Heat-mass Transfer Analogy Research Articles

Measured Film Cooling Effectiveness of Three Multihole Patterns

As an advanced cooling scheme to meet increasingly stringent combustor cooling requirements, multihole film cooling has received considerable attention. Experimental data of this cooling scheme are limited in the open literature in terms of different hole patterns and blowing ratios. The heat-mass transfer analogy method was employed to measure adiabatic film cooling effectiveness of three multihole patterns. Three hole patterns differed in streamwise row spacing (S), spanwise hole pitch (P), and hole inclination angle (α), with the first pattern S∕P=2 and α=30°, the second S∕P=1 and α=30°, and the third S∕P=2 and α=150°. Measurements were performed at different blow ratios (M=1-4). Streamwise coolant injection offers high cooling protection for downstream rows. Reverse coolant injection provides superior cooling protection for initial rows. The effect of blowing ratio on cooling effectiveness is small for streamwise injection but significant for reversion injection.

Performance investigation of plain circular and oval tube evaporatively cooled heat exchangers

The performance of two evaporatively cooled heat exchangers is analysed, one has plain circular tubes while the other one has plain oval tubes. Both are investigated under similar operating conditions in relation to airflow rates and inlet hot water temperatures. The circular tube is 10 mm o.d., and the oval tube (axes ratio 3.085) is formed from an 18 mm o.d. circular tube whose perimeter is preserved after forming. It is concluded that the average mass transfer Colburn factor ( j m) for the oval tube is 89% of that for the circular tube, while the average friction factor ( f) for the oval tube is 46% of that for the circular tube. The ratio ( j m/ f) for the oval tube is 1.93–1.96 times that for the circular tube. This means that the oval tube has a better combined thermal–hydraulic performance. The heat-mass transfer analogy showed lower values for the mass transfer coefficient estimated from dry heat transfer correlations when compared with wet measurements.

Adequacy of the Heat-Mass Transfer Analogy to Simulate Containment Atmospheric Cooling in the New Generation of Advanced Nuclear Reactors: Experimental Confirmation

Driving forces of passive cooling systems of advanced reactor containments are substantially weaker than those brought in by active systems of operating power plants. This fact along with the new geometries being used suggest the need either to develop new reliable simulation techniques or to adapt and validate traditional approaches. Suitability of the heat-mass transfer analogy for this purpose is investigated based on previous authors’ experience. Major analogy drawbacks are identified and overcome by supplementing it with analytically derived factors. By comparing against experimental data available, the heat-mass transfer analogy is demonstrated to be a sound, configuration-independent, and accurate-enough theoretical approximation.

Fouling in enhanced tubes using cooling tower water: Part II: combined particulate and precipitation fouling

This work addresses fouling in a family of seven internally helically ridged tubes, which have different ridge heights, helix angles, and a number of ridge starts. Of specific interest are long term, combined precipitation and particulate fouling (P&PF) in cooling tower systems, and accelerated particulate fouling. The comparison of the P&PF and accelerated particulate fouling data shows a unique relationship. This allows one to infer the relative long-term P&PF performance of different enhanced tube geometries from accelerated particulate fouling data. For a small number of ridge starts (less than 25) and helix angles below 35°, the fouling resistance is proportional to the heat transfer coefficient (or the mass transfer coefficient, via the heat–mass transfer analogy). However, for a large number of starts and high helix angles (e.g., 45°), the fouling factor is considerably higher than one would predict, based on the mass transfer coefficient. It appears that this occurs because of low shear stress (affecting the foulant removal rate) in the interfin region. Recommendations are offered on geometries that will avoid high fouling penalty.

Film Cooling on a Gas Turbine Rotor Blade

The film cooling effectiveness on a low-speed stationary cascade and the rotating blade has been measured by using a heat-mass transfer analogy. The film cooling effectiveness on the suction surface of the rotating blade fits well with that on the stationary blade, but a low level of effectiveness appears on the pressure surface of the rotating blade. In this paper, typical film cooling data will be presented and film cooling on a rotating blade is discussed.

