TechnicalPapers

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Keihin Technical Review Vol.6 (2017)

Investigation of CFD Temperature Prediction for

HVAC Units※

Technical Paper

1. Introduction

In recent years , due to h igh per formance

requirements of air conditioning systems, the

c o m p l ex i t y o f H VAC i n t e r n a l f l ow p a t h i s

progressing, i.e. leaf/right independent process

control type system for automobile, and rear air

conditioning for the rear seat passengers, etc.,

furthermore, despite speeding up in development,

the demand for quality assurance, performance

improvement and cost reduction is increasing.

Therefore, in the development project of HVAC

units, it is necessary to ensure target performance

at an early stage and to make efforts to improve

quality.

In o rder to ach ieve the demand ta rge t in

performance improvement at an early stage of

development, i t is indispensable to grasp the

information on flow and temperature field using CFD

simulation. However, in the case where warm air

and cool air mixed inside HVAC units, if utilization

of a default simulation condition in the commercial

CFD software to predict temperature at duct outlet,

in which the default setting of Prandtl number is

usually set to about 0.7 to 0.9 as laminar airflow(1),

there is a big difference between the simulation

result and the measured data, and the quantitative

evaluation is very difficult and a hard task, because

the airflow inside HVAC units has a very complex

turbulence vortex structure(2), and moreover the

structure of the turbulence airflow changes with

the variation of the gap between the temperature

control damper and the associated shut rib, due to

the various air mixing opening degrees. Therefore,

the determination of the turbulent Prandtl number

is a key point for improvement of CFD simulation

accuracy.

According to our previous s tudies , i t has

been confirmed that some simulation results for

temperature are close to the measured valves

by adjusting the turbulent Prandtl number to an

arbitrary constant of 0.7 or less, and it is also known

that the precision of simulation results deteriorates

depending on the position of measurement point, the

reason for this is that the turbulent Prandtl number

is not a constant value but is considered to be

change with variation of the flow and temperature

field. For instance, Kitada et al.(3) determined a

function of the turbulent Prandtl number with eddy

viscosity coefficient and the temperature gradient by

an experimental studies of air mix basic model, and

applied in CFD simulation to improve temperature

prediction accuracy.

In the study, a functionalized Prt is proposed by

theoretical analysis using the numerical results of

velocity and the measured data of temperature in a

Key Words: Air conditioning system, HVAC unit, CFD, Turbulent prandtl number

Koei ITO＊１ Jun LIU＊１ Jun ONODERA＊１

＊１ Air-conditioning System Development Department, Air-conditioning System Business Operations

※ Received 19 June 2017, Reprinted with permission from paper No. 20175127, proceedings of technical session No. 25-17, 2017 JSAE Annual Congress (Spring). Further use or distribution is not permitted without permission from JSAE.

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Investigation of CFD Temperature Prediction for HVAC Units

transport terms (u'v', T'v') and utilization of the

definition of the eddy diffusivity, which gives

dy

duε

ρτ t = u'v' = εm (5)

dy

dTρq t = T'v' = εh (6)

then substituting the Eqs. (5) and (6) into Eq. (1)

yields

dU

dT

dU

dy

dy

dT

T'v'

u'v'

T'v'

u'v'Prt = = (7)

thus, if the velocity and temperature fields, and the

turbulent fluctuating terms are known, the Prt can be

evaluated.

The latter method will be used here.

3. Investigation Using an Air Mix Model

3.1. Experimental Verification

As shown in Fig. 1, create a simple experimental

model to imitate the air mix condition inside

the HVAC units, two heat exchangers are placed

in model, one heat exchanger with warm water

generates a warm air flow, and mixing with a cold

air flow is performed by a guide near the confluence

on the downstream, mult iple sensor pins are

arranged in lattice pattern in air mix region.

T Sensor V Sensor

Sensor Pin

IN-Flow

Out-Flow

Observation area

Heat Exchanger

Warm water

h

b

t

Air mix Guide

Fig. 1 Air mix model for Experiment

simple air mix model. In addition, the functionalized

Prt was applied in CFD simulation to predict the

temperature of the air flow inside HVAC units,

and the simulation accuracy will be verified by the

comparison between the experimental data and the

simulated result.

