1、3.1CHAPTER 3FLUID FLOWFluid Properties 3.1Basic Relations of Fluid Dynamics . 3.2Basic Flow Processes 3.3Flow Analysis 3.6Noise in Fluid Flow. 3.13Symbols . 3.14LOWING fluids in HVAC gasesmay range from compressible to nearly incompressible. Liquidshave unbalanced molecular cohesive forces at or nea
2、r the surface(interface), so the liquid surface tends to contract and has propertiessimilar to a stretched elastic membrane. A liquid surface, therefore,is under tension (surface tension).Fluid motion can be described by several simplified models. Thesimplest is the ideal-fluid model, which assumes
3、that the fluid hasno resistance to shearing. Ideal fluid flow analysis is well developede.g., Schlichting (1979), and may be valid for a wide range ofapplications.Viscosity is a measure of a fluids resistance to shear. Viscouseffects are taken into account by categorizing a fluid as either New-tonia
4、n or non-Newtonian. In Newtonian fluids, the rate of deforma-tion is directly proportional to the shearing stress; most fluids in theHVAC industry (e.g., water, air, most refrigerants) can be treated asNewtonian. In non-Newtonian fluids, the relationship between therate of deformation and shear stre
5、ss is more complicated.DensityThe density of a fluid is its mass per unit volume. The densitiesof air and water (Fox et al. 2004) at standard indoor conditions of68F and 14.696 psi (sea-level atmospheric pressure) arewater= 62.4 lbm/ft3air= 0.0753 lbm/ft3ViscosityViscosity is the resistance of adjac
6、ent fluid layers to shear. A clas-sic example of shear is shown in Figure 1, where a fluid is betweentwo parallel plates, each of area A separated by distance Y. The bot-tom plate is fixed and the top plate is moving, which induces a shear-ing force in the fluid. For a Newtonian fluid, the tangentia
7、l force Fper unit area required to slide one plate with velocity V parallel to theother is proportional to V/Y:F/A = (V/Y )(1)where the proportionality factor is the absolute or dynamic vis-cosity of the fluid. The ratio of F to A is the shearing stress , andV/Y is the lateral velocity gradient (Fig
8、ure 1A). In complex flows,velocity and shear stress may vary across the flow field; this isexpressed by = (2)The velocity gradient associated with viscous shear for a simple caseinvolving flow velocity in the x direction but of varying magnitude inthe y direction is illustrated in Figure 1B.Absolute
9、 viscosity depends primarily on temperature. Forgases (except near the critical point), viscosity increases with thesquare root of the absolute temperature, as predicted by the kinetictheory of gases. In contrast, a liquids viscosity decreases as temper-ature increases. Absolute viscosities of vario
10、us fluids are given inChapter 33.Absolute viscosity has dimensions of force time/length2. Atstandard indoor conditions, the absolute viscosities of water and dryair (Fox et al. 2004) arewater= 6.76 104lbm/fts = 2.10 105lbfs/ft2air= 1.22 105lbm/fts = 3.79 107lbfs/ft2Another common unit of viscosity i
11、s the centipoise (1 centipoise =1 g/(sm) = 1 mPas). At standard conditions, water has a viscosityclose to 1.0 centipoise.In fluid dynamics, kinematic viscosity is sometimes used inlieu of absolute or dynamic viscosity. Kinematic viscosity is the ratioof absolute viscosity to density: = /At standard
12、indoor conditions, the kinematic viscosities of waterand dry air (Fox et al. 2004) arewater= 1.08 105ft2/sair= 1.62 104ft2/sThe stoke (1 cm2/s) and centistoke (1 mm2/s) are common unitsfor kinematic viscosity.The preparation of this chapter is assigned to TC 1.3, Heat Transfer andFluid Flow.Fig. 1 V
13、elocity Profiles and Gradients in Shear Flowsdvdy-3.2 2013 ASHRAE HandbookFundamentalsNote that the inch-pound system of units often requires the con-version factor gc= 32.1740 lbmft/s2lbfto make some equationscontaining lbfand lbmdimensionally consistent. The conversionfactor gcis not shown in the
14、equations, but is included as needed.BASIC RELATIONS OF FLUID DYNAMICSThis section discusses fundamental principles of fluid flow forconstant-property, homogeneous, incompressible fluids and intro-duces fluid dynamic considerations used in most analyses.Continuity in a Pipe or DuctConservation of ma
15、ss applied to fluid flow in a conduit requiresthat mass not be created or destroyed. Specifically, the mass flowrate into a section of pipe must equal the mass flow rate out of thatsection of pipe if no mass is accumulated or lost (e.g., from leak-age). This requires thatdA = constant (3)where is ma
16、ss flow rate across the area normal to flow, v is fluidvelocity normal to differential area dA, and is fluid density. Both and v may vary over the cross section A of the conduit. When flowis effectively incompressible ( = constant) in a pipe or duct flowanalysis, the average velocity is then V = (1/
