### 5.3.3. General Connection

The `General Connection` interface model is a powerful way to connect regions together. A general connection can be used to:

- Apply a frame change at the interface between a rotor and stator

- Connect non-matching grids

- Apply fully transient sliding interfaces between domains

Pitch change can also be applied. For example, a domain interface can connect a stator domain with a rotor domain where the number of stator blades is not equal to the number of rotor blades, even if the mesh contains only one blade from each side.

Examples of the general connection type are shown below:

Figure 5.2: General Connection: No Frame Change

Figure 5.3: General Connection: Frame Change and Pitch Change

The `General Connection` option is necessary when the frame of reference or pitch changes across the interface. For example, the general connection option must be used in the following cases:

- One side is in a stationary frame of reference and the other side is in a rotating frame of reference

- Both sides are in a rotating frame of reference but each with a different rate of rotation

- Both sides are in the same frame of reference but have unequal pitches. In this situation, the flows through the interface must account for pitch change.

When a general connection is selected, the following details need to be specified:

- Frame Change/Mixing Model

- Pitch Change

#### 5.3.3.1. Frame Change/Mixing Model

There are three types of frame change/mixing models available in ANSYS CFX:

- `Frozen Rotor`

- `Stage (Mixing-Plane)`

- `Transient Rotor-Stator`

Each side of the interface must be a surface of revolution and both sides must sweep out the same surface of revolution.

##### 5.3.3.1.1. None

Select `None` when there is no frame change or pitch change.

##### 5.3.3.1.2. Frozen Rotor

The frame of reference and/or pitch is changed but the relative orientation of the components across the interface is fixed. The two frames of reference connect in such a way that they each have a fixed relative position throughout the calculation. If the frame changes the appropriate equation transformations are made. If the pitch changes, the fluxes are scaled by the pitch change.

This model produces a steady-state solution to the multiple frame of reference problem, with some account of the interaction between the two frames. The quasi-steady approximation involved becomes small when the through flow speed is large relative to the machine speed at the interface. `Frozen Rotor` analysis is most useful when the circumferential variation of the flow is large relative to the component pitch. This model requires the least amount of computational effort of the three frame change/mixing models.

The disadvantages of this model are that the transient effects at the frame change interface are not modeled. Modeling errors are incurred when the quasi-steady assumption does not apply. Also, the losses incurred in the real (transient) situation as the flow is mixed between stationary and rotating components is not modeled.

###### 5.3.3.1.2.1. Rotational Offset

The Rotational Offset settings control the angle by which the side 1 or side 2 domains are rotated before the interface calculation is performed. The domain axis of rotation is used to perform the rotation. The rotational offset that is applied to the domains on side 1 or 2 depends on whether domains are rotating on side 1, 2, both, or none. The ways in which rotational offsets are stored in results file and are interpreted by CFD-Post are:

- If the side 1 domains are rotating and the side 2 domains are stationary then a rotational offset will be written for the side 1 domains, and interpreted by CFD-Post.

- If the sides 1 and 2 domains are rotating then a rotational offset will be written for the side 1 domains, and interpreted by CFD-Post.

- If the side 1 domains are stationary and the side 2 domains are rotating then a rotational offset will be written for the side 2 domains, and interpreted as a counter-rotation by CFD-Post.

- If the sides 1 and 2 domains are stationary then a rotational offset will be written for the side 1 domains, but not interpreted by CFD-Post; the rotational offset will not be applied.

You can use a rotational offset if you want to change the relative position of the components on each side of the interface without altering the position of the meshes. The positive direction for an offset is determined by the right-hand rule. Figure 5.4: Rotational Offset shows how a rotational offset will alter the relative position of a rotor and stator component.

Note: As an alternative to the Rotational Offset parameter, you can also apply a domain rotation in CFX-Pre and create a new CFX-Solver input file.

Figure 5.4: Rotational Offset

By default, the domain positions are stored in their original (non-offset) location. To have the domains appear in their offset positions in CFD-Post, include the expert parameter `rotational offset for post=t` in the problem definition and, in CFD-Post, open Edit > Options, then set the CFD-Post option Angular Shift for Transient Rotating Domains to Always Rotate. Click OK to save the change.

##### 5.3.3.1.3. Stage (Mixing Plane)

The Stage model (also known as the Mixing-Plane model) is an alternative to the Frozen Rotor model for modeling frame and/or pitch change. Instead of assuming a fixed relative position of the components, the Stage model performs a circumferential averaging of the fluxes through bands on the interface. Steady-state solutions are then obtained in each reference frame. This model enables steady-state predictions to be obtained for multi-stage machines. The stage averaging at the frame change interface incurs a one-time mixing loss. This loss is equivalent to assuming that the physical mixing supplied by the relative motion between components is sufficiently large to cause any upstream velocity profile to mix out prior to entering the downstream machine component. `Stage` analysis is most appropriate when the circumferential variation of the flow is of the order of the component pitch.

