Manufacturers often assume that the quickest way to reduce dishwasher energy use is to use new and relatively untested motor technologies. Unfortunately, they almost always come with larger price tags, increased complexity, numerous failure modes, and higher electromagnetic emissions from additional electronics. Choosing a new motor may give a 10 to 20% increase in electrical efficiency, but it does nothing to reduce the amount of shaft power required to drive the circulation pump or the noise generated by the pump. The motor itself may or may not be any quieter (from reduced torque pulsations), depending on the design.
By optimizing the dishwasher's wash system hydraulics, engineers can fundamentally reduce energy use, noise, and heat rise, regardless of what motor is used. Unlike upgrading the motor, improving the hydraulic efficiency can actually reduce cost while providing many benefits.
Overview of Dishwasher Mechanisms
Before analyzing the hydraulics, it will be useful to discuss the mechanisms at work in a typical dishwasher. Several processes work together to clean dishes during the typical wash cycle. The most obvious is the mechanical impulse of the jets of water from the sprayarms directly impacting the food soil and knocking it off the dishes.
Figure 1. Dishwasher diagram.


Another vital mechanism is the combined effect of saturating the food soil with a hot detergent and water solution. The action of the hot water and detergent continually wetting the dishes eventually brings the dishes and food to the same temperature as the water. After some time, the food soil becomes saturated, expands, and then finally loosens or becomes easier to remove with the mechanical action of the spray jets.
It is important to note that the process of wetting dishes and food soil and raising the temperature is only loosely dependent on continual direct hits from highpressure jets. Over time, wash water deflected off other dishes, obstacles, or the interior of the dishwasher tub is almost as effective at wetting and heating the food soil as direct hits of water from sprayarm jets. The main performance benefit of having high flow rate and pressure (power) from the sprayarm jets is removing the last bits of food. Because of this, having only one sprayarm in operation at a time does relatively little, if anything, to decrease the overall wash performance. In practice, the wash performance of an alternatingarm system and a simultaneousarm system tend to converge fairly rapidly. Therefore, a welldesigned alternatingarm system does not need to operate much, if any, longer than a system that operates both sprayarms at the same time.
Figure 2. Alternating sprayarm system (before modifications).


The third key mechanism at work is the dilution ratio. Dishwasher wash cycles are divided into phases of differing lengths, each preceded with a fresh water fill. During the circulation phase, food soil is removed from the dishes and becomes dissolved or suspended in the wash water. After the wash water has been circulated though the system numerous times, the soilladen water is drained at the end of the phase. At the end of the drainage, there is always a small amount of wash water left in the bottom of the sump, along with wash water that coats the interior of the tub and the dishes. This dirty wash water left in the sump and coating the interior of the dishwasher is called carryover water. The dishwasher's dilution ratio is the ratio of carryover water divided by the volume of fresh fill water added at the beginning of each phase raised to the power of the number of wash phases. The higher the dilution ratio, the cleaner the wash water will be, and, therefore, there will be less food soil redeposited on the dishes.
There are several ways to increase the dilution ratio. One is by designing the drainage system to leave as little carryover water in the sump as possible. While this is an energyefficient way of increasing the dilution ratio, there is little that can be done about the wash water coating the dishes and the interior of the tub. This tends to set a lower limit on the reduction of carryover water. Another way is to increase the number of fills, but this method significantly increases water and energy use. A third method is to increase the volume of fill water at the beginning of each wash phase. Once again, this method is not energy or waterefficient.
Figure 3. Alternating sprayarm system (after modifications).


A fourth method is filtering the wash water. Technically, it does not reduce the dilution ratio as defined, but it removes much more food soil earlier in the wash cycle than can be simply dissolved or suspended in the wash water and then pumped down the drain at the end of each cycle. Filtering the water is an effective and energyefficient way of increasing the performance without adding larger fills. The downside is that the filter may become clogged, especially in the early wash phases when the soil load in the water is at its highest. The higher the flow rate of soilladen wash water drawn through the filter, the more difficult it is to keep the filter from becoming clogged. To keep the filter clean, some of the wash water is usually diverted to clean the filter. Unfortunately, the water diverted to cleaning the filter does nothing to clean the dishes and has the counterproductive effect of increasing the total flow through the filter.
Types of Dishwasher Wash Systems
There have been many novel wash systems in dishwashers over the years, but three types have been the most successful:
 Systems utilizing simultaneous sprayarm operation.
 Systems that alternate the use of sprayarms.