17、A)vdA, and the massflow rate can be written as= VA (4)orQ = = AV (5)where Q is volumetric flow rate.Bernoulli Equation and Pressure Variation inFlow DirectionThe Bernoulli equation is a fundamental principle of fluid flowanalysis. It involves the conservation of momentum and energyalong a streamline
18、; it is not generally applicable across streamlines.Development is fairly straightforward. The first law of thermody-namics can apply to both mechanical flow energies (kinetic andpotential energy) and thermal energies.The change in energy content E per unit mass of flowing fluidis a result of the wo
19、rk per unit mass w done on the system plus theheat per unit mass q absorbed or rejected:E = w + q (6)Fluid energy is composed of kinetic, potential (because of elevationz), and internal (u) energies. Per unit mass of fluid, the energychange relation between two sections of the system is = EM + q (7)
20、where the work terms are (1) external work EMfrom a fluidmachine (EMis positive for a pump or blower) and (2) flow workp/ (where p = pressure), and g is the gravitational constant. Re-arranging, the energy equation can be written as the generalizedBernoulli equation: = EM+ q (8)The expression in par
21、entheses in Equation (8) is the sum of thekinetic energy, potential energy, internal energy, and flow work perunit mass flow rate. In cases with no work interaction, no heat trans-fer, and no viscous frictional forces that convert mechanical energyinto internal energy, this expression is constant an
22、d is known as theBernoulli constant B:+ gz + = B (9)Alternative forms of this relation are obtained through multiplica-tion by or division by g:p + + gz = B (10)(11)where = g is the weight density ( = weight/volume versus =mass/volume). Note that Equations (9) to (11) assume no frictionallosses.The
23、units in the first form of the Bernoulli equation Equation(9) are energy per unit mass; in Equation (10), energy per unit vol-ume; in Equation (11), energy per unit weight, usually called head.Note that the units for head reduce to just length (i.e., ftlbf/lbfto ft).In gas flow analysis, Equation (1
24、0) is often used, and gz is negli-gible. Equation (10) should be used when density variations occur.For liquid flows, Equation (11) is commonly used. Identical resultsare obtained with the three forms if the units are consistent and flu-ids are homogeneous.Many systems of pipes, ducts, pumps, and bl
25、owers can be con-sidered as one-dimensional flow along a streamline (i.e., variationin velocity across the pipe or duct is ignored, and local velocity v =average velocity V ). When v varies significantly across the crosssection, the kinetic energy term in the Bernoulli constant B isexpressed as V2/2
26、, where the kinetic energy factor ( 1)expresses the ratio of the true kinetic energy of the velocity profileto that of the average velocity. For laminar flow in a wide rectangu-lar channel, = 1.54, and in a pipe, = 2.0. For turbulent flow in aduct, 1.Heat transfer q may often be ignored. Conversion
27、of mechanicalenergy to internal energy u may be expressed as a loss EL. Thechange in the Bernoulli constant (B = B2 B1) between stations 1and 2 along the conduit can be expressed as+ EM EL= (12)or, by dividing by g, in the form+ HM HL= (13)Note that Equation (12) has units of energy per mass, wherea
28、seach term in Equation (13) has units of energy per weight, or head.The terms EMand ELare defined as positive, where gHM= EMrep-resents energy added to the conduit flow by pumps or blowers. Aturbine or fluid motor thus has a negative HMor EM. Note the sim-plicity of Equation (13); the total head at
29、station 1 (pressure headplus velocity head plus elevation head) plus the head added by apump (HM) minus the head lost through friction (HL) is the totalhead at station 2.Laminar FlowWhen real-fluid effects of viscosity or turbulence are included,the continuity relation in Equation (5) is not changed
30、, but V must bemv =mmmv22- gz u+ p-v22- gz up-+v22-p-v22-p-v22g- z+Bg-=p- V22- gz+1p- V22- gz+2p- V22g- z+1p- V22g- z+2Fluid Flow 3.3evaluated from the integral of the velocity profile, using local veloc-ities. In fluid flow past fixed boundaries, velocity at the boundary iszero, velocity gradients
31、exist, and shear stresses are produced. Theequations of motion then become complex, and exact solutions aredifficult to find except in simple cases for laminar flow between flatplates, between rotating cylinders, or within a pipe or tube.For steady, fully developed laminar flow between two parallelp
32、lates (Figure 2), shear stress varies linearly with distance y fromthe centerline (transverse to the flow; y = 0 in the center of the chan-nel). For a wide rectangular channel 2b tall, can be written as = w= (14)where wis wall shear stress b(dp/ds), and s is flow direction. Be-cause velocity is zero
