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)
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 = Q t o t a l A L arg e I n l e t = 0.475   m / s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGrb WaaSbaaSqaaiaadYeaciGGHbGaaiOCaiaacEgacaWGLbGaamysaiaa d6gacaWGSbGaamyzaiaadshaaeqaaOGaeyypa0JaamyqamaaBaaale aacaWGmbGaciyyaiaackhacaGGNbGaamyzaiaadMeacaWGUbGaamiB aiaadwgacaWG0baabeaakiaadAfadaWgaaWcbaGaamitaiGacggaca GGYbGaai4zaiaadwgacaWGjbGaamOBaiaadYgacaWGLbGaamiDaaqa baaakeaacaWGrbWaaSbaaSqaaiaadofacaWGTbGaamyyaiaadYgaca WGSbGaamysaiaad6gacaWGSbGaamyzaiaadshaaeqaaOGaeyypa0Ja amyqamaaBaaaleaacaWGtbGaamyBaiaadggacaWGSbGaamiBaiaadM eacaWGUbGaamiBaiaadwgacaWG0baabeaakiaadAfadaWgaaWcbaGa am4uaiaad2gacaWGHbGaamiBaiaadYgacaWGjbGaamOBaiaadYgaca WGLbGaamiDaaqabaaakeaacaWGrbWaaSbaaSqaaiaadsfacaWGVbGa amiDaiaadggacaWGSbaabeaakiabg2da9iaadgfadaWgaaWcbaGaam itaiGacggacaGGYbGaai4zaiaadwgacaWGjbGaamOBaiaadYgacaWG LbGaamiDaaqabaGccqGHRaWkcaWGrbWaaSbaaSqaaiaadofacaWGTb GaamyyaiaadYgacaWGSbGaamysaiaad6gacaWGSbGaamyzaiaadsha aeqaaaGcbaaabaGaamOvamaaBaaaleaacaWGWbGaamyAaiaadchaca WGLbaabeaakiabg2da9maalaaabaGaamyuamaaBaaaleaacaWG0bGa am4BaiaadshacaWGHbGaamiBaaqabaaakeaacaWGbbWaaSbaaSqaai aadYeaciGGHbGaaiOCaiaacEgacaWGLbGaamysaiaad6gacaWGSbGa amyzaiaadshaaeqaaaaakiabg2da9iaaicdacaGGUaGaaGinaiaaiE dacaaI1aGaaGjbVlaad2gacaGGVaGaam4Caaaaaa@AF83@

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 = ρ V D μ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOuaiaacw gacqGH9aqpdaWcaaqaaiabeg8aYjaadAfacaWGebaabaGaeqiVd0ga aaaa@3DE7@

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.