Best Practice Advice AC3-01
Buoyancy-opposed wall jet
Application Challenge 3-01 © copyright ERCOFTAC 2004
Best Practice Advice for the AC
Key Fluid Physics
The key fluid physics and flow regimes which influence the design or assessment parameters (the jet spreading rate and the jet penetration depth) for this AC are:
- the jet Reynolds number
- the ratio of the background (upward) flow velocity to the jet (downward) flow velocity
- the buoyancy of the jet flow relative to the background flow, and
- near-wall flow effects
Underlying flow regime (UFR) documentation that has been consulted when preparing this best practice advice (BPA) includes:
- the confined buoyant plume (UFR4-09)
- natural and mixed convection boundary layers on vertical heated walls (UFR3-07)
The plane wall jet (UFR3-10) is also relevant, but the D32 for this UFR was not available at the time of preparation of this D34. With regard to the confined buoyant plume (UFR4-09), there are significant differences in the flow physics relative to this AC which means that best practice advice for the UFR is not directly applicable (see section below on physical modelling). It is also worth noting that an attempt to prepare a UFR document for a plane wall jet in a counter-current flow was unsuccessful due to the lack of experimental and CFD results, apart from those reported in this AC. This is another indication that most of the BPA for this AC has to come from the AC itself, together with the underlying research work that has been continuing in parallel with the QNET-CFD project for a number of years.
It should also be noted that the following Best Practice Advice is specific to this AC.
This is a deceptively simple flow which presents a substantially greater challenge to CFD modelling than might at first appear. The experiments and associated modelling have revealed several areas where application uncertainties exist, for example:
- The flow is fairly unsteady with large velocity and temperature fluctuations, particularly when buoyancy effects are small.
- The background upward flow has only about two channel widths to develop before meeting the downward-flowing jet. Hence conditioning of the inlet flow in the experiments and the choice of inlet values for this flow in the modelling may be important.
- Due to practical limitations, measurements were not made at either the background flow or wall jet flow inlets, or very close to the wall itself. There are therefore no data against which CFD calculations can be compared in these important regions.
- The potential significance of 3D effects has to be recognized. This relates not only to 2D modelling of a 3D experiment (i.e. end wall effects), but also to the fluctuating 3D effects, revealed by the large eddy simulation (LES) calculations, which would occur even if the experimental test rig was infinitely wide.
The net effect of these uncertainties on the experimental DOAP evaluation is fairly small provided appropriate precautions are taken, e.g. comparison of integrated velocity profile data with overall rig flow rate measurements, sampling at measurement locations for long enough to obtain appropriate time-average results, etc.
Likewise, the DOAP predictions should not be unduly sensitive to these uncertainties as long as some care is taken over the choice of boundary condition values, e.g. matching the velocity and turbulence values at the background flow inlet, and performing a separate calculation for the wall jet to define its flow parameters at inlet to the main test section.
Computational Domain and Boundary Conditions
- 2D idealisation of this AC can provide reasonably realistic results and is computationally efficient when comparing different calculational methods. However, this idealisation over-constrains the flow as in 2D the background flow and jet flow cannot pass one another in the third dimension, artificially increasing the overall pressure drop and probably also having some influence on the DOAPs. As noted in the previous section, 3D effects may be important to obtain accurate DOAP predictions and any further work (see below) should seek to assess the importance of these.
- The primary computational domain for this AC (i.e. excluding the wall jet inlet section) needs to extend horizontally for the full width of the test section. Vertically, the extent required is dependent on whether the flow is isothermal or non-isothermal. For isothermal flows, it should extend from the background flow inlet (1.3m below the bottom of the splitter plate) to at least 0.4m above the bottom of the splitter plate. For non-isothermal flows, the vertical extent below the splitter plate may be reduced (e.g. to 0.6m), but the extent above the splitter may need to be increased (e.g. to 2.4m) to avoid inadvertent inflow at the exit boundary. The wall jet development section needs to be extended sufficiently far above the bottom of the splitter plate (e.g. to about 50 jet widths or 0.9m above the bottom of the splitter plate) to generate a fully-developed profile at the wall jet outlet. Alternatively, a separate calculation of the developing profile of the jet should be performed and the resulting profiles applied at the jet outlet.
