scholarly journals A Revised Equation for Heat Flux Reduction in Film Cooling Studies and Discussion of Its Applications

2011 ◽  
Author(s):  
Ting Wang ◽  
Lei Zhao
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Wall Temperature ◽  
Film Cooling ◽  
Surface Heat Flux ◽  
Experimental Studies ◽  
Flux Ratio ◽  
Surface Heat ◽  
Implicit Assumption ◽  
Film Cooling Effectiveness

In film cooling experimental studies, due to the difficulty in measuring the surface heat flux variation, a Heat Flux Ratio (HFR) equation originally derived by Mick and Mayle [1], has been widely employed to calculate the surface heat flux distribution using the measured adiabatic film effectiveness and surface temperature. A close examination of the derivation process and applications of the HFR equation reveals two issues of concern. First, an implicit assumption was introduced by letting the wall surface temperature of the system without-film be the same as that which would occur with a film-cooled condition. A revised equation is then derived by removing this implicit assumption and incorporating the wall temperature change due to film cooling Secondly, a uniform value of the non-dimensional metal temperature φ (or film cooling effectiveness) has been used in all the previous applications of the HFR equation. This practice implicitly implies that a uniform wall temperature is distributed throughout the entire surface under film cooling, which is usually not the case in real conditions. A series of computational experiments are conducted to verify the revised HFR equation under different conditions as well as examine the validity of using a constant surface temperature in the HFR equation. Results reveal that using a constant value of φ (0.5 ∼ 0.7) to calculate surface heat flux may result in a negative HFR in some simulated cases showing the commonly adopted value φ = 0.5∼0.7. This could induce errors and give false HFR. The error is reduced in 3D cases because the streamwise wall temperature becomes more uniform than 2D cases. The difference between the old and new equations can reach about 20%. A conjugate wall cooling simulation shows negative HFR is possible in the region close to the film hole due to the heat conduction from the downstream hotter region into the cooler region near the film hole. Using the actual wall temperature as the φ-value, the newly revised HFR equation produces the exact heat flux as calculated by CFD including the correct calculation of negative heat flux caused by the conjugate wall.

Laminar Natural Convection About Downward Facing Heated Blunt Bodies to Liquid Metals

1976 ◽  
Vol 98 (2) ◽  
pp. 208-212 ◽  
Author(s):  
G. M. Harpole ◽  
I. Catton
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Series Expansion ◽  
Surface Heat Flux ◽  
Liquid Metals ◽  
Surface Heat ◽  
Surface Shape ◽  
Boundary Layer Equations ◽  
Stagnation Points ◽  
Shape Dependence

The laminar boundary layer equations for free convection over bodies of arbitrary shape (i.e., a three-term series expansion) and with arbitrary surface heat flux or surface temperature are solved in local Cartesian coordinates. Both two-dimensional bodies (e.g., horizontal cylinders) and axisymmetric bodies (e.g., spheres) with finite radii of curvature at their stagnation points are considered. A Blasius series expansion is applied to convert from partial to ordinary differential equations. An additional transformation removes the surface shape dependence and the surface heat flux or surface temperature dependence of the equations. A second-order-correct, finite-difference method is used to solve the resulting equations. Tables of results for low Prandtl numbers are presented, from which local Nusselt numbers can be computed.

scholarly journals Seasonality of Decadal Sea Surface Temperature Anomalies in the Northwestern Pacific

2006 ◽  
Vol 19 (12) ◽  
pp. 2953-2968 ◽  
Author(s):  
Takashi Mochizuki ◽  
Hideji Kida
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Mixed Layer ◽  
Surface Heat Flux ◽  
Heat Budget ◽  
Surface Heat ◽  
Sea Surface ◽  
Northwestern Pacific ◽  
Sst Anomaly

