You should consider turbulent a bouyancy-driven flow at high Ra when the flow becomes unsteady and 3d. You can do a spectral analysis to check the turbent spectrum.

There is a lot of literature for such problem.

Yes, using the Rayleigh number (Ra) to identify the flow regime in buoyancy-driven flows is a standard approach, and a threshold of Ra>10e9 is typically considered indicative of turbulence in many systems. However, when working with liquid phase change materials (PCMs), there are some nuances to consider:

1. Thermophysical Properties of PCMs

• Liquid PCMs often have temperature-dependent thermophysical properties (e.g., viscosity, thermal conductivity, and specific heat). These variations can affect the transition point to turbulence.
• If the PCM exhibits significant variations in these properties, it may alter the critical Ra threshold for turbulence.

2. Geometry and Boundary Conditions

• The geometry of the domain (e.g., rectangular cavity, cylindrical enclosure) and boundary conditions (e.g., uniform heating, localized heating) influence the critical Rayleigh number for transition to turbulence.
• For certain confined or anisotropic systems, the onset of turbulence might deviate from the classical 10e9 threshold.

3. Influence of Phase Change

• Phase change processes (melting or solidification) can introduce complex flow patterns due to latent heat release or absorption.
• These processes may dampen or enhance convection, potentially delaying or advancing the transition to turbulence compared to systems without phase change.

4. Practical Considerations

• Experimental and numerical studies specifically focused on liquid PCMs might reveal deviations from the standard Ra>10e9 criterion.
• For instance, the critical Rayleigh number for turbulence in PCM flows might depend on the Prandtl number (Pr), which is typically very high for PCMs.

Suggested Approach:

you can identify that by using

How to Simulate Heat Transfer Through a 3D Hollow Shape in COMSOL Multiphysics:

Tips:

• Couple heat transfer with fluid flow if needed using Conjugate Heat Transfer.
• Validate the setup using simpler cases to ensure model accuracy.

A buoyancy-driven flow is often turbulent because the inherent instability created by density differences within the fluid leads to the formation of rising plumes and descending currents, which readily break down into smaller eddies, causing chaotic and irregular flow patterns as the fluid mixes due to these buoyant forces; this is particularly pronounced at high Rayleigh numbers, where the buoyancy forces significantly outweigh viscous damping effects.

Key points about buoyancy-driven turbulent flow:

• Density variations:The primary driver of turbulence in buoyancy-driven flow is the difference in density within the fluid, usually caused by temperature gradients.
• Plume formation:As less dense fluid rises, it forms buoyant plumes which can interact with each other, creating instability and turbulence.
• Rayleigh number:The level of turbulence in a buoyancy-driven flow is often characterized by the Rayleigh number, which compares the buoyancy forces to viscous forces. Higher Rayleigh numbers indicate a greater potential for turbulent flow.
• Anisotropic nature:Buoyancy-driven turbulence tends to be anisotropic, meaning the flow patterns are not uniform in all directions due to the influence of gravity.
• Computational study of buoyancy driven turbulence in statistically homogeneous bubbly flows - ScienceDirect📷ScienceDirect.com
• Turbulence modelling in buoyant flows - HZDRWhile commercial CFD codes in general can treat buoyancy effects e.g. within the Boussinesq approximation, there are defeciencies ...📷Helmholtz-Zentrum Dresden-Rossendorf (HZDR)
• Physics of Buoyant Flows - World Scientific PublishingChapter 15: Anisotropy in Thermally-Driven Turbulence ... Buoyancy-driven flows are anisotropic due to the gravitational force. In...

World Scientific Publishing

• Show all

Generative AI is experimental.

As complement to Ahuja's detailed discussion: Turbulence is the result of flow instability. It is found in any flows with velocity gradient normal to the flow direction (shear layers, jets, boundary layers...). In natural convection along a wall we have a wall jet (boundary layer on one side and shear layer on the other side). When plumes are created, these are essentially jets delimited by shear layers. The Grashof number Gr compares buoyancy to viscous forces and is analogue to the Reynolds number comparing inertial forces to viscous forces. For a heated vertical wall, the transition between laminar to turbulent for occurs in the range 1E8< Gr

The flow regime in buoyancy-driven flows can be identified using the Rayleigh number (Ra) and Reynolds number (Re):

• Rayleigh Number (Ra): Ra>109Ra > 10^9Ra>109 typically indicates turbulence.
• Reynolds Number (Re): Re>1600Re > 1600Re>1600 also suggests turbulent flow.
• Flow Patterns: Look for unsteady, 3D flow with plumes and eddies.

