Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Reynolds critical

H. L. Reynolds,"Critical Measurements and Calculations for Enrtched-Uranium j Graphite-Moderated Systems, HCRL-5175 (1958), k>. 2-7. [Pg.45]

Consider the case of the simple Bunsen burner. As the tube diameter decreases, at a critical flow velocity and at a Reynolds number of about 2000, flame height no longer depends on the jet diameter and the relationship between flame height and volumetric flow ceases to exist (2). Some of the characteristics of diffusion flames are illustrated in Eigure 5. [Pg.519]

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. [Pg.632]

Laminar and Turbulent Flow Below a critical Reynolds number of about 2,100, the flow is laminar over the range 2,100 < Re < 5,000 there is a transition to turbulent flow. For laminar flow, the Hagen-Poiseuille equation... [Pg.636]

The critical Reynolds number for transition from laminar to turbulent flow in noncirciilar channels varies with channel shape. In rectangular ducts, 1,900 < Re < 2,800 (Hanks and Ruo, Ind. Eng. Chem. Fundam., 5, 558-561 [1966]). In triangular ducts, 1,600 < Re < 1,800 (Cope and Hanks, Ind. Eng. Chem. Fundam., II, 106-117 [1972] Bandopadhayay and Hinwood, j. Fluid Mech., 59, 775-783 [1973]). [Pg.638]

Here the second term accounts for the laminar leading edge of the boundaiy layer and assumes that the critical Reynolds number is 500,000. [Pg.666]

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... [Pg.666]

Continuous Cylindrical Surface The continuous surface shown in Fig. 6-48b is apphcable, for example, for a wire drawn through a stagnant fluid (Sakiadis, AIChE ]., 7, 26-28, 221-225, 467-472 [1961]). The critical-length Reynolds number for transition is Re = 200,000. The laminar boundary laver thickness, total drag, and entrainment flow rate may be obtained from Fig. 6-49 the drag and entrainment rate are obtained from the momentum area 0 and displacement area A evaluated at x = L. [Pg.667]

Turbulent flow occurs when the Reynolds number exceeds a critical value above which laminar flow is unstable the critical Reynolds number depends on the flow geometry. There is generally a transition regime between the critical Reynolds number and the Reynolds number at which the flow may be considered fully turbulent. The transition regime is very wide for some geometries. In turbulent flow, variables such as velocity and pressure fluctuate chaotically statistical methods are used to quantify turbulence. [Pg.671]

The value of the Reynolds number which approximately separates laminar from turbulent flow depends, as previously mentioned, on the particular conhg-uration of the system. Thus the critical value is around 50 for a him of liquid or gas howing down a hat plate, around 500 for how around a sphere, and around 2500 for how tlrrough a pipe. The characterishc length in the dehnition of the Reynolds number is, for example, tire diameter of the sphere or of the pipe in two of these examples. [Pg.59]

Coefficient A and exponent a can be evaluated readily from data on Re and T. The dimensionless groups are presented on a single plot in Figure 15. The plot of the function = f (Re) is constructed from three separate sections. These sections of the curve correspond to the three regimes of flow. The laminar regime is expressed by a section of straight line having a slope P = 135 with respect to the x-axis. This section corresponds to the critical Reynolds number, Re < 0.2. This means that the exponent a in equation 53 is equal to 1. At this a value, the continuous-phase density term, p, in equation 46 vanishes. [Pg.297]

The first critical values of the dimensionless sedimentation numbers, S, and Sj, are obtained by substituting for the critical Reynolds number value, Re = 0.2, into the above expressions ... [Pg.298]

The turbulent regime for Cq is characterized by the section of line almost parallel to the x-axis (at the Re" > 500). In this case, the exponent a is equal to zero. Consequently, viscosity vanishes from equation 46. This indicates that the friction forces are negligible in comparison to inertia forces. Recall that the resistance coefficient is nearly constant at a value of 0.44. Substituting for the critical Reynolds number, Re > 500, into equations 65 and 68, the second critical values of the sedimentation numbers are obtained ... [Pg.298]

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). [Pg.725]

Linear jet attachment to a plane not parallel to the supply direction was studied by Katz. The critical angle, 9, of the plane to the jet supply direction, as indicated in Fig. 7.33, was found to be dependent on the supply velocity (Reynolds number). It also depends on the distance of the plane edge from the supply outlet (see Fig. 7.34). [Pg.473]

The Reynolds number, which is directly proportional to the air velocity and the size of the obstacle, is a critical quantity. According to photographs presented elsewhere, a regular Karman vortex street in the wake ot a cylinder is observed only in the range of Reynolds numbers from about 60 to 5000. At lower Reynolds numbers, the wake is laminar, and at higher Reynolds numbers, there is a complete turbulent mixing. [Pg.930]

It is necessary to study the Reynolds number independence in the hill scale and in the model as part of a complete model experiment. The threshold or the critical Reynolds number, Re, for the problem considered should be found by the experiments, and measurements should be made at either the same Reynolds number as in the full scale or at a Reynolds number equal to or larger than Re if the Reynolds number in the full scale is larger than Re. for the problem considered. [Pg.1184]

