**Author details**

R. C. Mehta1,2

Address all correspondence to: drrakhab.mehta@gmail.com

1 Department of Aeronautical Engineering, Noorul Islam University, Kumaracoil, Tamil Nadu, India

2 School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore

### **References**


[5] Bogdonoff, S. M. Some experimental studies of the separation of supersonic turbu‐ lent boundary layer, Heat Transfer and Fluid Mechanics Institute, University of Cali‐ fornia, Los Angles, June 1955, pp.1-23.

**Subscripts** *D* = diameter

*t* = turbulent ∞ = freestream **Superscripts** − = time mean

**Acknowledgements**

114 Computational and Numerical Simulations

**Author details**

R. C. Mehta1,2

Nadu, India

Singapore

**References**

13:1411-1413.

Rockets, 2006; 43(1):147-160.

*rms* = root-mean-square

' = turbulent fluctuation

Address all correspondence to: drrakhab.mehta@gmail.com

Mach Number Range. AIAA 75-83, 1975.

The author is indebted to his parents and Vikram Sarabhai Space Centre, Trivandrum, India for their valuable encouragement, support and contributions to build the research career.

1 Department of Aeronautical Engineering, Noorul Islam University, Kumaracoil, Tamil

2 School of Mechanical & Aerospace Engineering, Nanyang Technological University,

[1] Hsieh, T. Flowfield about Hemispherical Cylinder in Transonic and Low Supersonic

[2] Hsieh, T. Hemisphere-Cylinder in transonic flow, M∞ = 0.7−1.0, AIAA Journal, 1975;

[3] Brower, T. L. Titan Launch Vehicle: Ground test history. Journal of Spacecraft and

[4] Awrejcewicz, J. and Krysko, V.A., Nonclassical Thermoelastic Problems in Nonlinear

Dynamics of Shells, Springer-Verlag, Berlin 2003, pp. 43-120.


[21] Mair, W. Experiments on Separation of Boundary Layers on Probes in front of Blunt-Nosed Bodies in Supersonic Air Stream. Philosophy Magazine, 1952; 43: 695-716.

[37] MaCormack, R. W. Numerical Methods for Compressible Flow, Workshop-cum-Seminar on Computational Fluid Dynamics, Vikram Sarabhai Space Centre, Trivan‐

Unsteady Flowfield Characteristics Over Blunt Bodies at High Speed

http://dx.doi.org/10.5772/57050

117

[38] Mehta, R. C. Block structured finite element grid generation method, Computational

[39] Shang, J. S. Numerical simulation of wing-fuselage aerodynamic interference,

[40] Mehta, R. C. Numerical Simulation of Wall Pressure Fluctuations on Hemisphere-Cylinder at Transonic Mach Numbers, Computational Fluid Dynamics Journal, 2000;

[41] E. Isaacson and H. B. Keller, Analysis of Nonlinear Methods, Wiley, New York, 1966,

[42] Marple Jr., S. L., Digital Spectral Analysis with Applications, Prentice-Hall, Inc., NJ,

[43] Mehta, R. C. Influence of Geometrical Parameters of Heat Shield on Flow Character‐ istics at Transonic Mach Number, International Review of Aerospace Engineering,

[45] Kenworthy, M. A. A Study of Unstable Axisymmetric Separation in High Speed Flows, Ph. D. thesis, Virginia Polytechnic Institute and State University, 1978.

[46] Yamauchi, M., Fujii, K., Tamura, Y. and Higashino, F. Numerical Investigation of Su‐

[47] Hankey, W. L. and Shang, J. S. Numerical Simulation of Self Excited Oscillations in Fluid Flows, in Habashi W. G., (ed) Computational Methods in Viscous Flows, Vol. 3,

[48] Mehta, R. C. High Speed Flow over Spiked-blunt body and Representation of Shock

[49] Ames Research Staff, Equations, Tables and Charts for Compressible Flow, NACA

[50] Greensite, A. L., Elements of Nonlinear Control Theory, Vol. 1, Spartan Books, New

[51] Kreyszig, E., Advanced Engineering Mathematics, 5th ed., Wiley, New Delhi, 1985,

[44] MATLAB User's Guide, pp. 2.47-2.51, The Math Works Inc., USA, 1992.

personic Flows Around a Spiked-blunt body, AIAA 93-0887, 1993.

Polar, Computational Fluid Dynamics Journal, 2009; 18(1:3): 22-30.

Pineridge Press, Swansea, 1984, 543-582.

drum, Dec. 14-21, 1981.

8(4): 511-520.

pp.489.

USA 1987.

2013; 6(1), 69-75.

report 1135, 1953.

pp. 135.

York, 1970, pp. 215−232.

Fluid Dynamics Journal, 18(2)2011.

AIAAJ,1984; 22(10):1345−1353.


[37] MaCormack, R. W. Numerical Methods for Compressible Flow, Workshop-cum-Seminar on Computational Fluid Dynamics, Vikram Sarabhai Space Centre, Trivan‐ drum, Dec. 14-21, 1981.

