SysML4Mathematica: Example 08a: Humidification: Drying lumber with air: required volumetric air flow rate

The '@' prefix in some of the ConstraintBlocks and OpaqueBehaviors indicate that they are (typically trivial) maths operations that aren't represented by dedicated functions in the Webel Psy Mathematica code library:

Webel: SysML4Mathematica: An '@' prefix in the name of a ConstraintBlock, Activity, or OpaqueBehavior indicates that it is a "@pseudo" function not represented directly in the Wolfram Language or Webel code libraries (typically for minor maths or logic)

The inclusion of such fine-grained @dw for w2-w1 in the example diagrams here is purely for demonstration of that naming policy; one could instead simply pass w1 and w2 to the dryingAirMassRate calculation (with more concise model diagrams).

At the top we see a SysML Parametric Diagram representing a network of equations for the psychrometric properties obtained from low-level CoolProp wrappers for Mathematica, and some ConstraintBlock usages for calculating the volumetric humid air flow rate for achieving a desired degree of drying of another object.

In the middle and bottom Activity Diagrams we see how the problem can be setup instead using Webel MPsy objects, which encapsulate the lower level CoolProp calls. Together, they represent this Mathematica invocation:


ex8$psy1 = newPsy[asDegF[80.6], $opt$psy$r -> 0.8];
ex8$psy2 = newPsy[asDegF[140], $opt$psy$twb -> asDegF[125.6]];

psy$humidification$vfr$via$waterMassRate[
 ex8$psy1,
 ex8$psy2,
 5.68 unitPoundPerHour,
 $opt$psy$doShowAsIP -> True
 ]

1058.7950696434616 ft^3/hr

Here unitPoundPerHour is a pre-built Mathematica Quantity[1.0, ("Pounds")/("Hours")]:

Webel Best Practice: Mathematica: The Webel Units` package has Quantity variables for frequently used units using a naming convention 'unit$[Symbol]' or 'unit[DescriptiveName]' or unit[Acronym], each with a corresponding '$unit...' for the units identifier String(s).

And the units utility function asDegF[magF_Real] similarly creates a Quantity for °F.

Note that:

Psychrometrics: The volumetric flow rate of a humid air mixture MAY change between a State1 and State2 (but the mass flow rate of dry air does not under steady state)! This is sometimes "glossed over" in some online calculators and less formal guides.

Psychrometrics: Calculations of the mass flow rate of the dry air component (assumed constant under steady state) from the ENTRY volumetric flow rate of the humid air mixture MUST use the INITIAL state variables!

Up next

SysML4Mathematica: Example 09: Moisture added to air: Amount (mass)

Notes

[MODELLING, NAMING, TIP]{RECOMMENDED} SysML Parametrics: You can use custom stereotypes keywords «i» and «o» on constraint parameters to indicate their intended use (causality) as (i)nputs and (o)utputs on ConstraintBlocks

[CONVENTION]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: CONVENTION: 'Q' as a quantity symbol in equations indicates the energy GAINED BY the system as heat energy transfer; 'W' indicates the work DONE BY the system on its external surroundings.

[CONVENTION]{STRICT} Webel: Psy/MPsy: Psychrometrics for Mathematica: Transferred heat (energy "Q") has field names with lower case 'qTot', 'qSen', 'qLat'. Heat rates (energy per time) have field names 'qDotTot', 'qDotSen', 'qDotLat' (to avoid clashes with Mathematica core)