Flow In Round Tubes Research Articles

Modeling local interfacial area concentration for adiabatic and boiling bubbly flows

Bubbly flows appear in various heat and mass transfer systems, and interfacial area concentration (IAC) is a critical geometrical parameter for the flows. The fidelity of accurately computed IACs is essential for reliable three-dimensional computational fluid dynamics analyses of bubbly flows because the IACs directly affect the interfacial force and interfacial heat and mass transfer rates. This study targeted development of a simple and robust model for predicting the local IAC under steady-state bubbly flows with and without phase change. The dependent two-phase flow parameters of the IAC were derived by considering bubble coalescence and breakup rates. The IAC transport equation simplified under steady-state conditions was used for this purpose. A simplified turbulence model was introduced to formulate the energy dissipation rate per unit mass necessary for computing the bubble coalescence and breakup rates. The prediction accuracy of the local IAC model for bubbly flow conditions with area-average void fraction values less than 10 % was estimated to be 20 % based on 803 local data collected for adiabatic air–water bubbly flows in round tubes with diameters ranging from 9.0 to 200 mm. The model was also applied to predict the local IAC data of subcooled boiling flows in heated channels with hydraulic diameters ranging from 18.5 to 22.2 mm. The test conditions covered pressures from 0.1 to 1.46 MPa. The model prediction accuracy for bubbly flow conditions with area-average void fraction values less than 10 % was estimated to be 40 % based on 155 subcooled boiling flow data.

Development of correlation for critical heat flux for vertically downward two-phase flows in round tubes

ABSTRACT Critical Heat Flux (CHF) is one of the catastrophic failure modes encountered in two-phase flows in nuclear, chemical, and power industries. Considerable research was carried on CHF in last few decades in horizontal, inclined, and vertically upward flows. Only limited information, mostly at atmospheric pressure conditions and including CHF enhancers like inlet throttling, was available on CHF in vertical pipes with flow directed downwards. The complexity associated with vertically downward two-phase flows, due to flow instabilities and premature tube burnout, dictates for stringent design considerations, especially, from CHF perspective. As a result, accurate estimation of CHF is a requirement not only from performance, but also more significantly from safety perspective. The objective of this paper is to develop a correlation for CHF in vertical tubes in which the fluid flow was directed downward. As part of these investigations, a versatile test rig was designed and developed. Experiments were conducted in the pressure range of 1 to 5 bar and a CHF correlation is proposed as a function of inlet fluid temperature, mass flux and pressure in the absence of inlet throttling or other similar effects. The new correlation developed agrees well with the data from current experiments with a mean deviation of 13.87% and standard deviation of 18.71%. The uncertainty analysis revealed a 90% confidence level on the CHF estimate due to variation in the input variables.

Modeling of Incompressible Fluid Flows in a Round Tube in Laminar, Transient, and Turbulent Regimes using the Conv-3d Code

The results of using the CONV-3D code to model incompressible fluid flows in round tubes in laminar, transient, and turbulent regimes are presented. The results of modeling with different Reynolds numbers are compared with the Poiseuille parabola and the Blasius formula. It is shown that the code satisfactorily models the flow of an incompressible fluid in laminar, transient, and turbulent regimes and can be used to analyze such flows in different applications.

A Historical Misperception on Calculating the Average Convection Coefficient in Tubes With Constant Wall Heat Flux

The historical approach to averaging the convection coefficient in tubes of constant wall heat flux leads to quantitative errors in short tubes as high as 12.5% for convection into fully developed flows and 33.3% for convection into hydrodynamically developing flows. This mistake can be found in teaching texts and monographs on heat transfer, as well as in major handbooks. Using the correctly defined relationship between local and average convection coefficients, eight new correlations are presented for fully developed and developing flows in round tubes and between parallel plates for the constant wall heat flux condition. These new correlations are within 2% of exact solutions for fully developed flows and within 6% of first principle calculations for hydrodynamically developing flows.