[21] Mair, W. Experiments on Separation of Boundary Layers on Probes in front of Blunt-Nosed Bodies in Supersonic Air Stream. Philosophy Magazine, 1952; 43: 695-716.

[22] Wood, C. J., Hypersonic Flow over Spiked Cones, Journal of Fluid Mechanics, 1961;

[23] Bogdonoff, S.M. and Vas, I.E. Preliminary Investigations of Spiked Bodies at Hyper‐

[24] Crawford, D. H., Investigation of the flow over a spiked-nose hemisphere-cylinder,

[25] Kabelitz., H., Zur Stabilität Geschlossener Greznschichtablösegebeite an Konischen

[26] Feszty, D., Badcock, K. J., and Richards, B. E. Driving Mechanism of High-Speed Un‐

[27] Kistler, A. L. Fluctuating Wall Pressure under a Separated Supersonic Flow, Journal

[28] Badcock, K. J., Richards, B. E., and Woodgate, M. A. Elements of Computational Flu‐ id Dynamics on Block Structured Grids Using Implicit Solvers, Progress in Aero‐

[29] Feszty, D., Badcock, K.J., Richards, B.E. Driving Mechanisms of High-Speed Unstea‐ dy Spiked Body Flows, Part 1: Pulsation Mode, AIAA Journal; 2004 42(1): 95-106

[30] Panaras, D., and Drikakis, D. High Speed Unsteady Flows Around Spiked-Blunt

[31] Baldwin, B. S., and Lomax, H. Thin Layer Approximation and Algebraic Model for

[32] Purohit, S. C., Shang, J. S., and Hankey, W. L. Effects of Suction on the Wave Struc‐

[33] Liu, F., and Jameson, A. Multgrid Navier-Stokes Calculations for Three-Dimensional

[34] Peyret, R., and Vivind, H., Computational Methods for Fluid Flows, Springer, Berlin,

[35] Blazek, J. Computational Fluid Dynamics: Principles and Applications, 1st Editon,

[36] Jameson, A, Schmidt, W. and Turkel, E. Numerical Simulation of Euler Equations by Finite Volume Methods using Runge-Kutta Time-Stepping Scheme, AIAA 81-1259,

Drehkörpern bei Hyperschallströmung, DLR, FB: 71-77, Germany, 1971.

steady Spiked Body Flows, Part 1 & 2, AIAA Journal, 2004; 42(1): 95-106.

of Acoustic Society of America; 1964; 36: 543-550.

Bodies, Journal of Fluid Mechanics, 2009; 632: 60-96.

ture of a Three-Dimensional Turret, AIAA 83-1738, 1983.

Separated Turbulent Flow, AIAA 78-257, 1978.

sonic Speeds, Journal of the Aero/Space Sciences, 1959; 26(2): 65-74.

12: 614 - 624.

116 Computational and Numerical Simulations

NASA TND-118, Dec. 1959.

space Sciences, 2000; 36: 351-392.

Cascades, AIAA 92-0190, 1992.

Elsevier Science Ltd, Oxford, 2001.

1993.

1981.


**Chapter 6**

**Computer Modelling of Radial-Direct Extrusion of**

Improving the competitiveness of engineering products related to enhancement of extrusion technologies using computer modelling of the material behaviour that allows production of

It is well known that a wide range of complex-shaped parts with flanges and spherical cavities are applied in machine-building and operating at variable loadings and high wear conditions. This is why the mentioned parts are produced of compact materials by various types of extrusion. The extrusion techniques are less used for production parts from powder materials due to presence of residual porosity and density variation. The extrusion technologies for parts with spherical cavities producing in the automotive industry have studied insufficiently. Production of parts may be carried out using various deformation schemes by selection the optimal initial shape and porosity of billets, as well as the deformation temperature. The most common process flowsheet for parts from powder materials is the scheme involving pressing of billet (compact), sintering and subsequent final stamping to obtain the necessary accuracy

Finite element simulation is the most effective way for determination of optimal process variables of forming operations. However, simulation of extrusion of porous billets from powder materials with taking into account dependences of mechanical properties from porosity, thermal and strain rate deforming conditions does not allow to estimate the conver‐ gence of finite element method (Awrejcewicz et al., 2004; Awrejcewicz & Pyryev, 2009). Mathematical formulation of the nonlinear coupled thermal plasticity problem makes necessary implementation of advanced solution methods for systems of linear algebraic

> © 2014 Ryabicheva and Usatyuk; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

high-quality products (Aliev et al., 2001; Favrot et al., 1997, Ryabicheva, 2012).

**Porous Powder Billets**

http://dx.doi.org/10.5772/57142

and density (Ryabicheva et al., 2011).

equations (Awrejcewicz et al., 2007).

**1. Introduction**

Lyudmila Ryabicheva and Dmytro Usatyuk

Additional information is available at the end of the chapter
