System Description

3. GEOMETRY

The first task for a user of the SES program is to prepare a schematic diagram of the physical system to be simulated. This schematic diagram will facilitate considerably the preparation of the geometry descriptive data, and will assist the user in understanding the operational requirements of the program. In broad terms, the subway system must be divided into: (1) sections in which airflows must be uniform, (2) nodes which signify the connecting points of these sections, (3) segments which have uniform geometrical properties (and therefore uniform air velocities), and (4) subsegments which are subdivisions of segments and which are assumed to have uniform temperature and humidity conditions. These four geometrical properties (sections, nodes, segments and subsegments) are the basic geometrical building blocks of the simulated subway system. An actual physical subway system must be converted into a schematic representation using these four geometric units before the user can proceed further with the simulation, since all other input data required by the program must be referenced to these parameters.

A brief description of these four geometrical properties will be provided here, followed by an example of the reduction of an actual system to a schematic representation using these building blocks.

3.1 System Description

The term “system” is used to describe the entire track and tunnel network, both above and below the ground. The above-ground portion of the system may be either at grade, on a elevated structure, or in a trench-like open cut. The below-ground portion, or tunnel system, is composed of a network of tunnels and passageways. Some parts of the tunnel system contain tracks for train operation; some are designed to allow passengers and employees to enter, exit, and move about within the system, and other parts permit the exchange of air with the atmosphere.

The analysis of a system which is composed of two or more separate tunnel systems must be performed in two or more parts since airflows and temperatures occurring in one tunnel system do not influence other systems. The independent simulation of each tunnel system does not introduce any error into the results. The user may simulate each tunnel system with track on each route extending outside the tunnel portion of the system so that the train operation within the tunnel system can be arranged to be the same as if the entire system was simulated as a whole.

The basic geometrical unit for the simulation of the below-ground portion of the system is the segment. There are two categories of segments: line segments and ventilation shaft segments.

Line Segment

A line segment is a continuous length of station or tunnel which has the following geometric properties “uniform” over its length: type (tunnel or station), cross-section, perimeters, and roughness length.

Since a line segment is a physically uniform length of tunnel, the velocity of airflow in a line segment will also be constant over its length at any given instant in time, when no trains are present within it.

Ventilation Shaft Segments

A ventilation shaft is a structure that permits movement of air or patrons between the below-ground tunnel system and the outside atmosphere, and may be any stairway, walkway, or tunnel. A ventilation shaft cannot contain tracks for train operation, but may contain a fan. It is important to note that within the SES program, the term “ventilation shaft” is an inclusive term for both the structures that are designed for the movement of air and the structures for passenger movement such as stairways and walkways. In most cases a ventilation shaft connects between a point in the system and the atmosphere.

However a ventilation shaft may also be connected between two points within the system, as would be the case for a passageway between parallel tunnels. Ventilation shafts differ from line segments in four ways:

(1) trains cannot operate in ventilation shafts, (2) fans can be placed in a ventilation shaft (provided it is not a stairway), (3) neither steady nor unsteady state heating or cooling sources can be located within a ventilation shaft, and (4) the viscous friction between the air and the ventilation shaft walls is assumed to be negligible compared to the “minor” head losses, and is therefore ignored in the ventilation shaft airflow calculations. (“Minor” head losses refers to those losses caused by other than frictional effects, such as turns. Minor does not refer to the magnitude of the losses.)

Ventilation shaft structures may be assigned one or more segments, each of which may have a different area or perimeter. Furthermore, ventilation shafts are sometimes constructed of segments which are connected at various angles in order to satisfy physical clearance problems and alignment with surface geometry, reflecting the fact that, in general, gratings are preferably located in the sidewalk rather than in the street.

Each ventilation shaft segment has the following uniform properties: length, area, and perimeter.

These properties are defined in a manner identical to those of line segments. The following additional properties must be defined once for each ventilation shaft: section type, grate-area, and design maximum outflow air velocity at grate.

