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## Understanding Dynamic Simulations

### Dynamic Simulations and Unsteady Flows

The Simscape™ Fluids™ software models time-dependency within components and systems. Fluid flow within Simscape networks may, however, be either steady or unsteady with respect to time. During the course of the simulation, after initial simulation transients dissipate, if the network fluid variables do not change or do not contribute to periodicity within the simulation, the flow is considered to be steady-state. A steady-state flow indicates a steady-state simulation, however, unsteady flows may occur in both steady and dynamic simulations.

Before assuming a flow is steady-state, it is important to verify that the relationship between components is truly steady. The simulation length may also be critical: fluid dynamics with lower periodicity may require a longer period to be exposed within simulation. Finally, the boundary conditions of your simulation may themselves be time-dependent, as is the case in the Brayton Cycle refrigeration model discussed below.

### Observing Unsteady Boundary Conditions

The design criteria of a heating-cooling system are based on the pressure-enthalpy diagram of the system working fluid:

HVAC System p-H Plot

Each corner of the cycle indicates the fluid state after a dynamic process:

1. Cool vapor at low pressure

2. Hot vapor at high pressure

3. Hot liquid at high pressure

4. Mixed vapor and liquid at low pressure

These points become the design criteria for an HVAC system, which can be recreated in the Simscape Fluids Two-Phase domain by:

• An expansion valve (state 4 to state 3)

• A condenser (state 3 to state 2)

• A compressor (state 2 to state 1)

• An evaporator (state 1 to state 4)

Brayton Cycle HVAC System

During the simulation, however, the quality of the working fluid at each design point may vary depending on the dynamic processes occurring in the rest of the cycle. For example, when compressor dynamics are not assumed to be steady, the fluid qualities at the four points of the cycle are influenced:

Note that the cycle temperature in the example above remains between 275 and 325 K. This is an efficiency design point: icing forms at sustained temperatures lower than 275 K, which in turn lowers the evaporator heat conductivity and efficiency. At temperatures higher than 325 K, the condenser capacity for heat shedding is reduced, along with the overall cycle efficiency.

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