Momentum Transfer Coefficient Research Articles

Experimental and Numerical Simulation of Ejecta Size and Velocity of Hypervelocity Impact Rubble-Pile Asteroid

Rubble-pile asteroids may be the type of near-Earth object most likely to threaten Earth in a future collision event. Small-scale impact experiments and numerical simulations for large-scale impacts were conducted to clarify the size ratio of the boulder/projectile diameter effects on ejecta size–velocity distribution. A series of small-scale impact cratering experiments were performed on porous gypsum–basalt targets at velocities of 2.3 to 5.5 km·s−1. Three successive ejection processes were observed by high-speed and ultra-high-speed cameras. The momentum transfer coefficient and cratering size were measured. A three-dimensional numerical model reflecting the random distribution of the interior boulders of the rubble-pile structure asteroid is established. The size ratio (length to diameter) of the boulder size inside the asteroid to the projectile diameter changed from 0.25 to 1.7. We conducted a smoothed particle hydrodynamics numerical simulation in the AUTODYN software to study the boulder size effect on the ejecta size–velocity distribution. Simulation results suggest that the microscopic porosity on regolith affects the propagation of shock waves and reduces the velocity of ejecta. Experiments and numerical simulation results suggest that both excavation flow and spalling ejection mechanism can eject boulders (0.12–0.72 m) out of the rubble-pile asteroid. These experiments and simulation results help us select the potential impact site in a planetary defense scenario and reduce deflection risk. are comprised primarily of boulders of a range of sizes.

A numerical model for calculating velocity distribution in cross-section of an open channel

Flow velocity in open channels is a fundamental hydraulic parameter with wide-ranging applications, including the development of rating curves and the study of sediment transport. While some river engineering projects may only require the calculation of average flow velocity, others, such as the design of hydraulic structures and stable channels, as well as the assessment of boundary shear stress, necessitate a more comprehensive understanding of flow dynamics, including the two-dimensional velocity distribution within open channels. To address this, various mathematical models have been proposed for estimating the two-dimensional distribution of flow velocity across transverse and depth directions. However, these models often come with complexities that hinder their practical application. In this research, we introduce a simplified numerical model that combines simplified Navier–Stokes equations with an eddy viscosity formula. This innovative approach aims to estimate velocity distribution in both rectangular and trapezoidal channels. The accuracy of our developed model hinges on the momentum transfer coefficient used in the eddy viscosity formula. Through the execution of the numerical model and the utilization of observational data, we determined the optimal value of the momentum transfer coefficient to be 0.241. To validate the effectiveness of our numerical model, we compared its predictions with laboratory data encompassing diverse hydraulic conditions. The results demonstrated a high level of accuracy, with the calculated velocity distribution and flow discharge differing by no more than 7.6% and 6.8%, respectively.

Effect of Oldroyd-B fluid on thermal convection stability in a bidispersive porous media with relatively large macropores

This study investigates the effect of Oldroyd-B fluids on the thermal convection instability in a bi-disperse porous medium with relatively large macropores. The modified momentum equation of Oldroyd-B fluid in the macro- and micropores is first derived, assuming local thermal equilibrium. The Orr–Sommerfeld (O–S) equation is derived using the new modified incompressible Navier–Stokes equations of Oldroyd-B fluid. The Chebyshev collocation method is employed to solve the generalized eigenvalue problem, and the neutral stability curves and temporal growth rates are obtained. The results demonstrate that the relaxation time enhances the convective instability, while the retardation time suppresses it. Furthermore, the effect of relaxation time is generally small for smaller wave number, but the effect of relaxation time is significant for large wave number, and this effect becomes accentuated as the wave number increases. The retardation time does not have any influence when the wavenumber is small, and the influence of retardation time becomes small with the large relaxation time. Moreover, the convection instability is enhanced with the higher micropermeability and a higher ratio of momentum transfer coefficient between the macro- and microphases will suppress the instability.

