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

REYNOLDS-STRESS MODELLING OF FLOW AND THERMAL FIELDS IN
AN IC-ENGINE-RELATED COOLING CHANNEL

Sebastian Wegt, Maximilian Bopp, Louis Krüger, Suad JakirlićInstitute of Fluid Mechanics and Aerodynamics
Technical University of Darmstadt
Alarich-Weiss-Str. 10 64287 Darmstadt
wegt@sla.tu-darmstadt.de, jakirlic@sla.tu-darmstadt.de

ABSTRACT

new reference test sample in relation to the cooling systems of
IC engines in practice and is topologically intended to mimic
the coolant flow around the cylinder head (see Fig. 8 upper).
According to the position of the cylinder chamber in the IC
engines relevant to the cylinder head, a one-sided heating of
the WSG is experimentally prescribed. This results in a nonuniform heat load on the surface of the WSG leading to ahighly complex conjugate heat transfer problem. Apart fromthe intensive development of an isothermal reference databasefor the WSG and its constituting flow guiding elements (Tjunction, deflections and reverse T-junction), treated in an isolated manner, by a high-fidelity Large Eddy Simulation (LES)
within the work of Wegt (2021), a RANS (Reynolds-averaged
Navier-Stokes) model formulation, requiring substantially lesscomputer resources for computing the flow field in the WSG,
was also proposed on the basis of an elliptic-blending-related
Reynolds-stress model (EBM) having the ωh quantity as thescale-supplying variable. The extensive validation study performed so far was limited to isothermal flow conditions, however the quality of the results obtained supports further efforts
towards the extension of the validation study to non-isothermal
flow conditions. For this purpose, the perpendicular impingement of a jet originating from a fully-developed channel flow
onto a heated wall according to the investigations of Hattori& Nagano (2004) represents a suitable reference case. Finally,
the flow in the heated WSG is considered presently in conjunction with the EBM.

The present work represents an extension of the validation
study of a newly developed ωh -based elliptic-blending-related
Reynolds-stress model (EBM) elaborated by Wegt (2021). The
EBM formulation has been intensively validated for a multitude of well-known isothermal flow benchmarks involving
basic flow scenarios encountered in some canonical fullydeveloped flow configurations, as e.g. in plane channels andpipes, in developing boundary layers subjected to zero- andadverse-pressure gradients, as well as in flows separating fromsharp-edged and curved continuous surfaces, as in flow past
periodically arranged hills, over a backward facing step andin differently configured 3D diffusers. The validation studyof the EBM formulation in non-isothermal flow conditions is
the subject of the present study with the wall impingement ofa jet discharging from a fully-developed channel flow serving as a preliminary reference case. This represents the next
logical step in approaching the complex flow topology withincooling systems of internal combustion (IC) engines, which is
the main goal in relation to the EBM development. Consequently, the non-isothermal analysis is subsequently extended
to the so-called WSG (’Water-Spider’ Geometry), which represents a generic cooling channel configuration of IC engines.
The WSG was designed and developed within the frameworkof a BMWi project (Klink et al. (2021)) and investigated in theframework of isothermal flow simulations by Wegt (2021) andWegt et al. (2022).

INTRODUCTIONCOMPUTATIONAL MODEL

The steadily rising requirements for internal combustion(IC) engines imposed by the European union (EU, Heibel(2009) and Gruden (2008)) and the associated manufacturerrelated measurements (intelligent thermal management anddownsizing, see van Basshuysen (2013) and Lunanova (2009))
cause enhanced thermal loads on IC engines. The cooling system is forced to its failure limit by increased thermal
stresses representing subsequently one of the restricting elements within the IC engines and its performance capability.
For the best possible design and exploitation of the existing
potential of the cooling systems, a test methodology for cooling systems of IC engines as well as for the applied coolants
is developed within a complementary experimental and numerical BMWi project (Klink et al. (2021)). A part of thisintensive cooperation study is the resource-efficient determination of the flow topology within the so-called ’Water Spider Geometry’ (WSG). The WSG is designed to serve as a

The newly developed ωh -based elliptic-blending-related
Reynolds-stress model (EBM) by Wegt (2021) represents a
synthesis of the second moment closure (SMC) proposals by
Jakirlić & Maduta (2015), Maduta et al. (2015) and Manceau& Hanjalić (2002) combining the advantages of the homogeneous dissipation concept and the robust elliptic-blending
procedure for the pressure redistribution term. The EBM is
implemented in the finite-volume-based, opensource toolbox
OpenFOAM® and, as previously mentioned, has been validated by computing a variety of isothermal flow configurations. To extend the validation study to non-isothermal flow
conditions, the Reynolds-averaged temperature equation

