Hydraulic Simulation Model for Dishwasher

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IN

DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2018,

Hydraulic Simulation Model for Dishwasher

SEYED MORTEZA HABIBI KHORASANI

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Hydraulic Simulation Model for Dishwasher

SEYED MORTEZA HABIBI KHORASANI

M.Sc. in Engineering Mechanics Date: October 17, 2018

Supervisors at Electrolux: Mathias Belin, Antonios Monokrousos Supervisor at KTH: Shervin Bagheri

Examiner: Shervin Bagheri KTH Royal Institute of Technology

School of Engineering Sciences

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Abstract

This thesis project concerns the creation of a simulation model for the hydraulic system of a commercial dishwasher machine. A 1D model was created using the Simscape physical network modeling tool integrated into the widely used MATLAB software environment.

The resultant model can predict the hydraulic performance of the dishwasher for various cases of input parameters. It can also simulate certain state varying aspects of the dishwasher such as its flow controller which opens and shuts off flow to different parts of the system.

The model can achieve sufficiently low runtimes where it can be faster than the real‐time operation of the target system. The modularity of the physical network approach allows for the quick testing of changes to the overall design of the hydraulic system, a useful attribute when it comes to investigating performance requirements.

The results of this work show promise in Simscape as a modeling tool for multi‐physics systems. The model developed can serve as a foundation for further development to be carried out and more aspects of the dishwasher machine, such as its heating, be added to the model so it can cover a

broader range of the dishwasher’s behavior.

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Acknowledgments

This project was carried out at the Stockholm headquarters of AB Electrolux among the Advanced Development group of the Global R&D Dish Care department.

I would like to express my gratitude to several people who were involved in project.

 The head of Advanced Development, Mathias Belin, for granting me the opportunity to do this project and be a part of his splendid team of talented individuals.

 Antonios Monokrousos, who helped supervise the project at Electrolux and provided the CFD model and leakage measurements while also giving advice at various points during the project.

 Magnus Wahlberg, who was responsible for the principle idea behind the test rig for the water distribution measurements and made the many hours spent within the lab enjoyable through stimulating conversations.

 Anders Haegermarck, for his expertise on all matters concerning the dishwasher and generously imparting his knowledge whenever I had questions.

 Charlie Johansson, for preparing the Arduino board and who’s excellent Python firmware emulator facilitated the task of carrying out the measurements.

 All other members of the Advanced team during this time: Marie Hakkarainen, Simon Trbojevic, Eduardo Martinez, Kristian Reunanen, Ivar Siösteen and Johan Eed for making this a memorable experience.

Finally, I would like to thank Shervin Bagheri who was my supervisor and examiner at KTH for this project.

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Nomenclature

Notation Description Unit

𝐴 Area [m²] or [mm²]

α Kinetic energy coefficient [‐]

𝐶

Contraction coefficient [‐]

𝐶 Discharge coefficient [‐]

𝐷 Diameter [m]

𝑒 Pipe roughness [m] or [mm]

𝑓 Friction factor [‐]

𝑔 Gravitational acceleration [m/s²]

ℎ Total hydraulic head loss [m]

ℎ Major hydraulic head losses [m]

ℎ Minor hydraulic head losses [m]

𝐾

Head loss coefficient [‐]

𝐿 Length [m]

𝜇 Dynamic viscosity [kg/(m s)]

𝑝 Static pressure [N/m²] or [mbar]

𝑄 Flow rate [m³/s] or [lpm]

𝑉 Velocity [m/s²]

𝜔 Angular velocity [rad/s] or [rpm]

𝑧 Elevation [m]

𝜌 Density [kg/m³]

𝛾 Specific weight [N/m³]

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1

Introduction

1.1 A Brief History of Simulations

The advent of computers during the second half of the 20^th century represented the prelude to what would become a dramatic change in almost every known facet of human society. Initially designed as analogue machines to tackle specific scientific problems, early computers were limited in capabilities and functionality, their greatest shortcoming being a lack of programmability. Analogue computers were made obsolete by their digital counterparts which superseded them by the 1950s [1]. The development of these machines was largely propelled due to war time impetus during the events of the second World War.

The growth of computer technology saw another discipline grow alongside it, that of simulations. A simulation is a computer program which executes a model of the desired system, the model itself being a mathematical representation of said system. Simulations and modeling quickly found applications in tackling scientific and engineering problems which were unwieldy or improbable to be carried out by human efforts alone. A typical case where simulations are widely used is solving systems of equations which cannot be solved analytically, requiring a high volume of recursive numerical calculations.

With computer resources continuing to grow at an accelerating rate and the technology itself becoming more accessible by exiting the exclusive confines of scientific establishments, many engineering and technologically driven sectors began to leverage it as a tool in their day to day operations. Today, any industry has made computer modeling and simulations an integral part of their development and production processes. Consumer demands, competitors, market dynamics, regulations, etc. necessitate that the development pipeline be adaptive to changes in these factors and adjust accordingly. The rate at which such adjustments must take place grows continuously, straining the conventional approach of product development which relies on real prototyping and experimental efforts. Resources are not in infinite supply and their expenditure should be streamlined

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1.2 Why Modeling is Utilized

A proven way of dealing with the complexity of engineering systems is to find a suitable abstraction level to work with [2]. Higher abstraction layers obscure details and provide a broad picture of the system under consideration, as depicted in Figure 1.

Figure 1: Evolution of abstraction layer in the modeling of physical systems. From general purpose code (FORTRAN), to computing software (MATLAB), to graphical software (Simulink), to physical modeling [3].

This persistent pursuit of abstraction was motivated by the need to make the model separable from the simulation and to also reduce the level of difficulty involved in developing a computer simulation.

Engineers faced the arduous task of programming everything from the ground‐up, involving the mathematical equations, discretization, numerical solver, etc. The advent of numerical computing environments such as MATLAB allowed for the model to become separate from the simulation due to the existence of its built‐in differential equation solvers.

