How to Read Heat Transfer Factor on a Graph With Reynolds Number

Situational Bug in MPD

Bill Rehm , ... Jerome Schubert , in Managed Pressure level Drilling, 2008

Reynolds Number

The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number is a dimensionless number used to categorize the fluids systems in which the effect of viscosity is of import in controlling the velocities or the flow blueprint of a fluid. Mathematically, the Reynolds number, N _Re, is defined as

(2.6) $N_{\mathrm{Re}}=\frac{\rho \upsilon d}{\mu }$

where

$\begin{array}{l}\rho =\mathrm{density}\\ v=\mathrm{velocity}\\ d=\mathrm{diameter}\\ \mu =\mathrm{viscosity}\end{array}$

The Reynolds number is used to determine whether a fluid is in laminar or turbulent menstruation. Based on the API 13D recommendations, it is causeless that a Reynolds number less than or equal to 2100 indicates laminar menstruation, and a Reynolds number greater than 2100 indicates turbulent menstruation. In field units, the equation for calculating the Reynolds number becomes

(2.7) $N_{\mathrm{Re}}=\frac{928\rho \upsilon d}{\mu }$

where

$\begin{array}{l}\rho =\mathrm{density},\mathrm{ppg}\\ v=\mathrm{velocity},\mathrm{ft}/\text{s}\text{e}\text{c}\\ d=\mathrm{diameter},\mathrm{in}.\\ \mu =\mathrm{viscosity},\mathrm{cp}\end{array}$

Depending on which rheological model is used, the associated correlation for the Reynolds number may vary. Table 2.1 presents the different expressions, which correlate the Reynolds number.

Table 2.1. Reynolds Number Terms

Pipage	Annulus
Newtonian model:
${\mathrm{Due\; north}}_{\mathrm{Re}}=\frac{928\rho {\upsilon }_{p}d}{{\mu }_a}$	$N_{\mathrm{Re}}=\frac{757\rho {\upsilon }_a\left(d_2-d_1\right)}{{\mu }_a}$
Bingham plastic model:
$N_{\mathrm{Re}}=\frac{928\rho {\upsilon }_{p}d}{{\mu }_a}$	${\mathrm{Due\; north}}_{\mathrm{Re}}=\frac{757\rho {\upsilon }_a\left(d_{\mathrm{ii}}-d_1\right)}{{\mu }_a}$
Power law model:
${\mathrm{Northward}}_{\mathrm{Re}}=\frac{89,100\rho {\upsilon }_p^{\mathrm{two}-n}}{k}{\left[\frac{0.0416d_p}{3+\frac{1}{\mathrm{northward}}}\right]}^n$	${\mathrm{Due\; north}}_{\mathrm{Re}}=\frac{109,000\rho {\upsilon }_p^{2-n}}{k}{\left[\frac{0.0208\left(d_2-d_1\right)}{2+\frac{\mathrm{ane}}{n}}\right]}^{\mathrm{north}}$
API 13D model (2003):
$N_{\mathrm{Re}}=\frac{928\rho {\upsilon }_{p}d}{{\mu }_e}$	$N_{\mathrm{Re}}=\frac{757\rho {\upsilon }_a\left(d_{\mathrm{ii}}-d_{\mathrm{i}}\right)}{{\mu }_e}$
${\mu }_{\mathrm{due\; east}}=100m_p{\left[\frac{96{\upsilon }_p}{d_p}\right]}^{n_p^{-\mathrm{ane}}}{\left[\frac{3n_p+1}{4{\mathrm{north}}_p}\right]}^{{\mathrm{northward}}_p}$	${\mu }_e=100k_a{\left[\frac{144{\upsilon }_a}{\left(d_{\mathrm{ii}}-d_1\right)}\right]}^{{\mathrm{north}}_a^{-1}}{\left[\frac{2n_a+1}{\mathrm{iii}{n}_a}\right]}^{{\mathrm{northward}}_a}$
Herschel–Bulkley model:
${\mathrm{North}}_{\mathrm{Re}}=\left[\frac{\mathrm{ii}\left(3\mathrm{north}+\mathrm{one}\right)}{n}\right]\times \left\{\frac{\rho {\upsilon }_p^{\left(2-n\right)}{\left(\frac{d_p}{2}\right)}^n}{{\tau }_0{\left(\frac{d_p}{2{\upsilon }_p}\right)}^n+\mathrm{chiliad}{\left[\frac{\left(3n+1\right)}{\mathrm{north}{C}_c}\right]}^{\mathrm{due\; north}}}\right\}$	${\mathrm{Northward}}_{\mathrm{Re}}=\left[\frac{4\left(2\mathrm{northward}+\mathrm{ane}\right)}{\mathrm{north}}\right]\times \left\{\frac{\rho {\upsilon }_a^{\left(2-\mathrm{due\; north}\right)}{\left(\frac{d_2-d_1}{2}\right)}^{\mathrm{due\; north}}}{{\tau }_0{\left(\frac{d_{\mathrm{two}}-d_1}{2{\upsilon }_a}\right)}^{\mathrm{northward}}+k{\left[\frac{2\left(2n+1\right)}{n{C}_a}\right]}^{\mathrm{due\; north}}}\right\}$