DΘ
∂
∂Θ
∂Θ
⇒
+U i
=
Dt
∂t
∂ xi
∂ xi

1



ν ∂Θ
− ui θ
Pr ∂ xi

(1)

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
is included in the set of governing equations with the mean
temperature Θ (xi ,t), the kinematic viscosity ν and the Prandtl
number Pr. Here, the temperature Θ is treated as a passive
scalar, implying a negligible temperature dependence on thefluid properties. Within the Reynolds averaging procedure an
additional term on the right-hand side of Eq. (1) appeared,
denoting the turbulent transport of temperature field and requiring a modeling approach. Thus, the turbulent heat flux
ui θ = Di j ∂ Θ/∂ x j modeled by the gradient approach requires
special attention. Presently, the diffusion coefficient Di j is expressed in terms of turbulent viscosity νt , but also in terms of
the Reynolds stress tensor ui u j .

D
inlet
y

H
z

x

LH
Figure 1. Schematic of the flow impingement configuration
with D representing the width of the inlet channel flow, H theheight of the outlet gap and LH the spatial expansion of theheated area. The fully-developed channel inflow is highlighted
in blue and the heated area in red.

FLOW IMPINGEMENT
In order to investigate the predictive capabilities of the
EBM formulation under thermal flow conditions and with respect to the multitude of flow impingement events within the
WSG configuration, the impingement of a jet resembling afully-developed channel flow with Reb = Ub D/ν = 4560 onto
a partially heated wall and the resulting gap flow toward theoutlets are considered in the following. The adopted computational domain is schematically illustrated in Fig. 1, where D
denotes the width of the inlet channel, H the height of the outlet gap, and LH the spatial expansion of the heated area. This
flow impingement configuration is based on the detailed DNS
study of Hattori & Nagano (2004), whose database serves asa reference for the evaluation of the EBM formulation. The
DNS study considers three configurations differing in the gap
width H between the partially heated wall and the opposite
iso-thermal wall, representing actually the distance between
the channel-shaped nozzle and the impinging target, as wellas in the spatial expansion of the heated area LH . All threecases are considered within this validation study; the geometrical details are summarized in Table 1. The partially heatedarea is subjected to a constant wall heat flux, realized numerically by prescribing a Neumann boundary condition for thetemperature equation (∂ Θ/∂ y|heatedwall = q̇/λ = 1K/m). The
remaining wall segments of the partially heated wall toward
the configuration outlets (|x| > LH /2) and the opposite wall are
not heated. The comparatively small temperature gradient on
the heated wall allows the temperature to be treated as a passive scalar, allowing the temperature dependence on the flow
properties to be neglected. The unclosed turbulent heat flux
ui θ in Eq. (1) is modeled by applying the General-GradientDiffusion-Hypothesis (GGDH) with the diffusion coefficient
written as Di j = Cgg ui u j /ω h . The value of the model constantis set to Cgg = 0.3.
The computational domain illustrated in Fig. 1 is meshedby a two-dimensional, block-structured, fully-hexahedral gridwith the OpenFOAM own meshing tool ’blockMesh’. The
wall-next cells are clearly positioned within the viscous sublayer (y+ < 1) to satisfy the low-Reynolds number character of the EBM formulation and to enable the capturing of
the boundary layer in its entirety. The grid resolutions used
are listed in Table 1 for all three cases. The SIMPLE (SemiImplicit Method for Pressure Linked Equations) procedure forthe pressure-velocity coupling is applied and the discretization
for the convective term is done with a second-order upwind
scheme. The fully-developed channel flow conditions at the
inlet into the flow domain are realized by a separate computation of a channel element by applying the periodic inlet/outlet
conditions. The flow thus generated is subsequently mapped
onto the domain inlet.
A detailed discussion of the flows structural properties, as

H

LHnx x ny

Case 1

0.5 D

21 D

510 x 50

Case 2

1.0 D

21 D

510 x 100

Case 3

2.0 D

26 D

560 x 150

Table 1. Geometrical details of the three flow impingement
configurations according to Hattori & Nagano (2004) and thepresently applied grid resolution; nx and ny denote the grid cellnumber in x- and y-directions respectively.

