Air distribution measurement in a room with a sidewall jet: A 3D benchmark test for CFD validation

Accepted Manuscript Air Distribution Measurement In A Room With A Sidewall Jet: A 3d Benchmark Test For Cfd Validation M. Hurnik, M. Blaszczok, Z. Popiolek PII:

S0360-1323(15)30052-4

DOI:

10.1016/j.buildenv.2015.07.004

Reference:

BAE 4182

To appear in:

Building and Environment

Received Date: 7 April 2015 Revised Date:

19 June 2015

Accepted Date: 5 July 2015

Please cite this article as: Hurnik M, Blaszczok M, Popiolek Z, Air Distribution Measurement In A Room With A Sidewall Jet: A 3d Benchmark Test For Cfd Validation, Building and Environment (2015), doi: 10.1016/j.buildenv.2015.07.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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AIR DISTRIBUTION MEASUREMENT IN A ROOM WITH A SIDEWALL JET: A 3D BENCHMARK TEST FOR CFD VALIDATION M. Hurnik*, M. Blaszczok, Z. Popiolek Department of Heating, Ventilation and Dust Removal Technology, Silesian University of

44-100 Gliwice, Poland __________________________________

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* Corresponding author, E-mail address: [email protected]

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Technology, Konarskiego 20,

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Keywords: sidewall jet, occupied zone, laser Doppler anemometer, low velocity thermal anemometer, CFD predictions, 3D benchmark

Highlights

New 3D benchmark for validating CFD predictions of room air movement is proposed

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Axial velocity component in jet is measured with laser Doppler anemometry

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Air speed in the occupied zone is measured with low velocity thermal anemometers

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Methods to validate CFD results in the jet and the occupied zone are proposed

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ABSTRACT

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In mixing ventilation systems, diffusers are often located on side walls and supply quasi-free air jets above the occupied zone. The aim of the current research was to create a new CFD 3D benchmark with two well-defined characteristic zones in the room, i.e., the quasi-free jet zone and the occupied zone. The measurements were performed in a physical scale model (1:5) of the room. The kinematic similarity criterion was fulfilled by the equality of the Reynolds numbers in the model and in the prototype. Measurement methods adequate for air velocity and speed measurement were applied: laser Doppler anemometry for the axial velocity component in the jet and low velocity

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thermal anemometry for the air speed in the occupied zone. The novelty of the paper is the identification of the evolution of the air mean velocity distribution with distance from the supply opening. In the distance of 15 to 30 equivalent diameters, the jet behaves as a free turbulent axisymmetric jet; its momentum flux is conserved and fixed at approximately 80% of the inlet

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momentum flux. At higher distances from the inlet, the confinement effect of partitions is observed. The CFD results validation and reporting methods applicable for the benchmark data are proposed. The new 3D benchmark can be useful for CFD researchers, engineers and students for testing

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different CFD modelling aspects and thus may contribute to the improvement of CFD prediction

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accuracy. The benchmark results are available in the Data in Brief article.

Nomenclature A area (m2) a inlet width (m)

B velocity decay coefficient D diameter (m)

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f weighing factor

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b inlet height (m)

k kinetic turbulence energy (m2/s2)

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M mean motion momentum flux in the axial direction (kg⋅m⋅s-2) m velocity distribution coefficient n exponent

R radial width of the jet (m) Tu turbulence intensity U velocity (m/s)

u velocity fluctuations (m/s) V volume flow rate (m3/s)

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W speed (m/s) x, y, z Cartesian coordinates (m) Greek symbols:

ρ density (kg/m3)

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Subscripts: o inlet e equivalent

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m maximum

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p point source of momentum model (PSM)

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Introduction

Computational fluid dynamics (CFD) is a useful tool supporting the design and optimization of ventilation systems in rooms. CFD is used to predict air movement, contamination dispersion, fire and smoke spread and indoor air quality and thermal comfort analysis [1, 2]. In many cases, CFD

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predictions may replace expensive and time-consuming full-scale or model measurements, especially in the case of large enclosures, rooms of complicated geometry and rooms with high internal or solar heat gains [3]. A very detailed review of CFD applications for room air movement

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is given by Awbi [4]. In the CFD modelling process, assumptions of steady or transient analysis and 2D or 3D approach must be made. A calculation grid and turbulence and radiation models must be

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selected. Wall treatment, boundary conditions and the discretization scheme have to be assumed as well. These assumptions yield different simplifications, and consequently, the CFD results contain uncertainties. Thus, the validation of a CFD program and training of CFD users are necessary. Validation is defined as the uncertainty assessment of a computational simulation by comparison with benchmark experimental data [5, 6]. The aim of validation is to prove that both the user and

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the CFD code have the ability to properly perform simulations [7]. The data used as a benchmark for CFD validation should contain complete and detailed information on simulated object geometry,

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initial conditions, boundary conditions and measurement results with their uncertainties. In mixing ventilation systems, diffusers are often located on side walls and supply the quasi-free air

