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

INTEGRATION OF PIV DATA INTO THE SIMPLE ALGORITHM FOR 2D
TIME-AVERAGED TURBULENT FLOWS

Nikolaos-Petros Pallas
School of Mechanical Engineering
National Technical University of Athens
9 Heroon Polytechniou, 15773 Zografou, Greece
Email: npallas@mail.ntua.gr

Demetri Bouris
School of Mechanical Engineering
National Technical University of Athens
9 Heroon Polytechniou, 15773 Zografou, Greece
Email: dbouris@fluid.mech.ntua.gr

ABSTRACT

vestigation over the last decades, being able to extract instantaneous velocity fields simultaneously over large domains ofinterest. Hence, the PIV technique is a natural selection forthe purpose of combining measurements with CFD codes.
The fundamental idea has been introduced in the past.
Hayase and Hayashi (1997) proposed a methodology where
the SIMPLER algorithm uses partial experimental information as feedback for the reconstruction of the boundary conditions of turbulent simulations. Two other attempts may also
be noted: Jaw et al. (2009) implemented a SIMPLER based
method where 2D PIV data are integrated and the respective pressure fields of steady-state, incompressible, laminarflows are calculated, while Gunaydinoglu and Kurtulus (2020),
again with a SIMPLER-based algorithm, extracted pressure
fields of incompressible, laminar, steady as well as unsteadyflows, utilising 2D PIV velocity data. Although the methodology of the two forenamed attempts is quite similar to the one
presented here, they do not include turbulence closure. Regarding the computation of the pressure fields from PIV data,
numerous endeavours based on the solution of a Poisson pressure equation can be found (Vanierschot and Van den Bulck,
2008, Suryadi and Obi, 2011 , Van der Kindere et al., 2019).
It has to be noted though that in these methods PIV velocity
fields remain unchanged and thus do not constitute measurement integration into CFD calculations per se.
The methodology that is implemented in the present endeavour is a SIMPLE algorithm-based one, where a finite volume method is applied for the discretisation of the 2D RANS
equations, boundary conditions are imposed from unchanging PIV data and turbulence is included through the Reynolds
Stresses, calculated directly from the statistics of the PIV experiment. The calculation procedure thus includes turbulence
effects, avoiding the assumptions related to numerical turbulence closure models, and ensures conservation of mass andmomentum through the solution of the corresponding equations. Furthermore, it arguably ensures better compliance of
the CFD solution to the inherent physics of the flow being
studied, since turbulence models are usually calibrated in order
to be consistent with the prediction of fundamental flows e.g.
homogeneous isotropic turbulence, logarithmic law boundary

The merging of diverse sources of information describing thesame phenomenon is currently an active area of scientific research. In this scope, an attempt based on the SIMPLE algorithm is presented for the integration of time-averaged planar PIV velocity measurements into a CFD code. The measurements are adjusted/corrected by the CFD calculation of
the time-averaged velocity fields through which the respective
pressure fields are also computed. Boundary conditions are applied based on the PIV data by imposing a layer of constant velocity values near the boundaries i.e. constant first and second
normal derivatives. The novelty of this approach derives not
only from the integration of PIV measurements but also fromthe utilisation of PIV statistics for the direct computation of the
Reynolds Stresses and their introduction into the source termsof the Reynolds averaged equations. This permits application
to steady state turbulent flow fields without the need for a numerical turbulence closure model. The application is the caseof a cube with openings, immersed in a boundary-layer flow at
an angle of attack equal to 0 degrees. The calculated velocity
fields as well as the respective pressure fields are found to bephysically consistent, while the inherent turbulent structure of
the flow is taken into account.

