CFD and CHT Code Validation

1D Finite Slab Validations
Case 1D finite slab with fixed boundary conditions on both ends. This model is used to test the time-space accuracy of a solver. The comparison is made to the exact solution.

Case 1D Finite Slab Sine Distribution

Analytical Solution

TFS Numerical Solution

Case 1D Infinite Slab

Analytical Solution

TFS Numerical Solution

Burger's Equation SS

Steady State Analytical

Analytical (Pe = 10)

TFS Numerical (Pe = 10)

Cavity Flow BCs

3D Vector Field

Corner Vortex

Contour plot u

Comparison to Ghia data

Burger's Equation TR

Analytical (Pe = 10)

TFS Numerical (Pe = 10)

Solidification Model

Analytical Solutions

TFS Numerical Solution

Natural Convection Geometry

Boundary Conditions

Velocity Field

Temperature Field

Comparison with Experiment

Boundary Conditions

Velocity Field

Temperature Field

Comparison with Experiment

Turbulent Viscosity

The following page presents an abbreviated collection of the validations used to benchmark the Hyperion-TFS CFD and CHT analysis code. Where possible, the validations are compared to both analytical and experimental data. All validations presented on this page were computed with the Hyperion-TFS CHT-CFD solver engine. The solidification solutions were computed with the same ADI sweep algorithm and diffusion matrices and therefore represent the TFS code and are included.

1D Infinite Slab Validations
Case 1D infinite slab with fixed boundary conditions on the left end and a far field boundary condion on the right. This model is used to test the time-space accuracy of a solver. The comparison is made to an error function solution. It shows that the finite domain rendered in the computational model impacts the solution at later times.

1D Finite Slab Validations (Burger's Equation - Steady State)
Case 1D finite slab with fixed temperature boundary conditions on both ends, modelled using Burger's equation. This model is used to test the space accuracy of a solver including advection and diffusion processes. The comparison is made to the exact solution at steady state conditions.

1D Finite Slab Validations (Burger's Equation - Transient)
Case 1D finite slab with time-dependant temperature boundary conditions on both ends, modelled using Burger's equation. This model is used to test the time and space accuracy of a solver including advection and diffusion processes. The comparison is made to the exact solution at a transient select time as indicated.

Lid Driven Cavity Flow (Reynolds Number 100)
The data are compared to the classical Ghia experimental measurements. Plot shows the u velocity taken through the centerline of the cavity. The data points are scaled to the velocity scale and length scale in the TFS simulation. Data are compared to the Ghia et al. data in forth figure. Reynolds number based on lid length and velocity is 100.
Ghia, Ghia, and Shin (1982), "High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method", Journal of Computational Physics, Vol. 48, pp. 387-411.

Natural Convection Between Eccentric Cylinders
A 2D model of the eccentric cylinder geometry was constructed and simulated in TFS to predict the coupled velocity and temperature fields. The following plots show the model, the recirculation vortices and the temperature field. The temperature of the fluid above the heated cylinder is in close agreement with the experimental data derived from the following reference.
Kuehn, T.H. and Goldstein, R.J., An Experimental Study of Natural Convection Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli, Journal of Heat Transfer, 100:635-640, 1978.

Natural Convection in a Vertical Cavity
A 2D model of the tall vertical cavity geometry was constructed and simulated in TFS to predict the coupled velocity and temperature fields. The following plots show the model, the velocity field and the temperature field. The velocity field is in close agreement with the experimental data derived from the following reference.
Cheesewright, R., King, K. J. and Ziui, S., "Experimental Data for the Validation of Computer Codes for the Prediction of Two-Dimensional Buoyant Cavity Flows," ASME Winter Annual Meeting, HTD-60, December, 1986.

Solidification Front Propagation
In this analysis both a flat front and cylindrical front propagation are analyzed. The generic case of a cylindrical propagation is derived and then extended to a flat front by applying a large base radius (both models become self-similar). An analytical solution is compared to the TFS numerical solution, plotting nondimensional front position or radius as a function of non-dimensional time. The flat front is solved in rotated XY space to fully test the ADI solver in TFS. In this fashion, the front must diffuse in both directions and invokes cross component flows in the sweep equations.

Geometry

Geometry 3D

Data Product Ls

Transient Ls Overlay

Data Comparison

Forced Convection over a Cylinder (Reynolds number 135)
A 3D model of a cylinder in a crossflow as constructed in Mesh3D and simulated in TFS to predict the coupled velocity and temperature fields. The air inflow is set at 20 deg. C and the cylinder wall is set at 100 deg. C. The following plots show the model, the velocity field, temperature field. The predicted heat transfer coefficient coefficient (cylinder-average) compares to within 5% of the value predicted by Hyperion-TFS.
Kreith, F., Principles of Heat Transfer, 3d Edition, Harper and Row Publishers, Inc., 1973.

Geometry and BC

PCM Temperature Response

Movie (3.5 MB)

Solidification PCM Module (Case Study)
In this analysis a generic PCM module is analyzed. A sine function heat load is applied to the module. The TFS solution tracks the transient response. A GIF movie is included to show the PCM response. The significant feature to this analysis is the application of the ADI solution method to generate the field simulation in a computationally efficient manner.

Geometry Model and BC

Velocity Field

Temperature Field

Convection Heat Transfer Coefficients

Impulsively Started Impinging Flow
A 2D model of a small vertical flat plate is rendered and the flow impinges on this flat plate in a larger domain. The data product in this simulation is the time-transient length of the recirculation bubble behind the plate - Ls(t). The following plots show the model, the velocity field, recirculation zone and comparison with experiment. The Hyperion-TFS predicted Ls(t) values match the experimental data very closely. In this comparison, the experimental data are taken from the following reference:
Taneda, S., and Honji, H., "Unsteady Flow Past a Flat Plate Normal to the Direction of Motion," J. Phys. Soc. Japan , Vol. 30, pp. 262-273, 1971.

Geometry

Analytical Solutions

TFS Numerical

Poiseuille Flow
A 3D model of a tube was constructed of a fixed length. A fixed pressure was applied at both ends of the tubes. The inlet pressure was 0.04 Pa and the outlet was set to 0. The simulation seeks to find the fully developed velocity profile that would exist in the tube (assuming a laminar flow). Analytical solutions exist for the maximum velocity and mass flowrate thru the tube. The TFS simulation results compare very closely with the analytical solutions.

Boundary Conditions and mu Turbulent

Log Wall Velocity at midpoint

Cf CFD versus Analytical

h.CV CFD versus Analytical

Flat Plate - Turbulent
A 2D model of a horizontal flat plate is simulated. The inflow flow velocity over the 1 meter plate is set to 40 m/s, resulting in a Reynolds number of approximately 1.5E6. The model is setup to create a leading edge region to allow the ellipticity of the flow field to begin the stretch of the flow prior to the leading edge located at 10 cm from the left boundary. The mixing lenth model is compared to the the analytical predictions. The Hyperion-TFS predicted Cf and heat transfer coefficient values match the experimental data very closely.