Numerical and Experimental Investigation Of Mixing Enhancement Using A Stepped Cavity With A Three Lobbed Clover Nozzle

Numerical and Experimental Investigation Of Mixing Enhancement Using A Stepped Cavity With A Three Lobbed Clover Nozzle

Krishnaraja D.a and Z. A. Samithab

aM.Tech. student, Propulsion Engineering, College of Engineering Trivandrum, Thiruvananthapuram- 695016, India

bProfessor, Dept. of Mechanical Engineering, College of Engineering Trivandrum, Thiruvananthapuram

-695016,India

Abstract

Proper mixing between two high speed coaxial streams in a short mixing chamber is a necessity in hypersonic air breathing engines. To enhance mixing active and passive methods of mixing are employed together. The present study investigates a three lobbed clover nozzle with stepped cavity. Numerical investigations were carried out by varying the step ratio of the axisymmetric cavity. The mixing effectiveness of various configurations were analysed with the help of mixing parameters. The results indicate uniformity of mixing is better with clover nozzle with stepped cavity of step ratio 0.33. The experimental validation of the numerical analysis has been done.

1. Introduction

   In hypersonic air breathing engines, the short residence time of air in supersonic combustor, the efficient mixing between coaxial flows is a challenge. Hypersonic propulsion devices like Air Augmented Rocket (AAR) and Dual Combustor Ramjet (DCR) having advantages of high impulse and high. altitude flight proper mixing of supersonic coaxial flows plays an important role in efficiency. In an AAR configuration as in figure 1 the combustion products fuel rich mixture at supersonic speed, enters secondary combustor mixes with the atmospheric air induced through converging air intake.

   In a Dual Combustor Ramjet (DCR) as in fig 2, the air enters through a ramjet inlet and helps to burn fuel rich exhaust from primary in a secondary chamber. The mixing of supersonic flow in short residence time, the rate and uniformity of mixing has a major influence in the efficiency of combustion, heat release, size of combustion chamber and many other critical parameters.

   Figure 1 Air Augmented Vehicle

   Figure 2 Dual Combustor Ramjet

   Experimental studies showed that high speed jets shear mixing is retarded due to slow growth rate of shear layers as a result of compressibility [1]. Vorticity dynamics have a strong influence in mixing process. The stream wise vortices generated in a flow, in addition to the span wise (planar shear layer) or ring type ( in axisymmetric shear layers ) vortex rollup processes, have been found to mix fluid streams quickly and efficiently.

   Mixing enhancement is brought by the introduction of active and passive methods. Active methods include inducing turbulence, shock, swirls by components like cavities, struts ramps etc. The passive methods include changing initial condition of the jet by changing geometry.

   S.Jeyakumar and Balachandran.P [2] conducted an experimental study on mixing enhancement in supersonic streams with axisymmetric cavities. It is

   observed that wall mounted cavities enhance momentum mixing of two supersonic streams within a mixing tube at the cost of marginal stagnation pressure drop. Ben-Yakar and Hanson [3] investigated a high speed, high temperature flow over cavities to understand the fluid dynamics and flame holding characteristics. The shock wave structure around the cavity changes from compressive to expansive in nature as the ratio of length to depth of cavity increases from l/d = 3 to 7. For large values of l/d, the leading edge shock pattern gets diminished. Deepu et al [4] numerically studied that shock included vortex generation enhance mixing and reaction. They concluded that the shock reflections are responsible for blocking the development of jets and thereby creating the low velocity region. This increases the residence time of flow and hence increases mixing and reaction.

   Three lobbed clover nozzle is introduced to add passive mixing. Studies [5] proved that a clover nozzle, radially lobbed nozzle provides better pressure recovery compared to lobbed nozzle. The clover nozzle can enhance mixing at high speed jet at marginal stagnation pressure loss compared to circular. The effectiveness is also been experimentally proved [6, 7].

   Samitha et al. [8] experimentally and numerically studied the mixing performance of three lobbed clover with cavity configuration. Rectangular cavities with different l/d ratio, l/d =1 and l/d =1.66 are compared with conical nozzle with cavity in coaxial supersonic streams. Clover nozzle with L/D=4 and l/d=1.66 gave flat momentum flux distribution in the radial direction at the end of the mixing tubes.

   From the literature, the mixing tube with L/D=4 and l/d= 1.66 is chosen for the work as it gives better performance with DOM and PDF in earlier comparisons.

   In this study the effect of stepped cavity along with clover nozzle and circular nozzle in coaxial supersonic stream is analyzed by varying the step ratio of the stepped cavity.

   The numerical results obtained are all experimentally validated.

2. Computational Methodology

   Numerical analysis has been done using commercial CFD software ANSYS FLUENT. The grid generation and modelling is done using the pre-processor GAMBIT 2.4.6. The computational domain for numerical analysis is shown in fig 3.