INTRODUCTION
The traditional approach in the field of Fluid Mechanics
treats the solutions acquired through CFD and Experimental
Fluid Mechanics as discrete and separate sources of information, even though they may refer to a common phenomenon.
For that reason, the integration of measurements into a CFD
code is a significant advancement, in order to capitalise on
both these disciplines. Moreover, for problems concerning
real flows, the imposition of exact boundary conditions on theequations of a CFD code is not always feasible as turbulencemodels are not always capable of encapsulating the inherent
structure of the flow (Hayase, 2015).
As van Oudheusden et al. (2007) mention, the PIV
measurement technique constitutes a non-intrusive method tostudy very complex flows and has emerged as an accurate andcredible tool for fundamental and industrial fluid dynamics in-1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
boundary nodes (i.e. constant velocities, u and v with respect
to the x and y directions, and constant convective terms) were
ineffective.
The modified SIMPLE iterative algorithm for the extraction of the results consists of the following steps:

layer etc. (Duraisamy et al., 2019). The aforementioned
methodology is applied for three regions lying on the symmetry plane of the flow around a cube with openings, immersed ina boundary-layer at an angle of attack equal to 0 degrees, utilising PIV data originating from the experiment of Manolesos
et al. (2018).

1. The pressure correction equation is solved, after having
introduced as initial velocity fields those emanating fromthe PIV measurements.
2. The adjusted/corrected velocity and pressure fields arecalculated by implementing the standard SIMPLE correction equations.
3. The RANS momentum equations are solved with respect
to the x and y direction with Reynolds Stresses included in
the source terms of the discretised form of the equations.
4. The aforementioned iterative steps are repeated until thereis the best possible convergence.

EQUATIONS AND ITERATIVE METHOD
In this section, the basic equations that are solved arepresented. Firstly, the 2D steady-state Reynolds-Averaged
Navier-Stokes (RANS) momentum equation (1) in tensor form
is given along with the continuity equation (2), for incompressible flow. Although the continuity equation is not solved directly throughout this method, it is a key component as it isimperative for the deduction of the pressure correction equation (Patankar, 1980).

ρu j 0 0
∂ ui u j∂ ui∂p=+ µ∆ui − ρ
∂xj
∂ xi
∂xj

∂ ui
=0
∂ xi

The method was developed using an in-house code, which
is a standard finite volume implementation of the SIMPLE
algorithm on a Cartesian grid with collocated variables andhas been used in numerous studies e.g. Bouris and Bergeles(1999), Jurelionis and Bouris (2016) and Konstantinidis andBouris (2016).

(1)

(2)

RESULTS
Configuration of the experiment
The configuration of the experiment that Manolesos
et al. (2018) conducted at the National Technical University of Athens wind tunnel, in the large test section(2.5m×3.5m×12m) is given in Figure 1.

Here i, j = 1 or 2 (with respect to x and y direction), ∆is the Laplace operator, ρ and µ are the density and dynamic
viscosity respectively and the last term on the right hand-sideof the equation corresponds to the Reynolds Stress gradients.
By deploying the finite volume method in equation (1),a pentadiagonal linear system for each direction (x and y) is
derived, which is solved by the Alternating-Direction Implicit
Method (ADI). Here, the terms corresponding to the Reynolds
Stresses are included in the source terms of the discretised
momentum equations, instead of being modelled. An analogous pentadiagonal linear system, corresponding to the pressure correction can be extracted (Patankar, 1980).
The Reynolds Stresses terms can be computed directlyfrom the statistics of the experiment. If N is the total numberof PIV snapshots then the equation, in tensor form, of theseterms is written as follows:N

u0i u0j = ∑k=1

u0i,k u0j,kN

Figure 1. Geometry and configuration of the PIV experiment (Manolesos et al., 2018). Left: side view with upstream velocity profile, Right:
top view.

