.. _sr1: Monitoring and analyzing CFD runs ================================= By the animated icons |running| and |waiting| and the status symbols in the **workspace tree** **CFturbo BLADERUNNER** provides a perfect overview of which flow simulation is currently running, which simulations are scheduled and which have already been completed. The **Convergence plots** tab immediately reveals whether a flow simulation will be successful or not by showing a live view of the current simulation that gives trends of important quantities such as efficiency and of the residuals. In the **Performance curves** tab, the characteristic curves for all variants, denominated **performance curves** in **CFturbo BLADERUNNER**, are shown in direct comparison. The value currently computed by means of CFD is displayed in real time, so that the **performance curve** dynamically emerges before the user's eyes making the turbomachine's behavior clear during the ongoing CFD run. .. |running| image:: images/status_running.gif :align: middle :scale: 33 .. |waiting| image:: images/status_waiting.gif :align: middle :scale: 25 .. _sr2: Convergence plots ----------------- Two diagrams - **Convergence** and **Residuals** ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The **Convergence plots** tab is divided into two diagrams. The **Convergence** diagram at the top shows the development of **variables** and **expressions** over the number of iterations for **steady-state** simulations or over the simulated time for **transient** simulations. **Variables** are integral quantities calculated by the **Simerics MP/MP+** solver at interfaces and surfaces, such as - **mass flow**, **total pressure**, **average static pressure** or **torque** **Expressions** are other integral quantities that are calculated from these **variables** and defined in the **.spro** project file, such as - **efficiency** or **total pressure rise** The **Residuals** diagram below shows the development of the **residual** of one of the solution variables - **pressure** - **velocity** - **turbulent kinetic energy** or - **turbulent energy dissipation** over the number of iterations for **steady-state** simulations or over the simulated time for **transient** simulations. The curves displayed are based on the object selected in the **workspace tree**. .. figure:: images/conv_fine3.png :align: center **Convergence** diagram (top) and **Residuals** diagram (bottom): data set **Fine**, **steady-state** simulation: development of expression **efficiency (t-t)** and residuals over the number of iterations In this case, the **total to total efficiency** curves and the **pressure residuals** for all the operating points of the **Fine** variant of the centrifugal pump **CP nq37 (end-suction)** are shown in the course of a mesh independence study. The rapid convergence of the **total to total efficiency** curves to a constant value is clearly visible. After approximately 350 iterations the residuals have reached the convergence criteria, and the simulations are terminated. The exception is the partial load case Q = 160 m³/h, which runs through to 637 iterations before reaching the convergence criteria. With the checkbox **Show convergence criteria** enabled, the **convergence criterion** for each solution variable is plotted as a thin, dashed line. By grabbing the invisible frame line between the diagrams, where the cursor changes, and dragging it up or down one diagram is enlarged to better examine its content while the other is reduced in size. .. image:: images/conv_minmax2.png :align: center Another way to maximize the diagrams is to separate the **Convergence** diagram from the tab by left-clicking the icon in the upper right corner. Click again to re-attach it. .. image:: images/conv_separate3.png :align: center **Convergence** - displaying exact values ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The exact value of a **variable** or **expression** that **Simerics MP/MP+** returns for an **operating point** for each iteration can be obtained by moving the cursor close to the corresponding curve. A hint then appears and displays, among other things, the iteration value and the value of the **variable** or **expression** closest to the cursor position. .. figure:: images/conv_value2.png :align: center **Hint** showing the iteration number and the value returned for the respective **operating point** .. _sr3: **Convergence** - formatting the diagram ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In the Convergence diagram, the **variable** with its associated location or the **expression** to which the curves refer is displayed at the top left. Left-clicking on this information or on the numbering of the Y-axis opens a configuration menu on the right, which allows these values to be changed. Also the Y-axis and its label may be formatted here. .. image:: images/conv_yaxis2.png :align: center The **Plot type** option is used to select either a **variable** or an **expression**. .. image:: images/conv_plottype2.png :align: center The **Variable** list shows all the variables used in the object that has been selected in the **workspace tree**. Once a variable has been chosen, the corresponding location can be selected from the **Location** list. Only locations where the variable is defined are displayed. The variable **Mass flow rate +** is limited to MGIs, for example. .. image:: images/conv_variables_locations.png :align: center Please note that when selecting a **study** or a whole **project** onl y locations common to all variants of this study or project are listed. As long as the standard **CFturbo** nomenclature is used, **Impeller_1**, **Stator_1** etc., the names of the locations will most probably match. But when renaming **Stator_1** to just **Stator**, for example, two different inflow boundary names occur, **Stator_1-Flow domain-Inflow** and **Stator-Flow domain-Inflow**, which are not visible in the list since they cannot be selected at the same time. So the curves of the variables at these locations can only be evaluated on the variant level. ***OPEN boundary 1** and ***OPEN boundary 2** are names defined by **Simerics MP/MP+** which correspond to the inflow and outflow boundary, respectively. In this example these boundaries are identical to those named **Stator_1-Flow domain-Inflow** and **Volute_1Extension-CFD Flow domain-Outflow** in **CFturbo**. The **Expression** list shows all expressions used in the selected object. .. image:: images/conv_expression2.png :align: center The **Average** value of the selected variable or expression is very useful for evaluating the convergence of flow simulations. It is calculated from the specified number of **most recently stored values** of the respective variable or expression and displayed as a thin, dashed line. The default value for averaging is 50. When moving the cursor close to the line, the **average value** of the variable or expression is displayed. .. image:: images/average_diagram1.png :align: center .. image:: images/average_diagram2.png :align: center The **unit** of a **variable** or **expression** can be changed at any time, regardless of its original definition in **CFturbo**, in order to make simulation results comparable with other data or to use units that are common in the respective country. .. image:: images/conv_unit2.png :align: center A **font size** of up to 14 px can be set for the **title** and the **numbers** of the **X-axis** and **Y-axis**. The default settings are 11 px for the title and 9 px for the numbers. As with the Y-axis, left-clicking the title **Iterations [-]** or the numbers of the **X-axis** opens a configuration menu. .. figure:: images/font_sizes.png :align: center **Font sizes** of the X-axis and Y-axis: standard size (left), maximum size (middle and right) Clicking on a **curve** also opens a configuration menu on the right of the diagram to edit the **label** shown in the **legend** and to change the appearance of the line. Modifications also apply to the associated curve in the **Residuals** diagram. .. figure:: images/curve_label2.png :align: center **Pair of Curves** with their color changed to red and their label changed to **TEST** A variety of **pen styles** is available to set the curve apart from others. .. image:: images/pen_style2.png :align: center While the **pen width** is set directly, a dialog window opens when clicking on the color field to change the **color**, and **transparency (alpha channel)** of the curve. An alpha value of 0 provides complete transparency, while a value of 255 makes the curve opaque. .. figure:: images/pen_color2.png :align: center Dialog window to set the **RGBA (red-green-blue-alpha)** values of the **curve**: range 0 .. 255 Clicking on the **legend** also opens a configuration menu on the right of the diagram to define its **position**, **font size** and the **colors** of its border and the background. .. figure:: images/legend_position2.png :align: center Various position options for the **legend** A high alpha value for low transparency is sometimes useful to make the legend easier to read in front of the curves. .. figure:: images/legend_overview2.png :align: center Different border options and maximum font and border size for the **legend**, opaque background In all cases, the configuration menu can be closed by clicking on **X** in the upper right corner or on the diagram area. **Convergence** - scaling the axes ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Both the **X-axis** and the **Y-axis** scale automatically during a simulation. For a more detailed analysis of curve trajectories, you can easily **zoom in** and **out** using the **mouse wheel** or by spreading two fingers on a **touchscreen** or **touchpad**. The curves can be moved by left-clicking and dragging or by tapping on a **touchscreen** or **touchpad** with a finger and dragging. .. image:: images/conv_zoom_move.png :align: center For more targeted zooming, select the **Zoom window** option from the context menu of the diagram area and then draw a box around the area you want to enlarge. .. image:: images/conv_zoom_context.png :align: center .. image:: images/conv_zoom_box.png :align: center .. figure:: images/conv_zoom_view.png :align: center **Zoom in** on an area using **Zoom window** in the context menu (top) and dragging a box (center) to get the enlarged view (bottom) Using **Fit view** in the context menu of the diagram area, the diagram can be reset to the original axis limits. .. image:: images/conv_fitview.png :align: center To get a precisely defined area the diagram can also be **scaled manually** by specifying the **Minimum** and **Maximum** values for each axis. The number of intervals between them is defined by **Major ticks**. If the checkboxes are enabled the values entered for **Minimum** and **Maximum** apply, and