Experimental and numerical study of double
5
backward-facing step ow
AFTER demonstrating the development of the mixing JICF in Chapter 4, the current chapter extends the experimental and numerical investigation to a single injector, as outlined by the blue lines in Figure 5.1. Basically, the geometry of a single injector consists of an air guiding gate and graded series of two backward-facing steps: air guiding gate step yAGG and liner step yL. To the best of the author's knowledge, no predictions of ow downstream of consecutive backward-facing steps is reported on in literature. Therefore the chapter is introduced by the description of the ow structure behind a single backward- facing step in Paragraph 5.1. After looking at the experimental set-up in Paragraph 5.2, the double backward-facing step injector ow behavior is addressed in Paragraph 5.3. At rst a scaled up geometry is investigated experimentally and numerically, focusing on ame stabilization and checking up on the previous inow estimations. Subsequently, the eect of step heights is explored and linked up with single backward-facing step observations.
Figure 5.1: Schematic of single injector research approach
93
dimensional (Armaly et al. (1983), Thangam and Knight (1989) and Kaiktsis et al. (1996)).
A schematic of a backward-facing step and associated ow features is shown in Figure 5.2.
The incoming boundary layer (a) separates at the edge (b). The shear layer impinge- ment onto the bottom wall (c), followed by a boundary layer recovery (d), denes the reattachment length xr. Multiple regions of recirculating ow are observed. A primary recirculation region develops adjacent to the step (e). A small corner eddy (f) in the opposite rotation with respect to the primary recirculation ow develops adjacent to the bottom corner where the step and the bottom wall intersect. A roof eddy (g) is found next to the upper wall. The position of the reattachment point is considered the cru- cial feature of this type of ow. It depends primarily on the specic geometry and the uid Reynolds number Re = U s/ν, based on the step height s and the mean upstream velocityU. Available published data (Mouza et al. (2005), Armaly et al. (1983) and Lee and Mateescu (1998)) on the dependence of the reattachment length, normalized with re- spect to the step height, onReis shown in Figure 5.3. It becomes apparent that the ratio xr/sincreases almost linearly withRe, reaches a peak value of approximately 17 and then
Figure 5.2: Schematic of backward-facing step ow features
Figure 5.3: Dependence of the reattachment lengthxronRe(data reproduced from Mouza et al. (2005))
5.2. Set-up and procedure 95
decreases irregularly to reach a value close to 7 at Re≈2000.
5.2 Set-up and procedure
Analogous to the JICF research, the experimental and numerical study were done without combustion in cold ow on the injector geometry scaled up by a factor 33, resulting in an yAGG and yL of 88 mmand 174 mmrespectively.
To allow for a wide range of step heights, the PIV experiments were conducted in a plexiglas channel (92 mmin width,620 mmin height and2300 mmin length). A front and side view photograph of the experimental set-up are produced in Figure 5.4. The steps are formed by movable plexiglas plates covering the downstream section allowing to varyyAGG andyL. The rear wall was covered with black cardboard to reduce background noise. The reader is referred to Paragraph 3.1.2 for the overall description of the experimental facility and technique. In particular, the channel upstream section length ensured developed ow conditions before the abrupt contraction through the air guiding gate. Inow conditions were set to bring about the U∞= 2.5 m/s JICF characteristic free-stream velocity at the jet exit. Concentrating on the ow past a double backward-facing step, and keeping in mind resolution constraints, the jet-free-stream interaction was disregarded. Despite the three-dimensionality of the ow eld, and taking into account measurement equipment characteristics, measurements were limited to 2D-PIV on the centre-plane. The image size in physical dimensions for the large recording planes and close-ups was approximately 500×400 mm and 110×90 mm, yielding a spatial resolution of about 7 mm and 1.5 mm respectively.
For the numerical counterpart, reference is made to Paragraph 4.2 for the general computational method. Grid specically, the mesh was smoothly connected to the JICF grid, and a high density in the regions near the step walls was insured. The time increment was set at5 10−4sand the transient simulation was terminated att= 12.5 s, corresponding approximately to 2.5 ow through times. In contrast to the JICF numerics, the STAR-CD simulation codes and algorithms are exclusively validated by comparison to experiments.