The present 2D method is applied to the case of highshear flow around the surface mounted cube immersed in aboundary-layer flow. The method has already been successfully applied to the case of a solid cube (Pallas and Bouris,2022) but here, a more complex situation is considered wherea thin vertical opening is present at the center of the upstream
and downstream face of the cube (see Manolesos et al., 2018).
A, B and C are planes of symmetry and they are parallel to thevector of the free stream velocity. Owing to the assumed twodimensional nature of the mean flow on these planes, resultsfor plane A, B and C will be presented. Table 1 illustrates thebasic grid and geometric parameters for the three planes. It isnoted that the CFD spatial resolution is the same as the PIV
one and that the PIV/CFD grid is uniform and collocated.
Apart from the PIV experiment, pressure taps, were
utilised for the extraction of profiles of the pressure coefficient,
CPexp (Manolesos et al., 2017) along the plane of symmetry, on
the centre line of the front, the roof and the back face walls of
the cube (Figure 2), so they could be compared with the CFDcalculated CP profiles. It should also be noted that the maximum experimental error of the pressure coefficient is equal to
4.5 %, (the maximum measurement errors of the pressure andthe reference velocity are 3 % (Manolesos et al., 2018) and1.67 %, respectively).
It has to be clarified that the coordinates X, Y in all theforthcoming figures are non-dimensionalised with the heightof the cube, Hc = 0.11 m, whilst the thick black line represents the boundary of the cube. Moreover, the distance of(3)

The computational grid is almost identical to the PIV one,so interpolation is not necessary to produce the initial CFD values. The initial velocity field and of course the statistics for the
Reynolds Stresses, for the commencement of the iterative algorithm, are provided by the PIV data.
This direct calculation of Reynolds Stresses from PIVdata is evidently limited by the PIV resolved length/timescales, therefore a number of higher frequencies intrinsicallylinked to the nature of turbulent flows cannot be included.
However, in the examined case, where the CFD grid is almost
identical to the PIV one, the aforementioned physical limitation is assumed not to be crucial, since the CFD solution is notexpected to resolve sub-PIV length/time scales.
The type of boundary conditions (BC) that is deployed
imposes constant velocities and convective terms on a boundary zone which contains three lines/layers of grid points andtwo finite volumes adjacent to each boundary, respectively.
Initial attempts to use Dirichlet boundary conditions at the212th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
The normalised continuity residual, CRN, which is derived by implementing the discretised form of the continuity
equation, using the PIV velocities on plane A before nondimensionalising it with a characteristic velocity gradient i.e.
< ut,PIV > /(2∆x), is shown in the form of contours in Figure 4b. Similar to the error of Figure 4a, CRN reaches its
highest values near the solid boundary of the cube, whereas
its maximum appears near the top upstream corner. Owing
to the strong coupling between the continuity residual and the
SIMPLE pressure correction equation, one can contend thatthe appearance of the maximum relative error near the top upstream corner of the cube is partially justified by the fact that
CRN also reaches its highest value there. The higher CRN
values near the upstream wall of the cube could be attributed
to three-dimensional structures of the flow, since the third velocity component, w is not included in the calculation of thecontinuity residual. More specifically, the ratio of the third,
not included, velocity component, w (Manolesos et al., 2018,
performed Stereo-PIV), over the u velocity component reaches
its maximum value, namely 60%, near the top upstream cornerof the cube.

the three planes from every solid boundary (i.e. the groundand the respective walls of the cube) is close to 1cm (or 0.09
in non-dimensional form, so, e.g., for plane A, the point with
X = Xmax , Y = 0.91 corresponds to the upper edge of the cube).
The Reynolds number at cube height exceeded 2 · 104 throughout the realisation of the experiment, namely it was over thesuggested limit for Reynolds number independence in windtunnel tests on buildings (Castro and Robins, 1977). It is notedthat from now on, the overbar denoting time-averaged velocities will be omitted.

Plane
A
B
C

NI
98
99
110

NJ
95
104
105

Xtot /Hc
1.68
1.52
1.67

Ytot /Hc
1.63
1.60
1.59

Table 1. Basic geometric and grid parameters: NI and NJ are thenumbers of the grid lines with respect to the x and y direction, while
Xtot and Ytot are the x and y dimensions of the computational domain.

