Turbulent Flow: Physics and Methods of Investigations

Turbulent Flow:

Physics and Methods of Investigations

By

 Dr. Sharad N. Pachpute (PhD, IIT Delhi)

1. Physics of Turbulence

 i) Turbulent flows are chaotic 

  •         turbulent flows show  irregularity or randomness in measured quantities
  •          A full deterministic approach to determine flow quantities is not possible for all cases
  •         High velocity turbulent flows are observed to be more chaotic
  •         Turbulent flows are generally described statistically
  •        Example: Buoyant plume of smoke rising from a stick of incense 

ii) Turbulent flows are dissipative

  •  Kinetic energy of low gets converted into heat due to viscous shear stresses (viscous heating)
  •  Turbulent flows end  quickly when energy is not supplied to the flow
  • Example: Tugboat riding on the turbulent wake of a ship, in this turbulent flow is created by the motion of ship over the surface of ocean
  • The diffusivity of turbulence results in rapid mixing and enhances the rate of  momentum, heat, and mass transfer
  • Example: Wake turbulence behind individual wind turbines

iii)  Rotation and vorticity  
  •  Turbulent flows are highly rotational and they have non-zero vorticity.
  •  vortex stretching of three-dimensional flows play a key role in turbulence flows
  • Example (1): Vortex formation in a free jet is caused by Kelvin-Helmholtz instability
 
  • Example (2): Von Karman Vortex Streets in the northern Pacific  (Picture taken by from the International Space Station)
 
 
  • Example (30): Vortices on a 1/48-scale model of an F/A-18 aircraft inside a Water Tunnel (Photo credit: NASA Dryden Flow Visualization Facility)

iv)  In-compressible vs compressible  

  • Most of low speed flows are in-compressible
  • high speed flows are compressible which is decided based on the Mach number (M = fluid velocity/sonic velocity). If mach number is greater than 0.2 , then flow is treated as compressible flow
  • Examples for representation of compressible and in compressible flow

 2. Fluctuations and Scaling of Turbulence 

• Relative magnitude of inertial and viscous terms is called as  Reynolds number
Increasing Reynolds number, the  non-linearity inertia term of Navier-Stokes(NS) equations. This results in  flow disturbances
 

 i) Turbulence – fluctuations

  • Turbulence is defined as a deterministic chaos. Velocity and pressure fields are unsteady (non-stationary):  dU/dt is non zero) even though,  flow rate and boundary conditions are constant.
  • Palatines of all particles depend on initial conditions (even the particles that are very close at some moment diverge apart during time evolution)
  • Velocities, pressures, temperatures and species transport are still solutions of NS and energy equations, however they are non-stationary and form chaotically oscillating vortices (eddies)
  • Time and spatial profiles of transported properties are characterized by fluctuations

ii) Turbulent eddies – scales

• Kinetic energy of turbulent fluctuations is also defined as  the sum of energies of turbulent eddies of different sizes

  • Turbulent energy spectrum is given below. The large eddies depends on boundary conditions and geometry of flow. These large eddies carried flow from mean flow and transfer to intermediate size eddies, then to smaller eddies. However, smallest eddies are independent of boundary conditions and determined by fluid viscosity and dissipation rate.
  • L F Richardson defined the energy cascade of turbulent flows as
“Big whirls have little whirls 
Which feed on their velocity
Little whirls have lesser 
whirls And so on to viscosity – in the molecular sense”
 

  3.  Methods for Turbulent Flow Investigations  

  •  Based on experimental and numerical methods, investigation of turbulent flow is classified as follows
  • In experimental methods, hot wire anemoetry (HWA) and particle image velocity-metry (PIV) are widely used due their accuracy and reliability
  • In CFD modelings, RANS models are preferred in industries for complex and large scale problems, but LES and DNS are used in academic research to improve RANS models
 
 

3.1 Experimental Approach:

A) Laser Doppler Velocimetry (LDV):

  • LDV is a useful technique and widely used for accurate measurements of fluid velocity in liquid or gaseous flows
  • In this method,  a pair of coherent beams of laser raditaion are focused down to generate  interference fringes at the optical probe volume which are  formed by the intersection of the two beams in fluid flows
  • The fringe spacing is a strong function the angle between the beams and  optical wavelength a
  • Scattered light from particles passing through the probe volume includes a Doppler frequency:  Doppler frequency (f)  is proportional to the particle velocity (v).
x
  •  Use of LDV for turbulent jet velocity measurement
 
                   

B) Particle Image Velocimetry (PIV):

  • Particle Image Velocimetry (PIV) is a flow visualization technique which is commonly used to measure instantaneous velocity vector a cross-section of a flow
  • This is an optical method for flow visualization
  • This technique is  a non-intrusive  method
  • The PIV is quite useful in high speed flows and boundary layer studies of fluids.
  •   Principle of PIV  for velocity measurement is shown below

Limitations of PIV:

  • The time delay between the laser pulses should be long enough to capture of the displacement of the tracer particles and short enough so that the particles with an out-of-plane velocity component leaving the light sheet.
  •  With the use of high power lasers, the tracer particles size can be reduced. The accuracy of the PIV measurements will drastically improve as the particles will follow the flow more closely.
  •  The size of the interrogation area should be small such that there is no significant velocity gradient within the interrogation area.