(a) (b)
Figure 5.4: Experimental set-up: (a) front view (b) side view
5.3 Results
5.3.1 Scaled geometry
Dening x and y as the stream-wise and transverse coordinates, U, V-streamlines over- laying the mean stream-wise velocity component U are reproduced in Figure 5.5a. The
(a) (b)
Figure 5.5: Single injector scaled geometry averaged velocity eld; U-velocity and U, V-streamlines:
(a) Overall ow eld; (b) Reattachment close-up
marked discontinuity in the velocity eld near the liner edge results from laser light re- ections. The incoming ow stays attached to the bottom wall, separates at the edge of the liner step, deects upwards and impinges onto the top wall. A primary recirculation zone develops adjacent to the air guiding gate step. A secondary recirculation zone is observed downstream of the liner step, spanning the whole ow domain. The resolution did not allow to draw any conclusion about a corner eddy. The reattachment length was quantied by close-up averagedU-velocity elds (Figure 5.5b). A common concept to characterize the reattachment location is the point where theU-velocity changes its value from positive to negative. To account for wall reections, the criterion was applied5 mm o the ceiling, yielding a xr of 337 mm. Looking into the Reynolds dependence of the reattachment length normalized with respect to the air guiding gate step height returns xr/yAGG= 3.83forRe≈14000. Although lacking in comparative data in this ow regime, the reattachment length is in line with the observations in Figure 5.3 and suggests that in our ow conguration the double backward-facing step behaves like a single backward- facing step with respect to the air guiding gate step height. This supposition is veried in Paragraph 5.3.2 by varying yAGG. As a consequence, the ow behind the liner step is expected to behave free surface separation like. For the combustion computations in Chapter 6, considering the impaction of the ow on the upper wall, the extension of the domain to two single injectors across from each other is indispensable to account for ow interaction.
Distribution of z-vorticity is given in Figure 5.6. As it is clearly seen, the maximum vorticity develops along the separating shear layers, thereby identifying the edge of the liner step, which is identical with the outer border of the turbulent free shear layer, and the inner border of the shear layer as potential ame anchoring locations. A stabilization in the inner border of the shear layer only exists on the condition of recirculating exhaust gases, ensuring continuous ignition in the inner border shear layer. In rst approximation, the primary recirculation zone seems to provide for those conditions. Further evidence of the feasibility of ame anchoring in the inner border of the shear layer is given by the image map in Figure 5.7. The high particle density in the region enclosed by the inner border shear layer indicates free-stream uid recirculating and collecting in the primary recirculation zone. In addition, one notices the ow modulation past the air guiding gate and shear layer roll-up at the inner and outer border.
5.3. Results 97
Figure 5.6: Single injector scaled geometry averagedz-vorticity eld
Figure 5.7: Single injector scaled geometry image map
The numerical study details the ow structures and is used as the basis for their tem- poral evolution. For code validation the measured and predicted U- and V-velocitiesare compared. Unfortunately, as much as 900 PIV recordings did not allow for a converged uctuating velocity eld, making a uctuating velocity eld validation impracticable. The mean velocities resemblance is examined in Figure 5.8 by overlaying measured data by com- puted isolines. In general, the turbulence model is seen to reproduce the measurements rather well. In particular, the reattachment points compare very well.
Beginning, more information about the observed ow structures in Figure 5.7 is given.
Next, their temporal evolution is looked into. In Figure 5.9 instantaneous u-velocity is combined with z-vorticity isosurfaces (+z-vorticity in red and −z-vorticity in blue) and overlaid by u, v-streamlines. First, vortical shedding at the air guiding gate and liner step becomes apparent (A, B). Second, the oscillatingu-velocity and saw-like prole past the air guiding gate arm the ow modulation observed in Figure 5.7. The oscillation is visually enhanced by the streamline bordering the inner shear layer. Third, the−z-vorticity pattern indicates that the incoming boundary layer separates upstream the liner edge step, contrasting with theoretical single backward-facing step ow. The temporal evolution of u-velocity at the air guiding gate, liner step and reattachment zone (C) and its frequency spectra are represented in Figure 5.10. The respective monitoring locations are marked in Figure 5.9. In all positions, the velocity oscillates, while changing of sign, around a mean value (Figures 5.10a, c and e). Besides the signature of vortical activity in points A
(a)
(b)
Figure 5.8: Comparison of mean velocity quantities: (a)U-velocity; (b)V-velocity: LES (lines), Experiments (map)
and B, this indicates that the reattachment aps for and aft with reference to the mean reattachment point. While the peaks in Figures 5.10b and d correspond to the shedding frequencies, no dominant peak is observed in the reattachment zone (Figure 5.10f). This points out that the inner and outer shear layer interact in an unpredictable manner. In Figure 5.10b, the highest peaks around 14.5 and4 Hzare thought to correspond to the air guiding gate contraction prole instability and apping. This supposition is discussed by comparison to ow characteristic Strouhal numbers. For the sharped-edged air guiding gate contraction, aStH = 0.37, based on the exit centre-line mean velocity and gate height is in
Figure 5.9: Single injector scaled geometry instantaneous velocity and vorticity eld: u-velocity,
−z-vorticityisosurface (blue),+z-vorticityisosurface (red) andu, v-streamlines
5.3. Results 99
(a) (b)
(c) (d)
(e) (f)
Figure 5.10: Time evolution and spectra of stream-wise velocity: (a), (b) air guiding gate step (A);
(c), (d) liner step (B); (e), (f) reattachment (C)
excellent agreement with Tsuchiya and Horikoshi (1986), who measured from sharp-edged rectangular nozzles aStH of 0.4. Wall-bounded separation exhibits a shedding normalized Sts=fss/U of approximately 0.130 (Mehrez et al., 2010). For the present backward-facing step, a Sts = 0.137is computed. At the liner step (Figure 5.10d), and in the assumption of an unbounded ow, the frequencyfI of the shear layer instability, when scaled with the boundary layer thickness and shear layer velocity, is proposed to be close to StI = 0.017 (Michalke, 1965). StI at the liner step equals 0.016, associating the vortices with shear layer instability.
