Variations of local heat transfer coefficient in piped flow of viscous liquids

Measurements were carried out to determine local coefficients of heat transfer in short lengths of horizontal pipe, and in the region of an discontinuity in pipe diameter. Laminar, transitional and turbulent flow regimes were investigated, and mixtures of propylene glycol and water were used in the experiments to give a range of viscous fluids. Theoretical and empirical analyses were implemented to find how the fundamental mechanism of forced convection was modified by the secondary effects of free convection, temperature dependent viscosity, and viscous dissipation. From experiments with the short tube it was possible to determine simple empirical relationships describing the axial distribution of the local 1usselt number and its dependence on the Reynolds and Prandtl numbers. Small corrections were made to account for the secondary effects mentioned above. Two different entrance configurations were investigated to demonstrate how conditions upstream could influence the heat transfer coefficients measured downstream In experiments with a sudden contraction in pipe diameter the distribution of local 1u3se1t number depended on the Prandtl number of the fluid in a complicated way. Graphical data is presented describing this dependence for a range of fluids indicating how the local Nusselt number varied with the diameter-ratio. Ratios up to 3.34:1 were considered. With a sudden divergence in pipe diameter, it was possible to derive the axial distribution of the local Nusse1t number for a range of Reynolds and Prandtl numbers in a similar way to the convergence experiments. Difficulty was encountered in explaining some of the measurements obtained at low Reynolds numbers, and flow visualization techniques wore used to determine the complex flow patterns which could lead to the anomalous results mentioned. Tests were carried out with divergences up to 1:3.34 to find the way in which the local Nusselt number varied with the diameter ratio, and a few experiments were carried out with very large ratios up .to 14.4. A limited amount of theoretical analysis of the 'divergence' system was carried out to substantiate certain explanations of the heat transfer mechanisms postulated.

Measurements of stress-optic coefficient in polymer optical fibers

We have systematically measured the differential stress-optic coefficient, ?C, in a number of poly(methyl methacrylate) (PMMA) fibers drawn with different stress, ranging from 2 up to 27 MPa. ?C was determined in transverse illumination by measuring the dependence of birefringence on additional axial stress applied to the fiber. Our results show that ?C in PMMA fibers has a negative sign and ranges from -4.5 to -4.5×10-12 Pa-1, depending on the drawing stress. Increase of the drawing stress results in greater initial fiber birefringence and lower ?C.

Local heat transfer coefficient in a baffled shell and tube heat exchanger

Local shell side coefficient measurements in the end conpartments of a model shell and tube heat exchanger have been made using an electrochemical technique. Limited data are also reported far the second compartment. The end compartment average coefficients have been found to be smaller than reported data for a corresponding internal conpartment. The second compartment data. have been shown to lie between those for the end compartments and the reported internal compartment data. Experimental data are reported fcr two port types and two baffle orientations. with data for the case of an inlet compartment impingement baffle also being given . Port type is shown to have a small effect on compartment coefficients, these being largely unaffected. Likewise, the outlet compartment average coefficients are slightly snaller than those for the inlet compartment, with the distribution of individual tube coefficients being similar. Baffle orientation has been shown to have no effect on average coefficients, but the distribution of the data is substantially affected. The use of an impingement baffle in the inlet compartment lessens the efect of baffle orientation on distribution . Recommendations are made for future work.

Creep and fatigue of a single crystal nickel base superalloy

The introduction of single crystal casting techniques has led to the development of existing nickel-base superalloys to produce materials with optimum mechanical properties in the single crystal condition. As single crystals are known to be anisotropic, a study is needed to determine the general mechanical properties of these materials, and determine the effects of crystal orientation upon them. A study has been carried out to identify the effect of orientation and temperature on the creep and fatigue properties of a development single crystal superalloy, SRR 99. Creep testing and crystal rotation experiments have been made on SRR 99 and an earlier development alloy, SRR 9. Fatigue experiments at elevated temperatures have been carried out on both notched and un-notched specimens of alloy SRR 99. To aid in this analysis, several analytical techniques have been employed including Laue x-ray orientation analysis, measurement of strain by photographic methods and microstructural examination. Crystal rotation experiments have indicated that shear of 1 precipitates by lbrace111rbrace< 112> slip systems is operative during primary creep deformation at temperatures of 750oC and 850oC. The effect of orientation variation obtained by standard casting practices was not found to be significant. Creep rupture was found to be associated with multiple crack initiation from micropores. Fatigue crack initiation in un-notched specimens was found to be related to microporosity and microstructural defects. Failure was predominantly by crystallographic crack growth on lbrace111rbrace planes. The use of linear elastic fracture mechanics to describe fatigue crack propagation in alloy SRR 99 was found to be acceptable at temperatures up to 850oC. Variation of temperature, frequency and crystal orientation was found to have only moderate effect upon crack propagation rates.