Read full chapter

URL:

https://www.sciencedirect.com/scientific discipline/article/pii/B9781933762241500085

Fluid Flow in Pipes

Due east. Shashi Menon , in Transmission Pipeline Calculations and Simulations Manual, 2015

3 Liquid: Reynolds Number

Period in a liquid pipeline may be polish, laminar period also known as glutinous flow. In this type of catamenia, the liquid flows in layers or laminations without causing eddies or turbulence. If the pipe is transparent and we inject a dye into the flowing stream, it would flow smoothly in a directly line confirming smooth or laminar flow. Every bit the liquid menstruum rate is increased, the velocity increases and the period will change from laminar menstruation to turbulent flow with eddies and disturbances. This tin be seen clearly when a dye is injected into the flowing stream.

An important dimensionless parameter called the Reynolds number is used in classifying the blazon of flow in pipelines.

Reynolds number of menstruation, R, is calculated every bit follows:

(5.14) $\mathrm{R}=\text{VD}\mathrm{\rho }/\mathrm{\mu }$

where:

V – average velocity, ft/southward

D – pipe internal bore, ft

ρ – liquid density, slugs/ft³

μ – accented viscosity, lb-southward/ft²

R – Reynolds number is a dimensionless value

Because of, the kinematic viscosity ν   =   μ/ρ, the Reynolds number can also be expressed as

(5.15) $\mathrm{R}=\mathrm{VD}/\mathrm{\nu }$

where:

ν – kinematic viscosity, ft²/s

Care should exist taken to ensure that proper units are used in Eqns (v.14) and (5.fifteen) such that R is dimensionless.

Menstruation-through pipes are classified into three main flow regimes.

1.

Laminar flow – R   <   2000

two.

Disquisitional catamenia – R   >   2000 and R   <   4000

3.

Turbulent period – R   >   4000

Depending upon the Reynolds number, flow-through pipes will fall in i of these three flow regimes. Let us starting time examine the concepts of the Reynolds number. Sometimes an R value of 2100 is used as the limit of laminar flow.

Using customary units in the pipeline manufacture, the Reynolds number tin can be calculated using the post-obit formula:

(5.16) $\mathrm{R}=92.24\mathrm{Q}/\left(\mathrm{\nu D}\right)$

where:

Q – menses rate, bbl/day

D – internal diameter, in

ν – kinematic viscosity, cSt

Equation (5.16) is only a modified course of Eqn (5.fifteen) subsequently performing conversions to commonly used pipeline units. R is still a dimensionless value.

Another version of the Reynolds number in English units is as follows:

(5.17) $\mathrm{R}=\mathrm{iii,160}\mathrm{Q}/\left(\mathrm{\nu D}\right)$

where:

Q – flow rate, gal/min

D – internal bore, in

ν – kinematic viscosity, cSt

A similar equation for the Reynolds number in SI units is

(five.18) $\mathrm{R}=\mathrm{353,678}\mathrm{Q}/\left(\mathrm{\nu D}\right)$

where

Q – flow rate, m³/h

D – internal diameter, mm

ν – kinematic viscosity, cSt

Every bit indicated previously, if the Reynolds number is less than 2000, the flow is considered to be laminar. This is besides known as sticky catamenia. This means that the various layers of liquid menstruation without turbulence in the form of laminations. We volition now illustrate the diverse flow regimes using an example.

