Heat Transfer Coefe Cient Research Articles

Experimental Frossling Numbers for Ice-Roughened NACA 0012 Airfoils

Experimental Frossling numbers are presented for two aluminum castings of ice-roughened NACA 0012 airfoil surfaces at 0-deg angle of attack for chord Reynolds number ranging from 4.00 £ £10 5 to 1.54£10 6 . The castings were meticulously obtained from actual ice accretions representing mildly rough glaze and rough glaze ice with horns. A modie ed investment casting technique wasused to capture all of the surface roughness details. The rough glaze ice with horns produced higher heat-transfer rates than those for the mildly rough glaze ice, especially at the horns. Immediately downstream of the horns, stagnation air gaps resulted and caused lower heat-transfer coefe cients. For both types of ice, higher Reynolds numbers in general produced higher heat-transfer coefe cients. For the samechord Reynoldsnumberand at thesameposition on the airfoil, theFrossling numbersweregenerally higher than those for the smooth case and those for the hemispherical roughness elements of previous studies. A maximumincreaseofapproximately306%overthesmoothcaseand192%overthedensehemisphericalroughness case was recorded at one rough glaze ice horn. This work provides some directly measured values of the Frossling number needed to improve the prediction of some icing codes. Such icing codes help in the effective design of some deicing systems of aircraft.

Thermal Performance of a Triple-Glazed Exhausting and Ventilating Airflow Window System

The thermal performance and optimum design of a triple-glazed exhausting and ventilating aire ow window system arestudied numerically using a e nitevolume method. Exhausting and ventilating aire ow rate, solarinsolation, and aspect ratio are identie ed as important governing parameters. Effort is directed toward the reduction in space cooling and heating load. It is found that both space-heat gain and space-heat loss are reduced considerably by increasing the exhausting and ventilating aire ow rate. The optimum aire owrate(Reynolds number) and aspect ratio are found to be about 600 and 0.05, respectively. Comparisons between the aire ow window system and the enclosed window system are madequalitatively and quantitatively. The aire ow window system with zero Reynolds number corresponds to the enclosed window case. The present aire ow window model can be used year round, as an exhausting aire ow type in summer and as a ventilating aire ow type in winter. Nomenclature A = area of glazing, m 2 C = heat capacity, kJ/m 3 ¢K Cp = specie c heat, kJ/kg ¢K c = clearance, m Gr = Grashof number g = gravitational acceleration, m/s 2 H = height of the window, m h = convective heat transfer coefe cient, W/m 2 ¢ ± C It = solar insolation per unit area, W/m 2 k = thermal conductivity, W/m ¢K

Heat (Mass) Transfer on Effusion Plate in Impingement/Effusion Cooling Systems

The local heat/masstransfercharacteristics on an innersurfaceoftheeffusion platein an impingement/effusion cooling system have been investigated. Two perforated plates are installed in parallel position to simulate the impingement/effusioncooling system.Theexperimentshavebeenconductedforthreedifferentholearrangements, staggered, square, and hexagonal, with various gap distances of 1, 2, 4, and 6 times the effusion hole diameter. The Reynolds number based on the effusion hole diameter is e xed at 1 £ £10 4 . A naphthalene sublimation method is used to determine the local heat/mass transfer coefe cients on the effusion plate. For all of the tested cases, high transfer regions are formed near the stagnation points and at the midline region of the adjacent impinging jets due to secondary vortices and e ow acceleration to the effusion holes. The heat/mass transfer coefe cient in the whole region increases with decreasing gap distance. The staggered hole arrangement shows the highest average heat transfer coefe cient due to the largest area ratio of the effusion to the injection hole; however, the heat/mass transferon theeffusionplateismoreuniform forthesquareand hexagonalholearrangementsbecausethenumber of injection holes is increased. Nomenclature Ae = total hole area of effusion plate Ai = total hole area of injection plate D = effusion hole diameter d = injection hole diameter H = gap distance between injection and effusion plates hm = local mass transfer coefe cient Knaph = mass diffusion coefe cient of naphthalene vapor in air ND = number of effusion holes Nd = number of injection holes Nu = Nusselt number based on effusion hole diameter P = pitch of array holes Pr = Prandtl number ReD = Reynolds number based on effusion hole diameter and the average velocity in the hole Red = Reynolds number based on injection hole diameter and the average velocity in the hole Sc = Schmidt number Sh = Sherwood number based on effusion hole diameter, Eq. (2) Sh = average Sherwood number x;z = distance from the center of a hole (Fig. 2)

