AixLib.Fluid.Actuators.BaseClasses.PartialDamperExponential

# .AixLib.Fluid.Actuators.BaseClasses.PartialDamperExponential

Partial model for air dampers with exponential opening characteristics

## Information

Partial model for air dampers with exponential opening characteristics. This is the base model for air dampers. The model implements the functions that relate the opening signal and the flow coefficient. The model also defines parameters that are used by different air damper models.

The model is as in ASHRAE 825-RP except that a control signal of `y=0` means the damper is closed, and `y=1` means the damper is open. This is opposite of the implementation of ASHRAE 825-RP, but used here for consistency within this library.

For `yL < y < yU`, the damper characteristics is:

kd(y) = exp(a+b (1-y))

where kd is the loss coefficient (total pressure drop divided by dynamic pressure) and y is the fractional opening.

Outside this range, the damper characteristics is defined by a quadratic polynomial that matches the damper resistance at `y=0` and `y=yL` or `y=yU` and `y=1`, respectively. In addition, the polynomials are such that kd(y) is differentiable in y and the derivative is continuous.

The damper characteristics is then used to compute the flow coefficient k(y) as:

k(y) = (2 ρ ⁄ kd(y))1/2 A

where A is the face area, which is computed using the nominal mass flow rate `m_flow_nominal`, the nominal velocity `v_nominal` and the density of the medium.

ASHRAE 825-RP lists the following parameter values as typical (note that the default values in the model correspond to opposed blades).

| opposed blades | single blades
yL | 15/90 | 15/90
yU | 55/90 | 65/90
k1 | 0.2 to 0.5 | 0.2 to 0.5
a | -1.51 | -1.51
b | 0.105*90 | 0.0842*90

(The loss coefficient in fully closed position `k0` is computed based on the leakage coefficient and the coefficient in fully open position.)

#### References

P. Haves, L. K. Norford, M. DeSimone and L. Mei, A Standard Simulation Testbed for the Evaluation of Control Algorithms & Strategies, ASHRAE Final Report 825-RP, Atlanta, GA.

## Revisions

- September 21, 2021, by Michael Wetter:
  Corrected typo in comments.
  This is for #1525.
- December 23, 2019, by Antoine Gautier:
  Removed the equations involving `m_flow` and `dp` that now need to be added in each derived damper model.
  Added the declaration of `dpDamper_nominal` and `dpFixed_nominal`.
  Replaced `k0` by leakage coefficient.
  Modified the limiting values for `k0` and `k1`.
  This is for #1188.
- March 22, 2017, by Michael Wetter:
  Added back `v_nominal`, but set the assignment of `A` to be final. This allows scaling the model with `m_flow_nominal`, which is generally known in the flow leg, and `v_nominal`, for which a default value can be specified.
  This is for #544.
- October 12, 2016 by David Blum:
  Removed parameter `v_nominal` and variable `area`, to simplify parameterization of the model. Also added assertion statements upon initialization for parameters `k0` and `k1` so that they fall within suggested ranges found in ASHRAE 825-RP. This is for #544.
- January 27, 2015 by Michael Wetter:
  Set `Evaluate=true` for `use_constant_density`. This is a structural parameter. Adding this annotation leads to fewer numerical Jacobians for `Buildings.Examples.VAVReheat.ClosedLoop` with `Buildings.Media.PerfectGases.MoistAirUnsaturated`.
- December 14, 2012 by Michael Wetter:
  Renamed protected parameters for consistency with the naming conventions.
- January 16, 2012 by Michael Wetter:
  To simplify object inheritance tree, revised base classes `AixLib.Fluid.BaseClasses.PartialResistance`, `AixLib.Fluid.Actuators.BaseClasses.PartialTwoWayValve`, `AixLib.Fluid.Actuators.BaseClasses.PartialDamperExponential`, `AixLib.Fluid.Actuators.BaseClasses.PartialActuator` and model `AixLib.Fluid.FixedResistances.PressureDrop`.
- August 5, 2011, by Michael Wetter:
  Moved linearized pressure drop equation from the function body to the equation section. With the previous implementation, the symbolic processor may not rearrange the equations, which can lead to coupled equations instead of an explicit solution.
- June 22, 2008 by Michael Wetter:
  Extended range of control signal from 0 to 1 by implementing the function exponentialDamper.
- June 10, 2008 by Michael Wetter:
  First implementation.

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