presented in Hattori & Nagano (2004), is omitted here and thefocus is set on the predictive capability of the EBM formulation in reproducing the main flow topology. A first impressionof the flow topology dependence on the distance H between
the channel-shaped nozzle and the bottom wall, characterizing the three flow-impingement cases, is provided in Fig. 2 byillustrating the iso-contours of the velocity magnitude U/Ub(right half) and turbulence kinetic energy k/Ub2 (left half). The
mean flow streamlines originating from the inlet provide adeeper insight into the flow pattern around the stagnation area.
The streamline pattern illustrates a severe right-angled skewing of the incoming channel-related flow stream, indicating astrong alternation of flow deceleration and subsequent acceleration in the immediate region around the stagnation point(x/D = 0). The incoming perpendicularly-directed flow, featured by a pronounced velocity gradient within this discharging zone, as well as the outflowing wall-bounded jet, resulting
from the impingement event, exhibit a clear demarcation fromthe remaining low-velocity flow region located near the upper wall. Downstream of the impingement region an intense
spreading of the wall jet can be observed by the broadeningof the streamlines, which is accompanied by the flow relaxation characterizing the post-acceleration region immediately
after the impingement occurrence. This relaxation is strongly
confined by the presence of the upper wall, which can be especially observed for the Case 1 with the lowest gap heightof H/D = 0.5 (cf. Table 1). The strongly varying velocity
gradient within the shear layer aligned with the streamline dividing the high-velocity flow stream, with respect to both thedischarging free jet and the wall-bounded jet, from the weakflow intensity region represents a source of enhanced turbulent
activity. This can be clearly seen at the iso-contours of the turbulence kinetic energy in Fig. 2 around and downstream of the
sharp edge of the inlet channel. Here, the fast developing free2

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

Figure 2. Iso-contours of the turbulence kinetic energy k/Ub2 (left) and velocity magnitude U/Ub (right) and associated streamlines
depicted for the three flow impingement cases considered. The magenta dotted lines mark the line plot positions for Figures 3, 5 and 6.

shear layer between the fully-developed inlet flow and the region of low velocity causes steep changes in the velocity field
increasing subsequently turbulence production in this region.
The turbulence production is even much more pronounced in
the zone bordering the wall-bounded jet and the low-velocity
flow region. This wall-jet cross-sectional area extends along
the outlet gap, with the outcome being especially pronounced
within the Case 1, and represents the location of highest turbulence activity within the flow impingement configuration.
The mean flow topology interpretation allows identification of characteristic flow locations within immediate impingement and wall-jet regions, enabling a more focused assessment and classification of the EBM’s predictive performance. For this purpose, the mean flow and turbulence quantity profiles determined with the EBM formulation are compared with the DNS data at three selected cross-sections at
x/D = 0.5, 1.0, 3.0 downstream the impingement center, denoted by the magenta-dotted lines in Fig.2. The selection of
the cross-sectional locations is in accordance with the available DNS data. Since a detailed discussion of the entire flow
field is beyond the scope the present (6-page long) manuscript,
a representative selection of some essential flow quantities ismade with the velocity magnitude U/uτ (U = (Ux2 +Uy2 )1/2 ),√the wall-normal Reynolds stress intensity vv/uτ and the temperature Θ. The corresponding line plots are depicted in Figures 3, 5 and 6 in direct comparison with the DNS data.
Fig. 3 shows very good agreement of the EBM-related
velocity magnitude profiles with the DNS data for all three
configurations considered in three characteristic flow regions,the region of immediate impingement (x/D = 0.5), the region representing the transition from flow deceleration due
to impingement to the flow acceleration and wall-jet formation (x/D = 1.0), and within the developing wall-jet region(x/D = 3.0). The velocity profiles exhibit strong gradientsin both wall-normal and wall-parallel directions. The differently intensive flow acceleration toward and within the walljet region in terms of the nozzle-to-wall distance is obtainedin close agreement with the DNS study, apart of some slightdeparture at x/D = 3.0. The strongest relative (in relation to

Figure 3. Line plots of the velocity magnitude U normalized
by the local friction velocity uτ depicted at locations x/D =0.5, 1.0, 3.0 (according to Fig. 2). The DNS data of Hattori &Nagano (2004) are represented by symbols.

