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RE: [EnergyPlus_Support] Airflow Distribution Network L-U Factorization Error





Like Dave, I work with CONTAM, but am becoming more familiar with E+.

   ** Severe  ** AirflowNetworkSolver: L-U factorization in Subroutine FACSKY.

   **   ~~~   ** The denominator used in L-U factorizationis equal to 0.0 at node = AIRLOOPZONESPLITTEROUTLETNODE3.

   **   ~~~   ** One possible cause is that this node may not be connected directly, or indirectly via airflow network connections

   **   ~~~   ** (e.g., AirflowNetwork:Multizone:SurfaceCrack, AirflowNetwork:Multizone:Component:SimpleOpening, etc.), to an external

   **   ~~~   ** node (AirflowNetwork:MultiZone:Surface).

 

The message above and the fact that a valid SVG node diagram is not being produced would lead me to believe that your node connectivity is not quite right.

You might want to go back to an example file and review proper connectivity, e.g., AirflowNetwork_Simple_SmallOffice.idf.

 

- Stuart

 

From: EnergyPlus_Support@xxxxxxxxxxxxxxx [mailto:EnergyPlus_Support@xxxxxxxxxxxxxxx]
Sent: Wednesday, October 05, 2016 7:13 PM
To: EnergyPlus_Support@xxxxxxxxxxxxxxx
Subject: Re: [EnergyPlus_Support] Airflow Distribution Network L-U Factorization Error

 

 

Hello,

> So I have been trying to model a simple building with an airflow distribution network, however I keep getting the L-U factorization numerical error, it says that one of the nodes is not connected to the outside via an opening or something similar. I have tried to add window openings with different configurations but the error doesn't go away.

Your problem might be in a few places. If I was more familiar with
E+, I could do better than this, but here goes:

(1) Those window models need to include an airflow path, i.e., not
just be an energy model for the window. I assume that's what you
meant when you said you added "window openings", but I figured it
would be best to be explicit. An appropriate airflow path will have
some kind of leakage parameter you can adjust.

(2) If you get a numerical error from the factorization routine, it
may mean that you have met the *legal* but not the *practical*
requirement.

Legal requirement -- you must connect every node to the outside via a
flow path, or a series of flow paths, with a positive pressure-flow
relation (i.e., increasing the pressure drop through the path
increases the flow through it).

Practical requirement -- a modest change in pressure drop through the
path can't produce such a huge or such a tiny change in airflow,
compared to the other paths, that the solver simply can't choose
numbers that make the whole system work.

I don't know whether E+ enforces the legal requirement. The main
software I work with, CONTAM, analyzes the network before it tries to
solve the network. Therefore it reports unconnected zones before it
gets to the factorization stage. That means that, when CONTAM finds a
problem, you always start off knowing whether you've hit the legal or
the practical limit.

However, the E+ airflow solver is based on an early version of the
CONTAM solver -- so it's possible that network analysis isn't in
there. If E+ does not do the network analysis, that makes it hard to
say whether your error comes from violating the legal or from the
practical requirement. Maybe somebody else can comment on this.

(3) The salient point of the "legal" vs "practical" distinction is
that you might have the sorts of paths that the solver needs to form a
legal network, but that the parameters make one of the paths so tight
that the solver just can't figure it out. LU factorization isn't the
best game in town, but it should be sufficient for the small problem
you have defined, if you have sensible leakage parameters.

I believe (not having encountered this problem in a long time) that if
you run into a factorization problem, it means one of the paths is far
too tight (i.e., a huge change in pressure hardly changes the airflow
rate). A path that is too loose (small change in pressure causes
large change in airflow) will cause numerical numerical problems, but,
I think, not at the factorization stage (the numerical problem would
show up as too many solver iterations). So I would begin by looking
at the paths to make sure your leakage parameters are all reasonable,
with a focus on finding one that's set too small.

(4) Note that the requirement isn't as simple as "there's an airflow
path to the outside". In fact, you need an airflow path that is able
to respond to changes in pressure, by changing the airflow rate. To
take a practical example, think of a room with a fan blowing into it,
and no other airflow path. Sure the room connects to outdoors via a
path (the fan), but there's no relief path. Without a way for air to
escape the room as a result of the fan pressurizing it, you end up
with a singular matrix of d(airflow)/d(pressure drop) entries. Hence
the LU solver will blow up.

In the system you drew (nice diagram, by the way), there is a
possibility that the offending node is between two flow paths that are
both trying to set the airflow rate. So for example if you had a
supply fan and a terminal unit, which were both trying to establish
the airflow, then they would try to over- or under-pressurize the
duct, in a way exactly analogous to the simple room example I gave
above. Again I'm not familiar with E+, so I don't know the models
here.

So I would look for some node that is caught between two fans, and
with no way for air to escape.

This last one, by the way, is why your window models need airflow
paths -- otherwise, your supply and extract fans can get into in a war
to see who will blow up or depressurize the building (they don't have
to be in a war, if you define them right, but fan models that fix the
flow aren't good enough).

(5) You can always "shotgun" the problem by adding leakage paths
(independent of the windows) that go from each zone to the outdoors.
If that doesn't solve the problem, then the problem is in the duct
system (nobody models duct leakage, even though we should). If it
does solve the problem, then take one path out at a time, and see when
the error re-establishes itself. Note, however, that the problem
doesn't necessarily exist in just the zone from which you removed the
last leakage path. If it's a numerical problem, then it can be a
problem of the whole system, not just of one path or another.

Hope something here helps.

-Dave

> My building is originally 13 levels, which I reduced to 3 for testing, with square geometry (66x66x5 m per floor). It has 50% glazing on all 4 sides. The plan is to model an airflow distribution network the models the HVAC air distribution in these zones, then I'm going to add external zones to model a double skin facade (DSF), which means outside each facade in the inner zones, there will be a cavity zone that has ~100% glazing, the main idea is to direct the exhaust air of the AHU of the inner zones into the DSF zones, where the exhaust ideally will be blowing from the bottom, and an open window will be at the top of the DSF cavity. My HVAC system is a Single Duct VAV with reheat terminal, and an AHU with heat recovery, along with supply and extract fans.
>
> I'm using Energyplus V8.2 because my final system will be connected to BCVTB.
>
> At this stage, I'm just trying to model the basic airflow distribution network of the inner building (without the DSF) but its giving me that error, I went over all examples in Energyplus, I believe my airflow network structure is complete but maybe there is something I'm missing. an anyone help me figure out what this error means?
>
> I have attached the schematic of the nodes and components in the AFN, and the idf file I'm using.



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Posted by: "Dols, William Stuart (Fed)" <william.dols@xxxxxxxx>


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