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jets above the occupied zone. This system is used in offices, conference rooms, auditoriums and concert and sport halls. In this system, two well defined characteristic zones, i.e., the quasi-free jet zone and the zone of induced secondary flows (occupied zone), occur in the room. Despite the fact that this case is often used in practice, it has not yet been described. The objective of the present study was to identify turbulent diffusion of the air in the 3D jet supplied from a sidewall diffuser, to determine the impact of room partitions on the jet confinement and to identify the air speed distribution within the occupied zone. The authors’ intention was to create a new 3D benchmark useful for CFD beginners and advanced researchers, students and engineers. The benchmark can be

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used to test different CFD modelling aspects, such as steady or transient approach, calculation grid, turbulence model, wall treatment, boundary conditions, discretization scheme etc. The new 3D benchmark test for CFD validation, i.e., the 3D jet supplied from a sidewall diffuser, and the other most representative experiments listed below that were used to validate the CFD

used in the experiments are also indicated in Fig. 1.

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predictions are schematically presented in Fig. 1. The methods for air velocity/speed measurements

2D case -The first CFD simulations of the air distribution in a room were performed by Nielsen [8].

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A detailed description of this test is available on the website http://cfd-benchmark.com and in the papers [9, 10]. So far, this two-dimensional benchmark test has been used approximately 50 times

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for different studies [1].

3D jet in enclosure - Hjertager et al. [11] measured the air velocity in a jet injected into a square sectioned enclosure. The measurement results were compared to CFD predictions [12]. 2D & 3D wall jet with separation - 2D and 3D wall jets in an empty room and in the same room with obstacles were tested by Awbi et al. [4].

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Large flow obstruction - The air distribution in a room with a large flow obstruction was tested by Posner et al. [13]. Rectangular inlets and outlets were located at the ceiling, and the air was supplied

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vertically downwards.

3D non-isothermal jet - A full-scale test room was used to validate CFD with four different RANS

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turbulence models [14]. The jet was supplied horizontally from a round nozzle located below the ceiling. Three cases were experimentally tested: isothermal, “hot” and “cold”. 2D&3D airflow and heat exchange - 2D and 3D cases simulating a twin-aisle airline cabin were used to validate 12 different turbulence models [15]. Airflow from diffusers - Different types of diffusers, also called air terminal devices or ATDs, which often have complex geometry, are used to supply air into rooms. Many researchers have modelled the airflow supplied from diffusers [16-22].

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Full-scale measurements - The air temperature and velocity distributions in full-scale rooms were tested by many researchers [23-29]. The CFD benchmarks of simulated sitting and standing people in cases of mixing, displacement and personal ventilation are available on http://cfd-

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benchmarks.com [30-31] and in the paper [32].

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Fig. 1. CFD benchmarks: a) 2D case, b) 3D jet in enclosure, c) 2D & 3D wall jet with separation, d) large flow obstruction, e) 3D non-isothermal jet, f) 2D&3D airflow and heat exchange, g) airflow from diffusers, h) full-scale measurements in climate chambers, i) 3D jet supplied from sidewall,

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the benchmark test presented in the paper; HWA - hot-wire anemometer, LDA - laser Doppler

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anemometer, HFA - hot-film anemometer, PIV - particle image velocimetry, UA - ultrasonic anemometer, LVTA - low velocity thermal anemometer

Fig. 1 shows the wide variety of the tested air distribution systems and flow elements as well as the measurement methods used for CFD validation. Using laser Doppler anemometry (LDA), particle image velocimetry (PIV) and ultrasonic anemometry (UA), the results of velocity component measurements can be directly compared to the CFD prediction results. Hot-wire anemometry (HWA) and hot-film anemometry (HFA) are directionally sensitive and at turbulence intensities

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higher than 25%, tend to overestimate the velocity. Thus, additional uncertainty caused by these factors has to be considered. Low velocity thermal anemometers (LVTAs) measure the air speed (the magnitude of the instantaneous velocity vector), and the measurement results can be compared to the CFD prediction results only if the air speed is estimated from CFD results using the methods

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presented in [33, 34] and in section 3.2. LVTAs are recommended by international standards [35] for measuring the air speed in occupied zones for assessing thermal comfort.

In the presented benchmark tests, adequate measurement methods for air velocity/speed

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measurement were applied: laser Doppler anemometry for the axial velocity component in the jet and low velocity thermal anemometry for the air speed in the occupied zone. The tested enclosure

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had dimensions corresponding to the average sized office or residential room. The supply nozzle construction guaranteed uniform velocity distribution and low turbulence in the supply opening. Thus, the boundary values of the air jet volume and the momentum fluxes could be accurately measured. The novelty of the paper is the identification of the evolution of the air mean velocity distribution with the distance from the supply opening. The measurements in the jet region were

supply opening [36].

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focused on determining the jet volume and the momentum flux changes with the distance from the

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This paper also presents a method for CFD results validation and reporting, relevant for the new benchmark. CFD calculations were performed for two cases. In case “A”, the boundary conditions

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were exactly the same as in the benchmark experiment. However, a higher momentum flux in the jet and a higher speed in the occupied zone were obtained. In case “B”, the initial momentum flux was reduced (by enlarging the supply opening and reducing the velocity), and in result, the values of the momentum flux in the jet and the speed in the occupied zone were close to the measured values.