 Singlesprayarm systems utilizing a “spray tower” to reach dishes in the upper rack.
Simultaneous SprayArm Systems. This type of system operates both sprayarms at the same time during the wash cycle. This system consumes the most hydraulic power, and consequently electrical power, of the three. Usually the circulation pump is mounted underneath the dishwasher tub (see Figure 1) with the pump discharge positioned vertically along the centerline of the dishwasher tub (dishwasher tub and racks not shown). The lower sprayarm is located directly under the lower dish rack and atop a relatively short, straight, feed tube extending from the pump discharge to the lower sprayarm’s inlet. In this position, the lower sprayarm is ideally positioned to give maximum coverage to the lower rack while wash water pumped to the lower sprayarm undergoes minimal hydraulic loss. Wash water is supplied to the upper sprayarm by a feedtube system that branches off of the wash pump’s discharge.
This type of system is relatively simple because no control system is required to switch water flow from the upper to the lower sprayarm. But it consumes the most hydraulic power of the three and requires the most powerful motor, which in turn consumes the most energy during the wash cycle. Also, because of the relatively high flow rate, it is more difficult to keep the filter from clogging during the earlier phases of the wash cycle. At first glance, it may seem that an advantage of this type of system is the potential for shorter wash cycles when compared with an alternatingarm system. However, in practice, there is not nearly enough of a reduction in cycle time to offset the increase in power and energy usage.
Alternating SprayArm System. The alternating sprayarm system is very similar to the simultaneous system, except that there is some means, usually an electrically actuated valve near the pump’s discharge, to switch the flow of wash water from the lower sprayarm to the upper sprayarm.
This system has several advantages. It consumes much less power than the other systems. Besides, the wash filter only needs to handle half the flow rate of a simultaneousarm or tower system, making it much easier to keep the filter from clogging. Finally, both types of twosprayarm systems have the advantage of offering better coverage to the upper rack without forcefully spraying water against the inner door or sides of the dishwasher tub. This means lower noise, better wash performance, and a reduced tendency for the door gasket to leak.
SingleSprayArm and Tower System. The tower system uses a lower sprayarm much like the first two systems, except it has no upper sprayarm or feed system for the upper sprayarm. In order to clean the dishes in the upper rack, it utilizes a spray tower mounted to the center of the lower sprayarm with spray nozzles aimed at the upper rack. When the lower sprayarm rotates, so does the tower. The advantage of a tower system is simplicity and lower cost. The disadvantages are increased noise from the spray hitting the dishwasher tub and inner doors at a more direct angle; reduced lowerrack capacity; reduced wash performance from relatively poor coverage of the upper rack; high power consumption; and a relatively high flow rate, which makes it more difficult to keep a filter clean. Hydraulically, tower systems are a special case of the lower sprayarm mode in an alternating system. Tower systems were once very popular but now play a decreasing role in new dishwasher design.
Analysis of Important Hydraulic Characteristics
In order to understand the total amount of hydraulic power a given wash system consumes—how much of that power actually gets used to clean the dishes, how well the operating point of the system matches the best efficiency point of the pump, and finally, where opportunities may be to reduce wasted power—the system head, power, and pump curves need to be examined.
System Head
AlternatingArm Wash System. Deriving the system curve for the wash system and plotting it over the pump’s head and efficiency curves provides a great deal of insight into the operation of the wash system.
With an alternatingsprayarm system, the approach is to treat each wash mode—upper sprayarm in operation and lower sprayarm in operation—independently. By examining the upper sprayarm mode (see Figure 1), a few simplifying assumptions can be made to make the equations less cumbersome. The inner diameters of the conduits, elbows, and fittings for the upper sprayarm system, D_{2U}, are all assumed to be the same. The Darcy friction factor will be treated as a constant for the flow rates encountered in normal operation. Also, for purposes of a general analysis, all of the holes in the sprayarms will be treated as one large hole with the same open area as the sum of all of the smaller holes in the sprayarm.
Although a real sprayarm with multiple small holes would have more losses than this simplified case, the error is relatively small and the assumption has the benefit of making the equations less cumbersome.