Buoyancy-driven flow occurs when fluid motion is triggered by density differences resulting from temperature differences. A characteristic of buoyancy-driven flow is its ability to transition from laminar to turbulent regimes, which is strongly influenced by several parameters specific to each case used. In buoyancy-driven turbulent flow, the fluid exhibits chaotic and irregular fluctuations, leading to increased mixing and increased heat transfer rates. This behavior contrasts sharply with laminar flow, where fluid particles move in parallel layers with minimal mixing. The transition to turbulence can be characterized by observational and computational techniques, such as particle image velocimetry (PIV) or large eddy simulation (LES), which can distinguish the presence of eddies and vortices that define turbulent flow. The Reynolds number (Re), another dimensionless quantity, can also play an important role in determining flow characteristics. In conjunction with the Rayleigh number, a high Re is often associated with a tendency toward turbulent flow. When the momentum of the fluid flow becomes large enough for the viscous forces, review the Rayleigh, Reynolds, Neber, and Grashof numbers.

Turbulence emerges when inertial forces dominate over viscous forces. And you can see in your flow :

Plumes breaking into smaller fragments.

Swirling, irregular motion with a wide range of scales (from large thermal plumes to small eddies).

Enhanced mixing, where hot and cold regions become indistinct over time.

Some criteria you can consider to determine if the flow regime in buoyancy-driven flow is turbulent:

Dimensionless Numbers

1. *Grashof Number (Gr)*: Gr > 10^9 indicates turbulent flow.

2. *Rayleigh Number (Ra)*: Ra > 10^9 indicates turbulent flow.

3. *Reynolds Number (Re)*: Re > 4000 indicates turbulent flow.

Flow Regime Maps

1. *Gr-Re map*: Plot Gr vs. Re. Turbulent flow typically occurs at Gr > 10^6 and Re > 4000.

2. *Ra-Re map*: Plot Ra vs. Re. Turbulent flow typically occurs at Ra > 10^6 and Re > 4000.

Experimental and Numerical Indicators

1. *Velocity fluctuations*: Measure or simulate velocity fluctuations. Turbulent flows exhibit random, chaotic fluctuations.

2. *Vorticity and eddies*: Visualize or simulate vortices and eddies. Turbulent flows exhibit complex, three-dimensional flow structures.

3. *Power spectral density*: Analyze the power spectral density of velocity or temperature fluctuations. Turbulent flows exhibit a -5/3 power-law decay in the inertial subrange.

Other Indicators

1. *Flow visualization*: Use techniques like dye injection, PIV, or LIF to visualize the flow. Turbulent flows exhibit complex, chaotic flow structures.

2. *Pressure drop measurements*: Measure the pressure drop along the flow direction. Turbulent flows typically exhibit higher pressure drops than laminar flows.

How to Identify Turbulence in Buoyancy-Driven Flow

Good morning, Eddie! Hope you're doing well. When it comes to understanding turbulence in buoyancy-driven flows, it all boils down to a few key principles and numbers that describe how heat, momentum, and fluid movement interact. Let’s break it down in a way that still keeps it highly technical but feels more natural.

1. What Makes a Flow Turbulent?

In buoyancy-driven (natural convection) flows, turbulence isn’t always obvious at first glance. You might see swirling motion, feel temperature variations, or even detect oscillations in experimental setups. But to really determine if a flow is turbulent, we rely on some fundamental dimensionless numbers.

2. The Rayleigh Number (Ra) – The First Indicator

The Rayleigh number (Ra) tells us how strong the buoyancy forces are compared to the stabilizing effects of viscosity and thermal diffusion. The formula is:

Ra=gβ(Ts−T∞)L3ναRa = \frac{g \beta (T_s - T_\infty) L^3}{\nu \alpha}Ra=ναgβ(Ts​−T∞​)L3​

where:

• ggg is gravity (9.81 m/s²)
• β\betaβ is the thermal expansion coefficient (depends on the fluid, for air it's ~3×10−33 \times 10^{-3}3×10−3 K−1^{-1}−1)
• TsT_sTs​ and T∞T_\inftyT∞​ are the surface and ambient temperatures
• LLL is the characteristic length (height of the heated surface)
• ν\nuν is kinematic viscosity
• α\alphaα is thermal diffusivity

Now, the rule of thumb:

• If Ra is less than 10910^9109, the flow is mostly laminar.
• If Ra is greater than 10910^9109, you’re almost certainly dealing with turbulence.

For example, in a heated vertical wall, once Ra passes this threshold, the smooth rising air layers break down into swirling eddies and chaotic motion.

3. The Grashof Number (Gr) – The “Buoyancy vs. Viscosity” Test

Another key indicator is the Grashof number (Gr), which compares the buoyancy force to the opposing viscous force. The equation looks a lot like Rayleigh:

Gr=gβ(Ts−T∞)L3ν2Gr = \frac{g \beta (T_s - T_\infty) L^3}{\nu^2}Gr=ν2gβ(Ts​−T∞​)L3​

This tells us how much the fluid wants to rise. If Gr exceeds 10810^8108, that’s another strong signal that the flow is turbulent.

