Apparatus:
Crossflow Tube and fin HX. (liquid-to-air Intercooler),
Hot Side: Tube side, gas flowing internally
Cold Side: fin side, water flowing in crossflow
Goal:
Generate an environment in "OpenAI gym" where the agents actions:
are moving the valve (1),(0) fully open, fully closed on the inlet stream.
Observation:
outflow temperature
Problem:
Generate a formula for the change in
$$\Delta{\dot V in} = \Delta{Tout}$$
where:
$$\Delta{\dot V in}$$ is the flow rate inside the tube &
$$\Delta{Tout}$$ is the temperature out of the tube.
Its understood that this is one of the most common process control problems: feedback or feedforward valve that controls inlet flowrate to regulate outlet temperature. Temperature is sensed by a thermocouple.
Understanding:
Mass balance:
F-F = 0
Energy balance:
$$V \cdot \rho\cdot c_p \cdot \frac{dT_{out}}{dt} = F \cdot \rho \cdot c_p \cdot T_{out} - F \cdot \rho \cdot c_p \cdot T_{in}$$ This can be rearranged to make $$T(out)=f(T(in))$$ Its further understood that the change in Tin can be proportional to the pressure or height change at the valve.
Im looking for a solution that ties this whole process together. Better yet if someone knows a textbook (process control, instrumentation engineering, Linear models etc.) where this problem similar to this is solved and the logic is stepped out would be even better. Thank you all for your time.