SYSTEMS MODELING

Stress Engineering Services regularly develops special-purpose time-domain dynamic simulation programs for our clients. These programs allow the user to vary the important parameters of the systems such as dimensions, fluid properties, fluid volumes, and flow resistance coefficients. The output of these programs provides time-history traces of variables such as pressure and flow rate throughout the device being modeled. This technology has been applied to single-phase and two-phase modeling in a variety of industries. Stress Engineering has developed dynamic simulation programs for the following:

An example of a systems model is presented below. The model simulates the priming and normal operation of a trigger sprayer. The figure below shows the sprayer with the critical flow, pressure, and displacement variables labeled. The objective of a dynamic systems model is to reduce this complex fluid/mechanical system to a set of equations that accurately captures the physics of the device while remaining simple enough to allow a large number of designs to be evaluated on an office PC in a short period of time.

The user is given a panel such as that shown below allowing input of a variety of dimensional and process information. In this case one of the critical parameters is the cross sectional area of the air vent which allows fresh air into the package through the Q1 flow path at the end of each stroke.

The results of the simulation at the end of each of the first four priming strokes are shown below. In this simulation the air vent area was set to 0.07 mm^2 as shown above. Notice that as the pump primes the air pressure in the bottle decreases. This can lead the sides of the bottle to pull in (paneling) and is undesirable.

The above results are shown in graphical form below. In this graph the blue trace shows the motion of the piston and the red line shows the pressure in the bottle. The pressure in the bottle drops sharply during each stroke as liquid is drawn up the dip tube during the suction portion of the stroke. The bottle pressure stays constant during the first part of the discharge portion of the stroke. As the piston reaches the end of the discharge stroke the air vent opens, the bottle vents, and the pressure in the bottle increases. However, because the air vent is undersized the pressure never recovers completely and the vacuum in the bottle increases with each stroke.

The problem described above can be corrected by opening the vent from 0.07 mm^2 to 0.14 mm^2. The results of the simulation with this increased vent area are shown below. Note that in this case the pressure in the bottle returns to zero at the end of each discharge stroke.

A similar series of simulations can be done to optimize other features of the design such as the number of strokes to prime and to insure the performance of the sprayer for products having a wide variety of densities and viscosities.