Comprehensive evaluation of typical planetary boundary layer (PBL) parameterization schemes in China – Part 1: Understanding expressiveness of schemes for different regions from the mechanism perspective

Abstract. The optimal choice of the planetary boundary layer (PBL) parameterization scheme is of particular interest and urgency to a wide range of scholars, especially for many works involving models. At present, there have been many works to evaluate the PBL schemes. However, little research has been conducted into a more comprehensive and systematic assessment of the performance capability of schemes in key regions of China, especially when it comes to the differences in the mechanisms of the schemes themselves, primarily because there is scarcely sufficient observational data, computer resources, and storage support to complete the work. In this companion paper (i.e., Part 1), four typical schemes (i.e., YSU, ACM2, BL, and MYJ) are selected to systematically analyze and evaluate near-surface meteorological parameters, PBL vertical structure, PBL height (PBLH), and turbulent diffusion coefficient (TDC) in five key regions of China (i.e., North China Plain, NCP; Yangtze River Delta, YRD; Sichuan Basin, SB; Pearl River Delta, PRD and Northwest Semi-arid region, NS) in different seasons (i.e., January, April, July, and October). The differences in the simulated 2 m temperatures between the nonlocal closure schemes are mainly affected by the downward shortwave radiation, but to compare the nonlocal closure schemes with the local closure schemes, the effect of sensible heat flux needs to be further considered. The 10 m wind speed is under the influence of factors like the momentum transfer coefficient and the integrated similarity functions at night. The wind speeds are more significantly overestimated in the plains and basin, while less overestimated or even underestimated in the mountains, as a result of the effect on topographic smoothing in the model. Moreover, the overestimation of small wind speeds at night is attributable to the inapplicability of the Monin–Obukhov similarity theory (MOST) at night. The model captures the vertical structure of temperature well, while the wind speed is outstandingly overestimated below 1000 m, largely because of the TDC. The difference between the MOST and the mixing length theory, PBLH, and Prandtl number is cited as the reason for the difference between the TDC of the YSU and ACM2 schemes. The TDCs of the BL and MYJ schemes are affected by the mixing length scale, which of BL is calculated on the basis of the effect of buoyancy, while MYJ calculates it with the consideration of the effect of the total turbulent kinetic energy. The PBLH of the BL scheme is better than the other schemes because of the better simulation results of temperature. In general, to select the optimal scheme, it is necessary to offer different options for different regions with different focuses (heat or momentum). The first focus is on the temperature field. The BL scheme is recommended for January in the NCP region, especially for Beijing, and the MYJ scheme is better for the other 3 months. The ACM2 scheme would be a good match for the YRD region, where the simulation differences between the four schemes are small. The topography of the SB region is more complex, but for most of the areas in the basin, the MYJ scheme is proposed, and if more stations outside the basin are involved, the BL scheme is recommended. The MYJ scheme is applied to the PRD region in January and April, and the BL scheme in July and October. The MYJ scheme is counseled for the NS region. The second focus is the wind field. The YSU scheme is recommended if the main concern is the near-surface layer, and the BL scheme is suggested if focusing on the variation in the vertical direction. The final evaluation of the parameterization scheme and uncertainties will lay the foundation for the improvement of the modules and forecasting of the GRAPES_CUACE regional model developed independently in China.

Two Random Forest Models for the Non‐Iterative Parametrization of Surface‐Layer Turbulent Fluxes

AbstractThis study investigated two random forest (RF) models for the non‐iterative parametrization of surface‐layer turbulent fluxes: (a) the RF scheme, a calculation model that is directly trained using correlated variables, and (b) the RF_Li10 scheme, a random forest correction model based on the Li10 scheme (Li et al., 2010, https://doi.org/10.1007/s10546-010-9523-y). A comparison between these two new models and the Li10 scheme against an iterative scheme revealed the hierarchy of maximum relative errors in estimating stability parameters, as well as momentum and heat transfer coefficients. This hierarchy is as follows: the Li10 scheme is the greatest, followed by the RF scheme, with the RF_Li10 scheme exhibiting the least errors.

