HYDRODYNAMICS · CFD · EXPERIMENTAL METHODS
Hydrodynamics, CFD & Experimental Methods
Hydrodynamics, CFD & Experimental Methods provides engineering calculators for scaling and similarity, towing-tank corrections, model-to-ship full-scale extrapolation, CFD wall and time-step metrics, verification and validation, experimental uncertainty, and flow-field, wake and turbulence analysis. The calculators bring key physical, numerical and experimental relationships into one structured browser-based environment.
Use the seven modules below to establish geometric and dynamic similarity, assess towing-tank corrections and model-to-ship extrapolation, evaluate CFD near-wall resolution, discretization and V&V metrics, quantify experimental uncertainty and interpret flow-field measurements. Results should be used with consistent reference quantities, scale, fluid properties, numerical settings and experimental definitions.
ENGINEERING MODULES
From similarity and model testing to CFD verification and full-scale prediction
Seven coordinated modules connect similarity theory, towing-tank corrections, full-scale extrapolation, CFD setup and verification, experimental uncertainty analysis, and measured flow-field and turbulence quantities.
Scaling & Similarity Calculators
Work with scale ratio, geometric and mass scaling, Froude similarity, Reynolds mismatch, time/frequency scaling and force, moment and power scaling.
Model Testing & Towing-Tank Corrections
Evaluate towing-tank geometry and blockage ratio, depth Froude number, Schuster/Scott/Tamura blockage corrections, corrected resistance, equivalent speed and Nyquist sampling requirements.
Model-to-Ship / Full-Scale Extrapolation
Calculate full-scale friction coefficient, roughness and correlation allowances, air-resistance coefficient, total resistance, effective power, appendage scaling and temperature-corrected model resistance.
CFD Core Calculations
Evaluate friction velocity, wall y+, first-cell height, u+, wall shear, dynamic pressure, pressure coefficient, Courant number and CFD time step.
CFD Verification & Validation
Evaluate grid spacing and refinement ratio, convergence behavior, observed order, Richardson extrapolation, numerical uncertainty and CFD validation against reference data.
Experimental Calculations & Uncertainty
Calculate sample statistics, Type A and Type B standard uncertainty, sensitivity coefficients, independent/correlated combined uncertainty, relative uncertainty and expanded uncertainty.
Flow Field, Wake & Turbulence Analysis
Analyze Reynolds decomposition, mean and weighted LDV statistics, turbulence intensity, turbulent kinetic energy, axial vorticity, wake fraction and LDV Doppler velocity.
Scaling & Similarity Calculators
Research-grade hydrodynamic scaling calculators for model–ship scale ratio, geometric similarity, Froude and Reynolds similarity, time and frequency scaling, and force, moment and power conversion.
Scale Ratio
Calculate the ship-to-model linear scale ratio from corresponding characteristic lengths.
Engineering note: This suite uses λ = LS/LM, so λ > 1 for a conventional reduced-scale model. Use corresponding geometric lengths for model and ship.
Geometric & Mass Scale Factors
Calculate area, volume and density-adjusted mass scale factors from the linear scale ratio.
Engineering note: Geometrically similar quantities scale with λ for length, λ² for area and λ³ for volume. Mass additionally depends on the density ratio.
Model Testing & Towing-Tank Correction Calculators
Practical calculators for towing-tank geometry, blockage ratio, depth Froude number, Schuster, Scott and Tamura corrections, equivalent speed, corrected resistance coefficient and Nyquist sampling checks.
Tank Cross-Section
Calculate the rectangular towing-tank cross-sectional area from tank breadth and water depth.
Engineering note: Uses A = b h for a rectangular towing-tank section. If the facility has a non-rectangular section, enter its true cross-sectional area directly in calculators that request A.
Blockage Ratio
Calculate the blockage parameter from the model maximum transverse area and towing-tank cross-sectional area.
Engineering note: ITTC defines the blockage parameter as m = AX/A, where AX is the model maximum transverse section and A is the towing-tank section.
Model-to-Ship / Full-Scale Extrapolation Calculators
Practical full-scale extrapolation calculators for ship friction, roughness and correlation allowances, air resistance, resistance prediction, effective power, appendage scaling and temperature correction.
Full-Scale Friction Coefficient
Calculate full-scale Reynolds number and the ITTC-1957 frictional resistance coefficient.
Engineering note: Uses the ITTC-1957 model-ship correlation line CFS = 0.075 / (log10 ReS − 2)². The entered length should match the characteristic length used for the Reynolds number in the extrapolation.
CFD Core Calculators
Practical CFD calculators for near-wall resolution, wall shear, dynamic and pressure coefficients, Courant control and time-step estimation in marine and general fluid-flow simulations.