1.3 Modeling Approaches

Many modeling approaches exist, from general‐purpose code (FORTRAN, C etc.) to signal‐based or input‐output (causal) methods in graphical software tools (Simulink, etc.) and the physical network

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In input‐output based methods signals are transmitted through links between individual blocks. The signals serve to transfer values of individual variables from the output of one block to inputs of other blocks. Input information is processed in the blocks to output information. Interconnection of blocks therefore reflects rather the calculation procedure than the very structure of the modeled reality. This is known as the causal approach to modeling, where the causal way of calculating the different model variables must be expressed [4]. Causal modeling has been used to model physical systems for quite some time [5]. One of the main reasons this method is used is because it is the natural language of control engineers. In a standard control loop, the plant (the controlled physical system) is represented as a transfer function with an input and an output, as depicted in

Figure 2. Finding a mathematical representation composed of blocks with inputs and outputs fits naturally into this system and is easy for a control engineer to use and understand [6].

Figure 2: A typical control loop [7].

The causal modeling approach has disadvantages when attempting to model complex systems. Often, a significant effort in terms of analysis and analytical transformations is needed to model in this form.

This procedure requires a lot of engineering skills and manpower as well as being error‐prone [8]. Such an approach also tends to obscure the physical topology of the system and make it less intuitive to the unfamiliar eye. Model components developed in such a way are also not reusable as they are defined based on their connection to other components. These impediments gave rise to the acausal modeling approach where equations can be stated in a neutral form without any consideration of the computational order. Systems in nature can be thought of as acausal. Causality is artificially made because physical laws must be transformed into a convenient computational description [8].

Due to these reasons, engineers began looking for a better method for modeling these types of systems. For purely electrical systems, Kirchoff’s laws have been used for quite a long time to express the equations for an entire system by applying a few basic mathematical rules to a network of electrical components represented by their individual mathematical models [9]. For example, the component model of a resistor was represented by 𝑣 𝑖𝑅, and this component model of an ideal resistor was identical for all resistors in the electrical network, independent of where the resistors were placed in the circuit. The equations for the entire system could be derived by applying Kirchoff’s laws at the nodes of the electrical circuit. This method permits the component models to be modular

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physical elements, such as pumps, motors, etc. These blocks are linked to each other in a way which corresponds to the physical connections that transmit power. This approach allows for describing the physical structure of a system, rather than the underlying mathematics. Such an approach makes the resultant model more intuitive and highly modular. Since the actual geometry of the components are not resolved, this approach falls within the category of 1D simulation methods.

As an example of utilizing such an approach for industrial purposes, Miele® made use of Siemens’

Amesim simulation platform to create a model of the hydraulics of their washer‐disinfectant machines to reduce their need for physical prototypes in the design stage of their product [10].

Figure 3: Model of the inner wash cycle of the Miele large‐capacity disinfector PG8528 [10].

Figure 4: The wash cages component from Figure 3 [10].

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It is clearly evident from Figure 3 and Figure 4 how the actual components of a hydraulic circuit are represented by discernable counterparts within the model, demonstrating the advantage of physical modeling in creating intuitive representation of the real‐life system.

The physical network approach is further elaborated in section 4.

1.5 Objective

The primary aim of this Thesis work is to develop a simulation model of a dishwasher’s hydraulic system which can evaluate its performance during operation. The model should allow for simulating the hydraulic system under different operating conditions and predict the hydraulic variables, pressure and flow rate, at different points of the system.

For this project, it was opted to make use of MathWorks’ Simscape software. Almost every engineering software developer provides their own software environment for physical modeling (such as Amesim from Siemens). The author decided upon using Simscape due to it being a part of the MATLAB software package which they had access to through the academic licensing made available by KTH, and due to some prior familiarity with MATLAB itself. In any case, deliberating the choice of tool for carrying out this thesis work would have deviated from the main objective and consumed valuable time.

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2

The Dishwasher Appliance

2.1 The Dishwasher Appliance

A dishwasher is a mechanical device for cleaning dishware and cutlery. Unlike manual dishwashing, which relies largely on physical scrubbing to remove soiling, the mechanical dishwasher cleans by spraying hot water mixed with detergent at the dishes [11]. A frontal view of an open dishwasher with its components visible is shown in Figure 5. A description of these components is shown in Figure 6.

Figure 5: A dishwasher along with its components [12].

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Figure 6: Dishwasher component descriptions [13].

2.2 The Hydraulic System

The Hydraulic system supplies pressurized water to the spray arms where it becomes discharged into the tub and enables the process of dishwashing. This system is comprised of the following components:

 Circulation pump

 Flow (direction) controller

 Sump

 Delivery tube

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Figure 7: CAD rendering of hydraulic system.

2.2.1 Circulation Pump

The pump used within the dishwasher is of the centrifugal type. The theory regarding these types of pumps within hydraulic systems is described in section 3.5.

Figure 8 shows the pump component, consisting of both the mechanical section and electrical motor.

Top spray arm

Upper spray arm

Delivery tube

Lower spray arm

Circulation pump Sump

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The impeller within the pump housing is shown below.

(a) (b)

Figure 9: (a) Transparent CAD render of pump with impeller visible. (b) Actual pump’s “eye” inlet with impeller visible.

The pump is operated up to rotational speeds of 3300 rpm in the dishwasher. The performance curves of the pump, detailing the possible combinations of total pressure and flow rate for it, are shown in Figure 10. These curves were generated through measurements which had been previously carried out at Electrolux.

The declining trend of the energy imparted to the fluid (pressure difference) with increasing flow rate is a general attribute of centrifugal pumps used in hydraulic systems. This is due to the geometrical design of the impeller within the pump which has backward facing vanes (observable in Figure 9), resulting in less work being done on the fluid by the pump as flow rate increases. The reason behind this is to prevent the motor of the pump from being overloaded at higher flow rates which could damage it. The interested reader may find more information about the turbomachinery theory of centrifugal pumps in fluid mechanics textbooks such as [14] and [15].