Computational modelling of the impact of particle size to the heat transfer coefficient between biomass particles and a fluidised bed

The fluid–particle interaction and the impact of different heat transfer conditions on pyrolysis of biomass inside a 150 g/h fluidised bed reactor are modelled. Two different size biomass particles (350 µm and 550 µm in diameter) are injected into the fluidised bed. The different biomass particle sizes result in different heat transfer conditions. This is due to the fact that the 350 µm diameter particle is smaller than the sand particles of the reactor (440 µm), while the 550 µm one is larger. The bed-to-particle heat transfer for both cases is calculated according to the literature. Conductive heat transfer is assumed for the larger biomass particle (550 µm) inside the bed, while biomass–sand contacts for the smaller biomass particle (350 µm) were considered unimportant. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. Biomass reaction kinetics is modelled according to the literature using a two-stage, semi-global model which takes into account secondary reactions. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase. FLUENT 6.2 has been used as the modelling framework of the simulations with the whole pyrolysis model incorporated in the form of User Defined Function (UDF).

Mass transfer coefficient for drying of moist particulate in a bubbling fluidized bed

Experiments on drying of moist particles by ambient air were carried out to measure the mass transfer coefficient in a bubbling fluidized bed. Fine glass beads of mean diameter 125?µm were used as the bed material. Throughout the drying process, the dynamic material distribution was recorded by electrical capacitance tomography (ECT) and the exit air condition was recorded by a temperature/humidity probe. The ECT data were used to obtain qualitative and quantitative information on the bubble characteristics. The exit air moisture content was used to determine the water content in the bed. The measured overall mass transfer coefficient was in the range of 0.0145–0.021?m/s. A simple model based on the available correlations for bubble-cloud and cloud-dense interchange (two-region model) was used to predict the overall mass transfer coefficient. Comparison between the measured and predicted mass transfer coefficient have shown reasonable agreement. The results were also used to determine the relative importance of the two transfer regions.

The creep behaviour of pressure diecast zinc-aluminium based alloys

The creep behaviour of three pressure diecast commercial zinc-aluminium based alloys: Mazak 3, corresponding to BS 1004A, and the new alloys ZA.8 and ZA.27 with a series of alloys with compositions ranging from 0% to 30% aluminium was investigated. The total creep elongation of commercial alloys was shown to be well correlated using an empirical equation. Based on this a parametrical relationship was derived which allowed the total creep extension to be related to the applied stress, the temperature and the time of test, so that a quantitative assessment of creep of the alloys could be made under different conditions. Deviation from the normal creep kinetics occurred in alloys ZA.8 and ZA.27 at very low stresses, 150°C, due to structural coarsening combined with partial transformation of ε -phase into T' phase. The extent of primary creep was found to increase with aluminium content, but secondary creep rates decreased in the order Mazak 3, ZA.8 and ZA.27. Thus, based on the above equation, ZA.8 was found to have a substantially better total creep resistance than ZA.27, which in turn was marginally better than Mazak 3 for strains higher than 0.5%, but inferior for smaller strains, due to its higher primary creep extension. The superior creep resistance of ZA.8 was found to be due to the presence of strictly-orientated, thin plate-like precipitates of ε(CuZn4) phase in the zinc matrix of the eutectic and the lamellarly decomposed β phase, in which the precipitation morphology and orientation of ε in the zinc matrix was determined. Over broad ranges of temperature and stresses, the stress exponents and activation energies for creep were found to be consistent with some proposed creep rate mechanisms; i.e. viscous glide for Mazak 3, dislocation climb over second phase particles for ZA.8 and dislocation climb for ZA.27, controlled by diffusion in the zinc-rich phase. The morphology of aluminium and copper-rich precipitates formed from the solid solution of zinc was clearly revealed. The former were found to further increase the creep rate of inherently low creep resistant zinc, but the latter contributed significantly to the creep resistance. Excess copper in the composition, however, was not beneficial in improving the creep resistance. Decomposition of β in copper-containing alloys was found to be through a metastable Zn-Al phase which is strongly stabilised by copper, and the final products of the decomposition had a profound effect on the creep strength of the alloys. The poor creep resistance of alloy ZA.27 was due to the presence of particulate products derived from decomposed β-phase and a large volume of fine, equiaxed products of continuously decomposed α-dendrites.

