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ABSTRACT
Heat transfer coefficient measurements for jet impingement onto the concave surface of a cone with apex angles equal to 30° and 70° are reported in this study. Static pressure measurements along the cone surface are also reported which aid in explaining the results from the heat transfer measurements. The conical geometry finds application for the heating of aircraft gas turbine engine nose bullet region which could experience ice formation whenever aircraft operates at higher altitudes. The concave surface of the cone is heated by impinging hot air tapped from the compressor. The heat transfer coefficients, which are significantly different compared to flat surface impingement, and are scarcely available, are reported in this study. The influence of the jet axis coincident with the cone axis and impinging into apex region was studied first. The methodology where a thin stainless-steel foil is heated with a known heat flux by passing electric current through it and then measuring the detailed surface temperature using an infrared thermal camera, was used to compute the wall Nusselt distribution. The Nusselt number variation is presented as a function of nondimensional apex to nozzle spacing (L/D) and the nondimensional axis displacement (O/D). Three different diameter (D equal to 10 mm,14 mm and 20 mm) pipes were used for the concentric impingement case and the Nusselt number distribution was observed not depend on the injection diameter. The jet Reynolds number was varied between 25000 and 82000. The peak Nusselt number values are similar to those for flat plate impingement and do not occur at the cone apex, but at a nondimensional distance between 3.2 and 3.9 for 4.25 < L/D < 10.25 for the 30° cone. The peak Nusselt number values increase by almost 30% with decrease in the L/D from 10.2 to 3.0. Wall static pressure measurements indicated that the peak Nusselt number values occur in regions where the interaction between the incoming and outgoing streams is strongest – these regions occur at distances downstream from the stagnation region toward cone exit. The peak heat transfer coefficient location could not be obtained for the 70° cone, but the measured maximum values are higher by 30–50% compared to those for the 30° case. The jet is able to penetrate further toward the apex of the cone for 70° cone compared to 30° cone shifting the peak heat transfer locations closer to the apex for larger apex angle case. There is insignificant influence of jet diameter on Nusselt number variation for the three diameter values investigated in this study. The influence of displacing the jet axis by a distance equal to half the jet diameter in a direction perpendicular to the cone axis was also studied but detailed measurements were possible only for the 30° cone. Two semi-circular regions, one close to the impingement tube and the other away from the tube, displaying similar heat transfer coefficient behavior were observed. A peak in the Nusselt number occurs in each semi-circular region and the magnitude of the peaks are nearly same and they lie on either side of the peak location observed for the concentric impingement case when the flow geometric parameters are similar for the two cases. The measurements for the 70° cone exhibited all features of the 30° cone but the maximum values were higher by nearly 40% for this case.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Nomenclature
| Cp | = | Coefficient of pressure [(pw-pa)/(ptot-pa)] |
| D | = | Diameter of pipe (m) |
| dox, dix | = | Outer and inner diameter respectively of cone at any location X |
| DPT | = | Differential Pressure Transducer |
| G | = | Gravitation acceleration (9.8m/s2) |
| h | = | heat transfer coefficient (W/(m2K)) |
| hx | = | Heat transfer coefficient at a location x on the wall (W/(m2K))(see in eq.(3)) |
| I | = | Electrical current (A) |
| ka | = | Thermal conductivity of air(W/mK) |
| KSS | = | Thermal conductivity of stainless steel |
| L | = | Distance along cone axis between jet exit and the target surface (m) |
| L1 | = | Distance along cone axis between jet exit and cone exit (m) |
| m | = | Mass flow rate (kg/s) |
| Nu | = | Nusselt number (hxD/k) |
| NuMax | = | Maximum Nusselt Number |
| O | = | Offset of jet from the cone axis (m) |
| Pa | = | Ambient pressure (N/m2) |
| Pj | = | Static pressure at jet exit (N/m2) |
| Ptot | = | Total pressure at jet exit (Pj+ρVj2/2) |
| Pw | = | Static pressure at wall (N/m2) |
| qconx | = | Heat flux carried away by fluid at a given location x (W/m2) |
| qlossx | = | Heat flux loss to ambient at a given location x (W/m2) |
| qtotx | = | Heat flux input to the wall at a given location x (W/m2) |
| Re | = | Jet Reynolds number (ρaVjD/ μa) |
| SS | = | Stainless steel |
| Ta | = | Ambient air temperature (K) |
| Tj | = | Jet temperature (K) |
| Twox, Twix | = | Temperature of cone wall at dox and doi resp. at a given X(K) |
| T | = | Thickness of SS foil (m) |
| Vj | = | Jet Velocity (m/s) |
| X | = | Stream wise coordinate along cone slant length |
Greek symbols
| β | = | Electrical Resistivity (Ωm) |
| μa | = | Dynamic Viscosity of fluid (Ns/m2) |
| Ø | = | Apex angle of conical test section |
| ρa | = | Density of fluid (Kg/m3) |
| θ | = | Angle in the circumferential direction at any given location ‘X’ (See ) |