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2.2.2 Flow Controller

The flow controller is 3‐position valve which distributes water to the various parts of the system.

(a) (b)

Figure 11: (a) Flow controller outlets. (b) Flow controller motor.

As shown in Figure 11 (a), the flow controller has two outlets. One outlet provides flow to the “Lower”

region of the hydraulic system, where the lower spray arm is present, while the other provides flow to the “Upper” region, where the “Upper” and “Top” spray arms are present. The incoming flow can be redirected to either a single outlet or both giving a total of 3 possible positions.

The flow controller position is set by a circular disc with 3 annular openings, similar to the sketch shown in Figure 12.

Figure 12: Flow controller position disc.

Position changes are made through the rotation of this disc. As indicated in Figure 11 (b), the flow controller motor rotates counter‐clockwise. On average, every quarter rotation (90°) of the disc takes 6 seconds. The amount of time it takes for a position change (switching) to take place is dependent on the combination of initial and final positions.

Table 1: Flow Controller switching times

From To Time (s)

Lower Upper 12

Upper Lower 12

Lower Both 6

Both Upper 6

Upper Lower

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The shortest switching time is when only a single quarter rotation is required for the change to take place, while the longest occurs over the span of three‐quarter rotations. Figure 13 and Figure 14 demonstrate two cases.

Both Upper Lower

Figure 13: Switching from “Both” to “Lower”.

Upper Lower Both

Figure 14: Switching from “Upper” to “Both”.

Any switching which takes more than one quarter rotation will pass over other positions and momentarily allow water to pass on through them.

2.2.3 Sump

The sump is where the intake water is accumulated to then be circulated by the pump. During a dishwasher’s operation, the run‐off water from the dishware, baskets and other elements within the dishwasher tub gathers within the sump and is recirculated by the pump for continuous washing.

Figure 15 and Figure 16 depict the sump and its different parts.

6 seconds

Connection to Upper region Connection to

Lower region

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Figure 16: Underside view of sump (CAD render).

The sump as it is connected to other components in an actual machine is shown in Figure 17.

Figure 17: The sump along with the other dishwasher components as they are installed in the machine.

2.3 Delivery Tube

The delivery tube transports water to the “Upper” and “Top” spray arms. One can see from Figure 18 the geometrical variance of the delivery tube along its length.

Connection to Upper region Connection to

Lower region

Connection to drain pump

Connection to circulation pump

pump Connection to

water softner Pressure sensor port

Turbidity sensor port

Drain pump

Circulation pump Flow

controller Water softner Turbidity

sensor Pressure

sensor

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Figure 18: CAD render of the delivery tube.

2.4 Spray Arms

2.4.1 Lower Spray Arm

The “lower” spray arm washes the dishware in the “lower” basket by spraying water upward. It also sprays water towards the “tub” floor and flat filter to wash away any accumulated soil. The spray arm consists of two main parts: the “sun” arm and the “satellite” arm.

Connection to Top spray arm Connection to

Upper spray

Connection to Flow Controller

Sun arm nozzle

(top) Satellite arm

nozzles

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Figure 20: Underside view of the lower spray arm.

Figure 21: Side view of bottom spray arm.

2.4.2 Upper Spray Arm

The “Upper” spray arm discharges water both upward and downward contributing to the cleaning of the dishware in the “lower” and “upper” baskets.

Figure 22: Top view of upper spray arm.

Sun arm nozzle (underside)

Inlet

(from flow controller)

Bottom spray arm collar

Snap‐fit pieces for mounting onto sump

Nozzles (Top)

Snap‐fit pieces for mounting onto upper

basket Inlet

(from delivery tube)

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Figure 23: Underside view of upper spray arm.

The underside nozzles shown in Figure 23 rotate the upper spray arm during dishwashing action.

2.4.3 Top Spray Arm

The “top” spray arm washes the cutlery in the cutlery drawer by spraying water downward.

Figure 24: Top view of top spray arm.

Nozzles (Underside) Nozzle

(side)

Nozzles (underside)

Nozzle (side) Inlet (from delivery tube)

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3

Theory

3.1 Pipe Flow

In the hydraulic system of a dishwasher the fluid, before reaching the tub, is flowing in closed conduits.

Depending on the type of cross‐section, this type of flow is called pipe or duct flow [14]. A typical pipe system along with some of the usual components they consist of is depicted in Figure 26.

Figure 26: A pipe system and its components [14].

In this section, the pertinent fluid dynamics theory concerning pipe flow is recounted.

3.2 Flow Regime in Pipe Flow

In fluid mechanics this type of flow is divided into two distinct regimes, denoted as Laminar and Turbulent flow. These classifications where established through the experiments of British scientist Osborne Reynolds (1842‐1912). In laminar flow, fluid flows in parallel layers, with no disruption between them [16]. In contrast, turbulent flow is marked by chaotic behavior with lateral mixing of the fluid layers occurring.

The above classification applies to flow within pipes, with there being both laminar and turbulent flows. The important dimensionless quantity called the Reynolds number, is also the most important when it comes to pipe flows. For a pipe of diameter 𝐷 with an average velocity 𝑉, the Reynolds number is expressed as:

𝑅𝑒 𝜌𝑉𝐷

(1)

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With 𝜌 and 𝜇 being the fluid density and dynamic viscosity, respectively.

The Reynolds number ranges for laminar or turbulent pipe flows cannot be precisely given. The actual transition from laminar to turbulent flow may take place at various Reynolds numbers, depending on how much the flow is disturbed by vibrations of the pipe, roughness of the entrance region, and the like. For general engineering purposes the following values are appropriate: The flow in a round pipe is laminar if the Reynolds number is less than approximately 2100. The flow in a round pipe is turbulent if the Reynolds number is greater than approximately 4000 [14]. In the intermediate range between these two thresholds, the flow is in a transitional state and strongly affected by disturbances.