Experimental and calculation investigations of hydrodynamics and heat exchange in liquid metal turbulent flows in fast reactor fuel assemblies

The formation of velocity and temperature fields in the fuel assemblies of fast reactor core occurs under the influence various factors. It is shown, that the most important factors include a complex multiply connected geometry, subject to deformation during the campaign under the influence of temperature non-uniformity and radiation effects. The results of studies of the velocity fields and shear stress, turbulence microstructure are presented. An intensification of turbulent momentum transfer in channels in azimuthal and radial directions in the area of gaps between the rods is demonstrated. The performed analysis is indicate that there are a significant difference between the experimental dependences for turbulent momentum transfer coefficients in the radial and azimuthal directions and calculated within the framework of semi-empirical models of turbulent momentum transfer as well as the anisotropy coefficients of the turbulent momentum transfer in rod bundles. The results of benchmark on the fuel assembly thermohydraulics showed that the common commercial codes describe experimental data only approximately. It is shown, that the intensification of turbulent momentum transfer in the channels of rod bundles is due to the appearance of large-scale turbulent momentum transfer (secondary flows). The contribution of large-scale turbulent momentum transfer to the turbulent momentum transfer coefficients in the channels of rod bundles is calculated. The dependence for coefficient of inter-channel turbulent exchange of momentum is obtained and the intensification of inter-channel turbulent exchange in close-packed rod lattices is explained. A dependence for the dissimilarity coefficients of forced inter-channel convective exchange of momentum and mass, as well as energy and mass in rod bundles spaced by wire winding is obtained. The calculation methods and the numerical modeling results for temperature regime of fuel assemblies with randomly distributed initial parameters by the Monte Carlo method are presented as well as the thermomechanical analysis of the temperature field in the fuel assemblies during the campaign. An idea about the equilibrium configuration of a rod bundle in a hexagonal jacket during irradiation, the stress–strain state of an individual fuel rod and a fuel assembly jacket is obtained. The tasks of further investigations discussed.

Effects of projectile parameters on the momentum transfer and projectile melting during hypervelocity impact

The effects of projectile/target impedance matching and projectile shape on energy, momentum transfer and projectile melting during collisions are investigated by numerical simulation. By comparing the computation results with the experimental results, the correctness of the calculation and the statistical method of momentum transfer coefficient is verified. Different shapes of aluminum, copper and heavy tungsten alloy projectiles striking aluminum, basalt, and pumice target for impacts up to 10 km/s are simulated. The influence mechanism of the shape of the projectile and projectile/target density on the momentum transfer was obtained. With an increase in projectile density and length-diameter ratio, the energy transfer time between the projectile and targets is prolonged. The projectile decelerates slowly, resulting in a larger cratering depth. The energy consumed by the projectile in the excavation stage increased, resulting in lower mass-velocity of ejecta and momentum transfer coefficient. The numerical simulation results demonstrated that for different projectile/target combinations, the higher the wave impedance of the projectile, the higher the initial phase transition velocity and the smaller the mass of phase transition. The results can provide theoretical guidance for kinetic impactor design and material selection.

Parameterization and Remote Sensing Retrieval of Land Surface Processes in the Gurbantunggut Desert, China

The exchange of energy between the land surface and atmosphere is dependent upon crucial parameters, including surface roughness, emissivity, bulk transfer coefficients for momentum (CD) and heat (CH). These parameters are calculated through site observation data and remote sensing data. The following conclusions are drawn: (1) the aerodynamic roughness of the Gurbantunggut Desert measures 1.1 × 10−2 m, which is influenced by the varying conditions of the underlying surface. The roughness decreases as wind speed increases and is seen to be directly proportional to the growth of vegetation. From April to June, the aerodynamic roughness increases with increasing vegetation cover, but begins to gradually decrease after July. Spatially, the middle regions show higher roughness values than the eastern and western areas. In the central part of the desert, the roughness is between 2.37 × 10−2 m and 2.46 × 10−2 m from April to November. The northwest and northeast regions measure 1.41 × 10−2 m–2.04 × 10−2 m and 1.53 × 10−2 m–2.39 × 10−2 m, respectively. (2) The surface emissivity is 0.93, and it varies depending on the snow and vegetation present in the underlying area. (3) CD and CH exhibit an inverse relationship with wind speed. When wind speed falls below 6 m/s, the CD declines rapidly as wind speed increases. In contrast, once wind speed surpasses 6 m/s, the propensity for the CD to decrease with increasing wind speed slows down and approaches stability.