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Experiment

2.1 Tested room The measurements were carried out in isothermal conditions in a room with dimensions of 6×6×3 m

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(length × width × height), as shown in Fig. 2.

Fig. 2. Tested ventilated room and the coordinate systems

The jet was generated by a diffuser with a rectangular nozzle of the dimensions 0.144×0.096 m,

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(equivalent diameter De=0.133 m) positioned on the wall at half of the room width and at 2.35 m above the floor. The nozzle profile was calculated using the third order polynomial equation [36]. The contraction ratio of the nozzle was equal to 5.2.

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The air supply velocity Uo was equal to 5.16 m/s, and the corresponding air change rate was equal

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to 2.4 h-1. The exhaust opening had the same dimensions as the supply opening and was positioned near the floor on the same wall as the supply opening. The measurements were carried out in a physical scale model (1:5) of the room. The kinematic similarity criterion was fulfilled by the equality of the Reynolds numbers in the model and the prototype, ReM = ReP = 45,300. This yielded five times higher velocity and 52 faster turbulent fluctuations in the scale model than in the prototype and, consequently, resulted in lower uncertainties of the air speed measurement in the occupied zone and lower uncertainties of the statistical estimators of the mean and standard deviation (uncertainties due to the limited averaging time). Although the measurements were

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performed in the 1:5 physical model, all of the results presented in the paper and attachments were recalculated for the prototype conditions.

2.2 Measurement methods

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The measurements of the airflow in the presented benchmark tests were performed in two zones: the quasi-free jet zone and the occupied zone. To identify the boundary conditions, additional measurements were carried out in the inlet region (as close as possible to the supply opening). The

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measurement methods were selected depending on the flow characteristics in each zone. Jet zone

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The airflow in the jet zone is characterised by high velocity, exceeding 0.2 m/s, and relatively welldefined flow direction. Three regions can be distinguished in the jet: the initial region, the turbulent free jet region and the attachment/impingement jet region. In the initial region the potential core is observed; the zone of turbulent mixing of supplied air and ambient air increases with distance from the opening, and the jet becomes axisymmetric. In the turbulent free jet region, high turbulence

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intensity Tu occurs. Test results have shown that in a free jet Tu changes from approximately 25% in the jet axis and 43% at the radial distance r/R=1 to more than 100% at the jet edge [37]. For high

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turbulence intensity, it is difficult to interpret the signal from a hot-wire anemometer (HWA) [38] and, in general, the measured velocity can be overestimated. The jet momentum determined based

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on the velocity measured with a stationary hot-wire anemometer was equal to106% of the source momentum. In comparison, when the results obtained with a so-called flying hot-wire anemometer or an LDA method were used, the jet momentum was only 85% of the source momentum [37]. Thus, in the jet region, the methods allowing measurement of the axial velocity component are preferred. The air velocity components can be measured using the LDA, ultrasonic anemometer and particle image velocimetry methods. In the present benchmark tests, LDA was used to measure two selected air velocity components [36]. The uncertainty of the velocity measurement with LDA was

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assessed by the manufacturer to be lower than 5% of the mean velocity value [39]. The LDA measurement results and the CFD prediction results could be directly compared. The benchmark room model was made of organic glass, and the air was seeded with paraffin fog. The seeding particles were mixed with the air in a special mixing chamber, as shown in Fig. 3. The

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particles were produced by a Safex Fog Generator located in the chamber. The supply and exhaust fans, controlled by two frequency converters, were connected to the mixing chamber and the room model. The supply velocity was controlled by a static pressure measurement at the nozzle inlet.

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Zero static pressure difference between the model of the room and the surrounding laboratory hall was maintained. At each measurement point, samples were collected during the period of 300 s.

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Axial and lateral velocity components were measured at 222 points in two perpendicular planes that crossed at the middle of the supply opening. The velocity measurement results are presented in the

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file LDA&LVTA_results.xlsx, which is attached to the article [36].

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Fig. 3. Scheme of the experimental setup

Occupied zone

The air speed measurements in the occupied zone were performed in a uniform measurement grid, and 200 measurement points were located on eight horizontal planes (25 points on each plane) at heights from 0.1 m to 1.8 m and 0.5 m away from the walls. Omnidirectional hot sphere low velocity thermal anemometers (LVTA), recommended for air speed measurement in the occupied zone, were used. The uncertainty of the mean speed measurement was lower than 0.01 m/s (see 10

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chapter 5). The results of the mean speed and the speed standard deviation measurements in the occupied zone are presented in the file LDA&LVTA_results.xlsx [36].

Boundary conditions in the supply opening

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The measurements were carried out in the inlet region as close as possible to the supply opening. The aim of these measurements was to identify the boundary conditions at the inlet, such as the inlet mean velocity, inlet volume flux, inlet momentum flux, turbulence kinetic energy and turbulence

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intensity. Two measurement series were performed. The velocity measurement was performed in a regular grid of 12.5×12.5 mm (96 points) using a micro Pitot tube at the distance x=12.5 mm from

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the nozzle (0.094 De) with expanded uncertainty of 0.5%; the other measurement was carried out using LDA. The axial and lateral velocity components were measuredin418 points (a regular grid of 10×10 mm) at the distance x=145 mm (1.1 De) from the nozzle. The results are presented in the file

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CFD predictions

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Inlet_boundary_cond.xlsx [36].