Section and Nodes

A section is a length of tunnel within which the air moves at a uniform flow rate. It may contain one or more contiguous segments. If these segments are of different cross-section area, the air velocity will change for each segment, but the bulk airflow rate will be uniform throughout the section. A line segment may comprise all or part of any given section, but it cannot be part of more than one section. A section is

3-3 The aerodynamic portion of the SES simulation program computes an airflow rate for each line section and ventilation shaft section in the system. The rate of airflow in the section is a function of train piston action, fans, buoyancy, viscous damping, “minor” head losses and inertial effects. These factors are all considered in the calculations of the airflows which are continuously varying over the simulation

interval.

A section may be connected to other sections or to the atmosphere. In addition, sections must not terminate at a “dead end,” that is, it must not have a closed end which does not permit air to flow either into or out of the section. When simulating a system which is composed of a tunnel network, there must be a flow path available from any node to all other points in the tunnel system. This flow path may pass through one or more sections, but may not pass through the atmosphere. In short, the tunnel system must be an interconnected network of sections, each with a uniform airflow rate at any given time. Examples of possible sections are shown in Figure 3.1.

A “node” is a reference point which is used to relate the interconnections of the sections in a system. A node must be defined at each junction of three or more sections as well as at each portal and opening to the atmosphere. A node may also optionally be located at a junction of two sections if the user wishes.

A “portal” is formed when a line segment is terminated at the atmosphere. Since line segments may have trains operating in them, trains can enter or leave the tunnel system through portals. The point where a ventilation shaft terminates at the ground surface is called an “opening to the atmosphere.”

Nodes may have from one to five sections attached. (This upper limit may be changed as described in Appendix A.) However, a node with a single section attached is always either a portal or an opening to the atmosphere.

The airflows at each node must satisfy the law of conservation of mass. That is, at any instant, the amount of air flowing toward the node is always equal to the amount of airflow leaving the node. The law of conservation of thermal energy is also maintained. The thermal energy flowing toward the node is always equal to that leaving the node.

NOTE: In the following discussion, and throughout this manual, the term “fan” refers to a conventional supply/exhaust fan, unless otherwise specified.

NODE

NODE SECTION

NODE NODE

SEGMENT

SECTION

NODE NODE

SEGMENT

SEGMENT SEGMENT

SEGMENT

NODE NODE

SECTION SECTION

NODE SECTION

NODE

NODE NODE

SECTION

SECTION

SECTION

3-5 3.2 Schematic Diagram

As an aid to setting up the system geometry and understanding the interrelation between the sections in the system, the user is advised to prepare a schematic or line diagram of the system. In the schematic diagram, each section is represented by a line and the intersections of sections (at nodes) are also identified. Each of the sections and nodes are then numbered for purposes of identification in the program. Each section number is unique to that section; that is, no other section in the system can have the same identification number. Sections need not be consecutively numbered (although this is advisable to assist in data review as the print out supplies the information within the sections sequentially according to the section identification numbers); the user may choose any number as long as the number has not been used previously and lies between the limits of 1 and an upper limit described in Appendix A. There is no relationship between section numbers and their physical location within the system. These numbers are used solely for identification, and the physical arrangement of the sections is described in the geometry data.

In a manner similar to section numbers, the node identification numbers need not be consecutive, but they must be unique. Node numbers do not describe the physical location of the sections within the system, but are only a means of referring to a particular node.

Unlike sections and nodes, segment identification numbers are not limited by the limit in Appendix A, but may range from 1 through 999. However, the total number of segments is limited to the amount specified in Appendix A. Section, node, and segment identification numbers are entirely independent.

Therefore sections, nodes and segments may, if desired, be referenced by the same identification number.

Sample System

Figure 3.2 provides an isometric sketch of a sample subway system which is used as the basis for the preparation of the schematic diagram of the system also shown in Figure 3.2. This figure shows several of the geometrical situations that one would expect to encounter in a subway. In the schematic diagram the nodes are represented by numbered points, the sections are represented by numbered lines, and the segments are represented by portions of the numbered lines used to describe the sections. It can be seen that the system shown has been represented by 18 sections and 18 nodes.