C) Hot Wire Anemometry (HWA):

Scope of HWA:

  • Intrusive Technique
  • Measurement of instantaneous velocities and temperature at a point in a flow.
  • Hot wire anemometry is an ideal tool for measurement of velocity fluctuations in time domain in turbulent flows
  • Principal tool for basic studies of physics of turbulent flows.
  • Development of realistic turbulence models, HWA necessary to carry out fundamental turbulence studies

Working Principle of HWA:

  •  CTA (constant temperature  anemometer) is on hand for an experiment, while it is more seldom that selecting and purchasing an anemometer is part of the experimental planning
 

For more details Click here : Dantec_HWA_CTA_Principle

Advantage of HWA:

  • Good Frequency response: Measurements to several hundred kHz possible, 1 MHz also feasible
  • Velocity Measurement: measures magnitude and direction of velocity and velocity fluctuations, Wide velocity range
  • Temperature Measurements
  • Two Phase Flow: Measurements in flows containing continuous turbulent phase and distributed bubbles.

3.2 Statistical Analysis of Turbulent Flow 

After getting the instant nous velocity data from experiments, we can find the average and turbulent statistic   

For more details Click here:

  4. Numerical Modeling of Turbulence

 

4.1 Critical Reynolds Number

  • The Reynolds number is generally use to determine whether the flow is laminar or turbulent
  • The Reynolds number is based on the length scale of geometry (length or hydraulic diameter for internal flow) velocity of fluid and viscosity of fluid
  • Transition to turbulence varies depending on the type of flow

Important Notes for Critical Reynolds number:

  • There is no a fixed critical Reynolds number for all kind of flows.
  • The critical Reynolds (from laminar to turbulent flow) depends on geometries (its cross sectional area, shape, size and shape). Check the geometry across the flow is streamlined or not. For non streamlined body, the flow can become turbulence in the wake region at low velocity at upstream of obstacle
  • Maximum velocity in a lower cross section may lead to turbulence flow
  •  Inlet turbulent conditions (turbulent intensity) and properties of fluid
  • Disturbances or vibration to the flow system can make flow turbulence
  • Surface roughness/projections/fins of wall boundaries can make flow turbulence
  • Presence of moving wall like stirrer or rotor, the flow can become turbulence at low velocity of fluid

4.2 CFD Modeling of Turbulent Flow

4.3 Turbulence Models Available in ANSYS FLUENT

The following models are available in ANSYS FLUENT.
For more details click : FLUENT_Turbulence_Models_v12

Note for Selection of RANS Models  in FLUENT:

  • The SST k-w model with low Reynolds number correction with enhanced wall treatment is commended for adverse /wake region to correctly predict wall shear stress and wall heat flux (keeping note of  y+ value for first wall adjacent cell <1)
  • The SST k-w IDDES model with low Reynolds number correction with enhanced wall treatment is commended for adverse /wake region to correctly predict wall shear stress and wall heat flux (keeping note of  time or  surface averaged y+ value for first wall adjacent cell <1)

 

4.4 Turbulence Models Available in OpenFOAM

Click here for turbulence models in OpenFOAMOpenFOAM_Turbulence_Model_V1912

a) RANS: Linear eddy viscosity turbulence model in OpenFOAM

  1. k-epsilon
  2. k-epsilon-phit-f
  3. k-kl-omega
  4. Langtry-Menter k-omega Shear Stress Transport (SST)
  5. k-omega Shear Stress Transport (SST)
  6. Lien-Leschziner
  7. q-zeta
  8. Realizable k-epsilon
  9. RNG k-epsilon
  10. Spalart-Allmaras
  11. v2-f

Note: The v2-f model is recommended for turbulent jet impingement problems where pressure gradients (in the impingement region) is significant.

b) RANS: Non-linear eddy viscosity turbulence model in OpenFOAM

c) Hybrid RANS/LES Models in OpenFOAM

  •  Near the wall the size of eddy is very small. Hence, the computational cost of scale resolving simulations (LES) increases with an increase in the Reynolds number.
  • To avoid high computational cost of scale resolving, hybrid RANS/LES or detached eddy simulation (DES) approach is used.
  • In this case, RANS is used adjacent to the wall (approximately within a viscous sub-layer) and above it LES resolve the scales in turbulent flow
  • The size of grid decides the resolution of turbulent scales.
  • List of Hybrid RANS/LES models in OpenFOAM: Click here for model setting
  1. k-omega-SST Delayed Detached Eddy Simulation (DDES)
  2. k-omega-SST Delayed Eddy Simulation (DES)
  3. k-omega-SST Improved Delayed Detached Eddy Simulation (IDDES)
  4. Spalart-Allmaras Delayed Detached Eddy Simulation (DDES)
  5. Spalart-Allmaras Detached Eddy Simulation (DES)
  6. Spalart-Allmaras Improved Delayed Detached Eddy Simulation (IDDES)
Note: The k-Omega SST IDDES model with low Reynolds number correction is commended  to correctly predict wall shear stress and wall heat flux (keepingnote of  time or  surface averaged y+ value for first wall adjacent cell <1)
 

    d) LES-SGS Models in OpenFOAM

  1. Dynamic k eqn
  2. k Equation
  3. Smagorinsky
  4. WALE

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