Jet Decay Characteristics of Convergent Nozzle for Uncontrolled Jets

JET DECAY CHARACTERISTICS OF CONVERGENT NOZZLE FOR UNCONTROLLED JETS

AIM:

• To find the jet decay characteristics of the convergent nozzle for free jets at Mach 0.6, 0.8, and 1.

Do the following steps:

• Grid dependency test

1. To validate the mesh sizing more finer to get an accurate result.

• Post-processing Result

1. Pressure and Velocity contour
2. Centerline plots
3. Radial plots

• Validation

1. Centerline Decay
2. Radial Decay

COMPUTATIONAL SET UP:

Computations are performed using ANSYS–Fluent and the meshing part is done by cut-cell structural mesh and K- omega SST Turbulence model is used. The cut-cell Cartesian approach makes handling complex and moving geometries much easier and accurate by cutting the cells rather than stretching and compressing the cells to fit.

DOMAIN SPECIFICATION:

• Inlet diameter of the nozzle(D') - 40mm
• Exit diameter of the nozzle (D) - 20mm
• Length of the nozzle(L) - 50mm
• The radius of the domain - 16D - 300mm
• The length of the domain - 60D - 1200mm

The primary jet is discharged through a straight pipe with a length of 50mm. The nozzle diameter D is 20mm.

The radius of the domain is set at 16D and the length is set at 60D. This can ensure enough space for the spreading of the jet and keeping the influence of the artificial boundaries to a minimum.

COMPUTATIONAL SET UP:

Computations are performed using ANSYS–Fluent and the meshing part is done by cut-cell structural mesh and K- omega SST Turbulence model is used. The cut-cell Cartesian approach makes handling complex and moving geometries much easier and accurate by cutting the cells rather than stretching and compressing the cells to fit.

BOUNDARY CONDITIONS:

General

• Type: Pressure based
• Time: Steady
• Models: K- omega SST Turbulence model
• Materials: fluid (Air)
• Boundary conditions: Inlet – pressure inlet

outlet – pressure outlet

wall – stationary

• Solution methods: SIMPLE SCHEME
• Solution Initialization: HYBRID

The inflow boundary is the gauge total pressure and the outflow boundary is set as gauge pressure. The no-slip boundary condition is defined at the nozzle wall.

COMPUTATIONAL MESH AND SOLVER:

The mesh for the computational domain is made with cut-cells, as the geometry is complex. The element size settings were used from the grid independency study, and the optimum grid was generated.

The pressure-based solver, chosen by with implicit and absolute velocity formulation. SIMPLE SCHEME algorithm is used for coupling the pressure and velocity terms. The first order upwind differencing scheme is used for the turbulence quantities in order to enhance the numerical accuracy of the computational results.

STRUCTURED MESH (CUT - CELL APPROACH)

Advantages of the cut cell approach

• The benefits of the cut-cell Cartesian approach is the fact that you have a body-fitted mesh.
• This ultimately means that your mesh fits perfectly with your geometry, reducing the number of inaccuracies that propagate through the rest of the domain.
• Because of this, the cut-cell Cartesian approach makes handling complex and moving geometries much easier and accurate by cutting the cells rather than stretching and compressing the cells to fit.

Independent resolution:

• Because this method cuts the volume cells at the wall, the mesh resolution is then independent of the geometry resolution.
• This can help speed up run-time calculations.

Lack of skewness:

• The mesh remains stationary and as the geometry moves the cells are cut and no compressing or stretching of the volume mesh occurs.
• This lack of skewness increases the accuracy of the results and makes it the preferred method when dealing with moving geometries.

Near-wall flow:

• The other benefit of the cut-cell Cartesian method is added cell refinement at the wall, as this will have a positive impact on accuracy.

STUDY OF AXIS SYMMETRY FLOW:

Structure and Development of a Free Jet

A free jet is a fluid mass that discharges into an infinitely large environment of ambient fluid. The flow structure in a free jet has been studied by many researchers and four distinct zones have been identified from these studies. As per studies, the development of a jet is divided into four zones, related to centerline velocity decay.

Zone 1: The convergent zone: This region is called the potential core of the jet, Where the centerline velocity is equal to the nozzle outlet velocity. This region normally extends up to 4d to 6d, where d is the diameter of the nozzle exit.

Zone 2: This transition zone: It is the region in which the centerline velocity starts to decay. The velocity decay can be approximated as proportional to x^-0.5, where x is the axial distance. This usually corresponds to a region from 6d to 20d, and it is known as the interaction region where shear layers from both sides merge.