To show how CFD results can be validated with the presented experimental data, exemplary CFD

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predictions of the benchmark case were performed. The new benchmark geometry is intentionally very simple and can be modelled with any CFD code. The CFD modelling method presented in this

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paper is also simple and widely used in engineering applications.

3.1 Method

The standard two equation k-ε turbulence model with enhanced wall treatment included in the Fluent Airpak 3.0.16 commercial code was applied [40]. The simulations were performed under isothermal conditions, so only the flow variables (velocity and pressure) were calculated. The second-order upwind discretization scheme and the SIMPLE algorithm for coupling pressurevelocity [40] were used. The under-relaxation factors were set to 0.3 for the pressure, 0.7 for both

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the momentum and turbulence dissipation rate ε, and 0.5 for the turbulence kinetic energy k. Taking into account the modelled room symmetry, the calculations were only performed in half of the room. The Cartesian grid was selected, and to minimize numerical diffusion, a fine grid was used in the regions with high gradients, i.e., at the supply opening, in the jet and near the walls. The

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dimensions of the modelled half of the supply opening (width/2 × height) were 0.072×0.096 m in case “A” and 0.0858×0.1148 m in case “B”. The inlet air velocities Uo were equal to 5.16 and 3.621 m/s for cases “A” and “B”, respectively. In both cases, the initial air volume flux was the

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same, Vo=0.0713 m3/s. Within the modelled half of the supply opening 9×12=108 cells were created in case “A” and 11×14=154 cells were created in case “B”. The size of the cells near all of

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the walls was set to 0.01m. The smallest cells size was at the supply opening: 0.008 m in the y and z directions and 0.01 m in the x direction. The cell size increased with the distance from the inlet and the walls, and the size ratio was equal to 1.05. The maximum size of the cells in the x, y and z directions was set to 0.06 m. The total number of the cells was approximately 2×106 in both cases. The number of cells was ten times higher than the minimum number required by German guideline

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VDI 6019 [1]. To show the independence of the results from the mesh size, the CFD calculations were performed with 50% larger cell size, i.e., 0.012 m in the y and z directions and 0.015 m in the

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x direction at the supply opening and 0.015 m near all of the walls. The maximum cells size in all directions was set to 0.09 m. In that case, the total number of the cells was approximately 1×106.

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The comparison of the CFD prediction results obtained for 2×106 cells and 1×106 cells is shown in Fig. 4. The CFD prediction results are practically independent from the cells size for cases with more than 1×106 cells.

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Fig. 4. Comparison of CFD prediction results obtained using meshes with 2·106 and 1·106 cells: a) jet region - distributions of axial mean velocity component Ux , b) occupied zone - cumulative distributions of mean speed W e

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The turbulence intensity in the supply opening was set equal to 4.1% (as for the value measured at the nozzle outlet, see the file Inlet_boundary_cond.xlsx [36]), and turbulence length scale was set to 0.1×opening height.

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After approximately 1.2×104 iterations, the converged solutions were obtained. The residuals stabilized on the levels of 3-7×10-7 for the mean velocity components, 3-5×10-8 for k and ε and

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8×10-4 for continuity (pressure). The mean velocity values monitored in the jet and the occupied zone regions stabilized after approximately 4×103 iterations. Generally, all of the requirements concerning the CFD quality control presented in the REHVA guidebook [1] were fulfilled.

3.2 Estimation of air speed in the occupied zone Speed, i.e., the magnitude of the velocity vector, measured by low velocity thermal omnidirectional anemometers cannot be directly compared to the velocity predicted by CFD simulation. Due to fluctuations in the magnitude and direction of the instantaneous velocity, the mean speed W will be 13

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different than the mean velocity U from CFD predictions. The standard deviation of speed ∗ fluctuations w will also be different than the average standard deviation of the velocity predicted

(

)

by CFD simulations (2k/3)0.5, where k = u x2 + u y2 + u z2 / 2 is a turbulence kinetic energy. Thus, the velocity turbulence intensity, determined based on the turbulence kinetic energy and the mean

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velocity, Tu = (2k / 3)0.5 / U , will be different from the speed turbulence intensity, TuW = w∗ /W . To ∗ compare the CFD and measurement results, W and w need to be estimated from the CFD results.

