12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

HEAT TRANSFER MECHANISMS IN SEPARATED TURBULENT FLOWS

Rozie Zangeneh
Department of Mechanical Engineering
Lawrence Tech University
Southfield, MI, USA, 48075
rzangeneh@ltu.edu

ABSTRACT

predicting the pressure fluctuations generated within the flowthat is central to the acoustic source generation along the solid
surfaces. Wall pressure fluctuations are related to the motion oflarge-scale vortices, especially hairpin vortices in the reattachment region that produce large amplitude fluctuations ( Figure1). Two main mechanisms govern the flow in the unsteadinessin the separation bubble: the shedding of large-scale vortices
downstream of the separation and a low-frequency unsteadiness called flapping, linked to the shredding and enlargementof the bubble. These two mechanisms also can couple; however, the connection is still not clear.
Several works discussed the existence of vortex shedding and low frequency shear layer flapping in separated flows(Tenaud et al. (2016)). Previous simulations are devoted to describing better the relationship between pressure fluctuationsand vortex dynamics for separated-reattached flow over a flat
plate (Minsuk & Wang (2010)). However, all these studies addressed the case of adiabatic wall conditions, and to our knowledge, no high-fidelity simulations have been carried out to explore heat transfer mechanisms in unsteady separated flows.

This study aims to gain insights into the underlying mechanism of heat transfer characteristics in separated flows using a reduction model through Dynamic Mode Decomposition
Reduced-Order Models. To this end, highly resolved Large
Eddy Simulations (LES) are performed to explore the effectof wall thermal conditions on the behavior of a separated flow
on a flat surface. Various wall-to-recovery temperature ratios
and an adiabatic surface will be considered. Next, we use thedynamic mode decomposition (DMD) to identify the structures generated by the shear layer and the exposed bluntness.
This modal decomposition analysis will be deployed here tocontribute to a better understanding of the interrelated mechanisms between eddy structures and wall pressure fluctuations.
Therefore, a thorough understanding of heat transfer effects on
turbulence structures near the wall will be achieved.

Introduction
Separated flows have engineering concerns since they canoccur in many aerodynamic applications. Examples include
separated flow around ground vehicles, trains, or aircraft bodies. Controlled separation, however, may be advantageous asin the case of slender delta wings, spoilers used on wings forcontrol purposes and transverse fins used to improve the heattransfer performance of nuclear reactor fuel elements.
There are two significant challenges associate with the unsteady behavior of separated flows. Mechanisms driving theacoustic propagation in the far-field surrounding these aerodynamic bodies can impact the system’s structural integrity. Another one is the sound propagation toward the vehicle’s interior, which has the same range of frequencies as voice. Therefore a thorough understanding of mechanisms underlying theacoustic and noise generations and their transmissions are essential for designing of controlling acoustic disturbances anddeveloping noise reduction process techniques. On the otherhand, separation of flow may be used as a means of controlling the heat transfer to a surface and for aerodynamic control
purposes. Heat-transfer characteristics of separated flows areof considerable interest in the design of heat exchangers, aircraft and space vehicles.
A mechanistic understanding of interrelated mechanismsthat couples heat transfer and flow unsteadiness in separated
flows leads to engineering advanced control systems for separated and attached boundary layers that are solutions for noise
reduction techniques and surface heat transfer controlling.
Since the source noise is essentially the coupling between
turbulence structures and the unsteady pressure field in thecore of the flow, previous studies were devoted to accurately

Results
The separated–reattached turbulent flow over a blunt, flat
plate with a right-angled leading edge is the subject of thisstudy. It is equipped with a right-angled corner leading-edge.
This flat plate spans the computational domain horizontally in
its centerline, as seen in Fig 1. The inlet boundary is located
10H upstream of the sharp leading edge to minimize its influence on the uniform inlet boundary condition. The flat plate
has a streamwise length of 25H, extending up to the streamwise outlet boundary. The computational domain sizes we retained to analyze LES results are Lx = 35H in the streamwise
direction, Ly = 5H in the spanwise direction and Lz = 17H in
the normal to the flat plate direction. These domain sizes provide with blockage ratio that are equivalent to previous studiesTenaud et al. (2016).
Numerical predictions using Large-eddy simulation(LES) will provide the base data for the dynamical analysis in
this study. We solve the filtered compressible Navier–Stokes
equations following an LES approach with k-equation subgrid
model (Chai & Mahesh (2012)).
Simulations will be carried out at various values of thewall-to-recovery-temperature ratio, representing cooled, adiabatic, and heated walls as shown in Table 1.
An in-house finite-volume code will be used to carry out
LES. The flow is assumed as Newtonian with a specific heat ratio and Prandtl number of γ = 1.4 and Pr = 0.72, respectively.
A detailed comparison of the present LES and experimental

1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

Figure 1.
Table 1.

Simulation Domain

Flow parameters for LES simulations.

Test case

ReHT∞ (K)Tw (K)

δs (mm)Cooled

7500

300

290

3

Adiabatic

7500

300

300

3

Heated7500300

330

3of the velocity field separated by ∆t, X1N = {v1 , v2 , ..., vN }(Hemati et al. (2017)). When applied to a linear system, the equation is exact. In this case, the computedmodes/eigenvalues represent the physically correct structures
and their growth rates, frequencies. For non-linear systems,
it represents a best linear map that links all snapshots. If theflow is characterized by periodically repeatable and persistent(i.e., neutrally stable) structures, the DMD method should be
able to detect these and the associated frequencies. This modal
decomposition analysis is proposed here to contribute to abetter understanding of the interrelated mechanisms between
eddy structures and wall pressure fluctuations. Therefore, athorough understanding of heat transfer effects on turbulence
structures near the wall will be achieved.

results for the reattaching free shear layer, including the reattachment process and downstream boundary layer growth, waspreviously published by the author (Zangeneh (2020a, 2021,2020b, 2021 doi=10.1115/1.4048611)).
Next, we use the Dynamic Mode Decomposition (DMD)
to identify the structures generated by the shear layer and theexposed bluntness. We will use the DMD method proposedby Schmid (Schmid & Peter (2010)). The method provides
a set of non-orthogonal modes, each having a characteristicfrequency. The temporal and spatial variations are therefore
fully coupled.

