Experimental investigations on overall cooling effect of ribbed channel with air bleeds

An experimental investigation on overall heat transfer performance of a rectangular channel, in which one wall has periodically placed oblique ribs to enhance heat exchange and cylindrical film holes to bleed cooling air, has been carried out in a hot wind tunnel at different mainstream temperatures, hot mainstream Reynolds numbers, coolant Reynolds numbers and blowing ratios. To describe the cooling effect of combined external coolant film with the internal heat convection enhanced by the ribs, the overall cooling effectiveness at the surface exposed in the mainstream with high temperature was calculated by the surface temperatures measured with an infrared thermal imaging system. The total mass flow rate of cooling air through the coolant channel was regulated by a digital mass flow rate controller, and the blowing ratio passing through the total film holes was calculated based on the measurements of another digital-type mass flow meter. The detailed distributions of overall cooling effectiveness show distinctive peaks in heat transfer levels near the film holes, remarkable inner convective heat transfer effect over entire channel surface, and visible conductive heat transfer effect through the channel wall; but only when the coolant Reynolds number is large enough, the oblique rib effect can be detected from the overall cooling effectiveness; and the oblique bleeding hole effect shows the more obvious trend with increasing blowing ratios. Based on the experimental data, the overall cooling effectiveness is correlated as the functions of Re_m (Reynolds number of hot mainstream) and Re_c (Reynolds number of internal coolant flow at entrance) for the parametric conditions examined.     

Heat transfer model with two heat transfer coefficients along a multiperforated plate — Application to combustion chamber wall cooling

Walls‘ cooling of aeronautic propeller combustion chamber is performed with the injection, through the combustion chamber wall, of a part of the air coming from compressors placed upstream. Measurements of the wall thermal fields are made by infrared thermography along the injection wall. This injection wall is pierced by 9 rows of 8 holes (α=90°) in staggered configuration (p/D=s/D=6). We propose a model using two heat transfer coefficients to represent the convective exchanges. The results are non-dimensioned and presented in comparison with the case without holes. The use of this model allows us to define 4 zones. Those 4 zones exist for the 5 blowing rates.     

KI–T estimations for embedded flaws in pipes – Part I: Axially oriented cracks

This study reports a numerical investigation on the linear-elastic K_I and T-stress values over the front of elliptical cracks axially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs an interaction integral approach to compute the linear-elastic stress intensity factor (SIF) K_I and T-stress values from very detailed crack-front meshes. The verification study confirms the accuracy of the adopted numerical procedure in computing the K_I values based on existing results for external axial surface cracks in the wall of a cylindrical structure. The parametric investigation covers a wide range of geometric parameters including: the wall thickness to the inner radius ratio of the pipe (t/R_i), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the crack location measured by the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (e_M/t). Subsequent efforts develop, from a nonlinear curve-fitting procedure, a new set of equations to estimate the T-stress and K_I values at three critical front locations of the axial elliptical cracks: the crack-front point O nearest to the outer surface of the pipe, the crack-front point I nearest to the inner surface of the pipe and the crack-front point M on the centerline of the axial crack. These equations combine a second-order polynomial with a power-law expression to predict the pronounced variations in the T-stress and K_I values with respect to the geometric parameters. The coefficients of the new K_I and T-stress equations either take a constant value or incorporate the linear variation with respect to the pipe wall thickness over the inner radius ratio, t/R_i. The proposed equations demonstrate a close agreement with the finite element (FE) results, which indicate very strong dependence of the T-stress and K_I values at point O and point I on the corresponding ligament lengths, e_O and e_I.     