In the dishwasher, the Reynolds number ranges between 3000 to 20000 for a pump speed of 1800 rpm to between 8000 to 30000 for a pump speed of 2800 rpm, making the flow predominately turbulent.

3.3 Energy Considerations in Pipe Flow

One of the principle conservation laws of physics is that of conservation of energy. Therefore, it is important to examine pipe flows from an energy perspective. For an incompressible fluid flowing within a pipe, if the effects of friction are ignored (inviscid flow) and steady flow along a streamline is considered, the well‐known Bernoulli equation can be applied.

𝑝

𝜌 𝑉

2 𝑔𝑧 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (2)

This equation demonstrates the causes of pressure loss for inviscid flow along a streamline: a reduction of area causing an increase in the velocity V, or the pipe having a positive incline so 𝑧 increases. Conversely, the pressure will tend to increase if the flow area is increased or the pipe slopes downward [15].

However, flows in pipes and ducts experience significant friction and are often turbulent, so the Bernoulli equation does not apply. In effect, friction effects lead to a continual reduction in the value of the Bernoulli constant of Equation (2), causing a loss of mechanical energy. The Bernoulli equation must be replaced with an energy equation that incorporates the effects of friction [15]. To this end we consider the energy equation for incompressible, steady flow between two locations as given below.

𝑝

𝜌𝑔 𝛼 𝑉

2𝑔 𝑧 𝑝

𝜌𝑔 𝛼 𝑉

2𝑔 𝑧 ℎ (3)

α and α are kinetic energy coefficients and compensate for the fact that the velocity profile across the pipe is not uniform. For uniform velocity profiles 𝛼 1, whereas for any nonuniform profile 𝛼 1. Because 𝛼 is reasonably close to unity for high Reynolds numbers, and because the change in kinetic energy is usually small compared with the dominant terms in the energy equation, the approximation 𝛼 1 is widely used in pipe flow calculations [15]. The head loss term ℎ , accounts for any energy

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3.4.1 Major Head Loss

For fully developed flow through a constant‐area horizontal pipe, ℎ 0 and 𝛼 𝛼 ; Equation (3) reduces to:

𝑝 𝑝

𝜌𝑔

∆𝑝

𝛾 ℎ (4)

The major head loss is then the pressure loss for fully developed flow through a horizontal pipe of constant area.

Since head loss represents the energy converted by frictional effects from mechanical to thermal energy, head loss for fully developed flow in a constant‐area duct depends only on the details of the flow through the duct. Head loss is independent of pipe orientation [15].

For laminar flow through a pipe, the major head loss can be calculated using the analytical relation given in Equation (5).

ℎ 64

𝑅𝑒 𝐿 𝐷

𝑉

2𝑔 (5)

In turbulent flow the pressure drop cannot be evaluated analytically. Experimental results must be used along with dimensional analysis to correlate the experimental data. In fully developed turbulent flow, the pressure drop, ∆𝑝, caused by friction in a horizontal constant‐area pipe is known to depend on pipe diameter, 𝐷; pipe length, 𝐿; pipe roughness, 𝑒; average flow velocity, 𝑉; fluid density, 𝜌; and fluid viscosity, 𝜇 [15]. This may be written in functional form as Equation (6).

∆𝑝 ∆𝑝 𝐷, 𝐿, 𝑒, 𝑉, 𝜌, 𝜇 (6)

Using Equations (1) and (4) this can be rewritten in non‐dimensional form as Equation (7).

ℎ

𝑉 𝑔  𝑅𝑒,𝐿 𝐷,𝑒

𝐷 (7)

The dimensionless parameter, 𝑒 𝐷, is called the relative roughness and is not present in the laminar formulation, Equation (5), because fully developed laminar pipe flow is independent of it. Dimensional analysis establishes the functional relationship, but the actual values must be obtained experimentally.

Experiments show that the non‐dimensional head loss is directly proportional to 𝐿 𝐷, giving

ℎ 12 𝑉

𝑔 𝐿

𝐷 𝑅𝑒,𝑒

𝐷 (8)

The constant, 1 2, is introduced to the left side of Equation (8) so that the left side is the ratio of the head loss to the kinetic energy per unit mass of the flow. The undetermined function, , is defined as the Darcy friction factor, 𝑓, and is determined experimentally [15].

𝑓  𝑅𝑒,𝑒

𝐷 (9)

Equation (8) can thus be rewritten as

ℎ 𝑓𝐿

𝐷 𝑉

2𝑔 (10)

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The functional dependence of the friction factor on the Reynolds number and relative roughness was an arduous task that required extensive experiments to be carried out. Such experiments were conducted by Nikuradse in 1933 [17]. In 1944, Lewis Ferry Moody plotted the Darcy–Weisbach friction factor against Reynolds number, 𝑅𝑒, for various values of relative roughness, 𝑒 𝐷, [18]. The resultant graph is called the Moody diagram and can be viewed in appendix 1.

To determine head loss for fully developed flow with known conditions, the Reynolds number is evaluated first. Roughness, 𝑒, is obtained from available tabulated data such as those in Table 2. Then the friction factor, 𝑓, can be read from the appropriate curve in the Moody diagram, at the known values of 𝑅𝑒 and 𝑒 𝐷. Finally, the head loss can be found using Equation (10).

Table 2: Roughness for New Pipes, data from [19] and [18].

Pipe material Pipe roughness, 𝒆 (mm)

Riveted steel 0.9 – 9.0

Concrete 0.3 – 3.0

Wood stave 0.18 – 0.9

Cast iron 0.26

Galvanized iron 0.15

Commercial steel 0.045

Drawn tubing 0.0015

Plastic, glass 0.0 (smooth)

The Moody Diagram has many interesting aspects which can be discussed at length, and the interested reader is directed towards any fluid mechanics text‐book, such as [14] and [15], for greater information. A summary of the most notable features of the Moody diagram are as follows, as the Reynolds number is increased, the friction factor decreases if the flow remains laminar. In the turbulent flow regime, the friction factor decreases gradually and finally levels out at a constant value for large Reynolds numbers. The most important conclusion to be made is that the head loss always increases with flow rate, and more rapidly when the flow is turbulent.

