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.

Heat transfer from a rotating disk

1956 ◽  
Vol 236 (1206) ◽  
pp. 343-351 ◽  
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Outer Part ◽  
Rotating Disk ◽  
Friction Torque ◽  
Practical Applications ◽  
A Value ◽  
Flow Heat

The flow due to a disk rotating in its own plane has been investigated theoretically by von Kármán, Goldstein, and others, but little has been published on the heat transfer. For laminar conditions theoretical solutions have been given by Millsaps & Pohlhausen and by Wagner, but for conditions when the flow is turbulent over the outer part of the disk there is no previous information. The present paper describes an experimental investigation of the heat transfer for a range of conditions from entirely laminar flow to conditions when the outer 80% of the disk area is under turbulence. For laminar flow the heat transfer agrees with Wagner’s results, but Millsap’s theory is found to give too low values and an explanation is given. For the turbulent case, which occurs in most practical applications, values are given for the heat transfer which is found to approach the expression N = 0∙015 R 0∙8 for all-turbulent flow. An attempt is made to deduce the turbulent flow heat transfer theoretically by assuming a 1/7 power law of temperature distribution, but this gives too low a value. Some measurements of the velocity and temperature profiles both for laminar and for turbulent conditions are given. For laminar flow these show fair agreement with the theoretical values. For turbulent flow the temperature ratios are higher than those of velocity, which explains the low heat transfer values calculated assuming a 1/7 power temperature distribution. The relation between heat transfer and friction torque is also discussed.

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.

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.

Burnout in Turbulent Flow—A Droplet Diffusion Model

1961 ◽  
Vol 83 (2) ◽  
pp. 158-162 ◽  
Author(s):  
K. Goldmann ◽  
H. Firstenberg ◽  
C. Lombardi
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Physical Model ◽  
Diffusion Model ◽  
Two Phase Flow ◽  
Flow Regimes ◽  
Phase Flow ◽  
Two Phase ◽  
Order Of Magnitude ◽  
Simplifying Assumptions

Two-phase flow regimes are reviewed briefly. A physical model, which is based on the concept that droplet diffusion through a steam boundary layer is the limiting mechanism for burnout in turbulent flow, is described. An equation is derived relating burnout to other parameters in fog flow. With simplifying assumptions, an order-of-magnitude agreement between analysis and experimental burnout data in fog flow is demonstrated.

scholarly journals An Experimental Study of Gas Flow Regime and Pressure Drop in a Random Packed Bed with Sinter Particles

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 872
Author(s):  
Zude Cheng ◽  
Haitao Wang ◽  
Junsheng Feng ◽  
Hui Dong
Keyword(s):  
Pressure Drop ◽  
Turbulent Flow ◽  
Flow Regime ◽  
Gas Flow ◽  
Particle Diameter ◽  
Flow Regimes ◽  
Packed Bed ◽  
Superficial Velocity ◽  
Experimental Conditions ◽  
Gas Flow Regime

The gas flow regime and pressure drop in a gas–solid packed bed with irregularly shaped sinter particles were experimentally investigated. Using a self-made experimental facility for data measurement, the gas flow pressure drop in a sinter bed layer was determined for various experimental conditions. According to the changes in the modified coefficients, α and β, for different flow regimes, the flow transitions from one regime to another in packed beds with different particle diameters were described. Furthermore, the pressure drop correlations for different flow regimes were determined, and the reliabilities of the obtained correlations were contrastively analyzed. The results show that, when the particle diameter is constant, the modified pressure drop per unit height, ΔP/Hu, increases linearly with the increasing gas superficial velocity. When the gas superficial velocity is larger than 1.15 m/s under atmospheric conditions, the gas flow regime in the sinter bed layer is the turbulent flow. Compared with the experimental correlation of the whole flow, the pressure drop correlations obtained by the piecewise fitting method provided a better prediction of the experimental values, and the average deviations of the obtained correlations for the Forchheimer flow and the turbulent flow were 5.31% and 4.07%, respectively.

scholarly journals Color Response Modification of Encapsulated Liquid Crystals Used in Rotating Disk Heat Transfer Studies

1995 ◽  
Author(s):  
Cengiz Camci ◽  
Boris Glezer
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Liquid Crystals ◽  
Rotational Speed ◽  
Rotating Disk ◽  
Point Of View ◽  
Centrifugal Acceleration ◽  
Relative Shift ◽  
Color Response ◽  
Stationary Conditions

The liquid crystal thermography can be successfully used in both transient and steady-state heat transfer experiments with excellent spatial resolution and good accuracy. Although most of the past liquid crystal based heat transfer studies are reported in the stationary frame, measurements from the rotating frame of turbomachinery systems exist The main objective of the present investigation is to determine the influence of rotation on the color calibration of encapsulated liquid crystals sprayed on the flat surface of a rotating aluminum disk. The investigation is performed for a rotational speed range from 0 rpm to 7500 rpm using three different liquid crystal coatings displaying red at 30, 35 and 45° C, under stationary conditions. An immediate observation from the present study is that the color response of liquid crystals is strongly modified by the centrifugal acceleration of the rotating environment. It is consistently and repeatedly observed that the hue versus temperature curve is continuously shifted toward lower temperatures by increasing rotational speed. The relative shift of the display temperature of the green can be as high as 7°C at 7500 rpm when compared to the temperature of the green observed under stationary conditions. The present study shows that relative shift of the liquid crystal color has a well-defined functional dependency to rotational speed. The shift is linearly proportional to the centrifugal acceleration. It is interesting to note that the individual shift curves of the green for all three liquid crystal coatings collapse into a single curve when they are normalized with respect to their own stationary green values. When the color attribute is selected as “intensity” instead of “hue”, very similar shifts of the temperature corresponding to the intensity maximum value appearing around green is observed. An interpretation of the observed color shift is made from a thermodynamics energy balance point of view.

The influences of bathymetry and flow regime upon the morphology of sublittoral sponge communities

2000 ◽  
Vol 80 (4) ◽  
pp. 707-718 ◽  
Author(s):  
James J. Bell ◽  
David K.A. Barnes
Keyword(s):  
Turbulent Flow ◽  
Flow Regime ◽  
Current Flow ◽  
Volume Ratio ◽  
Basal Area ◽  
Morphological Diversity ◽  
Flow Regimes ◽  
High Energy ◽  
Similarity Analysis ◽  
Lough Hyne

Sponge communities were sampled at 3 m depth intervals at six sites experiencing different flow regimes at Lough Hyne, Ireland. Sponges were identified and classified within the following morphological groups: encrusting, massive, globular, pedunculate, tubular, flabellate, arborescent, repent and papillate morphological types on both vertical (≈90°) and inclined (≈45°) surfaces.Differences in the proportional abundance of the sponge body forms and density (sponge m−2) were observed between sites and depths. The density of sponges increased with depth at sites of slight to moderate current flow, but not at the site where current flow was turbulent. Morphological diversity of sponge communities decreased with increasing current flow due to the removal of delicate forms such as pedunculate and arborescent shaped sponges. Massive and encrusting morphologies dominated at the high-energy sites (fast and turbulent flow regimes) due to a high basal area to volume ratio, which prevents removal from cliff surfaces. However, pedunculate, papillate and arborescent types dominated at the low current sites as these shapes may help to prevent the settlement of sediment on sponge surfaces. Bray–Curtis Similarity analysis and Correspondence Analysis were used to distinguish between five different morphological communities.

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