the diagram can no longer be zoomed or moved in the according axis using the mouse or your fingers. .. image:: images/minmax_ticks2.png :align: center **Residuals** - analyzing single or multiple operating points ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The selection of variants, studies, entire projects, or even a single operating point made for the **Convergence** diagram also applies to the **Residuals** diagram, with one detail: While all **solution variables** are shown for a single **operating point**, only the **solution variable** chosen in the dropdown menu is displayed for multiple selections. On one hand, this provides a **detailed view** on the convergence of each solution variable for a **single operating point**. On the other hand, a **comparison** of the convergence behavior of **many operating points** is possible, and **operating points** with poor convergence can be reworked by changing the solver settings. .. figure:: images/conv_singleOP2.png :align: center Convergence of a **single** operating point: all solution variables shown in the **Residuals** diagram The image above shows the convergence behavior of a **single** operating point. The **steady-state** flow simulation ended after 928 iterations when the convergence criterion of 0.001 was reached for all four solution variables. **Turbulent kinetic energy** was the last to reach this criterion and thus determined the duration of the simulation. .. figure:: images/conv_multipleOP2.png :align: center Convergence of **turbulent kinetic energy** of an **entire** performance curve The second image shows the residual curves for **all** operating points of the performance curve. In these cases, too, **turbulent kinetic energy** is the decisive factor for terminating the flow simulations. Monitoring **transient** flow simulations ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The previous sections have focused on the convergence of **steady-state** flow simulations. As soon as the first **transient time step** has been computed, indicated by |running|, or **transient results** are available, indicated by check marks in column **T** of the **workspace tree**, the corresponding curves can be selected by choosing the **transient** option at the top left of the **Convergence** or the **Residuals** diagram. .. image:: images/transient_res_available.png :align: center There are some differences in the visualization of **transient** simulations: In the **Convergence** diagram, the value of a **variable** or **expression** is plotted over the simulated time span, as are the **residuals** of the solution variables in the **Residuals** diagram. The simulation converges when this variable or expression reaches a constant value over time or oscillates periodically around an average value. The frequency of this oscillation directly corresponds to a blade passage frequency or the frequency of a rotor-stator interaction. The **Residuals** diagram shows the residuals of the solution variables at each time step after a loop of **inner iterations**. Ideally, the simulation converges so well that the convergence criteria, residuals smaller than 0.001, for example, are met. .. figure:: images/transient_eff.png :align: center **Convergence** and **Residuals** diagrams of a **transient** flow simulation: transient response of the **efficiency** over three revolutions (top), **velocity** residuals well below the convergence criterion of 0.001 (bottom) In the image above, the transient response of the **total-to-total efficiency** over time using the example of the centrifugal pump **CP nq37 (end-suction)** is displayed. Three revolutions of the six-bladed impeller at a rotational speed of 3600 rpm, resulting in a simulation time of 0.05 s, were set and are sufficient for the **efficiency (t-t)** to reach a stable level, while the residual of the **velocity** already meets the convergence criterion after two blade passes at the volute's cutwater. Resolving each rotation into 120 angular steps is therefore completely sufficient for excellent convergence and a detailed view on the transient process. The **efficiency (t-t)** is a calculated value that, for centrifugal pumps, sets the total pressure built up over the entire stage, including the total pressure losses in the volute, and the volumetric flow rate for a specific operation point in relation to the required shaft power. The total pressure rise **Delta p (t-t)** and the shaft power **Power, Impeller_1** both experience periodic fluctuations. However, the shaft power oscillation decreases from the partial load range at Q = 160 m³/h to the design point at Q = 227 m³/h, since backflow in the impeller then usually disappears in contrast to the partial load flow field. Thus the static pressure on the blade surfaces is less affected when the blade passes the cutwater. .. image:: images/transient_dptot.png :align: center .. figure:: images/transient_Pshaft2.png :align: center **Total pressure rise** of the entire stage (top) and **shaft power** (bottom) for **CP nq37 (end-suction)** Performance curves ------------------ **Performance** diagram - overview ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The **Performance** diagram in the **Performance curves** tab is the main tool in **CFturbo BLADERUNNER** for describing and analyzing the behavior of turbomachines by displaying **performance curves** obtained from flow simulations. It