0. Introduction
Comparison of results with Westegaard’s added mass
The objective of this verification study is to model a 3D sloshing fluid domain using the slosh ing element tool available in Midas GTS NX and Midas FEA NX. A linear time-history dynamic analysis is carried out to simulate the hydrodynamic effects generated by ground motion.
1. Problem Statement
The primary intention of this report is to:
- Determine sloshing pressures on the vertical wall of a reservoir-like fluid domain in Midas GTSNX/FEANX.
- Extract the pressure distribution with depth along the upstream face of the wall.
- Perform a comparative verification against the classical Westergaard’s added-mass formulation for hydrodynamic pressure under seismic loading.
This comparison enables validation of the 3D sloshing fluid element and confirms the numerical model’s fidelity relative to established analytical solutions.
2. Model Creation
Step 1: Creating a New Model
Open a new file in Midas GTS NX. Select the Model Type as 3D and click OK.
Creating a new 3D model in Midas GTS NX
Step 2: Geometry Creation
Use the geometry creation tools to construct the model geometry as shown in Figure 3.
Model specifications
Step 3: Material and Element Property Definition
3D model showing water volume and wall
Define the Wall, Water, Fluid-Structure-Interface and Free Surface properties as per Table.1 and Table.2.
| Material | Material Type | Elastic Modulus | Bulk Modulus | Poisson's ratio | Unit weight |
| Wall | Isotropic-Elastic | 30 GPa | - | 0.2 | 20 kN/m3 |
| Water | Sloshing Medium | - | 2.2 GPa | - | 9.8 kN/m3 |
Table.1. Material properties used in the model
| Element Property | Element Type | Material |
|
Wall |
3D Solid | Wall |
| Water | 3D Sloshing | Water |
| Fluid Boundary | Plane-Free Surface | - |
| Fluid Boundary | Plane-FSI | - |
Table.2. Element properties used in the model
Step 4: Mesh Generation
A structured hexahedral mesh is generated for both the wall and fluid regions. The meshing strategy for the model incorporates the following features:
- 3D mesh for wall and a continuous 3D mesh for water capable of supporting realistic sloshing wave propagation,
- FSI interface mesh,
- Planar mesh elements that accurately represent the free surface boundary.
Fixed Boundary Definition
Meshed model
Step 5: Boundary Conditions
Fixed Boundary (Wall)
- All translational degrees of freedom (DOFs) are constrained.
- Ensures that the wall behaves rigidly.
Sloshing Fluid Boundary (Fluid End Face)
- Applied to the far end of the water domain.
- Allows the water to respond dynamically without introducing wave reflection artifacts.
- Implements the appropriate hydraulic boundary behavior for sloshing analysis.
Fixed Boundary Definition
Sloshing Constraint Boundary Definition
3. Load Case Definition
Dynamic Load Case Definition
Adynamic ground acceleration load is defined to simulate earthquake-induced excitation of the fluid domain. The applied sinusoidal forcing function provides a controlled and repeatable excitation mechanism, enabling the generation of sloshing waves within the fluid.
Ground Motion Characteristics
- Acceleration amplitude: 0.3g
- Frequency: 5Hz (five cycles per second)
- Time variation: Pure sinusoidal loading
Time forcing function input window
4. Analysis Case Definition
A linear time-history (Direct) analysis is defined to compute the dynamic response of the fluid domain under the prescribed ground motion. The key analysis settings are as follows:
- Activated Elements: All mesh sets, boundary conditions and load definitions are activated.
- Time-step definition: The time step(0.1 sec) and time increment(0.001 sec) is selected to accurately capture half-cycle oscillations of the sinusoidal input, which is essential for re solving sloshing dynamics and results comparison.
Since Westergaard’s formulation represents the impulsive component of the hydrodynamic pressure—i.e., the pressure generated by the instantaneous inertial response of the reservoir during ground acceleration—the dynamic loading is applied only over the half–cycle of the excitation.
For an excitation frequency of 5Hz, the duration of one half–cycle is
Therefore, the hydrodynamic pressure is applied over a time period of 0.1s.
Analysis case definition
5. Results Extraction
After the dynamic analysis is completed, the following results are extracted to evaluate the hydro
dynamic behavior of the fluid:
(a) Sloshing Pressure
- • FromtheResultsworktree navigate to Absolute Max and select the 3D Pressure from Slosh ing Fluid Results,
- • Thepressure variation with depth can be seen from the contours.
(b) Pressure vs. Depth Plot
Using the Cutting Diagram tool, the following steps are carried out:
• A vertical cutting plane is defined along the wall surface and pressure values are sampled continuously along the fluid depth.
• The tabulated dataset is exported for comparison.
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