Figure 2. Pressure measurement locations (Manolesos et al., 2017).
(a) ε (%)

Plane A

Figure 4. Contours of: (a) the non-dimensional error between the CFD
total velocity, ut,CFD , and the PIV one, ut,PIV , on plane A, (b) the nondimensional continuity residual derived by the discretised continuity
equation, CRN, on plane A. X and Y are non-dimensional coordinates,
whereas the thick black line denotes the upstream boundary of the
cube. Flow is from left to right.

Figure 3a, presents the contours of the CFD total velocity
Ut,CFD , extracted with the above-mentioned iterative methodology, whilst in Figure 3b those of the uncorrected PIV total
velocity Ut,PIV are given, for the experiment on plane A.
As expected, the CFD-calculated velocity field is similar
to the PIV one. More specifically, the position of the stagnation point, namely at approximately (Xmax , 0.7), and thevelocity range remain almost invariant after the deploymentof the CFD methodology. Figure 4a, where the relative error εut (%) = 100 · |ut,CFD − ut,PIV |/| < ut,PIV > | is presented(ut,CFD and ut,PIV are local, total, CFD and PIV velocities, respectively, whilst < ut,PIV > is the time and spatially averaged
PIV total velocity), further supports the aforementioned argument. That is to say, its value is maximum only in the area
near the top upstream corner of the cube where the flow accelerates, whereas in the rest of the domain the error remains
below 10 − 20%. This possibly indicates that the CFD spatial
resolution is inadequate to capture the physics of the flow near
the cube’s upstream corner.

The pressure field of the experiment on plane A, with respect to a reference pressure located at the upstream boundary of the plane, chosen as the least disturbed point of
the flow, is illustrated in Figure 5a. From the calculatedpressure fields, the profile of the pressure coefficient CP =(P − Pre f )/(1/2ρU 2 ) (where Pre f = 0 and Pdyn = 1/2ρU 2 =5.99Pa) is extracted along the boundary that corresponds tothe upstream face of the cube (at a distance of approximately
1 cm) and compared with the experimental CPexp , (Manolesos
et al., 2017) in Figure 5b.

(a) P (Pa)(a) Ut,CFD (m/s)(b) CRN (%)(b) CPexp and CP

Figure 5. (a) Relative pressure contours extracted by the developed
methodology, on plane A, (b) comparison between CPexp and CP ,where the Y-axis corresponds to the non-dimensional distance fromthe bottom boundary of the domain (Y = 0.91 denotes the upper edgeof the cube), for plane A. Flow is from left to right for (a).

(b) Ut,PIV (m/s)

Figure 3. Contours of the total velocity extracted by: (a) CFD methodology, (b) PIV experimental technique, on plane A. X and Y are nondimensional coordinates, whereas the thick black line denotes the upstream boundary of the cube. Flow is from left to right.

The pressure contours, shown in Figure 5a, indicate thestagnation point (i.e. (Xmax , 0.7)), since the pressure reaches

312th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
its maximum value near this point, in line with the velocity behaviour shown in Figure 3. Near the corner, there is a pressure
drop, due to flow acceleration.
Figure 5b, shows that there is a slight difference between the CFD-calculated pressure coefficient, CP , and the experimental one, CPexp , i.e. the maximum difference is about
5 − 10% of CPexp , which is probably caused by: (i) the reference pressure is not exactly the same as the experimental reference one, which was outside the experimental domain available here, (ii) CP is calculated at a distance of approximately
1 cm and not exactly on the upstream wall, (iii) numerical andexperimental errors, (iv) 3D effects (leading to increased PIV
mass residual).

(a) P (Pa)

Figure 8. (a) Relative pressure contours extracted by the developed
methodology, for plane B, (b) comparison between CPexp and CP ,where the X-axis corresponds to the non-dimensional distance fromthe upstream boundary of the domain, for plane B. Flow is from left toright for (a).