Polyimide degradation under atomic oxygen attack

Procedures are developed for accelerated laboratory tests of spacecraft polymers for resistance to long-term exposure to hyperthermal atomic oxygen (AO) with the use of high-energy AO ions of a rarefied plasma and Kapton-H polyimide as the reference material. The parameters that characterize physico-chemical, thermo-optical, and aerodynamic AO – Kapton-H interaction (surface roughness, solar absorptance, and normal infrared emittance) are determined at different values of the AO fluence. To do this, use was made of the data of tests onboard spacecraft in the Earth's atmosphere and the authors and others' laboratory tests. The normal and the tangential momentum transfer coefficient and the energy transfer coefficient are reported as a function of the AO bombardment angle. The obtained data on the AO-induced degradation of the parameters that characterize AO–polyimide dynamic interaction allow one to predict the behavior of the polyimide thermo-optical and aerodynamic properties during a long-term service in the Earth's upper atmosphere and ionosphere.

ONSET OF DARCY-BRINKMAN CONVECTION IN A ROTATING BIDISPERSIVE POROUS MEDIUM

The onset of Darcy-Brinkman convection in a rotating bidispersive porous layer is studied for different boundary configurations. Rotating bidispersive porous layer manifests in many applications such as food and chemical processes, rotating machinery, the petroleum industry, solidification and centrifugal casting of metals, biomechanics, and geophysical problems. Three types of boundary configurations are considered, namely rigid-rigid, rigid-free, and free-free boundaries. The fluid motion is characterized using the Brinkman-Darcy equation with a single temperature in macro and micro phases. The linear stability theory is used, and the obtained eigenvalue problem is addressed analytically for the free-free boundary conditions. The eigenvalue problems for the rigid-rigid and rigid-free boundaries are solved numerically. The effects of the Taylor number, momentum transfer coefficient, permeability ratio, Darcy number, and porosity ratio on the system's stability are graphically explored. The Darcy number, permeability ratio, and Taylor number are found to have a stabilizing influence on the system. Further, it is found that the momentum transfer coefficient shows destabilizing effect. The porosity ratio is found to have a stabilizing impact on the system.

A Package of Momentum and Heat Transfer Coefficients for the Stable Surface Layer Extended by New Coefficients over Sea Ice

The bulk transfer coefficients of momentum, heat, and humidity belong to the main ingredients of numerical weather prediction and climate models. They are needed for the calculation of turbulent fluxes in the surface layer and often rely on the Monin–Obukhov similarity theory requiring universal stability functions. The problem of a derivation of transfer coefficients based on different stability functions has been considered by many researchers over the years but it remains to this day. In this work, dedicated to the memory of S.S. Zilitinkevich, we also address this task, and obtain transfer coefficients from three pairs of theoretically derived stability functions suggested by Zilitinkevich and co-authors for stable conditios. Additionally, we construct non-iterative parametrizations of these transfer coefficients based on earlier work. Results are compared with state-of-the-art coefficients for land, ocean, and sea ice. The combined parametrizations form a package in a universal framework relying on a semi-analytical solution of the Monin-Obukhov similarity theory equations. A comparison with data of the Surface Heat Budget of the Arctic Ocean campaign (SHEBA) over sea ice reveals large differences between the coefficients for land conditions and the measurements over sea ice. However, two schemes of Zilitinkevich and co-authors show, after slight modification, good agreement with SHEBA although they had not been especially developed for sea ice. One pair of the modified transfer coefficients is superior and is compatible to earlier SHEBA-based parametrizations. Finally, an algorithm for practical use of all transfer coefficients in climate models is given.

