Handbook of air conditioning and refrigeration / Shan K

25.18 CHAPTER TWENTY-FIVE
Physical Modeling
the catalog data or actual performance into a regression equation, to mathematically relate the dependent
variable z to independent variable x in steady-state simulation as follows:
z � a 0 � a 1x � a 2x 2 � a 3x 3 (25.4)
To relate a dependent variable with two independent variables x and y, the polynomial expression is
z � b 0 � b 1x � b 2x 2 � b 3y � b 4y 2 � b 5xy � b 6x 2 y � b 7xy 2 � b 8x 2 y 2 (25.5)
where a 0, a 1,...,a 3, b 0, b 1,...,b 8 � coefficients. Computer programs are available to solve
the coefficients according to the data from the manufacturer or actual performance data.
Modeling. Setting up a component or a system model is the first step of energy simulation by
physical modeling. Modeling includes the following:
● Description of system or component configuration whether it is an air, water, refrigeration, or
heating system, or whether it consists of many components or only contains a single device.
● Description of the operating characteristics of the system or component, and the interaction between
system components, whether it can be simplified to a steady-state model or a dynamic
model. A simplification of the physical model that results in an error of only few percent of the final
result is recommended, in order to simplify the calculation and analysis.
Developing Mathematical Equations. Mathematical equations are developed to describe the operating
characteristics of the working substance, and work and energy transfer.
Solving for Outputs. Computer programs are used to solve equations simultaneously, in sequence,
or by iteration. The required operating parameters, the outputs, can thus be obtained. Sometimes performance
equations are used to link the required outputs with one or two operating parameters.
Verification. The results of predicted performance during energy simulation can be verified
against actual measured readings of similar models and operating conditions. According to Scientific
Computing (1997), using performance equations to simulate the energy use of an HVAC&R
system or component is simple, and lumps the capacity, energy use, or other required operating parameters
in one performance equation. The disadvantage is that the performance data must be provided
to create the performance equations. Physical modeling allows more freedom in configuring
the characteristics of the system or equipment.
Steady-State and Dynamic Simulation
According to its operating characteristics, energy simulation can be classified as steady-state or dynamic
simulation.
Steady-State Simulation. In steady-state simulation, the relationship between various operating
parameters within a certain time increment is described by mathematical equations independent of
time, such as
z � F(x, y, ...) (25.6)
where x, y, z � operating variables that are not a function of time. Steady-state simulation always
simulates relatively long-term system or component characteristics, such as annual or seasonal energy
simulation. A time increment of 1 h is typically used for analysis. Within the time increment,
the operating parameters are independent of time. However, the magnitude of the same operating
parameter may be different in successive hours.