The compressive creep and load relaxation properties of a series of high aluminium zinc-based alloys

A new family of commercial zinc alloys designated as ZA8, ZA12, and ZA27 and high damping capacity alloys including Cosmal and Supercosmal and aluminium alloy LM25 were investigated for compressive creep and load relaxation behaviour under a series of temperatures and stresses. A compressive creep machine was designed to test the sand cast hollow cylindrical test specimens of these alloys. For each compressive creep experiment the variation of creep strain was presented in the form of graphs plotted as percentage of creep strain () versus time in seconds (s). In all cases, the curves showed the same general form of the creep curve, i.e. a primary creep stage, followed by a linear steady-state region (secondary creep). In general, it was observed that alloy ZA8 had the least primary creep among the commercial zinc-based alloys and ZA27 the greatest. The extent of primary creep increased with aluminium content to that of ZA27 then declined to Supercosmal. The overall creep strength of ZA27 was generally less than ZA8 and ZA12 but it showed better creep strength than ZA8 and ZA12 at high temperature and high stress. In high damping capacity alloys, Supercosmal had less primary creep and longer secondary creep regions and also had the lowest minimum creep rate among all the tested alloys. LM25 exhibited almost no creep at maximum temperature and stress used in this research work. Total creep elongation was shown to be well correlated using an empirical equation. Stress exponent and activation energies were calculated and found to be consistent with the creep mechanism of dislocation climb. The primary α and β phases in the as-cast structures decomposed to lamellar phases on cooling, with some particulates at dendrite edges and grain boundaries. Further breakdown into particulate bodies occurred during creep testing, and zinc bands developed at the highest test temperature of 160°C. The results of load relaxation testing showed that initially load loss proceeded rapidly and then deminished gradually with time. Load loss increased with temperature and almost all the curves approximated to a logarithmic decay of preload with time. ZA alloys exhibited almost the same load loss at lower temperature, but at 120°C ZA27 improved its relative performance with the passage of time. High damping capacity alloys and LM25 had much better resistance to load loss than ZA alloys and LM25 was found to be the best against load loss among these alloys. A preliminary equation was derived to correlate the retained load with time and temperature.

The creep properties of a series of zinc-rich zinc-aluminium alloys

The compressive creep behaviour of six sand cast zinc-rich alloys: No3 and No5, corresponding to BS 1004A and BS 1004B, respectively, alloy No2, ILZRO,.16 and two newer alloys ACuZinc5 and ACuZinc10 was investigated. The total creep contraction of the alloys was found to be well correlated using an empirical equation. On the basis of this equation, a parametrical relationship was derived which allowed the total creep contraction to be related to the applied stress, the temperature and the time of test, so that a quantitative assessment of compressive creep of the alloys could be made under different testing conditions. The primary creep and secondary creep rates were found for the alloys at different temperatures and stresses. Generally, the primary creep contraction was found to increase with copper content, whereas secondary creep rates decreased in the order No3, ACuZinc10, ACuZinc5 and No2. ILZRO.16 was tested only at the highest stress and two higher temperatures. The results showed that ILZRO.16 had higher creep resistance than all the other alloys. Thus, based on the above empirical equation, alloy No2 was found to have a substantially better total creep resistance than alloys No3 and No5, and slightly better than ACuZinc5 and ACuZinc10 for strains up to 1%. Both ACuZinc alloys had higher creep strength than commercial alloys No3 and No5. Alloy No5 had much higher creep resistance than alloy No3 under all conditions. The superior creep resistance of alloy No2 was considered to be due to the presence of small precipitates of -phase in the zinc matrix and a regular eutectic morphology. The stress exponents and activation energies for creep under different testing conditions were found to be consistent with some established creep-controlling mechanisms; i.e. dislocation climb for alloy No3, dislocation climb over second phase particles for alloys No5, No2, ACuZinc10, controlled by lattice diffusion in the zinc-rich phase. The lower creep resistance of alloy No3 was mainly due to the lower creep strength of copper-free primary particles having greater volume than eutectic in the microstructure. Alloys No5, ACuZinc5 and ACuZinc10 showed much better creep resistance than alloy No3, based on the precipitation-hardening due to the presence of small -phase precipitates. The primary dendrites in both ACuZinc alloys however were not of much benefit in improving the creep resistance of the alloys.

