1、13.1CHAPTER 13INDOOR ENVIRONMENTAL MODELINGCOMPUTATIONAL FLUID DYNAMICS 13.1Meshing for Computational Fluid Dynamics 13.4Boundary Conditions for Computational Fluid Dynamics 13.6CFD Modeling Approaches . 13.9Verification, Validation, and Reporting Results 13.9MULTIZONE NETWORK AIRFLOW AND CONTAMINAN
2、T TRANSPORT MODELING 13.14Multizone Airflow Modeling 13.14Contaminant Transport Modeling 13.16Multizone Modeling Approaches 13.16Verification and Validation. 13.17Symbols 13.20HIS chapter presents two common indoor environmental model-Ting methods to calculate airflows and contaminant concentra-tion
3、s in buildings: computational fluid dynamics (CFD) and multi-zone network airflow modeling. Discussion of each method includesits mathematical background, practical modeling advice, model val-idation, and application examples.Each modeling method has strengths and weaknesses for study-ing different
4、aspects of building ventilation, energy, and indoor airquality (IAQ). CFD modeling can be used for a microscopic view ofa building or its components by solving Navier-Stokes equations toobtain detailed flow field information and pollutant concentrationdistributions within a space. Its strengths incl
5、ude the rigorous appli-cation of fundamental fluid mechanics and the detailed nature of theairflow, temperature, and contaminant concentration results. How-ever, these results require significant time, both for the analyst tocreate a model and interpret the results and for the computer to solvethe e
6、quations. This time cost typically limits CFD to applications in-volving single rooms and steady-state solutions.In contrast, multizone airflow and pollutant transport modelingcan yield a macroscopic view of a building by solving a network ofmass balance equations to obtain airflows and average poll
7、utant con-centrations in different zones of a whole building. This entire processtakes much less time, making whole-building modeling, includingvarious mechanical systems, possible over time periods as long as ayear. This methods limitations include far less-detailed results (e.g.,no internal-room a
8、irflow details, a single contaminant concentrationfor each room), which poorly approximate some modeling scenarios(e.g., atria, stratified rooms). Although modeling software is widely available, successfulapplication of either indoor environmental modeling method is stillchallenging. A strong grasp
9、of fundamental building physics anddetailed knowledge of the building space being modeled are bothnecessary. (Also see Chapters 1, 3, 4, 6, 9, 11, 16, and 24 of this vol-ume.) Successful modeling also starts with planning that considersthe projects objectives, resources, and available information. W
10、henmodeling existing buildings, taking measurements may significantlyimprove the modeling effort. Modeling is particularly useful whenknown and unknown elements are combined, such as an existingbuilding under unusual circumstances (e.g., fire, release of an air-borne hazard). However, even for hypot
11、hetical buildings (e.g., in thedesign stage), knowledge gained from a good modeling effort can bevaluable to planning and design efforts.COMPUTATIONAL FLUID DYNAMICSComputational fluid dynamic (CFD) modeling quantitativelypredicts thermal/fluid physical phenomena in an indoor space. Theconceptual mo
12、del interprets a specific problem of the indoor envi-ronment through a mathematical form of the conservation law andsituation-specific information (boundary conditions). The governingequations remain the same for all indoor environment applications ofairflow and heat transfer, but boundary condition
13、s change for eachspecific problem: for example, room layout may be different, orspeed of the supply air may change. In general, a boundary conditiondefines the physical problem at specific positions. Often, physicalphenomena are complicated by simultaneous heat flows (e.g., heatconduction through th
14、e building enclosure, heat gains from heatedindoor objects, solar radiation through building fenestration), phasechanges (e.g., condensation and evaporation of water), chemicalreactions (e.g., combustion), and mechanical movements (e.g., fans,occupant movements).CFD involves solving coupled partial
15、differential equations,which must be worked simultaneously or successively. No analyticalsolutions are available for indoor environment modeling. Computer-based numerical procedures are the only means of generating com-plete solutions of these sets of equations.CFD code is more than just a numerical
16、 procedure of solving gov-erning equations; it can be used to solve fluid flow, heat transfer,chemical reactions, and even thermal stresses. Unless otherwiseimplemented, CFD does not solve acoustics and lighting, which arealso important parameters in indoor environment analysis. DifferentCFD codes h