To avoid having to use a graphical method for obtaining the friction factor, 𝑓, for turbulent flows, various mathematical expressions have been fitted to the data. The most widely used formula for the friction factor is from Colebrook [19],

1

𝑓 2.0 𝑙𝑜𝑔

𝑒 𝐷 3.7

2.51

𝑅𝑒 𝑓 (11)

Equation (11) is valid for the entire nonlaminar range of the Moody chart. The Moody chart is essentially a graphical representation of this equation, which is an empirical fit of the pipe flow pressure drop data [14]. It is implicit in 𝑓 and must be solved iteratively.

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head loss. These losses are referred to as minor losses. Similar to major head losses, a theoretical analysis of such losses does not exist and they are represented in dimensionless form using experimental data. Minor head losses are expressed by a loss coefficient, defined as:

𝐾 ℎ

𝑉 2𝑔

∆𝑝 12 𝜌𝑉

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Which can be re‐written to give:

ℎ 𝐾𝑉

2𝑔 (14)

The value of 𝐾 is strongly dependent on the geometry of the component considered and fluid properties, 𝐾  𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦, 𝑅𝑒 . For most practical scenarios, the Reynolds number is large enough so that inertial effects are dominant and viscous effects are negligible. Therefore, in most cases the loss coefficient is a function of geometry only, 𝐾  𝑔𝑒𝑜𝑚𝑒𝑡𝑟𝑦 [14].

Minor losses may also be expressed in terms of an equivalent length, meaning the head loss through a component is given in terms of the equivalent length of pipe that would produce the same head loss as the component.

ℎ 𝐾𝑉

2𝑔 𝑓𝑙 𝐷

𝑉

2𝑔→ 𝑙 𝐾 𝐷

𝑓 (15)

3.4.2.1

Losses in Bends

Bends in pipes cause greater head loss than if the pipe were straight. The separated region of flow near the inside of the bend and the swirling secondary flow caused by the imbalance of centripetal forces from the pipe curvature are responsible for the losses. These effects and corresponding values of 𝐾 for large Reynolds number flows through a bend are shown in Figure 27. The friction loss from the length of the pipe bend must also be calculated and added to that given by the loss coefficient of Figure 27 [14].

Figure 27: Character of the flow in a 90° bend and the associated loss coefficient, reproduced with permission

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3.4.2.2

Losses in Exit Flows

Another scenario of interest is the flow leaving a confined space, resulting in a jet of fluid. If the exit is not a smooth, well‐contoured nozzle, but rather a flat plate as shown in Figure 28, the diameter of the jet, 𝑑 , will be less than the diameter of the hole, 𝑑 . This phenomenon, called a vena contracta effect, is the result of the inability of the fluid to turn the sharp corner, as indicated by the dotted lines in the Figure 28 [14].

Figure 28: Vena contracta effect for a sharp‐edged orifice, reproduced with permission from [14].

The vena contracta effect is a function of the geometry of the outlet. Some typical configurations are shown in Figure 29 along with typical values of the experimentally obtained contraction coefficient,

𝐶 𝐴

𝐴 , where 𝐴 and 𝐴 are the areas of the jet at the vena contracta and the area of the hole respectively [14].

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Another non‐dimensional coefficient is more typically used when describing the behavior of nozzles and orifices. This coefficient is known as the discharge coefficient, 𝐶 , and is the ratio of mass flow rate at the discharge end of the nozzle to that of an ideal nozzle (no energy loss) which expands an identical working fluid from the same initial conditions to the same exit pressures.

𝐶 𝑄

𝑄 (16)

Some typical values for the discharge coefficient are shown in Figure 30.

Figure 30: Discharge coefficients for various exit configurations [21].

The relation between the loss coefficient, 𝐾, and the discharge coefficient, 𝐶 , is such

𝐾 1

𝐶 (17)

3.5 Centrifugal Pump

One of the most common pump types is the centrifugal pump. There are two main components to this type of pump: an impeller attached to a rotating shaft, and a stationary casing enclosing the impeller. The impeller is comprised of several curved blades, arranged in a regular pattern around the shaft. The rotation of the impeller causes fluid to be sucked in through the “eye” of the casing and flow radially outward. Energy is added to the fluid by the rotating blades, and both pressure and absolute velocity are increased as the fluid flows from the eye to the edge of the blades [14].

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3.5.1 Pump Characteristics

The head rise, ℎ , gained by a fluid flowing through a pump can be expressed using the energy equation, (3).

ℎ 𝑝 𝑝

𝜌𝑔

𝑉 𝑉

2 𝑧 𝑧 (18)

Figure 32: Head rise gained by a fluid flowing through a pump, reproduced with permission from [14].

Typically, the differences in elevation between the pump inlet and outlet are negligible simplifying equation (18) to:

ℎ 𝑝 𝑝

𝜌𝑔

𝑉 𝑉

2

𝑝 𝑝

𝛾

𝑉 𝑉

2 (19)

Performance characteristics for a given pump geometry and operating speed are usually depicted as plots of ℎ versus flowrate, 𝑄, as shown in Figure 33.

,

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3.5.2 System Characteristics and Operating Point

A typical flow system is depicted in Figure 34.

Figure 34: A typical flow system, reproduced with permission from [14].

Application of the energy equation, (3), to this system gives the “system equation”.

ℎ 𝑧 𝑧 ℎ (20)

Where ℎ is the head provided by the pump as described in section 3.5.1 and ℎ is the total head loss accounting for all major and minor frictional losses as covered in section 3.4. Expanding equation (20) using equations (10) and (14) from sections 3.4.1 and 3.4.2 gives:

ℎ 𝑧 𝑧 𝑓 𝑙

𝐷 𝐾 𝑉

2𝑔 (21)

Equation (21) demonstrates that ℎ is proportional to velocity squared, 𝑉 , making it proportional to flowrate squared, 𝑄 .