Friction Velocity
Calculate friction velocity from wall shear stress and fluid density.
Engineering note: Uses uτ = √(τw/ρ). Friction velocity is a velocity scale derived from wall shear stress; it is not the physical fluid velocity at the wall.
Wall y+
Calculate the non-dimensional wall distance from first-cell wall-normal distance, friction velocity and kinematic viscosity.
Engineering note: y+ depends on the wall treatment and turbulence model. Wall-resolved RANS commonly targets y+ near unity, while wall-function approaches require the first cell to lie in the model's intended wall-function region.
First-Cell Height
Estimate first-cell wall-normal height for a target y+ using the ITTC-1957 friction line as a practical skin-friction estimate.
Engineering note: Uses Cf = 0.075/(log10 Re − 2)², uτ ≈ U√(Cf/2), and y = y+ν/uτ. This is an engineering estimate for mesh planning; local wall shear can differ substantially over a hull or complex geometry.
Dimensionless Wall Velocity u+
Compare dimensionless local wall velocity with a logarithmic-law estimate at a specified y+.
Engineering note: The logarithmic law is an idealized wall-law relation. Its use is appropriate only where the selected wall treatment and local flow conditions support a logarithmic-layer interpretation.
Wall Shear from Skin Friction
Calculate wall shear stress and friction velocity from density, reference velocity and skin-friction coefficient.
Engineering note: This calculator uses the conventional skin-friction definition Cf = τw/(½ρU²). Ensure the coefficient and velocity reference are consistent with each other.
CFD Verification & Validation Calculators
Research-grade calculators for grid metrics, refinement studies, convergence assessment, Richardson extrapolation, numerical uncertainty and CFD validation against experimental data.
Grid Characteristic Spacing
Estimate a representative three-dimensional grid spacing from computational-domain volume and total cell count.
Engineering note: Uses h = (V/N)^(1/3) as a single representative spacing for a three-dimensional grid. It is most meaningful when grids are generated with systematic refinement.
Grid Refinement Ratio
Compare fine, medium and coarse characteristic spacings and quantify how closely the two refinement ratios match.
Engineering note: Uniform refinement uses approximately equal ratios h₂/h₁ and h₃/h₂. A refinement ratio near √2 is commonly practical for industrial ship CFD, while the exact choice remains case-dependent.
Experimental Calculations & Uncertainty Calculators
Research-grade calculators for experimental statistics, Type A and Type B standard uncertainty, sensitivity coefficients, uncertainty propagation, correlation and expanded uncertainty.
Arithmetic Mean
Calculate the arithmetic mean of five repeated experimental observations and report the observed range.
Engineering note: Uses the arithmetic mean q̄ = (1/n)Σqᵢ. All five observations are treated as equally weighted repeated measurements.
Sample Variance & Standard Deviation
Calculate unbiased sample variance and sample standard deviation from five repeated observations.
Engineering note: Uses s² = Σ(qᵢ − q̄)²/(n − 1). This is the unbiased sample-variance form for repeated observations.
Type A Standard Uncertainty
Calculate the standard uncertainty of a sample mean from sample standard deviation and number of independent observations.
Engineering note: Uses u(q̄) = s/√n for independent repeated observations. Correlated time-series data require additional treatment.
Flow Field, Wake & Turbulence Analysis Calculators
Research-grade hydrodynamic calculators for Reynolds decomposition, velocity statistics, LDV weighted processing, turbulence intensity, turbulent kinetic energy, axial vorticity, wake fraction and Doppler velocimetry.
Reynolds Decomposition
Separate an instantaneous velocity sample into mean and fluctuating components.
Engineering note: Uses Reynolds decomposition Vᵢ = V̄ + V′. Relative fluctuation is reported only when the mean velocity is non-zero.
ENGINEERING GUIDANCE
Using Hydrodynamics, CFD & Experimental Methods Calculators
Reliable hydrodynamic analysis depends on consistent reference scales, fluid properties, geometry, numerical resolution and measurement definitions. Model tests and CFD results should be interpreted within Froude/Reynolds similarity assumptions, facility corrections, numerical convergence behavior and experimental/numerical uncertainty limits.
Define scale, reference quantities and test conditions
- Keep model and full-scale length, speed, density and viscosity definitions consistent.
- Check Froude and Reynolds similarity before applying extrapolation relationships.
- Document CFD grid spacing, refinement ratio, wall y+, time step and convergence assumptions.
- Use the same measurand and reference condition throughout uncertainty calculations.
Separate physical trends from numerical and experimental error
- Check whether towing-tank corrections are significant relative to the measured quantity.