Ship-based estimates of momentum transfer coefficient over sea ice and recommendations for its parameterization

Abstract. A major source of uncertainty in both climate projections and seasonal forecasting of sea ice is inadequate representation of surface–atmosphere exchange processes. The observations needed to improve understanding and reduce uncertainty in surface exchange parameterizations are challenging to make and rare. Here we present a large dataset of ship-based measurements of surface momentum exchange (surface drag) in the vicinity of sea ice from the Arctic Clouds in Summer Experiment (ACSE) in July–October 2014, and the Arctic Ocean 2016 experiment (AO2016) in August–September 2016. The combined dataset provides an extensive record of momentum flux over a wide range of surface conditions spanning the late summer melt and early autumn freeze-up periods, and a wide range of atmospheric stabilities. Surface exchange coefficients are estimated from in situ eddy covariance measurements. The local sea-ice fraction is determined via automated processing of imagery from ship-mounted cameras. The surface drag coefficient, CD10n, peaks at local ice fractions of 0.6–0.8, consistent with both recent aircraft-based observations and theory. Two state-of-the-art parameterizations have been tuned to our observations, with both providing excellent fits to the measurements.

7 February Chamoli (Uttarakhand, India) Rock-Ice Avalanche Disaster: Model-Simulated Prevailing Meteorological Conditions

The present study aims to analyze the high-resolution model-simulated meteorological conditions during the Chamoli rock-ice avalanche event, which occurred on 7 February 2021 in the Chamoli district of Uttarakhand, India (30.37° N, 79.73° E). The Weather Research and Forecasting (WRF) model is used to simulate the spatiotemporal distribution of meteorological variables pre- and post-event. The numerical simulations are carried out over two fine resolution nested model domains covering the Uttarakhand region over a period of 2 weeks (2 February to 13 February 2021). The model-simulated meteorological variables, e.g., air temperature, surface temperature, turbulent heat flux, radiative fluxes, heat and momentum transfer coefficients, specific humidity and upper wind patterns, were found to show significant departures from their usual patterns starting from 72 h until a few hours before the rock-ice avalanche event. The average 2 m air and surface temperatures near the avalanche site during the 48 h before the event were found to be much lower than the average temperatures post-event. In-situ observations and the ERA5-Land dataset also confirm these findings. The total turbulent heat flux mostly remained downward (negative) in the 72 h before the event and was found to have an exceptionally large negative value a few hours before the rock-ice avalanche event. The model-simulated rainfall and Global Precipitation Measurement (GPM, IMERG)-derived rainfall suggest that the part of the Himalayan region falling in the simulation domain received a significant amount of rainfall on 4 February, around 48 h prior to the event, while the rest of the days pre- and post-event were mostly dry. The results presented here might be helpful in further studies to identify the possible trigger factors of this event.

Mathematical model of supersonic jet centerline velocity for multi-nozzle oxygen lance

The supersonic jet characteristics of multi-nozzle oxygen lance are the key to the quality of converter steelmaking. It is of great significance to clarify the velocity distribution characteristics of multi nozzle jet centerline to guide the production practice of converter steelmaking. Taking the oxygen lance for 260 t converter as the object, a three-dimensional geometric model is established to study the distribution characteristics of jet centerline velocity under different Mach number and inclination. The synergistic effect of Mach number and orifice inclination on jet attenuation is mainly studied. The mathematical expressions of jet deflection, Mach number and jet inclination are established, the calculation method of jet centerline deviation is proposed, and the previous mathematical model of jet centerline velocity is improved. The results show that the momentum transfer coefficient Kj of multi-nozzle oxygen lance is not only related to Mach number, but also affected by jet inclination. The deviation between the corrected mathematical model and the field measured results is 4.3%.

