ME7724 - Computational Fluid Dynamics for Engineering Application - Engineering Assignment Help

Assignment Task

Module Learning Outcomes

The following module learning outcomes and professional body learning outcomes are tested in this assessment:

(LO1) Define and analyse engineering fluid flow problems using the Navier Stokes equations. Simplify flow problems and solve them exactly. (SM1m, SM2m, G1)

(LO2) Construct appropriate solid models for CFD analysis, setup the solution domain and generate suitable surface and volume grids via meshing tool. (SM3m, SM5m)

(LO3) Understand both flow physics and mathematical properties of governing Navier-Stokes equations and define appropriate boundary conditions. (EA3m)

Assessment task and specific terms

The aims of this individual assignment are twofold:

(1) to investigate the analytical solution derived from Navier-Stokes (NS) equations through simplification process

(2) to construct mesh over typical curved geometry models, reflecting known physical flow features of near wall viscous layer and run simple CFD simulations

Question 1

The analytical solution of laminar flow through infinitely long ‘parallel plates’ (also called plain channel) can be derived from the full 3-D Navier-Stokes (NS) governing equations via simplification with given boundary conditions. Fig. 1a below shows an upper plate driven flow with the bottom plate fixed. Fig. 1b shows a pressure driven flow with both upper and lower plates fixed. The channel height is 2h (h=10 mm) and the flowing fluid is water at a constant temperature of 25 °C. Ignore the effects of gravity.

(1. a) Using Cartesian coordinates, simplify the full 3-D unsteady compressible NS equations into 1-D (one dimensional) steady incompressible laminar flow equations. You should clearly explain and justify all steps and the reasons for the simplifications. (13 marks)

(1.b) Considering the boundary conditions in Fig. 1a (fixed bottom plate, moving upper plate at constant velocity V), with zero pressure gradient along streamwise direction (dp/dx=0):

(1.b.i) Derive the analytical solution of the streamwise velocity profile u(y) and the general formula of the volumetric flow rate Q (7 marks) Question 1 Continued…

(1.b.ii) For V= 0.1m/s, calculate the flow Reynolds number (based on density, mean velocity, channel height, viscosity) and determine the value of the volumetric flow rate Q. Take the water properties (density, viscosity etc...) at 25 °C from the literature. For the volume flow rate calculations, you may assume a unit width of the plate.

(1.c) Considering the boundary conditions in Fig. 1.b (fixed bottom and fixed upper plate), water flow driven by a non-zero constant pressure gradient dp/dx (with dp/dx=-1 Pa/m):

(1.c.i) Derive the analytical solution of the streamwise velocity profile u(y) and the general formula of the volumetric flow rate Q (8 marks)

(1.c.ii) Calculate the flow Reynolds number (based on density, mean velocity, channel height, viscosity) and determine the value of the volumetric flow rate Q. Take the water properties (density, viscosity etc...) at 25 °C from the literature. For the volume flow rate calculations, you may assume a unit width of the plate. (5 marks)

(1.d) We now consider a flow condition which is a combination of the above conditions: fixed bottom plate, moving upper plate at constant velocity V, a non-zero constant pressure gradient dp/dx along the streamwise direction.

(1.d.i) Derive the analytical solution of the streamwise velocity profile u(y) and the general formula of the volumetric flow rate Q; (8 marks)

(1.d.ii) Calculate the flow Reynolds number (based on mean/bulk velocity) and determine the volumetric flow rate Q for the following parameters: V= 0.1m/s, dp/dx=-1 Pa/m. (4 marks)

(1.e) Plot the velocity profiles obtained in questions (1.b.i), (1.c.i) and (1.d.i) together with a sketch showing the flow domain and specific boundary conditions. Compare the velocity profiles and discuss thoroughly the effects of moving wall, pressure gradient and both.

This ME7724 - Engineering Assignmen has been solved by our Engineering Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.