To complete the numerical analysis, the air injection contraction coecient, estimated at 0.7 in Chapter 2, needs verication to prove the free-stream velocity set atU∞= 2.5 m/s valid. Figure 5.11 showsU-velocityend views at the air guiding gate exit, entry and150 mm upstream with streamlines on top. While the contraction is best viewed by the streamlines
Figure 5.11: Contraction ratio: averaged end views, air guiding gate exit, entry and x = −150 mm, U-velocityand streamlines
shape, theU-velocityend views demonstrate the uid acceleration through the air guiding gate. The contraction coecient, computed as the ratio of the ideal velocity by the mass ow weighed averaged actual velocity at the air guiding gate exit, is approximately 0.8.
Since the a priori estimation and actual value are only slightly out of line, the impact on the momentum ratio and backward-facing step Reynolds number is insignicant. As such, the dierence in contraction ratio is expected to have no eect on the previous JICF and backward-facing step investigation.
5.3.2 Eect of step heights
Oriented towards optimization, and aware of the air guiding gate step and liner step height as design parameters,yAGGwas varied in the rst place. Afterwards the parametrical study was concisely extended to the liner step height.
Air guiding gate step height
Air guiding gate steps were set at 45, 71, 88, 154, 180, 211, 265 and 343 mm keeping the liner step height at the nominal value. For clarity, the baseline air guiding gate step height is typed in bold face. U-velocity is overlaid by U, V-streamlinesin Figure 5.12 for yAGG = 45, 88 and180 mm. The slight shift in data in Figure 5.12c aroundx= 560 mm originates from separate observation planes brought together. Independent of air guiding gate step height, the baseline ow topology is observed: separation at the edge of the liner step, upwards deection and impingement onto the top wall. On the one hand, the reattachment length xr, with reference to the air guiding gate, is seen to increase with the step height. On the other hand, the size of the primary recirculation region increases both in length and in height with the increase in step height. The reattachment length andRe-dependenceis graphically presented in Figure 5.13. A linear increase with a slope close to 1 is observed in Figure 5.13a. The Re-dependence is given in Figure 5.13b. In contrast to Figure 5.3, to cover theRe-rangedistinctly, thex-axisis scaled logarithmically.
A reattachment length close to 7 at low Re, decaying with increasing Re, corresponds in character to the literature results, arming the behavior as a single backward-facing step with respect to the air guiding gate step height.
Directing the attention to NOxproduction, the residence time in the primary recircula-
5.3. Results 101
(a) (b)
(c)
Figure 5.12: Velocity eld dependence on air guiding gate step height;U-velocityandU, V-streamlines (a)yAGG= 45 mm; (b)yAGG= 88 mm; (c)yAGG= 180 mm
(a) (b)
Figure 5.13: Reattachment length dependence: (a) on air guiding gate step height (b) onRe; comparison to literature
tion zone was gone about. The residence time of particles was considered to be proportional to the recirculation time, calculated along the outer boundary streamline in Figure 5.14a of
(a) (b)
Figure 5.14: Recirculation computational approach: (a)|U|andU, V-streamline; (b)+z-vorticityand U, V-streamlines
the zone comprising+z-vorticity in the region delimited by the collection of points where the U-velocity component switches from negative to positive (Figure 5.14b). The circu- lation time is shown in Table 5.1. As withxr, a linear growth with air guiding gate step height shows up. Having identied the inner shear layer as potential ame stabilization region, and in the assumption of high temperature in the primary recirculation zone, an increase in air guiding gate step height would result in NOx emissions step-up.
