^{1}

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In this paper, an extensive numerical study on pressure characteristics in the configuration of sudden expansion with central restriction and suction has been carried out. During study, Reynolds numbers (Re) are considered from 50 to 200, suction (S) from 2% to 10% of inlet mass flow, percentage of central restriction (CR) from 0% to 40% and aspect ratio (AR) from 2 to 6. The effects of each variable on average static pressure distribution and average stagnation pressure distribution have been studied in detail. The results have been compared with the configuration of plain sudden expansion, and sudden expansion with central restriction only. From the study, it is noted that maximum magnitude of average static pressure rise from throat increases with the increase in percentage of suction, flow Reynolds number and percentage of central restriction. This magnitude is higher at lower aspect ratio. Also, it is observed that maximum magnitude of average static pressure rise from throat is always more in case of suction configuration compared to the case of configuration of without suction. Average stagnation pressure drop at any section increases with the increase in percentage of suction and percentage of central restriction, but it decreases with the increase in Reynolds number. It is noted that higher pressure drop at any section occurs at higher aspect ratio. This pressure drop at a section is more in case of suction configuration compared to the case of without suction.

In plain sudden expansion configuration, the fluid is required to flow through a passage of sudden increasing cross-sectional area; this results in a recovery of static pressure. Because, significant amount of energy is transferred from the main flow irreversibly to the recirculating eddies. However, since the flow is subjected to adverse pressure gradient, the flow separates from the walls resulting in substantial loss of stagnation pressure. As stagnation pressure is a matter of utmost significance in assessing the performance of various components and the cycle of a gas turbine based power plant, such losses in stagnation pressure in sudden expansion geometry may drop the overall plant efficiency. In this paper, study on pressure characteristics of fluid passing through sudden expansion configuration has been carried out by incorporating central restriction in the inlet zone and suction at the top corner on side wall. The most remarkable feature of this study is that it clearly shows the advantages of sudden expansion with central restriction and suction over the plain sudden expansion configuration or sudden expansion with central restriction only as far as the maximum magnitude of the static pressure rise is concerned.

From a brief review of literature, it appears that the first work in the field of plain sudden expansion configuration has been carried out by Macagno and Hung [

Sheen et al. [^{5}. For 10 deg inlet swirl, they have observed that AR = 1.91 diffuser gives highest performance. Taamallah et al. [

As per brief review of literature, it is noted that a number of researchers have studied the flow characteristics of fluid passing through plain sudden expansion configuration. But, the numerical or experimental study on plain sudden expansion configuration with some modifications is very few [

Schematic diagrams of the computational domain for flow through plain sudden expansion, sudden expansion with central restriction only, and sudden expansion with central restriction and suction are illustrated in

The following dimensionless variables are defined to obtain the governing conservation equations in the non- dimensional form;

Lengths:

Velocities:

Pressure:

With the help of these variables, the non-dimensional mass and momentum conservation equations are written as follows:

where, the flow Reynolds number,

Four different types of boundary conditions are applied to the present problem. They are as follows:

1) At the walls: No slip condition is used, i.e.,

2) At the inlet: Axial velocity is specified and the transverse velocity is set to zero, i.e.,

3) At the exit: Fully developed condition is assumed and hence gradients are set to zero, i.e.,

4) At the line of symmetry: The normal gradient of the axial velocity and the transverse velocity are set to zero, i.e.,

The partial differentials Equations (1), (2) and (3) are discretised by a control volume based finite difference method. Power law scheme is used to discretise the convective terms (Patankar, [^{−8}.