`Stage` averaging between blade passages accounts for time average interaction effects, but neglects transient interaction effects. `Stage` analysis is not appropriate when the circumferential variation of the flow is significant relative to the component pitch (for example, a pump and volute combination at off-design conditions).

The Stage model usually requires more computational effort than the Frozen Rotor model to converge, but not as much as the transient rotor-stator model. You should obtain an approximate solution using a Frozen Rotor interface and then restart with a Stage interface to obtain the best results.

###### 5.3.3.1.3.1. Pressure Profile Decay

The pressure profile at a Stage (Mixing-Plane) interface is determined by extrapolation from the pressure profile just inside the interface location (just upstream or just downstream of the Stage interface, for the upstream and downstream sides respectively). Sometimes, this procedure is unstable and a small amount of stiffness must be added to the pressure profile rather than just letting it float. By default, the pressure profile is decayed by 5% towards a constant value. The amount of decay can be controlled by this setting. Using a 5% pressure profile decay is recommended.

###### 5.3.3.1.3.2. Downstream Velocity Constraint

At a Stage (Mixing-Plane) interface, the average static pressure within each band on both the upstream and downstream side of the interface is set to the average band pressure. Here are possible treatments for velocity on the downstream side:

- It may be calculated as the average band velocity. (`Stage Average Velocity`)

- It may be calculated from the average band total pressure and direction in the relative frame (`Constant Total Pressure`). Note that, in this case, the frame type will be rotating.

The constant total pressure options permit the downstream velocity profile to naturally adjust to downstream influences. For tightly-coupled components, the `Constant Total Pressure` option provides a better approximation than the `Stage Average Velocity` option. To obtain results comparable to CFX-TASCflow, use `Constant Total Pressure`, `Frame Type=Rotating`.

###### 5.3.3.1.3.3. Implicit Stage Averaging

This option helps to improve the convergence of the Stage (Mixing-Plane) model and minimizes reflection on the upstream side of the interface due to locally supersonic flow that is subsonic in the direction normal to the interface.

##### 5.3.3.1.4. Transient Rotor-Stator

This model should be used any time it is important to account for transient interaction effects at a sliding (frame change) interface. It predicts the true transient interaction of the flow between a stator and rotor passage. In this approach the transient relative motion between the components on each side of the GGI connection is simulated. It ultimately accounts for all interaction effects between components that are in relative motion to each other. The interface position is updated each timestep, as the relative position of the grids on each side of the interface changes. It is possible to use a transient sliding interface anywhere a `Stage` or `Frozen Rotor` sliding interface could be used.

The principle disadvantage of this method is that the computer resources required may be large, in terms of simulation time, disk space and quantitative postprocessing of the data. The resource requirement problem is exacerbated if unequal pitch between components occurs. In these situations, spatial periodicity cannot formally be used to limit the analysis to a single blade passage per component. Often the problem of unequal pitch is addressed by modifying the geometry to the nearest integer pitch ratio, which may affect the validity of the analysis. In practice, components of unequal pitch can be treated by solving N passages on one side and M passages on the other side, with N and M determined such that the net pitch change across the interface is close to unity. As with a Frozen Rotor interface, pitch change is automatically accounted for by scaling of flows by the pitch ratio.

It is possible to start a `Transient Rotor-Stator` computation from a simple initial guess, or from an existing prediction. If you are interested in the start-up transient of the machine, then start from the appropriate physical initial conditions. If you are interested in simulating a periodic-in-time quasi-steady-state, then it may be helpful to first obtain a steady-state solution using `Frozen Rotor` interfaces between components. This solution will contain most of the overall flow features, and should converge to the desired transient simulation in the fewest transient cycles.

Translational relative motion is not supported at a transient sliding interface (only rotational motion is supported).

#### 5.3.3.2. Pitch Change

To connect dissimilar meshes, an intersection algorithm is used to find the overlapping parts of each mesh face at the interface; for details, see GGI and MFR Theory in the CFX-Solver Theory Guide. The CFX-Solver must decide the most appropriate way to perform this intersection. The choices are:

- Intersect in physical space. The connection will be made as is with no correction for pitch change or rotational offset. This method is used when the pitch change model is set to `None`.