Measurements of mass transfer coefficient and effectiveness in the recovery region of a film-cooled surface

Mass transfer coefficients and film cooling effectiveness are measured downstream of a single row of holes (recovery region) inclined 30° with the surface and inline with the main turbulent boundary layer flow. The mass transfer coefficients are measured using a naphthalene sublimation technique. The effectiveness is determined through the injection of a trace gas into the secondary flow and measuring its concentration at the impermeable wall. Experiments are carried out in a subsonic, zero pressure gradient turbulent boundary layer, under isothermal conditions with three blowing ratios (U_j/U_∞): 0.4, 0.8, and 1.2. The data is collected in a region 7–80 jet diameters downstream of the injection location. From the data on mass transfer coefficients and effectiveness obtained under the same flow conditions a general mass transfer equation is derived. This paper presents extensive data and discussions; and is believed to be one of the few studies in which both of these variables are measured on the same surface and in a large area in the recovery region.     

Film cooling on a gas turbine blade pressure side or suction side with axial shaped holes

The film cooling effectiveness on the surface of a high pressure turbine blade is measured using the pressure sensitive paint (PSP) technique. Four rows of axial laid-back, fan-shaped cooling holes are distributed on the pressure side while two such rows are provided on the suction side. The coolant is only injected to either the pressure side or suction side of the blade at five average blowing ratios ranging from 0.4 to 1.5. The presence of wakes due to upstream vanes is simulated by placing a periodic set of rods upstream of the test blade. Effect of the upstream wakes is recorded at four different phase locations with equal intervals along the pitch-wise direction. The freestream Mach numbers at cascade inlet and exit are 0.27 and 0.44, respectively. Results reveal that the tip leakage vortices and endwall vortices sweep the coolant film on the suction side to the midspan region. The film cooling effectiveness on the suction side is usually higher than that on the pressure side except the regions affected by the secondary vortices. The presence of upstream wakes results in lower film cooling effectiveness on the blade surface. The moderate blowing ratios (M = 0.6 or M = 0.9) give higher film cooling effectiveness immediately downstream of the film cooling holes. Further downstream of the holes, higher blowing ratios cover wider surface area.     

Film cooling characteristics of rows of round holes at various streamwise angles in a crossflow: Part II. Heat transfer coefficients

Measurements of heat transfer coefficient (h) are presented for rows of round holes at streamwise angles of 30°, 60° and 90° with a short but engine representative hole length (L/D = 4). The study began with a single row of holes with pitch-to-diameter ratios of 3 and 6, followed by two inline and staggered rows for each hole spacing and streamwise inclination, which amount to 105 different test cases in addition to the 21 test cases presented on the single hole [C.H.N. Yuen, R.F. Martinez-Botas, Film cooling characteristics of a single round hole at various angles in a crossflow: Part I. Effectiveness, Int. J. Heat Mass Transfer, in press; C.H.N. Yuen, R.F. Martinez-Botas, Film cooling characteristics of a single round hole at various angles in a crossflow: Part II. Heat transfer coefficients, Int. J. Heat Mass Transfer, in press]. The present investigation is a continuation of the previous work [Yuen and Martinez-Botas, Parts I and II, in press] with the same test facility, operating conditions (freestream Reynolds number, Re_D of 8563, and blowing ratio, 0.33 ⩽ M ⩽ 2), and measurement technique of liquid crystal thermography and the steady-state heat transfer method, therefore the results presented in the form of h/h₀, which is the ratio of heat transfer coefficient with film cooling to that without, are directly comparable. Both local values and laterally averaged ones are presented, the latter refers to the averaged value across the central hole. The corresponding measurements of effectiveness for the rows of holes are presented in a companion paper [C.H.N. Yuen, R.F. Martinez-Botas, Film cooling characteristics of rows of round holes at various angles in a crossflow: Part I. Effectiveness, Int. J. Heat Mass Transfer, submitted for publication]. The low effectiveness observed with the 90° holes in the companion paper [Yuen and Martinez-Botas, submitted for publication] and the relatively large heat transfer coefficient presented here, suggest that the normal injection should only be used in situations where shallower holes are not feasible. The combined performance of effectiveness and heat transfer coefficient suggests that the two inline rows are likely to be advantageous in the film cooling of turbine blades with good coverage per unit mass flow of cooling air and lower thermal stresses due to the smaller heat load.     

