Generating a Model

Abstract

This chapter develops an example in fluid mechanics using Comsol Multiphysics^®. Fluid flow around a sphere in a tube is developed. The simulation is created from scratch and in detail. This helps to develop a measure of expertise in the use of this computational tool. The flow lines are determined in laminar flow. The example is enhanced by adding the effect of heat transfer. The sphere is the heat source. An anisotropic problem is generated, more representative of real applications, by giving a higher temperature only a lateral portion of the surface of the sphere. The viscous and thermal boundary layers are shown and evidenced without the need of any assumptions other than those applied to the Navier–Stokes equation and its boundary and initial conditions. The mesh used in the process of finite-element analysis is shown. Times for computations and number of nodes are given in the examples what in turn serves as a guide for the level of computational demand of the problem. All results are generated using Azure’s resources. Batch processing and parametric sweep are discussed using a more complex example of fluid flow using a computer fan. Flow around a computer fan demonstrated the case of a much more complex problem for which laminar and turbulent flows are discussed. The increasing size and selection of virtual workstations of up to 64 vCPUs to meet high computational demands are discussed, and results are presented.

Important Equations: Laminar Flow (spf)

2.1.1 Appendix

2.1.1.1 Equation 1. Navier–Stokes Equation

$$ \rho \left(\mathbf{u}\cdot \nabla \right)\mathbf{u}=\nabla \cdot \left[-\rho \mathbf{l}+\mu \left(\nabla \mathbf{u}+{\left(\nabla \mathbf{u}\right)}^{\mathrm{T}}\right)-\frac{2}{3}\mu \left(\nabla \cdot \mathbf{u}\right)\mathbf{l}\right]+F $$

2.1.1.2 Equation 2. Continuity Equation

$$ \nabla \cdot \left(\rho \mathbf{u}\right)=0 $$

2.1.1.3 Inlet

2.1.1.3.1 Equation 3. Inlet Velocity Equation

$$ \mathbf{u}=-{U}_0\mathbf{n} $$

2.1.1.4 Outlet

2.1.1.4.1 Equation 4. Pressure Equation

$\left[-\rho \mathbf{l}+\mu \left(\nabla \mathbf{u}+{\left(\nabla \mathbf{u}\right)}^{\mathrm{T}}\right)-\frac{2}{3}\mu \left(\nabla \cdot \mathbf{u}\right)\mathbf{l}\right]\mathbf{n}=-{\hat{\rho}}_0\mathbf{n}$; $-{\hat{\rho}}_0\le {\rho}_0$

2.1.1.5 Important Equations: Heat Transfer in Solids (ht)

2.1.1.5.1 Equation 5. Heat Transfer in Solids Equation

$$ \rho {C}_p\mathbf{u}\cdot \nabla T=\nabla \cdot \left(k\nabla T\right)+Q $$

2.1.1.5.2 Equation 6. Thermal Insulation Equation

$$ -n\cdot \left(-k\nabla T\right)=0 $$

2.1.1.5.3 Equation 7. Heat Transfer in Fluids

$$ \rho {C}_p\mathbf{u}\cdot \nabla T=\nabla \cdot \left(k\nabla T\right)+Q+{Q}_{vd}+{Q}_p $$