Laminar and turbulent flows

There are two distinct modes of flow, laminar and turbulent. Fluid inertia tends to allow fluctuations to grow and give rise to turbulent eddies. Viscosity on the other hand, tends to damp out these fluctuations. A ratio of forces, inertial to viscous, is used to characterise the nature of the flow and is called the Reynolds Number, Re. For pipe flow this takes the form  

The Reynolds Number being a ratio of like quantities, forces in this case, is dimensionless. At low Re, flows tend to be laminar, and at high Re, flows tend to be turbulent. As we shall see later, the limiting values of Re for laminar and turbulent flow and the transition between these modes of flow is a function of the flow geometry. 

In all following calculations, we assume that the flow is laminar and not turbulent. In laminar flow, the different layers do not mix due to hydrodynamic flow. Mixing is possible only by diffusion. Laminar flow dominates if the inertial components of the flow are low compared to frictional effects. Inertial forces become apparent due to the transformation from the comoving to the laboratory reference frame. They are represented by the term q(7 V)7, which is a force density in N m. If we denote a typical velocity by v and I is the length scale over which the velocity changes, we can approximate V7 v/I and q(7 V)7 qv /L 

Frictional forces are due to the viscous term qV 7. It can be approximated by qV 7 PS qv/I. The ratio between both force densities is Reynolds number  

5) Osborne Reynolds, 1842-1912. Irish physicist, professor in Manchester. 

Reynolds number allows us to predict what kind of flow we expect. Asa rule of thumb, turbulences occur for large Reynolds numbers. Re 3 1. Laminar flow dominates for Re 1. 

In a microfluidic device, water flows through channels of 50 (un width at a central velocity 100 pm/s. Would you expect laminar flow or turbulences to occur Compare it to normal household water pipe 1 cm diameter in which water flows with a central speed of 0.2 m s. The viscosity of water at 20 °C is t] = 0.001 Pa s. 

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Petera,. 1. and Nassehi, V., 1993. Flow modelling using isoparametric Hermite elements. In Taylor C. (ed.), Numerical Methods in Laminar and Turbulent Flow, Vol. VIII, Part 2, Pineridge Press, Swansea. 

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

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. 

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... 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

Leva et al (1949) and Ergun (1952) developed similar useful equations. Later, these were refined and modified by Handley and Heggs (1968 ) and by MacDonald et al (1979). All these equations try to handle the transient regime between laminar and turbulent flow somewhat differently but are based on the same principles. 

Flow in empty tubes has a relatively narrow band of velocities—or Reynolds numbers from 2000 to 10000—wherein the character changes from laminar to turbulent. In packed beds, even the laminar flow does not mean that motion is linear or parallel to the surface. Due to the many turns between particles, stable eddies develop and therefore the difference between laminar and turbulent flow is not as pronounced as in empty tubes. 

Fauske [32] represented a nomograph for tempered reaetions as shown in Figure 12-35. This aeeounts for turbulent flashing flow and requires information about the rate of temperature rise at the relief set pressure. This approaeh also aeeounts for vapor disengagement and frietional effeets ineluding laminar and turbulent flow eonditions. For turbulent flow, the vent area is... 

The flow region between laminar and turbulent flow is called transitional flow. It is three dimensional and varies with time. 

Dckker, E. (1961). Transition between laminar and turbulent flow in human trachea./. Appl. Physiol. 16, 1060-1064. 

Transitional flow The nature of flow in the zone between laminar and turbulent flow. 

The general form of the population balance including aggregation and rupture terms was solved numerically to model the experimental particle size distributions. While excellent agreement was obtained using semi-empirical two-particle aggregation and disruption models (see Figure 6.15), PSD predictions of theoretical models based on laminar and turbulent flow considerations... 

Liquids in motion have characteristics different from liquids at rest. Frictional resistances within the fluid, viscosity, and inertia contribute to these differences. Inertia, which means the resistance a mass offers to being set in motion, will be discussed later in this section. Other relationships of liquids in motion you must be familiar with. Among these are volume and velocity of flow flow rate, and speed laminar and turbulent flow and more importantly, the force and energy changes which occur in flow. 

However, on die basis of the relation between pressure drop and die minimum fluidisation velocity of particles, the point of transition between a packed bed and a fluidised bed has been correlated by Ergun41 using (17.7.2.3). This is obtained by summing the pressure drop terms for laminar and turbulent flow regions. 