In the computation, flow is assumed fully developed at the inlet and exit. Therefore, exit is chosen far away from the throat. The distribution of grid nodes is non-uniform and staggered in both coordinate direction allowing higher grid node concentrations in the region close to the step and walls. During computations, the non-di- mensional inlet (_{max}. Finally in our work we have considered the meshes comprising of 41 × 37 grid nodes in the inlet section and 221 × 121 grid nodes in the exit section in the x- and y-directions, respectively. For higher aspect ratio like AR = 4, 5 and 6, the grid sensitivity study has been performed considering typical aspect ratio of 5, Reynolds number of 100% and 20% central restriction. For these aspect ratios, the non-dimensional inlet and the exit lengths are considered as 1 and 200 respectively. The meshes comprising of 41 × 37 grid nodes in the inlet section and 457 × 193 grid for the exit section in the x- and y-directions, respectively are used. This study_{ }has been discussed in detail by Das and Chakrabarti [

Sheen et al. [

Battaglia and Papadopoulos [

The important results of the present study are reported in this section. The parameters those affect the flow characteristics are identified as,

AR | Present Study | Battaglia and Papadopoulos [ | Percentage Deviation |
---|---|---|---|

1.61 | 1.8294 | 1.655 | 9.53 |

2 | 4.5248 | 4.316 | 4.61 |

AR | Present Study | Battaglia and Papadopoulos [ | Percentage Deviation |
---|---|---|---|

1.61 | 1.1362 | 1.028 | 9.52 |

2 | 2.262 | 2.154 | 4.77 |

a) Reynolds number, 50 ≤ Re ≤ 200,

b) Central restriction, CR = 0 to 40%,

c) Suction, S = 2% to 10% of inlet mass flow,

d) Aspect ratio, AR = 2 to 6.

A sudden expansion configuration creates a separation of the boundary layer from the wall which results positive and negative pressure zone at the post throat region. This post throat region greatly influence the static pressure which is considered an important parameter in assessing the performance of various components of gas turbine engine such as diffuser, combustor etc. In the present work, the average static pressure at any cross section is determined by the following expression:

The average static pressure distribution curves along the axial distance for sudden expansion with 40% central restriction with 0% (i.e. without suction), 2%, 4%, 6%, 8% and 10% suction are shown in

Reynolds number and aspect ratio, the magnitude of average static pressure rise at a section is more in case of sudden expansion with central restriction and suction configuration compared to the case of configuration of sudden expansion with central restriction only. The probable reason may be that, when suction is considered the recirculating bubble size decreases. Because of that, the effect of diffusion should decrease. But, suction at the top of the vertical wall decreases the outer layer of corner recirculation zone which are the main cause of dominating frictional effect with the wall. This combined effect increases the magnitude of average static pressure at any section. The effect of central restriction on average static pressure distribution along the axial distance for sudden expansion with different percentages of central restrictions and 10% suction and without suction configurations is illustrated in

When sudden expansion with central restriction with and without suction configurations are compared, maximum magnitude of average static pressure rise from throat is always more in case of suction configuration compared to without suction one for a fixed value of Reynolds number. The effect of aspect ratio on average static pressure distribution with axial distance for sudden expansion with typically 40% central restriction and sudden expansion with typically 40% central restriction for 10% suction is presented in

Therefore, from the study, it may be mentioned that sudden expansion with central restriction and suction configuration will give more benefit in terms of the maximum magnitude of average static pressure rise from throat compared to the sudden expansion with central restriction configuration only or configuration of plain sudden expansion.

Stagnation pressure is one of the important parameter to determine the performance of the various components of a gas turbine cycle as well as the cycle itself. The computation of average stagnation pressure at any section should take into considerations of the direction of the velocity vector particularly in a flow situation, like the present case where the flow is the recirculating type. After performing the energy balance, Chakrabarti et al. [

The suffix “e” represents the plane of measurement. Stagnation pressure is constant in a stream flowing without heat or work transfer only if friction is absent, i.e., the stagnation pressure drop can be used as a measure of fluid friction. In the present problem the stagnation pressure at any location is computed using the dimensionless form of the above equation. It is obvious that according to the present definition, average stagnation pressure, should always drop along the axial length.