the Uτ value) acceleration at the last location corresponds, inaccordance with the DNS, to the Case 2. Differences observedat the velocity profiles in the immediate wall region are reflected in the friction coefficient distribution (Cf ) at the partially heated wall, which is depicted for all three flow configurations in Fig. 4. The EBM results follow closely the DNS data
for all three cases concerning both the very strong Cf variationin the immediate impingement region, characterized by a distinct peak, and a flattened Cf development within the far walljet region. The deviation far downstream of the impingement isobserved for the Case 1 featured by the narrowest gap between
the upper plate and lower impingement plate (H/D = 0.5) andare directly connected to the characteristic second peak of thefriction coefficient development. The EBM is in general capable of reproducing this second peak, but its magnitude isslightly underpredicted and the position is shifted downstream.
The performance assessment of the EBM toward to cap-3

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

Figure 4. Friction coefficient Cf depicted over x for all threeflow impingement configurations. The DNS of Hattori &Nagano (2004) are represented by symbols.

Figure 6. Line plots of the temperature Θ normalized adequately by the inlet Θinlet and wall temperatures Θwall depicted
at locations x/D = 0.5, 1.0, 3.0 (according to Fig. 2). The
DNS data (symbols) are from Hattori & Nagano (2004).

Figure 5. Line plots of the wall-normal Reynolds stress in√tensity vv normalized by the local friction velocity uτ depicted at locations x/D = 0.5, 1.0, 3.0 (according to Fig. 2).
The DNS data (symbols) are from Hattori & Nagano (2004).

Figure 7. Nusselt number (Nu) distribution over bottom wall
for all three flow impingement configurations. The DNS of
Hattori & Nagano (2004) are represented by symbols.

turing of the turbulence field is presently
focused on the wall√
normal Reynolds stress intensity vv as this is one of thedominant components in the diffusion coefficient in the flow
impingement configuration within the so-called gradient approach used for the turbulent heat flux modeling. The corresponding line plots are depicted in Fig. 5. With the exception of the near field of the channel-discharging jet (atH/D = 0.5 and y/D ≈ 1.5 − 2), the EBM returns correctly thereference DNS data over the entire configurations√range underconsideration. The corresponding EBM-related vv profile at
x/D = 0.5 exhibits a peak value near the top wall that is notreflected in the DNS data. This suggests an overestimation of
the turbulent production at the transition of the fully-developed
channel flow discharging into the domain (the Reynolds stress
distribution within the channel - not shown here for brevity shows excellent agreement with the respective DNS data).
Finally, the focus is placed on the thermal field that is induced at the partially heated wall. The variations in the temperature field can be observed mainly in the immediate wall vicinity; accordingly, the temperature profiles are depicted within
the wall-nearest region in Fig. 6 (y/D < 0.1). Starting from theimpingement area center, a continuously increased influenceof the wall heating on the temperature profile can be observed.
This behavior is qualitatively and partially quantitatively correctly reproduced by the EBM, with a somewhat more pro-nounced departure pertinent to the Case 1 (H/D = 0.5). The
latter is reflected in a correspondingly enhanced heat propagation into the interior of the flow domain, which is accompanied by a temperature gradient weakening. This is further
reflected in the Nusselt number (Nu) distribution at the partially heated wall, depicted for all three cases in Fig. 7. The
Nusselt number, correlated directly with the near-wall behavior of the temperature field and its gradient, is reasonably well
reproduced by the EBM. Certain deviations are visible in relation to a slight overestimation of the Nusselt number maximum
around the impingement center. A well-known characteristics
of impingement configurations is the formation of the second
Nusselt number peak, the occurrence of which is dependent
on nozzle-to-wall distances. Accordingly, it is clearly visible
in the Cases 1 and 2, analog to the behavior of the friction
coefficient in Fig. 4. This feature represents large challenge
for RANS-based turbulence models. In both Cases 1 and 2
the second peak can be indeed observed at the EBM-related
results, whereas no peak can be seen in the Nusselt number
evolution of the Case 3 in accordance to the DNS study. Although the EBM peaks deviate quantitatively in magnitude andposition from the DNS result, their qualitative reproductionin the Cases 1 and 2 can be certainly treated as a reasonably
good outcome. This smooth jump at the Nu distribution is, ac-4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
cording to Hadziabdic & Hanjalic (2008, JFM 596), the consequence of a very small detachment of the instantaneous flow
field at this location, being beyond the reach of the presently
applied steady RANS framework