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For this estimation, the method suggested by Koskela et al. [33] and Popiołek et al. [34] can be applied. The method proposed by Koskela et al. [33] is based on theoretical studies and

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experimental laboratory tests. A theoretical correlation was developed by statistical calculations with the assumption of normally distributed and uncorrelated turbulent velocity components. A 3D ultrasonic anemometer was used for air velocity measurement. Popiolek at al [34] experimentally identified the differences between velocity and speed based on 3D LDA measurements performed

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in the occupied zones of two full-scale test rooms with different ventilation systems, diffusers, air exchange rates, air temperatures etc. A comprehensive database of 291 instantaneous velocity measurements collected in the tests [41] was analysed. The LDA measurements of three

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instantaneous velocity components were used to identify the instantaneous speed W, the mean speed ∗

W , and the standard deviation of the speed fluctuations w . The 3D LDA data makes it possible to

(

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calculate the mean velocity components U x , U y and U z the mean velocity U = U x2 + U y2 + U z2 the three components of the standard deviation of the velocity fluctuations

Popiołek et al. [34] proposed a set of two equations to estimate the mean speed. The present research found that these two equations can be replaced by a single equation that fits the

[

(

)]

W e U = 1 + 1 .2668 1 − EXP − (Tu 1.0979 ) Tu 1.051

(1) 14

0.5

and

u∗x , u∗y and u∗z , which are

used to calculate the turbulence kinetic energy.

experimental data slightly better:

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The results shown in Fig. 5 illustrate the accuracy of the estimation. Fig. 5a shows the difference between the estimated mean speed W e (based on the mean velocity and the turbulence intensity, Eq. 1), and the mean speed W obtained directly from the LDA measurements analyses. The results

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show that the mean speed can be estimated by Eq. 1 with an uncertainty of 0.0058 m/s.

Fig. 5. a) Difference between the estimated mean speed W e calculated by Eq. 1 and the mean speed

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W obtained from the LDA measurements analyses; b) Relative difference between we* (estimated standard deviation of speed, calculated from Eq. 3) and the measured speed standard deviation w* ; the dotted lines define the uncertainty of the W e and we* estimation. The mean squared value of the speed can be calculated from the equation: 2

2

W e2 = We + we2 = U + 2k

(2)

Then, the speed standard deviation can be found:

(

2

)

2 0.5

w∗e = we2 = U + 2k − W e

(3)

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The results in Fig. 5b illustrate the accuracy of the standard deviation of the speed estimation using Eq. 3. The results show that the standard deviation of the speed can be predicted with an uncertainty of 25%.

Validation of the CFD results

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4.

The presented benchmark has two characteristic airflow zones: the quasi-free jet zone with a relatively high velocity and a well-defined flow direction and the occupied zone with low velocity,

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high turbulence, recirculating and induced secondary flow. In the jet zone, the CFD results can be validated by comparison to the LDA measurement data of the mean axial velocity component U x ,

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the volume flux V and the mean motion momentum flux in the axial direction M. The air speed W measured with LVTAs is one of the main physical parameters that is needed to assess thermal comfort and draught rating. Thus, comparison of the speed distributions is an appropriate method

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for CFD validation in the occupied zone.

4.1 Determination of the maximum mean velocity, volume flux and momentum flux in the jet In the benchmark tests, the jet is supplied from the rectangular opening and affected by the ceiling;

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therefore, it cannot be treated as an axisymmetric jet. Due to the Coanda effect, the jet axis position , z m and the position of the point of maximum velocity ym change with the distance from the opening

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and have to be identified.

The values of the mean axial air velocity component U x measured and calculated in several crosssections of the turbulent jet region at the distance 5-43 De from the supply opening were approximated using a quasi-Gaussian exponential curve:

U x,apr

  r = U xm ⋅ exp−    Rα

  

n

  

(4)

where the radial distance from the jet axis position equals r = [( z − zm )2 + ( y − ym, )2 ]0.5 . To describe the velocity distribution in an asymmetric air jet, the angular change in the velocity profile width 16

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should be considered. In the case of the CFD results, it was possible to analyse the radial changes of the velocity in a 360° range (180°covered by the CFD data and 180° covered by the assumption of flow symmetry in the z plane). In this case, the angular changes were analysed in detail, and the jet profile width was calculated as a trigonometric series of six harmonic components: (5)

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Rα = R (1 + a1 cos α + a 2 cos 2α + a 3 cos 3α + a 4 cos 4α + a 5 cos 5α + a 6 cos 6α )

where α = arctan2[( z − z m ), ( y − ym, )]

The LDA measurements were performed in two perpendicular axes in the z and y’ directions. Thus,

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using the experimental data was able to find only the profile width changes in these directions. The amplitude of the second harmonic component a2 was calculated, and the other amplitudes were set

axis was assumed).

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equal to 0 (symmetry of the velocity distribution in the vertical and horizontal planes across the jet

In the proposed method, only the velocity results U x >0.2 m/s measured or calculated at the distance r/Rα<1.5 were used in the approximation. The approximation error was calculated as:

Σ(

)

(6)

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∆1 min

 n 2 = U x,i - U x,apr ,i   min  i=1

The least squares method was used to find the axial mean velocity component in the jet axis U xm ,

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the position of the maximum jet velocity z m and ym, , the exponent n, the jet profile average width R

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and the amplitudes a1-a6.

The results of the benchmark test LDA measurements of U x in the jet and their approximations using Eqs. 4 and 5 are shown in Fig. 6.