Abstract The seasonality of the decadal sea surface temperature (SST) anomalies and the related physical processes in the northwestern Pacific were investigated using a three-dimensional bulk mixed layer model. In the Kuroshio–Oyashio Extension (KOE) region, the strongest decadal SST anomaly was observed during December–February, while that of the central North Pacific occurred during February–April. From an examination of the seasonal heat budget of the ocean mixed layer, it was revealed that the seasonal-scale enhancement of the decadal SST anomaly in the KOE region was controlled by horizontal Ekman temperature transport in early winter and by vertical entrainment in autumn. The temperature transport by the geostrophic current made only a slight contribution to the seasonal variation of the decadal SST anomaly, despite controlling the upper-ocean thermal conditions on decadal time scales through the slow Rossby wave adjustment to the wind stress curl. When averaging over the entire KOE region, the contribution from the net sea surface heat flux was also no longer significantly detected. By examining the horizontal distributions of the local thermal damping rate, however, it was concluded that the wintertime decadal SST anomaly in the eastern KOE region was rather damped by the net sea surface heat flux. It was due to the fact that the anomalous local thermal damping of the SST anomaly resulting from the vertical entrainment in autumn was considerably strong enough to suppress the anomalous local atmospheric thermal forcing that acted to enhance the decadal SST anomaly.

3D Heat Transfer Assessment of Full-Scale Inlet Vanes With Surface-Optimized Film Cooling: Part 1 — Experimental Results

2019 ◽  
Author(s):  
R. J. Anthony ◽  
J. P. Clark ◽  
J. Finnegan ◽  
J. J. Johnson
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
High Frequency ◽  
Film Cooling ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Full Scale ◽  
Pressure Side ◽  
Flux Measurements ◽  
Real Hardware

Abstract Full-scale annular experimental evaluation of two different high pressure turbine first stage vane cooling designs was carried out using high frequency surface heat-flux measurements in the Turbine Research Facility at the Air Force Research Laboratory. A baseline film cooling geometry was tested simultaneously with a genetically optimized vane aimed to improve efficiency and part life. Part 1 of this two-part paper describes the experimental instrumentation, test facility, and surface heat flux measurements used to evaluate both cooling schemes. Part 2 of this paper describes the result of companion conjugate heat transfer posttest predictions, and gives numerical background on the design and modelling of both film cooling geometries. Time-resolved surface heat flux data is captured at multiple airfoil span and chord locations for each cooling design. Area based assessment of surface flux data verifies the genetic optimization redistributes excessive cooling away from midspan areas to improve efficiency. Results further reveal key discrepancies between design intent and real hardware behavior. Elevated heat flux above intent in some areas led to investigation of backflow margin and unsteady hot gas ingestion at certain film holes. Analysis shows areas toward the vane inner and outer endwalls of the aft pressure side were more sensitive to reduced aft cavity backflow margin. In addition, temporal analysis shows film cooled heat flux having large high frequency fluctuations that can vary across nearly the full range of film cooling effectiveness at some locations. Velocity and acceleration of these large unsteady heat flux events moving near the endwall of the vane pressure side is reported for the first time. The temporal nature of the unsteady 3-D film cooling features are a large factor in determining average local heat flux levels. This study determined this effect to be particularly important in areas on real hardware along the HPT vane pressure side endwalls towards the trailing edge, where numerical assumptions are often challenged. Better understanding of the physics of the highly unsteady 3D film cooled flow features occurring in real hardware is necessary to accurately predict distress progression in localized areas, prevent unforeseen part failures, and enable improvements to turbine engine efficiency. The results of this two-part paper are relevant to engines in extended service today.

Film Cooling Effectiveness and Heat Transfer Near Deposit-Laden Film Holes

2009 ◽  
Author(s):  
Scott Lewis ◽  
Brett Barker ◽  
Jeffrey P. Bons ◽  
Weiguo Ai ◽  
Thomas H. Fletcher
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Film Cooling ◽  
Density Ratio ◽  
Flux Ratio ◽  
Deposition Pattern ◽  
Primary Flow ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
The Impact