33、 at the wall ( y = b), Equation (14) can be inte-grated to yieldv = (15)The resulting parabolic velocity profile in a wide rectangularchannel is commonly called Poiseuille flow. Maximum velocityoccurs at the centerline (y = 0), and the average velocity V is 2/3 ofthe maximum velocity. From this, the
34、 longitudinal pressure drop interms of V can be written as(16)A parabolic velocity profile can also be derived for a pipe ofradius R. V is 1/2 of the maximum velocity, and the pressure dropcan be written as(17)TurbulenceFluid flows are generally turbulent, involving random perturba-tions or fluctuat
35、ions of the flow (velocity and pressure), character-ized by an extensive hierarchy of scales or frequencies (Robertson1963). Flow disturbances that are not chaotic but have some degreeof periodicity (e.g., the oscillating vortex trail behind bodies) havebeen erroneously identified as turbulence. Onl
36、y flows involving ran-dom perturbations without any order or periodicity are turbulent;velocity in such a flow varies with time or locale of measurement(Figure 3).Turbulence can be quantified statistically. The velocity mostoften used is the time-averaged velocity. The strength of turbulenceis chara
37、cterized by the root mean square (RMS) of the instantaneousvariation in velocity about this mean. Turbulence causes the fluid totransfer momentum, heat, and mass very rapidly across the flow.Laminar and turbulent flows can be differentiated using theReynolds number Re, which is a dimensionless relat
38、ive ratio ofinertial forces to viscous forces:ReL= VL/ (18)where L is the characteristic length scale and is the kinematic vis-cosity of the fluid. In flow through pipes, tubes, and ducts, the char-acteristic length scale is the hydraulic diameter Dh, given byDh= 4A/Pw(19)where A is the cross-sectio
39、nal area of the pipe, duct, or tube, and Pwis the wetted perimeter.For a round pipe, Dhequals the pipe diameter. In general, laminarflow in pipes or ducts exists when the Reynolds number (based onDh) is less than 2300. Fully turbulent flow exists when ReDh10,000. For 2300 3 105Sphere 0.36 to 0.47 0.
40、1Disk 1.12 1.12Streamlined strut 0.1 to 0.3 0), flow decays exponentially as e.Turbulent flow analysis of Equation (42) also must be based onthe quasi-steady approximation, with less justification. Daily et al.(1956) indicate that frictional resistance is slightly greater than thesteady-state result
41、 for accelerating flows, but appreciably less fordecelerating flows. If the friction factor is approximated as constant,= A BV2(50)and for the accelerating flow, = (51)orV = (52)Because the hyperbolic tangent is zero when the independentvariable is zero and unity when the variable is infinity, the i
42、nitial(V = 0 at = 0) and final conditions are verified. Thus, for long times(),ReFig. 19 Flowmeter Coefficientsd24-R2D- 2 ghd24-2 P1P2 1 4-dVd-1-dpds-fV22D-+dVd-pL-fV22D-=dVd-pL-32VD2-=dVdABV-1B-=pL-D232- 1Lp-32D2-exppL-D232- pL-R28- =1Lp-fV2D-exp64VD-dVd-pL-fV22D-=1AB- t a n h1V BA-AB tanh AB3.12 2
43、013 ASHRAE HandbookFundamentalsV= (53)which is in accord with Equation (30) when f is constant (the flowregime is the fully rough one of Figure 13). The temporal velocityvariation is thenV = Vtanh ( fV/2D) (54)In Figure 20, the turbulent velocity start-up result is compared withthe laminar one, wher
44、e initially the turbulent is steeper but of thesame general form, increasing rapidly at the start but reaching Vasymptotically.CompressibilityAll fluids are compressible to some degree; their density dependssomewhat on the pressure. Steady liquid flow may ordinarily betreated as incompressible, and
45、incompressible flow analysis is sat-isfactory for gases and vapors at velocities below about 4000 to8000 fpm, except in long conduits.For liquids in pipelines, a severe pressure surge or water hammermay be produced if flow is suddenly stopped. This pressure surgetravels along the pipe at the speed o
46、f sound in the liquid, alternatelycompressing and decompressing the liquid. For steady gas flows inlong conduits, pressure decrease along the conduit can reduce gasdensity significantly enough to increase velocity. If the conduit islong enough, velocities approaching the speed of sound are possiblea
47、t the discharge end, and the Mach number (ratio of flow velocity tospeed of sound) must be considered.Some compressible flows occur without heat gain or loss (adia-batically). If there is no friction (conversion of flow mechanicalenergy into internal energy), the process is reversible (isentropic), aswell, and follows the relationshipp/k= constantk = cp/cvwhere k, the ratio of specific heats at constant pressure and volume,has a value of 1.4 for air and diatomic gases.The Bernoulli equation of steady flow, Equation (21), as an inte-gral of the