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Fig. 6. Radial distribution of the axial mean velocity component U x in the jet from the LDA measurement results

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Based on the above approximation results, the axial mean velocity component U x was calculated in n uniform elementary areas ∆S=0.01×0.01 m in size; then, the volume flux V and momentum flux

V = ∆S

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M in a cross-section of the jet were determined: n

∑U

(7)

x ,i

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i =1

M / ρ = ∆S

n

∑U

2 x ,i

(8)

i =1

Fig. 7 shows the results of the LDA measurement and the CFD prediction of parameters of the axial mean velocity component determined using the above method. Additionally, to identify the inlet boundary conditions such as the inlet velocity Uo, the inlet volume flux Vo, the momentum flux Mo and the inlet turbulence kinetic energy ko, the measurements were performed at distances equal to 0.09 De and 1.1 De (De =0.133 m) using a Pitot tube and the LDA method, respectively. The results are presented in the benchmark Excel file Inlet_boundary_cond.xls [36]. 18

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Fig. 7a shows that within the range of x/De =10-36, the maximum axial mean velocity component U xm changes inversely as a function of the distance from the supply opening. The results presented

in Figs. 7b and 7c illustrate that within the range of x/De=10-31, the jet spreads and the air volume flux increases linearly. Qualitatively, the U xm , R and V changes are similar for the measurement and

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CFD results. The LDA results show that the momentum flux M in the potential core and in the initial region x/De=0 -15 decreases by approximately 20% of its initial value. In the range of x/De=15-30, the momentum flux M stabilizes and drops down in the jet impingement region. For the

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CFD prediction, the momentum flux M increases with the distance from the supply opening, reaching its maximum value of approximately 23% higher than the initial value at x/De=33 and

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dropping down near the opposite wall, as in the case of the LDA results.

Fig. 7. LDA measurement and CFD prediction results, comparing the mean axial velocity component parameters 19

ACCEPTED MANUSCRIPT Significant differences between the measurement and CFD results are observed for the volume flux V and momentum flux M (see Fig. 7c and Fig. 7d). When using the point source of the momentum model of a free axisymmetric jet (PSM), the volume flux V and the momentum flux M depend on

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the maximum axial mean velocity U xm and the jet width R as follows: V ~ U xm ⋅ R 2 and M ~ U xm2 ⋅ R 2 . For CFD “A”, the measured and predicted U xm agree well, but the predicted jet width R is on average 23% higher than the measured one. Thus, both the predicted V and M values are 50%

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higher than the measured ones. For CFD “B”, the predicted U xm is on average 15% lower than the measured one and the predicted jet width R is on average 20% higher than the measured one. This

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difference results in a 23% higher predicted V and a 4% higher predicted M on average. The main reason for the discrepancies between the CFD predictions and measurements is the much higher jet spread in the CFD predictions.

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4.2 Approximation of the velocity distribution in the jet using the PSM model For a quantitative comparison of the LDA benchmark, the CFD results and the data available from other tests, the LDA and CFD results were approximated using a point source of momentum (PSM)

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model. In the case of the presented benchmark test, the jet can be considered a free turbulent jet at distances from the supply opening x of 10 to 31De (see Fig. 7). The PSM model assumes self-

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preservation of the flow in the jet and conservation of the mean motion momentum flux in the axial direction M. A Gaussian shape of the mean velocity radial distribution is typically assumed. In this case, the mean axial velocity component U x in a turbulent region can be described using the equation: U x = k M B U o ( x − xo )

−1

where k M = (M M o )0 .5

2  r   2   De exp  − 2 B    x − xo  

(9)

(10)

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The PSM model has three parameters: B - the velocity decay coefficient (throw constant), xo- the origin position (the position of the virtual point source of momentum) and kM - the momentum loss coefficient. Instead of coefficient B, the velocity decay coefficient BU = k M ⋅ B and the velocity distribution coefficient m = 2B2 are often used.

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The characteristic parameters of the PSM jet model were identified based on U xm and V changes as a function of the distance from the supply opening and based on M. These parameters are described by the equations: = k M B U o ( x − x o ) D e = BU U o ( x − x o ) D e −1

xm , p

−1

(11)

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U

Mp ρ =

π 4

k M2 D e2 U o2

(13)

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V p = 2 k M B −1 V o (x − x o ) D e (12)

The values of B, xo and kM were obtained through optimisation using the least squares method:

(14)

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2 2   U xm, p − U xm 2  Vp −V   Mp − M    + ∑  + ∑   ∆2 min = ∑   U xm  M i min  V i i

Then, the changes in the jet width Rp can also be found: R p = 2 − 0 .5 B − 1 ( x − x o ) (15)

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The values of xo/ De, B, km and m obtained from the LDA measurement and the CFD prediction

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results are given in Tab. 1.

Table 1. The values of the characteristic parameters of the PSM jet model obtained for the LDA measurement and the CFD prediction results

xo/ De B BU km m

LDA 0.7 6.4 5.7 89% 81

CFD “A” CFD “B” -0.2 0 5.3 5.3 5.8 4.8 109% 91% 56 57

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prediction results, the method of the mean air speed W and standard deviation w estimation based

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on mean air velocity U and turbulence kinetic energy k presented in chapter 3.2 was used. The ∗ measured and predicted values of W and w were used to calculate the cumulative distribution

functions of these parameters in the occupied zone, as shown in Fig. 8. Additionally, the percentage

(

) (0.37 w 0.62

∗

+ 3.14 )/ 100

(16)

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DR = (34 − ta ) W − 0.05

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of people dissatisfied due to draught sensation DR was calculated [35]:

where ta is the air temperature, and ta=23°C was assumed

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The cumulative distribution function of DR in the occupied zone is also shown in Fig. 8.