The general equation for the upper sprayarm system head is:
Because the pressure at the surface of the sump (location 1) and the upper sprayarm discharge (location 3U) are both atmospheric, P_{3U} – P_{1}= 0. It can also be assumed that the velocity of the surface of the water in the sump is small enough to be disregarded; therefore, V_{1}= 0. Taking this into account, the upper system equation becomes:
Let’s take a look the head loss in the upper sprayarm system, h_{LU}, and what contributes to it:
Because the inner diameters of the upper sprayarm supply tubes, D_{2U}, and fittings are the same, the average velocity, V_{2U}, is the same everywhere. Additionally, it is assumed that the Darcy friction factor, f, is the same along all of the inner surfaces. Taking this into account, equation 3 simplifies to:
Substituting equation 4 back into equation 2 results in:
Noting that for a round conduit where Q is the flow rate:
Substituting equation 6 into equation 3 and simplifying puts the upper spraysystem head in a more useful form:
As expected, equation 7 shows the system head being proportional to the square of the flow rate and inversely proportional to the equivalent sprayjet hole diameter raised to the fourth power, D_{3U}^{4}. Equation 7 also reveals how critically important the choice of inner diameters of the supply conduits, D_{2U}, is, since all the local loss coefficients are multiplied by the inverse of the inner diameter raised to the fourth power. Delta z_{U} is defined as the change in elevation of the upper sprayarm system, z_{3U} – z_{1}.
The derivation of the equation for the lower sprayarm system head is the same as it was for the upper sprayarm system. The lower sprayarm system mode is therefore:
The only differences between the system heads for the upper and lower sprayarm modes are the values of the sprayarm hole diameter, inner diameter of the conduit, sum of local loss coefficients, and total length of conduit.
SimultaneousArm Wash System. Solving for the system head curve of a simultaneously operating upper and lower wash system is essentially a twobranch parallel piping problem. The key to solving this type of problem is to recognize that the head is the same for both branches. They both originate at the sump’s surface (location 1) and exit at atmospheric pressure (locations 3_{U} and 3_{L}). The total flow rate for a simultaneous system, Q_{T}, is the sum of the flow in each branch—the upper sprayarm branch, Q_{U}, and the lower sprayarm branch, Q_{L}, as shown below.
The next step is to equate the upper system head, h_{U}, with the lower system head, h_{L}, then solve for the relationship between Q_{U} and Q_{L}.
Substituting the expressions for the upper and lower system curves from equations 7 and 8 into equation 10 results in:
To simplify the equation, the change in the elevation for the upper and lower branches will be assumed to be the same, allowing the elevation, z, to drop out of the equation. In our hypothetical system, there is a 14in. difference in elevation, but that is small in comparison to the system head at the operating point. So equation 11 simplifies to:
Where
Solving equation 12 for QL:
Substituting equation 15 into equation 9 and solving for Q_{U} and Q_{L}:
Substituting equation 16a into the system head equation for the upper sprayarm branch, equation 7, gives the head equation for the simultaneous system in terms of the total flow rate for the system.
Also note that for a simultaneous system that:
Washing Power
AlternatingArm Wash System. Washing power is defined as the hydraulic power of the spray jets as they exit the sprayarm. Washing power is only dependent on flow rate and the diameter of the sprayjet hole. The washing power would be the same as the input power if there were no local losses, zero friction factor, and no change in elevation for the system.
The hydraulic power of the spray jets is the pressure just before the jet discharge, h_{dis}, multiplied by the flow rate; therefore, the washing power of the upper sprayarm is:
Noting that the flow rate through a round hole in a pressurized vessel is:
Which can be solved for h_{dis} giving:
Substituting equation 21 into equation 19 gives the washing power of the upper sprayarm as a function of flow rate and equivalent hole diameter:
The washing power of the lower sprayarm system is derived in the same way and is:
SimultaneousArm Wash System. The washing power for a simultaneous system is the sum of the washing power of the upper and lower systems.
Substituting equations 22 and 23 into equation 24 gives:
In order to get the total washing power for the simultaneous system as a function of the total flow rate, substitute equations 16a and 16b into equation 25 and simplify:
Input Hydraulic Power
AlternatingArm Wash System. The power input, P_{I}, to the wash system by the pump is derived the same way as the washing power: The flow rate is multiplied by the pressure, where the pressure is the system head multiplied by the weight density of water. The input power for the upper spray arm is:
Substituting equation 7 for h_{su} in equation 14 yields the following expression for the upper sprayarm system input power as a function of flow rate.