Pressure drop and heat transfer of arrays of in-line circular blocks on the wall of parallel channel

Pressure drop and heat transfer of arrays of in-line circular blocks on the wall of a parallel channel are measured. Diameter and height of the blocks are 40 and 18 mm, respectively, while pitches of the blocks are varied. The effects of the number of lines and rows and other factors on pressure drop and heat transfer are investigated. The pressure loss coefficient ζ is the sum of the pressure drop across three regions, the inlet, intermediate and outlet regions, and is formulated as an empirical equation that agrees with experimental data to within ±10%. Average heat transfer coefficient of the first row of blocks is 10% lower than that of the second row. Coefficients of the first 5 rows Nu_mi, are approximated to within ±10% by Nu_mi=0.118(Re/β)^0.75, where β is the opening ratio. The average Nusselt number of the second to fifth rows is also correlated to fan power, P_w, to within 5% by Nu_ave=190P_w^0.25, where P_w=ΔPU_mA₀,ΔP is the pressure difference, U_m is the mean velocity and A₀ is the cross-sectional area of the duct. Finally, the Nusselt number is represented by a non-dimensional expression as Nu_ave=0.134(ζ^1/3Re)^0.75.     

Natural convection in a partially open square cavity with internal heat source: An analysis of the opening mass flow

A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra_e = 10³–10⁵, while the influence of the heat source was evaluated through the relation R = Ra_i/Ra_e, investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra_e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra_e whereas these features are absent at higher Ra_e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.     

KI–T estimation for embedded flaws in pipes – Part II: Circumferentially oriented cracks

This paper, in parallel to the investigation on axially embedded cracks reported in the companion paper, presents a numerical study on the linear-elastic K_I and T-stress values over the front of elliptical cracks circumferentially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs the interaction-integral approach to compute the linear-elastic stress-intensity factor (SIF) K_I and T-stress values for embedded cracks with practical sizes at different locations in the wall of the pipe. The parametric study covers a wide range of geometric parameters for embedded cracks in the pipe, including: the wall thickness to the inner radius ratio (t/R_i), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (e_M/t). The parametric investigation identifies a significant effect of the remaining ligament length on both the T-stress and K_I values at the crack-front location (denoted by point O) nearest to the outer surface of the pipe and at the crack-front location (denoted by point I) nearest to the inner surface of the pipe. The numerical investigation establishes the database to derive approximate functions from a nonlinear curve-fitting procedure to predict the T-stress and K_I values at three critical front locations of the circumferentially embedded crack in a pipe: points O, I and M. The proposed T-stress and K_I functions utilize a combined second-order polynomial and a power-law expression, which presents a close agreement with the T-stress and K_I values computed from the very detailed finite element models. The comparison between the circumferentially embedded crack and the axially embedded crack indicates that both the T-stress and K_I values at crack-front points O and I in a circumferential crack equal approximately 50% the T-stress and K_I values at the corresponding front locations in an axial crack with the same crack depth ratio, the same crack aspect ratio and the same pipe wall thickness to the inner radius ratio.     

Validation of three dimensional film cooling modeling on convex surface for gas turbine blade

In this study, three dimensional computational predictions on the film cooling performance of single row and simple cylinder on the convex surface have been studied and compared with corresponding experimental data reported in the literature to validate the model. This computational prediction serves as the baseline for future studies of optimization in determining the film cooling effectiveness. Realizable κ–? turbulent model has been employed and energy equation has been solved. Grid independence study has been fulfilled using two kinds of meshing approach for the plenum and the cooling holes. Results of grid independence study showed that fine meshed plenum and cylinders of tetrahedral grids case have provide a good agreement with the related experimental data. Study of temperature ratio between the coolant and mainstream hot gas T_c/T_g has been performed using four values of temperature ratios that are 0.5, 0.6, 0.7, and 0.8. In all of these tests the mainstream duct of the models was generated with multigrid hexahedral mesh. Based on the heat-mass transfer analogy, results of this study showed good agreement of the film cooling effectiveness and temperature distribution in comparison to the related experimental data. The case in which combination of both plenum and cylinders in one volume with tetrahedral fine mesh generation and temperature ratio of T_c/T_g = 0.6 was found to be in good agreement with the experimental data among all of the other models. Computational prediction results have found an agreement with the experimental data, thus the approach is verified.     

