scholarly journals Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

2018 ◽  
Vol 8 (11) ◽  
pp. 2036 ◽  
Author(s):  
Dejan Brkić ◽  
Pavel Praks
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Pipe Flow ◽  
Flow Regimes ◽  
Hydraulic Model ◽  
Friction Model ◽  
Newtonian Fluids ◽  
Turbulent Regime ◽  
Flow Friction ◽  
Switching Functions

This paper provides a new unified formula for Newtonian fluids valid for all pipe flow regimes from laminar to fully rough turbulent flow. This includes laminar flow; the unstable sharp jump from laminar to turbulent flow; and all types of turbulent regimes, including the smooth turbulent regime, the partial non-fully developed turbulent regime, and the fully developed rough turbulent regime. The new unified formula follows the inflectional form of curves suggested in Nikuradse’s experiment rather than the monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula uses switching functions and interchangeable formulas for the laminar, smooth turbulent, and fully rough turbulent flow regimes. Thus, the formulation presented below represents a coherent hydraulic model suitable for engineering use. This new flow friction model is more flexible than existing literature models and provides smooth and computationally cheap transitions between hydraulic regimes.

scholarly journals Unified Friction Formulation from Laminar to Fully Rough Turbulent Flow

2018 ◽  
Author(s):  
Dejan Brkić ◽  
Pavel Praks
Keyword(s):  
Turbulent Flow ◽  
Pipe Flow ◽  
Flow Regimes ◽  
Hydraulic Model ◽  
Newtonian Fluids ◽  
Turbulent Regime ◽  
Switching Functions

This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent regimes: smooth turbulent regime, partial non-fully developed turbulent and fully developed rough turbulent regime. The formula follows the inflectional form of curves as suggested in Nikuradse’s experiment rather than monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula consists of switching functions and of the interchangeable formulas for laminar, smooth turbulent and fully rough turbulent flow. The proposed switching functions provide a smooth and a computationally cheap transition among hydraulic regimes. Thus, the here presented formulation represents a coherent hydraulic model suitable for engineering use. The model is compared to existing literature models, and shows smooth and computationally cheap transitions among hydraulic regimes.

Effects of Roughness on Turbulent Flow in Microchannels and Minichannels

2008 ◽  
Author(s):  
Timothy P. Brackbill ◽  
Satish G. Kandlikar
Keyword(s):  
Experimental Study ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Roughness Parameter ◽  
Reynolds Numbers ◽  
Turbulent Regime ◽  
Roughness Effects ◽  
Relative Roughness ◽  
Roughness Elements ◽  
Moody Diagram

The effect of roughness ranging from smooth to 24% relative roughness on laminar flow has been examined in previous works by the authors. It was shown that using a constricted parameter, εFP, the laminar results were predicted well in the roughened channels ([1],[2],[3]). For the turbulent regime, Kandlikar et al. [1] proposed a modified Moody diagram by using the same set of constricted parameters, and using the modification of the Colebrook equation. A new roughness parameter εFP was shown to accurately portray the roughness effects encountered in laminar flow. In addition, a thorough look at defining surface roughness was given in Young et al. [4]. In this paper, the experimental study has been extended to cover the effects of different roughness features on pressure drop in turbulent flow and to verify the validity of the new parameter set in representing the resulting roughness effects. The range of relative roughness covered is from smooth to 10.38% relative roughness, with Reynolds numbers up to 15,000. It was found that using the same constricted parameters some unique characteristics were noted for turbulent flow over sawtooth roughness elements.

A Functional Scaling Relationship for Laminar to Turbulent Flow Regimes

2011 ◽  
Author(s):  
George Papadopoulos
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Flow Characteristics ◽  
Flow Region ◽  
Flow Regimes ◽  
Transitional Flow ◽  
Turbulent Regime ◽  
Flow Profile ◽  
Scaling Relationship

A dimensional analysis that is based on the scaling of the two-dimensional Navier-Stokes equations is presented for correlating bulk flow characteristics arising from a variety of initial conditions. The analysis yields a functional relationship between the characteristic variable of the flow region and the Reynolds number for each of the two independent flow regimes. A linear relationship is realized for the laminar regime, while a nonlinear relationship is realized for the turbulent regime. Both relationships incorporate mass-flow profile characteristics to fully capture the effects of initial conditions on the variation of the characteristic variables. The union of these two independent relationships is formed utilizing the concept of flow intermittency to further expand into a generic scaling relationship that incorporates transitional flow effects to fully encompass solutions spanning the laminar to turbulent flow regimes. The results of the analysis are discussed within the context of several flow phenomena (e.g. pipe flow, jet flow & separated flow) resulting from various initial and boundary conditions.