The mechanics of creep crack growth in a Magnox alloy

Magnox AL80 has been used for a study of creep crack propagation. A number of variables have been considered such as specimen geometry,notch root radius, material thickness, creep prestrain and stress level.The work has covered the material behaving under two values of the creep exponent, n=3.5 and n=7, according to the stress level. As well as observing initiation times and crack growth rates, scribed grids have been used to examine the near crack tip strain levels and distributions. It was shown that estimations of COD from notch flank opening can give misleading indications of material behaviour and that a more informative method was to monitor displacements in the material surrounding the crack tip. Strong evidence was found for crack advance being displacement controlled, however it was shown that the COD approach should be considered geometry dependant. The summation of ∈xx and ∈yy provided the most successful description of crack advance as it produced a single value that described propagation in all the cases concidered. The strain distributions indicates that σyy was related to distance from a point ahead of the crack tip by the exponent - (l/n+l) and that σxx is proportional to σyy. The constraint stresses arising in the DEN and CN specimens were evaluated. Initiation time was found to be principally affected by the stress level but was modified by the constraints arising from specimen geometry. Crack growth was found not to obey either the empirical K or σpett relationships but was reviewed in context of the observed strain behaviour.

Creep crack growth in cast steam turbine casing steels

The creep rupture properties of cast ½Cr½Mo¼V and 1Cr1Mo¼V alloy steel used in the manufacture of power station steam generating plant. have been investigated. The effects of constraint and geometry on the creep rupture properties are also considered. The validity of various criteria controlling macroscopic creep crack growth in cast CrMoV alloys has been examined. It is found that neither the stress intensity factor nor reference stress correlate satisfactorily the creep crack growth rates at the test temperature of 550°C. Certain minimum displacements must be achieved for crack initiation and propagation. It is found that this displacement as measured by crack opening displacement or crack aspect ratio, is the same in both compact tension and centre-cracked panel geometries, is invariant with crack length and decreases with increasing constraint. The effect of constraint on creep crack growth rate in the two geometries is less conclusive. A new model describing creep crack growth in cast CrMoV alloy steels has been developed. The model is based on the results from a numerical finite element creep analysis of the relaxation and redistribution of stress ahead of an incubating creep crack . It is found that macroscopic creep crack growth in a material undergoing either plane stress or plane strain deformation can be described by a fracture stress which is based on the Von Mises equivalent stress. It has been shown that this model is capable of rationalising all of the experimental crack velocity data from the cast CrMoV alloys. The resultant degree of data correlation is far superior to that obtained when using the stress intensity factor or reference stress. A cumulative damage creep fracture model based upon the results from the numerical analysis has been developed. It is found that the model is capable of predicting the behaviour of propagating creep cracks in cast CrMoV alloys from smooth bar creep rupture data.

Estimation of TFP growth:a semiparametric smooth coefficient approach

This article uses a semiparametric smooth coefficient model (SPSCM) to estimate TFP growth and its components (scale and technical change). The SPSCM is derived from a nonparametric specification of the production technology represented by an input distance function (IDF), using a growth formulation. The functional coefficients of the SPSCM come naturally from the model and are fully flexible in the sense that no functional form of the underlying production technology is used to derive them. Another advantage of the SPSCM is that it can estimate bias (input and scale) in technical change in a fully flexible manner. We also used a translog IDF framework to estimate TFP growth components. A panel of U.S. electricity generating plants for the period 1986–1998 is used for this purpose. Comparing estimated TFP growth results from both parametric and semiparametric models against the Divisia TFP growth, we conclude that the SPSCM performs the best in tracking the temporal behavior of TFP growth.