Zone 3: The self-similar zone: In this region, transverse velocity profiles are similar at different values of x and the centerline velocity decay is approximately proportional to x^-1.

Zone 4: The termination zone: In this region, the centerline velocity decays rapidly. Although this zone has been studied by several researchers, the actual mechanisms in this zone are not understood properly.

VALIDATION OF GRID INDEPENDENCY TEST:

Mesh or Grid independent solution is a solution that does not vary significantly even when you refine your mesh further.

The trend of centerline velocity decay is done for different meshing cells of the same inlet at Mach 0.8, thus we conclude that 9.2 and 11.1 lakh mesh cells follow the same trend even after refining the mesh.

RESULTS AND DISCUSSION:

The results from the computations carried out on free jet are discussed below. The results are categorized according to Mach numbers, wherein each different graphs have been plotted. Centreline jet decay, the jet spread is plotted for Mach numbers 0.6, 0.8, and 1.0. The curves are drawn with height variation are compared.

CONTOURS:

Velocity magnitude contours for Axial jet decay

In the below contours, velocity along the axial flow direction of the jet is displayed for the free jet with height variation for Mach number 0.6, 0.8, and 1.0.

(a) At Mach Number 0.6

Fig. 1.1. Axial velocity magnitude contour for the free jet at Mach number 0.6

(b) At Mach Number 0.8

Fig. 1.2. Axial velocity magnitude contour for the free jet at Mach number 0.8

(c) At Mach Number 1

Fig. 1.3. Axial velocity magnitude contour for the free jet at Mach number 1

Velocity magnitude contours for Radial jet spread

In the below contours, velocity along the axial flow direction of the jet is displayed for the free jet with height variation for Mach number 0.6, 0.8, and 1.0.

(a) At Mach Number 0.6

Fig. 2.1. Radial velocity magnitude contour for the free jet at Mach number 0.6

(b) At Mach Number 0.8

Fig. 2.2. Radial velocity magnitude contour for the free jet at Mach number 0.8

(c) At Mach Number 1

Fig. 2.3 Radial velocity magnitude contour for the free jet at Mach number 1

VALIDATION:

i. AXIAL DECAY CHARACTERISTICS

The measured centreline Mach number distributions along the jet centreline were made non- dimensional with the nozzle exit Mach number. The axial distance X is non- dimensionalized with the nozzle exit diameter D.The centreline Mach number decay is a measure of jet propagation that is, the faster the decay, the faster the jet mixing with entrained fluid mass and so on.

From the plots, we see that the centreline Mach number initially remains constant and then continuously decreases as we move away from the nozzle exit. The length over which the centreline Mach number initially remains more or less constant is known as the core length.

• At Mach number =0.6

The centreline Mach number decay for M=0.6 fig: shows that the core length for the uncontrolled jet extends to about 5.67D.

Fig. 3.1. Nondimensional Mach no vs. nondimensional distance for centerline jet decay comparison at M=0.6.

• At Mach number=0.8

The centreline Mach number decay for M=0.8 fig: shows that the core length for the uncontrolled jet extends to about 6.13D.

Fig 3.2. Non-dimensional Mach no vs. non-dimensional distance for centerline jet decay comparison at M=0.8.

• At Mach number=1

The centreline Mach number decay for M=1 fig: shows that the core length for the uncontrolled jet extends to about 6.47D.

Fig 3.3. Non-dimensional Mach no vs. non-dimensional distance for centerline jet decay comparison at M=1.

ii. RADIAL DECAY CHARACTERISTICS

To gain an insight into the jet flow development without control, the Mach number profiles along the radial direction, for the uncontrolled jet, were taken at different axial locations, for all the Mach numbers of the present study.

• At Mach number = 0.6

Non-dimensionalized Mach number is measured at various axial distances for the exit Mach number Me = 0.6. The Mach number is measured at axial distances of Z/D = 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, and 10.

Fig 4.1. Non-dimensional Mach no vs. nondimensional distance for the jet spread of free jet in tabbed direction at M=0.6

• At Mach number = 0.8

Non-dimensionalized Mach number is measured at various axial distances for the exit Mach number Me = 0.8. The Mach number is measured at axial distances of Z/D = 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, and 10.

Fig 4.2. Nondimensional Mach no vs. nondimensional distance for the jet spread of free jet in tabbed direction at M=0.8.

• At Mach number = 1

Non-dimensionalized Mach number is measured at various axial distances for the exit Mach number Me =1. The Mach number is measured at axial distances of Z/D = 0.5, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 8, and 10.

Fig 4.3. Nondimensional Mach no vs. nondimensional distance for the jet spread of free jet in tabbed direction at M=1.