Plane BIn Figure 6a, the contours of the CFD-calculated total velocity Ut,CFD are given, while in Figure 6b those of the PIV total velocity Ut,PIV are illustrated, for the experiment on plane
B.

(a) Ut,CFD (m/s)

Figure 7a, where the error/difference between the initial
PIV and the CFD-estimated velocities is shown, further supports that no significant corrections take place. More specifically, the maximum error is about 10% and appears in thearea of flow acceleration. Generally, a comparison between
the error of plane B and that of plane A, reveals that lesser correction takes place in plane B. This can be partially attributed
to the much lower continuity residual, as its maximum value,
shown in Figure 7b, is about ten times less than that in plane
A. The ratio of the third, not included, velocity component,w (Manolesos et al., 2018, performed Stereo-PIV), over the uvelocity component (not shown) is close to zero in most partsof the examined domain except for the region near the roof ofthe cube where it is about 24%. This is generally better than inplane A and may partially justify the lower values of CRN for
plane B in comparison with those for plane A.
The relative pressure field of the experiment on plane B,
with respect to a reference pressure located at the top upstream
corner of the domain (where the flow can be considered freestream) is illustrated in Figure 8a, whereas in Figure 8b a comparison between CP and CPexp (Manolesos et al., 2017) is presented for plane B. It should be noted that the reference pressures in planes A, B (and C, presented following) could besignificantly different.
Figure 8a presents a physically consistent behaviour ofpressure. That is to say, it reaches its maximum value near the
inlet, namely 5 Pa above the free stream value, as it is influenced by the stagnation that takes place on the upstream solidboundary of the cube. After the region of positive pressures,
there is a pressure drop due to flow acceleration, a conclusion
in line with the results of other researchers, such as Hölscher
and Niemann (1998), Castro and Robins (1977).
Regarding the comparison between CPexp and CP , it canbe said that the calculated pressure coefficient is close to themeasured values with an exception being the first measurement
point where a large difference can be observed. This probably
indicates that the spatial resolution in conjunction with Neumann boundary conditions, are incapable of depicting suitably
the local physics of the flow, i.e. the steep pressure gradient.
The fact that velocity measurements could not be performed
up to the surface where pressure was measured exacerbates
this. Indicative remedies for this drawback of the developed
approach will be given in the section of conclusions.

(b) Ut,PIV (m/s)

Figure 6. Contours of the total velocity extracted by: (a) CFD methodology, (b) PIV experimental technique, on plane B. X and Y are nondimensional coordinates (non-dimensional distance of 1 corresponds
to 1 cube height), whereas the thick black line denotes the roof of the
cube. Flow is from left to right.

Similar to the case of plane A, the iterative method does
not seem to change significantly the velocities on plane B.
More specifically, the region of low velocities near the solidboundary of the cube remains almost invariant while the velocity range is almost the same for the CFD and PIV velocity
fields. This indicates the potential of the proposed approach interms of universality and independence of the specific characteristics of the flow velocities.

(a) ε (%)(b) CPexp and CP(b) CRN (%)

Figure 7. Contours of: (a) the non-dimensional error between the CFD
total velocity, ut,CFD , and the PIV one, ut,PIV , for plane B, (b) the nondimensional continuity residual derived by the discretised continuity
equation, CRN, for plane B. X and Y are non-dimensional coordinates(non-dimensional distance of 1 corresponds to 1 cube height), whereas
the thick black line denotes the roof of the cube. Flow is from left toright.

Plane C
Figure 9 illustrates the contours of the CFD-calculated total velocity Ut,CFD as well as those of the PIV total velocity
Ut,PIV , for plane C.

412th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
The relative pressure field of the measurements on planeC, with respect to a reference pressure located at the top downstream corner of the domain, again different from planes A andB but chosen as the point where the flow is the least disturbed,
is illustrated in Figure 11a, whereas in Figure 11b a comparison between CP and CPexp is presented.