Heat transfer and hydraulic resistance of supercritical-pressure coolants. Part II: Experimental data on hydraulic resistance and averaged turbulent flow structure of supercritical pressure fluids during heating in round tubes under normal and deteriorated heat transfer conditions

Methodological basis and results from the experimental studies on hydraulic and friction resistances under turbulent supercritical-pressure (SCP) fluids flow in round tubes under adiabatic and heating conditions are presented. The experimental technique and results from sounding studies of the averaged turbulent SCP fluids flow under normal and deteriorated heat transfer conditions are given. The possible sources of large errors in hydraulic resistance calculations, when using one-dimensional (homogeneous) flow model, are pointed out. The interdependence between the heat transfer deterioration and significant changes in the averaged flow structure due to fluid thermal acceleration and Archimedes forces effects is analyzed.

Decaying swirl flow in round tubes with short-length twisted tapes

This paper presents experimental and numerical results of the local heat transfer coefficient and flow characteristics of decaying turbulent swirl flow generated by short-length twisted tapes (STs). The STs with three different twist ratios (y/W=3, 4 and 5) were applied at the entrance of the test section. The experiments were conducted under uniform heat flux conditions for water flow rates in the range of 5200≤Re≤15,300. The results of the tube without swirl generator as well as the ones with full-length twisted tape (TTs) are also reported as the reference cases. The experimental results reveal that the tube with STs consistently yields higher local Nusselt number than that the one without swirl generator. The local Nusselt numbers decrease with increasing axial distance (x/D) due to the decaying effect. Although, STs consistently provide poorer heat transfer than TTs over the range studied, the STs with y/W=4 and 5 yield superior thermal performance factors to the TTs at the same twist ratios, for Reynolds numbers beyond 10,000 due to the prominent effect of heat transfer improvement over that of the increase of friction factor. For better understanding, the visualization of flow structure (pathline and vector plot) in the tubes with STs is also presented.

Correlation for Flow Boiling Critical Heat Flux in Thin Rectangular Channels

The effect of heated length on critical heat flux (CHF) in thin rectangular channels under atmospheric pressure has been studied. CHF in small channels has been widely studied in the last decades but most of the studies are based on flow in round tubes and number of studies focused on rectangular channels is relatively small. Although basic triggering mechanisms, which lead to CHF in thin rectangular channels, are similar to that of tubes, applicability of thermal hydraulic correlations developed for tubes to rectangular channels are questionable since heat transfer in rectangular channels are affected by the existence of nonheated walls and the noncircular geometry of channel circumference. Several studies of CHF in thin rectangular channels have been reported in relation to thermal hydraulic design of research reactors and neutron source targets and correlations have been proposed, but the studies mostly focus on geometrical conditions of the application of interest and therefore effect of channel parameters exceeding their interest is not fully understood. In his study, CHF data for thin rectangular channels have been collected from previous studies and the effect of heated length on CHF was examined. Existing correlations were verified with data with positive quality outlet flow but none of the correlations successfully reproduced the data for a wide range of heated lengths. A new CHF correlation for quality region applicable to a wide range of heated lengths has been developed based on the collected data.

A complex but accurate correlation for predicting critical heat flux in a round tube for low and medium pressures under circumferentially non-uniform heating conditions

This paper presents an empirical correlation for predicting the critical heat flux (CHF) of vertical, upward, steam–water flows in round tubes for low and medium pressures under circumferentially non-uniform heating conditions. This correlation is based on experiments carried out with test sections having an inner diameter of 22mm and heated lengths ranging from 1.8 to 3.5m. The ratios between the maximum and the minimum heat fluxes were 1.0, 4.7 and 8.3. The experiments were carried out for outlet pressures and mass fluxes ranging from 10 to 40bar and 300 to 1600kgm−2s−1, respectively. The root mean square error of predicted CHF values by using the proposed correlation and applying the heat balance method is 3.7%.

Modélisation dynamique des structures d’interface via l’équation de transport de l’interface

The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes.

Development of One-Group and Two-Group Interfacial Area Transport Equation

A dynamic approach employing the interfacial area transport equation is presented to replace the static flow regime dependent correlations for the interfacial area concentration. The current study derives the transport equations for the bubble number, volume, and interfacial area concentration. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, both one-group and two-group interfacial area transport equations are developed along with the necessary constitutive relations. The framework for the complicated source and sink terms in the two-group transport equation is also presented by identifying the major intragroup and intergroup bubble interaction mechanisms. In view of evaluating the theoretical model, the one-group interfacial area transport equation is benchmarked based on the available data obtained in a wide range of air-water bubbly flow in round tubes of various diameters. In general, the results show good agreement within the measurement error of ±10%.

