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From: Narek on 5 Aug 2010 11:37
Hi,

I am currently trying to model the bypass flow in a turbofan engine. In order to do this I am using a performance map which is approximated via a 2nd degree polynomial. All the components are currently highly simplified.

I have created my own nozzle, diffuser and fan components for now using isentropic thermodynamic equations. I get one of the two following errors depending on whether the solver is set to sparse or full respectively

Nonlinear solver: Linear Algebra error. Failed to solve using iteration matrix.
Initial conditions solve failed to converge.

or

Nonlinear solver: failed to converge, residual norm too large.
Initial conditions solve failed to converge.
Here is the set of components with unconverged equations:
'Fan/Diffuser'
'Fan/Fan'

The rotational speed is set as an initial condition via an inertia.

The mass flow through the fan is dependent on the pressure ratio and the pressure ratio dependent in turn on the mass flow (because the mass flow is also a function of the pressure ratio across the nozzle).

Is this coupling, which is physical property of the fan, at the heart of the issue?

If we take into account regions of operation where the fan flow goes to Mach one then than for a given speed and mass flow the pressure ratio is essentially undefined (contour lines go vertical on the performance map).

To combat this an additional beta coordinate system can be introduced which intersects contour lines on the map at unique pressure ratios, speeds and mass flows. Given a nozzle area and initial speed one can iterate in beta until the error in the two mass flows (the mass flow dictated by the fan map and the one dictated by the pressure ratio across the nozzle) is brought to zero. A solution exists (I have checked via a matlab script) but the solver in Simscape gives the latter of the two errors.

My main question would be following:

Can the Simscape solver fundamentally deal with cross coupled systems which also require one or more iteration variables such as beta?

Many thanks
From: Arnaud Miege on 9 Aug 2010 12:24
"Narek " <narek.shougarian07(a)imperial.ac.uk> wrote in message <i3elr1$mri$1(a)fred.mathworks.com>...
> Hi,
>
> I am currently trying to model the bypass flow in a turbofan engine. In order to do this I am using a performance map which is approximated via a 2nd degree polynomial. All the components are currently highly simplified.
>
> I have created my own nozzle, diffuser and fan components for now using isentropic thermodynamic equations. I get one of the two following errors depending on whether the solver is set to sparse or full respectively
>
> Nonlinear solver: Linear Algebra error. Failed to solve using iteration matrix.
> Initial conditions solve failed to converge.
>
> or
>
> Nonlinear solver: failed to converge, residual norm too large.
> Initial conditions solve failed to converge.
> Here is the set of components with unconverged equations:
> 'Fan/Diffuser'
> 'Fan/Fan'
>
> The rotational speed is set as an initial condition via an inertia.
>
> The mass flow through the fan is dependent on the pressure ratio and the pressure ratio dependent in turn on the mass flow (because the mass flow is also a function of the pressure ratio across the nozzle).
>
> Is this coupling, which is physical property of the fan, at the heart of the issue?
>
> If we take into account regions of operation where the fan flow goes to Mach one then than for a given speed and mass flow the pressure ratio is essentially undefined (contour lines go vertical on the performance map).
>
> To combat this an additional beta coordinate system can be introduced which intersects contour lines on the map at unique pressure ratios, speeds and mass flows. Given a nozzle area and initial speed one can iterate in beta until the error in the two mass flows (the mass flow dictated by the fan map and the one dictated by the pressure ratio across the nozzle) is brought to zero. A solution exists (I have checked via a matlab script) but the solver in Simscape gives the latter of the two errors.
>
> My main question would be following:
>
> Can the Simscape solver fundamentally deal with cross coupled systems which also require one or more iteration variables such as beta?
>
> Many thanks

It's difficult to answer without seeing the model. I would try to simplify the model as much as possible for debugging purposes in order to separate the two issues (the circular variable dependency and vertical contour lines). My guess is that the first one should be easily dealt with by Simscape. I am not so sure about the second one. My best suggestion would be to contact technical support:
http://www.mathworks.co.uk/support/contact_us/index.html

HTH,

Arnaud
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