ℎ 𝑧 𝑧 𝐶𝑄 (22)

This “system equation” thus demonstrates how the pump head is related to the system parameters, or how the head gained by the fluid is related to the flowrate [14]. The plotted curve of equation (22) is shown in Figure 35.

, ,

h z z CQ

z z

𝑄

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There also exists a unique relationship between the pump head given to the fluid and the flowrate, which is governed by the pump design. Selecting a pump for a particular application, requires using both the system curve, as determined by the system equation, and the pump performance curve.

When both curves are plotted on the same graph, as shown in Figure 36, their intersection (point A) gives the operating point for the system. This point gives the head and flowrate that satisfies both the system equation and the pump equation [14].

Figure 36: The operating point for a hydraulic system, reproduced with permission from [14].

The theory covered thus far suffices for the purposes of this thesis. At this point, it is important to state that the theory for internal incompressible flows covered in this section is for conventional pipe systems which are circular in geometry. As will be seen further‐in, the geometry of the dishwasher hydraulic components does not conform to that of a typical pipe system. Therefore, the non‐dimensional coefficients cannot be readily taken from tables within literature and assumed to be

appropriate.

,

𝑸

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4

Simscape

4.1 Background

Simscape is a set of block libraries and special simulation features for modeling physical systems in the Simulink® environment. It employs the Physical Network approach (acausal approach), which differs from the standard Simulink modeling approach (casual approach) and is particularly suited to simulating systems that consist of real physical components. Simulink blocks represent basic mathematical operations. When Simulink blocks are connected, the resulting diagram is equivalent to the mathematical model, or representation, of the system under design. Simscape allows for creating a network representation of the system under design, based on the Physical Network approach.

According to this approach, each system is represented as consisting of functional elements that interact with each other by exchanging energy through their ports [22].

These connection ports are nondirectional. They mimic physical connections between elements.

Connecting Simscape blocks together is analogous to connecting real components, such as pumps, valves, and so on. In other words, Simscape diagrams mimic the physical system layout. If physical components can be connected, their models can be connected too. It is not necessary to specify flow directions and information flow when connecting Simscape blocks, just as they are not specified when connecting real physical components. The Physical Network approach, with its nondirectional physical connections, automatically resolves all the traditional issues with variables, directionality, and so on [22].

4.2 Variable Types

The Physical Network approach supports two types of variables, as described in [22]:

 Through Variables that are measured with a gauge connected in series to an element.

 Across Variables that are measured with a gauge connected in parallel to an element.

These definitions are based on Kirchoff’s Current and Voltage law which, respectively, state that the sum of electrical currents into and out from a single node must be equal, and that the sum of the electrical potential differences around any closed circuit must also be zero.

The equivalent of the Current and Voltage quantities in Simscape are the “through” and “across”

variables. These are conjugate variables whose product is the energy flow between the components.

4.3 Physical Domains

Simscape offers separate component libraries for different physical domains. Each physical domain has its own set of conjugate variables along with constraints which determine the rules by which those variables can operate. The domain provides the environment in which components can be connected to each other.

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Since the topic of this thesis concerns hydraulics, the hydraulics domain of the Simscape library was utilized. The conjugate variables of this domain can be ascertained by applying Kirchoff’s laws.

Restating the voltage law, it establishes that the voltage of all components’ ports attached to an electrical node must be the same. Extending this definition to the hydraulics domain, this means that the pressure at all the components’ ports attached to that node must be the same. Pressure is therefore, the “across” variable of the hydraulics domain.

Similarly, the current law establishes that the sum of currents flowing towards an electrical node is equal to the sum of currents flowing away from that node. Extending this to the hydraulic domain, it means that the amount of fluid flowing into a node must be equal to the amount of fluid flowing out of that node. This makes the flow rate the “through” variable of the hydraulics domain.

Table 3: Across and Through variables of the hydraulic domain.

Physical Domain Across Variable Through Variable

Hydraulic Pressure Flow rate

These variables are defined in the domain declarations of Simscape. As an example, the declaration of the hydraulics domain is shown in Listing 1.

Listing 1: hydraulic domain declaration.

domain hydraulic

% Hydraulic Domain

parameters

density = { 1000 , 'kg/m^3' }; % Fluid density

viscosity_kin = { 8.887e-7 , 'm^2/s' }; % Kinematic viscosity

bulk = { 0.8e9 , 'Pa' }; % Bulk modulus at atm. pressure and no gas

alpha = { 0.005 , '1' }; % Relative amount of trapped air range_error = { 2 , '1' }; % Pressure below absolute zero end

variables

p = { 0 , 'Pa' }; % Pressure end

variables(Balancing = true)

q = { 0 , 'm^3/s' }; % Flow rate end

end

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The parameters block simply defines a set of default fluid properties to be used in case they are not defined by the user in their model.

4.4 Component Definition

Components are defined as belonging to a certain physical domain and inherit their variables from their parent domain. The components are the building blocks of the physical network and are connected to other components. They contain the necessary balance equations which determine the behavior of those connections. The Simscape code implementing a simple resistor can be seen in Listing 2.

Listing 2: Component definition of a simple electrical resistor [24]

component resistor nodes

p = foundation.electrical.electrical; % +:left n = foundation.electrical.electrical; % -:right end

variables

i = { 0, 'A' }; % Current v = { 0, 'V' }; % Voltage end

parameters

R = { 1, 'Ohm' }; % Resistance end

branches

i : p.i -> n.i;

end equations

v == p.v - n.v;

v == i*R;

end

The nodes

section declares the physical connection ports of the resistor. The variables section contains the (in this case) two principle variables which are used in the equations. In the parenthesis facing each variable is an initial value and the variable unit. The parameters

section is where the electrical resistance is defined, which is used as a coefficient in the equations. The branch

section defines the direction of the current of the component. Since the through variable in the electrical domain is the current, the declaration in the branch section also ensures compliance with Kirchoff’s Current Law. Lastly, the equations

section is where the familiar Ohm’s law is declared along with the relation determining the across variable (voltage) of the component, with p.v and n.v

being the across variable values at ports p and n.