Flow regime transition criteria for upward two-phase flow in vertical narrow rectangular channels

In relation to the cooling system of high performance microelectronics, a high power research reactor with plate type fuels and plasma facing components of a fusion reactor, study of two-phase flow in a narrow rectangular channel has been paid considerable attention, recently. For the two-fluid model, direct geometrical parameters such as the void fraction should be used in flow-regime criteria. From this point of view, flow-regime transition criteria for vertical upward flows in narrow rectangular channels have been developed considering the mechanisms of flow-regime transitions. The basic concept of the present modeling followed the Mishima and Ishii model for vertical upward two-phase flows in round tubes. Newly developed criteria have been compared with the existing experimental data for air–water flows in narrow rectangular channels with the gaps of 0.3–17 mm. The present criteria showed satisfactory agreements with those data. Further comparisons with data for steam–water in a rectangular channel at relatively high system pressures have been made. The results confirmed that the present flow-regime transition criteria could be applied over wide ranges of parameters as well as to boiling flow.

Approximate method for measurement of phase-distribution in multiphase materials with small neutrondashattenuation using a neutron beam as a probe

Abstract An approximate method for the quantification of a neutron radiography image was proposed for measuring the phase-distribution of multiphase materials with small neutrondashattenuation. Since it is not necessary for this method to put a standard calibration sample in a field of a view, this method has an advantage of measuring the phase-distribution of multiphase materials with unknown internal-structure and neutrondashattenuation in the object in an enlarged field of view. Although its application is limited to an object with small neutrondashattenuation, it was revealed from a numerical analysis that the approximate method can be applicable to heavy water, liquid sodium andliquid potassium, which are important materials in relation to research on the thermalhydraulics of the nuclear reactor. The validity of the approximate method was also confirmed experimentally by comparing the void fraction of air-water flows in round tubes measured by the approximate method with those by the other more-accurate method.

Theoretically Based Correlating Equations for the Local Characteristics of Fully Turbulent Flow in Round Tubes and between Parallel Plates

Comprehensive correlating equations that incorporate all of the known theoretical structure, namely, the asymptotic behavior near the wall, the asymptotic behavior near the center line, and the speculative intermediate behavior, have been devised for the local time-averaged velocity and the local time-averaged turbulent shear stress in smooth round tubes. These expressions are postulated to apply directly for parallel plates on the basis of the analogy of MacLeod. The expression for the local time-averaged velocity for smooth surfaces is extended for naturally rough surfaces on the basis of the analogy of Colebrook for the friction factor, while that for the local turbulent shear stress is directly applicable without modification. Separate correlating equations for the time-averaged velocity and the turbulent shear stress are suggested on grounds of convenience and accuracy despite the one-to-one correspondence of these quantities. Correlating equations for the eddy viscosity and the mixing length follow directly but are shown to be redundant

Improved Correlating Equations for the Friction Factor for Fully Turbulent Flow in Round Tubes and between Identical Parallel Plates, both Smooth and Naturally Rough

Mixed-mean velocities were computed by numerical integration using a comprehensive correlating equation for the velocity distribution, and independently using a corresponding correlating equation for the local turbulent shear stress. As contrasted with earlier analytical integrations for grossly simplified velocity distributions, these calculations take into account the effects of the boundary layer near the wall and the wake in the central region. The resulting sets of numerical values for the mixed-mean velocity are correlated almost exactly in terms of equations with a theoretically derived structure. On the basis of the generally overlooked analogy of MacLeod, the same distributions for the velocity and the turbulent shear stress are used for both round tubes and parallel plates, but of course, the expressions for the mixed-mean velocity differ because of the different areas of integration. The analysis reveals inter alia that the hydraulic-diameter and laminar-equivalent-diameter concepts are fundamentally unsound. The correlating equations for the mixed-mean velocity are extended for the transition engendered by naturally rough surfaces using the speculation of Colebrook, and are reexpressed directly in terms of the friction factor and the Reynolds number for convenience

