Since the generation of green and clean renewable energy is a major concern in the
modern era, solar energy conversion technologies such as the solar chimney power plant
are gaining more attention. In order to accurately predict the performance of these power
plants, hydrodynamic instabilities that can lead to large-scale coherent structures which
affect the mean flow, have to be identified and their onset has to be predicted accurately.
The thermal stratification of the collector flow (resulting from the temperature difference
between the heated bottom surface and the cooled top surface) together with the opposing
gravity can lead to buoyancy-driven instability. As the flow accelerates inside the collector,
the Reynolds number can get large enough for viscous (Tollmien-Schlichting) instability to
occur. A new highly accurate compact finite difference Navier-Stokes code in cylindrical
coordinates has been developed for the spatial stability analysis of such radial flows. The
new code was validated for a square channel flow. Stability results for different stable and
unstable Reynolds/Rayleigh number combinations were in good agreement with temporal
stability simulations as well as linear stability theory. To investigate the radial flow effect,
spatial stability simulations were then carried out for a computational domain with constant
streamwise extent and different outflow radii. The Reynolds and Rayleigh number were
chosen such that buoyancy-driven instability occured. For cases with significant radial flow
effect, the spatial growth rates of the azimuthal modes were found to vary considerably in
the streamwise direction.
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Numerical Investigation of Radial Flow in Solar Chimney Power Plant Collector
The hydrodynamic stability of the radial Rayleigh-Benard-Poiseuille flow inside the collector of solar chimney power plants has not attracted much attention in the literature. Because the ground is heated, buoyancy driven instability is possible. In addition, viscosity driven instability may occur. Temporal and spatial simulations are employed for investigating the hydrodynamic stability of the radial flow. Towards this end a new compact finite difference Navier-Stokes code is being developed. Square channel ow simulations were performed for code validation purposes using both the new code and an existing finite-volume code. For certain Reynolds and Rayleigh number combinations transverse rolls or longitudinal rolls appear while for others the ow remains stable. A Fourier mode decomposition of the wall-normal velocity component at mid-channel height reveals linear (exponential) growth for the unstable modes and nonlinear interactions once the mode amplitudes exceed a certain threshold. The present square channel flow results are consistent with the neutral curves from the linear stability theory analysis by Gage and Reid. Simulations were also carried out for the collector of a 1:30 scale model of the Manzanares solar chimney power plant at the University of Arizona. The Rayleigh number is well above the critical Rayleigh number and steady longitudinal rolls appear shortly downstream of the collector inflow.
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- Award ID(s):
- 1510179
- NSF-PAR ID:
- 10025303
- Date Published:
- Journal Name:
- 55th AIAA Aerospace Sciences Meeting, AIAA SciTech Forum
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Inward radial Rayleigh-Be'nard-Poiseuille flow can exhibit a buoyancy-driven instability when the Rayleigh number exceeds a critical value. Furthermore, similar to plane Rayleigh-Be'nard-Poiseuille flow, a viscous Tollmien-Schlichting instability can occur when the Reynolds number is high enough. Direct numerical simulations were carried out with a compressible Navier-Stokes code in cylindrical coordinates to investigate the spatial stability of the inward radial flow inside the collector of a hypothetical solar chimney power plant. The convective terms were discretized with fifth-order-accurate upwind-biased compact finite-differences and the viscous terms were discretized with fourth-order-accurate compact finite differences. For cases with buoyancy-driven instability, steady three-dimensional waves are strongly amplified. The spatial growth rates vary significantly in the radial direction and lower azimuthal mode numbers are amplified closer to the outflow. Traveling oblique modes are amplified as well. The growth rates of the oblique modes decrease with increasing frequency. In addition to the purely radial flow, a spiral flow with swept inflow was examined. Overall lower growth rates are observed for the spiral flow compared to the radial flow. Different from the radial flow, the relative wave angles and growth rates of the left and right traveling oblique modes are not identical. A plane RBP case with viscosity-driven instability by Chung et al. was considered as well. The reported growth rate and phase speed were matched with good accuracy.more » « less
