In a dishwasher or washing machine, performance is a combination of four variables: temperature, chemistry, time and mechanical action. The side the design can control, and where analysis contributes directly, is the mechanical action.
Dishwasher: the spray coverage
Jets from rotating arms strike the surfaces and dislodge soil. The critical question is which surfaces stay under a jet, and for how long.
The difficulties:
- Shadowing. A plate in front blocks the one behind. Basket geometry and loading pattern are therefore part of the performance.
- Arm rotation speed. A slower arm dwells longer at each point but completes its revolution later. The optimum is in between.
- Hole pattern. The number, diameter and angle of the holes set both the flow rate and the impact intensity. More holes means less energy per jet.
- Water temperature and foam. Affect whether the jet disperses before reaching the target.
A jet striking a surface is directly an impinging jet problem — with shear stress sought instead of heat transfer.
Washing machine: a different mechanism
Here cleaning comes not from jets but from the laundry being lifted and dropped by the drum, and from detergent solution passing through the fabric. The analytical question is more about wetting uniformity and water circulation: is all the laundry wetted equally, does the detergent reach everywhere?
The laundry mass is a porous medium that resists the flow and retains water; as the load fraction rises the circulation becomes harder and performance falls.
Modelling
Both problems involve a free surface and are transient. See the multiphase note. The rotating arm and drum require a moving boundary approach.
The output sought is not a single number but a coverage map accumulated over the surfaces: the total mechanical action each surface receives through the cycle.
References
- Hirt, C. W. & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201–225. DOI: 10.1016/0021-9991(81)90145-5
- Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48(2), 89–94.