17、ave different capabilities: a simple code may solve onlylaminar flow, whereas a complicated one can handle a far more com-plex (e.g., compressible) flow.Mathematical and Numerical BackgroundAirflow in natural and built environments is predominantly tur-bulent, characterized by randomness, diffusivit
18、y, dissipation, andrelatively large Reynolds numbers (Tennekes and Lumley 1972).Turbulence is not a fluid property, as are viscosity and thermal con-ductivity, but a phenomenon caused by flow motion. Research onturbulence began during the late nineteenth century (Reynolds 1895)and has been intensive
19、ly pursued in academia and industry. For fur-ther information, see Corrsins (1961) overview; Hinzes (1975) andTennekes and Lumleys (1972) classic monographs; and Bernardand Wallace (2002), Mathieu and Scott (2000), and Pope (2000).Indoor airflow, convective heat transfer, and species dispersionare c
20、ontrolled by the governing equations for mass, momentum ineach flow direction, energy (Navier-Stokes equation), and contam-inant distribution. A common form is presented in Equation (1),relating the change in time of a variable at a location to the amountof variable flux (e.g., momentum, mass, therm
21、al energy). Essen-tially, transient changes plus convection equals diffusion plussources:(1)The preparation of this chapter is assigned to TC 4.10, Indoor EnvironmentalModeling.wwt- UI wwxj- UUjI +wwxj- *IwIwxj-SI+=13.2 2013 ASHRAE HandbookFundamentals (SI)wheret = time, sU = density, kg/m3I = trans
22、port property (e.g., air velocity, temperature, species concentration) at any pointxj= distance in j direction, mUj= velocity in j direction, m/s*I= generalized diffusion coefficient or transport property of fluid flowSI= source or sinkLocal turbulence is expressed as a variable diffusion coefficien
23、tcalled the turbulent viscosity, often calculated from the equationsfor turbulent kinetic energy and its dissipation rate. The totaldescription of flow, therefore, consists of eight differential equa-tions, which are coupled and nonlinear. These equations containfirst and second derivatives that exp
24、ress the convection, diffusion,and source of the variables. The equations can also be numericallysolved see the section on Large Eddy Simulation (LES).Direct solution of differential equations for the rooms flowregime is not possible, but a numerical method can be applied. Thedifferential equations
25、are transformed into finite-volume equationsformulated around each grid point, as shown in Figure 1. Convec-tion and diffusion terms are developed for all six surfaces around thecontrol volume, and the source term is formulated for the volume(see Figure 1B).Assuming a room is typically divided into
26、90 u 90 u 90 cells,the eight differential equations are replaced by eight differenceequations in each point, giving a total of 5.8 u 106equations withthe same number of unknown variables.The numerical method typically involves 3000 iterations, whichmeans that a total of 17 u 109grid point calculatio
27、ns are made for theprediction of a flow field. This method obviously depends heavily oncomputers: the first predictions of room air movement were made inthe 1970s, and have since increased dramatically in popularity, espe-cially because computation cost has decreased by a factor of 10 everyeight yea
28、rs. Baker et al. (1994), Chen and Jiang (1992), Nielsen(1975), and Williams et al. (1994a, 1994b) show early CFD predic-tions of flow in ventilated rooms, and Jones and Whittle (1992) dis-cuss status and capabilities in the 1990s. Russell and Surendran(2000) review recent work on the subject.Turbule
29、nt flow is a three-dimensional, random process with awide spectrum of scales in time and space, initiated by flow insta-bilities at high Reynolds numbers; the energy involved dissipates ina cascading fashion (Mathieu and Scott 2000). Statistical analysis isused to quantify the phenomenon. At a given
30、 location and time, theinstantaneous velocity uiisui= (2)where is the ensemble average of v for steady flow, and isfluctuation velocity. Through measurement, is obtained as thestandard deviation of ui. The turbulence intensity TI is(3)The turbulent kinetic energy k per unit mass is(4)To quantify len
31、gth and time, velocity correlations and highermoments of uiare commonly used (Monin and Yaglom 1971).Those scales are essential to characterize turbulent flows and theirenergy transport mechanisms. With its turbulent kinetic energyextracted from the mean flow, large eddies cascade energy tosmaller e
32、ddies. In the smallest eddies, viscous dissipation of the tur-bulent kinetic energy occurs. By equating the total amount of energytransfer to its dissipation rate H, based on Kolmogorovs theory(Tennekes and Lumley 1972), a length scale K is defined as(5)where Q is the fluids kinematic viscosity. The
33、 Kolmogorov lengthscale K is used to determine the smallest dissipative scale of a tur-bulent flow; it is important in determining the requirements of gridsize see the sections on Large Eddy Simulation (LES) and DirectNumerical Simulation (DNS).For an incompressible fluid, the governing equations of