Similarity analysis of model experiments for film cooling in gas turbines

This report investigates our present ability to predict the thermal performance of film cooling arrangements used to protect the hot components of gas turbines. The required information is usually obtained by model experiments carried out at near room temperature as opposed to the high temperature encountered in the gas turbines. Dimensional or similarity analysis is used to develope the functional relationships for film effectiveness and convective heat transfer and the use of mass transfer experiments with foreign gas injection and naphthalene sublimation based on the heat-mass transfer analogy is discussed. The law of superposition is used to describe the combined effects of film cooling, surface convection or radiation and frictional heating. An order of magnitude estimate indicates to what extent local temperature gradients are alleviated in the cooled walls by internal heat conduction.

On the rate balance between impingement water evaporation and heat transfer

An experimental investigation of impingement water evaporation under single and multiple air jets was made. Similar studies of impingement heat transfer from solid surfaces were also carried out; the heat transfer areas were nearly the same as those for evaporation. It is established that evaporative fluxes can be calculated from the rate balance between evaporation and heat transfer via heat-mass transfer analogy.

The Effect of Density Ratio on the Heat Transfer Coefficient From a Film-Cooled Flat Plate

The effect of density ratio of cooling films on the heat transfer coefficient on a flat plate is investigated using a heat-mass transfer analogy. The experimental technique employed uses a swollen polymer surface and laser holographic interferometry. A density ratio of 1.0 was achieved using air as the injectant. Density ratios of 1.38 and 1.52, representative of turbine operating conditions, were obtained by using foreign gases. The coolant fluids were injected at various blowing rates through a single normal hole or through a row of holes spaced at three-diameter intervals, and inclined at 35 or 95 deg to the mainstream direction. The experiments were conducted under isothermal conditions in a subsonic, zero mainstream pressure gradient turbulent boundary layer. The results indicated large differences in behavior between the two injection angles. For normal injection, the heat transfer coefficient at a fixed blowing parameter was insensitive to the variation of density ratio, whereas for 35 deg injection strong dependence was observed. Scaling parameters for the heat transfer data have been proposed so that use can be made of data obtained at density ratios not representative of gas turbine practice. In addition, a correlation for normal injection data has been formulated.

High-Rayleigh-number convection in a horizontal enclosure

A review of the literature on natural convection in a horizontal layer heated from below shows the need for reliable data at high Rayleigh number (Ra) to determine the asymptotic Nusselt number (Nu) variation with Rayleigh number. The present study expands the data base by the use of an electrochemical mass transfer technique to determine the asymptotic dependence of the Sherwood number (Sh) on Ra at high Schmidt number (Sc). The results of the present study give Sh = 0.0659 for Sc ≈ 2750, 3 × 109 < Ra < 5 × 1012. Using the heat-mass transfer analogy, this indicates the high Prandtl number variation of Nu with Ra.

Occupational hot exposures: a review of heat and mass transfer theory.

The assessment and control of hot working environments is based on an appraisal of the thermal interaction between an individual and the surroundings. This paper examines in detail the processes of convection, radiation and evaporation which constitute the principal mechanisms for this interaction. The defining equations are discussed with particular attention given to the appropriate numerical values of body heat and mass transfer coefficients. The use of the heat-mass transfer analogy for the prediction of the mass transfer coefficient is introduced and verified. Finally, recommendations are given as to the most appropriate set of energy exchange equations for use in the analysis of high-temperature environments. The physiological criteria involved in hot working conditions, and the generation of a suitable assessment procedure based on the energy exchange equations, are the subject of a companion paper.

Effects of Cooling Films on the Heat Transfer Coefficient on a Flat Plate With Zero Mainstream Pressure Gradient

The influence of injection of cooling films through a row of holes on the heat transfer coefficient on a flat plate is investigated for a range of mass flux ratio using a heat-mass transfer analogy. Injection angles of 35 deg and 90 deg are covered. The experimental technique employed uses a swollen polymer surface and laser holographic interferometry. The results presented show the change in local heat transfer coefficient over the no-injection values at the centerline and off-centerline locations for various streamwise stations. The effect of injection on laterally averaged heat transfer coefficients is also assessed.