Experimental Study of Evaporative Heat Transfer in Sintered Copper Bidispersed Wick Structures

An experiment has been carried out on evaporative heat transfer in rectangular bidispersed wick structures heatedbya groovedblock from thetop. Threebidispersedwick structures,havinglarge/smallpore-diameterratios of 200/80, 400/80, and 800/80 πm, were formed by sintering copper powder. For comparison, two monodispersed wick structures having pore diameters of 80 and 800 πm, respectively, were also tested. It was found that the heat transfer coefe cient and the critical heat e ux of a bidispersed wick are much higher than that of a monodispersed wick having its pore diameter equal to the smaller pore diameter of the bidispersed wick. It is also found that for bidispersed wicks with the same small-pore diameter there exists an optimal large-pore diameter that gives both the highest heat transfer coefe cient and the highest critical heat e ux. Finally, the effect of the adverse hydrostatic head on the heat transfer performance in the wick is shown. Nomenclature Ah = heating surface area, m 2 a = length of heating block, m h = heat transfer coefe cient, W/m 2 K K = permeability, m 2 P m = mass e ow rate, kg/m 2 s Q = heat power, W Tl = temperature of the subcooled liquid water, ± C Ts = saturation temperature, ± C Tv = temperature of the exhaust vapor, ± C TW = temperature of the heating block, ± C 1H = adverse hydrostatic head, mm = porosity Subscripts l = liquid s = saturation v = vapor w = wall

Optimization of Micro Heat Pipe Radiators in a Radiation Environment

Acombined numericaland experimentalinvestigation wasconducted to predict, measure,and optimize theheat transfer performance of a novel micro heat pipe radiator design that utilized an array of metal wires sandwiched between two thin sheets. The numerical model indicated that the maximum heat transport capacity for a single micro heat pipe increases proportionally to the square of the wire diameter, that the optimal charge volume decreased with increasing heat e ux, that the maximum heat transport capacity increases with increasesin thewire spacing, and that the overall maximum heat transport capacity of the radiator is strongly governed by the spacing of the wires, the length of the radiator, and the radiation capacity of the radiator surface. These numerical results are consistent with the experimental results, which indicated that the uniformity of the temperature distribution and the radiation efe ciency both increased with increasing wire diameter, resulting in a maximum heat transport capacity for radiators utilizing a wire diameter of 0.635 mm of 15.2 W. Additional experimental tests conducted on radiators utilizing wire diameters of 0.813 and 1.016 mm illustrated similar trends; however, for micro heat pipes with wire diameters largerthan 0.813 mm, the maximum heat transport capacity was not reached within the operating temperature of the acetone working e uid. Comparison of the proposed micro heat pipe radiators with solid conductors and uncharged versions indicated signie cant improvements in the temperature uniformity and overall radiation efe ciency. A maximum radiation efe ciency of 0.95 was observed. Nomenclature A = surface area of the radiator, m 2 Ac;l = liquid-phase cross-sectional area, m 2 Ac;v = vapor-phase cross-sectional area, m 2 Ar = surface area of the radiator, m 2 dw = wire diameter, m F = view factor g = gravitational acceleration, m/s 2 hc;o = heat transfer coefe cient outside of the condenser, J/m 2 K h fg = latent heat of vaporization, J/kg N

Heat Transfer Correlation for Anti-icing Systems

Nomenclature Aimp = total area of jet impingement a;b;c = constants C = constant Cp = specie c heat capacity of air Cx = distance between the holes d = hole diameter G = mass e ow per unit area of impingement h = heat transfer coefe cient N = average heat transfer coefe cient, q=Aimp.Tpiccolo i N Tlipskin) L = length of nozzle N = number of holes Nu = local Nusselt number Nu = average Nusselt number Pr = Prandtl number q = heat transfer from impinging air, w £Cp £.Tpiccolo i N Texhaust/£3600 Re = Reynolds number based on hole diameter, .w=Nholes/£.d=Aholeπ/ ReG = Reynolds number based on impingement area, 4Gd=oπ T = temperature N T = average temperature w = mass e ow rate Zn = perpendicular distance from hole to lipskin µ = jet impingement angle π = dynamic Viscosity

