|Year : 2016 | Volume
| Issue : 2 | Page : 75-79
Overstable convection in a double-diffusive, salt-stratified system heated from below
Karim Alwani Choubani1, Mohammed Abdulrahman Almeshaal2
1 Department of Mechanical, Riyadh College of Technology, Technical and Vocational Training Corporation, Riyadh, Saudi Arabia
2 Department of Mechanical Engineering, College of Engineering, Al Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
|Date of Submission||05-Sep-2016|
|Date of Acceptance||13-Jun-2017|
|Date of Web Publication||21-Aug-2017|
Karim Alwani Choubani
Department of Mechanical, Riyadh College of Technology, Technical and Vocational Training Corporation, Riyadh
Source of Support: None, Conflict of Interest: None
Introduction: The salt-stratified solution destabilized by bottom heating is a double-diffusive system, which is characterized by conditions similar to those found in salt gradient solar ponds. Although many of its features are well understood, controversy still exists concerning the mechanisms responsible for the growth of the first mixed layer. This growth strongly influences overall system performance. The solar pond is a complex system that is coupled to ambient conditions and where several different inputs can destabilize the stratification. This complexity cannot be reflected in the idealized analytical description of the mixing mechanisms. In spite of these difficulties, the experimental description seemed necessary. Our objective is to make a laboratory scale flow visualization experiments using shadowgraph, to understand the occurrence of overstability and the layer motion in a simulated solar ponds. Laboratory experiments were made to investigate further the stability and occurrence of convective regimes, as a function of density and heat constraints.
Methodology: In this paper, the overstable convection in a linearly salt-stratified system with a free surface and heated from below at constant temperature is studied. In the experimental studies, almost the same conditions and same stability parameter that we can find in a real salt-stratified solar pond was considered.
Results: It is found that the oscillatory motion appeared in the bottom of the stratification seems to be the main mechanism responsible for the growth of the first mixed layer which strongly influences overall system performance.
Conclusion: In this work, the onset and the development of the first mixed layer were studied for small stability parameter Λ. No investigation has been performed, to our knowledge, regarding the occurrence of overstability for small values of Λ.
Keywords: Double diffusion, flow visualization, overstability, solar pond
|How to cite this article:|
Choubani KA, Almeshaal MA. Overstable convection in a double-diffusive, salt-stratified system heated from below. Imam J Appl Sci 2016;1:75-9
|How to cite this URL:|
Choubani KA, Almeshaal MA. Overstable convection in a double-diffusive, salt-stratified system heated from below. Imam J Appl Sci [serial online] 2016 [cited 2019 Feb 21];1:75-9. Available from: http://www.e-ijas.org/text.asp?2016/1/2/75/213392
| Nomenclature|| |
A - Aspect ratio
C (%) - Concentration
Cp (J/kg°C) - Specific heat - uncertainty ± 0.2%
G (m/s 2) - Gravitational acceleration
H (m) - Stratified layer height
kT (m 2/s) - Coefficient of thermal diffusion
kS (m 2/s) - Coefficient of solute diffusion - uncertainty ±5%
RaT= αg Δ TH 3/kTν - Thermal Rayleigh number where
ΔT = Tb − Tu
RaS= αgΔCH 3/kSν - Solute Rayleigh number where
ΔC = Cb − Cu
Pr= ν/kT Prandtl number
Sc = ν/kS Schmidt number
T (°C) - Temperature
t (s) - Time
X (mm) - Horizontal coordinate
Z (mm) - Vertical coordinate
α (°C − 1) - Thermal expansion coefficient - uncertainty ±3%
β (m 3/kg) - Saline expansion coefficient - uncertainty ±3%
ν (m 2/s) - Kinematic viscosity - uncertainty ±2%
ρ (kg/m 3) Density - uncertainty ±0.2%
Λ = RaT/RaS - Stability parameter
| Introduction|| |
The convection instability in a stratified-systems heated from below has many important applications, such as convection in oceans, atmosphere, lakes, and solar ponds.,,,,
We consider initially a linear saline stratification, where salinity and temperature are both increasing downward. When a small element of fluid is displaced upward a small distance during a short time interval and then released. As it moves away from its equilibrium position, it will exchange its temperature and salinity with the surrounding fluid. Since the temperature diffusivity is greater than the salinity diffusivity, the upward displaced fluid element will change very little in salt content during the displacement, but it will lose considerable heat to the surrounding fluid. In consequence, it will become denser that it was, and in falling down, it will gain more energy than was used in displacing it upward. When the fluid element reaches its initial position, it will overshoot, then will gain heat and rise up again.
The same process will be repeated, and the net result is that a small disturbance to the system will create a growing oscillation in amplitude, resulting eventually in mixing. This phenomenon is often called overstability.
Theoretically, overstability is only possible if:
Moreover, then a much stronger condition for overstability was made:
Salinity gradient solar ponds are used as low-cost solar collectors, with integrated long-term storage. The energy stored, is used in different applications.
