Modeling Rapid Condensation of Steam in a 2D Laval Nozzle

Transcription

Tutorial: Modeling Rapid Condensation of Steam in a 2D
Laval Nozzle
Introduction
Modeling wet steam is very important in the analysis and design of steam turbines. Wet
steam refers to the two-phase mixture of saturated vapor and fine liquid droplets formed
during rapid condensation of steam.
The purpose of this tutorial is to demonstrate the mechanics of running a non-equilibrium
steam condensation problem using the wet steam model in FLUENT.
This tutorial demonstrates how to do the following:
• Set up a non-equilibrium steam condensation problem using the wet steam model.
• Specify wet steam modeling parameters.
• Solve and postprocess the wet steam case.
• Set up and solve a non-condensing problem.
• Compare the results obtained for the wet and dry (non-condensing) cases.
Prerequisites
This tutorial assumes that you are familiar with the FLUENT interface and have completed
Tutorial 1 from the FLUENT 6.3 Tutorial Guide. You should also be familiar with the wet
steam model. Refer to Section 23.13: Setting Up the Wet Steam Model in the FLUENT 6.3
User’s Guide for more information.
Problem Description
This problem considers steam condensation in a Laval converging-diverging nozzle. A
schematic of the problem is shown in Figure 1. The nozzle geometry is two-dimensional.
The throat height is 1 cm. Because of the symmetry of the nozzle geometry, only half of
the nozzle is modeled.
c Fluent Inc. September 27, 2006
1
Axis of symmetry
Inlet
Outlet
Figure 1: Problem Schematic
The fluid entering the nozzle is dry steam. As the flow accelerates and clears the throat
area, rapid condensation occurs. The steam first subcools and then nucleates, forming a
two-phase mixture of steam (gas phase) and fine water droplets (liquid phase). The wet
steam model will solve transport equations for conservation of mass fraction of the condensed
phase and conservation of number density of the droplets per unit volume. These equations
will not be solved for the non-condensing case.
Preparation
1. Copy the file 2dlaval.msh to your working folder.
2. Start the 2DDP (2ddp) version of FLUENT.
Setup and Solution
Step 1: Grid
1. Read the mesh file 2dlaval.msh.
File −→ Read −→Case...
2. Check the grid.
Grid −→Check
FLUENT will perform various checks on the mesh and report the progress in the console. Make sure that the minimum volume reported is a positive number.
2
3. Display the grid (Figure 2).
Display −→Grid...
(a) Retain the default settings.
(b) Click Display and close the Grid Display panel.
Grid
FLUENT 6.3 (2d, dp, pbns, lam)
Figure 2: Grid Display
3
Extra: You can use the right mouse button to check the zone number corresponding
to each boundary. If you click the right mouse button on one of the boundaries
in the graphics window, its zone number, name, and type will be printed in the
FLUENT console. This feature is especially useful when you have several zones
of the same type and you want to distinguish between them.
Step 2: Units
1. Change the unit of measurement for pressure to torr.
The pressure for this problem is specified in torr, which is not the default unit in
FLUENT. You will need to define the unit for pressure as torr.
Define −→Units...
(a) Select pressure from the Quantities list.
Scroll down the Quantities list to find pressure.
(b) Select torr from the Units list.
(c) Close the Set Units panel.
4
Step 3: Models
1. Enable the density-based solver with implicit formulation.
Define −→ Models −→Solver...
(a) Select Density Based from the Solver list.
!
The wet steam model can only be used with the density-based solver.
(b) Retain the default selection of Implicit in the Formulation list.
(c) Click OK to close the Solver panel.
5
2. Enable the wet steam model.
Define −→ Models −→Multiphase...
(a) Select Wet Steam from the Model list.
(b) Click OK to close the Multiphase Model panel.
FLUENT will report in the console that the material properties have been set to
wet steam and that the energy equation has been enabled.
FLUENT will use the built-in property data for the wet steam model. Hence, the access
to the Materials panel (from the Define menu and Fluid panel) is restricted. Set the
solid properties (if any) before activating the wet steam model. If required, you can
also specify a different set of properties using user-defined functions (UDFs).
3. Enable inviscid flow.
Define −→ Models −→Viscous...
(a) Select Inviscid from the Model list.