Effect of Film-Hole Shape on Turbine-Blade Heat-Transfer Coefficient Distribution

Detailed heat-transfer coefe cient distributions on the suction side of a gas turbine blade were measured using a transient liquid crystal image method. The blade has only one row of e lm holes near the gill-hole portion on the suction side of the blade. Studies on three different kinds of e lm-cooling hole shapes were presented. The hole geometriesstudied includestandard cylindricalholesand holeswith adiffuser-shaped exitportion (i.e., fan-shaped holes and laidback fan-shaped holes ). Tests were performed on a e ve-blade linear cascade in a low-speed wind tunnel. The mainstream Reynolds number based on the cascade exit velocity was 5 :3 ££ 10 5 . Upstream unsteady wakes were simulated using a spoke-wheel-type wake generator. The wake Strouhal number was kept at 0 and 0.1. The coolant-to-mainstream blowing ratio was varied from 0.4 to 1.2. The results show that unsteady wake generally tends to induce earlier boundary-layer transition and enhance the surface heat-transfer coefe cients. When compared to the cylindrical hole case, both the expanded hole injections have much lower heat-transfer coefe cients over the surface downstream of the injection location, particularly at high blowing ratios. However, the expanded hole injections induce earlier boundary-layer transition to turbulence and enhance heat-transfer coefe cients at the latter part of the blade suction surface.

Insights in Turbulence Modeling for Crossing-Shock-Wave/Boundary-Layer Interactions

The impact of turbulence modeling on the numerical simulation of the crossing-shock-wave/boundary-layer interactionsoccuringinaMach4e owon7 ££ 7deg,7 ££ 11deg,and15 £ 15degdouble-sharpe nplatesisanalyzed. The full Reynolds-averaged Navier ‐Stokes equations are solved with linear and weakly nonlinear formulations of the k‐! turbulence model, on grids up to 4 ££ 10 6 cells. The overpredicted heat transfer on the bottom plate is shown to be closely related to the main three-dimensional features developing in these e ows. The stronger the interaction, the more the numerical solutions violate the realizability principles. By introducing a dependence of cµ on the velocity gradients, realizable solutions are obtained and analyzed. The heat-transfer coefe cients are effectively lowered but not sufe ciently to meet the experimental data. The expected impact of other corrections, based on a limitation of the turbulent length scale or some compressibility effects, is evaluated and shown to be insufe cienttoe llthegapbetweencomputedandmeasuredheat-transfercoefe cients.Thestreamlinesarriving near the wall in the regions of overpredicted heat transfer are shown to originate from the very narrow regions close to the e n leading edges, in the upper part of the incoming boundary layer, and to be associated with an increase of turbulent kinetic energy when approaching the bottom wall, rather than when crossing the shock waves.

Solid-Fuel Ramjet Regulation by Means of an Air-Division Valve

An in-e ight regulation technique, which can provide an optimal operation of a solid-fuel ramjet (SFRJ) motor over a wide e ight envelope, has been analyzed. Regulation capability is essential for an efe cient use of the SFRJ propulsionforapplicationsinvolvingvariablee ightandoperatingconditions.Themethodisbasedonacontrollable air-division valve, which drivespart of the inlet airinto thesolid-fuel port, whiletherest of the aire ow ischanneled through a bypass to the aft-mixing section of the combustor. The model takes into account parameters ine uencing the burning rate of the solid fuel (e.g., port-e ow rate, port diameter ) and formulates a general regulation law in terms of the instantaneous opening state of the division valve fora constant fuel-to-air ratio operation. The control lawwascheckedforcertaincases,considering typicaltrajectories.Ithasdemonstrated agoodregulationcapability over a broad operational range (between sea level and 15-km altitude ). Nomenclature A = area d = diameter f = fuel-to-air ratio f (h) = function of altitude in the regulation law, Eq. (22) G = air mass e ux g(M) = function of Mach number in the regulation law, Eq. (23) H = inlet step height h = heat-transfer coefe cient; altitude L = fuel grain length M = Mach number m = temperature exponent C m = mass-e ow rate n = mass-e ow rate or mass e ux exponent C