Consider a 16-in pipeline, 0.250-in wall thickness transporting a liquid of viscosity 250   cSt. At a flow rate of fifty,000   bbl/24-hour interval, the Reynolds number is, using Eqn (5.16),

$\mathrm{R}=92.24\left(\mathrm{50,000}\right)/(250\times \mathrm{xv.5})=\mathrm{1,190}$

Because R is less than 2000, this menstruation is laminar. If the menses rate is tripled to 150,000   bbl/twenty-four hour period, the Reynolds number becomes 3570 and the flow will exist in the critical region. At flow rates above 168,040   bbl/24-hour interval, the Reynolds number exceeds 4000 and the menses volition be in the turbulent region. Thus, for this sixteen-in pipeline and given liquid viscosity of 250   cSt, flow volition be fully turbulent at flow rates above 168,040   bbl/twenty-four hour period.

As the menses charge per unit and velocity increase, the menses regime changes. With a change in period government, the free energy lost from pipe friction increases. At laminar flow, there is less frictional energy lost compared to turbulent menstruation.

Read full chapter

URL:

https://www.sciencedirect.com/science/commodity/pii/B9781856178303000055

Fluids

Bastian E. Rapp , in Microfluidics: Modelling, Mechanics and Mathematics, 2017

nine.nine.viii Reynolds Number

The Reynolds number is one of the most important dimensionless quantities in microfluidics. It correlates the inertia forces to the gummy forces. The Reynolds number was offset described by Reynolds in 1883 [5], although others have used the quantity before, eastward.thou., Stokes [6]. It is defined equally

(Eq. 9.20) $\text{Re}=\frac{\rho \upsilon L_{\text{char}}}{\eta }=\frac{\upsilon {\mathrm{Fifty}}_{\text{char}}}{v}=\frac{\text{inertia}\text{forces}}{\text{viscous}\text{forces}}=\frac{\text{Pe}}{\text{Se}}$

The Reynolds number is important for describing the ship properties of a fluid or a particle moving in a fluid. Every bit an example, for very modest organism, e.thousand., leaner, the Reynolds number is very small, typically in the range of 1 × 10⁻⁶. Given the minor dimensions, these objects do not have a significant inertia and are thus mainly driven past the viscous forces of the fluid. For such objects, a fluid would feel significantly more rigid, i.e., it would exist hard for a bacteria to forcefulness a path through a moving fluid non following the streamlines. As the objects abound larger, their inertia starts to dominate over the viscous forces. For most fish, the Reynolds number is in the range of i × 10^v, for a homo it is in the range of 1 × ten⁶. At higher Reynolds numbers, an object is able to force its way through a catamenia field even beyond the streamlines. A good case is a big vessel or ship (with Reynolds numbers in the range of one × 10⁹) compared to a folded origami or paper boat: the large vessel can force its way through the electric current and the waves, whereas the light paper boat would non exist able to practice and so. Rather it has to stay with the streamline and will be dragged along.

Every bit the Reynolds number is so of import for microfluidics, we will particular its meaning and application when discussing the concept of dimensional analysis in section 11.viii.three.

Read total chapter

URL:

https://world wide web.sciencedirect.com/science/article/pii/B9781455731411500095

Vertical Axis Wind Turbines

Robert Whittlesey , in Wind Energy Engineering, 2017

10.iii.6 Blade Reynolds Number

The Reynolds number is a commonly used nondimensional parameter in fluid mechanics, which describes the ratio of inertial forces to viscous forces. In the context of VAWTs, the Reynolds number is defined using the kinematic viscosity of the air, the freestream velocity of the wind, and the chord length of the bract every bit follows:

$\mathit{Re}=\frac{c\cdot U_{\mathrm{\infty }}}{\nu }$

where c is the chord length, $U_{\infty }$ is the freestream velocity of the current of air, and $\nu$ is the kinematic viscosity. Using this definition of the Reynolds number, Kirke suggests that low Reynolds numbers contribute to difficulty in the self-starting of a VAWT. Hence larger Reynolds numbers are desired. Additional research in this area by Brusca et al. constitute a similar result: increasing the Reynolds number increased the power coefficient of a given VAWT [18].

In practice, this advice is synonymous with ensuring that (1) the current of air velocity magnitude is high and (2) the blade chord, which is proportional to the blade expanse, is big. Even so, it is not clear if the fault is in the wind velocity or if at that place is actually a Reynolds number dependence on operation (e.thou., transition to turbulence or elevate buckets). This should also be considered in more particular.