Experimental and CFD Investigations of Heat Transfer in Helical Coils for the Development of Correlations for Newtonian and Non-Newtonian Fluids in Transient State-Space Conditions

2013 ◽  
Author(s):  
Sandipan S. Pawar ◽  
Vivek K. Sunnapwar ◽  
Vivek K. Yakkundi
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Turbulent Flow ◽  
Transfer Coefficient ◽  
Flow Regimes ◽  
Newtonian Fluids ◽  
Water Mixture ◽  
Glycerol Water ◽  
Laminar And Turbulent Flow ◽  
Helical Coils

Experimental studies and CFD investigations were carried out under laminar and turbulent flow regimes in isothermal steady state and non-isothermal unsteady state conditions in helical coils for Newtonian and non-Newtonian fluids. Water and glycerol-water mixture (10 and 20 % glycerol) as Newtonian fluids and dilute aqueous polymer solutions of sodium carboxymethyl cellulose (SCMC), sodium alginate (SA) as non-Newtonian fluids were used in this study. The experiments were performed for three helical coils of coil curvature ratios as 0.0757, 0.064 and 0.055 in laminar and turbulent flow regimes. For the first time, two innovative correlations to calculate Nusselt number (Nu) in terms of new dimensionless ‘M’ number, Prandtl number and coil curvature ratio under different conditions for Newtonian fluids are proposed in this paper. Third correlation of Nu vs. Graetz number (Gz) including the effects of coil curvature on heat transfer coefficient which was not considered by earlier investigators is developed based on tests conducted in laminar flow for Newtonian fluids. All these three innovative correlations developed based on experimental data which were not found in the literature. These correlations were compared with the work of earlier investigators and were found to be in good agreement. The CFD analysis for laminar and turbulent flow was carried out using the CFD package FLUENT 12.0.16. The CFD calculation results (Nui, U) for laminar and turbulent flows were compared with the experimental results, and also the work of earlier investigators was found to be in excellent agreement. Further, the effect of helix diameter on heat transfer for Newtonian and Non-Newtonian fluids are also presented in this paper and it was observed that as helix diameter increases, overall heat transfer coefficient decreases.

Performance of Lightly Loaded Gas Journal Bearings in the Slip-Flow and Turbulent-Flow Regimes

1968 ◽  
Vol 10 (4) ◽  
pp. 363-366
Author(s):  
M. D. Wood
Keyword(s):  
Steady State ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Reynolds Equation ◽  
Dynamic Performance ◽  
Slip Flow ◽  
Flow Regimes ◽  
Journal Bearings ◽  
Performance Parameters ◽  
Existing Data

The note compares recently published versions of the governing gas film equations for slip-flow and turbulent flow with Reynolds equation for laminar flow. The comparison shows how approximate values of steady-state and dynamic performance parameters may be deduced for the new conditions from existing data.

Experimental Investigation on Flow Characteristics in a Tube-Bundle Channel

2012 ◽  
Author(s):  
Zhan Li ◽  
Guangyao Lu ◽  
Wenyuan Xiang
Keyword(s):  
Heat Exchange ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Circular Tube ◽  
Tube Bundle ◽  
Flow Characteristics ◽  
Phase Flow ◽  
Flow Friction ◽  
Annular Channels ◽  
Flow Directions

Experiments were carried out to investigate the flow characteristics with/without heat exchange in vertical and inclined tube-bundle channels. In the experiments, the influences of flow directions and heat exchange upon the flow characteristics were studied. Experiments showed that the flow friction in tube-bundle channels had relations to the flow directions, and the liquid temperature difference at the inlet and outlet of tube-bundle channels. And these influences were comparatively obvious in the laminar flow regime. In the experiments, the transition from laminar to turbulent flow was carefully observed. The flow characteristics of single phase flow through tube-bundle channels were different from those in circular tubes and those in annular channels. The flow friction in tube-bundle channel is larger than that in normal circular tube. And the transition from laminar flow to turbulent flow in tube-bundle channel is different from that in normal circular tube. The influences of flow direction and heat exchange on the friction were also studied. The results were gained to provide the basis for the further investigations on the two-phase flow in tube-bundle channels.

Turbulent Flow Behaviour in a Pipe Fully Submerged in a Hot Fluid

2017 ◽  
Author(s):  
Benjamin Steen ◽  
Kamran Siddiqui
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Vertical Plane ◽  
Flow Behaviour ◽  
Turbulent Regime ◽  
Fluid Temperature ◽  
Cross Sectional ◽  
Turbulence Transition ◽  
Flow Mixing

We report on an experimental study conducted to investigate the flow behaviour in a heat exchanger pipe submerged in a hot stagnant fluid. Particle Image Velocimetry (PIV) was used to measure the two-dimensional velocity field in the mid-vertical plane of the tube. Fluid temperatures in the cross-sectional plane were also measured using thermocouples. The mode of heat transfer into the pipe was mixed convection where both inertia and buoyancy contributed to the convection. The results show that when the contribution of buoyancy-driven flow (natural convection) was smaller than that of the inertia-driven flow (forced convection), in an originally turbulent flow, the shear-induced turbulence dominated the flow and the turbulent velocity profile was not influenced by the heat input. In an originally laminar flow, the role of buoyancy was primarily limited to the initiation of instabilities in the laminar flow to trigger the turbulence transition. The temperature profiles indicate the presence of stably stratified layer inside the pipe in originally laminar flow regime that suppressed the heat transfer rate. In originally turbulent regime, the fluid temperature field was nearly uniform indicating efficient flow mixing.