CFD simulation of continuous non-catalytic gas–solid reaction with uniform particle size distribution

Non-catalytic fluidized bed reactors (FBRs) have been utilized in various industries. In this study, a computational fluid dynamics (CFD) model, involving a combination of transport processes, intrinsic kinetics, and flow structure, is established and validated to investigate the continuous gas–solid reaction. The simulated results indicate that the solid conversion rate is determined by the solid reaction rate and the mass flow rate. Traditional interphase transfer models have been proven to overestimate the momentum and mass transfer coefficients, and cause deviations in the predicted results. The gas–solid reaction rate, obtained from the structure-based model, depends on reaction time and bed position owing to the variations in the overall reaction rate constant and the non-uniform gas–solid flow structure. The period longer than twice the time required for complete conversion of particle has little effect on the solid conversion process, because of the higher internal diffusion resistance and the wider residence time distribution of particles. The mass transfer during the bubble phase also contributes to the reaction process. Therefore, this study provides a methodology for the CFD simulation of continuous non-catalytic FBRs.

Sensitivity to changes in the surface‐layer turbulence parameterization for stable conditions in winter: A case study with a regional climate model over the Arctic

AbstractThe modeling of the atmospheric boundary layer over sea ice is still challenging because of the complex interaction between clouds, radiation and turbulence over the often inhomogeneous sea ice cover. There is still much uncertainty concerning sea ice roughness, near‐surface thermal stability and related processes, and their accurate parameterization. Here, a regional Arctic climate model forced by ERA‐Interim data was used to test the sensitivity of climate simulations to a modified surface flux parameterization for wintertime conditions over the Arctic. The reference parameterization as well as the modified one is based on Monin–Obukhov similarity theory, but different roughness lengths were prescribed and the stability dependence of the transfer coefficients for momentum, heat and moisture differed from each other. The modified parameterization accounts for the most comprehensive observations that are presently available over sea ice in the inner Arctic. Independent of the parameterization used, the model was able to reproduce the two observed dominant winter states with respect to cloud cover and longwave radiation. A stepwise use of the different parameterization assumptions showed that modifications of both surface roughness and stability dependence had a considerable impact on quantities such as air pressure, wind and near‐surface turbulent fluxes. However, the reduction of surface roughness to values agreeing with those observed during the Surface Heat Budget of the Arctic Ocean campaign led to an improvement in the western Arctic, while the modified stability parameterization had only a minor impact. The latter could be traced back to the model's underestimation of the strength of stability over sea ice. Future work should concentrate on possible reasons for this underestimation and on the question of generality of the results for other climate models.

A Universal Approach for the Non‐Iterative Parametrization of Near‐Surface Turbulent Fluxes in Climate and Weather Prediction Models

AbstractWeather prediction and climate simulations need reliable parameterizations of turbulent fluxes in the stable surface layer. Especially in these conditions, the uncertainties of such parametrizations are still large. Most of them rely on the Monin‐Obukhov similarity theory (MOST), for which universal stability functions (SFs) represent important ingredients. The SFs are nonlinear, if so, a numerical iteration of the MOST equations is required. Moreover, presently available SFs are significantly different at large stability. To simplify the calculations, a non‐iterative parametrization of fluxes is derived and corresponding bulk transfer coefficients for momentum and heat for a package of five pairs of state‐of‐the‐art SFs are proposed. For the first time, a parametrization of the related transfer coefficients is derived in a universal framework for all package members. The new parametrizations provide a basis for a cheap systematic study of the impact of surface layer turbulent fluxes in weather prediction and climate models.

ГИДРОДИНАМИКА ТУРБУЛЕНТНЫХ ПОТОКОВ В ТВС БЫСТРЫХ РЕАКТОРОВ (ПОЛЕ СКОРОСТИ И МИКРОСТРУКТУРА ТУРБУЛЕНТНОСТИ)