Read full chapter

URL:

https://world wide web.sciencedirect.com/science/article/pii/B9780128094518000102

Bones Menstruation Measurement Laws

Paul J. LaNasa , East. Loy Upp , in Fluid Flow Measurement (Third Edition), 2014

Reynolds Number

The Reynolds number is a useful tool for relating how a meter volition react to a variation in fluids from gases to liquids. Since an impossible amount of inquiry would be required to test every meter on every fluid we wish to measure out, it is desirable that a relationship between fluid factors be known. Reynolds' work in 1883 defines these relationships through his Reynolds number, which is defined by the equation:

(2.6) $\mathit{Re}=\frac{\rho \mathit{Dv}}{\mathit{\mu }}$

where:

Re=Reynolds number, a dimensionless number;

ρ=density of the fluid;

D=diameter of the passage way;

v=velocity of the fluid;

μ=viscosity of the fluid.

Notation: All parameters are given in the same units, so that when multiplied together they all cancel out, and the Reynolds number has no units. Units in the pound, human foot, second system are shown below:

Re=no units;

ρ=#/cubic feet;

D=feet;

v=feet/sec;

μ=#/pes-sec.

Based on Reynolds' work, the menstruation profile (which affects all velocity-sensitive meters and some linear meters) has several important values. At values of ii,000 and below, the period profile is bullet-shaped (parabolic). Between 2,000 and 4,000 the flow is in the transition region. At 4,000 and above the flow is in the turbulent flow surface area and the profiles are fairly apartment. Thus, calculation of the Reynolds number volition define the period velocity pattern and gauge limits of the meter's application. To completely define the meter'south application at that place must be no deformed profiles, such as after an elbow or where upstream piping has imparted swirl to the stream.

These effects volition exist farther discussed in the sections roofing the description and application of unlike meters, in Chapters 8, 9, and ten Chapter 8 Chapter ix Chapter 10 , and the equations will be covered more than thoroughly after in this book.

These equations tin can be combined and rewritten in simplified forms. However, information technology is of import to recognize the assumptions which have been made, and so that if a metering situation deviates from what has been assumed, a "flag will go up" to betoken that the outcome of Reynolds number must be evaluated and treated.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780124095243000022

Transportation

Dr. Boyun Guo , Dr. Ali Ghalambor , in Natural Gas Engineering science Handbook (Second Edition), 2005

11.2.one.2 Reynolds Number

The Reynolds number (N _Re ) is defined equally the ratio of fluid momentum strength to gluey shear force. The Reynolds number tin can be expressed every bit a dimensionless group defined every bit

(11.5) ${\mathrm{Northward}}_{Re}=\frac{Du\rho }{\mu }$

where

D = pipage ID, ft

u = fluid velocity, ft/sec

ρ = fluid density, lb_m/ft^three

μ = fluid viscosity, lb_{one thousand}/ft-sec

The Reynolds number can exist used as a parameter to distinguish between laminar and turbulent fluid flow. The alter from laminar to turbulent flow is usually causeless to occur at a Reynolds number of 2,100 for period in a circular piping. If U.Due south. field units of ft for diameter, ft/sec for velocity, lb_m/ftⁱⁱⁱ for density and centipoises for viscosity are used, the Reynolds number equation becomes

(11.six) $N_{R\mathrm{due\; east}}=1,488\frac{Du\rho }{\mu }$

If a gas of specific gravity γ_chiliad and viscosity μ (cp) is flowing in a pipe with an inner bore D (in) at flow rate q (Mcfd) measured at base conditions of T_b (°R) and p_b (psia), the Reynolds number can be expressed as:

(11.7) $N_{Re}=\frac{711p_{b}q{\gamma }_{\mathrm{thou}}}{T_{b}D\mu }$

As T_b is 520 °R and p_b varies only from 14.4 psia to 15.025 psia in the U.s., the value of 711p_b/T_b varies between 19.69 and xx.54. For all practical purposes, the Reynolds number for natural gas menses problems may be expressed equally

(11.8) $N_{Re}=\frac{\mathrm{xx}q{\gamma }_g}{\mu D}$

where

q = gas flow rate at lx °F and 14.73 psia, Mcfd

γ _thou = gas-specific gravity (air = 1)

μ = gas viscosity at in-situ temperature and pressure, cp

D = piping diameter, in

Read total chapter

URL:

https://www.sciencedirect.com/science/commodity/pii/B9781933762418500186

Liquids—Hydraulics

In Pipeline Rules of Thumb Handbook (Eighth Edition), 2014

Nomograph for calculating Reynolds number for menstruum of liquids and friction factor for clean steel and wrought iron pipe

The nomograph (Figure 1) permits calculation of the Reynolds number for liquids and the corresponding friction factor for clean steel and wrought iron pipe.