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∗ Fig. 8. Cumulative distributions of W , w and DR in the occupied zone, comparing the LVTA

measurements and the CFD predictions

4.4. Maps of mean air velocity and speed contours The LDA measurement results in the jet region, the LVTA measurement results in the occupied zone, and the CFD prediction results are presented as contour maps of the mean air velocity and the mean air speed in Figs. 9-11.

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Fig. 9. Maps of the axial mean air velocity component contours in selected x-plane cross sections, comparing the LDA measurements and the CFD prediction results

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Fig. 10. Maps of the axial mean air velocity component contours in the z = 0 plane cross section, a) LDA measurement, b) CFD prediction results for case “A”, c) CFD prediction results for

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case “B”

Fig. 11. Maps of the mean air speed contours in the x = 0 plane cross section, a) LVTA measurement, b) CFD prediction results for case “A”, c) CFD prediction results for case “B”

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Discussion

Jet zone Both the benchmark test and the CFD “A” prediction results showed that the jet core zone length was approximately 5De (Fig. 7a). Both results showed the maximum jet axis deflection at a distance

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from the supply opening of x = 4.7 m (35 De); at this distance, the jet axis is shifted up approximately 0.17 m (1.3 De). At the distance x/De <31 from the supply opening (2/3 of the room length), the jet behaved as a quasi-free jet, the maximum axial mean velocity component changed

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inversely to the distance from the opening, and the jet spread and the air volume flux increased linearly.

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The CFD predicted a higher than measured spread ratio of the jet. The discrepancies start close to the supply opening in the core and transition zones. This result implies that at the distance x=10 De in CFD “A”, the jet is more symmetrical but wider than the measured jet (Fig. 9). The higher spread ratio in the case of CFD “A” is also observed at longer distances from the supply opening. The jet attaches to the ceiling in the LDA measurements at the distance x equal to approximately 3.5 m (26

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De) and at one meter closer at x=2.5 m (20 De) in the case of CFD “A” (Fig. 10). In both cases, the jet impingement zone, which is characterized by a decrease in the volume and momentum flux

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values, begins at the distance x=4.3 m (33 De) (Fig. 7c, d). Unlike the discrepancies in the jet width, good agreement between the measured and predicted (CFD “A”) values of the maximum axial

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mean velocity component U xm is observed (Fig. 7a) that is confirmed by the agreement between the

BU velocity decay coefficients of the LDA and CFD “A” (Tab. 1). The velocity decay coefficients B and BU determined based on the LDA results are equal to 6.4 and 5.7, respectively, corresponding to a velocity distribution coefficient of m=82. The above coefficient values are generally in good agreement with previous tests of axisymmetric free jet discharged nozzles with low turbulence intensity, i.e., Hussein et al. [37] with BU=5.8, Panchapakesan et al. [42] with BU=6.06 and Malmström et al. [43] (for Re=4.5×104) with BU=5.8.

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In chapter 4.1, the measured and predicted (CFD “A”) jet momentum flux values were compared. In the case of the benchmark test, the momentum loss coefficient kM (Eq. 10) is approximately 0.89 (Tab. 1). Hussein et al. [28] analysed the effect of jet confinement on momentum conservation. They

2  4  x  Ao   M M ' = 1 + 2    BU  De  AR 

−1

(17)

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where M’ is the jet momentum without the confinement effect.

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proposed the following equation for the momentum loss caused by the reverse flow:

In their experimental facilities, for Ao=4.9×10-4 m2, AR=23.9 m2and x/De=70, the loss due to the

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effect of confinement was identified as 0.99 and the total momentum loss was equal to 0.85. Thus, based on the jet tests [37], approximately 14% of the initial momentum was lost in the core and in the transition zones of the jet and an additional 1% of momentum was lost by the generation of the reverse flow. Taking into account the benchmark data (Ao = 1.38×10-2 m2, AR = 18 m2, x/De = 33),

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the momentum loss coefficient can be estimated as M/M’= 0.905 according to Eq. 17. Thus, in the benchmark, the total momentum loss can be found as equal to M/Mo = 0.86×0.905 = 0.78

→kM = 0.88. The identified coefficient of the total momentum loss kM = 0.89 agrees with the data of

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Hussein et al. [37].

Compared to the benchmark test results, the momentum fluxes M identified based on the CFD “A”

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results at the distances x/De = 10, 15 and 30 are approximately 20%, 40% and 60% higher, respectively. In the quasi-axisymmetric free jet region, i.e., x/De =10-30, the momentum flux M from CFD “A” is approximately 43% higher on average than the measured one. Moreover, in the case of CFD“A”, the jet momentum flux M is much higher than the momentum at the supply opening Mo in all of the jet zones except the impingement zone. The higher momentum flux may be caused by several reasons such as the turbulence model, the grid system, the numerical scheme, etc. The purpose of the present study was not to find these reasons.