(b) Click OK to close the Viscous Model panel.
6
Step 4: Operating Conditions
Define −→Operating Conditions...
1. Enter 0 torr for Operating Pressure.
2. Click OK to close the Operating Conditions panel.
Step 5: Boundary Conditions
You will set inlet and outlet boundary conditions in this step.
Define −→Boundary Conditions...
7
1. Set the boundary conditions for the inlet (pressure inlet.3).
(a) Enter 530.5 torr for both, Gauge Total Pressure and Supersonic/Initial Gauge
Pressure.
(b) Retain the selection of Normal to Boundary in the Direction Specification Method
drop-down list.
(c) Retain the default setting of 0 for both, Liquid Mass Fraction and Log 10 (Droplets
Per Unit Volume).
(d) Click the Thermal tab and enter 377 K for Temperature.
(e) Click OK to close the Pressure Inlet panel.
8
2. Set the boundary conditions for the outlet (pressure outlet.4).
(a) Enter 37.50319 torr for Gauge Pressure.
(b) Click the Thermal tab and enter 377 K for Temperature.
(c) Retain the default settings for the remaining parameters.
(d) Click OK to close the Pressure Outlet panel.
3. Retain the default conditions for all other boundaries.
4. Close the Boundary Conditions panel.
9
Step 6: Solution
1. Set the discretization scheme for wet steam.
Solve −→ Controls −→Solution...
(a) Retain the default settings for the under-relaxation factors.
(b) Retain the default setting of 5 for Courant Number.
(c) Select Second Order Upwind from the Wet Steam drop-down list in the Discretization group box.
(d) Click OK to close the Solution Controls panel.
10
2. Initialize the solution.
Solve −→ Initialize −→Initialize...
(a) Enter the following initial values:
Parameters
Gauge Pressure
X Velocity
Temperature
Initial Values
530.5 torr
53 m/s
377 K
(b) Click Init.
(c) Close the Solution Initialization panel.
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3. Enable the plotting of residuals.
Solve −→ Monitors −→Residuals...
(a) Enable Plot in the Options group box.
(b) Enter 0.0001 for Absolute Criteria for continuity.
(c) Click OK to close the Residual Monitors panel.
4. Save the case file (moses-stein 410.cas.gz).
File −→ Write −→Case...
5. Start the calculation by requesting 1000 iterations.
Solve −→Iterate...
(a) Enter 1000 for Number of Iterations.
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(b) Click Iterate.
The solution will converge in approximately 800 iterations.
(c) Close the Iterate panel.
Residuals
continuity
x-velocity
y-velocity
energy
wsb
wsn
1e+06
1e+04
1e+02
1e+00
1e-02
1e-04
1e-06
0
100
200
300
400
500
600
700
800
900
Iterations
Scaled Residuals
FLUENT 6.3 (2d, dp, dbns imp)
Figure 3: Scaled Residuals
6. Save the data file (moses-stein 410.dat.gz).
File −→ Write −→Data...
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Step 7: Postprocessing
1. Display filled contours of static pressure (Figure 4).
Display −→Contours...
(a) Enable Filled in the Options group box.
(b) Select Pressure... and Static Pressure from the Contours of drop-down lists.
(c) Click Display.
(d) Change the view to mirror the display across the symmetry plane.
Display −→Views...
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i. Select symmetry.2 from the Mirror Planes selection list.
ii. Click Apply (Figure 4) and close the Views panel.
5.30e+02
5.10e+02
4.90e+02
4.70e+02
4.50e+02
4.30e+02
4.10e+02
3.90e+02
3.70e+02
3.50e+02
3.30e+02
3.10e+02
2.90e+02
2.70e+02
2.49e+02
2.29e+02
2.09e+02
1.89e+02
1.69e+02
1.49e+02
1.29e+02
Contours of Static Pressure (torr)
Figure 4: Contours of Static Pressure
2. Display filled contours of temperature (Figure 5).
(a) Select Temperature... and Static Temperature from the Contours of drop-down
lists.
(b) Click Display.