Effigy 1. Reynolds number for liquid flow friction factor for clean steel and wrought iron pipage.

(Reproduced by permission, Tech. Paper, 410, Crane Co., copyright 1957).

The Reynolds number is defined as:

$\text{Re}=22\text{,}700\frac{\text{q}\rho }{\text{d}\mu }=\mathrm{fifty.6}\frac{\text{Q}\rho }{\text{d}\mu }=\mathrm{half-dozen.31}\frac{\text{W}}{\text{d}\mu }=\frac{\text{dv}\rho }{\mu \text{a}}$

where: Re   =   Reynolds number

d   =   Within pipe diameter, in.

q   =   Volumetric flow rate, cu. ft/sec

Q   =   Volumetric catamenia charge per unit, gal/min

ρ  =   Fluid density, lb/cubic ft

μ  =   Fluid viscosity, centipoise

μa   =   Fluid viscosity, lb/(ft)(sec)

5   =   Average fluid velocity, ft/sec

w   =   Mass rate of flow, lb/hr

Example

Given:

water at 200°F

d   =   4-in. schedule xl steel pipage

Q   =   415 gal/min

ρ  =   60.13 lb/cubic ft

μ  =   0.3 centipoises

Obtain the Reynolds number and the friction factor.

Connect	With	Mark or Read
Q   =   415	ρ  =   lx.thirteen	W   =   200,000
W   =   200,000	d   =   iv-in. schedule xl	Alphabetize
Alphabetize mark	μ  =   0.three	Re   =   1,000,000

At Re   =   ane,000,000 read f   =   0.017 from the graph on the center of the nomograph.

Effigy 2 is an enlarged version of the friction gene chart, based on Moody's data ⁱ for commercial steel and wrought iron. This chart can be used instead of the smaller version shown in Figure 1.

Figure two. Friction factors for clean commercial steel and wrought iron pipe.

(Reproduced past permission, Tech. Paper, 410, Crane Co., 1957.)

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780123876935000139

The Anatomy of the Airfoil

Snorri Gudmundsson BScAE, MScAE, FAA DER(ret.) , in Full general Aviation Aircraft Blueprint, 2014

Reynolds Number

The Reynolds number (R_e) is a measure of the ratio of inertial forces to viscous forces in a fluid menstruation. It is of nifty importance in the analysis of the purlieus layer. It is divers as follows:

Reynolds number:

(8-28) $R_{\mathrm{eastward}}=\frac{\rho 5\mathrm{50}}{\mu }$

where

L = reference length (e.g. wing chord being analyzed), in ft or m

V = reference airspeed, in ft/south or m/southward

ρ = air density, in slugs/ft³ or kg/thousand³

μ = air viscosity, in lb_f·southward/ft^two or N·south/m²

A simple expression, valid for the Britain system at sea-level weather only, is (V and L are in ft/s and ft, respectively):

(8-29) $R_e\approx 6400VC$

For the SI organisation at sea-level conditions only, the expression becomes (5 and L are in m/s and m, respectively):

(viii-30) $R_{\mathrm{due\; east}}\approx 68500\mathrm{Five}C$

Read full affiliate

URL:

https://world wide web.sciencedirect.com/science/article/pii/B9780123973085000088

Fluid Menstruation

A. Kayode Coker , in Fortran Programs for Chemic Process Design, Analysis, and Simulation, 1995

The Overall Force per unit area Drib

Designers involved in sizing process piping oftentimes apply trial and mistake procedure. The designer commencement selects a pipe size and so calculates the

Reynolds number, friction factor, and coefficient of resistance. The pressure drop per 100 anxiety of pipe is and so computed. For a given volumetric rate and concrete properties of a single-phase fluid, ΔP₁₀₀ for laminar and turbulent flows is:

laminar catamenia

(3-sixteen) $\Delta {\text{P}}_{100}=0.0273\frac{\mu \text{Q}}{{\text{d}}^{\mathrm{four}}},\text{psi}/100\text{ft}$

turbulent flow

(3-17) $\Delta {\text{P}}_{100}=0.0216{\text{f}}_{\text{D}}\frac{\rho {\text{Q}}^2}{{\text{d}}^{\mathrm{five}}},\text{psi}/100\text{ft}$

Alternatively, for a given mass flow rate and physical properties of a single-phase fluid, ΔP₁₀₀ for laminar and turbulent flows respectively is:

laminar menstruation

(three-18) $\Delta {\text{P}}_{100}=0.0034\frac{\mu \text{Westward}}{{\text{d}}^4\rho },\text{psi}/100\text{ft}$

turbulent menstruation

(3-19) $\Delta {\text{P}}_{100}=0.00036{\text{f}}_{\text{D}}\frac{{\text{W}}^2}{{\text{d}}^{\mathrm{five}}\rho },\text{psi}/100\text{ft}$

Multiplying Equations iii-xvi, iii-17, 3-18, and 3-19 by the total length between two points and adding the pipe elevation yields the overall pressure drop.