Figure 3.

Figure 2.

Amplitudes of difference modes for cooled wall.

Figure 2 shows the dominant frequencies, one at thefrequency of f1 H/U∞ = 0.06, another at a frequency off2 H/U∞ = 0.12 , still another at the frequency of f3 H/U∞ =0.23, and a distant peak at the frequency of f4 H/U∞ = 1.1.
The first three frequencies were also educed through a DMD
decomposition applied on the same configuration (Debesse etal., 2016). It can be attributed to the Kelvin–Helmholtz modeof the mixing layer edging the separation since f 4 matches theStrouhal number of the Kelvin–Helmholtz frequency recorded
experimentally by numerous authors.

Amplitudes of difference modes for adiabatic wall.

DMD approach assumes a series of N time snapshots2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

Figure 4.

Figure 5.

Dynamic load.

Figure 6.

Skin friction

Amplitudes of difference modes for heated wall.

Separated–reattached flows are characterized by two frequency modes which are related to shedding and flapping phenomena. The vortex shedding resulting from the large scale
motion of the mixing layer, is characterized by a frequency
peak band around f L/U∞ = 0.6 - 0.8 (corresponding to theshedding modes, f1 H/U∞ = 0.11 - 0.14) (Cherry et al., 1984;
Kiya and Sasaki, 1983, 1985). The flapping phenomenon isan overall dynamical mechanism linked to successive enlargements and shrinkage of the separated zone. Its characteristicfrequencies (corresponding to the flapping modes) are much
lower than those of the shedding modes, e.g. f L/U∞ = 0.12
( f H/U∞ = 0.024) (Cherry et al., 1984; Kiya and Sasaki, 1983;1985). The two lowest frequencies (f1 and f2) are the sameas those associated in the literature(Cherry et al., 1984; Kiyaand Sasaki, 1985) with the recirculation bubble (the third frequency f1 H/U∞ = 0.23 is simply likely to be a harmonic of
f2 H/U∞ = 0.12). The lowest frequency f1 H/U∞ = 0.06 canbe seen to correspond to the flapping frequency which is associated with the growth and shrinkage of the bubble (Fouras andSoria, 1995). In fact, if this frequency is renormalized with therecirculation length, we find a dimensionless frequency whichmatches results in the literature (Cherry et al., 1984; Kiya andSasaki, 1985).
Results show cooling the wall decreases the dominant frequencies and on the other hand heating the wall increase thefrequencies as shown in Figures .

Table 2.

Figures 7-9 show Q-criterion contoured by the modes 13, respectively. The first mode ( frequency) is not active inthe cooled wall case, the flapping frequency becomes intense
as the wall is heated. The second mode (shedding frequency)
extends on the wall for the heated wall. The third mode ( KH instability) is not affected significantly by the wall thermalcondition.

REFERENCES

Dominant frequencies for various wall.

Test case

f1

f2

f3

f4

Cooled

0.02

0.05

0.4.8

Adiabatic

0.06

0.12

0.23

1.1

Heated

0.17

0.56

1.1

1.4

Chai, Xiaochuan & Mahesh, Krishnan 2012 Dynamic kequation model for lage eddy simulation of compressible
flows. Journal of Fluid Mechanics 699, 385–413.
Hemati, Maziar, Rowley, Clarence & Cattafesta, Louis 2017
De-biasing the dynamic mode decomposition for applied
koopman spectral analysis. Theoretical and Computational
Fluid Dynamics 31.
Minsuk, JI & Wang, MENG 2010 Sound generation by turbulent boundary-layer flow over small steps. Journal of Fluid
Mechanics 654, 161–193.
Schmid & Peter, J. 2010 Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics
656, 5–28.
Tenaud, Christian, Podvin, Berengere, Fraigneau, Yann &Daru, Virginie 2016 On wall pressure fluctuations and theircoupling with vortex dynamics in a separated–reattached

Table 2 summarizes the frequencies.
Figures 5 show the dynamic load, Pw /P∞ at the wall forthree different wall condition. As the wall is cooled the dynamic load on the wall is increased. The skin friction value
is increased by heating the wall and decreased as the wall iscooled (Figure 6).

312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022

Figure 7.

Mode-1Figure 8.

Mode-2

Figure 9.

Mode-3turbulent flow over a blunt flat plate. International Journalof Heat and Fluid Flow 61, 730–748.
Zangeneh, R 2020a Evaluation of reattaching shear-layer incompressible turbulent flows; a large-eddy simulation approach. Proceedings of the ASME 2020 Fluids Engineering
Division 3 (V003T05A035).
Zangeneh, R 2020b A new framework for modeling shockturbulence interactions. SAE International Journal ofAerospace .
Zangeneh, Rozie 2021 Parametric study of separation and reattachment in transonic airfoil flows. AIAA Journal 59 (11),1–10.
Zangeneh, R 2021 doi=10.1115/1.4048611 Development of a
new algorithm for modeling viscous transonic flow on unstructured grids at high reynolds-numbers. Journal of Fluids
Engineering .

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