The average stagnation pressure distribution along the axis has been described in

fixed value of Reynolds number, the average stagnation pressure drop at any section increases with increase in percentage of central restriction for both the configurations. This is happening because, with increase in percentage of central restriction, the viscous dissipative effect dominates the effect of kinetic energy diffusion, this leads to increase in average stagnation pressure drop at a section. It is also noted that, at a particular value of Reynolds number and central restriction, more stagnation pressure drop occurs at a section in case of suction configuration compared to without suction configuration. The reason is explained earlier in this subsection. The effect of Reynolds number on average stagnation pressure distribution along the axis for sudden expansion with typically 40% central restriction only and sudden expansion with typically 40% central restriction and 10% suction has been investigated and illustrated in

The general characteristics of all the curves of both the considered configurations (i.e., with and without suction) are same in nature, i.e., average stagnation pressure drop at a section decreases with increase in Reynolds number. This can be reasoned as, for higher Reynolds number flow, the kinetic energy contribution towards the working fluid at a section will be higher leading to the possibility of higher average stagnation pressure at that section. Form the figure, it is also found that for all the considered Reynolds number, the average stagnation pressure drop at a section is more in case of sudden expansion with central restriction and suction configuration compared to the case of sudden expansion with central restriction only, like earlier observation. The reason is explained earlier. The variation of average stagnation pressure distribution along the axial distance for different aspect ratio of 2, 4 and 6 for sudden expansion with 40% central restriction and sudden expansion with 40% central restriction and 10% suction is shown in

In many flow situations, fluid is decelerated to ensure an increase in the static pressure and to get the recirculating bubbles for the mixing of two or several fluids as a mixing chamber in the decelerated zone. Among its many applications, particular mention may be made of the function as a diffuser, or mixing chamber and combustor. In this research activity, the effects of percentage of suction, percentage of central restriction, Reynolds number and aspect ratio on average static pressure distribution and average stagnation pressure distribution have been investigated for the configuration of sudden expansion with central restriction and suction configuration. This leads to the following important observations:

1) Maximum magnitude of average static pressure rise from throat increases with the increase in percentage of suction. This maximum magnitude also increases with the increase in Reynolds number and percentage of central restriction. The maximum magnitude of average static pressure rise from throat is less for higher aspect ratio. Again, this magnitude is always more in case of sudden expansion with central restriction and suction configuration compared to the case of without suction configuration.

2) Average stagnation pressure drop at any section increases with the increase in percentage of suction and percentage of central restriction, but it decreases with the increase in Reynolds number. The average stagnation pressure drop at a section increases with the increase in aspect ratio. When suction is considered, average stagnation pressure drop at a section increases in case of suction configuration compared to the case of without suction.

TridibeshDas,SomnathChakrabarti, (2016) Pressure Characteristics Study for the Configuration of Sudden Expansion with Central Restriction and Suction. Open Journal of Fluid Dynamics,06,30-41. doi: 10.4236/ojfd.2016.61003

L_{i}: Inlet length (i.e., length between inlet and throat sections), m

L_{ex}: Exit length (i.e., length between throat and exit sections), m

L_{R}: Reattachment length, m

p: Static pressure, [N/m^{2}]

Re: Reynolds Number

u: Velocity in x-direction, m∙s^{−}^{1}

v: Velocity in y-direction, m∙s^{−1}

U: Average velocity, m∙s^{−1}

W: Width of central restriction, m

W_{s}: Width of suction slot, m

W_{1}: Width of inlet duct, m

W_{2}: Width of exit duct, m

AR: Aspect ratio = W_{2}/W_{1}

CR: Percentage of central restriction = W/W_{1}

x, y: Cartesian co-ordinates

ρ: Density, kg∙m^{−3}

μ: Dynamic viscosity, kg∙m^{−1}∙s^{−1}

*: Dimensionless terms

1-1: Inlet

2-2: Exit