Thermodynamic Node Type (Input Forms 6A, 6B, 6C)

The air temperature and specific humidity of each subsegment are recomputed at every thermodynamic computation interval during the simulation. Three fundamental processes can occur to alter the temperature and humidity in each of these subsegments: (1) sensible and latent heat can be added directly from sources within the subsegment; (2) heat can be exchanged with the tunnel walls; and (3) there can be a net difference in the heat and moisture content between air flowing into the subsegment and air flowing out. Air flowing into a node from a subsegment bears the temperature and humidity of the subsegment from which it is leaving. Air flowing into a subsegment from a node bears the temperature and humidity either computed by the program or assigned by the user (e.g., outside ambient) depending on the number of subsegments joined by the node.

On Input Form 6A the user is required to indicate a thermal characteristic for each of the nodes in the system, by specifying whether the node is to be defined as a Type 1, Type 2, or Type 3

thermodynamic node. The Thermodynamic Type assigned to a node defines the manner in which the program determines the temperature and humidity of airflow leaving a node and entering a subsegment. A Type 1 may be assigned to a node which joins two, three, four, or five subsegments. A Type 2 may be assigned to a node which joins four or five subsegments. Type 1 and Type 2 differ in the method of computing the temperature and humidity of air leaving the nodes. These methods reflect the degree of thermodynamic mixing of the airflows at this confluence point. Type 3 must be assigned to nodes which are joined to only one subsegment and represent an opening to the atmosphere or any other boundary condition where the air entering the subsegment from this node is at a user-specified temperature and humidity.

Type 3 and Type 1 nodes occur in all subway systems, whereas Type 2 nodes are defined only for nodes joining four or five subsegments and then at the discretion of the user. Accordingly, these node types will be described in the order of increasing complexity.

Boundary Nodes (Type 3). A node defined as Type 3 may only be connected to one subsegment, and all airflows entering the subsegment from this node have the dry-bulb and wet-bulb temperatures at this boundary defined by the user on Input Form 6B. Air entering the subsegment through this node bears user-specified temperature and humidity boundary conditions, and air leaving the system through the Type 3 node is exhausted bearing the temperature and humidity computed for the terminal subsegment.

Mixing Nodes (Type 1). Prior to recomputing the air temperature and humidity of each

subsegment, the program first computes the instantaneous airflows in each section of the system. These computations insure continuity of flow about each node; i.e., the flow approaching a node equals the flow leaving. If a Type 1 is assigned to a node on Input Form 6A, the program automatically treats this node as one where complete thermodynamic mixing of the incoming airflows occurs. The temperature and

humidity of the airflows leaving this node are computed simply as the energy-based average of the temperature and humidities of the airflows approaching the node. Type 1 must be assigned to nodes which join either two or three subsegments, and may be assigned to any node which joins four or more subsegments.

Partial - Mixing Nodes (Type 2). For subway geometries where either four or five sections meet at a node, flow situations may occur where inflowing air from one section does not mix completely in a thermodynamic sense with other inflows before leaving the node. Typical circumstances where this may occur are tunnel-to-tunnel crossovers (4 sections meet) and ventilation shafts which connect to two separate tunnels (5 sections meet). The SES Program enables the user to address such complexities in a straightforward manner through the use of the Type 2 thermodynamic node.

A node assigned a Type 2 on Input Form 6A is internally represented in the program

thermodynamic network by a set of three thermodynamic “subnodes”. Unlike the nodes designated as Type 1, which may form a confluence of two- to five-system sections, Type 2 may only be assigned to nodes which joins either four or five system sections. The three thermodynamic “subnodes” of a Type 2 node are treated mathematically as though a minor network existed within the node which links the sections joined by the node in a special manner reflecting preferred intra-section flows.

Each thermal subnode behaves individually as a mixing, or Type 1 thermodynamic node; that is, the temperature and humidity of the airflows leaving a subnode are computed simply as the energy-based average of the temperature and humidity of the airflows entering the subnode. The Aerodynamic

Subprogram provides the magnitude and direction of airflow in each section. If the node is thermodynamic

5-17

“subnodes” in the minor network as A, B, and C it is possible to describe the “subnodes” as internally linked by two branches - one extending from A to B and the other from B to C.

