EXAMPLE $6\mathrm{.}1$

Determine the coil load, circulation and ventilation airflow rates and the thermodynamic states for a CAV system at design conditions for a commercial office building. The design ambient conditions are $\backslash (92^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ dry bulb and $\backslash (78^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )$ wet bulb. The building can be treated as a single zone with a total zone load of $\backslash (500,000\backslash$mathrm$\{$Btu$\}/\backslash )$ hr and a sensible heat ratio of $0\mathrm{.}8.$ The design occupancy is $80$ people and the corresponding ventilation air flow rate is $1600$ cfm $,$ which is based on $20$ cfm of outdoor air per person $($Section $7\mathrm{.}3).$ The zone temperature thermostat setting is $\backslash (77^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ),$ which is within the summer comfort zone $($Section $7\mathrm{.}2).$ The bypass factor for the coil is $0\mathrm{.}175$ and the chilled water temperature is $\backslash (50^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$

$1.$ Review Example $6\mathrm{.}1$ in the textbook. Write a Matlab code to solve the example, through an iterative calculation.

Follow these steps:

a$.$ Assume that there is no reheat.

b$.$ How many thermodynamic states of moist air, and how many flow rates must be known to specify the state of the system?

c$.$ List the variables that must be determined to specify the state of the system. Use the symbols of the textbook and lecture notes.

d$.$ Write all the fundamental conservation law equations connecting these variables, especially for the plenum that mixes ventilation air with recirculation air.

e$.$ Write any additional equations that relate the unknown variables to the data given in the problem.

f$.$ Discuss whether the number of remaining unknown variables and number of equations to be solved are equal, and whether any additional assumptions are needed.

g$.$ Considering that an explicit solution method may not be possible, make an approximate initial estimate for one of the unknowns:

i$.$ Either estimate the processed air state $($C$)$ as the saturated state corresponding to the cooling coil temperature $($ignoring coil bypass factor$)$

ii$.$ Or estimate the R$.$H$.$ of the zone air as $50\backslash \%($Don$\text{'}$t use both estimates$)$

h$.$ Using the psychrometric chart and method $($i$),$ obtain an initial estimate for air flow rates and the coil load.

i$.$ Discuss whether the ASHRAE equations $($Section $6\mathrm{.}5)$ can be used to solve the problem without iterative computation.

j$.$ Optional, best effort only: Write a Matlab code that takes the initial estimate, and uses the relevant equations to sequentially calculate unknown state and flow variables. Use the psychrometric functions that are provided in the set of Matlab codes available to you. Recalculate the value that was estimated initially, and repeat the calculation until it does not change significantly. If the computation does not converge, you may consider changing the order in which you calculate variables.

k$.$ Compare the final values with the solution given in the textbook.