Introduction of background knowledge regarding flow physics and CFD as well as detailed information about the use of AcuSolve and what specific options do.
Collection of AcuSolve simulation cases for which results are compared against analytical or experimental results to demonstrate the accuracy
of AcuSolve results.
In this application, AcuSolve is used to simulate the flow of water between concentric cylinders. The outer cylinder is held stationary while the
inner cylinder rotates with a constant speed. AcuSolve results are compared with analytical results as described in White (1991). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases containing thin annular gaps with flow induced by rotating walls.
In this application, turbulent flow of air through a pipe is simulated. AcuSolve results are compared with experimental results as described in White (1991) and extracted from the Moody chart. The
close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model turbulent flow within pipes.
In this application, AcuSolve is used to simulate the viscous flow of water between a moving and a stationary plate with an imposed pressure
gradient. AcuSolve results are compared with analytical results described in White (1991). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with imposed pressure gradients.
In this application, AcuSolve is used to simulate the flow of air in an enclosed cylindrical cavity with a rotating top and a fixed bottom.
AcuSolve results are compared with experimental data adapted from Michelsen (1986). The close agreement of AcuSolve results with experimental data validates the ability of AcuSolve to model cases containing enclosed cavities with flow induced by rotating walls.
In this application, AcuSolve is used to simulate natural convection in the annular space between a heated inner pipe and an outer concentric pipe.
AcuSolve results are compared with experimental results adapted from Kuehn and Goldstein (1978). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model cases with flow induced by natural convection.
In this application, AcuSolve is used to simulate laminar flow through a channel with two outlets forming a T-junction. AcuSolve results are compared with experimental results adapted from Hayes and others (1989). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model cases with multiple outlet paths.
In this application, AcuSolve is used to simulate high Peclet number laminar flow through a channel with heated walls. AcuSolve results are compared with analytical results adapted from Hua and Pillai (2010). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases involving heat transfer to a moving fluid with a high Peclet number.
In this application, AcuSolve is used to simulate turbulent flow of air through and behind a two dimensional open-slit V. AcuSolve results are compared with experimental results adapted from Yang and Tsai (1993). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model the Coandă effect.
In this application, AcuSolve is used to simulate turbulent flow of a fluid over a NACA 0012 airfoil at 3 angles of attack, 0 degrees, 10
degrees, and 15 degrees. AcuSolve results are compared with experimental results for coefficients of pressure, lift, and drag reported by NASA. The
close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model external aerodynamics.
In this application, AcuSolve is used to simulate the natural convection of a turbulent flow field within a tall rectangular cavity. AcuSolve results are compared with experimental results as described in Betts and Bokhari (2000). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model cases with natural convection of turbulent flow within a tall cavity.
In this application, AcuSolve is used to simulate the separation of laminar flow over a blunt plate. AcuSolve results are compared with experimental results as described in J.C. Lane and R.I. Loehrke (1980). The close
agreement of AcuSolve results with the experimental results validates the ability of AcuSolve to model cases with external laminar flow including separation.
In this application, AcuSolve is used to simulate fully developed turbulent flow through an asymmetric diffuser with a divergent lower wall and
a straight upper wall. AcuSolve results are compared with experimental results as described in Buice and Eaton (2000). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model cases with internal turbulent flow with flow separation and reattachment in an asymmetric diffuser.
In this application, AcuSolve is used to simulate fully developed turbulent flow through an axisymmetric diffuser with a divergent upper wall and
a straight lower wall. AcuSolve results are compared with experimental results as described in Driver (1991) and on the NASA Langley Research Center
Turbulence Modeling Resource webpage. The close agreement of AcuSolve results with experimental data and reference turbulence model performance validates the ability of AcuSolve to model cases with turbulent flow with separation due to an adverse pressure gradient within an axisymmetric
geometry.
In this application, AcuSolve is used to simulate fully developed turbulent flow over a backward-facing step. AcuSolve results are compared with experimental results as described in Driver (1985) and on the NASA Langley Research
Center Turbulence Modeling Resource web page. The close agreement of AcuSolve results with experimental data and reference turbulence model performance validates the ability of AcuSolve to model cases with turbulent flow that forms a shear layer, recirculates and then reattaches downstream
of the divergent step.
In this application, AcuSolve is used to simulate fully developed turbulent flow through a channel containing a convex curve in the lower wall.
AcuSolve results are compared with experimental results as described in Smits (1979) and on the NASA Langley Research Center
Turbulence Modeling Resource webpage. The close agreement of AcuSolve results with experimental data and reference turbulence model performance validates the ability of AcuSolve to model cases with turbulent flow moving past a convex curved wall.