Heat tranter. Experimental data for laminar and turbulent flow regimes... 

A study of forced convection characteristics in rectangular channels with hydraulic diameter of 133-367 pm was performed by Peng and Peterson (1996). In their experiments the liquid velocity varied from 0.2 to 12m/s and the Reynolds number was in the range 50, 000. The main results of this study (and subsequent works, e.g., Peng and Wang 1998) may be summarized as follows (1) friction factors for laminar and turbulent flows are inversely proportional to Re and Re ", respectively (2) the Poiseuille number is not constant, i.e., for laminar flow it depends on Re as PoRe ° (3) the transition from laminar to turbulent flow occurs at Re about 300-700. These results do not agree with those reported by other investigators and are probably incorrect. 

An experimental study of the laminar-turbulent transition in water flow in long circular micro-tubes, with diameter and length in the range of 16.6-32.2 pm and 1-30 mm, respectively, was carried out by Rands et al. (2006). The measurements allowed to estimate the effect of heat released by energy dissipation on fluid viscosity under conditions of laminar and turbulent flow in long micro-tubes. 

The dependence of the measured rise in fluid mixed-cup temperature on Reynolds number is illustrated in Fig. 3.12. The difference between outlet and inlet temperatures increases monotonically with increasing Re at laminar and turbulent flows. Under conditions of the given experiments, the temperature rise due to energy dissipation is very significant AT = 15—35 K at L/ i = 900—1,470 and Re = 2,500. The data on rising temperature in long micro-tubes can be presented in the form of the dependence of dimensionless viscous heating parameter Re/[Ec(L/(i)] on Reynolds number (Fig. 3.13). 

Once a scaleup strategy has been determined, Equation (3.17)—rather than the limiting cases for laminar and turbulent flow—should be used for the final calculations. 

P. Clavin. D)mamic behaviour of premixed flame fronts in laminar and turbulent flows. Progress in Energy and Combustion Science, 11 1-59,1985. 

The static inline mixer shown in Figure 10.53 is effective in both laminar and turbulent flow, and can be used to mix viscous mixtures. The division and rotation of the fluid at each element causes rapid radical mixing see Rosenzweig (1977) and Baker (1991). The... 

The transition from laminar to turbulent flow on a rotating sphere occurs approximately at Re = 1.5 4.0 x 104. Experimental work by Kohama and Kobayashi [39] revealed that at a suitable rotational speed, the laminar, transitional, and turbulent flow conditions can simultaneously exist on the spherical surface. The regime near the pole of rotation is laminar whereas that near the equator is turbulent. Between the laminar and turbulent flow regimes is a transition regime, where spiral vortices stationary relative to the surface have been observed. The direction of these spiral vortices is about 4 14° from the negative direction of the azimuthal angle,. The phenomenon is similar to the flow transition on a rotating disk [19]. 

Lla. Landau. U., LBL-2702 Ph.D. thesis. University of California, Berkeley, January 1976. Lib. Landau, U., and Tobias, C. W., Mass Transport and Current Distribution in Channel Type Electrolyzers in the Laminar and Turbulent Flow Regimes, Ext. Abstr., No. 266, Electrochemical Society Meeting, Washington D.C., May 1976, 663. 

Several correlating equations for the friction factor have been proposed for both the laminar and turbulent flow regimes, and plots of fM (or functions thereof) versus Reynolds number are frequently presented in standard fluid flow or chemical engineering handbooks (e.g., 96, 97). Perhaps the most useful of the correlations is that represented by the Ergun equation (98)... 

The expressions for the friction factor in both laminar and turbulent flow were combined into a single expression by Churchill (1977) as follows ... 

Equation (6-41) adequately represents the Fanning friction factor over the entire range of Reynolds numbers within the accuracy of the data used to construct the Moody diagram, including a reasonable estimate for the intermediate or transition region between laminar and turbulent flow. Note that it is explicit in /. 

Corresponding expressions for the friction loss in laminar and turbulent flow for non-Newtonian fluids in pipes, for the two simplest (two-parameter) models—the power law and Bingham plastic—can be evaluated in a similar manner. The power law model is very popular for representing the viscosity of a wide variety of non-Newtonian fluids because of its simplicity and versatility. However, extreme care should be exercised in its application, because any application involving extrapolation beyond the range of shear stress (or shear rate) represented by the data used to determine the model parameters can lead to misleading or erroneous results. 

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