.. _non_dim_output_userGuide: Non-Dimensional Outputs ======================= .. note:: With :ref:`User Variables `, manual dimensionalization is rarely needed — simply request the desired unit system and the conversion is automatic. The formulas below describe the underlying logic. All solver outputs are non-dimensional. To recover physical (SI) values, multiply by the appropriate reference quantity from the :ref:`Reference Quantities Table `. .. _tab_non_dim_output: .. csv-table:: Reference values for non-dimensional outputs :file: Tables/nondim_output.csv :widths: 10 10 60 :header-rows: 1 :delim: @ .. note:: Many output variables use the :ref:`reference velocity scaling ` :math:`U_\text{scale}` (not :math:`U_\text{ref}`). In the examples below we assume :math:`U_\text{scale}` has been computed as shown in the :ref:`Introduction `. Visualization Field Conversions ------------------------------- Flow360 exports ParaView (.pvtu) and Tecplot (.szplt) files. All exported fields are non-dimensional. The subsections below show how to recover dimensional values. .. _postprocess_tab_img: .. figure:: Figures/download_results_WebUI.png :scale: 20% :align: center Accessing case results. Velocity ^^^^^^^^ Reference value: :math:`U_\text{scale}`. If :code:`velocityX = 0.6` and :math:`U_\text{scale} = 340\;\text{m/s}`, then :math:`v_x = 0.6 \times 340 = 204\;\text{m/s}`. Pressure ^^^^^^^^ Reference value: :math:`\rho_\infty\,U_\text{scale}^2`. If :code:`p = 0.65`, :math:`\rho_\infty = 1.225\;\text{kg/m}^3`, and :math:`U_\text{scale} = 340\;\text{m/s}`: .. math:: p_\text{dim} = 0.65 \times 1.225 \times 340^2 = 92\,046.5\;\text{Pa} Node Force Per Unit Area ^^^^^^^^^^^^^^^^^^^^^^^^ :code:`nodeForcesPerUnitArea` is the total (pressure + friction) force at a node divided by the surface area attributed to that node. Integrating over the whole surface yields the total force. The reference value is the same as for pressure: :math:`\rho_\infty\,U_\text{scale}^2`. Temperature ^^^^^^^^^^^ Reference value: :math:`T_\infty`. Multiply the non-dimensional temperature by the freestream temperature to obtain Kelvin. Surface Coefficient Definitions ------------------------------- The following coefficients appear in both visualization files and CSV files. They all use the **reference velocity** :math:`U_\text{ref}` (accessed via ``case.params.reference_velocity``), which is different from :math:`U_\text{scale}`. .. tip:: Flow360's unit system carries SI units through arithmetic, so you can convert any coefficient to physical units in one step. For example, once ``q_ref`` and ``A_ref`` are retrieved from the API: .. code-block:: python tau_wall = (Cf * q_ref).to('Pa') # wall shear stress p_dim = (Cp * q_ref + p_inf).to('Pa') # static pressure We define the dynamic pressure for coefficients as: .. math:: q_\text{ref} = \tfrac{1}{2}\,\rho_\infty\,U_\text{ref}^2 Skin Friction Coefficient ^^^^^^^^^^^^^^^^^^^^^^^^^ The skin friction coefficient vector :math:`\mathbf{C_f}` and its magnitude :math:`C_f`: .. math:: :label: skinFrictionCoeffVecDef \mathbf{C_f} = \frac{\mathbf{\tau_\text{wall}}}{q_\text{ref}} To recover the dimensional wall shear stress: .. math:: :label: fricCoeff \tau_\text{wall}\;[\text{Pa}] = C_f \cdot q_\text{ref} .. _pressureCoefficientDefinition: Pressure Coefficient ^^^^^^^^^^^^^^^^^^^^ .. math:: :label: pressCoeffDef C_p = \frac{p - p_\infty}{q_\text{ref}} To recover the dimensional static pressure: .. math:: :label: pressDimm p\;[\text{Pa}] = C_p \cdot q_\text{ref} + p_\infty .. _totalPressureCoefficientDefinition: Total Pressure Coefficient ^^^^^^^^^^^^^^^^^^^^^^^^^^ .. math:: :label: totalPressCoeffDef C_{p_t} = \frac{p_t - p_{t,\infty}}{q_\text{ref}} To recover the dimensional total pressure: .. math:: :label: totalpressDim p_t\;[\text{Pa}] = C_{p_t} \cdot q_\text{ref} + p_{t,\infty} The total pressure coefficient can also be computed from the primitive variables as described in equations 26 and 29 of :ref:`this paper `: .. math:: :label: totalPressCoeff C_{p_t} = \frac{\gamma\,p\,\bigl(1 + \tfrac{\gamma-1}{2}\,\text{Ma}^2\bigr)^{\gamma/(\gamma-1)} - \bigl(1 + \tfrac{\gamma-1}{2}\,\text{Ma}_\infty^2\bigr)^{\gamma/(\gamma-1)}}{\tfrac{\gamma}{2}\,\text{Ma}_\infty^2} where :math:`\gamma = 1.4` for standard air. .. note:: Ensure :code:`Mach` and :code:`primitiveVars` are included in your :ref:`volume output ` configuration. CSV File Outputs ---------------- .. _ADoutput: Actuator Disk ^^^^^^^^^^^^^ The file ``actuatorDisk_output_v2.csv`` reports power, force, and moment for each disk. The power column contains a coefficient: .. math:: :label: defADPower C_p = \frac{\text{Power}\;[\text{W}]}{\rho_\infty\,U_\text{scale}^3\,L_\text{gridUnit}^2} To obtain dimensional power: .. code-block:: python actuator_disk_output = case.results.actuator_disks.averages density = case.params.operating_condition.thermal_state.density L_grid = project.length_unit C_p = actuator_disk_output['Disk0_Power'] power = C_p * density * U_scale**3 * L_grid**2 # W .. attention:: Actuator Disk forces and moments use :math:`U_\text{scale}`, **not** :math:`U_\text{ref}`. See :ref:`Converting to Physical Units ` for the general conversion formulas. .. _betDiskLoadingNote: BET Loading ^^^^^^^^^^^ The file ``bet_forces_v2.csv`` contains: 1. **Integrated forces and moments** per disk (``Disk0_Force_x``, ``Disk0_Moment_x``, …). These are non-dimensional raw values: .. math:: :label: defBETForce \text{Force}^* = \frac{F\;[\text{N}]}{\rho_\infty\,U_\text{scale}^2\,L_\text{gridUnit}^2} .. math:: :label: defBETMoment \text{Moment}^* = \frac{M\;[\text{N·m}]}{\rho_\infty\,U_\text{scale}^2\,L_\text{gridUnit}^3} .. note:: These values represent forces/moments on the **solid**. Forces on the **fluid** are the negative of the above. .. _pmoutput: .. note:: Equations :eq:`defBETForce` and :eq:`defBETMoment` also apply to Porous Media outputs in ``porous_media_output_v2.csv``. .. attention:: BET forces and moments use :math:`U_\text{scale}`, **not** :math:`U_\text{ref}`. The x, y, z components are in the global inertial frame defined by the mesh. .. _bet_section_ct_cq: 2. **Sectional thrust** :math:`C_t` **and torque** :math:`C_q` per blade at each radial station (``Disk0_Blade0_R0_ThrustCoeff``, …). .. math:: :label: defBETCt C_t(r) = \frac{\text{Thrust/span}\;[\text{N/m}]}{\tfrac{1}{2}\,\rho_\infty\,(\Omega r)^2\,\text{chord}_\text{ref}} \cdot \frac{r}{R} .. math:: :label: defBETCq C_q(r) = \frac{\text{Torque/span}\;[\text{N}]}{\tfrac{1}{2}\,\rho_\infty\,(\Omega r)^2\,\text{chord}_\text{ref}\,R} \cdot \frac{r}{R} Here :math:`r` is the dimensional distance from the rotation axis, :math:`\text{chord}_\text{ref}` the dimensional reference chord, and :math:`R` the rotor radius. .. note:: :math:`C_t` and :math:`C_q` are **sectional** loadings: :math:`C_t(r) = \text{d}C_T/\text{d}(r/R)` and :math:`C_q(r) = \text{d}C_Q/\text{d}(r/R)`. .. important:: All right-hand-side quantities in :eq:`defBETForce`–:eq:`defBETCq` are **dimensional**. The non-dimensional radius in the CSV must first be converted: :math:`r` = ``Disk0_Blade0_R0_Radius`` :math:`\times\, L_\text{gridUnit}`. .. warning:: For steady-state BET Disk simulations, :math:`C_t` and :math:`C_q` are written only for ``Blade0``; all other blades report zeros because the loading is identical. For unsteady BET Line simulations each blade has distinct values. **Python example** — dimensional force, moment, and sectional loading: .. code-block:: python bet_forces = case.results.bet_forces.averages density = case.params.operating_condition.thermal_state.density L_grid = project.length_unit # --- Integrated force & moment (Disk 0) --- force_x = bet_forces["Disk0_Force_x"] * density * U_scale**2 * L_grid**2 # N moment_x = bet_forces["Disk0_Moment_x"] * density * U_scale**2 * L_grid**3 # N·m # --- Sectional loading (Disk 0, Blade 0, radial station 1) --- bet_model = case.params.models[4] # index of the BETDisk model chord_ref = bet_model.chord_ref omega = bet_model.omega R = bet_model.entities.stored_entities[0].outer_radius r1 = bet_forces["Disk0_Blade0_R1_Radius"] Ct_r1 = bet_forces["Disk0_Blade0_R1_ThrustCoeff"] Cq_r1 = bet_forces["Disk0_Blade0_R1_TorqueCoeff"] thrust_r1 = Ct_r1 * 0.5 * density * omega**2 * r1 * L_grid * R * chord_ref # N/m torque_r1 = Cq_r1 * 0.5 * density * omega**2 * r1 * L_grid * R**2 * chord_ref # N Aeroacoustic Output ^^^^^^^^^^^^^^^^^^^ The file ``total_acoustics_v3.csv`` reports the non-dimensional acoustic pressure signal at each observer location. If :py:attr:`AeroacousticOutput.write_per_surface_output` is ``True``, per-surface files ``surface__acoustics_v3.csv`` are also written. Columns: ``time, physical_step, observer_0_pressure, observer_0_thickness, observer_0_loading, …`` for N+1 observers. .. note:: The observation time may fall outside the simulation time range because the acoustic signal takes a finite propagation time from the surface to each observer. Early and late time entries are zero-padded. Heat Transfer ^^^^^^^^^^^^^ The file ``surface_heat_transfer_v2.csv`` contains surface-integrated heat flux in non-dimensional form. To recover the dimensional heat transfer rate, multiply by :math:`\rho_\infty\,U_\text{scale}^3\,L_\text{gridUnit}^2`: .. code-block:: python surface_ht = case.results.surface_heat_transfer.averages density = case.params.operating_condition.thermal_state.density L_grid = project.length_unit q_nd = surface_ht["fluid/Interface_solid_HeatTransferRate"] q = q_nd * density * U_scale**3 * L_grid**2 # W .. _visualization_outputs: Visualization Tips ------------------ The sections below are not about conversion formulas but about using specific output fields effectively. Skin Friction — Detecting Separation ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The :code:`CfVec` vector is useful for locating boundary-layer separation. Fully attached flow follows the surface along the streamwise direction; separated flow produces local recirculation with reversed skin friction. For flow predominantly in the x-direction, regions of negative :code:`CfVecX` indicate separation. Visualizing with a three-level scale (e.g. −1e-6, 0, 1e-6) highlights separated vs. attached regions: .. _cfvecXrecirculation: .. figure:: Figures/surfaceRecirculation.png :scale: 70% :align: center x-component of skin friction showing attached (yellow) and separated (purple) flow at high angle of attack. Surface streamlines can also reveal recirculation. Since wall velocity is zero on a :code:`NoSlipWall`, use :code:`CfVec{X,Y,Z}` as the integration variable instead of velocity: .. figure:: Figures/surfaceRecirculationVec.png :scale: 70% :align: center Surface streamlines showing recirculation regions. Total Pressure — Visualizing Separation and Boundary Layers ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ :math:`C_{p_t}` reveals separation regions in volume slices and is effective for visualizing the boundary layer: .. figure:: Figures/CPT.png :scale: 50% :align: center Total pressure coefficient on a slice through a partially stalled wing. .. figure:: Figures/CPT_ZOOMED.png :scale: 50% :align: center Zoomed view showing the developing boundary layer (blue) near the leading edge. .. _knowledge_base_q_criterion: Q-Criterion — Visualizing Vortices ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The :code:`qcriterion` field identifies vortices via isosurfaces. Recommended isosurface values: - **Aircraft**: :math:`\text{Ma}^2 / \text{span}^2` - **Rotors**: :math:`\text{Ma}_\text{tip}^2 / D^2` Larger values show only strong vortices; smaller values reveal weaker structures. .. figure:: Figures/qcriterion.png :scale: 50% :align: center :code:`qcriterion` isosurface showing tip vortex and vortices from the separation region. .. figure:: Figures/qcriterion_mesh.png :scale: 50% :align: center Volume mesh coarsening away from the wing causes rapid vortex dissipation. After refining the far-field mesh: .. figure:: Figures/qcriterion_finer.png :scale: 50% :align: center Smoother isosurface with improved vortex resolution on a refined mesh. .. figure:: Figures/qcriterion_mesh_finer.png :scale: 50% :align: center Refined volume mesh reduces numerical dissipation. For more Q-criterion visualizations: - :ref:`BET Line flow visualization ` - :ref:`Wind turbine case study ` - :ref:`Hover prediction workshop (figs 9, 17) ` - :ref:`Rotor modeling techniques (figs 11, 12, 26, 27) ` - :ref:`Rotor5 tool (figs 4, 18, 19) ` - :ref:`XV15 DES simulations (figs 10, 14, 17) `