In this application, AcuSolve is used to simulate the heat transfer due to radiation between concentric cylinders. The inner and outer cylinders
are held at constant temperature and are defined to be radiation surfaces. AcuSolve results are compared with analytical results for temperature as described in Incropera (2006). The close agreement
of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with radiation heat transfer requiring view factor computation.
In this application, AcuSolve is used to simulate the mixing of two streams of fluid with different velocities moving past a splitter plate.
AcuSolve results are compared with experimental results as described in J. Delville, et al. (1989). The close agreement of
AcuSolve results with the experimental results validates the ability of AcuSolve to model mixing layers in the turbulent flow regime.
In this application, AcuSolve is used to solve for the flow field around a high lift airfoil with inflow conditions that lead to transitional flow
on the pressure and suction side of the airfoil's surface. The moderate level of turbulence intensity at the inlet,
low angle of attack and shape of the airfoil induce a transition to turbulent flow after a separation bubble develops
on the surface. The coefficient of pressure is compared against experimental data from laboratory experiments.
In this application, AcuSolve is used to simulate turbulent flow through a strongly curved two dimensional 180 degree U-duct channel. AcuSolve results are compared with experimental results adapted from Rumsey et al. (2000). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model turbulent cases with strong curvature effects.
In this application, AcuSolve is used to simulate the heat transfer due to conduction and radiation between concentric spheres. The inside surface
of the inner and the outside surface of the outer sphere are both held at constant temperature, while the gap between
them radiates the heat from one sphere to the other.
In this application, AcuSolve is used to simulate the heat transfer due to radiation through a specular interface within an absorbing, emitting,
but not scattering solid cube. One of the cube’s walls is modeled with an isotropic external radiation source while
the remainder of the cube is held at fixed temperature conditions and modeled with pure radiation, neglecting the
effects of conduction.
In this application, AcuSolve is used to simulate the wall heat flux due to nucleate boiling at a heated wall inside a rectangular channel with
water flow. Results are compared with experimental heat flux measurements as reported by Steiner, et al. (2005). The
close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model single phase nucleate boiling problems.
In this application, AcuSolve is used to simulate fully developed turbulent flow past a smooth hump on the lower wall of a flow domain. AcuSolve results are compared with experimental results as described in Seifert and Pack (2002) and on the NASA Langley Research
Center Turbulence Modeling Resource web page. The close agreement of AcuSolve results with experimental data and reference turbulence model performance validates the ability of AcuSolve to model cases with turbulent flow moving past a wall protrusion resulting in flow separation and recovery.
In this application, AcuSolve is used to solve for the flow and temperature field within a channel containing a heated wall. The wall is maintained
at a constant temperature, inducing heat flux into the fluid, to predict the thermal law of the wall. The non-dimensional
temperature versus the non-dimensional height above the wall is compared to the analytical correlation provided by
Kader.
In this application, AcuSolve is used to simulate the flow of a highly viscous fluid between a moving and a stationary plate with an imposed
pressure gradient and fixed temperature on the walls. AcuSolve results are compared with analytical results described in White (1991). The close agreement of AcuSolve results with analytical results validates the ability of AcuSolve to model cases with imposed pressure gradients and viscous heating.
This section includes validation cases that consider unbounded simulation domains where external flow is present over
solid bodies, leading to free boundary layer development.
This section includes validation cases containing conditions producing laminar to turbulent flow that are simulated
with a turbulence transition model.
This section includes validation cases that consider time dependent motion within the domain, requiring that the mesh
movement be modeled with a differential equation, a fully defined mesh motion or by interpolated mesh motion.
Collection of AcuSolve simulation cases for which results are compared against analytical or experimental results to demonstrate the accuracy
of AcuSolve results.
In this application, AcuSolve is used to solve for the flow and temperature field within a channel containing a heated wall. The wall is maintained
at a constant temperature, inducing heat flux into the fluid, to predict the thermal law of the wall. The non-dimensional
temperature versus the non-dimensional height above the wall is compared to the analytical correlation provided by
Kader.
In this application, AcuSolve is used to solve for the
flow and temperature field within a channel containing a heated wall. The wall is maintained
at a constant temperature, inducing heat flux into the fluid, to predict the thermal law of
the wall. The non-dimensional temperature versus the non-dimensional height above the wall
is compared to the analytical correlation provided by Kader.
Problem Description
The problem consists of a fluid having material properties close to air with a density of 1.0
kg/m3, molecular viscosity of 0.0001 kg/m-s, specific heat of 1005.0
J/kg-K and thermal conductivity of 0.139 W/m-K. The properties are specified to
obtain a Prandtl number of 0.72. The velocity is defined as periodic and is driven
by a constant acceleration body force equal to 2.0 m/s2. The temperature
is specified as periodic+unknown ratio allowing it to develop until it reaches a
steady solution. The simulation description is shown in the following image, which
is not drawn to scale. The model is simulated using the one equation Spalart
Allmaras turbulence model along with the advective-diffusive temperature equation.
