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Lab sheet for Computational Fluid Dynamics Government College of
Engineering and Research Avasari
Lab # 8: Solution of Navier-Stokes Equations for Flow in a
Square Cavity
Date: Time:
Testing of any in-house code, by comparing the simulated results
with the published results, is called as code-validation study. Lid
driven cavity flow is probably the most commonly used problem for
the code-validation; due to simplicity in the shape of the domain
and boundary conditions. It consists of a closed 2D Cartesian (x-y)
square domain of size LL, with all the boundaries as solid-wall.
The top wall is like a long conveyor-belt, moving horizontally with
a constant velocity U0; and other walls are stationary. The
objective of this lab session is to demonstrate the testing of an
in-house NS solver; developed on collocated grid. The code is to be
tested for isothermal flow, in problem # 1 below. For the remaining
problem, forced/mixed/natural convection heat transfer is tested.
The code is to be written in non-dimensional form, with Reynolds
number (Re=U0L/) as the governing parameter for isothermal flow.
For convective heat transfer problems, Prandtl number (Pr=/),
Grashoff number (Gr=g(TH-TC)L3/2) and Rayleigh Number
(Ra=g(TH-TC)L3/) comes as an additional governing parameters.
However, Gr=0 for forced and RePr=1 for natural convection heat
transfer. Note that the characteristic velocity considered here for
natural convection is equal to /L; thus, the diffusion-coefficient
is Pr for momentum and 1 for energy equation. The
benchmark/published results, used for code-validation are at
certain fixed value of the governing parameters. Thus, the
user-input in the problems below are those values only. However,
they are indeed applicable for other values of the parameters.
Moreover, all the problems below are to be solved on a coarser grid
size of imax=jmax=7 and larger steady state convergence criteria of
10-4, due to limited time available for the lab session; where the
simulated results follow the trend of the benchmark results. The
code needs to be run on a much finer, to get a better comparison
with the benchmark results. This will need a much larger
computational time. As a home-work, latter on you can run these
codes on a grid size of 1212, 3232 and 5252 (note that the finest
grid size may take 7-8 hours or more to converge to steady-state
results; be patient). Then show an overlap plot on the various grid
sizes, similar to that shown in lecture slide # T7_NS_stag. This is
called grid independence study. Isothermal Flow: Here, the walls of
the cavity are at the same temperature. Run the program
Lab5_1_Isothermal_Flow.sci,I. At Re=100. II. At Re=400. Report the
results asa) Plot and discuss the velocity (separate for U and V)
and stream-function contours for the Reynolds number (3+3
figures).b) Plot and discuss the variation of U-velocity along the
vertical and V-velocity along the horizontal centerline of the
cavity and its comparison with the benchmark results (2+2
figures).Refer code: Lab4_3_2DConvection.sci
Answer SheetProblem # 1: Isothermal Flow: a) Plot and discuss
the velocity (separate for U and V) and stream-function contours
for the different Reynolds number (3+3 figures).
Re = 100Re = 400(a1)(a2)(b1)(b2)(c1)(c2)Fig. 5.1: Steady state
contours obtained for an isothermal lid-driven cavity flow: (a1,a2)
U-velocity, (b1,b2) V-velocity, and (c1,c2) Stream-function; and
(a1-c1) Re=100 and (a2-c2) Re=400.
b) Plot and discuss the variation of U-velocity along the
vertical and V-velocity along the horizontal centerline of the
cavity and its comparison with the benchmark results (2+2
figures).
Re = 100Re = 400(a1)(a2)(b1)(b2)Fig. 5.2: Centreline velocity
plots obtained on an isothermal lid-driven cavity flow: variation
of(a1,a2) U-velocity along the vertical centreline (b1,b2)
V-velocity along the horizontal centerline, at (a1,b1) Re=100 and
(a2,b2) Re=400.
Discuss Fig. 5.1 and 5.2 here, limited inside this text box
only