The system shown in Figure 3.2 contains three portals which are located at nodes 1, 2, and 12.

These nodes can be immediately identified as either portals or openings to the atmosphere since only one line section is attached to them. The system contains six ventilation shafts which provide connections to the atmosphere. They have been designated as section numbers 5, 8, 11, 13, 15, and 17. These vent shafts all terminate at nodes with only one section attached. All portals or openings to the atmosphere must be represented by nodes with one section attached. This system contains one station composed of portions of sections 12 and 14.

2

3-7 The stairway which is located at the center of the station is connected to node number 9, which divides the station into two lines segments — one in line section 12 and other in line section 14. Both sections 12 and 14 are composed of two line segments — a station segment and a tunnel segment.

The system shown in Figure 3.2 contains both double-track tunnels and single-track tunnels. A double-track tunnel contains two or more tracks on which trains may operate. A tunnel is considered to be double-track if there is either no dividing wall between the trackways, or if a dividing wall of sufficient porosity is present so as to not significantly affect the bulk airflow rate in the section. Frequently trackway dividing walls are constructed with regularly spaced openings through the wall. These openings are placed for safety and access purposes; however, they also allow air to flow between the trackways. Porosity, which is a measure of the “openness” of the wall, is defined as the ratio of the open area of the holes to the area of the entire wall.

Scale model tests (Ref. 1) have shown that tunnels with porosity values from 0 to approximately 5 percent should be treated as two separate parallel segments with discrete openings between them. The airflow in the parallel tunnels exhibits some degree of asymmetry for porosity values on the order of 5 percent and greater, but the piston-action bulk tunnel airflow is essentially the same as if no dividing wall exists (see Ref. 1 for details). Thus, for normal operation simulations, tunnels with porosity over 5 percent can be adequately simulated as one double-track segment. (For emergency operation simulations, even tunnels with less than 5 percent porosity should be simulated as one double-track segment. See Chapter 9 for a more detailed discussion of emergency operations, and special cases.)

Referring to Figure 3.2, it can be seen that node 4 has four sections attached to it. In this case, three line sections and one ventilation shaft section meet at the node. Node 3, which is located at a junction of only two sections has been placed in the system at the user's option. If this node were not present, sections 2 and 3 would be combined into one section. This node was inserted in order to facilitate future modifications of the program to allow a new section, such as a ventilation shaft, to be added.

Addition of a ventilation shaft to an existing node requires only the definition of an additional ventilation shaft section which connects a new node, open to the atmosphere, and the existing node.

If an existing node is located at the point where a new ventilation shaft is to be connected into a system, the user need only define the new ventilation shaft to be connected to this existing node and enter the properties of this new shaft in the ventilation shaft data. The user will have fewer modifications to the input data than if a node was not placed in the original tunnel system in anticipation of the future addition of a vent shaft at that particular point. If no node exists at the point where the user wishes to add a ventilation shaft, there will be fewer modifications to the input data if the user adds the new node and the new vent shaft at the interface between two segments, rather than in the middle of a segment. The reasons that fewer modifications to the input data will be required if the new vent shaft is placed at the interface between two segments are as follows: When a new node is placed between two segments at the segment interface, it creates only one additional section and no additional segments. If the new node and vent shaft are placed in the middle of a segment, the segment in which they are to be located must be broken into two segments. Therefore, when the new node and vent shaft are placed in the middle of a

segment, one additional section and one additional segment will be created. It is always a good idea for the user to anticipate any possible future additions to the system as a great deal of time would be saved should modifications be necessary.

The cross passage represented by section 4 (see Figure 3.2) must be represented as a ventilation shaft segment if it is to contain a fan, or as a line segment if it is to include any steady-state heat loads. If calculations are desired to determine the heat created by viscous friction along the walls and for evaporation from the wall surface, the cross passage must be represented as a line segment. It is suggested that cross passages between tunnel sections be represented as ventilation shaft segments, while cross passages within stations be represented as line segments (unless they are expected to contain a fan). Stairways and actual ventilation shafts may also be represented as line segments if desired.