(3-twenty) $\Delta \text{P}=\Delta \text{P}•\frac{{\text{50}}_{\text{Total}}}{100}+\frac{\rho \Delta \text{Z}}{144},\text{psi}$

Equation 3-20 is valid for compressible isothermal fluids of shorter lines where pressure drops are no more than 10% of the upstream pressure. In general, pipe size for a given flow rate is often selected on the assumption that the overall pressure driblet is close to or less than the available pressure difference betwixt two points in the line.

Read full affiliate

URL:

https://www.sciencedirect.com/scientific discipline/commodity/pii/B9780884152804500042

Fly Design

Pasquale Sforza , in Commercial Airplane Blueprint Principles, 2014

v.4.5 Reynolds number in flight

The Reynolds number based on the chord length may be written in terms of the Mach number Five/V* equally follows:

(5.27) ${\text{Re}}_c=\frac{\mathit{Vc}}{\nu }=\mathit{Mc}\frac{5^{\ast }}{\nu }$

Using the information on the atmosphere presented in Appendix B, one may determine the ratio Five*/ν as a office of distance then show that Re _c /Mc  =   7   ×   ten⁶exp(−z/32,000), where z is the altitude in feet, represents a good fit to the atmospheric data. For typical commercial aircraft applications the Reynolds number per foot of chord length lies between 1.5 and 2   million per human foot, every bit illustrated in Effigy v.21. Note that for the major operations of takeoff and cruise, the unit Reynolds numbers for turboprop and turbofan airliners autumn in the range of 1.5–2   1000000 per foot. The data given in Table 5.five show that the mean aerodynamic chord for turboprop aircraft lies in the range 6.9   ft   < c_MAC   <   x.6   ft and for turbofan airliners in the range of 13.iii   ft   < cMAC  <   26.9   ft, while for very big shipping the range is xxx.6   ft   < c_MAC   <   40.33   ft. Thus the actual Reynolds number based on mean aerodynamic chord is 10–twenty   million for turboprop airliners, twenty–54   million for turbofan airliners, and 45–80   1000000 for very large aircraft like the B747 and A380. Note that for highly tapered wings the outboard chords may exist considerably smaller than the mean aerodynamic chord and will experience lower Reynolds numbers. For case, with a taper ratio λ  =   0.4 the tip chord c_t   ∼   0.fourc_MAC . During low-speed operations similar landing and takeoff, high lift devices such as flaps and slats are deployed. Because the characteristic lengths of these elements are considerably smaller than the local wing chord they will be operating at lower Reynolds number and therefore more than susceptible to flow separation and stalling.

Effigy five.21. The variation of unit Reynolds number Re/c_MAC is shown for typical commercial aircraft applications.

In the limited Reynolds number range achieved for the shine NACA airfoils, 3   ×   x^{half dozen}  <   Re _c   <   9   ×   ten⁶, the maximum elevator coefficient has its lowest value at 3   ×   ten⁶ and then increases to a constant value for Reynolds numbers of six   ×   10^half-dozen and 9   ×   10⁶. The general trend is for c_{fifty, max} to increase slowly, if at all, with increases in Reynolds number and for that increase to be more substantial for thicker sections. This is understandable considering as the Reynolds number increases the purlieus layer effects go relatively weaker assuasive the flow to remain attached to the airfoil for longer distances along the airfoil surface. The lift of an airfoil depends primarily on keeping the flow attached to the airfoil while friction elevate itself weakly influences the lift of an airfoil. Yet, little experimental data are available at higher Reynolds numbers, existence limited to about 25   one thousand thousand in the traditional variable-density wind tunnels, only ascension to as much as 100   million in cryogenic wind tunnels, every bit previously described in Department five.2.2.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B978012419953800005X

moonlartax1967.blogspot.com

Source: https://www.sciencedirect.com/topics/engineering/reynolds-number