An algorithm for sensor-less fuel control of direct methanol fuel cells

We report an algorithm for real-time control of the fuel of a DMFC. The MEA voltage decay coefficients [e₁, e₂], and I-V-T, M′-I-T, and W′-I-T curves (where I is the current, V the voltage, T the temperature, and M′ and W′ the methanol and water consumption rates, respectively) of n fuels with specified methanol concentrations C_M,k (k = 1, 2,…, n) are pre-established and form (I,V,T), (M′,I,T), and (W′,I,T) surfaces for each C_M,k. The in situ measured (I,V,T)_u after voltage decay correction is applied to the n preset (I,V,T) surfaces to estimate C_M,u (the C_M corresponding to (I,V,T)_u) using an interpolation procedure. The C_M,u is then applied to the n preset (M′,I,T) and (W′,I,T) surfaces to estimate cumulated “methanol” and “water” consumed quantities . Thus in a real-time system, the C_M and total quantity of fuel can be controlled using the estimated C_M,u and cumulated “methanol” and “water” consumed quantities.     

Numerical approach to film cooling effectiveness over a plate surface with coolant impingement

The aim of the present study is conducting the numerical approach to a combination of internal jet impingement and external film cooling over a flat plate. A multi-block three-dimensional Navier-Stokes code, CFX 4.4, with k-e turbulence model is used to simulate this complicated thermal-flow structure induced by the interaction of coolant jet and hot cross mainstream. By assuming the adiabatic wall boundary condition on the tested film-cooled plate, both the local and the spanwise-averaged adiabatic film cooling effectiveness are evaluated for comparison of the cooling performance at blowing ratios of Br=0.5, 1.0, and 1.5. Film flow data were obtained from a row of five cylindrical film cooling holes, inclined in angle of 35?and 0?in direction of streamwise and spanwise, respectively. The film cooling hole spacing between adjacent holes is 15 mm for all the holes. Before the coolant flow being injected through individual cooling hole then encountered with the mainstream, an impingement chamber containing an impingement plate with 43 holes is located on the path of coolant flow. Present study also focused on the effect of impingement spacing, 10mm, 20mm, and 30mm. Compare the results, we find the impingement jet has a significant effect on the adiabatic film cooling effectiveness. As the coolant impingement spacing is fixed, results indicated that higher blowing ratio would enhance the local and the spanwise-averaged adiabatic film cooling effectiveness. Moreover, neither uniform nor parabolic distribution of pressure distribution are observed within the coolant hole-pipe.     

Investigation of the Influence of Inclination Angle and Diffusion Angle on the Film Cooling Performance of Chevron Shaped Hole

The film cooling performance of chevron holes with different inclination angles and exit lateral diffusion angles has been studied experimentally and numerically. The inclination angles include 35° and 55°. The exit lateral diffusion angles include 20° and 25°. The film cooling effectiveness, heat transfer coefficient and discharge coefficient were measured on a flat plate model by transient liquid crystal measurement technique under four blowing ratios. The results show that the large inclination angle reduces the film cooling effectiveness. The influence of diffusion angle has two aspects: the large diffusion angle leads to mainstream ingestion and decreases film cooling effectiveness at M=1.0 and 1.5; however, the large diffusion angle increases the film cooling effectiveness at high blowing ratio of 2.0, because the larger hole exit area decreases the normal momentum component of the film jet. The large inclination angle decreases the heat transfer coefficient in the right downstream region at M=0.5 and 1.0. The large diffusion angle enhances the heat transfer in the right downstream of the holes in M=0.5～1.5 conditions. The chevron hole with large inclination angle generally has the highest discharge coefficient.     