2. Turbulent Prandtl Number

2.1. Definition of Turbulent Prandtl Number

The turbulent Prandtl number is a classical

approach for the heat transfer problem in turbulence,

similarly as in molecular Prandtl number, which is

defined as the ratio between the momentum eddy

diffusivity εm and the heat transfer eddy diffusivity

εh, which is

Prt = εh

εm (1)

using Boussinesq relation, the shear stress τ and

heat flux q can be written as follows(4).

dy

du = (ν + εm)

ρτ

(2)

dy

dT = (α + εh) ρCp

q (3)

There are basically two methods by which Prt

may be evaluated experimentally.

In one method, utilizing experimental time-

average velocity and temperature profiles together

with the integrated Reynolds equations. From

equations (2) and (3) to obtain

du – 1

dyρτ

dy

dT

ρCp

q – 1

Prt = (4)

thus, if the momentum and heat flux variation with

the distance from the wall are known, εm, εh, and

hence Prt can be evaluated.

Alternatively, direct measurement of the Reynolds

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Keihin Technical Review Vol.6 (2017)

The experiment was carried out on a test bench

that can be controlled the flow rate of air and

temperature of warm water, the temperature of

warm water is fixed and the inlet air volume is

set in 3 cases. A multi-channel wind velocity and

wind temperature sensor system is fixed on multiple

sensor pins to measure the velocity and temperature

field of the air mix region.

3.2. Validation by CFD

Since the wind velocity sensor is not able to

measure Reynolds stress u'v' of the air flow field,

after clarifying how much the CFD velocity result

correlates with the measured data, the CFD results

will be attempted to use instead of the measured

data.

3.2.1. Simulation Conditions

The 3D-CFD model completely reflects the

experimental model with the multiple sensor pins (see

Fig. 2). The heat exchanger is defined as a porous

body, and the permeability coefficient is calculated

from the experimental data of air flow resistance.

Additionally, the amount of heat generation per unit

volume is inputted as a quadratic function of air

velocity in the heat exchanger, and the maximum

heating temperature is limited so as to be equal

to the warm water temperature at inlet of heat

exchanger.

In this research, the CFD simulation is carried

out by commercial CFD software, and the simulation

conditions are listed in Table 1.

Fluid model

State

Mesh Structure

Turbulence model

Difference Scheme

Inlet volume flux [m3/h]

Air mix model

Unsteady

All Polyhedral

DES (SST k-ω)

2nd up wind scheme

200, 300, 400

Table 1 Simulation conditions

12

0 5

50V [m/s] T [°C]

Fig. 3 Velocity and temperature of CFD at 400m3/h

IN-Flow

Out-FlowAir mix Guide

PorousGeneration of heat

Porous

Sensor Pin

Fig. 2 Air mix model for CFD

ExperimentSimulation

20

15

10

5

0

Vel

ocity

[m/s

]

Measurement Point

200m3/h 300m3/h 400m3/h

Fig. 4 Correlation between experiment and CFD part1

3.2.2. A Comparison of Simulation and Experiment

Figure 3 present the flow field and temperature

f i e ld o f CFD resu l t s i n case o f 400m 3/h , i t

indicates that the mixing region has a non-uniform

temperature field, and at each measurement point in

grid pattern, there are temperature and flow fields

with different gradients, respectively.

A comparisons of velocity at each measured

point between simulat ion and experiment are

shown in Fig. 4-5, they show that the CFD results

of ve loc i ty g ive a c lose agreement wi th the

experimental data, the coefficient of determination

R2 equals 0.89 and the standard error of the mean is

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Investigation of CFD Temperature Prediction for HVAC Units

17.8%, in the study, the error rate level is acceptable

for determination of Prt.

coefficient, respectively, they can be determined

using separation of variables Re and Pr by simply

taking the natural logarithm to Eq. (8).

Equation (8) is applied to CFD simulation of the

simple air mix model, and compared to the case of

Prt = 0.9, maximum error decreased from 10.8°C to

8.0°C within the interval ±2σ as shown in Fig. 8,

and the probability of occurrence within the interval

V [m/s]

12

0

Velocity FieldExperiment

CFD

02468

1012141618

0 2 4 6 8 10 12 14 16 18

Vel

ocity

on

CFD

[m

/s]

Velocity on Experiment [m/s]

Fig. 5 Correlation between experiment and CFD part2

4. Determination of Functionalized Prt

As shown in Fig. 6, a new orthogonal coordinate

system (xi*, yi

*) which the xi* axis fixed along the

direction of main flow U at measurement point is

introduced, where subscript i denotes the number

of measurement point, and the coordinate system

(xi, yi) is the reference coordinate system in CFD

simulation.

