S. Dash, and P. Del Guidice, “Shock Capturing Finite-Difference and Characteristic Reference Plane Techiques for the Prediction of Threedimensional Nozzle- Exhaust,” NASA CR 145366, May 1978. P. D.
Thomas, “Numerical Method for Predicting Flow Characteristiccs and Performance of Nonaxisymmetric Nozzles, Part 2 – Application, NASA CR 3264, Oct. 1980. K. M. Peery, “Non-Axisymmetric Nozzle/Aftbody Flow Field Analysis,” AFWALTR- 81-3046, June 1981. D. E. Wolf, R. A. Lee, and S. M. Dash, “Parabolized Navier-Stokes Analysis of Scramjet Hypersonic Nozzle Flowfields,ll AIAA Paper No. 87-1897, AIAA/SAE/ASME/ASEE 23rd Joint Propulsion Conference, June 1987, San Diego, CA. C. F. Shieh, “Navier-Stokes Solutions of Transonic Nozzle Flow with Shock-Induced Flow Separationsr1I AIAA Paper No. 8-3614, AIAA/ASME/SIAM/APS 1st National Fluid Dynamics Congress, July 1988, Cincinnati, OH, USA. R. M. Beam, and R. F. Warming, “An Implicit Factored Scheme for the Compressible Navier-Stokes Equations,” AIAA Journal, Vo1. 16, April 1978, pp. 393-402. G. K. Cooper, “The PARC Code: Theory and Usage,” AEDC-TR-87-24, Oct. 1987. T. H. Pulliam, “Euler and Thin Layer Navier-Stokes Codes: ARC2D, ARC3D, Notes for Computational Fluid Dynamics User’s Workshop,” The University of Tennessee Space Institute, Tullahoma, Tn. , UTSI Pub. E02-4005-023-84, 1984, pp. 15. 1-15. 85. A. T. Hsu, and M. S.
Liou, “A Computational Analysis of UnderExpanded Jets in the Hypersonic regime,” NASA TM 101319, 1988. G. J. Harloff, H. T. Lai, and E. S. Nelson, “Two-Dimensional Viscous Flow Computations of Hypersonic Scramjet Nozzle Flow fields at Design and Off Design Conditions,” NASA TM 182150, June 1988. K. B. M. Q. Zaman, Flow-Field Surveys For Rectangular Nozzles, Glenn Research Center, Cleveland, Ohio, NASA/TM—2012-217410, AIAA– 2012–0069. Ganesh Raman, Michael Hailyef and Edward J. Rice, “Flip-Flop Jet Nozzle Extended to Supersonic Flows,” AIAA Journal, Vol. 31, No. 6, June 1993, pp. 1028-1035. M. Lozanova, P.
Stankov, “Experimental investigation on the similarity of a 3D rectangular turbulent jet,” Experiments in Fluids 24 (1998) 470478, Springer-Verlag 1998. A. Mohamed, A. Hamed, and T. Lehnig, “Supersonic Rectangular OverExpanded Jets of Single and Two-Phase Flows, ISABE 2003-1119. Mohammed Hamed Alnahhal, “Turbulent Rectangular Jets,” Ph. D Dissertation, Department of Mechanical Engineering and Aeronautics, University of Patras, Rio 26 504, Greece, 2010. Shantanu Khanna, “CFD Analysis of Super Critical Aerofoil over simple Aerofoil”, M. S Thesis, College of Engineering, University of Petroleum and Energy Studies, May 2011. 2] H. Lai and E. Nelson, “Comparison of 3D Computation and Experiment for Non-Axisymmetric Nozzles”, NASA Contractor Report 182245, NASA Lewis Research Center Group, Cleveland, Ohio, February 1989, AIAA-89-0007. Re, R. J. , and Leavitt, D. L. , “Static Internal Performance of SingleExpansion-Ramp Nozzles with Various Combinations Of Internal Geometric Parameters, NASA TM and 86270, 1984. 260 3rd International Conference on Trends in Mechanical and Industrial Engineering (ICTMIE’2013) January 8-9, 2013 Kuala Lumpur (Malaysia) Spare Parts Inventory Model for Auto Mobile Sector Using Genetic Algorithm S. Godwin Barnabas, I.
