1、3.1CHAPTER 3FLUID FLOWFluid Properties 3.1Basic Relations of Fluid Dynamics . 3.2Basic Flow Processes 3.3Flow Analysis 3.6Noise in Fluid Flow. 3.14Symbols . 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 (
8、Figure 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 shown in Figure 1B.Absolute visco
9、sity depends primarily on temperature. For gases(except near the critical point), viscosity increases with the squareroot of the absolute temperature, as predicted by the kinetic theory ofgases. In contrast, a liquids viscosity decreases as temperatureincreases. Absolute viscosities of various fluid
10、s are given in Chapter33.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 is the ce
11、ntipoise 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: = /The preparation of thi
12、s chapter is assigned to TC 1.3, Heat Transfer andFluid Flow.Fig. 1 Velocity Profiles and Gradients in Shear Flowsdvdy-=3.2 2017 ASHRAE HandbookFundamentals At standard indoor conditions, the kinematic viscosities of waterand dry air (Fox et al. 2004) arewater= 1.08 105ft2/sair= 1.62 104ft2/sThe sto
13、ke (1 cm2/s) and centistoke (1 mm2/s) are common unitsfor kinematic viscosity.Note 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 equation
14、s, but is included as needed.2. 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 mass ap
15、plied 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 mass fl
16、ow 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/A)vdA
17、, and the massflow rate can be written as= VA (4)orQ = = AV (5)where Q is volumetric flow rate.Bernoulli Equation and Pressure Variation in Flow DirectionThe Bernoulli equation is a fundamental principle of fluid flowanalysis. It involves the conservation of momentum and energyalong a streamline; it
18、 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 work p
19、er 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)wher
20、e 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.Rearranging, the energy equation can be written as the generalizedBernoulli equation: = EM+ q (8)The expression in parenthes
21、es 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 and is k
22、nown 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 units
23、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 (10) is
24、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 blowers
25、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, wher
26、e 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 of mec
27、hanicalenergy 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, whereaseach
28、term in Equation (13) has units of energy per weight, or head.The terms EMand ELare defined as positive, where gHM= EMrepresents energy added to the conduit flow by pumps or blowers. Aturbine or fluid motor thus has a negative HMor EM. Note themv =mmmv22- gz u+ p-v22- gz up-+v22-p-v22-p-v22g- z+Bg-=
29、p- V22- gz+1p- V22- gz+2p- V22g- z+1p- V22g- z+2Fluid Flow 3.3simplicity of Equation (13); the total head at 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
30、-fluid effects of viscosity or turbulence are included,the continuity relation in Equation (5) is not changed, but V must beevaluated from the integral of the velocity profile, using local veloc-ities. In fluid flow past fixed boundaries, velocity at the boundary iszero, velocity gradients exist, an
31、d 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 parallelplates (Fi
32、gure 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.Because velocity is zero at the wal
33、l ( y = b), Equation (14) can beintegrated 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 longitudinal
34、 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 fluctuations of the f
35、low (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. Only flows invol
36、ving 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 characterized by t
37、he 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 relative ratio ofi
38、nertial 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-sectional area of t
39、he 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 0.1Disk 1.12 1.
40、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 for accelera
41、ting flows, but appreciably less fordecelerating flows. If the friction factor is approximated as constant,Cd1 4-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-3.12 2017 ASHR
42、AE HandbookFundamentals = 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 initial(V = 0 at = 0) and final conditions are verified. Thus, for long times(),V= (53)which is i
43、n 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, where initially the turbulent is steeper but of thes
44、ame 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 incompressible flow analysis is sat-isfactory fo
45、r 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 of sound in the liquid, alternatelycompressing an
46、d decompressing the liquid. For steady gas flows inlong conduits, the pressure drop along the conduit can reduce gasdensity enough to increase the velocity. If the conduit is longenough, the velocity may reach the speed of sound, and the Machnumber (ratio of flow velocity to the speed of sound) must
47、 be con-sidered.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)and follows the relationshipp/k= constantk = cp/cvwhere k, the ratio of specific heats at constant pressure and volume,is 1.4 for air and diatomic gases.When the elevation term gz is neglected, as it is in most com-pressible flow analyses, the Bernoulli equation of steady flow,Equation (21), becomes= constant (55)For a frictionless adiabatic process,(56)Integrat
