Tumble/Swirl Ratio

This report is typically used for ICE applications and calculates swirl or tumble (dimensionless).

In the engine industries, typically three index numbers are used to quantify in-cylinder flow motion:

Swirl:
Rotational motion with its axis aligned with the cylinder axis.
Main-tumble:
Rotational motion with its axis normal to the cylinder axis and the symmetry plane of the ports (assuming a symmetric 4-valve engine).
Cross-tumble:
Rotational motion with its axis normal to the cylinder axis and parallel to the symmetry plane of the ports.

Using the Simcenter STAR-CCM+ swirl report, all three index numbers can be derived by adjusting the report properties accordingly:


Property	Value
Coordinate System	Set a local coordinate system with its Z-axis aligned with the cylinder axis and its X-axis parallel to the symmetry plane of the ports.
Axis	Set one of the following: [0,0,1] for swirl. [0,1,0] for main-tumble (also referred to as Y-tumble). [1,0,0] for cross-tumble (also referred to as X-tumble).

On the other hand, the Simcenter STAR-CCM+ tumble report can be used to calculate a combination of cross-tumble and main-tumble, as the formulation explains:

Tumble is defined as:

Figure 1. EQUATION_DISPLAY

T = \frac{1}{2} (T_{u}^{2} + T_{v}^{2} + T_{w}^{2})

(470)

with

Figure 2. EQUATION_DISPLAY

\begin{matrix} {\begin{matrix} T \end{matrix}}_{u} & = & {A x i s}_{y} \cdot S_{z} - {A x i s}_{z} \cdot S_{y} \\ {\begin{matrix} T \end{matrix}}_{v} & = & {A x i s}_{z} \cdot S_{x} - {A x i s}_{x} \cdot S_{z} \\ {\begin{matrix} T \end{matrix}}_{w} & = & {A x i s}_{x} \cdot S_{y} - {A x i s}_{y} \cdot S_{x} \end{matrix}

(471)

which, written in vector-form, corresponds to:

Figure 3. EQUATION_DISPLAY

T = A x i s \times S

(472)

Swirl is defined as:

Figure 4. EQUATION_DISPLAY

S w = {A x i s}_{x} \cdot S_{x} + {A x i s}_{y} \cdot S_{y} + {A x i s}_{z} \cdot S_{z}

(473)

where:

Figure 5. EQUATION_DISPLAY

S_{x} = \frac{M_{x}}{{ω_{c} I}_{x}} = \frac{\sum_{Cells}^{} ρ_{i} V_{i} [(Y_{i} - Y_{m}) w_{i} - (Z_{i} - Z_{m}) v_{i}]}{{ω_{c} \sum}_{Cells}^{} ρ_{i} V_{i} [{(Y_{i} - Y_{m})}^{2} + {(Z_{i} - Z_{m})}^{2}]}

(474)

Figure 6. EQUATION_DISPLAY

S_{y} = \frac{M_{y}}{{ω_{c} I}_{y}} = \frac{\sum_{Cells}^{} ρ_{i} V_{i} [(Z_{i} - Z_{m}) u_{i} - (X_{i} - X_{m}) w_{i}]}{{ω_{c} \sum}_{Cells}^{} ρ_{i} V_{i} [{(X_{i} - X_{m})}^{2} + {(Z_{i} - Z_{m})}^{2}]}

(475)

Figure 7. EQUATION_DISPLAY

S_{z} = \frac{M_{z}}{{ω_{c} I}_{z}} = \frac{\sum_{Cells}^{} ρ_{i} V_{i} [(X_{i} - X_{m}) v_{i} - (Y_{i} - Y_{m}) u_{i}]}{{ω_{c} \sum}_{Cells}^{} ρ_{i} V_{i} [{(Y_{i} - Y_{m})}^{2} + {(X_{i} - X_{m})}^{2}]}

(476)

where:


$ω_{c}$	Angular speed of crankshaft (rad/s)
$M_{x}, M_{y}, M_{z}$	Angular momentum about the x-, y-, and z-axes (kg m²/s)
$I_{x}, I_{y}, I_{z}$	Mass moment of inertia about the x-, y-, and z-axes (kg m²)
$X_{i}, Y_{i}, Z_{i}$	Centroid coordinate of cell (m)
$X_{m}, Y_{m}, Z_{m}$	Center of mass/volume/origin of the cylinder (m)
$u_{i}, v_{i}, w_{i}$	Velocity at cell (m/s)

Tumble/Swirl Report Properties


Units	Units that are used for specifying the quantity.
Evaluation Mode	Tumble	Selects the tumble report. Tumble is defined as the fluid rotation about the plane that contains the Tumble Origin and that is orthogonal to the cylinder Axis. For example, if the cylinder Axis is [0, 0, 1], that is, the Z direction, $T_{w} = 0$ and $T = \frac{1}{2} \sum_{Cells} (T_{u}^{2} + T_{v}^{2})$ as given by Eqn. (470) and Eqn. (471).
	Swirl	Selects the swirl report. Swirl is defined as the fluid rotation around the cylinder Axis. For example, if the cylinder Axis is [0, 0, 1], that is, the Z direction, swirl corresponds to $S w = S_{z}$ as given by Eqn. (473).
Origin Mode	Automatic	Uses the center of mass to calculate the origin.
	Manual	Uses the point that you specify for User Origin.
User Origin	When Origin Mode is set to Manual, specifies the point within the cylinder. This point is usually the center of the cylinder and corresponds to $X_{m}, Y_{m}, Z_{m}$ in Eqn. (474) to Eqn. (476). Defines the plane upon which the principal tumble axis lies. Tumble is calculated about this plane.
Rotational Rate	Rotational speed of the IC engine. See $ω_{c}$ in Eqn. (474) to Eqn. (476).
Axis	Defines the orientation, that is, the axis of the cylinder with respect to Coordinate System.
Coordinate System	A list of coordinate systems that this report can use.
Parts	Selects the regions and geometry parts for which Simcenter STAR-CCM+ computes the report. If multiple objects are selected, Simcenter STAR-CCM+ calculates the report for each object individually, and then sums the results.

Tumble/Swirl Report Expert Properties


Representation	Selects a representation. Additional selections appear as representations that are added to the simulation.