- Intersection in the radial direction. This method is used when the pitch change model is not `None` and the radial variation at the interface is larger than the axial (z-) variation. For example, this method is used for the surface of constant z in Figure 5.5: Radial vs. Z Direction.

- Intersect in the axial direction. This method is used when the pitch change model is not `None` and the axial variation at the interface is larger than the radial variation. For example, this method is used for the surface of constant radius in Figure 5.5: Radial vs. Z Direction.

If the pitch change model is not `None`, then the intersection algorithm will fail if the interface has any of the following:

- surfaces of zero radius

- surfaces of constant radius with surfaces of constant z

For example, an interface cannot contain both highlighted regions in Figure 5.5: Radial vs. Z Direction. Instead, two separate interfaces should be used.

In addition, for best accuracy, the interface should not be highly curved. For example, if a small change in radius produces a large change in z and a small change in z produces a large change in radius in the same interface, then separate interfaces should be used instead.

Figure 5.5: Radial vs. Z Direction

When there is pitch change, a transformation is also performed between components to account for the fact that they may not be rotationally aligned. This does not affect the relative position of the components. In Figure 5.6: Misaligned Components the components are not aligned; flow passes through the overlapping area as expected, but the flow that reaches the interface at 1 is transformed such that it emerges at 2 having crossed the interface.

Figure 5.6: Misaligned Components

##### 5.3.3.2.1. None

Using `None` as the pitch change option will cause the connection to be made “as is.” If you have non-aligned components, as shown in Figure 5.6: Misaligned Components, flow will only pass through the overlapping region. Therefore, this option should only be used when the overall extent and shape of each side of the interface perfectly match and the surfaces are aligned with each other. It may therefore be suitable when full 360 degree or exactly equal pitch components are being analyzed. A pitch change option of `None` cannot be used for a stage interface.

##### 5.3.3.2.2. Automatic

The `Automatic` pitch change option is the standard option for accounting for pitch change between components. The pitch ratio is taken to be the ratio of the areas of the two components. The two sides must each have the same radial or axial extent and can therefore only differ in extent in the direction of rotation of the frame of reference. This means that the surfaces on each side of a frame change interface must sweep on the same surface of revolution.

For the Frozen Rotor model, the flow variable profiles in the pitch-wise direction are stretched or compressed to the extent that there is pitch change across the interface. All flows (mass, momentum, energy, and so on) are scaled accordingly, based on the pitch change.

For the Stage (Mixing-Plane) model, the pitch change adjustment is made by applying average values calculated from the upstream side of the interface to the downstream side. The averaging is performed in a conservative manner. Meridional variation of the flow is maintained across the interface. Circumferential variation of all flow variables except pressure are removed across the interface. The average pressure is maintained at each meridional location across the interface, with independent local variation in pressure permitted.

The computational accuracy degrades rapidly with increasing pitch change. It is recommended that sufficient blade components be analyzed on each side of the interface to minimize pitch change. Any pitch change will result in a non-physical transient interaction: the entire 360 degree components must be solved for truly “accurate” transient interactions if the pitch ratio is non-integer. Small pitch changes will introduce relatively smaller errors, large pitch changes will introduce larger errors.

There are a number of scenarios where the algorithm used by the `Automatic` pitch change option is not valid, such as:

- When the vertices on the intersection of the hub and interface are not all at the same radial and axial position

- When one or both sides of the interface has a 360° or greater pitch angle

- When one or both sides of the interface has a zero radius

- When one or both sides of the interface has mesh faces normal and parallel to the rotation axis

- When one or both sides of the interface has mesh faces at the hub (that is, low radial or axial position) that are thin in the radial or axial direction

When using the `Automatic` pitch change option, you should examine the output file under the Mesh Information heading to confirm that the calculated pitch angles are sensible.

Using the `Automatic` pitch change option for determining the pitch change may result in failure of the solver or a solution that is completely wrong. An example of the flow solution being wrong is flow exiting a non-overlapping region of the interface or flow not exiting an overlapping area of the interface. In general if the flow solution through the interface does not make sense, or if the calculated pitch angles are not sensible in the output file, then you should use the `Value` or `Specified Pitch Angles` option.

##### 5.3.3.2.3. Value

This option enables you to explicitly provide the pitch ratio. This is the ratio of the pitch angle from the side with the larger pitch angle to the side with the smaller pitch angle across the domain interface. You can use this option when the precise pitch ratio is critical to the analysis; for example, in a closed system containing multiple pitched components.

##### 5.3.3.2.4. Specified Pitch Angles

This option enables you to specify the pitch angle on side 1 and side 2 of the domain interface. You can use this option when the precise pitch angle is needed or when the area ratio of the two sides is not equal to the pitch ratio.

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