Deciding Characteristic Length

Caner · October 18, 2010, 10:53

Hello everyone,
I am researching on jet impingement systems.I carry out numerical analysis to investigate flow field at the confined channel where dual jets impinge.I have a basic question about deciding characteristic length.

Basic drawing of my dual Nozzle can be seen here.There are 2 nozzles, one is(smaller diameter one-D1) in the another one(bigger diameter one-D2).
One of the parameter of my numerical simulation is Velocity ratio "VR" which means the ratio of V1 / V2.So in the case of VR=0,0.5,1.5,2,(which means V1 and V2 has a different velocity value) the question arises;

If there are two different velocities (V1 and V2) how should I determine the the characteristic length and Reynolds number in order to conduct numerical simulation?

Thank you very much in advance!

Regards,
Caner

mettler · October 20, 2010, 10:03

can you not use the respective diameter of the nozzle to determine your Re?

and, since the mdot doesn't change I would use

Re = (4*mdot)/(mu*pi*Diam)

Caner · October 20, 2010, 10:55

Quote:

Originally Posted by mettler

can you not use the respective diameter of the nozzle to determine your Re?

and, since the mdot doesn't change I would use

Re = (4*mdot)/(mu*pi*Diam)

Thanks mettler for your answer
I think, I can use D2-D1 as a characteristic length in my numerical analysis like other annular impinging jet studies did, but that D2-D1 cant be used to determine inner jet's reynolds number.
and could you please explain what mdot is?

mettler · October 20, 2010, 11:34

mdot is mass flow rate. I didn't see that diagram before my first post, so unless you know the mass flow rate thru the inner and outer channels you might not be able to use that.

azurespirit · December 2, 2010, 15:33

Hi,

I am conducting investigations into impinging jets as well. Most literature gives Re values used. For purpose of validation, I need to mimic these exact conditions, for that I wanted to know how to deduce the diameter value using the provided Re number.

The problem is both flow rate (or velocity) and diameter values are unknown, how can I go about this problem. Please help.

dandalf · December 3, 2010, 07:30

Hi

Caner you could simply switch to using the dimensional form of the equaions, and calculate your flow in real space, rather than non dimensional space.

That way the viscous term of your equatons depends on viscosity rather than Re.

Azurespirit, it sounds like your bench mark solution is in non dimensionl form. In which case if you are solving with the dimensionless from of the equations, your velocity and charecteristic length will both be 1.

mettler · December 3, 2010, 09:58

I think you just want to keep the Re the same - Reynolds Scaling, so you don't need to know any diameter or length. If you pick a diameter you will know what velocity you need to get the Re required.

azurespirit · December 3, 2010, 11:35

@dandalf

i dont think i can consider both diameter and velocity as 1 since i wont possibly obtain the desired Re number

@mettler

yeah that's what i've figured. it basically scales down to Re=v.d/constant

so maintain a v/d ratio to get the desired Re. thanks anyway.

dandalf · December 3, 2010, 12:32

Re is defined as,
$Re= \frac{\rho U D}{\mu}$

presumably you are solving a set of continuity equations of the form,
$\rho\left(\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j}\right)=\mu\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i} \right) - \frac{\partial p}{\partial x_i} - \rho g$
Which is the dimensional form of the navier stokes equation for the conservation of momentum.
However, if you non dimensionalize this, i.e. set
$\begin{array}{c} \rho=1\\ U =1 \\ D =1 \\ Re = \frac{1}{\mu}\end{array}$

giving the incompressible non dimensional from of of the equation,

$\left(\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j}\right)=\frac{1}{Re}\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i} \right) - \frac{\partial p}{\partial x_i} - g$

this is the form of the equation found in many books, but is only valid if your computational domain has, characteristic distance 1, velocity 1, and density 1.

I got tripped up by this myself,

Most bench mark solutions will be presented in this dimensionless form for obvious reasons.

Hope this helped,

Dandalf

Jade M · December 9, 2010, 12:04

I would use the length that gives you the largest Reynolds number and thus the smallest boundary layers. This way, I think that you can be sure to resolve all boundary layers. Good luck!