In the coordinate system (xi*, yi

*), the turbulent

fluctuating term (u'v', T'v') and spatial derivative

of velocity and temperature fields (dU, dT) at

each measurement point are calculated using CFD

numerical results of velocity and measured data of

temperature, respectively. Thereupon, according to

Eq. (7), Prt can be obtained with known Reynolds

transport terms and the velocity and temperature

fields.

H e r e , t h e r e l a t i o n s h i p o f P r t w i t h t w o

dimensionless numbers Reynolds number (Re) and

molecular Prandtl number (Pr) is plotted in Fig. 7,

and the Prt is assumed as a function of both Re and

Pr as follows

Prt = aReb Pr c (8)

where, the coefficients a, b and c are constant

Fig. 6 Components of velocity

Fig. 7 Plotting Prt with variation of Re and Pr

uxi

uyi

uxi*

=

uy

ux

cosθisinθi

cosθi − sinθiuxi*

uyi*

uyi*

θ

Prt

Prt

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

Re HighLow Pr HighLow

50

5

Experiment Prt = Function Prt =0.9T [°C]

Average Error

10.8°C

8.0°C

2σ (Prt = 0.9)

2σ (Prt = Function)

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Error [°C]

0

5

10

15

20

Freq

uenc

y

Prt = 0.9Prt = Function

Fig. 8 Comparison of temperature fields

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Keihin Technical Review Vol.6 (2017)

±5°C was upgraded 15%, which improves from

68.2% for Prt = 0.9 to 83.6% for functionalized Prt.

Consequently, utilization of the functionalized Prt is

effective for improving the temperature simulation

accuracy of air mix model.

5. Applied on CFD Simulation of HVAC Units

T h e f u n c t i o n a l i z e d P r t wa s e m p l oy e d t o

CFD simulation of HVAC units (see Fig. 9) for

verifying its simulation accuracy, and Table 2

shows the conditions of CFD simulation. Here, the

dimensionless temperature Td is defined by dividing

the air temperature T by the heater warm water

temperature TH.

F i g u r e 10 p r e s e n t t h e c h a r a c t e r i s t i c s o f

temperature varied with respect to damper open

degree changes in the Bi-Level (B/L) and the

Heat Differential (H/D) modes of HVAC units,

where solid line indicates measured data and dash

line indicates simulation results, respectively. It

shows that the inclination of the thermal control

characteristics at each blowing outlet are obtained,

and the tendency is approximately in agreement with

experimental data.

In regards to the probability distribution of errors,

in comparison to a default case of constant Prt = 0.9,

maximum error decreased from 11.2°C to 7.9°C

within the interval ±2σ as shown in Fig. 11, and the

probability of occurrence within the interval ±5°C

is 67.4% for Prt = 0.9 and 80.4% for functionalized

Prt, which was upgraded 13.4%, this demonstrates

1. VENT Dr2. VENT As3. HEAT Dr4. HEAT As5. R-HEAT Dr6. R-HEAT As7. DEF Dr8. DEF As

2

1

87

3

4

65

Fig. 9 HVAC model

00.10.20.30.40.50.60.70.80.9

1

0 10 20 30 40 50 60 70 80 90 100

Td

Air mix position [%]

00.10.20.30.40.50.60.70.80.9

1

0 10 20 30 40 50 60 70 80 90 100

Td

Air mix position [%]

B/L H/D

B/L H/D

ExperimentSimulation

ExperimentSimulation

HEAT DrHEAT As

VENT DrVENT AsR-HEAT DrR-HEAT AsDEF DrDEF As

Table 2 Simulation conditions

Fig. 10 Thermal control characteristics

Fluid model

State

Mesh Structure

Turbulence model

Difference Scheme

Semi center HVAC

Steady

All Polyhedral

Realizable k-ε

2nd up wind scheme

Fig. 11 Comparison of temperature

-7.9°C2σ (Prt = Function)

0

10

20

30

40

50

60

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14

Freq

uenc

y

Prt = 0.9Prt = Function

2σ (Prt = 0.9)

Average Error

Error [°C]

11.2°C

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Investigation of CFD Temperature Prediction for HVAC Units

that the functionalized Prt has been effective for

improving temperature prediction accuracy in CFD

simulation of the HVAC units.

