ACU-T: 2000 Turbulent Flow in a Mixing ElbowHyperWorks CFD

Prerequisites

Prior to starting this tutorial, you should have already run through the introductory HyperWorks tutorial, ACU-T: 1000 HyperWorks UI IntroductionPrior to starting this tutorial, you should have already run through the introductory tutorial, ACU-T: 1000 HyperWorks CFD UI IntroductionACU-T: 1000 Basic Flow Set UpHyperWorks CFD. To run this simulation, you will need access to a licensed version of HyperWorks CFD and AcuSolve.

Prior to running through this tutorial, click here to download the tutorial models. Extract from HyperWorksCFD_tutorial_inputs.zip.

Problem Description

The problem characteristics shown here determine if the flow is laminar or turbulent by calculating the Reynolds number in the pipe. The diameter of the large inlet is 0.1 m, and the inlet velocity (v) is 0.4 m/s. The diameter of the small inlet is 0.025 m, and the inlet velocity is 1.2 m/s.

Figure 1. Schematic of Mixing Elbow

The fluid in this problem is water with the following properties that do not change with temperature: a density (ρ) of 1000 kg/m³ and a molecular viscosity (μ) of 1 X 10^-3 kg/m-sec.

Based on mass conservation, the combined flow rate (Q) yields a pipe velocity of 0.475 m/s downstream of the small inlet. The following equations are used to calculate the pipe velocity:(1)

\begin{array}{l} Q_{L \arg e I n l e t} = A_{L \arg e I n l e t} V_{L \arg e I n l e t} \\ Q_{S m a l l I n l e t} = A_{S m a l l I n l e t} V_{S m a l l I n l e t} \\ Q_{T o t a l} = Q_{L \arg e I n l e t} + Q_{S m a l l I n l e t} \\ V_{p i p e} = \frac{Q_{t o t a l}}{A_{L \arg e I n l e t}} = 0.475 m / s \end{array}

$\begin{array}{l} Q_{L \arg e I n l e t} = A_{L \arg e I n l e t} V_{L \arg e I n l e t} \\ Q_{S m a l l I n l e t} = A_{S m a l l I n l e t} V_{S m a l l I n l e t} \\ Q_{T o t a l} = Q_{L \arg e I n l e t} + Q_{S m a l l I n l e t} \\ V_{p i p e} = \frac{Q_{t o t a l}}{A_{L \arg e I n l e t}} = 0.475 m / s \end{array}$

This value is useful in determining the Reynolds number, which in turn can be used to determine if the flow should be modeled as turbulent, or if it should be modeled as laminar.

In order to determine whether the modeled flow would be turbulent or whether it would be laminar, the Reynolds number (Re) should be calculated. The Reynolds number is given by:(2)

Re = \frac{ρ V D}{μ}

$Re = \frac{ρ V D}{μ}$

where ρ is the fluid density, V is the fluid velocity, D is the diameter of the flow region, and μ is the molecular viscosity of the fluid. When the Reynolds number is above 4,000, it is generally accepted that flow should be modeled as turbulent.

The Reynolds numbers of 40,000 at the large inlet, 30,000 at the small inlet, and 47,500 for the combined flow indicate that the flow is turbulent throughout the flow domain. The simulation will be set up to model steady state, turbulent flow.