Turbulent flow occurs if the Reynolds number as calculated above exceeds a certain critical value. Instead of calculating the Reynolds number, a critical flow velocity may be calculated and compared to the actual average flow velocity [60]. [Pg.836]

How does this relate to fluid turbulence The idea is that there exists a critical value of the Reynolds number, TZe, such that intermittent turbulent behavior can appear in the system for TZ > TZe- Moreover, if the behavior of the Lorenz system correctly identifies the underlying mechanism, it may be predicted that, as TZ changes, (1) the duration of the intermittently turbulent behavior will be random, and (2) the mean duration of the laminar phases in between will vary as... [Pg.474]

Laminar flow ceases to be stable when a small perturbation or disturbance in the flow tends to increase in magnitude rather than decay. For flow in a pipe of circular cross-section, the critical condition occurs at a Reynolds number of about 2100. Thus although laminar flow can take place at much higher values of Reynolds number, that flow is no longer stable and a small disturbance to the flow will lead to the growth of the disturbance and the onset of turbulence. Similarly, if turbulence is artificially promoted at a Reynolds number of less than 2100 the flow will ultimately revert to a laminar condition in the absence of any further disturbance. [Pg.82]

The critical value of the Reynolds number (Remit) for the transition from laminar to turbulent flow may be calculated from the Ryan and Johnson001 stability parameter, defined earlier by equation 3.56. For a power-law fluid, this becomes ... [Pg.138]

From equation 3.178, the critical Reynolds number for a Newtonian fluid is 2100. As n decreases, (ReMK)c rises to a maximum of 2400, and then falls to 1600 for n = 0.1, Most of the experimental evidence suggests, however, that the transition occurs at a value close to 2000. [Pg.138]

As an example, the flow of air at 293 K in a pipe of 25 mm diameter and length 14 m is considered, using the value of 0.0015 for R/pu2 employed in the calculation of the figures in Table 4.1 R/pu2 will, of course, show some variation with Reynolds number, but this effect will be neglected in the following calculation. The variation in flowrate G is examined, for a given upstream pressure of 10 MN/m2, as a function of downstream pressure P2. As the critical value of P /P2 for this case is 3.16 (see Table 4.1), the maximum flowrate will occur at all values of P2 less than 10/3.16 = 3.16 MN/m2. For values of P2 greater than 3.16 MN/m2, equation 4.57 applies ... [Pg.163]

The existence of roughness leads also to decreasing the value of the critical Reynolds number, at which transition from laminar to turbulent flow occurs. The character of the dependence of the friction factor on the Reynolds number in laminar flow remains the same for both smooth and rough micro-channels, i.e., X = const/Re. [Pg.113]

Li et al. (2003) studied the flow in a stainless steel micro-tube with the diameter of 128.76-179.8 jm and relative roughness of about 3-4%. The Poiseuille number for tubes with diameter 128.76 and 171.8 jm exceeded the value of Po corresponding to conventional theory by 37 and 15%, respectively. The critical value of the Reynolds number was close to 2,000 for 136.5 and 179.8 pm micro-tubes and about 1,700 for micro-tube with diameter 128.76 pm. [Pg.117]

The data on critical Reynolds numbers in micro-channels of circular and rectangular cross-section are presented in Tables 3.5 and 3.6, respectively. We also list geometrical characteristics of the micro-channels and the methods used for determination of the critical Reynolds number. [Pg.121]

Table 3.5 Critical Reynolds number in circular micro-channels... Table 3.5 Critical Reynolds number in circular micro-channels...
Thus, the available data related to transition in circular micro-tubes testify to the fact that the critical Reynolds number, which corresponds to the onset of such transition, is about 2,000. The evaluation of critical Reynolds number in irregular micro-channels will entail great difficulty since this problem contains a number of characteristic length scales. This fact leads to some vagueness in definition of critical Reynolds number that is not a single criterion, which determines flow characteristics. [Pg.123]

The data presented in the previous chapters, as well as the data from investigations of single-phase forced convection heat transfer in micro-channels (e.g., Bailey et al. 1995 Guo and Li 2002, 2003 Celata et al. 2004) show that there exist a number of principal problems related to micro-channel flows. Among them there are (1) the dependence of pressure drop on Reynolds number, (2) value of the Poiseuille number and its consistency with prediction of conventional theory, and (3) the value of the critical Reynolds number and its dependence on roughness, fluid properties, etc. [Pg.127]


See other pages where Reynolds critical is mentioned: [Pg.98]    [Pg.518]    [Pg.305]    [Pg.313]    [Pg.314]    [Pg.317]    [Pg.672]    [Pg.2003]    [Pg.278]    [Pg.1183]    [Pg.1186]    [Pg.119]    [Pg.174]    [Pg.498]    [Pg.109]    [Pg.64]    [Pg.69]    [Pg.664]    [Pg.122]    [Pg.128]   
See also in sourсe #XX -- [ Pg.3 , Pg.9 , Pg.19 , Pg.28 , Pg.31 , Pg.32 , Pg.91 , Pg.288 , Pg.304 , Pg.325 , Pg.364 ]




SEARCH



Reynold

© 2024 chempedia.info