The article describes the factors under the influence of which the formation of thermohydraulic characteristics occurs in the fuel assemblies of the core of fast reactors with liquid metal cooling. It is shown that one of the most important factors is a complex multiply connected geometry of a stochastic nature, subject to deformation during the campaign under the influence of temperature irregularities and radiation effects. The paper presents and analyzes the results of experimental and computational studies of the velocity field and shear stress, the microstructure of turbulence, momentum transfer in the central and peripheral regions of fuel assemblies without and with displacers, as well as in the case of deformation of the lattice of rods. The intensification of turbulent momentum transfer in the channels in the azimuthal direction in the area of the gaps between the rods is demonstrated. The anisotropy coefficient of turbulent momentum transfer reaches 30-40 units. The performed analysis indicated a significant difference in the calculated in the framework of semi-empirical models of turbulent transfer and experimental dependences of the coefficients of turbulent transfer of momentum in the radial and azimuthal directions and the coefficients of anisotropy of turbulent transfer of momentum in rod bundles. The results of an open benchmark on the thermohydraulics of fuel assemblies showed that common commercial computational thermohydraulic codes only approximately describe the experimental data. It is shown that the intensification of turbulent momentum transfer in the channels of rod assemblies is due to the appearance of large-scale turbulent momentum transfer (secondary flows). The contribution of large-scale turbulent momentum transfer to the kinetic energy of turbulent pulsations, azimuthal turbulent shear stresses, and turbulent momentum transfer coefficients in rod assemblies is calculated. An empirical dependence of the coefficient of interchannel turbulent impulse exchange in bundles of smooth rods is obtained, on the basis of a semi-empirical model, data on interchannel turbulent impulse exchange in assemblies of smooth rods are generalized, and the intensification of interchannel turbulent exchange in close lattices of rods is explained. Data on hydraulic resistance in bundles of smooth rods are analyzed. The tasks of further research are discussed.

Relationship Between Pressure Drop and Heat Transfer of Fully Developed Flow in Smooth Horizontal Circular Tubes and Spiral-Coiled Tubes in the Laminar Flow Regime

Abstract Studies on isothermal steady-state frictional pressure drop for flow of petroleum base oils SN70, SN150, diesel, and water are carried out in spiral coils with diameter to length ratio, 0.00042, 0.00047, 0.00073, 0.00164, 0.00189, 0.003, and 0.0037. An attempt is made to correlate friction factors with a better and more appropriate dimensionless group for flow of Newtonian fluids through spiral-coiled tubes. An innovative approach of correlating heat transfer data with the newly established dimensionless group is presented. Heat transfer experiments are performed for spiral coils with diameter to length ratio 0.000474, 0.00042, 0.001896, 0.00198, 0.000942, and 0.00164 in laminar flow regime. Suitable correlations for friction factors and Nusselt numbers are proposed. Relationship between pressure drop and heat transfer is studied. The incapability of the conventional analogy equations to estimate the heat and momentum transfer coefficients for laminar flow through straight or curved tubes is explained based on the viscous and form drag existing in straight and curved pipe flow. The limitations of the existing analogy equations are examined critically. A new general analogy equation is derived for laminar flow through spiral and straight tubes considering the influencing geometrical parameters of the tube.

Uncertainty in the Parameterization of Surface Fluxes under Unstable Conditions

AbstractIn this study, an attempt has been made to analyze the possible uncertainties in the parameterization of surface fluxes associated with the form of non-dimensional wind and temperature profile functions used in weather and climate models under convective conditions within the framework of Monin-Obukhov similarity theory (MOST). For this purpose, these functions, which are commonly known as similarity functions, are classified into four categories based on the resemblance in their functional behaviour. The bulk flux algorithm is used for the estimation of transfer coefficients of momentum and heat using four different classes of similarity functions. Uncertainty in the estimated values of fluxes is presented in the form of deviation in the predicted values of momentum and heat transfer coefficients and their variation with the Monin-Obukhov stability parameter. The analysis suggests that a large deviation in the values of estimated fluxes might occur if different forms of similarity functions are utilized for the estimation of surface fluxes. Recommendations are made for the form of similarity function for momentum based on the analysis of one year-long turbulence observations over an Indian region. The study suggests that there is a distinct need to carry out a careful analysis of turbulence data in free convective conditions for determining a consistent functional form of the similarity functions to be utilized in the atmospheric models universally.