A transfer of energy occurs between the mean flow and eddies of varying time and length scales, illustrated by the Kolmogorov turbulent energy cascade.
For most applications, the smaller details of turbulence are not important—what matters is the effect of turbulence on the main flow.
Turbulence causes pressure drop or drag increase, enhances heat transfer, and homogenizes the mixing of fluid/species.
Laminar vs. turbulent flow regime
According to the Second Law of Thermodynamics, the entropy of a system always increases, provided the process causing the change is irreversible. Although entropy represents the amount of unusable thermal energy that cannot be converted into mechanical work, increasing entropy is often taken to mean movement from a more stable to a more unpredictable, random, or chaotic state.
This physical reality has led to notions that the world is consistently moving toward chaos, as many processes release or lose energy as heat. An example of this is the heat generated by electrical current flow that is not available for work at the load. These dire predictions of the future are misplaced, as total energy is always constant and heat can be reconverted to usable energy. The Seebeck effect, where a temperature differential will introduce an electrical potential difference that can be utilized to generate current, illustrates this.
For fluid flow, there is a similar conversion from stability to chaos that occurs when changing from laminar to turbulent flow. The latter is highly undesirable, as turbulence can present problems such as increased drag for aircraft. Therefore, for system design, it is important to understand and analyze the turbulent flow regime, as this is the area in which these changes occur.
Turbulent Flow Regime Defined
In order to explain what a turbulent flow regime is, it is first necessary to define a fluid flow regime.
For the last classification, laminar flow is characterized by parallel streamlines and well-defined layers, while turbulent flow regimes have the following attributes:
- Non-parallel streamlines
- High rate of lateral mixing
- Layer disruption
- Chaotic changes in fluid properties such as temperature and pressure
Turbulent vs. laminar flow (Image from Thermal Engineering)
Turbulent flow regimes are marked by various fluid current changes or eddies, which vary in size as well as direction. Turbulence also differs from laminar flow in that the Reynolds number is significantly higher, as illustrated in the figure above. A better understanding of the turbulent flow regime can be reached by looking at a turbulent energy cascade.
Understanding the Turbulent Energy Cascade
In the figure below, a Kolmogorov turbulent energy cascade is shown.
Turbulent flow energy cascade (Image from “Towards a Comprehensive Modelling and Simulation Approach for Turbulent Nonequilibrium Plasma Flows”)
These representations seek to illustrate the activity--specifically changes in energy--that occurs during a turbulent flow regime. As shown, there are three intervals or ranges.
Energy Intervals During Turbulent Fluid Flow
- Generation - During this range, energy increases, and eddies are formed due to changes in velocity and other parameters.
- Inertial - This is a transformative range where large-scale eddies transfer energy to smaller ones (direct energy cascade) and vice-versa (reverse energy cascade). At some point along the cascade, after significant energy has been lost, this range transitions to the dissipation range. An important concept for modeling these transitions is self-similarity, which means that irrespective of the direction of change in scale, the created eddy is similar to the one from which it is formed.
- Dissipation - During the range, energy is being primarily dissipated due to viscosity.
The utilization of an energy cascade is important to the study of turbulent flow regimes, which is a critical analysis for designing systems that are resilient to fluid flow changes.
CFD Simulation Modeling of Turbulence
For system design, it is imperative to study how the system will respond to turbulence in order to make design decisions to optimize reliability. Although virtually all fluid dynamics analysis begins with the Navier-Stokes equations, which mathematically represent conservation of momentum and mass, there are several models used to study turbulence flow regimes.
Common Turbulence Flow Models
k - 𝛆 model
This is probably the most common model used in solvers. This 2-D model was initially developed to improve the mixing length model for moderate to highly complex fluid flows.
- k - 𝛚 model
This 2-D model is commonly used as closure for the Reynolds-averaged Navier-Stokes (RANS) equations.
- Reynolds stress equation model (RSM)
This model is typically used for highly complex turbulence modeling. It successfully addresses the shortcomings of other methods, such as the inability to model flows with large streamline curvature.
- Menter’s shear stress transport (SST) model
This is a popular model that combines the k - 𝛆 and k - 𝛚 models.
- Spalart-Allmaras (S-A) model
The Spalart-Allmaras (S-A) model, which was developed specifically for aerospace systems, is a single equation model that is good for solving adverse pressure boundary layer problems.
As shown, there are a number of models that may be employed to analyze turbulent flow regimes. However, the solver utilized is equally as important as the chosen model. Omnis from Cadence is an advanced tool for solving fluid flow problems of any level of complexity.