Thermal Behavior of Porous Plates Subjected to Air Blowing

The cooling of porous plates by air blowing is studied experimentally. The ine uences of the air injection rate, of the hot main e ow temperature, and of the internal heat exchange surfaces of porous media are determined. The experiments show high efe ciency for this cooling process, about 97%. Because of the radiative heat transfer occuring withinthetestsection,a largeinjectionrate (about5%)isrequired toreachsuch an efe ciency.Thecritical injection rate is highlighted. Beyond that value the convective heat transfer does not exist any more because the boundary layer is blown off. Our heat transfer model of the porous plate and its vicinity (convective and radiative transfer)emphasizes important temperaturegaps between the solid phase and the e uid phaseoftheporousmedia. Fitting the model with the experimental data permits an estimate of the internal heat transfer coefe cients.

Analysis of Transient Conjugate Heat Transfer to a Free Impinging Jet

Transient conjugate heat transfer during the impingement of a freejet of high Prandtl number e uid on a solid disk of e nite thickness is considered. When power is turned on at t =0, a uniform heat e ux is imposed on the disk surface. The numerical model considers both solid and e uid regions. Equations for the conservation of mass, momentum,andenergy aresolvedintheliquidregion,withthetransportprocessesattheinletand exitboundaries, as well as at the solid ‐liquid and liquid ‐gas interfaces taken into account. In the solid region, only heat conduction equation is solved. The shape and location of the free surface (liquid‐gas interface ) is determined iteratively as a part of the solution process by satisfying the kinematic condition as well as the balance of normal and shear forces at this interface. Computed results include the velocity, temperature, and pressure distributions in the e uid and the local and average heat transfer coefe cients at the solid ‐e uid interface. Computations are carried out to investigate the ine uence of different operating parameters such as jet velocity, disk thickness, and disk material. Nomenclature b = thickness of the disk, m cp = specie c heat at constant pressure, kJ/kg ¢ K dn = diameter of the nozzle, m Fo = Fourier number, a ft/d 2 n g = acceleration due to gravity, m/s 2 Hn = distance of the nozzle from the disk, m h = heat transfer coefe cient, qint/(Tint i Tj), W/m 2 ¢ K hav = heat transfer coefe cient, W/m 2 ¢ K:

Heat Transfer Coefficient Measurement on Iced Airfoil in Small Icing Wind Tunnel

The local convective heat transfer coefe cient distribution is measured on an iced airfoil in a small closed-loop icing tunnel at the Centre d’ Essais des Propulseurs, the French engine test center. The airfoil surface is heated with a modulated laser source, and the heat e ux variation of the ice is recorded with an infrared camera. The method is validated on a cylinderin dry air and in icing conditions. Themethod isthen applied to a 145-mm-chord airfoil covered with typical rime, glaze, and mixed ice shapes. The effect of air velocity is studied by performing tests at airspeeds from 80 to 123 m/s (Reynolds numbers from 1 :25 ££ 10 6 to 1:9 ££ 10 6). It was found that the heat transfer coefe cient strongly depends on the surface condition of the ice. In relatively smooth zones, values are approximately equal to 400 W/m 2± C, whereas values greater than 1000 W/m 2± C are observed in nonuniform and rough areas. Results and limitations of the method are discussed and compared to numerical results obtained on similar ice shapes.

Investigations on Transient and Steady-State Performance of a Micro Heat Pipe

A numerical study is presented of the vapor and liquid e ow in a micro heat pipe with triangular channels, utilizing water as the working medium. The governing equations are derived taking into account the variation in the e ow cross-sectional areas of the vapor and liquid phases and incorporating the phase change during the process. The velocity, pressure, and temperature distributions in the vapor and liquid, in the transient and steady states, are obtained from the analysis. The effective thermal conductivity of the micro heat pipe is calculated, and its dependence on the heat input and the heat transfer coefe cient at the condenser section is investigated. The results of the analysis are compared with those available in literature and discussed in the light of the assumptions made and the extensions incorporated in the present model. Nomenclature Ac = area of cross section of the heat-pipe channel, m 2 Cl = specie c heat of the liquid, J/kg K Cv = specie c heat at constant volume of the vapor, J/kg K DH = hydraulic mean diameter of the channel, m d = one side of the triangular channel, m El = total energy of the liquid per unit volume, q l(ClT + 1 u 2 ), J/m 3 Ev = total energy of the vapor per unit volume, q v(CvT + 1 u 2), J/m 3 f = friction coefe cient h fg = latent heat of vaporization, J/kg h0 = heat transfer coefe cient at the condenser, W/m 2 K k