SECTION 5 SECTION 5 SECTION 5

SECTION 4 SECTION 2

SECTION 3 SECTION 1

A

C B

The program user must designate on Form 6C the sections connected to thermal subnode A, thermal subnode B, and thermal subnode C. Two sections must be connected to each of the two end subnodes (A and C). If five sections are connected to the node, the remaining section may be connected to any of the three subnodes. By assigning certain sections connected to a common subnode, the user is indicating to the program that in circumstances where the aerodynamic subprogram computes airflow to be approaching the subnode in one of these sections and leaving in the other, the approaching air prefers to continue to the outflowing section without mixing thermodynamically with flows in sections connected to other subnodes. Whether or not mixing actually occurs will depend on the actual flow rates in the other sections; there may be crossflows among the subnodes as a consequence of continuity.

Since the internal geometric configuration of a Type 2 node may significantly affect the thermodynamic relationship among the subsegments adjacent to the node, it is necessary that this configuration reflect the physical nature of the junction to insure a valid thermodynamic simulation. The following examples will illustrate the use of a Type 2 thermodynamic node and the user discretion required.

Example 5.4 A common geometrical configuration in subway systems is illustrated by the following schematic of tunnel crossover, which shows a point at which two adjacent subway tunnels provide a brief area of communication at a point where no dividing wall exists; i.e., a “tunnel-to-tunnel crossover.”

SECTION 1

SECTION 3

SECTION 2

SECTION 4

L

This geometrical configuration would be represented in the system network by four line sections (1, 2, 3, and 4) which meet at a common node.

NODE SECTION 1

SECTION 3

SECTION 2

SECTION 4

In flow situations where the flow rate approaching subnode A in section 1 is the same as the flow rate leaving via section 2, there would be no thermodynamic mixing with the flow in sections 3 and 4. When the aerodynamic subprogram computes a greater approaching flow rate in section 1 than the leaving flow in section 2, the net difference in flow passes through subnode B to subnode C, to mix thermodynamically with other flows approaching subnode C.

If the distance L is relatively long (five or six tunnel diameters), the area of the system represented by the node is large, allowing the incoming flows the opportunity to intermix by virtue of the large, turbulence promoting, interface area of the various flows. In this case, the type 1 characteristic would be assigned and no thermal subnodes would be used. On the other hand, if the distance L were relatively short (one or two tunnel

diameters or less), there would be little opportunity for mixing of the incoming flows. The

5-19 thermodynamic mixing with the flow in sections 3 and 4. When the aerodynamic

subprogram computes a greater approaching flow rate in section 1 than the leaving flow in section 2, the net difference in flow passes through subnode B to subnode C to mix thermodynamically with other flows approaching subnode C. As another example, consider a configuration where a vent shaft is located directly above this break in the dividing wall. The user would connect this section to thermal subnode B; the

thermodynamic network created at this node would be as follows:

A

C B

SECTION 1 SECTION 2

SECTION 3

VENT SHAFT SECTION

SECTION 4

For the purposes of this example, let us assume the program has just computed the airflows in the sections joined by this node at an instant during the simulation and that these airflows are as shown.

SECTION 1 100 cfm SECTION 2 200 cfm @ 100^oF

SECTION 3 100 cfm @ 70^oF SECTION 4 150 cfm SECTION 5 50 cfm

Let us also assume that at this time the temperature of the air entering the node from sections 2 and 3 are 100 and 70ºF, respectively. If this node was defined as Type 1 (Mixing Node), the program would compute the temperature of the airflows entering sections 1, 4 and 5 as 90°F - the energy-based average of the temperatures of the airflows entering the node. If this node was defined as Type 2 (Partial-Mixing Node) having sections 1 and 2 connected to subnode A, sections 3 and 4 connected to subnode C and section 5 to subnode B, the program would first compute the flow from subnode A to subnode B as 100 cfm and from subnode B to subnode C as 50 cfm. The temperatures of the airflows leaving subnodes A, B, and C (to sections 1, 5,and 4) would be computed as 100, 100, and 80^oF, respectively - the energy-based averages of the temperatures of the airflows entering each subnode.

User Suggestions. It is important to remember that the use of the Type 2 node only need to be considered in situations where four or five sections are joined at a node. As the tunnel-to-tunnel crossover example shows, the criterion for selecting a Type 2 node over a Type 1 is based on the expected degree of mixing of incoming flows in all flow situations. The selection is to a certain extent dependent upon the judgement of the user. It is recommended that in cases where the type of a junction is uncertain, it should be assigned as a Type 1.

5.9 Environmental Control Load Evaluation