is identical in appearance and operation to the **Convergence** diagram in the **Convergence plots** tab, but shows complete **performance curves** consisting of several **operating points** rather than convergence curves for individual **operating points**. The display is **live**, i.e., the symbol of the operating point currently being computed moves across the diagram area with each iteration or time step according to its X and Y values. .. figure:: images/perf_conv_steady.png :align: center **Efficiency (t-t)** curve created by **steady-state** flow simulations (solid line) with previous computation steps of an **operating point** (dashed lines) **Performance** diagram - configuration ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Selecting **variables** and **expressions**, configuring the axes and formatting the curves and the legend is executed as described for the :ref:`Convergence diagram `. There is just one difference: In the configuration menu of the X-axis, you can choose between **mass flow rate** and **volumetric flow rate** as the **variable** and also specify the location where this **variable** is evaluated. .. image:: images/perf_X_variable2.png :align: center .. image:: images/perf_X_location2.png :align: center **Selection** of **steady-state** and **transient** data ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ As with the **Convergence** and **Residuals** diagrams, the **Performance** diagram displays the data selected in the **workspace tree**. This can be, for example, a single **performance curve** for a variant, or several **performance curves** for the same variant, which then form a characteristic map, or even a comparison of several variants. For each **operating point**, **steady** and/or **transient** results may be available, which can be selected using the drop-down menu at the top left. By activating the **Compare steady and transient** checkbox, the complementary data sets are also displayed, allowing a direct comparison of the results. .. image:: images/perf_options2.png :align: center The curves are then labeled **Steady** and **Transient**, respectively. .. figure:: images/perf_steady_transient_diagram2.png :align: center **Head** curve: comparison of **steady-state** and **transient** results If only a single **operating point** is selected in the **workspace tree**, the entire **performance curve** to which the operating point belongs is still displayed. To display only **individual operating points**, deselect the remaining operating points using the checkboxes. It is then advisable to display only these individual operating points instead of a shortened **performance curve**. To do this, click on the relevant **performance curve**, which will open the configuration menu on the right. There, you can set the **No line** option under **Pen style**. .. figure:: images/perf_singleOPs_diagram2.png :align: center Only three single **operating points** displayed by deselecting the other ones and by choosing **No line** **Uncertainty** of the displayed values ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ For each **operating point** Y-value, an **error bar** is displayed representing its uncertainty. It is formed from the minimum and maximum value of the last number of iterations or time steps defined by the **average** value. The value of the **variable** or **expression** itself is calculated as the average of precisely this number of calculation steps. The following image shows, as above, the convergence of the **Efficiency (t-t)** value of an **operating point** in a **steady-state** flow simjulation. The length of the **error bar** decreases continuously until convergence is reached. .. figure:: images/perf_error_steady.png :align: center **Efficiency (t-t)** curve curve created by **steady-state** flow simulations: development of error bars from bottom to top For well-converged **steady-state** simulations, there is of course a minimal error bar that barely extends beyond the symbol of the operating point's value. The value of the operating point also remains virtually unchanged, regardless of whether the averaging comprises 10 or 50 values. In **transient** simulations, the error bar captures a possible oscillation in the value of a **variable** or **expression**. In the example of **CP nq37 (end-suction)**, the rotation by one blade pitch is resolved with 20 time steps. An **average** value of 20 thus captures exactly one period of the oscillation and therefore also reliably its minimum and maximum, so the fluctuation range of the value is correctly displayed. When averaging over five time steps, the error bar shrinks noticeably and thus no longer reflects the possible fluctuation of the value, and the value itself changes. .. figure:: images/perf_avg_diagram.png :align: center **Head** curve created by **transient** flow simulations: fluctuation displayed depends on **average** value If you prefer not to display the error bars, you can deselect the **Show bars** option in the **Y-axis** configuration menu. .. image:: images/perf_show_bars2.png :align: center CFD data analysis ----------------- ... with Simerics MP ^^^^^^^^^^^^^^^^^^^^ As soon as simulation results are available for an operating point—as indicated by ✓ or ●/○—the flow field can be analyzed in **Simerics MP/MP+**. Depending on whether **steady-state** or **transient** data—or both—are available, selecting **Open steady