34、 the tur-bulent flow motion are= 0 (6)(7)where t is time, U is the fluid density, P is pressure, and Wijis the vis-cous stress tensor defined asWijPsij(8)Fig. 1 (A) Grid Point Distribution and (B) Control Volume Around Grid Point Puiuic+uiuicuicTIuiui- 100 in percentuk12-uic2 12- u1c2u2c2u3c2+ =KQ3H
35、-14-wuiwxi-Uwuiwt- Uujwuiwxj-+wPwxi-wWijwxj-+=Indoor Environmental Modeling 13.3where P is the dynamic viscosity and sijis the strain rate tensor,defined as(9)From Equations (6), (8), and (9), Equation (7) is rewritten as(10)Taking the ensemble average by using Equation (2), Equation (6)becomes(11)C
36、onsidering Equation (2), Equation (10) becomes the Reynolds-averaged Navier-Stokes (RANS) equation (Wilcox 1998):(12)The right-hand term is called the Reynolds stress ten-sor. To compute the mean flow of turbulent fluid motion, this addi-tional term causes the famous closure problem because of ensem
37、bleaveraging, and must be calculated. Much turbulence researchfocuses on the closure problem by proposing various turbulencemodels.Reynolds-Averaged Navier-Stokes (RANS) ApproachesThe most intuitive approach to calculate Reynolds stresses is toadopt the mixing-length hypotheses originated by Prandtl
38、. Manyvariants of the algebraic models and their applicability for varioustypes of turbulent flows (e.g., free shear flows, wakes, jets) are col-lected and provided by Wilcox (1998).Because of the importance of turbulent kinetic energy k in theturbulent energy budget, many researchers have developed
39、 mod-els based on k and other derived turbulence quantities for calcu-lating the Reynolds stresses. To solve the closure problem, thenumber of the additional equation(s) in turbulence models rangesfrom zero (Chen and Xu 1998) to seven Reynolds stress model(RSM) for three-dimensional flows (Launder e
40、t al. 1975); allequations in these approaches are time-averaged. Two-equationvariants of the k-H model (where H is the dissipation rate of turbu-lent kinetic energy) are popular in industrial applications, mostlyfor simulating steady mean flows and scalar species transport(Chen et al. 1990; Horstman
41、 1988; Spalart 2000). A widely usedmethod is predicting eddy viscosity Ptfrom a two-equation k-Hturbulence model, as in Launder and Spalding (1974). Nielsen(1998) discusses modifications for room airflow. The k-H turbu-lence model is only valid for fully developed turbulent flow.Flow in a room will
42、not always be at a high Reynolds number(i.e., fully developed everywhere in the room), but good predic-tions are generally obtained in areas with a certain velocity level.Low-turbulence effects can be predicted near wall regions with,for example, a Launder-Sharma (1974) low-Reynolds-numbermodel.More
43、 elaborate models, such as the Reynolds stress model(RSM), can also predict turbulence. This model closes the equationsystem with additional transport equations for Reynolds stressessee Launder (1989); it is superior to the standard k-H modelbecause anisotropic effects of turbulence are taken into a
44、ccount. Forexample, the wall-reflection terms damp turbulent fluctuationsperpendicular to the wall and convert energy to fluctuations parallelto the wall. This effect may be important for predicting a three-dimensional wall jet flow (Schlin and Nielsen 2003).In general, RSM gives better results than
45、 the standard k-H modelfor mean flow prediction, but improvements are not always signif-icant, especially for the velocity fluctuations (Chen 1996; Katoet al. 1994). Murakami et al. (1994) compared the k-H model, alge-braic model (simplified RSM), and RSM in predicting room airmovement induced by a
46、horizontal nonisothermal jet. RSMs pre-diction of mean velocity and temperature profiles in the jet showedslightly better agreement with experiments than the k-H modelsprediction.Large Eddy Simulation (LES)For intrinsically transient flow fields, time-dependent RANSsimulations often fail to resolve
47、the flow field temporally. Largeeddy simulation (LES) directly calculates the time-dependent largeeddy motion while resolving the more universally small-scalemotion using subgrid scale (SGS) modeling. LES has progressedrapidly since its inception four decades ago (Ferziger 1977; Smago-rinsky 1963; S
48、palart 2000), when it was mainly a research tool thatrequired enormous computing resources; modern computers cannow implement LES for relatively simple geometries in buildingairflow applications (Emmerich and McGrattan 1998; Lin et al.2001). For an excellent introduction to this promising CFD tech-n
49、ique, see Ferziger (1977).Filtering equations differentiate mathematically between largeand small eddies. For example,(13)where G(r,rc) is a filter function with a filter with length scale .G(r,rc) integrates to 1 and decays to 0 for scales smaller than (Chester et al. 2001). To resolve the SGS stresses, an analog tothe RANS approach for the Reynolds stress is implemented as(14)wher