Experiments were conducted to determine the impact of synfuel deposits on film cooling effectiveness and heat transfer. Scaled up models were made of synfuel deposits formed on film-cooled turbine blade coupons exposed to accelerated deposition. Three distinct deposition patterns were modeled: a large deposition pattern (max deposit peak ≅ 2 hole diameters) located exclusively upstream of the holes, a large deposition pattern (max deposit peak ≅ 1.25 hole diameters) extending downstream between the cooling holes, and a small deposition pattern (max deposit peak ≅ 0.75 hole diameter) also extending downstream between the cooling holes. The models featured cylindrical holes inclined at 30 degrees to the surface and aligned with the primary flow direction. The spacing of the holes were 3, 3.35, and 4.5 hole diameters respectively. Flat models with the same film cooling hole geometry and spacing were used for comparison. The models were tested using blowing ratios of 0.5–2 with a turbulent approach boundary layer and 0.5% freestream turbulence. The density ratio was approximately 1.1 and the primary flow Reynolds number at the film cooling row location was 300,000. An infrared camera was used to obtain the film cooling effectiveness from steady state tests and surface convective heat transfer coefficients using transient tests. The model with upstream deposition caused the primary flow to lift off the surface over the roughness peaks and allowed the coolant to stay attached to the model. Increasing the blowing ratio from 0.5 to 2 only expanded the region that the coolant could reach and improved the cooling effectiveness. Though the heat transfer coefficient also increased at high blowing ratios, the net heat flux ratio was still less than unity, indicating film cooling benefit. For the two models with deposition between the cooling holes, the free stream air was forced into the valleys in line with the coolant holes and degraded area-averaged coolant performance at lower blowing ratios. It is concluded that the film cooling effectiveness is highest when deposition is limited to upstream of the cooling holes. When accounting for the insulating effect of the deposits between the film holes, even the panels with deposits downstream of the film holes can yield a net decrease in heat flux for some cases.

Instantaneous Local Heat Flux Measurements in a Small Utility Engine

2009 ◽  
Author(s):  
Terry Hendricks ◽  
Jaal Ghandhi ◽  
John Brossman
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Numerical Model ◽  
Surface Temperature ◽  
Heat Transfer Rate ◽  
Surface Heat Flux ◽  
Transfer Rate ◽  
Surface Heat ◽  
High Load ◽  
Flux Measurements

Heat flux measurements were performed in an air-cooled utility engine using a fast-response coaxial-type surface thermocouple. The surface heat flux was calculated using both analytical and numerical models. The heat flux was found to be a strong function of engine load. The peak heat flux and initial heat flux rise rate increase with engine load. The measured heat flux data were used to estimate a global heat transfer rate, and this was compared with the heat transfer rate calculated by a single-zone heat release analysis. The measured values of heat transfer were higher than the calculated values largely because of the lack of spatial averaging. The high load data showed an unexplainable negative heat flux during the expansion stroke while the gas temperature was still high. A 1D and 2D finite difference numerical model utilizing an adaptive timestep Crank-Nicholson (CN) integration routine was developed to investigate the surface temperature measurement. Applying the measured surface temperature profile to the 1D model, the resultant surface heat flux showed excellent agreement with the analytical inversion solution and captured the reversal of the energy flow back into the cylinder during the expansion stroke. The 2D numerical model was developed to observe transient lateral conduction effects within the probe and incorporated the various materials used in the construction and assembly of the heat flux sensor. The resulting average heat flux profile for the test case is shown to be slightly higher in peak and longer in duration when compared with the results from the 1D analytical inversion, and this is attributed to contributions from the high thermal diffusivity constituents in the sensor. Furthermore, the negative heat flux at high load was not eliminated suggesting that factors other than lateral conduction may be affecting the measurement accuracy.

PHANTOM COOLING EFFECTS ON ROTOR BLADE SURFACE HEAT FLUX IN A TRANSONIC FULL SCALE 1+1/2 STAGE ROTATING TURBINE

2021 ◽  
pp. 1-13
Author(s):  
Richard J. Anthony ◽  
John Finnegan ◽  
John Clark
Keyword(s):  
Heat Flux ◽  
Air Force ◽  
Film Cooling ◽  
Surface Heat Flux ◽  
Rotor Blade ◽  
Surface Heat ◽  
Pressure Side ◽  
Blade Surface ◽  
Leakage Flows ◽  
Cooling Effects