October 18, 2010, 10:53	Deciding Characteristic Length	#1
Caner New Member Caner Join Date: Jan 2010 Posts: 8 Rep Power: 16	Hello everyone, I am researching on jet impingement systems.I carry out numerical analysis to investigate flow field at the confined channel where dual jets impinge.I have a basic question about deciding characteristic length. Basic drawing of my dual Nozzle can be seen here.There are 2 nozzles, one is(smaller diameter one-D1) in the another one(bigger diameter one-D2). One of the parameter of my numerical simulation is Velocity ratio "VR" which means the ratio of V1 / V2.So in the case of VR=0,0.5,1.5,2,(which means V1 and V2 has a different velocity value) the question arises; If there are two different velocities (V1 and V2) how should I determine the the characteristic length and Reynolds number in order to conduct numerical simulation? Thank you very much in advance! Regards, Caner

December 2, 2010, 15:33	determining diameter	#5
azurespirit New Member Shashank Join Date: Jul 2010 Posts: 18 Rep Power: 16	Hi, I am conducting investigations into impinging jets as well. Most literature gives Re values used. For purpose of validation, I need to mimic these exact conditions, for that I wanted to know how to deduce the diameter value using the provided Re number. The problem is both flow rate (or velocity) and diameter values are unknown, how can I go about this problem. Please help.

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October 20, 2010, 10:03		#2
mettler Senior Member Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 211 Rep Power: 18	can you not use the respective diameter of the nozzle to determine your Re? and, since the mdot doesn't change I would use Re = (4mdot)/(mupi*Diam)

October 20, 2010, 11:34		#4
mettler Senior Member Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 211 Rep Power: 18	mdot is mass flow rate. I didn't see that diagram before my first post, so unless you know the mass flow rate thru the inner and outer channels you might not be able to use that.

December 3, 2010, 07:30		#6
dandalf Member Dan Join Date: Oct 2010 Location: UK Posts: 41 Rep Power: 16	Hi Caner you could simply switch to using the dimensional form of the equaions, and calculate your flow in real space, rather than non dimensional space. That way the viscous term of your equatons depends on viscosity rather than Re. Azurespirit, it sounds like your bench mark solution is in non dimensionl form. In which case if you are solving with the dimensionless from of the equations, your velocity and charecteristic length will both be 1.

December 3, 2010, 09:58		#7
mettler Senior Member Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 211 Rep Power: 18	I think you just want to keep the Re the same - Reynolds Scaling, so you don't need to know any diameter or length. If you pick a diameter you will know what velocity you need to get the Re required.

December 3, 2010, 11:35		#8
azurespirit New Member Shashank Join Date: Jul 2010 Posts: 18 Rep Power: 16	@dandalf i dont think i can consider both diameter and velocity as 1 since i wont possibly obtain the desired Re number @mettler yeah that's what i've figured. it basically scales down to Re=v.d/constant so maintain a v/d ratio to get the desired Re. thanks anyway.

December 3, 2010, 12:32		#9
dandalf Member Dan Join Date: Oct 2010 Location: UK Posts: 41 Rep Power: 16	Re is defined as, $Re= \frac{\rho U D}{\mu}$ presumably you are solving a set of continuity equations of the form, $\rho\left(\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j}\right)=\mu\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i} \right) - \frac{\partial p}{\partial x_i} - \rho g$ Which is the dimensional form of the navier stokes equation for the conservation of momentum. However, if you non dimensionalize this, i.e. set $\begin{array}{c} \rho=1\\ U =1 \\ D =1 \\ Re = \frac{1}{\mu}\end{array}$ giving the incompressible non dimensional from of of the equation, $\left(\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j}\right)=\frac{1}{Re}\left(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i} \right) - \frac{\partial p}{\partial x_i} - g$ this is the form of the equation found in many books, but is only valid if your computational domain has, characteristic distance 1, velocity 1, and density 1. I got tripped up by this myself, Most bench mark solutions will be presented in this dimensionless form for obvious reasons. Hope this helped, Dandalf

December 9, 2010, 12:04		#10
Jade M Senior Member Join Date: Feb 2010 Posts: 148 Rep Power: 17	I would use the length that gives you the largest Reynolds number and thus the smallest boundary layers. This way, I think that you can be sure to resolve all boundary layers. Good luck!