results** or **Open transient results**, respectively, from the context menu of the according operating point launches **Simerics MP/MP+** directly with the corresponding latest SRES result file. .. figure:: images/CFD_analysis_Simerics.png :align: center Launching **Simerics MP/MP+** with the latest **steady-state** or **transient** SRES result file for analysis The flow-field analysis in **Simerics MP/MP+** offers extensive visualization options, such as streamline plots, multiple surface plots displayed simultaneously, and a perspective view. However, the analysis takes time, and the image data is not available in **CFturbo BLADERUNNER**. .. figure:: images/CFD_analysis_Simerics_perspective_view.png :align: center Extensive analysis capabilities in **Simerics MP/MP+** ... with CFturbo BLADERUNNER ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ An easier way to analyze flow fields than using **Simerics MP/MP+** is available via the **Postprocessing** tab, which appears when an **operating point** is selected in the **workspace tree**. Various settings can be used to generate the desired images, such as this one showing the static pressure reise in the impeller in a cascade view provided by the **Simerics MP/MP+ TurboPost** module. **CFturbo BLADERUNNER** calls **Simerics MP/MP+** in the background for this purpose and displays the images in a clear, organized list. .. figure:: images/CFD_analysis_BLADERUNNER_TurboPost.png :align: center Integrated flow-field analysis in **CFturbo BLADERUNNER** Currently, images are limited to surface plots. The first step is to specify the type of case to be analyzed—**steady-state** or **transient**—and the type of surface—**cross section** or **TurboPost**: .. image:: images/CFD_analysis_BLADERUNNER_step1.png :align: center - **Results** – analysis of the ""Steady**-state or **Transient** solution for an operating point - **Plot type** – either a plot on a **Cross section** or on a **TurboPost** surface - **Section** – the plane to be selected for a **Cross section**: either XY, XZ, or YZ - **Position** – the axial position of the **Cross section** plane selected - **TurboPost** – the **TurboPost** component to be shown either in a **meridional** section or in a **cascade** view In the second step, the image size is set and the variable or expression to be displayed selected. The value range at the current operating point is preset by default and can be changed manually: .. image:: images/CFD_analysis_BLADERUNNER_step2.png :align: center - **Zoom factor** – relative size of the plot on the drawing area - **Variable** – selection of the **Simerics MP/MP+** variable or expression to be displayed - **Min. value**/**Max. value** – value range of the **Variable** selected Once the settings are configured, clicking **+** adds the image to the **IMAGES** list. However, the image is only generated upon clicking the **Generate/update image** icon that is displayed in the **S** (steady-state result) or **T** (transient result) column. .. image:: images/CFD_analysis_BLADERUNNER_image_list.png :align: center One particularly convenient feature is the ability to apply the format of the generated images to all other operating points of the **Variant**, which ensures a consistent display and thus allows for a quick comparison of the flow fields of the various operating points. Of course, the images may also be exported. .. figure:: images/CFD_analysis_BLADERUNNER_toolbar.png :align: center Image management toolbar in the **Postprocessing** tab Comparison with measurement data ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Flow simulations provide flow fields for the various operating conditions of a turbomachine with unprecedented resolution and accuracy, and usually in much less time than would be possible with measurements. Nevertheless, bench tests are necessary to describe the actual behavior of the turbomachine and to identify any deviations from the simulations. Also extensive measurement data is often available for older designs, which can now be verified using flow simulations. **CFturbo BLADERUNNER** offers the ability to directly compare measurements and flow simulations by importing measurement data. To do this, characteristic curves are individually imported into the **workspace tree** via - importing a text file - pasting data from the clipboard - manual entry point by point for display alongside the simulation results. Measurement data is assigned to a **project** in the **workspace tree** under the **External curves** entry, directly below the project name. To import measurement data, first select **External curves** and then click **Add curve** in the **Settings**. .. image:: images/import_data_add_curve.png :align: center Data should be arranged in two columns of numerical values without caption to be imported via the clipboard or as a text file. .. image:: images/import_data_ext_data_file.png :align: center In this example, two data sets were imported that show the measured pressure ratio relative to the mass flow rate. Accordingly, **Mass flow rate** was selected for the X-axis and **Pressure ratio** for the Y-axis. The data sets were appropriately named under **Curve caption**, and the variant to which the measured values refer was specified under **Description**. The imported data is displayed as a curve in the diagram on the right and appears on the left in the **workspace tree** under **External