Table 5.1: Recirculation time dependence on air guiding gate step height
Air guiding gate step height, mm 45 88 180 265 343 Recirculation time, s 0.28 0.44 0.79 0.97 1.2
Liner step height
In his master thesis, Boonen (2010) put together air guiding gate step heightsyAGG = 71, 88 and154 mmwith liner step heights reaching from yL= 39to 164 mmwith intervals of 25 mm. In Figure 5.15 the ow behavior for the design scaled geometry is shown. Bringing in relation the ow pattern to the ratio of the liner step to the air guiding gate step height, he observed no relocation of the reattachment point down to yL/yAGG ratios of 1, as evidenced by comparing Figures 5.15a and b, corroborating again that the double backward-facing step at design conditions acts like a single backward-facing step, scaling with the air guiding gate step height. A further decrease revealed an unexpected down and back up clipping of the ow eld (Figures 5.15c and d). Beyond the scope of his thesis, at this time, the analysis was kept at a descriptive level.
To clear up this stream behavior, the ow over the double backward-facing step was reconsidered by looking into the modication of the separation phenomenon of the uid at the edge of the liner step by the periodic perturbation induced by the air guiding gate step (Figures 5.9 and 5.10b). Mehrez et al. (2010) investigated the active control of ow behind a backward-facing step by using a periodic perturbation. They found that the shedding process is signicantly modied by the perturbation amplitude and frequency. Figure 5.16 shows the variations of the Strouhal number of vortical shedding Sts as a function of Strouhal number of perturbationStp for various normalized perturbation amplitudesA/U
5.3. Results 103
(a) (b)
(c) (d)
Figure 5.15: Velocity eld dependence on air guiding gate step height and liner step height ratio:
yAGG = 88 mm: (a)yL/yAGG = 1.98(b)yL/yAGG= 1.30; (c)yL/yAGG= 0.68; (d)yL/yAGG= 0.44
and Re = 33000. The Strouhal numbers Stp = fps/U are dened by the step height, the mean velocity at step height and the perturbation frequency. A peak in shedding frequency is observed at Stp ≈0.25. At this so called optimum, the vortical structures become more intense and organized, leading to a reduction in reattachment length and recirculation zone size. The modications of the ow dynamics are more pronounced as the perturbation amplitude increases. With respect to Re, the peak zone is reported to
Figure 5.16: Strouhal number of vortical shedding frequency against Strouhal number of perturbation for various perturbation amplitudes (data reproduced from Mehrez et al. (2010))
dependence, the following mechanism is proposed. Initially, the outer shear layer behaves like a free shear layer. Bringing down the liner step height, and accordinglyStp, shifts the perturbation towards the preferred mode. The liner step starts dominating the air guiding gate step and the ow is forced down. Further decreasing the step height reducesStp and consequentlySts. The ow is once again driven by the air guiding gate step and the ow aps up. The periodic perturbation by the air guiding gate combined with the liner step height is retained as ow controlling.
Table 5.2: Strouhal number of perturbation against liner step height: yAGG= 88 mm
Liner step height, mm 174 114 64 39
Strouhal number of perturbation 0.96 0.64 0.35 0.21
Reynolds number 30000 19000 11000 6500
5.4 Intermediate conclusions
The injector characteristic double backward-facing step design was experimentally and nu- merically investigated by PIV measurements on a scaled geometry. A ow behavior similar to a single backward-facing step with respect to the air guiding gate step height showed up.
The ow impinging on the upper wall and primary recirculation zone connement demon- strated the need to extend the computational domain for the combustion simulations to a pair of opposite injectors to allow for ow interaction. Putting together the measurements and computations, validated by comparison to experiment, permitted to identify the inner and outer ow shear layer as potential ame anchoring locations. The inow condition estimate was formalized by comparing the approximate and actual contraction coecient through the air guiding gate. Extending the investigations towards varying step heights gave insight into double backward-facing step parametric ow behavior. On the one hand, at design scaled geometry liner step height, the ow behaves single backward-facing step like,Re-dependentwith the air guiding gate step height. An increase in step height results in a downstream displacement of the reattachment point, growth in recirculation zone size and larger residence time. As a consequence, in the event of a ame stabilization in the inner shear layer, higher NOx emissions are to be expected with larger air guiding gate steps. On the other hand, at design scaled geometry air guiding gate step height, the ow appears to be dependent on the periodic perturbation arising from the air guiding gate and liner step height. Their interrelation leads to an alternate upward and downward apping.