New and overlooked relationships for turbulent flow in channels

AbstractThis paper describes general, asymptotic and speculative relationships which can be deduced directly from the time‐averaged form of the basic, partial‐differential model for the conservation of mass and momentum in fully developed turbulent flow of constant‐property fluids through round and parallel‐plate channels. Such relationship are shown to provide insight as well as useful forms for correlation. Several analogies for flow in round tubes and between parallel plates which have generally been overlooked are reexamined and extended. A generally overlooked anomaly which occurs for flow in concentric, circular annuli, for flow between plates of non‐identical roughness, and for the combination of forced and wall‐Ind.uced flow between parallel plates is also is noted. The data needed to test the above analogies and to quantify the deviations, if any identified, as well as those needed to generalize the anomalous behavior.

Viscous flows: the practical use of theory

Part 1 One-dimensional laminar flows: momentum transfer viscosity and shear stress Newtonian flow between parallel plates Newtonian flow in round tubes and circular annuli forced flow on non-Newtonian fluids through channels thin films and other open, gravitational flows Couette flows. Part 2 The general equations of motion: derivation of the general mass and force-momentum balances modified forms of the general mass and force-momentum balances exact, closed-form solutions of the equations of motion the Blasius solution for laminar flow along a flat surface integral boundary layer solution for laminar flow along a flat surface experimental results and extended solutions for laminar flow along a flat surface laminar flow over wedges and discs, circular cylinders and solid spheres the motion of bubbles and droplets generalized methods and other geometrics. Part 3 Flow relative to dispersed solids: flow through porous media the relative motion of fluids and dispersed solids.

Two-phase hydrodynamic experiments with axial flow through seven-rod clusters

Hydrodynamic experiments have been carried out with upflow of air-water mixtures through vertical seven-rod clusters at atmospheric pressure. Results obtained from measurements of flow characteristics, including pressure drops, local velocity and voidage distribution, are discussed in terms of relations developed for two-phase flow in round tubes. Effects on the flow characteristics of spacer elements and bowing of a cluster are also discussed.

Concentration build-up in reverse osmosis in turbulent flow

The paper considers reverse osmosis in turbulent flow in round tubes. The problem of concentration build-up at the membrane surface in the mass-transfer entry length in fully developed turbulent flow is formulated, taking into account incomplete salt rejection at the membrane and axial variation of the osmotic pressure. The concentration boundary layer development is calculated numerically for representative values of the governing parameters. A limiting closed-form similarity solution is also presented and is used together with known results for the fully developed concentration profile to derive an approximate expression for the development length. It is suggested that the results be applied to the design of turbulence promoters for reverse osmosis systems.

Effect of Large Temperature Gradients on Convective Heat Transfer: The Downstream Region

The results of an experimental investigation of the frictional and heat transfer effects in air, nitrogen, and helium in steady, turbulent flow in round tubes are presented. Wall-to-bulk temperature ratios extend from near unity to 2.5, entering Reynolds numbers from 15,000 to 233,000. Dependence of the thermodynamic and transport properties on temperature is shown to be significant in both heat transfer and wall friction and is reflected in the empirical correlations for local and average coefficients which are developed. The results of other investigators who have analyzed or measured variable properties effects are recalculated where necessary to facilitate comparisons.

A Model for Correlating Two-Phase, Steam-Water, Burnout Heat-Transfer Fluxes

A simplified model for spray-annular flow in round tubes and rectangular channels and its use for the prediction of the maximum heat fluxes for steam- water flows is described. The data are for upward flow at 2000 psia for uniform and heat fluxes. The model is successfully applied to both uniform and nonuniform or hot-patch heat-flux tests. Burnout flux versus flow rate data obtained for uniform heat flux for a given iniet subcooling are sufficient for the evaluation of the characteristic parameters needed in the burnout model. Comparisons of predicted and experimental values of the bumout heat flux are encouraging, including 2 to 1 hot-patch tests. Further, the predictions for the 1.3 to 1 hot-patch tests are in accord with the experimental data that the hot- patch effectiveness is approximately zero. (N.W.R.)