Ambrose Edward, and S. Thandeeswaran Abstract—In this paper the objective is to determine the optimal allocation of spares for replacement of defective parts onboard of a usage. The optimal inventory control methodologies intend to reduce the supply chain cost by controlling the inventory in an effective manner, such that, the SC members will not be affected by surplus as well as shortage of inventory. In this paper, we propose an efficient approach that effectively utilizes the Genetic Algorithm for optimal inventory control. This paper reports a method based on genetic algorithm to optimize inventory in supply chain management.
We focus specifically on determining the most probable excess stock level and shortage level required for inventory optimization in the supply chain so that the total supply chain cost is minimized . So, the overall aim of this paper is to find out the healthy stock level by means of that safety stock is maintained throughout the service period. Keywords—Excess Stock, Genetic algorithm, Inventory, Optimization, Safety stock. service sector. Inventory is held throughout the supply chain in the form of raw materials, work in progress, and finished goods. II.
LITERATURE REVIEW Supply chain network is a complex network, which consists of multiple manufacturers, multiple suppliers, multiple retailers and multiple customers. The accomplishment of beam-ACO in supply-chain management has been proposed by Caldeira et al. . Beam- ACO has been used to optimize the supplying and logistic agents of a supply chain. A standard ACO algorithm has aided in the optimization of the distributed system. The application of Beam-ACO has enhanced the local and global results of the supply chain. A beneficial industry case applying Genetic Algorithms (GA) has been proposed by Wang et al. .
The case has made use of GAs for the optimization of the total cost of a multiple sourcing supply chain system. The system has been exemplified by a multiple sourcing model with stochastic demand. A mathematical model has been implemented to portray the stochastic inventory with the many to many demand and transportation parameters as well as price uncertainty factors. A genetic algorithm which has been approved by Lo  deals with the production inventory problem with backlog in the real situations, with time-varied demand and imperfect production due to the defects in production disruption with exponential distribution.
Besides optimizing the number of production cycles to generate a (R, Q) inventory policy, an aggregative production plan can also be produced to minimize the total inventory cost on the basis of reproduction interval searching in a given time horizon. P. Radhakrishnanet. al.  developed P. Radhakrishnan et. al.  developed a new and efficient approach that works on Genetic Algorithms in order to distinctively determine the most probable excess stock level and shortage level required for Inventory optimization in the supply chain such that the total supply chain cost is minimized.
Many well-known algorithmic advances in optimization have been made, but it turns out that most have not had the expected impact on the decisions for designing and optimizing supply chain related problems. Some optimization techniques are of little use 261 I. INTRODUCTION HE design and operation of spare part management systems is very important for automobile sector, Prior relevant system could be grouped in two categories. It is aimed to find optimal demand for a given spare parts management system; that is, how to determine optimal inventory level in order to reduce cost.
This paper attempts to solve a comprehensive design problem for a spare part management system. Every automobile sector should proceed systematically and establish an effective Spare parts management system. Inventory encompasses all raw materials, work in process, and finished goods within the supply chain. Changing Inventory policies can dramatically alter the supply chain’s efficiency and responsiveness. Inventory is an important cross functional driver of supply chain performance. An important role that can be satisfied by having the product ready and available when the customer wants it to reduce the customer waiting time in the S.
Godwin Barnabas 1. is an Assistant Professor, Mechanical Department in the Velammal College of Engineering and Technology,Madurai,Tamilnadu,India (Phone: +919943338837 ; e-mail: [email protected] com ). I. Ambrose Edward 2. is an Assistant Professor, Mechanical Department in the Velammal College of Engineering and Technology,Madurai,Tamilnadu,India (phone:+919952199565; e-mail:[email protected] com) S. Thandeeswaran 3. is an Assistant Professor, Mechanical Department in the Velammal College of Engineering and Technology,Madurai,Tamilnadu,India (Phone:+919790362087; e-mail: thandeeswaran. [email protected] com). T