UFR 4-18 Test Case

Flow and heat transfer in a pin-fin array

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Test Case Study

Brief Description of the Study Test Case

This should:

• Convey the general set up of the test-case configuration( e.g. airflow over a bump on the floor of a wind tunnel)
• Describe the geometry, illustrated with a sketch
• Specify the flow parameters which define the flow regime (e.g. Reynolds number, Rayleigh number, angle of incidence etc.)
• Give the principal measured quantities (i.e. assessment quantities) by which the success or failure of CFD calculations are to be judged. These quantities should include global parameters but also the distributions of mean and turbulence quantities.

The description can be kept fairly short if a link can be made to a data base where details are given. For other cases a more detailed, fully self-contained description should be provided.

General Description

The experiments from Ames et al. deal with the flow of air around 8 staggered rows of 7.5 heated pins, spaced at P=2.5D in both stream-wise and span-wise directions (based on center to center distances). The diameter of the pins is set to 0.0254 m (1 inch) and the channel height is twice the diameter (H=2D). The Reynolds numbers $Re_{D}$ based on the pin diameter and the average gap bulk velocity which have been tested are equal to 3,000, 10,000 and 30,000, respectively. The gap bulk velocity is determined between two adjacent pins of the same row. Taking $V_{0}$ and $V_{BG}$ as the inlet and gap velocities, respectively, and considering mass conservation, one obtains $V_{BG}=P/(P-D)V_{0}$.

A sketch of the original experimental configuration is given in Figure 1. In the experiment, the distance between the inlet (beginning of the test section; end of a converging nozzle) and the center of the first cylinders is equal to 7.75D. The distance between the center of the last cylinders and the test section is also equal to 7.75D.

The bottom wall is heated with a constant heat-flux whereas the other walls are adiabatic (Ames et al.). All the flow properties can be taken constant, the Prantl number is equal to 0.71.

Figure 1: Sketch of Ames et al. experiment

The principal measured quantities

All 1-D profiles are drawn along lines A1, B & C (see ). The main lines for the velocity components and the Reynolds stresses are A1 and B and the main one for the pressure coefficient is C (mid-span location).

The exact positions of the lines are the folowing :

• A1- Line at mid-span location (Y/D=5/4 from center of the pin or Y/D=3/4 from surface of the pin) between two adjacent pins of the same row along the channel height (Z-axis) for every row.
• B - Surface to surface line between two adjacent pins of the same row at mid height (Z/D=1.0) along the span (Y-axis).
• C - Circumferential line around the pin surface from 00-1800, at mid height of the pin (Z/D=1.0). Angle measurements are taken to be zero (00) on the leading edge of the pins with a counter-clockwise orientation.

Data will be shown for sevral rows mainly X/D=LU (row 1), X/D=LU+2.5 (row 2), X/D=LU+5.0 (row 3), and X/D=LU+10.5 (row 5).

When the wall heat flux $q_{w}$ is imposed, the Nussel number is given by $Nu=q_{w}/(\lambda (T_{w}-T_{ref})/D)$ where $T_{w}$ and $T_{ref}$ are respectively the temperature at the wall and a reference temperature and $\lambda$ the thermal conductivity. $T_{ref}$ is the increase of the temperature between the inlet and outlet of a pattern assuming that a statistically periodic flow is established. After integrating the energy equation using its conservative form (here the temperature equation), one obtains : Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle T_{ref} = q_{w}((P/D)^2-Π/2)D^2/(\rho C_p V_{BG}H(P-D))} .

When the wall temperature $T_{w}$ is imposed, the Nussel number is given by $Nu=D{\frac {\partial T}{\partial n}}/(T_{w}-T_{ref})$ where ${\frac {\partial T}{\partial n}}$ is the wall normal temperature gradient.