Drying characteristics of peppercorns in a rectangular fluidized-bed with triangular wavy walls

An experimental study on drying kinetics of peppercorns has been conducted in two different drying fluidized-bed configurations: rectangular fluidized-bed (RFB) and rectangular fluidized-bed with wavy walls (RFBW). In the RFBW, two opposite triangular wavy walls with three blockage ratios (e/H) are formed to produce vortex/swirl flows leading to stronger turbulence and longer residence time of the flow in the bed. For each bed, three inlet hot airs (T_in) at 60 °C, 80 °C and 100 °C and two superficial air velocity, U* of 1.2 and 2.0 (U* = U/U_mf) are introduced. The experimental results reveal that the air temperature and air velocity show significant effects on the drying rate of both beds, especially at T_in = 100 °C and U* = 2.0. The RFBW performs much better than the RFB due to shorter drying time. The average drying time of the RFBW with e/H = 0.3125, 0.3750 and 0.4375 is, respectively, around 29%, 36% and 43% less than that of the RFB. In addition, three mathematical drying models are offered for both the beds and the effect of the air temperature and velocity on the drying model constants was determined by fitting the experimental data using regression analysis techniques. The three models satisfactorily described the drying characteristics of peppercorns especially for the Henderson and Pabis model. The RFBW with e/H = 0.4375 is preferable in the study.     

Experimental and numerical determination of a new wall-heat-gain function

A new ‘wall-heat-gain function’ is developed, which provides the heat entering a space through a wall under periodic outdoor conditions and constant indoor air temperature. The proposed function, which is much simpler than the well-known conduction transfer function, contains three coefficients U, w₁ and w₂ characterizing the wall and three parameters T_M, T_C, and T_s characterizing the outdoor conditions (temperature and solar radiation). The wall coefficients U, w₁, and w₂ may be determined numerically by the use of the finite difference method or experimentally in the case of existing (built) walls of unknown properties. A related experimental set up has been developed. Ready to use values of the wall coefficients are provided for 15 typical wall constructions. The climatic parameters T_M, T_C and T_s either are available for some locations or may be easily calculated by least-squares fitting to local climatological data. In a modified form of the proposed function the three climatic parameters are reduced to two, which are available from ASHRAE for about 1000 stations around the world. The accuracy of the proposed wall heat gain function is very good for practical applications as proved by comparisons with corresponding finite difference solutions.     

Dynamic hydrogen sorption and its influence on metal hydride heat pump operation

Hydride units containing MmNi_4.5Al_0.5 (Mm = Mischmetall; MNA), LaNi₅ (LN) and LaNi_4.7Al_0.3 (LNA) as hydrogen storage materials were combined to simple heat pumps after the investigation of their dynamic sorption behaviour. These heat pumps were tested in the “upgrading” mode without any external user. The combination LNA/LN showed a maximum temperature increase of 13.9 K at inlet water temperatures of T_i = 286 K, T_m = 338.5 K (cycle time: 12 min); for the LNA/MNA combination at inlet water temperatures of T_i = 286 K and T_m = 353 K, the observed temperature increase was 12.3 K (cycle time: 12 min) and 17.6 K (cycle time: 19 min), respectively. The operation of the devices was found to be sensitive to characteristics of the hydride materials (e.g. hysteresis, plateau slope) as to those of the hydride bed and the container design (heat conductivity, heat capacity).     

Numerical approach to hole shape effect on film cooling effectiveness over flat plate including internal impingement cooling chamber