A characteristic element of the experiment on this domain, is the flow out of the opening on the downstream faceof the cube (at X = 0 and Y = 0 to 1).

(a) Ut,CFD (m/s)(b) Ut,PIV (m/s)

Figure 9. Contours of the total velocity extracted by: (a) CFD methodology, (b) PIV experimental technique, on plane C. X and Y are nondimensional coordinates, whereas the thick black line denotes thedownstream boundary of the cube. Flow is from left to right.

(a) P (Pa)

Figure 11. (a) Relative pressure contours extracted by the developed
methodology, on plane C, (b) comparison between CPexp and CP , where
the Y-axis corresponds to the non-dimensional distance from the bottom boundary of the domain (Y = 0.91 denotes the upper edge of thecube), for plane C. Flow is from left to right for (a).

Although the velocity range remains invariant after the iterative method, significant modifications are observed in theregion of low total velocities in the wake of the cube. Figure
10a supports the forenamed statement, since the normalised
error/difference between the PIV and CFD velocities reaches
a maximum value of 90 %. More specifically, there is an extended area coinciding with that of almost zero total velocities,
where the error is higher than 50%.
The fact that the continuity residual shown in Figure 10b
reaches a maximum value of 23%, namely a value of CRN
lower than that for plane A, probably indicates that the mass
residual of the domain does not constitute the most critical parameter for the departure of the CFD velocity field from thatof the PIV measurements. It has to be noted that the highest
CRN values are observed near the solid boundary of the cube,
which is in line with the results for plane A.
The ratio of the third velocity component, w, (Manolesos et al., 2018, performed Stereo-PIV), over the u velocity
component (not shown here) generally is higher than that of
the above-presented planes. However, the highest values areobserved at points where the u velocity component is close
to zero. Moreover, if three-dimensional flow structures werepredominant, this would also be manifested in an increase of
the values of CRN, whose values however, in this case, remain
moderate.
All the aforementioned analysis, indicates that one mightseek the reason for this discrepancy between the CFD and PIV
velocities in the low CFD spatial resolution, since it is probably inadequate to capture the complex physics of the flow
behind a bluff body such as the cube.

(a) ε (%)(b) CPexp and CP

In Figure 11a, a relatively small range of pressure can beobserved, namely about 2 Pa, indicating that the pressure is
generally constant in the wake of the cube, as expected, due
to flow separation. Two lobe-like structures with a pressure
difference equal to the pressure range, are located close to eachother on the downstream boundary of the domain, which areprobably caused by the inadequacy of the Neumann boundary
conditions that are imposed on this area.
Unlike the results shown for plane A and B, the comparison between CPexp (purple points) and CP (green line) reveals
a significant discrepancy between computational results andmeasurements. It has to be clarified that the most probable reasons are: (i) the reference pressure is not exactly the same as
the experimental reference one, which was outside the experimental domain available here, (ii) CP is calculated at a distanceof approximately 1 cm and not exactly on the downstream wall(iii) numerical and experimental errors and (iv) 3D effects.
The mean value of the difference ∆CP = CPexp −CP for every measurement point, is found to be equal to ∆CP = −0.3043
while its standard deviation in CP units is equal to 0.0197, results that correspond to 1.8 Pa and 0.12 Pa respectively (thedynamic pressure is once again equal to 5.99 Pa). Based on
the aforementioned results, it can be contended that the discrepancy between the two CP profiles has similar properties toa systematic error/bias, most probably corresponding to a difference between the experimental and computational reference
pressures.
The blue line, shown in Figure 11b, is produced by adding∆CP = −0.3043 to the CFD-calculated pressure coefficient.
The measurements almost coincide with the corrected pressure coefficient, with the maximum value of the relative error,∆CP /CPexp , derived about 7 %.
Generally, the results regarding plane C for the examinedcase where the apertures are open, demonstrate a larger, probably aberrant, velocity correction as well as a higher discrepancy between the experimental and CFD CP profiles, in comparison with the results extracted for the case where the appertures are closed (Pallas and Bouris, 2022).

