After i generate random numbers of x, how can i use this random x values to the rest of the code one by one. Because after that, I want to plot a friction factor-x number grapt with this different numbers

x = 0.05 + (0.1-0.05).*rand(10,1);
Perimeter = (pi*HydraulicDiameter); 
NumberOfCoolantChannels = 3; 
Npass = 1; ...Number of Passes
% Ac = (pi*(HydraulicDiameter^2)/(4)); ...Single channel flow cross section
Ac = 1.571e-5;
Atotal = NumberOfCoolantChannels*Ac; ... Total Flow Cross Section 
BladeMassFlow = (CoolantBleed/100)*(TurbineMassFlow/NumberOfBlades);
ChannelMassFlow = (BladeMassFlow/NumberOfCoolantChannels);
RibHeighHydraulicDiameterRatio = x;
FrictionFactor2 = 1.447*(1.14-2*log10(x))^-2; %transverse ribs

Answer 1

[Geoff Hayes]

isilay - since x is an array then you can use element-wise power to calculate the friction factor. Just change your line of code to

FrictionFactor2 = 1.447*(1.14-2*log10(x)).^-2; %transverse ribs

where a '.' is placed in front of the exponent operator.

[isilay aydin]

FrictionFactor2 = 1.447*(1.14-2*log10(x)).^-2; %transverse ribs
% OverallPressureDrop = FrictionFactor2*((Npass*BladeSpan*10^-3)/HydraulicDiameter)*CoolantDensity*((BulkVelocity^2)/2);
OverallPressureDrop = 8300;
BulkVelocity =((OverallPressureDrop/FrictionFactor2)*(HydraulicDiameter/(Npass*BladeSpan*10^-3))*(2/CoolantDensity))^0.5;
ChannelCoolantMassFlow = (CoolantDensity*Ac*BulkVelocity);
BladeCoolantMassFlow = NumberOfCoolantChannels*ChannelCoolantMassFlow;
PercentageCoolantBleed = 100*(BladeCoolantMassFlow*NumberOfBlades/TurbineMassFlow);
Re = (ChannelCoolantMassFlow/Ac)*(HydraulicDiameter/CoolantViscosity);
Nu = 0.15*Re^0.7; ...based on the Hydraulic Diameter
InternalHeatTransferCoefficient = Nu*(CoolantConductivity/HydraulicDiameter);
TechnologyFactor = (InternalHeatTransferCoefficient*Npass*Perimeter*NumberOfCoolantChannels)/(ExternalHeatTransferCoefficient*BladeExternalPerimeter*45*10^-3);
MassFlowFunction = (BladeCoolantMassFlow*CoolantSpecificHeat)/(BladeExternalPerimeter*BladeChord*10^-3*ExternalHeatTransferCoefficient*BladeSpan*10^-3);
ConvectionCoolingEfficiency = 1 - exp(-(TechnologyFactor)/(MassFlowFunction));
OverallEffectinevess = (MassFlowFunction*ConvectionCoolingEfficiency)/(1 + MassFlowFunction*ConvectionCoolingEfficiency);
MetalTemperature = (ExternalGasTemperature) - OverallEffectinevess*(ExternalGasTemperature-CoolantInletTemperature);
% FrictionFactor = 0.316*Re^-0.25; ...for smooth round pipe
% BulkVelocity = (ChannelMassFlow) / (CoolantDensity*Ac);
TemperatureSmooth = 1080.9;
TemperatureRipped = MetalTemperature;
RipEfficiency = ((TemperatureRipped-TemperatureSmooth)/TemperatureRipped)*100;

[isilay aydin]

thank you so much. i corrected the friction factor but now other variables has the same problem. ı am a new learner and i didnt get the logic. could you help me for the rest too please?

[Geoff Hayes]

isilay - it is probably a good idea if you post the error message and line of code that is causing the problem. You may want to review Array vs. Matrix Operations and pay particular attention to the array operators table. I also don't think I have all the values for each variable.

[isilay aydin]

Error using ^ (line 51)

Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To perform elementwise matrix powers, use '.^'.

[Geoff Hayes]

Can you post the line of code that this error corresponds to (I'm not sure which line is 51)?

[isilay aydin]

there is no line 51 in my code but when click on the message this is the result:

[Geoff Hayes]

so line 51 is in the mpower built-in MATLAB function, but there must be something more to the error message that indicates which line of your code is causing the problem.

[Geoff Hayes]

it may be that you just need to replace the exponent/power calls of ^ with .^...but this all depends upon whether you want to do an element-wise power (i.e. raise all elements in matrix to some power) or not.

[isilay aydin]

i really dont know because there is no other error in the code only this one

[Stephen23]

"ı am a new learner and i didnt get the logic"

MATLAB has two basic kinds of numeric operations:

• matrix operations are for doing linear algebra
• array operations are for element-wise numeic operations.