Descriptions regarding the Simscape environment, solvers, library and the blocks which were used in developing the model for the hydraulic system have been omitted from the main body of this text for the sake of brevity. The interested reader can refer to appendix 2 and acquire the information they seek.

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5

Model creation

The initial phase of creating the model involved replicating the hydraulic system in the same manner its components are connected to one another using the Simscape components described in appendix 2.

5.1 Pump

For the pump, the “Centrifugal Pump Block” was used. The required tabulated data (pressure difference, flow rate) were obtained from the pump characteristic curves depicted in section 2.2.1.

The equations of the 2^nd order polynomial fits representing the curves were extracted and used to generate vectors of pump pressure differentials for the different rotational speeds. These were then stored as MATLAB variables, as shown in Figure 38, within the model workspace to be read by the pump block as required.

Figure 37: Accessing the model workspace from within the model window menu bar.

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Figure 38: The pump parameters stored in the model workspace.

Therefore, instead of directly defining the vectors in the block settings, the names of the relevant MATLAB variables are instead input as shown in Figure 39.

Figure 39: Pump block settings.

The angular velocity of the pump must be supplied to it by a separate block through its “S” port. This block is called the “Ideal Angular Velocity Source” located at 𝑆𝑖𝑚𝑠𝑐𝑎𝑝𝑒  𝐹𝑜𝑢𝑛𝑑𝑎𝑡𝑖𝑜𝑛 𝐿𝑖𝑏𝑟𝑎𝑟𝑦  𝑀𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙  𝑀𝑒𝑐𝑎ℎ𝑛𝑖𝑐𝑎𝑙 𝑆𝑜𝑢𝑟𝑐𝑒𝑠. The desired angular velocity must itself be input to this model through its physical signal port “S”. The setup is depicted in Figure 40.

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Figure 40: The pump as represented within the model.

5.2 Flow Controller

The flow controller was represented using the “Fixed Orifice Block”. Two blocks in a parallel configuration were used to represent the flows discharging through the Flow Controller’s two outlets, shown in Figure 41.

Figure 41: The flow controller as represented in the model.

5.3 Delivery Tube

Due to the geometrical variance present throughout the delivery tube it was divided into several smaller sections, each of which were represented using a hydraulic block. For the lengthy parts of the tube the “Resistive Pipe LP Block”, while for the bends and cross‐sectional changes the “Local Resistance Block” were used. This setup is shown in Figure 42.

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Figure 42: The delivery tube as represented in the model.

5.4 Spray Arms

The spray arms are represented using a combination of “Local Resistance” and “Fixed Orifice” blocks.

The orifice blocks were used to represent the nozzles while the resistance blocks were used for the flow entering the different sides of the arms. The orifice blocks were connected to “Hydraulic Reference Blocks” in order to model discharging to atmospheric conditions.

Figure 43: The top spray arm as represented in the model.

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Figure 44: The upper spray arm as represented in the model.

Figure 45: The lower spray arm as represented in the model.

5.5 The Initial Hydraulic Circuit

The initial simple hydraulic circuit resulting from the connection of these different sections to each other is depicted in Figure 46.

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Figure 46: The hydraulic circuit.

The next phase was determining the loss coefficients and other loss parameters within the blocks, such that the behavior of the model conformed to that of the actual dishwasher system.

5.6 Evaluating the Loss Parameters

To determine the loss parameters (pressure loss coefficients, equivalent length of resistances, discharge coefficients) the pressure losses from different regions of the system were required. To this end, simulation results from a CFD model of the dishwasher hydraulic system were used. This CFD model had been previously developed and its veracity confirmed, making it a suitable source for extracting the desired hydraulic data.

The regions from which the pressure losses were extracted are depicted in Figure 47 to Figure 52.

These were than used in tuning the coefficients of the corresponding blocks in the Simscape model.

(a) (b)

Figure 47: Extracted pressure losses in the flow controller. (a) Between flow controller entry and outlet to lower spray arm, (b) Between flow controller entry and outlet to delivery tube.

Delivery tube

Pump

Flow Controller

Sump

Lower spray arm Upper spray

arm

Top spray arm

To lower spray arm

From pump From pump

To delivery

tube

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Figure 48: Extracted pressure loss in lower spray arm collar.

To lower spray

arm entry

From Flow Controller outlet

From lower arm entry

To “Sun” arm topside nozzle

From lower arm entry To “Satellite” arm

entry

“Satellite” arm entry To “Satellite” arm

side 1

To “Satellite” arm

side 2

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Delivery tube entry

To after delivery tube entry bend

After delivery tube entry bend To before lower tube lower bend

Before tube lower bend To after tube

lower bend

After tube lower bend To upper spray arm

junction

upper spray

To upper spray arm entry

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Figure 50: Extracted pressure losses in delivery tube.

upper spray arm junction To before tube

upper bend

Before tube upper bend To after tube upper bend

To divided cross‐section before top spray arm entry

After tube upper bend

Divided cross‐section before top spray arm entry

To top spray arm entry

To before upper

spray arm bend

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Figure 51: Extracted pressure losses in upper spray arm.

Figure 52: Extracted pressure losses in top spray arm.

Additionally, the nozzle flow rates of each spray arm were also extracted and used in tuning the discharge coefficients of the model orifice blocks representing the nozzles.

In total, 18 steady‐state CFD simulations covering different combinations of pump speed and flow controller positions served as the dataset for evaluating the loss parameters. For the full hydraulic system, meaning both outlets of the flow controller being open, 51 parameters required evaluation.

For the lower and upper parts only, the number of parameters was 15 and 37 respectively.

5.7 The Simulink Parameter Estimation Tool

Identifying the coefficients of a system of equations with parameter constraints by comparing its response to that of a reference system is known as “Gray Box” modeling. Therefore, the approach for evaluating the loss parameters of the hydraulic model constitutes this approach, with the reference system being the CFD model.