The thermal wall distribution is validated against correlation data published by
Kader 1981. Figure 1. Critical Parameters used For Simulating Periodic Flow Within a Heated
Channel Figure 2. Mesh used For Simulating Periodic Flow Within a Heated Channel
The simulation was performed as a two-dimensional problem by constructing a volume mesh that
contains a single layer of elements extruded in the cross-stream direction, normal
to the flow plane and by imposing periodic boundary conditions on the extruded
planes. The streamwise direction contains two elements allowing the flow and
temperature solution to develop. Only the lower half of the channel is modeled,
assuming the solution is mirror across the top slip plane.
AcuSolve Results
The AcuSolve solution converged to a steady state and the results
reflect the mean flow conditions within the channel. The simulation results
demonstrate that the channel wall induces a thermal flux into the flow field,
producing a temperature distribution dependent on the distance from the wall. The
thermal law of the wall computed from the AcuSolve
results is compared with correlation data for the corresponding Prandtl number, as
demonstrated in Kader 1981. The plot shown below gives the non-dimensional value of
T+ as a function of Y+, where T+ and Y+ are computed per the following
relationships:(1)
(2)
(3)
Where , is the fixed wall temperature,
T is the temperature away from the wall,
is the fluid density, is the fluid specific heat, is computed from the magnitude of the shear stress
and is the local surface heat flux.
The image below shows black circles representing the correlation data and a solid red line for
the AcuSolve results. The results demonstrate that the
temperature distribution away from the wall is resolved properly and compares well
with the correlation. Since an empirical relationship for T+ is used for comparison,
there will be minor discrepancies compared with the simulation results. Additional
comparisons have been made against DNS results for T+ from Kawamura et al. 1998. Figure 3. Thermal Boundary Layer Within the Heated Channel Compared Against the
Correlation Data Figure 4. Contours of Temperature and Vectors Representing the Fluid Velocity
Within the Channel
Summary
The
AcuSolve solution compares well with the correlation data for turbulent flow within a heated channel. In this application, the constant temperature wall induces a surface heat flux, giving rise to a temperature gradient within the channel.
AcuSolve can capture the correct temperature gradient at any location above the wall if an appropriate first layer height is selected to resolve a Y+ value of 1.0. The good agreement with correlation data for T+ demonstrates that
AcuSolve can predict the locally varying temperature distribution within a turbulent channel.
Simulation Settings for Turbulent Flow Through a Heated Periodic Channel
SimLab database file: <your working
directory>\channel_periodic_heat\channel_periodic_heat.slb
Global
Problem Description
Flow type - Steady State
Temperature equation - Advective Diffusive
Turbulence equation - Spalart Allmaras
Auto Solution Strategy
Max time steps - 50
Convergence tolerance - 0.0001
Relaxation Factor - 0.4
Temperature - On
Material Model
Fluid
Type - Constant
Density - 1.0 kg/m3
Viscosity - 1.0e-4 kg/m*sec
Specific Heat - 1005.0 J/kg*K
Conductivity - 0.139 W/m*K
Body Force
BodyForce
Gravity
X-component - 2.0 m/sec2
Model
Volumes
Fluid
Element Set
Material model - Fluid
Body force - BodyForce
Surfaces
Symmetry_1
Simple Boundary Condition - (disabled to allow for periodic
conditions to be set)
Symmetry_2
Simple Boundary Condition - (disabled to allow for periodic
conditions to be set)
Inflow
Simple Boundary Condition - (combination of integrated BC and
periodic BC set)
Advanced Options
Integrated Boundary Conditions - Temperature -
300.0 K
Outflow
Simple Boundary Condition - (disabled to allow for periodic
conditions to be set)
Slip_surface
Simple Boundary Condition
Type- Slip
Wall_surface
Simple Boundary Condition
Type- Wall
Temperature BC type - Value
Temperature - 350.0 K
Periodics
2D
Periodic Boundary Conditions
Type - Periodic
Flow
Periodic Boundary Conditions
Type - Periodic
Temperature
Individual Periodic BCs
Temperature: Type - Single Unknown Ratio
Nodes
Zero_z-velocity
Z-Velocity: Type - Zero
References
B.A. Kader, "Temperature and concentration profiles in fully turbulent boundary
layers", International Journal of Heat and Mass Transfer, Volume 24, Issue 9,
1981, Pages 1541-1544.
H. Kawamura, K. Ohsaka, H. Abe and K. Yamamoto, "DNS of turbulent heat transfer
in channel flow with low to medium-high Prandtl number fluid", International
Journal of Heat and Mass Transfer, 19:482-491, 1998.