The connection between Rayleigh and Grashof comes from the Prandtl number (Pr), which tells us how well heat diffuses through the fluid:

Ra=Gr⋅PrRa = Gr \cdot PrRa=Gr⋅Pr

For air, PrPrPr is about 0.7, while for water, it’s around 7. That means heat spreads differently in each case, affecting when turbulence kicks in.

4. Reynolds Number (Re) – The Classic Check for Flow Instability

The Reynolds number (Re) is a classic way to check for turbulence in any flow:

Re=ULνRe = \frac{U L}{\nu}Re=νUL​

For buoyant flows, you often use characteristic velocity UUU, which can be estimated using scaling laws from convection models.

• If Re > 4000, turbulence is almost a given.
• For natural convection surfaces, Re starts increasing when Ra > 10^9, meaning the flow will transition to turbulence.

5. How to Spot Turbulence in Experiments

Even if the math checks out, turbulence isn’t just a number—it’s something you can see and measure. Here are some real-world ways to detect it:

6. Common Flow Setups and Their Turbulent Thresholds

Here are some real scenarios where turbulence kicks in:

• Vertical heated wall: Turbulence forms when Ra>109Ra > 10^9Ra>109.
• Rayleigh-Bénard convection (heated bottom, cooled top):Convection starts at Ra>1708Ra > 1708Ra>1708, but turbulence happens around Ra>107Ra > 10^7Ra>107.
• Closed cavities (like enclosures): Turbulence starts around Ra>106−107Ra > 10^6 - 10^7Ra>106−107, depending on the aspect ratio.

Final Thoughts

If you’re working with buoyancy-driven flow and wondering if it’s turbulent, check:

✅ Ra > 10910^9109? You’ve got turbulence. ✅ Gr > 10810^8108? Viscosity isn’t stopping the chaos anymore. ✅ Re > 4000? Expect eddies and fluctuating velocities. ✅ Temperature fluctuations and spectral analysis confirm irregular motion.

Turbulent natural convection isn’t just a math problem—it’s something you can see, feel, and measure in real experiments.

Dear Edwin Pagan! Thank you for showing us how to use ChatGPT to answer common questions. Please at least edit the text you receive in the future to avoid the characteristic repetition of formulas and numerical values.

In my opinion, Grashoff number is enough to determine the transition from laminar to turbulence in buoyancy driven flow.

In absence of inertial force (or pressure difference driving the flow) for a buoyancy driven flow, strength of buoyancy force over viscosity determines the strength of turbulence.

Rayleigh number is for determining whether convection is Natural, mixed or forced (where there is inertial force and buoyancy force both plays some part).

1. Buoyancy-driven flow: This type of flow occurs when a fluid is driven by density differences, often due to temperature or concentration gradients.

2.Turbulent flow: Turbulent flow is characterized by chaotic, irregular motion, with eddies and swirls that can greatly enhance mixing and heat transfer.

3. Determining turbulence: To determine if the flow is turbulent, we often use dimensionless numbers, such as the Reynolds number (Re) or the Grashof number (Gr).

Criteria for turbulence:

1. Re > 4000: For pipe flow, a Reynolds number greater than 4000 typically indicates turbulent flow.

2. Gr > 10^9: For buoyancy-driven flow, a Grashof number greater than 10^9 often indicates turbulent flow.

Experimental methods:

1. Particle Image Velocimetry (PIV): PIV measures the velocity field of the flow, allowing us to visualize and quantify turbulent structures.

2. Laser Doppler Velocimetry (LDV): LDV measures the velocity of individual particles or fluid elements, providing detailed information about turbulent flow.

3. Flow visualization: Flow visualization techniques, such as dye or smoke injection, can help identify turbulent flow patterns.

Computational methods:

1. Computational Fluid Dynamics (CFD): CFD simulations can model turbulent flow using various turbulence models, such as the k-ε or k-ω models.

In free convection, the Grashof number (Gr) and the Rayleigh number (Ra=Gr*Pr) are used to describe the flow. Literature does not clearly indicate a preference for either in various applications; rather, it's influenced by historical background and authors' preferences. Two dimensionless numbers are needed to describe the flow: either Grashof and Prandtl numbers or Rayleigh and Prandtl numbers. However, there's a special case with highly viscous fluids where inertia forces can be neglected compared to viscous forces, eliminating the Prandtl number dependence in the equation. In this scenario, the flow can be described using only the Rayleigh number. Transition to turbulence is a complex phenomenon that cannot be characterized by a single Reynolds or Rayleigh number but rather spans a range. For free convection over a flat surface, the critical Rayleigh number varies widely for different fluids, typically ranging from 10^7 to 10^13. Therefore, it's common to discuss developed turbulence. On vertical surfaces, a sign of developed turbulence is when the heat transfer coefficient no longer depends on the linear dimension, resulting in a relationship like Nu=f(Gr^1/3).