Since the number of parameters is high and the hydraulic system represents a system of equations which are coupled to and constrained by each other, the parameters must be evaluated concurrently.

Simulink features a “Parameter Estimation” tool which can be used for this purpose. This tool can be

To upper spray arm side 1

After upper spray arm bend

To upper spray arm side 2 After upper spray

arm bend

From top spray arm entry

To top spray arm side 1

From top spray arm entry

To top spray arm

side 2

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Figure 53: Accessing the parameter estimation tool from the model window menu bar.

This opens the “Parameter Estimation” GUI shown in Figure 54.

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Figure 55: Select parameters window.

Opening “Select parameters” in this window displays a list of selectable parameters within the model.

Figure 56: Available parameters.

For parameters to show up in this list they must be defined as MATLAB variables, similar to what was described in section 5.1. Once selected, the parameters will appear in the previous window.

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Figure 57: Selected parameter(s) displayed in main window of “Select Parameters”.

The extremums of each parameter can be defined in their “Maximum” and “Minimum” fields. For the model parameters, the minimum was set to zero since loss parameters cannot be negative values. In the case of the nozzles, the maximum limit was set to 1 in accord with the theory covered in section 3.4.2.2. For the other parameters (pressure loss coefficients and equivalent lengths of resistances) no maximum limit was defined. The reasoning behind this is what was previously mentioned at the end of chapter 3; the components within the dishwasher system do not conform to those of typical piping systems, therefore it is not unreasonable to assume that the loss coefficients obtained for them will not conform to the typical values and limits found within pipe flow theory.

To estimate the parameters, the response of the model in its different parts needed to be monitored so they could be compared with the extracted data from the CFD model. This was achieved through the application of Sensor and Simulink Outport blocks which are described in appendix 2. After carrying out the required modifications, the model circuit became that shown in Figure 58.

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Figure 58: The modified model for parameter estimation.

Now the data from the CFD simulations must be input to serve as the reference against which the model response will be compared to. To do this, “New Experiment” is opened from the toolbar of the

“Parameter Estimation” GUI. The resulting window is shown in Figure 59.

Figure 59: The experiments window.

Opening “Select Measured Output Signals” displays a list of all selectable response signals of the

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Figure 60: The list of output signals from the model.

After selecting the desired output signals, they will appear in the previous window. Now the extracted data from the CFD model must be defined for each corresponding signal. This is done through the

“Edit signal data using variable editor” button as shown in Figure 61.

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e.g. 30 seconds, then view the simulation time data and use those for the time column of the time‐series matrix. An example is shown in Figure 62.

Figure 62: Representing the reference data in time‐series format.

The reference data can also be imported from CSV or Excel spreadsheet files should they exist.

Once this is done for all the output signals the parameter estimation can be carried out. The process is computationally intensive and therefore it is best to make use of parallel processing. The parameter estimation by default uses serial computing. Parallel computing can be enabled in “More Options”

accessible through the “Parameter Estimation” GUI and by checking the tick‐box next to “Use parallel pool during estimation”.

Figure 63: Enabling parallel processing in the parameter estimation options.

The other options such as the optimization method and algorithm were kept at their default settings.

After having carried out the previous tasks, the “Parameter Estimation” GUI is updated to reflect the

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Figure 64: Parameter estimation GUI with parameters and experiments sections updated.

Using the “Add Plots” menu on the toolbar the plots for the experiment (here the data from CFD) can be plotted. The “Plot Model Response” button also plots the current model response so its difference from the experiment data may be visually observed. This plot is continuously updated during the estimation process to reflect the changes in model response. Each set of model output and experiment data (the entries in Figure 61) are plotted separately within the GUI. An example of one such set of data plotted is shown in Figure 65.

Hydraulic Simulation Model for Dishwasher

Hydraulic Simulation Model for Dishwasher

SEYED MORTEZA HABIBI KHORASANI

Hydraulic Simulation Model for Dishwasher

SEYED MORTEZA HABIBI KHORASANI

Abstract

Acknowledgments

Contents

Nomenclature

𝐾

1

Introduction

1.1 A Brief History of Simulations

1.2 Why Modeling is Utilized

1.3 Modeling Approaches

1.5 Objective

2

The Dishwasher Appliance

2.1 The Dishwasher Appliance

2.2 The Hydraulic System

2.2.1 Circulation Pump

2.2.2 Flow Controller

2.2.3 Sump

2.3 Delivery Tube

2.4 Spray Arms

2.4.1 Lower Spray Arm

2.4.2 Upper Spray Arm

2.4.3 Top Spray Arm

3

Theory

3.1 Pipe Flow

3.2 Flow Regime in Pipe Flow

3.3 Energy Considerations in Pipe Flow

3.4.1 Major Head Loss

3.4.2.1

3.4.2.2

3.5 Centrifugal Pump

3.5.1 Pump Characteristics

3.5.2 System Characteristics and Operating Point

4

Simscape

4.1 Background

4.2 Variable Types

4.3 Physical Domains

4.4 Component Definition

5

Model creation

5.1 Pump

5.2 Flow Controller

5.3 Delivery Tube

5.4 Spray Arms

5.5 The Initial Hydraulic Circuit

5.6 Evaluating the Loss Parameters

To lower spray arm

From pump From pump

To delivery

tube

To lower spray

arm entry

From Flow Controller outlet

From lower arm entry

To “Sun” arm topside nozzle

From lower arm entry To “Satellite” arm

entry

“Satellite” arm entry To “Satellite” arm

side 1

To “Satellite” arm

side 2

Delivery tube entry

To after delivery tube entry bend

After delivery tube entry bend To before lower tube lower bend

Before tube lower bend To after tube

lower bend

After tube lower bend To upper spray arm

junction

upper spray

To upper spray arm entry

upper spray arm junction To before tube

upper bend

Before tube upper bend To after tube upper bend