3.77e+02
3.73e+02
3.70e+02
3.66e+02
3.62e+02
3.59e+02
3.55e+02
3.51e+02
3.48e+02
3.44e+02
3.40e+02
3.37e+02
3.33e+02
3.29e+02
3.25e+02
3.22e+02
3.18e+02
3.14e+02
3.11e+02
3.07e+02
3.03e+02
Contours of Static Temperature (k)
Figure 5: Contours of Static Temperature
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3. Display contours of Mach number (Figure 6).
(a) Select Velocity... and Mach Number from the Contours of drop-down lists.
(b) Click Display.
1.53e+00
1.45e+00
1.38e+00
1.31e+00
1.23e+00
1.16e+00
1.08e+00
1.01e+00
9.35e-01
8.61e-01
7.87e-01
7.13e-01
6.39e-01
5.64e-01
4.90e-01
4.16e-01
3.42e-01
2.68e-01
1.94e-01
1.20e-01
4.56e-02
Contours of Mach Number
Figure 6: Contours of Mach Number
4. Display contours of liquid mass fraction (Figure 7).
(a) Select Wet Steam... and Liquid Mass Fraction from the Contours of drop-down
lists.
(b) Click Display.
5.13e-02
4.88e-02
4.62e-02
4.36e-02
4.11e-02
3.85e-02
3.59e-02
3.34e-02
3.08e-02
2.82e-02
2.57e-02
2.31e-02
2.05e-02
1.80e-02
1.54e-02
1.28e-02
1.03e-02
7.70e-03
5.13e-03
2.57e-03
0.00e+00
Contours of Liquid Mass Fraction
Figure 7: Contours of Liquid Mass Fraction
16
5. Display contours of droplets nucleation rate (Figure 8).
(a) Select Wet Steam... and Log 10 (Droplets Nucleation Rate) from the Contours of
drop-down lists.
(b) Click Display.
2.28e+01
2.17e+01
2.05e+01
1.94e+01
1.82e+01
1.71e+01
1.60e+01
1.48e+01
1.37e+01
1.25e+01
1.14e+01
1.03e+01
9.12e+00
7.98e+00
6.84e+00
5.70e+00
4.56e+00
3.42e+00
2.28e+00
1.14e+00
0.00e+00
Contours of Log10(Droplets Nucleation Rate)
Figure 8: Contours of Droplets Nucleation Rate
6. Display contours of droplet average radius (Figure 9).
(a) Select Wet Steam... and Droplet Average Radius (microns) from the Contours of
drop-down lists.
(b) Click Display.
1.53e-02
1.45e-02
1.38e-02
1.30e-02
1.22e-02
1.15e-02
1.07e-02
9.94e-03
9.17e-03
8.41e-03
7.64e-03
6.88e-03
6.12e-03
5.35e-03
4.59e-03
3.82e-03
3.06e-03
2.29e-03
1.53e-03
7.64e-04
0.00e+00
Contours of Droplet Average Radius (microns)
Figure 9: Contours of Droplet Average Radius
17
(c) Close the Contours panel.
7. Define a custom field function for the ratio of static pressure to total inlet pressure.
Define −→Custom Field Functions...
(a) Select Pressure... and Static Pressure from the Field Functions drop-down lists
and click the Select button to add pressure (p) to the Definition field.
(b) Click the “/” button to add the division symbol to the Definition field.
(c) Enter 70727.32 (the SI value of total inlet pressure = 530.5 torr i.e., 70727.32 Pa)
using the calculator buttons.
You can use the DEL button to delete characters one at a time, if required.
(d) Enter p-ratio2 for New Function Name.
(e) Click Define and close the Custom Field Function Calculator panel.
8. Compare the results obtained for the simulation with available experimental data.
Plot −→XY Plot...
(a) Select Custom Field Functions... and p-ratio2 from the Y Axis Function drop-down
lists.
Custom Field Functions... is at the top of the upper Y Axis Function drop-down
list. Scroll up the list to select Custom Field Functions....
(b) Select symmetry.2 from the Surfaces selection list.
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(c) Click the Load File... button and select the experimental data file EXP-410-ppo.xy.
The plot title of the experimental data file (Exp-410 DATA P/Po) will be displayed
in the File Data list.
(d) Click Plot (Figure 10).
1.0
FLUENT
0.9
Exp-410
0.8
0.7
p-ratio2
0.6
0.5
0.4
0.3
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Position (m)
p-ratio2
Figure 10: Comparison of Results—Steam Condensation Case and Experimental Data
(e) Write the data to an output file.
i. Enable Write to File in the Options group box.