Anti-Icing System Simulation Using CANICE

A mathematical model of a hot air anti-icing system and its implementation in the ice accretion simulation code CANICEarepresented.Theicing codeisusedto predictthesurfacetemperatureandtheamount ofrunbackwater for given atmospheric conditions and heat e ux distribution from an anti-icing device. The external boundary layer is modeled with an integral method. Velocity and temperature distribution in the water e lm are estimated using a polynomial approximation. Conduction in the airfoil skin is taken into account with a one-dimension model. Numerical results are compared with experimental and numerical results from NASA for three different icing conditions. The comparison shows that surface temperatures are very sensitive to the water droplet impingement limits. The integral method used here failed to predict correctly the heat transfer coefe cients in the transition region of the boundary layer. When experimental heat transfer coefe cients are used, the model gives satisfactory results.

Evaluation of Stored Energy in Ultrafine Aluminum Powder Produced by Plasma Explosion

Ultrae ne aluminum powder produced by plasma explosion (ALEX) exhibits burn behavior unlike that of ordinary aluminum powders. Others have previously suggested that the source of this unique behavior might be stored internal energy. The objective of this study is to evaluate theoretically the feasibility of energy being stored in ALEX as a result of work performed by means of the compression of the liquid portion of an ALEX particle by its shrinking solid shell during rapid solidie cation of the particle. A theoretical model of this process of energy storage was developed. This model was then formulated and numerically solved on a computer for a variety of conditions. Results show that the postulated mechanism results in measurable stored energy for only unrealistically high cooling rates. It is concluded that, although the postulated mechanism could store energy, the amount of energy stored is realistically negligible. This theoretical e nding is in agreement with recent experiments that show no observable stored energy in ALEX particles. Nomenclature A = surface area, m 2 B = bulk modulus, N/m 2 Cp = specie c heat, J/kg ¢K D = diameter, m Est = thermal energy stored during solidie cation, J H f = latent heat of fusion, J/kg h = heat transfer coefe cient, W/m 2 ¢K k = thermal conductivity, W/m ¢K m = mass, kg N = surface node P = pressure, Pa r = radius,m T = temperature, K Ti = initial temperature, K V = volume, m 3 W = work, J ¯ = thermal coefe cient of expansion, 1/K 1t = time-step increment, s Ω = density, kg/m 3

Impingement Heat Transfer on a Target Plate with Film Cooling Holes

Detailedheat-transferdistributionsarepresentedforanarray ofjetsimpinging onatargetplatewithastaggered array of e lm cooling holes. The e ow impinges on the target plate through a row of impingement holes and exits the channel from the sides and through the e lm holes. The top plate has 12 rows of impingement holes, and the target platehas11 rows ofe lm holes. Theimpingementholes and the e lm holes have thesame diameterandarestaggered such that the air from the impingement hole does not exit directly through the e lm hole. The setup is typical of an impingement/transpiration cooled gas turbine airfoil. Additional to the e ow exiting through the e lm holes, there is an exit for crosse ow after impingement. The exit opening of the impingement channel is changed to provide three different spent air exit directions. The detailed heat-transfer coefe cient distributions were measured using a transient liquid crystal technique. Results are presented for a range of jet Reynolds numbers between 0.4 ££ 10 3 and 2.0 ££ 10 4 with different exit e ow orientations. Heat-transfer results for the target plate with e lm holes are compared with those without e lm holes under the same e ow conditions. Film extraction reduces crosse ow effects on jet impingement heat transfer. However, overall averaged heat-transfer rates on the target surface appear less affected by presence of e lm hole for cases where the crosse ow is generated in only one direction.