(b) CRN (%)

Figure 10. Contours of: (a) the non-dimensional error between the
CFD total velocity, ut,CFD , and the PIV one, ut,PIV , on plane C, (b) the
non-dimensional continuity residual derived by the discretised continuity equation, CRN, on plane C. X and Y are non-dimensional coordinates, whereas the thick black line denotes the downstream boundaryof the cube. Flow is from left to right.

CONCLUSIONS
Two-dimensional time-averaged PIV velocity fields alongwith PIV statistics have been integrated in a code based on the512th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
(Duraisamy et.al., 2019).

SIMPLE algorithm, and attempt is made to apply the methodology to three different data sets lying on the upstream, downstream and roof plane of symmetry, respectively, for the caseof turbulent flow around a surface-mounted cube, with upstream and downstream face vertical openings. The extractionof the respective pressure fields as well as the correction of the
PIV velocity fields in order to satisfy the continuity equation
are undertaken, whereas no model of turbulence is necessary,
since the closure of the equations is accomplished by directcomputation of the Reynolds Stresses, using the PIV statistics.
Profiles of the pressure coefficient near the upstream,
roof and downstream solid boundaries, calculated by the CFD
method, are compared with experimentally derived CP profiles, revealing that in most cases, the proposed approach is capable of producing reliable and physically consistent results.
Although the implementation of the approach to a more
complex case than in Pallas and Bouris (2022) and in three regions of the flow with different inherent physics does prove toa certain extent its flexibility and universality, several major issues remain, such as the availability of the experimental data,
the PIV temporal and spatial resolution as well as the CFD
spatial resolution, the uncertainties in the data and finally, thetwo-dimensionality assumption of the flow.
A prerequisite for the application of the developed approach, is the existence of PIV measurement data, which is
not always feasible, but even when a PIV experiment can be
carried out, optical access problems (predominant for casesof complex geometry) as well as limitations linked to the resolved PIV length/time scales can deteriorate the quality of
the results. The PIV-resolved length/time scales (and the respective frequencies) do not constitute an important limiting
factor, whenever the spatial PIV and CFD resolution are similar, since the CFD solution is not expected to resolve sub-PIV
length/time scales.
As seen in the presented results and especially for plane
C, the spatial PIV/CFD resolution is not always adequate tocapture complex physics of the flow in regions of steep gradients, e.g., the upstream corner or the wake of the cube. This
problem may be attenuated by applying interpolation of the
PIV data to a finer grid and/or by implementing CFD local
grid refinement techniques.
Finally, it should be noted that the violation of the assumption of two-dimensionality of the flow, can degrade thequality of the extracted results. The SIMPLE algorithm isbased on the solution of a pressure correction equation whichis strongly coupled with the continuity/mass residual throughits source terms. Owing to the non-inclusion of the third velocity component, w, it can be contended that the appearanceof three-dimensional flow structures can jeopardise the credibility of the the proposed approach, since they could lead toincreased values of the initial PIV continuity residual.
To conclude, the proposed method, in most cases, yielded
reliable and physically consistent results, showing the potential of performing adequately for different conditions and different intrinsic flow physics. Although several issues remain,
this attempt shows promise as a complementary source of information for experimental measurements, as a source of correction for numerical simulations and/or as a possible benchmark for numerical model development. More specifically, thefact that PIV-calculated Reynolds stresses are introduced in thesource terms of the RANS equations, overcomes any assumptions inherent in a turbulence model, and possibly leads tobetter compliance of the CFD solution to the inherent physics
of the flow, since turbulence models are usually calibrated inorder to be consistent in the prediction of fundamental flows

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