Volume No. 7 Issue No.: 4 Page No.: 1407-1412 April-June 2013

### MATHEMATICAL MODELLING OF SOLID PROPE-LLANT GRAIN GEOMETRY SUITABLE FOR MULTI BARREL ROCKET LAUNCHER APPLICATIONS

**Pandey K. M.* and Bose P.**

Department of Mechanical Engineering, National Institute of Technology, Silchar, Assam (INDIA)

**Received on :** December 10, 2012

### ABSTRACT

The purpose of the paper is to analyse as to why solid propellant is preferred in rockets to propel through Multi Barrel Rocket Launcher (MBRL) in military applications and the implications of grain geometry. In addition to high specific impulse capability, the solid propellant retains its usefulness even on prolonged storage and deployment in field condition. It has negligible toxicity/health hazards to the troops. Solid rocket propellant grain can be given desired grain geometry as it is manufactured by extrusion or casting process. It is possible to design the grain geometry keeping its end use in view. Mathematical modeling is done for composite solid propellant which is preferred in rocket launcher applications. There are various compositions of composite propellants and for MBRL applications it generally consist a crystalline oxidizers like Ammonium Perchlorate (AP), a metallic fuel like Aluminum (Al) in a resinous binder like Hydroxyl Terminated Poly Butadiene (HTPB). Composite propellant offers the advantages of higher specific impulse, possibility of case-bonding, burning rate independent of rocket motion and low cost of production. Pressure developed by the burning of propellant depends upon along with other parameters geometry of the grain which includes shape and size of the cross section, web and surface area dimensions. Mass burnt is proportional to exposed surface area which in turn responsible to the pressure developed by its burning. Relation between web and mass burnt is established by a parameter called form factor (θ). Mathematical modeling establishes that if θ is positive, the surface area decreases as the burning progresses. It is called propellant with regressive grain geometry and the propellant is suitable for artillery gun projectile. If θ is negative, it is progressive burning grain because in this case the surface area increases as the burning progresses. Propellant with this type of grain geometry is suitable for booster rockets in space applications. If θ = 0 the surface area remains constant as the burning progresses and the grain geometry provides neutral burning. Here the burning rate remains constant and thus suitable for MBRL as well as sustainer rocket in space applications. To extract the maximum chemical energy of a propellant in terms of heat, its complete combustion needs to be ensured. By suitably modifying the grain design 99% decomposition of propellant into gas can be achieved. One of the method is to design neutral burning surface having internal cross section of the grain such that negligible sliver is left after burning of the propellant. There is a requirement to inhibit the ends as well as the outer surfaces so that combustion can progress from inside.

**Keywords :** Solid rocket, MBRL, Grain geometry, Form factor, Composite propellant, Burning rate, Sliver, Mathematical modeling