Effects of the Condition of the Approach Boundary Layer and of Mainstream Pressure Gradients on the Heat Transfer Coefficient on Film-Cooled Surfaces

This paper describes an investigation of the sensitivity of the heat transfer coefficient under the film to the state of the approach boundary layer for injection through a row of holes on a flat plate. The investigation is done for a range of blowing parameters using a heat-mass transfer analogy. Injection angles of 35 deg and 90 deg are covered. Additionally, for the same injection geometries, the effect of injection in the presence of mild adverse, mild favorable, and strong favorable mainstream pressure gradients is investigated. The results indicate that the heat transfer coefficient under the film is sensitive neither to the condition of the approach boundary layer nor to the presence of a mild adverse pressure gradient, but it is significantly lowered by a favorable pressure gradient, particularly at low blowing parameters.

Heat and mass transfer in horizontal vapor phase epitaxy reactors

Heat and mass transfer processes were studied in a horizontal vapor epitaxy reactor with simultaneously developing velocity, temperature and concentration distributions. The susceptor placed in the reactor was either horizontal or slightly titled. An analytical solution was obtained using previous heat transfer results in entry length and fully developed duct flow, and the heat-mass transfer analogy for growth rate calculations. The mean concentration distributions along the susceptor are presented in dimensionless forms based on constant properties and laminar flow. The influences of axial temperature variation and wall cooling on the epitaxial growth rate distribution are examined in this study. Results of experimental studies of silicon growth from SiH 4 in hydrogen agree well with the analysis.

Measurements of Heat Transfer and Pressure Drop for an Array of Staggered Plates Aligned Parallel to an Air Flow

The heat transfer and pressure drop characteristics of an array of staggered plates, aligned parallel to the direction of a forced convection air flow, have been studied experimentally. During the course of the experiments, the plate thickness and Reynolds number were varied parametrically. Mass transfer measurements employing the naphthalene sublimation technique were made to obtain the heat transfer results via the heat-mass transfer analogy. For a given operating condition, the per-plate heat transfer coefficients were found to be the same for the second and all subsequent rows. The fully developed heat transfer coefficients increase with Reynolds number for all the plate thicknesses investigated, but in a different manner for the different thicknesses. In general, thicker plates give rise to higher heat transfer coefficients, especially at the larger Reynolds numbers. The measured friction factors also increase with plate thickness. For the thickest plates, the friction factor was found to be independent of the Reynolds number, signalling the dominance of inertial losses.

An experimental determination of heat transfer near the leading edge of a film-cooled gas turbine blade

This paper reports an experimental procedure for the determination of the local heat transfer coefficient in the vicinity of the leading edge of a film-cooled gas turbine blade. By invoking the heat-mass transfer analogy, and measuring the sublimation rate of naphthalene, the influence of film coolant ejection on the magnitude of the local transport coefficients is determined. A novel apparatus and experimental technique have been designed to eliminate the need to know the physical properties of the naphthalene. Results of experiments using a ‘relative mass transfer method’ for a blowing rate (injection velocity to mainstream velocity ratio) from 0·2 to 1·0 and a mainstream Reynolds number of 3·48 × 10 4 are presented and compared with previous heat transfer data.

A new approach to the correlation of boundary layer mass transfer rates with thermal diffusion and/or variable properties

A rational approach to the correlation of boundary layer mass transport rates, applicable to many commonly encountered laminar flow conditions with thermal diffusion and/or variable properties, is outlined. The correlation scheme builds upon already available constant property blowing/suction solutions by introducing appropriate correction factors to account for the additional (“pseudo” blowing and source) effects identified with variable properties and thermal diffusion. Applications of the scheme to the particular laminar boundary layer mass transfer problems considered herein (alkali and transition metal compound vapor transport) indicates satisfactory accuracy up to effective blowing factors equivalent to about one third of the “blow off” value. As a useful by-product of the variable property correlation, we extend the heat-mass transfer analogy, for a wide range of Lewis numbers, to include variable property effects.