Abstract An experimental and numerical investigation of phantom cooling effects on cooled and uncooled rotating high pressure turbine blades in a full scale 1+1/2 stage turbine test is carried out. Objectives set to capture, separate, and quantify the effects of upstream vane film-cooling and leakage flows on the downstream rotor blade surface heat flux. Multiple series of tests were carried out in the Air Force Research Laboratory, Turbine Research Facility, at Wright-Patterson Air Force Base, Ohio. A non-proprietary research turbine test article is uniquely instrumented with high frequency double-sided thin film heat flux gauges custom made at AFRL. High bandwidth, time resolved surface heat flux is measured on multiple film-cooled and non-film-cooled HPT rotor blades downstream of both film-cooled and non-film-cooled vane sectors. Upstream wake passing and heat flux is characterized on both rotor pressure and suction side surfaces, along with quantifying rotor phantom cooling effects from non-uniform 1st stage vane film cooling and leakage flows. Fast response heat flux measurements quantify how rotor phantom cooling impacts the blade pressure side greatest; increasing along the pressure side towards the trailing edge. It is discovered upstream vane film-cooling alone can account for 50% of the rotor blade cooling effect, and even outweigh the rotor blade film cooling effect far from the blade showerhead holes. Added unsteady numerical simulation demonstrates how variations in inlet total temperature and incidence angle can also contribute to circumferentially non-uniform rotor heat flux.

scholarly journals Surface Heterogeneity Effects on Regional-Scale Fluxes in Stable Boundary Layers: Surface Temperature Transitions

2009 ◽  
Vol 66 (2) ◽  
pp. 412-431 ◽  
Author(s):  
Rob Stoll ◽  
Fernando Porté-Agel
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Surface Temperature ◽  
Surface Heat Flux ◽  
Regional Scale ◽  
Potential Temperature ◽  
Surface Heterogeneity ◽  
Surface Heat ◽  
Average Surface ◽  
The Mean

Abstract Large-eddy simulation, with recently developed dynamic subgrid-scale models, is used to study the effect of heterogeneous surface temperature distributions on regional-scale turbulent fluxes in the stable boundary layer (SBL). Simulations are performed of a continuously turbulent SBL with surface heterogeneity added in the form of streamwise transitions in surface temperature. Temperature differences between patches of 6 and 3 K are explored with patch length scales ranging from one-half to twice the equivalent homogeneous boundary layer height. The surface temperature heterogeneity has important effects on the mean wind speed and potential temperature profiles as well as on the surface heat flux distribution. Increasing the difference between the patch temperatures results in decreased magnitude of the average surface heat flux, with a corresponding increase in the mean potential temperature in the boundary layer. The simulation results are also used to test existing models for average surface fluxes over heterogeneous terrain. The tested models fail to fully represent the average turbulent heat flux, with models that break the domain into homogeneous subareas grossly underestimating the heat flux magnitude over patches with relatively colder surface temperatures. Motivated by these results, a new parameterization based on local similarity theory is proposed. The new formulation is found to correct the bias over the cold patches, resulting in improved average surface heat flux calculations.

Effect of Subcooling and Nozzle Diameter on Heat Transfer Characteristics of Downward Facing Hot Surfaces Using Mist Jet

2018 ◽  
Author(s):  
Avadhesh Kumar Sharma ◽  
Monika Meena ◽  
Anirudh Soni ◽  
Santosh K. Sahu
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Stagnation Point ◽  
Surface Heat Flux ◽  
Jet Impingement ◽  
Surface Heat ◽  
Nozzle Diameter ◽  
Initial Surface ◽  
Ir Camera ◽  
Impingement Cooling

The jet impingement cooling is always preferred over the other cooling methods due to its high heat removal capability. However, rapid quenching may lead to the formation of cracks and poor ductility to the quenched surface. Mist jet impingement cooling offers an alternative method to uncontrolled rapid cooling, particularly in steel and electronic industries. In mist cooling, the droplets are atomized by compressed air. Experiments are performed under transient conditions using two full-cone spray nozzles (Lechler Pneumatic atomizing nozzle 136.115.xx.A2 and 136.134.xx.A2) to study the effect of subcooling and nozzle diameter on surface heat flux. The hot surface used for the experiment is a stainless steel foil (AISI-304) of thickness 0.15mm. The initial surface temperature of the plate is maintained at 500±10°C with the help of an AC transformer. Infrared thermal image camera (A655sc, FLIR System) is used for data estimation. The IR camera and the nozzle are positioned on either side of the plate. The variation in surface temperature has been acquired at 8 different spatial points. It has been observed that that as we move away from the stagnation point then irrespective of air and water flow rates surface heat flux decreases. The maximum surface heat flux obtained at the stagnation point. With the increase in diameter surface heat flux increases irrespective of pressure values. The correlation between qm/qstag experimental and predicted values has been shown.

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