If you are not doing linear algebra then using matrix operations is probably incorrect (but only you can know this!), and probably you should be using array operations. The different operators are explained here:

https://www.mathworks.com/help/matlab/matlab_prog/array-vs-matrix-operations.html

[isilay aydin]

thank you but i have checked this already

[Stephen23]

"but i have checked this already"

The code you showed in your new question has many locations where you are using matrix operators with arrays. I doubt that many (or any of those) operators are correct. For example:

BulkVelocity =((OverallPressureDrop/FrictionFactor2) ...
%                                  ^ here

Nu = 0.15*Re^0.7; ...based on the Hydraulic Diameter
%           ^ here

ConvectionCoolingEfficiency = 1 - exp(-(TechnologyFactor)/(MassFlowFunction));
%                                                        ^ here

OverallEffectinevess = (MassFlowFunction*ConvectionCoolingEfficiency)/(1 + MassFlowFunction*ConvectionCoolingEfficiency);
%                                       ^ here                       ^ here
etc. etc.

You need check the size of every variable and check all operations on that variable. It will take time.

[isilay aydin]

yes i have changed them because i thought that i should put dot every variables which affect the X and Friction factor. so i put almost everywhere

[isilay aydin]

this is my final version still idk if it is true

x = 0.05 + (0.1-0.05).*rand(10,1);
Perimeter = (pi*HydraulicDiameter); 
NumberOfCoolantChannels = 3; 
Npass = 1; ...Number of Passes
% Ac = (pi*(HydraulicDiameter^2)/(4)); ...Single channel flow cross section
Ac = 1.571e-5;
Atotal = NumberOfCoolantChannels*Ac; ... Total Flow Cross Section 
BladeMassFlow = (CoolantBleed/100)*(TurbineMassFlow/NumberOfBlades);
ChannelMassFlow = (BladeMassFlow/NumberOfCoolantChannels);
RibHeighHydraulicDiameterRatio = x;
FrictionFactor2 = 1.447*(1.14-2*log10(x)).^-2; %transverse ribs
% OverallPressureDrop = FrictionFactor2*((Npass*BladeSpan*10^-3)/HydraulicDiameter)*CoolantDensity*((BulkVelocity^2)/2);
OverallPressureDrop = 8300;
BulkVelocity =sqrt((OverallPressureDrop./FrictionFactor2)*(HydraulicDiameter/(Npass*BladeSpan*10.^-3))*(2/CoolantDensity));
ChannelCoolantMassFlow = CoolantDensity*Ac*BulkVelocity;
BladeCoolantMassFlow = NumberOfCoolantChannels*ChannelCoolantMassFlow;
PercentageCoolantBleed = (BladeCoolantMassFlow*NumberOfBlades/TurbineMassFlow)*100;
Re = (ChannelCoolantMassFlow/Ac)*(HydraulicDiameter/CoolantViscosity);
Nu = 0.15*Re.^0.7; ...based on the Hydraulic Diameter
InternalHeatTransferCoefficient = Nu*(CoolantConductivity/HydraulicDiameter);
TechnologyFactor = (InternalHeatTransferCoefficient*Npass*Perimeter*NumberOfCoolantChannels)/(ExternalHeatTransferCoefficient*BladeExternalPerimeter*45*10^-3);
MassFlowFunction = (BladeCoolantMassFlow*CoolantSpecificHeat)/(BladeExternalPerimeter*BladeChord*10^-3*ExternalHeatTransferCoefficient*BladeSpan*10^-3);
ConvectionCoolingEfficiency = 1 - exp((-TechnologyFactor)/(MassFlowFunction));
OverallEffectinevess = (MassFlowFunction*ConvectionCoolingEfficiency)/(1 + MassFlowFunction*ConvectionCoolingEfficiency);
MetalTemperature = (ExternalGasTemperature) - OverallEffectinevess*(ExternalGasTemperature-CoolantInletTemperature);

[Geoff Hayes]

isilay - I think that you need to step through each line of code (using the MATLAB debugger) and verify that all variables are as you expect and that, given their dimensions, the code is performing the correct operation.

[Stephen23]

"...i thought that i should put dot every variables which affect the X and Friction factor"

But those are not the only non-scalar variables in your code. These ones are too (or probably should be):

BulkVelocity
ChannelCoolantMassFlow
BladeCoolantMassFlow
PercentageCoolantBleed
Re
Nu
InternalHeatTransferCoefficient
TechnologyFactor
MassFlowFunction
etc. etc.

Why? Lets have a look at the definition of BulkVelocity:

BulkVelocity =sqrt((OverallPressureDrop./FrictionFactor2)*(HydraulicDiameter/(Npass*BladeSpan*10.^-3))*(2/CoolantDensity));
%                                        ^^^^^^^^^^^^^^^ non-scalar

Atleast one of its defining terms is non-scalar. There are no operations to reduce the size of that array, so BulkVelocity will also be non-scalar (with the same size as FrictionFactor2). And exactly the same for all the other variables listed and some more (because I stopped checking at that point).

You need to be much more thorough and actually look at the sizes of all of the variables, and then use the appropriate array operations. Note that if you are not perforning any linear algebra you could simply replace every matrix operation with an array operation (this would likely be much less effort than checking every variable).