Mandatory data for quantative comparisons

For all the cases, the following data need to be provided for every row (one can download experimental ASCII and Grace files on the TWiki (click on the link and download the file Exp_txt_grace.zip in the attachment table)). 0. The so called friction factor or headloss coefficient f =ΔP/(2 ρ V2BG N row ) where ΔP is the pressure drop between the planes X/D=LU-5 and X/D=LU+22.5 et N row the number of rows ( N row=8 for the present case. 1. Pressure Coefficient along line C for all rows: CP =2(P-Pmax)/ ρ V2BG where Pmax is the maximum pressure (at the stagnation point) 2. The mean stream-wise velocity profiles (U/VBG), mean cross-span velocity (V/VBG ), their r.m.s counterparts u'/V BG and v'/V BG respectively, w'/V BG and u'v'/ V2BG along lines A1, A2, A3 and B. 3. Nuav, the average of the Nusselt Coefficient on the bottom wall (specify the part of the bottom wall used for the averaging) or for every row when the pins are heated. 4. The Strouhal number(s) computed using either the time history of the lift coefficient (see below) or the stream-wise time history of a probe that “sees” the vortex shedding. If freq is an energetic frequency, the Strouhal number is St=freqD/ VBG 5. Nu/ Nuav along the lines y=0, y=P/4, y=P/2 on the bottom plate ( z=0) or along C when the pins are heated. When the pins are heated one can also provide Nu/ Re1/2D,VBG. 6. Turbulence intensity evolution in each direction ( u'/V BG , v'/V BG and w'/V BG ) as a fonction of the row. For every row, the definition of the turbulence intensity is : the average of the non-dimensional r.m.s. value over the 9 points shown in figure 2 taken from [2] (for every row, the points are in the plane containing the axis of two adjacent cylinders).

Optional data for quantative comparisons

The following data are not mandatory but the test-case coordinator highly recommend the participants to provide this set of data even if it is not complete. 1. The effective velocity for every row as described in [2]; if x stands for the distance from the stagnation point along the cylinder surfrace (if θ is the angle, x = θΠ/180*D/2 ), one has U(x)=3.63 Veff x/D where U(x) = (2(P(x)-Pmax )/ρ)^0.5. 2. u'w'/ V2BG and v'w'/ V2BG along lines A1 and B. 3. Lift and Drag coefficients CD and CL and their r.m.s. values for every row (or the time history of CD and CL ). Two coefficients may be given (we consider only the coefficients due to the pressure load): a. The one for the whole tube, for example, for the lift, one has CL = 2 ∫tube p/(ρ V2BG Π D H) where p is the pressure. b. If the disretization allows it (structured grid for example), the one obtained over the closest ring to line C (a ring is here a surface mesh which surround the tube). If dh stands for the height of the ring, one has CL = 2 ∫ ring p/( ρ V2BG Π D dh). 4. The mean and r.m.s. values of the temperature along lines A1, B’, B’’, B’’’ and B’’’’ (T/Tref and T’/Tref)._ If the center of the tube is the origin of a local frame, line B is at x=0 and z=0,05D (B’ is parallel to line B but at a distance of 0.05D from the bottom wall), B’’ at x=P/4 and z=0.05D, B’’’ at x=P/4 and z=0.05D and B’’’’ at x=3P/4 and z=0.05D. 5. The mean turbulent heat fluxes along lines A1, B’, B’’, B’’’ and B’’’’ and B ( u’T’/ (VBGTref) , v’T’/ (VBGTref) and w’T’/ (VBGTref)).

Qualitative Comparisons (figures)

The following figures are highly recommended, they contribute to a better understanding of the underlying physics. Mandatory qualitative comparisons 1. Mean velocity streamlines and/or vector, U/VBG, V/VBG, u'/VBG, v'/VBG, w'/VBG, u'v'/V2BG,(2/3k)^0.5/VBG on XY planes Z/D=1 and Z/D=0.05. For all the cases, the bounds have to respect the examples given in Figure 5 to Figure 11. 2. The projection of the mean velocity vectors on the planes shown in Figures 12 and 13 for all the rows. The first one allows to understand the dynamics of the flow upstream the pins (the horseshoe vortex, the other secondary motions, …) and the second one the mean recirculations downstream the cylinders. 3. Nu/Nuav on the bottom plate when it is heated as shown in [6] (see figures 14 and 15). For this point please respect the lower and upper bounds. Nu/Nuav on the pins when they are heated (here the average is computed using the whole pin surface), see figure 16 (the cylinder surface is projected on a plane)

Optional qualitative comparisons 1. The non dimensional pressure (Cp) on the bottom wall around the pins for all the rows as it was done in [4] (see figure 17). 2. 3-D views showing iso-Q in order to show the main structures. 3. The mean temperature T/Tref, its r.m.s value T’/Tref, the turbulent heat fluxes u’T’/ (VBGTref) , v’T’/ (VBGTref) and w’T’/ (VBGTref) on XY planes Z/D=1 and Z/D=0.05.