On the one hand, in the opening degree 70% of

the H/D mode, although the simulation temperature

(Td) of DEF was only 0.05 lower than the measured

data and it showed a relatively good results, but on

the other hand, in the opening degree 100%, the

simulation temperature of DEF and R-HEAT were

higher than the measured data, and that of HEAT

showed a tendency to be lower conversely, it is

considered that the correction of functionalized Prt

is insufficient for variation of thermal transfer and

diffusion, due to the reason that Re number of air

toward the DEF becomes high and exceeds the range

as shown in Fig. 12. This is probably due to the

fact that the air mix model which used in the study,

is relatively simple mixing with only one air mix

guide, and the application range of functionalized Prt

is the same length as the Prt distribution range (see

Fig. 7).

In order to improve adaptability to different

complex flow fields in each mode and opening

degree of HVAC units, the coefficients a, b and c in

Eq. (8) are considered to vary at a critical value of

Re number, and further verification is necessary.

and numerical results for velocity, and the turbulent

Prandtl number (Prt) can be expressed as a function

of both Reynolds number (Re) and molecular Prandtl

number (Pr).

In addition, the functionalized Prt was employed

to predict the temperature of the air flow at the

outlet with CFD simulation of HVAC units. As a

result, simulation results of the temperature field

were in relatively good agreement with experimental

data. This demonstrates that the functionalized

Prt has been effective for improving temperature

prediction accuracy in CFD simulation of the HVAC

units.

7. Future Tasks

As mentioned in chapter 5, since only one simple

flow field is discussed, and the applicability range to

CFD simulation of HVAC units was limited, then in

the future tasks, the applicability can be improved

with increasing of discussion cases, such as the

number of guides and variation of the temperature

difference between air and warm water.

Moreover, i t just set the wall heat transfer

coefficient as a constant in CFD simulation in the

study, however, the certainty of the constant has not

been clarified. Therefore, the other future challenge

is to elucidate the physical phenomenon concerning

heat exchange between the external environment

and HVAC case or the duct, and to identify the wall

heat transfer coefficient for further improvement in

simulation accuracy.

References

(1) Warren h. Giedt: Principles of Engineering Heat

Transfer, translation by Suzumu Yokohori, etc.,

Maruzen Press., p. 333 (1960)

(2) Jun Onodera, etc.: Numerical Simulation of Flow-

Induced Noise in Automotive HVAC Systems,

Fig. 12 Flow field of HVAC unit in H/D mode

Td Re PrtA/M

Position

70%

100%

1

0

High

Low 0

1

6. Conclusion

In the study, a functionalized Prt is obtained from

a combination of experimental data for temperature

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Keihin Technical Review Vol.6 (2017)

Authors

K. ITO J. LIU J. ONODERA

In the paper, a theoret ical-based approach

to identifying turbulent Prandtl number (Prt) in

air mixing is challenged, and a function of non-

unity Prt number is proposed. In addition, we are

also planning to improve the function of Prt with

increment of experimental conditions in the next

step, and to expand its application range on CFD

simulation of HVAC units. Finally, I would like to

thank everyone for their guidance and cooperation

during the research. (ITO)

Keihin Technical Review, Vol. 1, p. 19-24 (2012)

(3) M o t o h i r o K i t a d a , e t c . : D ev e l o p m e n t o f

Automotive A/C System Basic Performance

Simulator-Accuracy of Temperature Calculation

Technique Development, Proceeding of 2000

JSAE congress (Autumn), No. 169 (2000)

(4) Basim O. Hasan: Turbulent Prandtl Number and

its Use in Prediction of Heat Transfer Coefficient

for Liquids, Nahrain University, College of

Engineering Journal (NUCEJ) Vol. 10, No. 1

(2007)

(5) Shinobu Toshima: Yosetsu Hinshitsu Kanri, Japan

Standards Association, p. 13-23 (1967)