The input power for the lower system is derived in the same way:
SimultaneousArm Wash System. The total input power for a simultaneous system is derived the same way as the alternating system, except the flow rate and system head are for a simultaneous system:
Substituting equation 17 into equation 30 results in:
Wash System Efficiency
AlternatingArm Wash System. The wash system efficiency is defined as the system’s washing power, P_{W}, divided by the system’s input power, P_{I}. The wash system efficiency is an indication of how well the hydraulic power imparted to the system by the pump is converted into washing power at the spray jets. It does not include the efficiency of the pump or motor. Any pump or motor connected to a more efficient wash system will benefit from the reduced need for shaft power for the pump and electrical power for the motor. Therefore, the wash system efficiency of the upper sprayarm mode is:
And the lower wash system efficiency is:
SimultaneousArm System. The wash system efficiency for a simultaneous system is defined as equation 26 divided by 31:
Simplified Wash System Analysis Example
To show how small changes in the hydraulic characteristics can significantly reduce energy use while improving performance, a simple alternating system’s performance is analyzed before and after a set of changes.
Referring again to the simple system represented in Figure 1, the following values are chosen to represent a hypothetical wash system:
A few changes will be made to the system characteristics, and the performance will be evaluated for both systems, before and after the changes. The values that have changed are shown in red.
The system curves for the upper and lower systems, before and after, are plotted over the wash pump’s head/capacity and efficiency curves and show the system’s operating points and pump efficiency in each mode (see Figures 2 and 3). The graphs reveal the operating points for the upper and lower systems and the pump efficiency at those points. With this information, the washing power, power consumed, and efficiencies can be determined. Before calculating the system performance, the overall efficiency needs to be defined. The overall efficiency, η_{OA}, is the product of the wash system efficiency, η_{W}, the pump efficiency, η_{p}, and the motor efficiency, η_{m}.
To simplify the analysis, the motor efficiency will be assumed to be a constant 70% in all cases.
The system graphs and performance data show how performance and energy use can be improved from small changes: The change to the lower sprayarm hole equivalent diameter, D_{3L}, moved the operating point of the lower system much closer to the bestefficiency point of the pump, increasing the pump’s efficiency from 32 to 45.2%. The washing power increased from 20.9 to 25 W, and the lower system’s total electrical power consumption, P_{T}, dropped from 266 to 163 W.
Before, the upper system’s washing power was an anemic 8 W at a wash system efficiency of 16.3%. This implies that 83.7% of the hydraulic power input to the upper system was wasted before it reached the spray jets in the upper arm. Changes in the upper system’s conduit inner diameter and sprayjet hole equivalent diameter more than doubled the washing power and efficiency of the upper system without using any additional power.
Assuming that the upper and lower sprayarms operate the same amount of time, the average power consumption of this wash system went from 208 to 155 W, a reduction in overall power consumption of 25%, while improving the hydraulic washing power of the dishwasher—all without any increase to product cost or complexity.
To contact John Dries, please email lisa.bonnema@cancom.com.
Nomenclature
γ = weight density of water
g = acceleration due to gravity
V = average fluid velocity
D_{2U} = upper supply conduit inner diameter
D_{3U} = equivalent spray hole diameter for the upper spray arm
L_{TU} = total length of the upper supply conduits
K_{1U} = upper system's local loss coefficient for branch from the pump discharge
K_{2U} = upper system's local loss coefficient for the first elbow in the supply conduit
K_{3U} = upper system's local loss coefficient for the second elbow in the supply conduit
K_{4U} = upper system's local loss coefficient for the third elbow in the supply conduit
K_{5U} = upper system's local loss coefficient for the entrance to the upper spray arm
D_{2L} = lower spray arm supply conduit inner diameter
D_{3L} = equivalent spray hole diameter for the lower spray arm
L_{TL} = total length of the lower supply conduit
K_{1L} = lower system's local loss coefficient at the branch for the upper spray system
K_{2L} = lower system's local loss coefficient for the entrance to the lower spray arm
Q_{U} = upper system flowrate
Q_{L} = lower system flowrate
Q_{T} = total flowrate in a simultaneous system
h_{SU} = upper system head
h_{SL} = lower system head
h_{S} = system head for a simultaneous system
P_{IU} = input power to upper wash system
P_{WU} = washing power of the upper wash system
P_{WL} = washing power of the lower wash system
P_{W} = washing power of a simultaneous system
η_{WU} = upper system washing efficiency
η_{PU} =pump efficiency at the upper system's operating point
η_{M} = motor efficiency
P_{TU} = total electrical power consumed by the upper wash system
P_{TL} = total electrical power consumed by the lower wash system
P_{IL} = input power to lower wash system
η_{WL} = lower system washing efficiency
η_{PL} = pump efficiency at the upper system's operating point
η_{OA} = overall efficiency
F_{U} = upper system loss factor
F_{L} = lower system loss factor
h_{dis} = discharge head near a spray arm jet hole