Figure 2 :' Rows numbering and lines (A1, B and C) locations

Test Case Experiments

Provide a brief description of the test facility, together with the measurement techniques used. Indicate what quantities were measured and where.

Discuss the quality of the data and the accuracy of the measurements. It is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However, it should seek to address:

• How close is the flow to the target/design flow (e.g. if the flow is supposed to be two-dimensional, how well is this condition satisfied)?

• Estimation of the accuracy of measured quantities arising from given measurement technique

• Checks on global conservation of physically conserved quantities, momentum, energy etc.

• Consistency in the measurements of different quantities.

Discuss how well conditions at boundaries of the flow such as inflow, outflow, walls, far fields, free surface are provided or could be reasonably estimated in order to facilitate CFD calculations

General Description

The description given in the present section has been given by F. Ames during the $15^{th}$ Ercoftac SIG15 Workshop. More information could also be found in Ames et al. (2004, 2005, 2006, 2007). The objective of the experiments was to create a database that includes heat transfer distributions on the pin fins and endwall, pressure distributions on the pin fins and endwall, documentation of turbulence intensities and scales, and measurements of turbulence and velocity distributions across the channels. The research was conducted in a small bench top wind tunnel (see Figure 2) which included a small blower capable of producing a flow of $0.3m^{3}/s$ at a static pressure rise of 2000 Pa. The pin fin array was designed in an 8 row, 7 1/2 pin per row staggered arrangement. Both the cross passage (S/D) and stream-wise (X/D) pin spacing were equal to 2.5 while the pin height to diameter (H/D) was 2. The pin diameter was chosen to be equal to 2.54 cm. The flow conditioning system first spreads out the flow from the blower to the width of the array using a two-stage multi-vane diffuser. A heat exchanger was installed in the system downstream from the diffuser to control the tunnel temperature in order to impose a constant value. The heat exchanger discharges the flow into a screen box consisting of three nylon window screens to reduce the cross stream velocity variations in the flow. Directly downstream of the screens, the flow enters a smooth 2.5 to 1 area ratio nozzle prior to entering the test section. The pin fin array test section begins 7.75 D upstream of the centerline of the first row of pins and ended 7.75 D downstream of the centerline of the last row of pins. The inlet total temperature and pressure and static pressures were measured 5 D upstream from the row 1 centerline and the exit static pressures were measured 5 D downstream from row 8. Downstream from the test section the flow was directed through a 90° rectangular elbow then a rectangular channel followed by a second 90° elbow before entering a 20.8 cm diameter orifice tube used to measure the array flow rate. Tests were conducted at three Reynolds numbers : 3 000, 10 000, and 30 000. The Reynolds number is based on the maximum velocity (also called the gap velocity $V_{G}$, see the previous section). Fluid properties were determined from the inlet conditions.

The remaining description will focus on the data which are used in the present work, the heat transfer on the pins, the pressure distributions on the endwalls, availabe spectra ... are not included.

Figure 2: Sketch of Ames et al. experimental rig (image taken from Ames et al. (2007))

Pin fin surface static pressure

The pins were fabricated from clear acrylic. The midspan surface static pressure distributions were acquired using a 2.54 cm diameter pin which contained 20 equally spaced 0.76 mm static pressure taps around the midspan perimeter. Measurements were made in 6° increments by indexing the pin. An example of pressure distribution is given in figure 3.