WATER SPIDER GEOMETRY (WSG)
Following the preliminary computed canonical flow impingement, which demonstrates the potential of the EBM formulation in capturing the thermal flow conditions, the WSG
configuration is considered next. We refer to Wegt (2021)
and Wegt et al. (2022) for more details about the WSG, including geometrical and operating parameters, as well as thecomprehensive reference LES study. Here, the double symmetric character of the WSG is exploited and the computational domain is reduced to a quarter, as illustrated in Fig. 8lower. The inlet conditions corresponds to a fully-developed
pipe flow with a bulk Reynolds number of Reb = 12600, whichis achieved by a mapping procedure from the pipe inflow immediately downstream onto the WSG inlet. The spatial discretization of the computational domain should ensure a gridindependent solution with the wall-next cells situated completely in the viscous sublayer (y+ < 1). A block-structured
fully-hexahedral grid with 1 million cells has been proven to
be of sufficient size. For the discretization of the convective
term, a blending procedure between the central differencing(CD) and upwind schemes is applied with the CD-fraction of
70 %. To make the convergence procedure more efficient, apseudo-transient approach is applied. The corresponding temporal terms are discretized with the implicit Euler method.
An intensive discussion about structural flow properties
within the WSG would go beyond the scope of the present
manuscript. Instead, a brief extraction of the mean flow,
turbulence and thermal fields within the y − z−symmetry
plane at characteristic locations (see Fig. 8 lower) is exemplary illustrated in Fig. 9 by displaying the profile development of the velocity magnitude U (upper), the streamwise
Reynolds stress component uu (middle) and the mean temperature [(Θ − Θinlet ) / (d√∂ Θ/∂ z)]. For the turbulence quantity,
the root mean square uu is presented to account suitably forthe significantly different turbulence levels within the WSG
and to ensure a meaningful comparison. The corresponding
results of the well-resolved, highly comprehensive reference
LES according to Wegt (2021) are depicted by symbols.
The flow topology within the WSG is characterized bysome typical geometry-driven flow re-directions including
flow division (T-junction), deflections and confluence (reverse
T-junction), which are closely related to the formation of adominant vortical topology causing a distinct flow structure.
These flow phenomena are the turbulence-driving flow mechanisms, especially related to the localities downstream the Tjunction and reverse T-junction contributing substantially tothe turbulence level variation within the WSG. These insights
are the result of the detailed flow discussion in Wegt (2021).
With focus on the predictive capabilities of the EBM formulation, the determination of the velocity field development depicted in Fig. 9 (upper) deserves special attention. The alternation of the velocity magnitude peak as well as its specifically varying behavior within shear layer regions are consistent
with the reference LES data. Merely a slight overestimationof the flow magnitude can be seen in the low-velocity region
downstream of the inner radius of the T-junction. Furthermore,
the highly anisotropic turbulence structure in Fig. 9 middle isa challenging task for RANS-based models, especially withrespect to the correct redistribution among the stress compo-

U/Ub

0

2

y − z−symmetry plane:
4

Ub 1

r

5

3

6

2

7
x − z−symmetry plane

8

Figure 8. Upper: Instantaneous velocity field visualized by
the iso-contours and Q-criterion colored by its magnitude
U/Ub ; results originate from the reference Large Eddy Simulation by Wegt (2021). Lower: Schematic of the Water Spider
Geometry (WSG) with characteristic locations highlighted bymagenta dotted lines (1: T-junction inlet; 2: T-junction outlet;
3: 1. deflection inlet; 4: 1. deflection outlet; 5: 2. deflection
inlet; 6: 2. deflection outlet; 7: reverse T-junction inlet; 8: reverse T-junction outlet).