The Plot button will be replaced by the Write... button.
ii. Click the Write... button to open the Select File dialog box.
19
iii. Enter moses-stein-ppo.xy for XY File and click OK to close the Select File
dialog box.
(f) Close the Solution XY Plot panel.
Step 8: Solution for the Non-Condensing Case
1. Read the case file moses-stein 410.cas.gz in a new FLUENT session.
2. Disable the solving of the wet steam equation.
Solve −→ Controls −→Solution...
(a) Deselect Wet Steam from the Equations selection list.
(b) Click OK to close the Solution Controls panel.
Note: The equations for wet steam (conservation of mass fraction of condensed phase
and conservation of number density of the droplets per unit volume) will not be
solved. See Section 23.6 of the FLUENT 6.3 User’s Guide for more information
on the wet steam model.
3. Save the case file (non-condensing.cas.gz).
File −→ Write −→Case...
4. Request 800 iterations.
Solve −→Iterate...
The solution will converge in approximately 750 iterations.
20
5. Save the data file (non-condensing.dat.gz).
File −→ Write −→Data...
Step 9: Postprocessing (Non-Condensing Case)
1. Display filled contours of Mach number (Figure 11).
Display −→Contours...
(a) Enable Filled in the Options group box.
(b) Select Velocity... and Mach Number from the Contours of drop-down lists.
(c) Click Display.
(d) Change the view to mirror the display across the symmetry plane.
Display −→Views...
i. Select symmetry.2 from the Mirror Planes selection list.
ii. Click Apply and close the Views panel.
1.78e+00
1.69e+00
1.61e+00
1.52e+00
1.43e+00
1.35e+00
1.26e+00
1.17e+00
1.09e+00
9.99e-01
9.13e-01
8.26e-01
7.39e-01
6.53e-01
5.66e-01
4.79e-01
3.92e-01
3.06e-01
2.19e-01
1.32e-01
4.56e-02
Contours of Mach Number
Figure 11: Contours of Mach Number
(e) Close the Contours panel.
21
2. Define a custom field function for the ratio of static pressure to total inlet pressure.
Define −→Custom Field Functions...
(a) Enter p/70727.32 in the Definition field.
Select Pressure and Static Pressure from the Field Functions drop-down lists and
click the Select button to add pressure (p) to the Definition field.
(b) Enter p-ratio2 for New Function Name.
(c) Click Define and close the Custom Field Function Calculator panel.
3. Compare the results obtained for the condensing and non-condensing cases.
Plot −→XY Plot...
(a) Select Custom Field Functions... and p-ratio2 from the Y Axis Function drop-down
lists.
Custom Field Functions... is at the top of the upper Y Axis Function drop-down
list. Scroll up the list to select Custom Field Functions....
(b) Select symmetry.2 from the Surfaces selection list.
(c) Click the Load File... button and select the data file moses-stein-ppo.xy.
Click the Free Data button to remove previously loaded data files from the File
Data selection list before loading the new file.
(d) Click Plot (Figure 12).
1.0
0.9
Wet-Steam Model
0.8
Isentropic Expansion
0.7
p-ratio2
0.6
0.5
0.4
0.3
0.2
0.1
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Position (m)
p-ratio2
Figure 12: Comparison of Results—Steam Condensation Case and Non-Condensing Case
The jump in pressure for the condensing case is due to the initiation of droplet
nucleation, which is absent in the non-condensing (isentropic expansion) case.
22
(e) Write the data to an output file.
i. Enable Write to File in the Options group box.
The Plot button will be replaced by the Write... button.
ii. Click the Write... button to open the Select File dialog box.
iii. Enter non-condensing-ppo.xy for XY File and click OK to close the Select
File dialog box.
(f) Close the Solution XY Plot panel.
Summary
This tutorial demonstrated the set up and solution for a non-equilibrium steam condensation problem using the wet steam model in FLUENT. The results for the steam condensation
case were compared with available experimental data. The problem was set up to exclude
calculation of the wet steam equations (i.e., for non-condensation) and results for the condensing and non-condensing cases were compared.
23

Modeling Rapid Condensation of Steam in a 2D Laval Nozzle

Transcription

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