- With regard to boundary conditions, the advice is as follows:
- Background flow inlet: reasonable predictions can be obtained with ‘top hat’ velocity, turbulence and temperature profiles. The results are not sensitive to the inlet turbulence levels, as described in the section on CFD simulations for this AC.
- Wall jet flow: as noted above, fully-developed velocity and turbulence profiles are required at the jet outlet, with a constant specified temperature.
- Outlet: there are no special requirements for modelling the flow outlet (e.g. zero gradient boundary condition will suffice), but the representation and location should avoid inadvertent inflow.
- Walls: satisfactory results are unlikely to be achieved on this AC using standard wall functions. Either more sophisticated wall function models or a low Reynolds number formulation are needed (see below) which reduce or eliminate the dependency on the near-wall mesh size. For accurate modelling, consideration should also be given to heat losses from the outside walls of the test rig (these were not completely adiabatic, even for the nominally isothermal test cases).
Discretisation and Grid Resolution
- Calculations to date on this AC have employed the QUICK scheme for solving the convective transport equations for mean quantities, but with a first order upwind scheme for the turbulence equations. The SIMPLE pressure coupling algorithm has been used.
- The horizontal grid size required for this AC is dependent on whether a low Reynolds number or other type of near-wall turbulence model is being used, with finer meshes being required for the former. The minimum mesh size used horizontally with the low Reynolds number turbulence model was 103 cells, compared to 75 cells with other models. In the vertical direction, the minimum mesh sizes were either 165 cells for the isothermal cases or 150 cells for the non-isothermal cases.
- These mesh sizes have produced satisfactory results with a near-wall non-dimensional cell size (y*) of 1 near the jet exit using the low Reynolds number turbulence model. If analytic wall functions are used, a near-wall mesh size giving y* values between 65 and 160 near the jet exit should be adequate.
- Various approaches to modelling turbulence and the near-wall region have been used in the analysis of the AC, and significantly different results can be obtained with different approaches.
- Although further work is recommended, the available evidence for isothermal flows is that either a low Reynolds number k-ε turbulence model is required, or an enhanced second moment closure approach should be used (e.g. analytic wall functions in combination with two component limit second moment closure). This is due to the need to resolve the anisotropy in the stress field in order to resolve adequately the velocity field. For non-isothermal flows, reasonable results have been obtained with the low Reynolds number k-ε model, or with the standard k-ε model with analytic wall functions (but see next section).
- The BPA for UFR 4-09 (confined buoyant plume), in which satisfactory results were obtained with both the standard k-ε model and the RNG enhancement are not directly applicable for this AC, mainly due to the significance of wall effects in this AC.
- The recommendations for this AC are compatible to those for UFR3-07 (natural and mixed convection boundary layers on vertical heated walls), in which good results were obtained using either a low Reynolds number k-ε model or a standard model with analytic wall functions.
Recommendations for Future Work
On the basis of the results presented for this AC, further work recommendations are:
- Generate further experimental and computational results for an opposed wall jet UFR, including both isothermal and non-isothermal cases and with a wider range of Reynolds numbers. As already noted, this is a challenging test case for RANS calculations and it therefore provides a useful benchmark for testing turbulence models.
- Apply more advanced (e.g. two component limit second moment closure + algebraic wall function) turbulence models to the non-isothermal cases investigated experimentally.
- Further investigate 3D effects.
Some further work on this AC, in the form of LES modelling of both isothermal and non-isothermal test cases, has already been undertaken at UMIST. The team at UMIST should be consulted for further details on this and associated research work.
© copyright ERCOFTAC 2004
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