Figure 3 : Midline pressure coefficient distribution, row 1-5, Re=10 0000 (image taken from Ames et al. (2005))

Pin fin array turbulence and velocity measurements

Array turbulence and velocity measurements were acquired using single and X wire hotwire probes powered by a TSI IFA 300 constant temperature anemometry unit. A special low velocity jet was developed to calibrate the wires from 0.4 m/s through 40 m/s to enable measurements of turbulence and velocity distributions over a 10 to 1 range in Reynolds number. An example of profile obtained along the line B1 for row 5 is given in figure 4

Figure 4 : Mean and r.m.s. stream-wise velocity component along line B for different Reynolds numbers - row 5 (image taken from Ames et al. (2006))

Endwall heat transfer measurements

Full surface endwall heat transfer measurements were acquired using a constant heat flux test surface and a FLIR SC500 IR camera. A constant surface heat flux boundary condition was generated using three, 15.28 cm wide by 68.58 cm long, 0.023 mm thick Inconel foils with 0.127 mm thick Kapton backing and 0.05 mm thick acrylic adhesive. The three foils were adhered to a 0.89 mm thick sheet of fiberglass epoxy board which in turn was epoxied to a 3.81 cm thick section of isocyanurate foam. The three foils were connected in series. The current through the foil and the voltage across the center foil was used to determine the surface heat flux. The surface heat flux was corrected for both local radiation and conduction loss. The radiation loss assumed the emissivity of the surface was 0.96 and the conduction loss was based on a simple 1-D model. The camera was equipped with a special lens which allowed a much wider angle (45°) and a much closer focal plane (6.35 cm) than the tandard lens. This allowed the camera to acquire a 130 by 260 pixel image (3.175 cm by 6.35 cm) through a 5.08 cm diameter zinc selenide window. At each measurement location, the camera location was indexed on the pins to ensure a consistent camera location for all the measurements. The accuracy of the surface temperature measurement was enhanced by the calibration of the camera on a calibration surface through the same zinc selenide window, the manual resetting of the camera every three or four pictures, and the averaging of 9 images for each heat transfer realization. The driving force temperature difference was calculated as heated endwall surface temperature corrected for the inlet temperature during the test and for the local calibration less the unheated endwall surface temperature corrected for the inlet temperature and the local calibration. The temperature difference also accounted for the bulk temperature rise of the air due to endwall heating.

Figure 5 : The normalized Nusselt number for different Reynolds numbers (image taken from Ames et al. (2007))

Data uncertainties

Uncertainties in the reported values were estimated based on the root sum square method described by Moffat (1988). The uncertainty in the reported Reynolds number was determined to be +/- 3% due to the possible error in the flow rate measurement. The largest uncertainty for the midspan pressure coefficient was estimated to be +/- 0.075 due to the very low dynamic pressure at the low Reynolds number condition (Re = 3 000). However, the uncertainty in the pressure coefficient was no more than +/- 0.025 at the higher two Reynolds numbers. Uncertainty in the measurement of velocity using a hot wire was estimated to be +/- 3% except in the near wall region where positional and conduction effects could substantially increase the possible error. Additionally, at high turbulence levels single wire velocities can be significantly overestimated if traverse fluctuation velocities, normal to the wire become high. For example at 30% intensity levels velocities can be overestimated by 4%. The reported value of turbulence intensity had an uncertainty of approximately +/- 3%. The reported uncertainties in Nusselt number are estimated to be as high at +/- 12%, +/-11.4%, and +/-10.5% for the 3 000, 10 000, and 30 000 Reynolds numbers respectively in the endwall regions adjacent to the pins and +/- 9% away from the pin. Note that the combination of several methods reduced the uncertainty band of the surface temperature measurement from about +/-2 °C to about +/- 0.7 °C. Uncertainty estimates were determined using a 95% confidence interval.

CFD Methods

Provide an overview of the methods used to analyze the test case. This should describe the codes employed together with the turbulence/physical models examined; the models need not be described in detail if good references are available but the treatment used at the walls should explained. Comment on how well the boundary conditions used replicate the conditions in the test rig, e.g. inflow conditions based on measured data at the rig measurement station or reconstructed based on well-defined estimates and assumptions.

Discuss the quality and accuracy of the CFD calculations. As before, it is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However the following points should be addressed:

• What numerical procedures were used (discretisation scheme and solver)?

• What grid resolution was used? Were grid sensitivity studies carried out?

• Did any of the analyses check or demonstrate numerical accuracy?

• Were sensitivity tests carried out to explore the effect of uncertainties in boundary conditions?

• If separate calculations of the assessment parameters using the same physical model have been performed and reported, do they agree with one another?

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Contributed by: Sofiane Benhamadouche — EDF

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