curves**. .. figure:: images/import_data_ext_curves.png :align: center Imported external measurement data that appear as **External curves** It is important to note that the **External curves** will only appear if the correct units have been selected for both the X-axis and the Y-axis. In the following example, the two imported curves for 100,000 rpm and 120,000 rpm are shown in combination with simulation data. .. figure:: images/import_data_combined_curves.png :align: center External measurement data in comparison with simulation results **External curves** can be deleted using the **Remove file** option. If you simply want to hide them in a diagram, you can do so by deactivating them in the **workspace tree**. .. image:: images/import_data_remove_curve.png :align: center CFD cases - mesh independence and transient effects --------------------------------------------------- A brief mesh study ^^^^^^^^^^^^^^^^^^ A brief study is conducted to show the dependence of flow simulation results on coarse meshes and on flow modeling by analyzing the shapes of the **performance curves** and by taking a look at the flow fields. For this purpose, three different meshes are generated for the centrifugal pump **CP nq37 (end-suction)** by selecting the presets **Medium** and **Fine** in the **GLOBAL MESH PARAMETERS**. A further refined mesh, **User-defined #1**, is created using the following **GLOBAL MESH PARAMETERS**: - **Specific length calculation:** Using all CAD surfaces - **Cell size on surfaces:** 0.002 - **Maximum cell size:** 0.004 - **Minimum cell size:** 0.0001 .. image:: images/analysis_CP_meshMedium.png :align: center .. image:: images/analysis_CP_meshFine.png :align: center .. figure:: images/analysis_CP_meshNo1.png :align: center Meshes **Medium**, **Fine**, and **User-defined #1** (top to bottom) All of these meshes can be considered coarse. Their number of cells remains below 1,000,000 whereas mesh independence is expected at about 3,500,000 cells for this model. However, the number of cells in the volume and on the surface of the blades, and thus the resolution of the flow field and of the surface pressure distributions, increases systematically from grid to grid. By applying the same numeric schemes the conditions for the flow simulations are kept constant for both **steady** and **transient** flow simulations: .. image:: images/analysis_CP_num_scheme2.png :align: center In case the convergence criterion is not reached for the **steady** simulations in the partial load regime due to residuals settling at a higher level, the **blending factor** of the **velocity** equation is gradually increased to a maximum of **0.6**. Converged solutions are thus obtained for all **operating points**. For the **transient** simulations, the settings shown are sufficient to reach the convergence criterion. 20 iterations or time steps, equal to one blade pass, are used for **averaging**. .. figure:: images/analysis_CP_conv_steady2.png :align: center Convergence of the **steady-state** simulations for the **Medium** mesh .. figure:: images/analysis_CP_conv_transient2.png :align: center Convergence of the **transient** simulations for the **Medium** mesh The most important performance curves for describing a centrifugal pump are **head** and **shaft power**, while the **total-to-total efficiency** is calculated from these values. In the **Performance** diagram, **steady-state** simulations with the three meshes provide almost identical curves for the **head** with a spread of only 0.5% at the design point. The exact value of a data point can be obtained by approaching the cursor. .. figure:: images/analysis_CP_head_s2.png :align: center Almost identical **head** curves obtained by **steady-state** simulations The **head** curves of the **transient** flow simulations are also almost identical. .. figure:: images/analysis_CP_head_t2.png :align: center **Head** curves obtained by **transient** flow simulations Combining the two sets of curves, the **head** curves obtained by **transient** flow simulations are very close to the **steady-state** results, but generally show a more linear progression with a minimum deviation of 3.0% for the **User-defined #1** mesh in partial-load operation. .. figure:: images/analysis_CP_head_stacked.png :align: center **Head** curves in a stacked view to directly compare **steady-state** (dashed lines) and **transient** simulations This deviation should be visible in the flow field. For this purpose the **steady-state** and **transient** results for the partial load point Q = 160 m³/h are directly opened in Simerics MP/MP+ via the context menu. .. figure:: images/analysis_CP_openSteady2.png :align: center Context menu of the **operating point** for visualizing results in **Simerics MP/MP+** The following image shows the **velocity** distribution in a section at half the blade height at the outlet. Even within the impeller **Simerics MP/MP+** displays the **velocity in stationary frame** rather than the relative velocity in the rotating frame. Nonetheless, the differences in the flow field between the **frozen rotor method** used for the **steady-state** simulation (left) and the **transient** simulation (right) are clearly visible both in the wake of the blades and in the volute, particularly at the cut-water. .. figure:: images/analysis_CP_velocity.png :align: center **Velocity** distribution on a section at half the outlet blade height