# Vortex Shedding in Solid Rocket Motor-1

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BY L.SWATHI 08951A21B1 B.TEJASWI 08951A21B3

ABSTRACT Vortex shedding inside SRM is a well-known phenomenon,

which is a leading cause of pressure oscillations in the motors. With the advent of high speed numerical techniques it has become possible to numerically simulate the flows of different regimes. CFD was one such tool which evolved as a consequence of these high speed numerical techniques. Vortex shedding phenomenon in SRM is predicted using this CFD tool. In this project , in order to gain confidence in fluent solver , it has been validated by predicting the vortex shedding phenomenon in the flow past a circular cylinder and a flat plate to establish the methodology and then extended to SRM.

VORTEX A vortex is a spinning, often turbulent, flow of fluid. Any

spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex. The speed and rate of rotation of the fluid in a free (irrotational) vortex are greatest at the center, and decrease progressively with distance from the center, whereas the speed of a forced (rotational) vortex is zero at the center and increases proportional to the distance from the center. Both types of vortices exhibit a pressure minimum at the center, though the pressure minimum in a free vortex is much lower.

PROPERTIES OF VORTICES The fluid pressure in a vortex is lowest in the

center and rises progressively with distance from the center. The core of every vortex can be considered to contain a vortex line, and every particle in the vortex can be considered to be circulating around the vortex line Two or more vortices that are approximately parallel and circulating in the same direction will merge to form a single vortex. The circulation of the merged vortex will equal the sum of the circulations of the constituent vortices. Vortices contain a lot of energy in the circular motion of the fluid. In an ideal fluid this energy can never be dissipated and the vortex would persist forever. However, real fluids exhibit viscosity and this dissipates energy slowly from the core of the vortex.

VORTEX SHEDDING Vortex shedding is caused when a fluid flows past a

blunt object. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object . If the frequency of vortex shedding matches the resonance frequency of the structure, the structure will begin to resonate and the structure's movement can become self-sustaining.

A vortex is in the process of formation near the top of

the cylinder surface. Below and to the right of the first vortex is another vortex which was formed and shed a short period before. Thus, the flow process in the wake of a cylinder or tube involves the formation and shedding of vortices alternately from one side and then the other. This phenomenon is of major importance in engineering design because the alternate formation and shedding of vortices also creates alternating forces, which occur more frequently as the velocity of the flow increases.

The frequency at which vortex shedding takes place for

a cylinder is related to the Strouhal number by the following equation

The Strouhal number depends on the body shape and on the Reynolds number. At low Reynolds number the flow is steady and laminar. With increasing Reynolds number the flow becomes unsteady in a twodimensional periodic manner with regular vortex shedding. . At even higher Reynolds number the flow becomes three-dimensional, and finally become chaotic and turbulent

DESIGN OF SRM

NUMERICAL SIMULATION OF VORTEX SHEDDING To numerically simulate vortex

shedding, CFD is used to calculate the unsteady flow that arises from a fluid moving past an obstruction. Downwind of the obstruction are regions of lower pressure which causes the fluid which initially was deflected around the obstruction to get sucked into these regions, begin to circulate, and form vortices.

Generally a fluid flow problem is governed by different governing equations such as Mass, Momentum, Energy, all these equations are PDEs which are difficult to solve. In CFD we discretize these partial differential equations into algebraic equations which can be solved easily by using different softwares on computers. CFD is used especially for some reasons because CFD allows numerical simulation of fluid flows, results for which are available for study even after the analysis is over.

Numerical Techniques In CFDFor solving numerical equations we have different types of methods available. They are: Finite Difference Method (FDM) Finite Volume Method (FVM) Finite Element Method (FEM)

FINITE DIFFERENCE METHOD In finite difference method the flow domain is

discretized into a series of grid points (a structured mesh (i, j, k) is required). And then the governing equations are converted to algebraic equations (using Taylors series) which are solved iteratively until the solution converged. In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.

FINITE VOLUME METHOD In FVM the flow domain is divided into finite number of control volumes using grid points then the integral form of equations are converted into algebraic equations and are solved until solution is converged. "Finite volume" refers to the small volume

surrounding each node point on a mesh.

FINITE ELEMENT METHOD The finite element method (FEM) is a numerical

technique for finding approximate solutions of partial differential equations (PDE) as well as integral equations. The solution approach is based either on eliminating the differential equation completely, or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler's method, Runge-Kutta, etc.

VORTEX SHEDDING IN FLOW PAST A FLAT PLATEThe width of the flat plate was about 5mm and the lateral width of the plate was about 30mm. The plate is placed at a distance of 60mm from the inlet and flow was computed over a length of 335mm after the plate in the axial direction.

A flat plate is placed at 90 to the oncoming fluid

stream to disrupt the flow and generate vortices of alternating rotation from the edges of the body. To model flat plate using GAMBIT software and

numerically simulate the flow past the flat plate using FLUENT software to obtain the frequency of pressure oscillations due to vortex shedding phenomenon

Quadrilateral mesh has been implemented for both the cases i.e., flat plate case and the circular cylinder case. The computational domain of the flat plate has 158594 cells, 318033 faces and 159435 nodes with mesh interval size of 1mm. The mesh details in the computational domain around the flat plate are as shown in fig. The magnified view of mesh details near the geometry of the flat plate is shown in this figure.

Boundary conditions and physical valuesVelocity inlet along x-direction

Velocity inlet along x-direction

Pressure outlet normal to boundary

Velocity inlet along x-direction

VORTICITY CONTOURS

VORTEX SHEDDING IN CIRCULAR CYLINDERThe radius of the circular cylinder was 15mm. The cylinder is placed at a distance of 100mm from the inlet and flow was computed over a length of 350mm beyond the aft end of the cylinder in the axial direction

Meshing is done using the GAMBIT 2.3.Quadrilateral mesh has been implemented within the computational domain and around the cylinder. The computational domain of the circular cylinder has 248544 cells, 498232 faces and 249688 nodes with mesh interval size of 1mm. The mesh details in the computational domain around the circular cylinder are as shown in fig. The magnified view of mesh details near the geometry of the circular cylinder is shown in the subsequent figure

Boundary conditions and physical valuesVelocity inlet along x-direction Velocity inlet along x-directionPressure outlet- normal to boundary

Velocity inlet along x-direction

VORTICITY CONTOURS

VORTEX SHEDDING IN SOLID ROCKET MOTOR The geometry of SRM considered for analysis has three segments namely head-end , middle and nozzle-end or aft-end.

The solid rocket motor combustion chamber is in the form of a circular cylinder of 150mm radius with 50mm radius left hollow (perforation) for the passage of combustion products

The other 100mm radius consists of the solid

propellant grain. Two inhibition regions (obstacle walls) are considered in the model one at the head end segment joint (Joint-1) and the other at the nozzle end segment joint (Joint-2).

COMPUTATIONAL DOMAIN Vortex shedding does not occur initially and to simulate the phenomenon of vortex shedding flow has to be considered after certain amount of propellant has been burnt. For this reason four different cases will be studied with different levels of propellant burnt and inlet conditions are imposed normally to side walls, simulating inlet due to solid propellant combustion .

CASE 1:

In this configuration 30mm of the propellant is burnt with inhibitors projecting out of the propellant surface without any erosion

CASE 2: In the second case the geometry of SRM after 30mm (in radial direction) of the propellant is burnt was considered for analysis with the assumption that the inhibitor at head end was eroding at the rate of 30% with respect to the propellant which appears to be 9mm. And the inhibitor at the nozzle end was eroding at the rate of 50% with respect to the propellant which appears to be around 15mm

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