Nucleate Pool Boiling over Vertical Steps

Nucleate subcooled pool boiling of water over vertical steps was carried out under atmospheric conditions. Two forward-facing steps of 0.8125 and 0.50 in. were considered. Data were statistically analyzed to determine samplingerror.Theebullitionwasqualitativelyexplainedintermsofthermal/e owe eldsandbubbledynamics.Plots of boiling heat e ux vs superheat and surface heat transfer coefe cient vs heat e ux have been provided. Empirical correlations, developed from the above-mentioned data, are also presented. Boiling on vertically extended surfaces showed an increase in heat e ux for a given superheat when compared with a plain vertical surface because of e uid agitation in the region of the step. The parameters associated with bubble dynamics and bubble interactions were also qualitatively discussed. Nomenclature C = correlation constant h = surface heat transfer coefe cient, kW/m 2 K n = exponential constant q = ebullition heat e ux, kW/m 2 T = temperature, K Subscripts p = pool conditions w = wall conditions

Global Aeroheating Wind-Tunnel Measurements Using Improved Two-Color Phosphor Thermography Method

Detailed aeroheating information is critical to the successful design of a thermal protection system (TPS) for an aerospace vehicle. NASA Langley Research Center’ s (LaRC) phosphor thermography method is described. Development of theory is provided for a new weighted two-color relative-intensity e uorescence theory for quantitatively determining surface temperatures on hypersonic wind-tunnel models and an improved application of the one-dimensional conduction theory for use in determining global heating mappings. The phosphor methodology at LaRC is presented including descriptions of phosphor model fabrication, test facilities, and phosphor video acquisition systems. A discussion of the calibration procedures, data reduction, and data analysis is given. Estimates of the total uncertainties (with a 95% cone dence level ) associated with the phosphor technique are shown to be approximately 7 ‐10% in LaRC’ s 31-Inch Mach 10 Tunnel and 8 ‐10% in the 20-Inch Mach 6 Tunnel. A comparison with thin-e lm measurements using 5.08-cm-radius hemispheres shows the phosphor data to be within 7% of thin-e lm measurements and to agree even better with predictions via a LATCH computational e uid dynamics (CFD) solution. Good agreement between phosphor data and LAURA CFD computations on the forebody of a vertical takeoff/vertical lander cone guration at four angles of attack is also shown. In addition, a comparison is givenbetween Mach 6phosphordata andlaminarandturbulentsolutionsgeneratedusing theLAURA,GASP, and LATCH CFD codes on the X-34 cone guration. The phosphor process outlined is believed to provide the aerothermodynamic community with a valuable capability for rapidly obtaining (three to four weeks ) detailed heating information needed in TPS design. Nomenclature A = area of camera array element, m 2 a = effective aperture factor of camera optics, sr b = vehicle wing span from wing tip to wing tip, m C = heat transfer coefe cient constant, h.iw=Tw/ c = specie c heat of model substrate, J/ (kg-K) D = driver constant, iaw.Tw=iw/iTinit F = e ux of light, W/m 2 h = heat transfer coefe cient, kg/ (m 2 -s) I = radiant intensity, W/ (m 2 -sr)

Investigation of Heat Transfer and Coking Characteristics of Hydrocarbon Fuels

In this paper, worldwide investigations of the cooling characteristics of hydrocarbon fuels are reviewed and results of Chinese experimental investigations are presented. The Chinese tests were conducted at pressures of 0.5 ‐30 MPa, e ow velocities of 2 ‐106 m/s, and heat e uxes up to 66 MW/m 2 . The heat transfer characteristics of methane, propane, no. 21 high-density kerosene, aerokerosene and rocket kerosene in stainless-steel and copper tubes, and the deposit formation rates for kerosene in stainless-steel tubes were investigated. Forced convective heat transfer correlations were obtained for liquid methane, propane, and kerosene. Heat e uxes at which test tubes burnt out were also investigated. The test results indicate that heat transfer coefe cients of methane and propane decrease at high wall temperatures, and that the coefe cients of kerosene increase at similar conditions because of boiling. No coking was detected in methane tests; coking temperature and coking rates were determined for kerosene in stainless-steel tubes.

Condensation in Rotating Stepped Wall Heat Pipes with Hysteretic Annular Flow

Hysteresis effects of annular e ow in rotating stepped wall heat pipes are addressed based on visualization and systematic experiments. The region of hysteretic annular e ow is dee ned. Experimental data relating the condensation heat transfer for annular e ow in a rotating stepped wall heat pipe are presented. A model for predicting the condensation heat transfer coefe cient is proposed. The theoretical result is compared with experimental data. The effect of vapor shear drag on the condensation heat transfer is discussed.