for the operating point Q = 160 m³/h Black and white stripes are useful to highlight the differences in the **pressure** field. In the **transient** simulation, a change to black can be seen near the cut-water, indicating a higher pressure build-up there than in the **steady-state** simulation. .. figure:: images/analysis_CP_pressureBW.png :align: center **Pressure** distribution on the same section: higher pressure rise with the **transient** solution (right) For the **shaft power**, **steady-state** simulations also provide almost identical curves with a spread of only 1.1% at the design point. .. image:: images/analysis_CP_power_s2.png :align: center The **power** curve obtained by **transient** flow simulations fully coincides with the **steady-state** curve for the **User-defined #1** mesh and shows a maximum spread at the design point of 2.1% for the **Fine** mesh. .. figure:: images/analysis_CP_power_stacked.png :align: center **Power** curves in comparison in a stacked view: **steady-state** (dashed lines) and **transient** simulations For this mesh and operating point the **pressure** distributions on the blades are visualized using **Simerics MP/MP+** but without a noticeable difference betwenn the **steady-state** and the **transient** results, neither on the pressure side nor on the suction side. .. figure:: images/analysis_CP_pressure_blades.png :align: center **Pressure** distribution on the impeller blades: barely perceptible difference (in circles) between **steady-state** (ledt) and **transient** (right) results This brief investigation is not yet sufficient to achieve mesh independence. However, it shows that even fairly coarse grids can reproduce the curves of important **expressions** quite well, and do so in a short computing time. The use of **transient** simulations, especially away from the design point, produces results that are closer to physical reality than **steady-state** simulations. A look at cavitation ^^^^^^^^^^^^^^^^^^^^ Turbopumps in rocket engines deliver fuel and liquid oxygen (LOX) from tanks that are pressurized to approximately 0.2 MPa (2 bar) above ambient pressure and feed the liquids to the combustion chamber. Each turbopump consists of a centrifugal pump with an upstream inducer, at the blade edge of which cavitation occurs, which can be controlled by local confinement. The difficulty lies in simulating the process. A **steady-state** simulation is quick to run, but may not accurately represent the **transient** process, as shown in the following **CFturbo design** of a LOX turbopump. .. image:: images/LOX_turbopump_meridional.png :align: center .. figure:: images/LOX_turbopump_3D.png :align: center Meridional section (top) and 3D view (bottom) of a **LOX turbopump** in CFturbo The **steady-state** simulation, with the Simerics MP/MP+ cavitation module activated, shows an efficiency curve that turns negative with the residuals of the solution variables diverging, indicating that cavitation is improperly computed. .. image:: images/analysis_cav_conv_steady.png :align: center .. figure:: images/analysis_cav_resid_steady2.png :align: center **Steady-state** simulation: total-to total efficiency turning negative (top), residuals diverging (bottom) In **Simerics MP/MP+**, the cavitation zone can be visualized by an isosurface with a **vapor volume fraction** of, for example, 80% and above. .. image:: images/analysis_cav_SMP_settings.png :align: center In the **steady-state** flow simulation, this cavitation zone extends through the entire inducer and then fills the blade channels of the impeller, which is unrealistic since a pressure of approximately 18.0 MPa (180 bar) builds up there. .. figure:: images/analysis_cav_steady.png :align: center **Steady-state** flow simulation: unrealistic expansion of the cavitation zone (light blue) into the impeller In contrast, the transient simulation already reaches an efficiency level of around 80% after just a few calculation steps, while the velocity and cavitation residuals have already decreased significantly. .. image:: images/analysis_cav_conv_transient.png :align: center .. figure:: images/analysis_cav_resid_transient.png :align: center **Transient** simulation: high total-to total efficiency (top), already low velocity and cavitation residuals (bottom) In the **transient** simulation, the cavitation zone remains limited to the area around the leading edge and outer edge of the inducer blading, which corresponds to the expected behavior. A pressure of 18.0 MPa (180 bar) builds up in the impeller. .. figure:: images/analysis_cav_transient.png :align: center **Transient** simulation: realistic limitation of cavitation (light blue) to the inducer inlet, development of wall pressure of the impeller Data export ----------- **CFturbo BLADERUNNER** offers the option of exporting the data displayed in the **Performance** diagram - as an **image** via the **clipboard** or as a file in **bitmap** or **vector** format, or - as structured **tables** in a spreadsheet of a **Microsoft Excel workbook file** To do this, **right-click** in an **empty area** to open the diagram's context menu and select one of the options: - **Copy to clipboard** - **Save diagram** as a bitmap or as vector graphics, or - **Export to Excel** .. image:: images/data_diagram1.png :align: center .. figure:: images/data_diagram2.png :align: center Options for exporting data from the **Performance** diagram