Required Input

A certain minimal amount of input information is needed to run a CFD case; more information can be provided to achieve higher-qualitv results. The data required are usually

• Geometric modeling

• Boundary conditions in space and time: thermal, flow (ventilation, mechanical, and natural), sources of contaminants

CFD results can only be as good as

1. Quality of geometric modeling and spatial resolution of computational mesh

2. Models involved in CFD code

3. Knowledge of boundary conditions

This is not as simple as it sounds, as the boundary conditions are very of­ten not well known. The number and distribution of heat sources and ven­tilation parameters, particularly in naturally ventilated surroundings, are very often not known or even vary. The CFD engineer has to cope with this situation and can do one of the following:

• Choose boundary conditions from his or her knowledge about the given information.

• Perform calculations with parameters varied to check their importance. The CFD results can possibly turn out to be helpful more comparatively (qualitatively) than quantitatively.

• Try to expand the system assumed so far to derive higher-quality boundary-condition values.

The latter is certainly the best if it can be done, which depends on the availability of suited models and resources. Examples of such procedures are

• The problem of unknown amounts of air leakage in the cold season in an industrial hall can be calculated by multizone airflow models during the whole year with local meteorological data.

• A similar approach for unknown temperatures on wall and glass faces can be addressed with the help of thermal building simulation programs.

• The distribution of solar radiation, including surface radiation exchange, can account for solar heat source variations in time and local space.

The following objects usually can be added to the geometric model:

• Bounding shapes of the rooms

• Inclined bounding faces can cause modeling failures in orthogonal meshes, as the face is modeled as a “stair” instead of a plane face. The wall friction of such a stair is sometimes not accounted for.

• Shapes of inside objects which are obstacles to the airflow (sometimes referred to as “blocked-off” objects), such as machine blocks, partition walls, etc.

• These objects can contain unused computation nodes, which possibly still occupy memory space, depending on the meshing method used.

• Within such objects, conductive heat flow can be solved as well. This is sometimes called Conjugate heat transfer in the literature.

• Shapes of inside objects which are only partly permeable to airflow (sometimes referred to as “porous” objects), such as inlet grills, vents, etc.

• Position of supply and exhaust openings

Note that the codes usually do not support moving objects with either adap­tive meshes or a stationary mesh.

11.2.3.2 Physical Boundary Conditions

These conditions govern the flow and are therefore of crucial importance. For each condition (see Table 11.2) the flow value and the scalar values are discussed separately. The table contains volumetric sources, which are not strictly speaking boundary conditions in a mathematical sense. For the CFD engineer they nevertheless define the problem and are therefore included in this table. The problem must also not be overspecified.

Usually the boundary conditions in the following subsections are used.

Inflow

• Used for air supply.

• Flow parameter specified is one of mass flow, velocity, or pressure. Usually mass flow or velocity is taken, as these values are known for air supplies.

• Associated scalar values include temperature, turbulence quantities, contaminant concentrations.

Outlet

• Used for air supply.

Parameters specified are mass flow or velocity. Usually at one outlet, pres­sure equal to a constant is specified in incompressible flow. If several outlets are present, this pressure boundary condition can only be applied to one out­let, as there are some (unknown) pressure differences between the different outlets. The flow conditions in the rooms are better represented by taking the outlet mass flows when they are known.

TABLE 11.2 Boundary Conditions

Boundary — Condition type

Flow value

Scalar value

Special issues in ventilation App.

Inflow

M, v, or P

T; C„ turb

Lnlet-box method

< )uttlow

M, v, or P

Large opening

Ptotlll

T, C, turb for inflow

Combination with outside flow 1

Wall

V = 0

T or Q

Heat flux or temperature

Volumetric sources

Q, •’v

Simplification

Svmmetrv

_

_

Can be used sometimes ‘

Periodicity

For subdivision ot large <■ halls

M — mass flow, v = velocity components, P pressure, T = temperature, Q = heat flux, C, = concentration of contaminant species I, Sr = contaminant source, turb = turbulent quantities (depend on the turbulence model used). ‘ Example in appendix.

Large Opening

In such openings, bidirectional flow driven by temperature differences be­tween the two rooms can occur. If a total pressure (static pressure plus dy­namic pressure) is specified, this phenomenon can be accounted for. For higher accuracy in the neighborhood of this opening, it is, however, recom­mended to expand the calculation domain beyond this opening.

Walls

Wall friction slows down the flow.

The temperature boundary condition is in many problems of buoyant How, e. g., heat sources (machines) or heat sinks (cold glazings), is of great im­portance.

Walls can also act as sources or sinks of gases or materials.

Moving Walls (Rotating Parts)

Moving wralls can be used to represent rapidly moving parts which induce flow in the considered space.

Volume Sources

Heat or contaminant sources can also be assigned to parts of the fluid vol­ume to account for very small real sources or a distribution of a large number of small sources. Care must be taken, however, to make sure that this repre­sentation of distributed sources describes correctly the real situation (see the earlier section “Geometric Modeling”).

Symmetry or Periodicity

These conditions can be used sometimes for a reduction of the full geome­try, but only if the problem is symmetrical or periodic from both the geometric and the physical points of view.