Newtonian and Non-Newtonian Fluids: Velocity Profiles, Viscosity Data, and Laminar Flow Friction Factor Equations for Flow in a Circular Duct

2008 ◽  
Author(s):  
Melissa M. Simpson ◽  
William S. Janna
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Newtonian Fluid ◽  
Velocity Profiles ◽  
Newtonian Fluids ◽  
Viscosity Data ◽  
Circular Duct ◽  
Flow Friction

Newtonian fluid flow in a duct has been studied extensively, and velocity profiles for both laminar and turbulent flows can be found in countless references. Non-Newtonian fluids have also been studied extensively, however, but are not given the same attention in the Mechanical Engineering curriculum. Because of a perceived need for the study of such fluids, data were collected and analyzed for various common non-Newtonian fluids in order to make the topic more compelling for study. The viscosity and apparent viscosity of non-Newtonian fluids are both defined in this paper. A comparison is made between these fluids and Newtonian fluids. Velocity profiles for Newtonian and non-Newtonian fluid flow in a circular duct are described and sketched. Included are profiles for dilatant, pseudoplastic and Bingham fluids. Only laminar flow is considered, because the differences for turbulent flow are less distinct. Also included is a procedure for determining the laminar flow friction factor which allows for calculating pressure drop. The laminar flow friction factor in classical non-Newtonian fluid studies is the Fanning friction factor. The equations developed in this study involve the Darcy-Weisbach friction factor which is preferred for Newtonian fluids. Also presented in this paper are viscosity data of Heinz Ketchup, Kroger Honey, Jif Creamy Peanut Butter, and Kraft Mayonnaise. These data were obtained with a TA viscometer. The results of this study will thus provide the student with the following for non-Newtonian fluids: • Viscosity data and how it is measured for several common non-Newtonian fluids; • A knowledge of velocity profiles for laminar flow in a circular duct for both Newtonian and non-Newtonian fluids; • A procedure for determining friction factor and calculating pressure drop for non-Newtonian flow in a duct.

Turbulence Leads to Overestimation of the Acid-Diffusion Coefficient at Typical Experimental Conditions Using the Rotating Disk Apparatus

2021 ◽  
Author(s):  
Igor Ivanishin ◽  
Abdelrahman Kotb ◽  
Hisham Nasr-El-Din
Keyword(s):  
Diffusion Coefficient ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Rotational Speed ◽  
Mass Transfer Rate ◽  
Flow Regimes ◽  
Rotating Disk ◽  
Experimental Conditions ◽  
Acid Diffusion ◽  
Order Of Magnitude

Abstract A rotating-disk apparatus (RDA) is used to determine the acid-diffusion coefficient. The equations to interpret RDA tests were previously derived assuming laminar flow to the disk, i.e. uniform accessibility with equal flux of the reactive species over the entire surface of the disk. Thus, the acid-diffusion coefficient is overestimated if the tests are run at transition or turbulent flow regimes. The present work validated laminar flow assumptions at typical RDA experimental conditions to optimize the acid-diffusion coefficient measurements. Disks of calcite marble with a diameter of 0.72, 1.11, and 1.46 in. were reacted in an RDA with hydrochloric acid at temperatures ranging from 73.4 to 100°F and disk rotational speeds ranging from 207 to 1,555 rpm. Transition to turbulent flow was observed at Reynolds numbers one order of magnitude lower than the universally accepted critical value of 3×105. Dissolution patterns on the disks after the experiments and the simulation results using a developed computational fluid-dynamics model confirm this conclusion. The turbulence created cavities near the edges of the 1.46 and 1.1 in. disks starting at rotational speeds of 587 and 829 rpm, respectively. The region of turbulent flow propagated toward the center of the disks with further increase of disk rotational speed. Because of the non-uniform (higher) mass-transfer rate, the diffusion coefficient is overestimated to a value of 6.71×10−5 and 5.01×10−5 cm2/s for the 1.46 and 1.11 in. disks, respectively. For the 0.72 in. disks, no turbulent flow was observed at all disk rotational speeds tested, and the calculated value of the diffusion coefficient was 3.08×10-5 cm2/s. Commercial RDA setups are often equipped with 1.0 or 1.5 in. coreholders and are capable of maintaining a disk rotational speed of up to 2,000 rpm. Thus, care must be taken not to run the tests at transition or turbulent flow regimes, as this will result in overestimation of the acid-diffusion coefficient. Preliminary results indicate that the observed phenomena also affect the RDA analysis of organic and other less reactive acid compositions. Presented results are integral for designing the RDA tests to improve the accuracy of the acid-diffusion coefficient calculations.

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