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ABSTRACT
In this paper, flow and heat transfer of a swirl chamber that models an internal cooling passage for a gas turbine airfoil leading edge is studied with numerical simulation. The geometry consists of a circular pipe, and rectangular section inlets that lead inlet flow to impinge tangentially on the circular pipe. The effects of the ratio of jet spacing to swirl chamber radius and Reynolds numbers on swirl cooling performance are investigated. The results indicate how the pressure loss and globally averaged Nusselt number on the swirl chamber wall increase with increases of Reynolds number and the ratio of jet spacing to swirl chamber radius. A Nusselt number correlation on these parameters is suggested. Also shown is how Nusselt numbers on the swirl chamber surface increase with the ratio of jet spacing to swirl chamber radius.
NOMENCLATURE
| A | = | area [m2], = πR2 |
| b | = | width of the coolant inlet duct [m] |
| C | = | jet spacing [m] |
| D | = | diameter [m] |
| d | = | height of the coolant inlet duct [m] |
| f | = | friction coefficient |
| f∞ | = | friction coefficient for fully developed, turbulent, nonswirling pipe flow |
| Gx | = | axial flux of linear momentum [kg/s2] |
| Gθ | = | axial flux of angular momentum [kg/s2] |
| h | = | heat transfer coefficient [W/(m2·K)], = qw/(Tj − Tw) |
| j | = | thermal performance factor |
| L | = | length (span) of swirl chamber [m] |
| L1 | = | length of inlet duct [m] |
| L2 | = | length from the outlet to the axis of the chamber [m] |
| L | = | length of swirl chamber (axially or circumferentially) [m] |
| li | = | circumferential length of the node (i) [m] |
| lj | = | axial length of the node (j) [m] |
| NuD | = | Nusselt number based on chamber diameter, = hD/ λ |
| Nuax | = | axial length-weighted average NuD, |
| Nucir | = | circumferential length-weighted average NuD, |
| Nug | = | global area-weighted average NuD, |
| Nu∞ | = | Nusselt number for fully developed, turbulent, nonswirling pipe flow |
| P | = | static pressure [Pa] |
| Pse | = | average static pressure at outlet [Pa] |
| Ptj | = | total pressure at inlet [Pa] |
| ΔP | = | pressure drop [Pa] |
| qw | = | wall heat flux [W/m2] |
| R | = | inner radius of the swirl chamber [m], = D/2 |
| r | = | distance from the vortex center to any position in the swirl chamber [m] |
| Re | = | Reynolds number based on mean axial velocity and swirl chamber diameter, = UD/ν |
| S | = | local swirl number |
| Tj | = | inlet coolant temperature [K] |
| Tw | = | swirl chamber wall temperature [K] |
| U | = | mean axial velocity [m/s] |
| U | = | axial component of a local helical velocity in the swirl chamber [m/s] |
| uτ | = | shear velocity [m/s] |
| V | = | velocity magnitude [m/s] |
| V | = | tangential component of a local helical velocity in the swirl chamber [m/s] |
| X | = | spanwise coordinate, swirl chamber axial direction [m] |
| Y | = | wall-normal coordinate [m] |
| y+ | = | nondimensional distance, = Yuτ/ν |
| β | = | angle in the swirl chamber [rad] |
| μ | = | dynamic viscosity of fluid [kg/m·s] |
| ν | = | kinematic viscosity [m2/s] |
| λ | = | thermal conductivity of fluid [W/m·K] |
NOMENCLATURE
| A | = | area [m2], = πR2 |
| b | = | width of the coolant inlet duct [m] |
| C | = | jet spacing [m] |
| D | = | diameter [m] |
| d | = | height of the coolant inlet duct [m] |
| f | = | friction coefficient |
| f∞ | = | friction coefficient for fully developed, turbulent, nonswirling pipe flow |
| Gx | = | axial flux of linear momentum [kg/s2] |
| Gθ | = | axial flux of angular momentum [kg/s2] |
| h | = | heat transfer coefficient [W/(m2·K)], = qw/(Tj − Tw) |
| j | = | thermal performance factor |
| L | = | length (span) of swirl chamber [m] |
| L1 | = | length of inlet duct [m] |
| L2 | = | length from the outlet to the axis of the chamber [m] |
| L | = | length of swirl chamber (axially or circumferentially) [m] |
| li | = | circumferential length of the node (i) [m] |
| lj | = | axial length of the node (j) [m] |
| NuD | = | Nusselt number based on chamber diameter, = hD/ λ |
| Nuax | = | axial length-weighted average NuD, |
| Nucir | = | circumferential length-weighted average NuD, |
| Nug | = | global area-weighted average NuD, |
| Nu∞ | = | Nusselt number for fully developed, turbulent, nonswirling pipe flow |
| P | = | static pressure [Pa] |
| Pse | = | average static pressure at outlet [Pa] |
| Ptj | = | total pressure at inlet [Pa] |
| ΔP | = | pressure drop [Pa] |
| qw | = | wall heat flux [W/m2] |
| R | = | inner radius of the swirl chamber [m], = D/2 |
| r | = | distance from the vortex center to any position in the swirl chamber [m] |
| Re | = | Reynolds number based on mean axial velocity and swirl chamber diameter, = UD/ν |
| S | = | local swirl number |
| Tj | = | inlet coolant temperature [K] |
| Tw | = | swirl chamber wall temperature [K] |
| U | = | mean axial velocity [m/s] |
| U | = | axial component of a local helical velocity in the swirl chamber [m/s] |
| uτ | = | shear velocity [m/s] |
| V | = | velocity magnitude [m/s] |
| V | = | tangential component of a local helical velocity in the swirl chamber [m/s] |
| X | = | spanwise coordinate, swirl chamber axial direction [m] |
| Y | = | wall-normal coordinate [m] |
| y+ | = | nondimensional distance, = Yuτ/ν |
| β | = | angle in the swirl chamber [rad] |
| μ | = | dynamic viscosity of fluid [kg/m·s] |
| ν | = | kinematic viscosity [m2/s] |
| λ | = | thermal conductivity of fluid [W/m·K] |