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Occupied zone

Jackman [44] tested the air movement in a room with sidewall mounted grilles. His work is reported in the Awbi textbook [4]. Jackman found that the average speed in the occupied zone depended on the square root of the jet momentum and on the room dimensions. Thus, if the predicted jet

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momentum flux is much higher than the momentum at the supply opening, a higher mean air speed in the occupied zone than the measured speed can be expected. Comparing the case of CFD “A” to the measurements (see Fig. 8) confirms this supposition. The measured mean air speed W in the

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occupied zone changed from 0.07 to 0.28 m/s depending on the location. The measured average value of Wz was equal to 0.145 m/s. In the case of CFD “A”, the predicted average value of Wz was

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0.044 m/s (30%) higher than the measured value. The uncertainty of the mean air speed measurement in the scale model using LVTA is 0.02+0.02·W m/s [45]. After the conversion of the air speed measurement results from the scale model (1:5) to the prototype, an uncertainty of the air speed measurement equal to 0.01 m/s can be expected (within the air speed range of 0.07 to

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0.28 m/s). As mentioned in chapter 3.2, the mean speed can be estimated based on the CFD results with an uncertainty of 0.0058 m/s. The difference between the predicted and measured average value of the mean air speed in the occupied zone (0.044 m/s) was three times higher than the sum of

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both uncertainties; thus, the difference was statistically significant. The measured average standard deviation of the air speed w z∗ in the occupied zone was equal to 0.049 m/s. The predicted (CFD

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“A”) w z∗ value was higher than the measured value at 0.063 m/s (28% higher). The uncertainty analysis cannot confirm whether this difference is statistically significant. ISO standard 7730 [35] defines three quality categories of indoor thermal environment referring to draught sensation: category A if DR<10%; B if DR<20% and C if DR<30%. When assessing the draught rate based on the LVTA measurement results, 43% of the occupied zone fulfilled the requirement of category A, and 82% of the space fulfilled the requirement of category B. In the CFD “A”, categories A and B included 5% and 67% of the occupied zone, respectively. 27

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To answer whether the improvement in the jet simulation will result in higher accuracy of the air speed prediction in the occupied zone, CFD “B” calculations were performed. The predicted momentum flux in the jet was 43% higher than the measured flux; therefore, the CFD calculations were repeated to reduce the momentum flux in the supply opening to 70% (1/1.43 times) compared

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to case “A”. In case “B”, the dimensions of the supply opening were enlarged to 0.0858×0.1148 m and the inlet air velocity was reduced to Uo = 3.621 m/s. The volume flux of the supplied air was not changed at Vo = 0.0713 m3/s. The comparison of the measured and predicted (case “B”) air

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speed in the occupied zone presented in Fig. 7 confirms that accurate reproduction of the jet momentum is a necessary condition for air speed modelling in the occupied zone. The difference

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between the predicted (CFD “B”) and measured mean air speed in the occupied zone was only 0.007 m/s. The differences between the predicted (CFD “B”) and measured average standard deviation of speed and average draught rate in the occupied zone were also small at 0.003 m/s and

6. Conclusions

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0.8%, respectively.

This paper presents a new 3D benchmark test for validating CFD predictions of room air

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movement. The benchmark data were used to validate the CFD results obtained using the standard two equation k-ε turbulence model with enhanced wall treatment. Different validation methods

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were proposed and applied to the jet region and occupied zones. Based on measurement and CFD prediction results, the following conclusions can be drawn:

•

In the jet zone, the CFD prediction results can be validated by comparison with LDA measurement results of the mean axial velocity component. Comparison of the mean speed cumulative distributions is an appropriate method of CFD validation in the occupied zone.

•

The good agreement between the measured and calculated maximum mean air velocity in the jet, which can be observed on the contour maps, does not confirm unambiguously that the

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airflow in the jet is properly simulated. Thus, the CFD results validation based on the comparison of the velocity contour maps is not conclusive.

•

The new validation method of the CFD prediction results in the free jet region using the point source of the momentum model was proposed. The comparison of the measured and predicted mean air speed in the occupied zone confirms

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•

that accurate reproduction of the jet momentum is a necessary condition for air speed modelling in the occupied zone.

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The tests confirmed that both the benchmark data and the proposed validation methods could be useful for validating different aspects of CFD prediction modelling. The 3D benchmark test results

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are attached to the article [36].

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Acknowledgements

This work was supported by Polish Ministry of Science and Higher Education – statute research BK254/RIE-1/2015

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[44] Jackman PJ. Air movement in rooms with side-wall mounted grilles – A design procedure; BSRIA Lab. Rep. No. 65, 1970,Building Services Research and Information Association, Bracknell, UK [45] Melikov AK, Popiolek Z, Silva MG, Care I, Sefker T. Accuracy limitations for low-velocity

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measurements and draught assessment in rooms HVAC&R Research 2007;13(6):971-86

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Axial velocity component in jet is measured with laser Doppler anemometry

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Air speed in the occupied zone is measured with low velocity thermal anemometers

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Methods to validate CFD results in the jet and the occupied zone are proposed

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•