Film Cooling With Large Density Differences Between the Mainstream and the Secondary Fluid Measured by the Heat-Mass Transfer Analogy

The effect of large density differences on film cooling effectiveness was investigated through the heat-mass transfer analogy. Experiments were performed in a wind tunnel where one of the plane walls was provided with a porous strip or a row of holes with three-diameter lateral spacing and inclined 35 deg into the main stream. Helium, CO2, or refrigerant F-12, was mixed with air either in small concentrations to approach a constant property situation or in larger concentration to produce a large density difference and injected through the porous strip or the row of holes into the mainstream. The resulting local gas concentrations were measured along the wall. The density ratio of secondary to mainstream fluid was varied between 0.75 and 4.17 for both injection systems. Local film effectiveness values were obtained at a number of positions downstream of injection and at different lateral positions. From these lateral average values could also be calculated. The following results were obtained. The heat mass-transfer analogy was verified for injection through the porous strip or through holes at conditions approaching a constant property situation. Neither the Schmidt number, nor the density ratio affects the film effectiveness for injection through a porous strip. The density ratio has a strong effect on the film effectiveness for injection through holes. The film effectiveness for injection through holes has a maximum value for a velocity ratio (injection to free stream) between 0.4 and 0.6. The center-line effectiveness increases somewhat with a decreasing ratio of boundary layer thickness to injection tube diameter.

Experiments on the Transfer Characteristics of a Corrugated Fin and Tube Heat Exchanger Configuration

Local and average air-side transfer coefficients have been measured for a one-row corrugated fin and tube heat exchanger configuration. The measurements were accomplished via the heat-mass transfer analogy in conjunction with the naphthalene sublimation technique. The local transfer coefficients revealed the presence of several vortex systems which are activated and strengthened with increasing Reynolds number. The vortices serve to augment the transfer coefficients. The windward or leeward orientation of the facets of the corrugated wall was found to have a decisive effect on the transfer characteristics, with appreciably higher transfer rates prevailing on the windward facets. The average transfer coefficients were compared with those for a corresponding plane-walled heat exchanger configuration. The comparison showed that the augmentation due to the corrugated fin surface increased with Reynolds number. At a Reynolds number of 1000, the average coefficient for the corrugated fin system was about 45 percent greater than that for the plane fin system.

Transfer characteristics of two-row plate fin and tube heat exchanger configurations

The heat-mass transfer analogy, in conjunction with the naphthalene sublimation technique, was used to investigate the transfer capabilities and transfer mechanisms in two-row plate fin and tube heat exchanger configurations. Local and average transfer coefficients were determined from measurements of the mass transferred in an analogical system consisting of a pair of naphthalene plates and an array of spacer disks. The analogical system modeled a typical heat exchanger flow passage. The results were presented in dimensionless form to facilitate their conversion to Nusselt numbers. Different transfer mechanisms were found to be operative on the portions of the fin which are respectively associated with the first and the second rows of tubes. For the portion associated with the first row, the two factors which provided high mass-transfer rates were the boundary layer on the forward part of the fin and a vortex system which develops in front of the tubes. On the other hand, for the portion of the fin associated with the second row, there is no boundary-layer regime, and it is the vortex system alone which is responsible for high transfer rates. At higher Reynolds numbers, the influence of the second-row vortex system is sufficient to cause a near equality in the transfer capabilities of the first-row and second-row fin surfaces.

Impingement transfer coefficients due to initially laminar slot jets

The transfer coefficients resulting from the impingement of a slot jet on a plane surface have been measured by the naphthalene sublimation technique. The experiments were performed with jets that are laminar at the exit of the duct from which the jet issues. In addition, the velocity profiles at the duct exit were fully developed. Distributions of the local mass-transfer coefficient on the impingement surface were determined for five Reynolds numbers and at five separation distances between the duct and the surface. The mass-transfer results can be converted to heat-transfer results by using the heat-mass transfer analogy. It was found that the transfer coefficients generally tended to decrease with increasing separation distance, but there was evidence of non-monotonic behavior owing to the opposite influences of mixing-induced turbulence and diminished jet velocity. Increases in Reynolds number tended to increase the transfer coefficients, and the stagnation point values were correlated with a 0·6-power dependence. The surface distributions of the transfer coefficient were bell-shaped, with the largest value at the stagnation point. Comparisons with available literature suggested that the shape of the initial velocity profile has a significant effect on the transfer characteristics of the impingement surface.