nents. The EBM can inherently cope with the anisotropic character of the turbulence, but tends to slightly underestimate theturbulence level. This can be observed around the emerging
shear layer downstream the T-junction and reverse T-junction.
The reproduction of the flow topology by the EBM formulation offers a valuable basis for the analysis of the thermal
flow field due to a constantly heated wall with the temperature
profiles depicted in Fig. 9 (bottom). In the absence of the thermal reference data, the analysis of the temperature field represents a kind of numerical experiment. The temperature fieldalso exhibits a clearly asymmetric characteristics across thepipe, which varies in the position of its extreme values along
the WSG. Here, an inverse response to the position of the velocity peaks in Fig. 9 (upper) can be observed, which can be
attributed to a more pronounced convective transport of temperature from the wall into the flow field by a more intensemean flow. The strongest thermal activity within the y − zsymmetry plane occurs in the near-wall region upstream anddownstream from the second deflection. Here, the temperature peak shifts from the outer radius at position 5 (r/R > 0.5)
to the inner radius at position 6 (r/R < 0) as a consequence ofthe flow deflection, which can probably be related to the acting
centrifugal forces and the movement of the forming Dean vortices. This brief illustration of the temperature field indicates
its structural complexity and gives an impression about the diversity of the flow phenomena interacting within the WSG.

5

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

6

7

6

6

8

7

7

8

8

√
Figure 9. Profile development of the velocity magnitude U/Ub (upper), streamwise Reynolds stress intensity uu/Ub (middle) andmean temperature (Θ − Θinlet ) / (d ∂ Θ/∂ y) (lower) across the pipe radius r/R at characteristic localities within the WSG according to
Fig. 8-lower predicted by EBM (solid lines) and LES (circles).

CONCLUSIONREFERENCES
van Basshuysen, R. 2013 Ottomotor mit Direkteinspritzung:Verfahren, Systeme, Entwicklung, Potenzial. Springer.
Gruden, D. 2008 Umweltschutz in der Automobilindustrie.
Vieweg+ Teubner.
Hattori, H. & Nagano, Y. 2004 Int. J. Heat and Fluid Flow
25 (5), 749–758.
Heibel, M. 2009 Das wahrgenommene Umweltbewusstsein
einer Automarke und dessen Effekt auf die Beziehung zum
Verbraucher. GRIN Verlag.
Jakirlić, S. & Maduta, R. 2015 Int. J. Heat and Fluid Flow 51,
175–194.
Klink, A., Wegt, S., Reitz, R., Jakirlic, S., Engler, T., Hussong, J. & Oechsner, M. 2021 Strömungsinduzierte Korrosion und Erosion in Kühlkanälen von Verbrennungskraftmaschinen, IGF-Vorhaben Nr. 20224 N/1 .
Lunanova, M. 2009 Optimierung von nebenaggregaten. In Optimierung von Nebenaggregaten, pp. 93–266. Springer.
Maduta, R., Jakirlić, S. & Ullrich, M. 2015 In Turbulence,
Heat and Mass Transfer 8, Hanjalic et al. (Eds.), Begell
House Inc., ISBN 978-1-56700-427-4, pp. 299–302.
Manceau, R. & Hanjalić, K. 2002 Physics of Fluids 14 (2),744–754.
Wegt, Sebastian 2021 Computational characterization of flow
and turbulence in IC engine-relevant cooling channels:
An LES- and Reynolds-stress-modeling study. PhD thesis,
Technische Universität Darmstadt, Darmstadt.
Wegt, S., Klink, A., Reitz, R., Hussong, J., Oechsner, M. &Jakirlic, S. 2022 SAE Technical Paper Series 2022-01-0394.

The present validation study has demonstrated the potential of the newly developed Elliptic-Blending Reynolds-stressmodel of turbulence in reproducing the complex flow topology within the Water Spider Geometry (WSG) under the nonisothermal flow conditions. Preliminary, a generic flow impingement configuration has been computed. The consideredflow configurations could be correctly reproduced by the EBM
formulation in accordance with the reference DNS and LES
studies of Hattori & Nagano (2004) and Wegt (2021), respectively. Some slight deviations, as e.g. in relation to the specific second peak at the Nusselt number distribution, originating mostly from the inherently unsteady character of theunderlying turbulence, are addressed to the presently applied
steady RANS framework. The thermal field characteristics ofthe WSG provided by the EBM computations gave an impression of the complex temperature field with changing peaking
over the flow pattern and showed the strong coupling with thevelocity field..
Acknowledgement Based on a decision taken by the German Bundestag, this project was supported by the Federal
Ministry for Economic Affairs and Energy (BMWi) and theAIF (German Federation of Industrial Research AssociationseV) within the framework of the industrial collective research(IGF) program (IGF- No.: 20224 N/2). Furthermore, the financial support of the German Research Foundation (DFG) for
the Collaborative Research Center/Transregio 150 (SFB-TRR
150, Project Number 237267381) is gratefully acknowledged.

6