Numerical approach have been conducted on a flat, three-dimensional discrete-hole film cooling geometries that included the mainflow, injection tubes, impingement chamber, and supply plenum regions. The effects of blowing ratio and hole’s shape on the distributions of flow field and adiabatic film cooling effectiveness over a flat plate collocated with two rows of injection holes in staggered-hole arrangement were studied. The blowing ratio was varied from 0.3 to 1.5, while the density ratio of the coolant to mainstream is kept at 1.14. The geometrical shapes of the vent of the cooling holes are cylindrical round, simple angle (CYSA), forward-diffused, simple angle (FDSA) and laterally diffused, simple angle (LDSA). Diameter of different shape of cooling holes in entrance surface are 5.0 mm and the injection angle with the main stream in streamwise and spanwise are 35° and 0° respectively. Ratio of the length of the cooling holes and the diameter in the entrance surface is 3.5. The distance between the holes in the same row as well as to the next row is three times the diameter of hole in the entrance surface.The governing equation is the fully elliptic, three-dimensional Reynolds-averaged Navier–Stokes equations. The mesh used in the finite-volume numerical computation is the multi-block and body-fitted grid system. The simulated streamwise distribution of spanwise-averaged film cooling effectiveness exhibited that low Reynolds number k–ε model can give close fit to the experimental data of the previous investigators. Present study reveals that (1) the geometrical shape of the cooling holes has great effect on the adiabatic film cooling efficiency especially in the area near to the cooling holes. (2) The thermal-flow field over the surface of the film-cooled tested plate dominated by strength of the counter-rotating vortex pairs (CRVP) that generated by the interaction of individual cooling jet and the mainstream. For LDSA shape of hole, the CRVP are almost disappeared. The LDSA shape has shown a highest value in distribution of spanwise-averaged film cooling effectiveness when the blowing ratio increased to 1.5. It is due to the structure of the LDSA is capable of reducing the momentum of the cooling flow at the vent of the cooling holes, thus reduced the penetration of the main stream. (3) The structure of the LDSA can also increase the lateral spread of the cooling flow, thus improves the spanwise-averaged film cooled efficiency.     

Compressible heat transfer computations by an adaptive finite element method

This paper presents adaptive finite element computations of laminar jet impingement heat transfer. Variable fluid properties and compressibility effects are considered. A unified formulation of the equations is used to treat the simultaneous presence of three flow regimes: incompressible (ρ=constant), compressible (ρ=ρ(p,T)), and anelastic (ρ=ρ(T)). The error estimator uses a local least squares projection method and accounts for errors in velocity, pressure and temperature. The performance of the methodology is verified by solving a problem possessing a closed form solution. Several applications are then considered. We study two different gases (air and CO₂), different conditions (heated, cooled or constant properties), compressibility and inlet velocity profile effects. Heat transfer is a key element of the study. Results indicate that the methodology can produce grid independent solutions even for derived quantities and in thin boundary layers.     

Heat transfer in porous cavity under the influence of radiation and viscous dissipation

Heat transfer under the influence of radiation and viscous dissipation in a square cavity filled with saturated porous medium is analysed. The flow is assumed to follow Darcy law. The governing equations are non-dimensionalised and solved numerically using finite element method. Left vertical surface of the square cavity is maintained at isothermal temperature T_h and right vertical surface at T_c. Results are presented in terms of Nusselt number at hot and cold wall of the cavity for various values of viscous dissipation parameter and radiation parameter. It is seen that the average Nusselt number at hot as well as cold wall increases with increase in radiation parameter.     

Validation of five global radiation models with measured daily data in China

Two sunshine based and three air temperature based global radiation models are calibrated using daily data in Jan. 1 1994–Dec. 31 1998 at 48 stations all over China. The Nash–Sutcliffe equation (NSE) is used as the model evaluation criterion. The sunshine based models are suitable for daily global radiation estimation. The averaged NSE value of the Angström model is 0.83, and the maximum value is 0.91. The maximum NSE value of the Bahel model is 0.92 with an averaged value of 0.84. The models that use air temperature as the input variable are not suitable for daily global radiation estimation in China. The averaged NSE values of the three air temperature based models (Bristow–Campbell model, Allen model and Hargreaves model) are not larger than 0.47. A logarithmic relationship between the daily global radiation/daily extra-terrestrial solar radiation (R_G/R_A) and the temperature difference between the maximum and minimum daily air temperature (T_M−T_m) is found in the present study. A new daily global radiation model that is a function of R_A, sunshine hours and T_M−T_m is designed, which gives an averaged NSE value of 0.85 and a maximum value of 0.92.