- Assess grid refinement, observed order, numerical uncertainty and time-step sensitivity before interpreting CFD differences.
- Report uncertainty with experimental results rather than presenting measurements as exact values.
- Compare simulation and experiment using compatible quantities, locations and reference definitions.
CALCULATION COVERAGE
What the hydrodynamics, CFD and experimental calculators cover
The seven modules follow a practical workflow from similarity and model testing through full-scale extrapolation, CFD setup and V&V, uncertainty analysis and flow-field, wake and turbulence interpretation.
Scaling & Similarity Calculators
Calculate scale ratio, geometric and mass scale factors, Froude number and Froude speed scaling, Reynolds similarity and mismatch, time/frequency scaling, and force, moment and power scaling.
Model Testing & Towing-Tank Corrections
Evaluate tank geometry and blockage ratio, depth Froude number, Schuster, Scott or Tamura blockage corrections, equivalent speed, corrected resistance and Nyquist sampling requirements.
Model-to-Ship / Full-Scale Extrapolation
Calculate full-scale friction coefficient, roughness and correlation allowances, air-resistance coefficient, full-scale resistance coefficient and resistance, effective power, appendage scaling and temperature-corrected model resistance.
CFD Core Calculations
Evaluate friction velocity, wall y+, first-cell height, dimensionless wall velocity u+, wall shear, dynamic pressure, pressure coefficient, Courant number and transient CFD time-step requirements.
CFD Verification & Validation
Evaluate grid characteristic spacing and refinement ratio, solution convergence, observed order of accuracy, Richardson extrapolation, numerical uncertainty and CFD validation against reference or experimental data.
Experimental Calculations & Uncertainty
Calculate sample statistics and Type A uncertainty, Type B standard uncertainty, sensitivity coefficients, independent or correlated combined uncertainty and relative or expanded uncertainty.
Flow Field, Wake & Turbulence Analysis
Analyze Reynolds decomposition, mean and weighted LDV velocity statistics, weighted variance, turbulence intensity, turbulent kinetic energy, axial vorticity, wake fraction and LDV Doppler velocity.
NUMERICAL & EXPERIMENTAL HYDRODYNAMICS
CFD and experiments are strongest when they are used together
Physical experiments provide measured response and flow-field data, while CFD provides detailed spatial and temporal information that can help explain the mechanisms behind those measurements. Neither approach is automatically exact: experiments contain measurement and facility uncertainty, while numerical solutions contain modeling, discretization and iterative errors.
Verification asks whether the numerical equations are being solved with adequate numerical control; validation asks whether the simulated physical response agrees acceptably with reference data. A strong engineering workflow therefore combines convergence assessment, uncertainty analysis and consistent comparison between numerical and experimental quantities.
ANALYSIS WORKFLOW
How to use CFD and experimental results
Define the reference condition
Establish geometry, scale, fluid properties, speed and reference quantities before comparing model, CFD or full-scale results.
Control numerical and test setup
Check tank effects, sampling, mesh resolution, wall treatment, time step and convergence before interpreting the final value.
Quantify uncertainty
Evaluate experimental and numerical uncertainty so differences can be interpreted relative to the confidence in each result.
Compare like with like
Use matched locations, definitions and reference quantities when validating CFD against experiments or extrapolating to full scale.
AUTHORITATIVE REFERENCES
CFD, model-testing & uncertainty references
Detailed hydrodynamic studies should be checked against recognized testing, CFD and uncertainty procedures. ITTC publishes recommended procedures and benchmark material for resistance, propulsion and CFD validation, while NIST provides established guidance for evaluating and reporting measurement uncertainty.
FREQUENTLY ASKED QUESTIONS
Hydrodynamics, CFD & Experimental Methods FAQ
What calculations are included in Hydrodynamics, CFD & Experimental Methods?
The page includes calculator modules for scaling and similarity, towing-tank corrections, model-to-ship / full-scale extrapolation, CFD core calculations, CFD verification and validation, experimental calculations and uncertainty, and flow-field, wake and turbulence analysis.
Can these calculators support comparison of CFD with towing-tank experiments?
Yes. They support preliminary comparison by helping define scaling, numerical uncertainty, experimental uncertainty and related reference quantities, provided the CFD and experimental data represent compatible conditions.
Do the calculators replace formal CFD verification or experimental procedures?
No. Final research, design validation and publication-quality analysis should follow the applicable procedures, documented uncertainty methods, convergence studies and project-specific experimental or numerical methodology.
ENGINEERING CALCULATOR LIBRARY
Continue beyond hydrodynamics and CFD
Explore ship design, marine machinery, offshore engineering, underwater systems and engineering fundamentals from the central calculator library.