   Figure 3 Schematic of circular nozzle configuration

   For circular nozzle, an axisymmetric model was used with structured grid system having quadrilateral cells as shown in fig 4. For Clover nozzle, the grid system consists of hexahedral cells as shown in fig 5. For primary nozzle, the pressure inlet boundary condition is 10bar, 300K imposed at primary inlet. For secondary nozzle, pressure inlet condition 2bar pressure and 300K is implied. Pressure outlet condition with atmospheric properties (1.01325bar and 300K) set at outlet. Analysis is done with k- turbulence model with coupled implicit solver. The literature cast that the 3 lobbed clover nozzle with an axisymmetric cavity of l/d

   = 1.66 has an optimized performance considering the

   DOM and PDF

   Figure 4 Grid system for cnical configuration

   Figure 5 Grid system for clover configuration

3. Grid Independence Study

   A grid sensitivity study has been conducted to arrive at an optimum grid for two dimensional and three dimensional numerical simulations. The grid independence study has been carried out in configuration with mixing tube L/D=4, axisymmetric

   cavity l/d= 1.66 table1. The results are found to be insensitive beyond 75470 cell for two dimensional

   5 3

   9 40

   * 9

   100

   1 * 1

   2 2

   conical nozzle and 172428 for the three dimensional clover cases.

   TABLE 1 Grid independence test

   Nozzle type	Number of cells	DOM
   Clover Nozzle	163230	0.8300
   	172428	0.8150
   	177464	0.8120
   	196400	0.8115
   Conical nozzle	53954	0.5632
   	68610	0.5520
   	75470	0.5468
   	79080	0.5421

4. Governing Equations

   Continuity equation

   .( U ) 0

   Momentum Equation

   .( UU) p .

   Energy Equation

   In addition to above equations, other relations are also used based on assumptions to simplify the problem.

   State equation for ideal gas.

   1. Calorically perfect gas- constant specific heat.

   2. Flow field is assumed to be steady, effect of gravity is neglected.

   3. Sutherland law for variation of viscosity with temperature.

5. Definitions of Mixing Parameters

   1. Momentum flux (µ)

      2

      The coaxial jet enters into the supersonic combustor with different momentum and stagnation pressures. The momentum flux distribution at the exit of the supersonic combustors in the radial direction is the measure of bulk mixing. Momentum flux is calculated as,

      .( Ue)

      .q .(U )

      ( pU )

      p 1 M

      where e is the total energy

      the viscous stress , ij 2 Sij *

      1

      ui

      the viscous strain rate , Sij *

      2 x j

      u j 1 uk

      ij

      xi 3 xk

      where p is the static pressure and M is the Mach number calculated from measured values of stagnation pressure. The momentum flux at which uniformity is attained indicates the axial distance where mixing is

      the heat flux , q j

      k T ,

      x j

      complete. In the Clover nozzle, momentum distribution was studied at major and minor planes.

   2. Degree of Mixing (DOM)

      Turbulence Transport Equations

      1. Kinematic eddy viscosity

         k

         T

      2. Turbulence Kinetic Energy

         To make a comparison between the mixing performance of clover and circular nozzle for different cavities based on a quantitative assessment of the level of mixing achieved, a dimensionless parameter called uniformity factor is defined as

         .( kU)

         .[(

         * T ) k]

         k

         U * k

      3. Specific Dissipation Rate 1 x

         .( U )

         .[(

         T ) ] U 2

         k k

         av x

      4. Closure coefficients

         where (x) is the standard deviation of the radial distribution of momentum flux at a given axial location

         in the mixing tube, av (x) is the average of momentum flux along radial line at the location considered. This factor is a measure of the uniformity of the momentum flux distribution in radial direction, at a given location. For perfectly mixed flow, the distribution has to be uniform. The uniformity factor is used to define a mixing parameter called Degree of Mixing (DOM).

   3. Pressure Drop Factor (PDF)

   Stagnation pressure loss indicates the measure of the efficiency of a process. The loss in stagnation pressure is characterized by defining a parameter called Pressure Drop Factor (PDF). In the case of Clover nozzle weighted averaged stagnation pressure is calculated along major and minor plane. The PDF is defined as the difference between the weighted average of stagnation pressure at the inlet and exit of the mixing tube, normalized by the weighted average of the mixing tube inlet stagnation pressure.

   Figure 6 Schematic of test setup

   6.2. Mixing tube

   Mixing tube made of mild steel shaft with axisymmetric stepped cavities inside it is designed. The aspect ratio of mixing tube is fixed as 4 (L/D=4) and

   where, P

   PDF 1

   P A P

   POE

   POI

   A

   the cavity with l/d=1.66. For the measurement of static pressure a static tap is provided with a diameter of 1mm since according to the usual standards the static

   OP P OS S

   tap should have dimensions in between 0.25mm and

   A

   A

   OI

   P S 2.5mm. A static tap of diameter 1mm is provided on

   Where POI and POE are the weighted average of total pressure at the supersonic combustor inlet and exit.

6. Experimental Setup