The salt gradient solar pond generally has three zones [Figure 1]: The Lower Convective Zone (LCZ), the Non-Convective Zone (NCZ) and the Upper Convective Zone (UCZ). The LCZ acts as a collection and storage area; the UCZ bears all the environmental influences while the NCZ called the gradient zone acts as an insulator to limit double diffusion of heat and salt from the LCZ to the UCZ.
In a real solar pond, we find these properties:
In the LCZ: Temperature rise from 40°C to 90°C and concentration rise from 20% to 26% in weight.
In the UCZ: Temperature rise from 15°C to 30°C and concentration rise from 1% to 3% in weight.
Stratified layer height rise from 1 to 3 m.
[Table 1] gives an example of real conditions in salt-stratified solar pond. [Table 1] shows why we emphasize in our experiments a small value of Λ. Indeed, the values of Λ used in our experiments are comparable of real Λ-values.
We can notice that if we change Tu, Tb, Cu, Cb, and the stratified layer height H values, we can find in another value of Λ comparable to those used in our experiences.
| Experimental Set-Up|| |
All experiments were carried out in a rectangular Plexiglas tank with 200 mm × 20 mm inner dimensions. The tank was fitted in the bottom with an aluminum heat exchanger thermally insulated, through which circulates water coming from an adjustable thermostat to provide heating at a constant temperature over the base. The instruction-temperature is obtained with a precision of ±0.2°C. A schematic sketch of the entire apparatus is shown in [Figure 2].
The desired linear salinity gradients were set up using a modified two-tank technique of Oster. The resulting concentration was varying from Cb at the bottom to zero at the surface. The temperature profile of the stratified solution was measured by copper-constantan thermocouples. The diameter of each thermocouple is about 0.2 mm. Temperature measurements were obtained with a precision of ±0.8%. Thermocouples were positioned at 4 mm intervals along the mid vertical axis, except for the lowest one which had been set at 2 mm above the bottom of the cell to depict probably three-dimensional regimes. All the thermocouples were connected to an Agilent data-logger. The measurements of density were made using a single-point conductivity probe of constant 0.954. Interface location and layer formation were monitored with a shadowgraph system. It uses the fact that the index of refraction of fluids is typically dependent on temperature.
Experimental conditions associated with the linearly salt-stratified solution heated from below at constant temperature are presented in [Table 2]. The stability and the qualitative behavior of the stratification are described by the ratio of the thermal to the solutal Rayleigh number Λ.
| Results and Discussion|| |
Once the heat is turned on, shadowgraph observations [Figure 3] show the occurrence of overstability near the tank bottom.
The oscillatory motion appeared in the bottom of the stratification seems to be the main mechanism responsible for the growth of the first mixed layer which strongly influences overall system performance.
Verification of overstability-condition given by Equation 1 [Table 3]:
These results showed that in the three experiences (E1, E2, and E3) we are:
, so overstability is possible.
Let us now verify the Equation 2 which is much stronger, for overstability:
We find and the overstability-condition is verified. Hence, the occurrence of the overstability type convection for small values of Λ [Table 4].
The predicted occurrence of overstability agrees well with shadowgraph observation. This agreement confirms the occurrence of oversatbility as the first kind of instability in the NCZ of a real solar pond.
| Conclusion|| |
This study presented experimental results of the overstability convection in a linearly stratified medium of a salt solution heated from below at a constant temperature. Initially, the salt solution was at rest, isothermal, and its density decreased linearly with distance from the bottom wall. Shadowgraph visualization and experimental results show the occurrence of overstable convection in linearly salt-stratified salt systems. Our system presents the particularity that it is at the free surface and heated from below at constant temperature (most of the theoretical and experimental investigations used a gradient layer heated from below at constant heat flux).
In this work, the onset and the development of the first mixed layer were studied for small stability parameter Λ. No investigation has been performed, to our knowledge, regarding the occurrence of overstability for small values of Λ.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
| References|| |
Akrour D, Tribech M, Kalache D. A theoretical and numerica study of thermosolutal convection: Stability of a salinity gradient solar pond. Therm Sci 2011;8015-67.
Anderson MD, Mcfadden BG, Coriell RS, Murray TB. Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer. J Fluid Mech 2010;647:309-33.
Choubani K, Zitouni S, Charfi K, Safi MJ, Akbarzadeh A. Experimental study of the salt gradient solar pond stability. J Sol Energy 2010;84:24-31.
Choubani K, Safi MJ. Experimental simulation of the salt gradient solar pond stability. J Renew Sustain Energy 2012;4:063143.
Gargett AE, Tanny J, Kelley DE, Fernando HJ, Ozsoy E. The diffusive regime of double-diffusive convection. Prog Oceanogr 2003;56:461-81.
Hull JR, Nielsen CE, Golding P. Salinity-Gradient Solar Ponds. Ch. 4. Boca Raton, Florida: CRC Press. Inc; 1989.
Platten JK, Legros JC. Convection in Liquids. Berlin-Heidelberg-New York-Tokyo: Springer-Verlag; 1984.
Oster G. Density gradients. Sci Am 1965;213:70-6.
[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2], [Table 3], [Table 4]