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null (Ed.)The flow through the collector of a solar chimney power plant model on the roof of the Aerospace and Mechanical Engineering building at the University of Arizona was investigated numerically for the conditions of the experiment. The measured wall temperature and inflow velocity for a representative day were chosen for the simulation. The simulation was performed with a newly developed higher-order-accurate compact finite difference code. The code employs fifth-order-accurate biased compact finite differences for the convective terms and fourth-order-accurate central compact finite differences for the viscous terms. A fourth-order-accurate Runge-Kutta method was employed for time integration. Unsteady random disturbances are introduced at the inflow boundary and the downstream evolution of the resulting waves was investigated based on the Fourier transforms of the unsteady flow data. Steady azimuthal waves with a wavenumber of roughly four based on the channel half-height are the most amplified as a result of Rayleigh-Benard-Poiseuille instability. Different from plane Rayleigh-Benard-Poiseuille flow, these waves appear to merge in the streamwise direction. Oblique waves are also amplified. The growth rates are however lower than for the steady modes. Because of the strong streamwise flow acceleration, the growth rates decrease in the downstream direction.more » « less
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This paper reports on an experimental investigation of the flow through the collector of a solar chimney power plant which has been constructed on the roof of the Aerospace and Mechanical Engineering building at the University of Arizona. This model contains a central chimney which is a long tubular structure located in the center and a circular collector that employs the greenhouse effect to heat up the air under it. The chimney is 5.9m high and the collector radius measured from the center of the chimney is 4.13m. Measurements were carried out from April to June 2019. Several types of J thermocouples were mounted inside the collector at various radial locations to measure the air temperature both near the ground and the ceiling of the collector. A hot-wire probe (anemometer) was employed to measure the airflow velocity under the collector near the chimney inlet. A traverse system was designed and constructed, which allows the anemometer to be moved in the radial and circumferential direction under the collector. The height of the probe position above the collector ground can be adjusted by rotating the probe support along its longitudinal axis. A digital analog conversion system was used to convert the thermocouple and hot-wire readouts into binary data for processing via a LabVIEW interface. In parallel to the experiments, high-fidelity numerical simulations are being carried out for the conditions of the experiments. The simulations show longitudinal flow structures near the collector outflow that likely result from a buoyancy-driven instability.more » « less
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For plane channel flow, thermal stratification resulting from a wall-normal temperature gradient together with an opposing gravitational field can lead to buoyancy-driven instability of three-dimensional waves. Moreover, viscosity-driven instability can lead to the amplification of two-dimensional Tollmien-Schlichting waves. Temporal stability simulations considering different combinations of Reynolds number and Rayleigh number were performed to investigate both the buoyancy and viscosity-driven instability of Rayleigh-Benard-Poiseuille flow. The investigated cases are either (1) stable, (2) unstable with respect to three-dimensional waves (buoyancy-driven instability), or (3) unstable with respect to two-dimensional waves (viscosity-driven instability). Two new and highly accurate computational fluid dynamics codes have been developed for solving the full and linearized unsteady compressible Navier-Stokes equations in Cartesian coordinates. The codes employ fifth-order-accurate upwind-biased compact finite differences for the convective terms and fourth-order-accurate compact finite differences for the viscous terms. For the case with buoyancy-driven instability, strong linear growth is observed for a broad range of spanwise wavenumbers and the wavelength of the spanwise mode with the strongest non-linear growth is gradually decreasing in time. For the case with viscosity-driven instability, the linear growth rates are lower and the first mode to experience non-linear growth is a higher harmonic with half the wavelength of the primary wave. The present results are consistent with the neutral curves from the linear stability theory analysis by Gage and Reid.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/http://dx.doi.org/10.2514/6.2017-1010
