diff --git a/_data/tutorials.yml b/_data/tutorials.yml index 069c9300..873857e1 100644 --- a/_data/tutorials.yml +++ b/_data/tutorials.yml @@ -19,6 +19,7 @@ - NICFD_nozzle - NICFD_nozzle_datadriven - Aachen_Turbine + - Actuator_Disk - title: Incompressible Flow tutorials: diff --git a/_tutorials/compressible_flow/ActuatorDisk_VariableLoad/ActuatorDisk_VariableLoad.md b/_tutorials/compressible_flow/ActuatorDisk_VariableLoad/ActuatorDisk_VariableLoad.md index f532d610..c1f7c967 100644 --- a/_tutorials/compressible_flow/ActuatorDisk_VariableLoad/ActuatorDisk_VariableLoad.md +++ b/_tutorials/compressible_flow/ActuatorDisk_VariableLoad/ActuatorDisk_VariableLoad.md @@ -55,8 +55,8 @@ The global propeller data are: - Advance Ratio = 2.81487 - Radius = 2.5146 m -The thrust coefficient is defined using the "Renard" definition: the reference force is , where *n* are the propeller rounds per second and *D* is the propeller diameter -The advance ratio is defined as . +The thrust coefficient is defined using the "Renard" definition: the reference force is $$\rho n^2D^4$$, where *n* are the propeller rounds per second and *D* is the propeller diameter +The advance ratio is defined as $$J=\frac{V_\infty}{nD}$$. ### Mesh Description @@ -167,16 +167,16 @@ The `MARKER_ACTDISK` option, as the same for the configuration file, is used to The `CENTER` option contains the coordinates of the actuator disk center, expressed in the grid reference system. The `AXIS` option contains the components of the unit vector normal to the actuator disk surface. The `RADIUS` option is used to specify the actuator disk radius. -The `ADV_RATIO` option contains the advance ratio of the propeller defined as , where *n* are the propeller rounds per second and *D* is the propeller diameter. +The `ADV_RATIO` option contains the advance ratio of the propeller defined as $$J=\frac{V_\infty}{nD}$$, where *n* are the propeller rounds per second and *D* is the propeller diameter. The `NROW` option isused to indicate the number of radial stations of the actuator disk in which we assign the load distribution. The next row is a dummy row, so it is skipped. Then there are 4 columns containing respectively: -- The non dimensional radial station -- The thrust coefficient distribution -- The power coefficient distribution -- The radial force coefficient distribution +- The non dimensional radial station $$\overline{r}=\frac{r}{R}$ +- The thrust coefficient distribution $$\frac{\mathrm{d}C_T}{\mathrm{d}\overline{r}}$$ +- The power coefficient distribution $$\frac{\mathrm{d}C_P}{\mathrm{d}\overline{r}}$ +- The radial force coefficient distribution $$\frac{\mathrm{d}C_R}{\mathrm{d}\overline{r}}$$ -These coefficients are defined using the "Renard" definition: the reference force is , while the reference power is reference force is +These coefficients are defined using the "Renard" definition: the reference force is $$\rho n^2D^4$$, while the reference power is reference force is $$\rho n^3D^5$$ *It is possible to append other propellers data at the end of the input file. Note that the order and the format of the options should not be changed.* @@ -195,13 +195,13 @@ This script allows the user to use the `VARIABLE_LOAD` actuator disk type also w The input is interactive, and requires the following data: 1. Number of radial stations (where local data should be generated). -2. CT: the total thrust coefficient defined using the "Renard" definition. -3. R: The propeller radius expressed in meters. -4. r_hub: the hub radius expressed in meters. -5. J: the advance ratio. -6. Vinf: the free-stream velocity expressed in m/s. +2. $$CT$$: the total thrust coefficient defined using the "Renard" definition. +3. $$R$$: The propeller radius expressed in meters. +4. $$r_{\textrm{hub}}$$: the hub radius expressed in meters. +5. $$J$$: the advance ratio. +6. $$V_{\textrm{inf}}$$: the free-stream velocity expressed in m/s. 7. Here, the script asks if you want to use the tip loss Prandtl correction (*yes* is the default choise). -8. N: if you chose yes in the previous stage, it requires also the number of propeller blades. +8. $$N$$: if you chose yes in the previous stage, it requires also the number of propeller blades. Once the input is given, the script provides 3 plots showing the tip loss Prandtl correction function, the axial and rotational interference factors and the thrust and power coefficients distributions along the non dimentional radius. The script also provides 2 files: diff --git a/_tutorials/index.md b/_tutorials/index.md index 0fa54c5a..0a0c86f1 100644 --- a/_tutorials/index.md +++ b/_tutorials/index.md @@ -54,6 +54,8 @@ Simulation of compressible flow in a nozzle using non-ideal thermodynamic models Demonstration of data-driven equation of state using a physics-informed neural network. * [Turbomachinery: Aachen Turbine stage with mixing plane](/tutorials/Aachen_Turbine/) Simulation of compressible flow of the Aachen turbine demonstrating turbomachinery application. +* [Actuator Disk with Variable Load](/tutorials/ActuatorDisk_VariableLoad/) +Simulation of an actuator disk with variable load. #### Incompressible Flow