I 1.2.3.3 Wall Boundary Conditions Wall Functions

The natural way to treat wall boundaries is to make the grid sufficiently fine that the sharp gradients prevailing near walls are resolved. When comput­ing complex three-dimensional flow, this often requires an excessive amount of computer resources. An alternative is to assume that the flow near the wall behaves like a fully developed turbulent boundary layer and prescribe bound­ary conditions employing wall functions. Given a maximum number of nodes that we can afford to use in a computation, it is often preferable to use wall functions, which allow us to use a fine grid in other regions far away from the walls where the gradients of the flow variables are large. In this way the CPU time can be reduced substantially. Using wall functions means that the bound­ary layer near a wall is not resolved, but the first node is located in the log-law region where 30 5=y+ 5=100 (the upper limit depends on the Reynolds num­ber). The flow between the first node and the wall is supposed to be as in flat — plate boundary layer flow. This assumption is often well satisfied, but in many flow situations it is not true at all. When applying boundary conditions using wall functions, the friction velocity is computed from the log-law, which reads2“4

Eu*y

подпись: eu*y

(11.8)

■ In

U* k

подпись: ■ in
u* k
UP _ 11

Where Up is the near-wall node velocity tangential to the wall, Y is the distance from the wall to the node, K is the von Karmann constant ( =0.41), and Ј = 9.0. The friction velocity U, has to be computed numerically. This is con­veniently done by first guessing a value for y+, then computing a friction veloc­ity (which we denote ). Then the new friction velocity is computed from Eq. (11.8).

KUp

U * =

In (Eu2^y/v)

The above equation is solved a few times by iteration, replacing m? IcI on the right-hand side in each iteration by the new «». Having obtained m*, the non­dimensional wall distance y+ = U*y/v can be computed.

For a discussion of wall functions, see refs. 2-4, e. g.

In ventilated rooms buoyant effects are often imported, and wall func­tions to take this into account are presented in ref. 5.

Low-Reynolds-Number Turbulence Models

In the previous section we discussed wall functions, which are used to re­duce the number of cells. However, we must be aware that this is an approxi­mation that, if the flow near the boundary is important, can be rather crude. In many internal flows—where all boundaries are either walls, symmetry planes, inlets, or outlets—the boundary layer may not be that important, as the flow field is often pressure determined. However, when we are predicting heat transfer, it is generally not a good idea to use wall functions, because the convective heat transfer at the walls may be inaccurately predicted. The rea­son is that convective heat transfer is extremely sensitive to the near-wall flow and temperature field.

When the wall is approached, the viscous effects become more important, and for Y* < 5 the viscous diffusion becomes comparable to the turbulent dif­fusion. Thus, the standard turbulence models (high-Reynolds-number models) are not correct since fully turbulent conditions have been assumed. The high­Reynolds-number models are modified so that they can be used all the way down to the wall. These modified models are termed low-Reynolds-number (LRN) models. Please note that “high-Reynolds-number” and “low-Reynolds — number” do Not refer to the global Reynolds number (for example, Re7, ReT, Re0); rather, here we are talking about the local turbulent Reynolds number Re< = °}L(/v formed by a turbulent velocity fluctuation °U and turbulent length scale Ђ. This Reynolds number varies throughout the computational domain and is proportional to the ratio of the turbulent and physical viscosity Vt/v, i. e., Ref <=c Vt/ v. This ratio is of the order of 150 or larger in fully tur­bulent flow6 and it goes to zero w’hen a wall is approached.

Examples of LRN K-e and K-o> models can be found in refs. 2 and 9-13. A review can be found in ref. 14.

Time-Scheduled Boundary Conditions

In time-dependent problems, all the above conditions can be time-dependent functions, such as a machine heating cycle or another time-dependent process under study.

Initial Conditions

In stationary problems the initial conditions are in theory not important, but a good guess gives faster convergence. It is even possible that a very bad guess can prevent convergence, if the convergence parameters are chosen a bit aggressively. A very bad guess can also be obtained as an intermediate result of a mistakenly ill-posed problem. A restart from a fresh initial guess is then required.

In time-dependent problems, of course, a good guess (or knowledge) of the initial conditions is much more important.

Data from Thermal Building-Dynamics Programs

In many cases, some boundary conditions are not well known or not known at all. Temperature boundary conditions can be obtained from thermal building-dynamics programs that allow the capture of spatial mean tempera­tures during a time period as long as a whole year. Some of these programs yield surface temperature values (e. g., TRNSYS), which can be used as tem­perature boundary conditions at the time of CFD study.

Data from Infiltration and Multizone Airflow Programs

Flow values (mass flows into and out of the CFD domain) can be obtained from infiltration and multizone airflow programs and used as boundary con ditions.

Geometry from CAD Database

CAD databases can be helpful, but this depends much on the software set available. Architectural CAD data often contain too many data that have to be simplified and reduced considerably.

When choosing CFD software, there are several aspects that should be taken into account. The most important aspect is probably how complex the configuration is, and what type of grid that complexity requires. An­other question is if radiation15’16 needs to be taken into account; if so, is it sufficient to take radiation between walls, ceiling, and floor into ac­count, or do we need to do ray tracing,17 including the effects of solid bodies in the room? Does the fluid in the room (for example, moisture) contribute to radiation?18 A third aspect is the turbulence model. In ven­tilation problems it is often sufficient to use simple eddy-viscosity mod­els. If heat transfer near surfaces is to be predicted with accuracy, low-Re number models should be used. More complex models, that are better in accurately modeling the physics are Reynolds stress models.115′ These models are often considerably more expensive, primarily because they are numerically more unstable. Simplified forms of Reynolds stress models are algebraic Reynolds stress models (ASMs),20’21 and explicit algebraic Reynolds stress models (EARSMs);22-24 EARSMs are also often referred to as nonlinear eddy-viscosity models.

Next, the choice of grid type is discussed.

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